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Monday, July 2, 2018

Strong versus weak hypothesis tests, risky predictions.

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Efficient Market Hypothesis (EMH)

Written by True Tamplin, BSc, CEPF®

Reviewed by subject matter experts.

Updated on July 12, 2023

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Table of contents, efficient market hypothesis (emh) overview.

The Efficient Market Hypothesis (EMH) is a theory that suggests financial markets are efficient and incorporate all available information into asset prices.

According to the EMH, it is impossible to consistently outperform the market by employing strategies such as technical analysis or fundamental analysis.

The hypothesis argues that since all relevant information is already reflected in stock prices, it is not possible to gain an advantage and generate abnormal returns through stock picking or market timing.

The EMH comes in three forms: weak, semi-strong, and strong, each representing different levels of market efficiency.

While the EMH has faced criticisms and challenges, it remains a prominent theory in finance that has significant implications for investors and market participants.

Types of Efficient Market Hypothesis

The Efficient Market Hypothesis can be categorized into the following:

Weak Form EMH

The weak form of EMH posits that all past market prices and data are fully reflected in current stock prices.

Therefore, technical analysis methods, which rely on historical data, are deemed useless as they cannot provide investors with a competitive edge. However, this form doesn't deny the potential value of fundamental analysis.

Semi-strong Form EMH

The semi-strong form of EMH extends beyond historical prices and suggests that all publicly available information is instantly priced into the market.

This includes financial statements, news releases, economic indicators, and other public disclosures. Therefore, neither technical analysis nor fundamental analysis can yield superior returns consistently.

Strong Form EMH

The most extreme version of EMH, the strong form, asserts that all information, both public and private, is fully reflected in stock prices.

Even insiders with privileged information cannot consistently achieve higher-than-average market returns. This form, however, is widely criticized as it conflicts with securities regulations that prohibit insider trading .

Assumptions of the Efficient Market Hypothesis

Three fundamental assumptions underpin the Efficient Market Hypothesis.

All Investors Have Access to All Publicly Available Information

This assumption holds that the dissemination of information is perfect and instantaneous. All market participants receive all relevant news and data about a security or market simultaneously, and no investor has privileged access to information.

All Investors Have a Rational Expectation

In EMH, it is assumed that investors collectively have a rational expectation about future market movements. This means that they will act in a way that maximizes their profits based on available information, and their collective actions will cause securities' prices to adjust appropriately.

Investors React Instantly to New Information

In an efficient market, investors instantaneously incorporate new information into their investment decisions. This immediate response to news and data leads to swift adjustments in securities' prices, rendering it impossible to "beat the market."

Implications of the Efficient Market Hypothesis

The EMH has several implications across different areas of finance.

Implications for Individual Investors

For individual investors, EMH suggests that "beating the market" consistently is virtually impossible. Instead, investors are advised to invest in a well-diversified portfolio that mirrors the market, such as index funds.

Implications for Portfolio Managers

For portfolio managers , EMH implies that active management strategies are unlikely to outperform passive strategies consistently. It discourages the pursuit of " undervalued " stocks or timing the market.

Implications for Corporate Finance

In corporate finance, EMH implies that a company's stock is always fairly priced, meaning it should be indifferent between issuing debt and equity . It also suggests that stock splits , dividends , and other financial decisions have no impact on a company's value.

Implications for Government Regulation

For regulators , EMH supports policies that promote transparency and information dissemination. It also justifies the prohibition of insider trading.

Implications of the Efficient Market Hypothesis

Criticisms and Controversies Surrounding the Efficient Market Hypothesis

Despite its widespread acceptance, the EMH has attracted significant criticism and controversy.

Behavioral Finance and the Challenge to EMH

Behavioral finance argues against the notion of investor rationality assumed by EMH. It suggests that cognitive biases often lead to irrational decisions, resulting in mispriced securities.

Examples include overconfidence, anchoring, loss aversion, and herd mentality, all of which can lead to market anomalies.

Market Anomalies and Inefficiencies

EMH struggles to explain various market anomalies and inefficiencies. For instance, the "January effect," where stocks tend to perform better in January, contradicts the EMH.

Similarly, the "momentum effect" suggests that stocks that have performed well recently tend to continue performing well, which also challenges EMH.

Financial Crises and the Question of Market Efficiency

The Global Financial Crisis of 2008 raised serious questions about market efficiency. The catastrophic market failure suggested that markets might not always price securities accurately, casting doubt on the validity of EMH.

Empirical Evidence of the Efficient Market Hypothesis

Empirical evidence on the EMH is mixed, with some studies supporting the hypothesis and others refuting it.

Evidence Supporting EMH

Several studies have found that professional fund managers, on average, do not outperform the market after accounting for fees and expenses.

This finding supports the semi-strong form of EMH. Similarly, numerous studies have shown that stock prices tend to follow a random walk, supporting the weak form of EMH.

Evidence Against EMH

Conversely, other studies have documented persistent market anomalies that contradict EMH.

The previously mentioned January and momentum effects are examples of such anomalies. Moreover, the occurrence of financial bubbles and crashes provides strong evidence against the strong form of EMH.

Efficient Market Hypothesis in Modern Finance

Despite criticisms, the EMH continues to shape modern finance in profound ways.

EMH and the Rise of Passive Investing

The EMH has been a driving force behind the rise of passive investing. If markets are efficient and all information is already priced into securities, then active management cannot consistently outperform the market.

As a result, many investors have turned to passive strategies, such as index funds and ETFs .

Impact of Technology on Market Efficiency

Advances in technology have significantly improved the speed and efficiency of information dissemination, arguably making markets more efficient. High-frequency trading and algorithmic trading are now commonplace, further reducing the possibility of beating the market.

Future of EMH in Light of Evolving Financial Markets

While the debate over market efficiency continues, the growing influence of machine learning and artificial intelligence in finance could further challenge the EMH.

These technologies have the potential to identify and exploit subtle patterns and relationships that human investors might miss, potentially leading to market inefficiencies.

The Efficient Market Hypothesis is a crucial financial theory positing that all available information is reflected in market prices, making it impossible to consistently outperform the market. It manifests in three forms, each with distinct implications.

The weak form asserts that all historical market information is accounted for in current prices, suggesting technical analysis is futile.

The semi-strong form extends this to all publicly available information, rendering both technical and fundamental analysis ineffective.

The strongest form includes even insider information, making all efforts to beat the market futile. EMH's implications are profound, affecting individual investors, portfolio managers, corporate finance decisions, and government regulations.

Despite criticisms and evidence of market inefficiencies, EMH remains a cornerstone of modern finance, shaping investment strategies and financial policies.

Efficient Market Hypothesis (EMH) FAQs

What is the efficient market hypothesis (emh), and why is it important.

The Efficient Market Hypothesis (EMH) is a theory suggesting that financial markets are perfectly efficient, meaning that all securities are fairly priced as their prices reflect all available public information. It's important because it forms the basis for many investment strategies and regulatory policies.

What are the three forms of the Efficient Market Hypothesis (EMH)?

The three forms of the EMH are the weak form, semi-strong form, and strong form. The weak form suggests that all past market prices are reflected in current prices. The semi-strong form posits that all publicly available information is instantly priced into the market. The strong form asserts that all information, both public and private, is fully reflected in stock prices.

How does the Efficient Market Hypothesis (EMH) impact individual investors and portfolio managers?

According to the EMH, consistently outperforming the market is virtually impossible because all available information is already factored into the prices of securities. Therefore, it suggests that individual investors and portfolio managers should focus on creating well-diversified portfolios that mirror the market rather than trying to beat the market.

What are some criticisms of the Efficient Market Hypothesis (EMH)?

Criticisms of the EMH often come from behavioral finance, which argues that cognitive biases can lead investors to make irrational decisions, resulting in mispriced securities. Additionally, the EMH has difficulty explaining certain market anomalies, such as the "January effect" or the "momentum effect." The occurrence of financial crises also raises questions about the validity of EMH.

How does the Efficient Market Hypothesis (EMH) influence modern finance and its future?

Despite criticisms, the EMH has profoundly shaped modern finance. It has driven the rise of passive investing and influenced the development of many financial regulations. With advances in technology, the speed and efficiency of information dissemination have increased, arguably making markets more efficient. Looking forward, the growing influence of artificial intelligence and machine learning could further challenge the EMH.

About the Author

True Tamplin, BSc, CEPF®

True Tamplin is a published author, public speaker, CEO of UpDigital, and founder of Finance Strategists.

True is a Certified Educator in Personal Finance (CEPF®), author of The Handy Financial Ratios Guide , a member of the Society for Advancing Business Editing and Writing, contributes to his financial education site, Finance Strategists, and has spoken to various financial communities such as the CFA Institute, as well as university students like his Alma mater, Biola University , where he received a bachelor of science in business and data analytics.

To learn more about True, visit his personal website or view his author profiles on Amazon , Nasdaq and Forbes .

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Efficient Market Hypothesis: Strong, Semi-Strong, and Weak

If I were to choose one thing from the academic world of finance that I think more individual investors need to know about, it would be the efficient market hypothesis.

The name “efficient market hypothesis” sounds terribly arcane. But its significance is huge for investors, and (at a basic level) it’s not very hard to understand.

So what is the efficient market hypothesis (EMH)?

As professor Eugene Fama (the man most often credited as the father of EMH) explains*, in an efficient market, “the current price [of an investment] should reflect all available information…so prices should change only based on unexpected new information.”

It’s important to note that, as Fama himself has said, the efficient market hypothesis is a model, not a rule. It describes how markets tend to work. It does not dictate how they must work.

EMH is typically broken down into three forms (weak, semi-strong, and strong) each with their own implications and varying levels of data to back them up.

Weak Efficient Market Hypothesis

The weak form of EMH says that you cannot predict future stock prices on the basis of past stock prices. Weak-form EMH is a shot aimed directly at technical analysis. If past stock prices don’t help to predict future prices, there’s no point in looking at them — no point in trying to discern patterns in stock charts.

From what I’ve seen, most academic studies seem to show that weak-form EMH holds up pretty well. (Take, for example, the recent study which tested over 5,000 technical analysis rules and showed them to be unsuccessful at generating abnormally high returns.)

Semi-Strong Efficient Market Hypothesis

The semi-strong form of EMH says that you cannot use any published information to predict future prices. Semi-strong EMH is a shot aimed at fundamental analysis. If all published information is already reflected in a stock’s price, then there’s nothing to be gained from looking at financial statements or from paying somebody (i.e., a fund manager) to do that for you.

Semi-strong EMH has also held up reasonably well. For example, the number of active fund managers who outperform the market has historically been no more than can be easily attributed to pure randomness .

Semi-strong EMH does not appear to be ironclad, however, as there have been a small handful of investors (e.g., Peter Lynch, Warren Buffet) whose outperformance is of a sufficient degree that it’s extremely difficult to explain as just luck.

The trick, of course, is that it’s nearly impossible to identify such an investor in time to profit from it. You must either:

Invest with a fund manager after only a few years of outperformance (at which point his/her performance could easily be due to luck), or
Wait until the manager has provided enough data so that you can be sure that his performance is due to skill (at which point his fund will be sufficiently large that he’ll have trouble outperforming in the future).

Strong Efficient Market Hypothesis

The strong form of EMH says that everything that is knowable — even unpublished information — has already been reflected in present prices. The implication here would be that even if you have some inside information and could legally trade based upon it, you would gain nothing by doing so.

The way I see it, strong-form EMH isn’t terribly relevant to most individual investors, as it’s not too often that we have information not available to the institutional investors.

Why You Should Care About EMH

Given the degree to which they’ve held up, the implications of weak and semi-strong EMH cannot be overstated. In short, the takeaway is that there’s very little evidence indicating that individual investors can do anything better than simply buy & hold a low-cost, diversified portfolio .

*Update: The video from which this quote came has since been taken offline.

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A good point to keep in mind is that even if the EMH models aren’t a perfect model of the stock market- if it is close enough that technical analysis or fundamental analysis won’t give you a real advantage then it doesn’t make sense to try them. A Random Walk Down Wall Street: The Time-Tested Strategy for Successful Investing presents that case very well.

-Rick Francis

Wonderfully concise summary, Mike.

Just for completeness, re: the Semi-Strong EMH, there’s a third option – you could try to invest in stocks and beat the market yourself.

I know, I know – but before I get my hat I’d argue that there’s benefits to this approach over picking one or more active fund managers, in that your dealing charges *may* be lower than the fund’s charges (and at least they’re transparent and under your control) and also you don’t have to try to predict two potentially understandable things – a manager’s performance AND the performance of the sort of stocks he invests in (or even a third – whether he or she is going to stick around).

Of course, a tracker fund sidesteps all of this for most people to deliver better than average results compared to funds, and only slightly worse results compared to the market. 🙂

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Writing a Strong Hypothesis Statement

All good theses begins with a good thesis question. However, all great theses begins with a great hypothesis statement. One of the most important steps for writing a thesis is to create a strong hypothesis statement.

What is a hypothesis statement?

A hypothesis statement must be testable. If it cannot be tested, then there is no research to be done.

Simply put, a hypothesis statement posits the relationship between two or more variables. It is a prediction of what you think will happen in a research study. A hypothesis statement must be testable. If it cannot be tested, then there is no research to be done. If your thesis question is whether wildfires have effects on the weather, “wildfires create tornadoes” would be your hypothesis. However, a hypothesis needs to have several key elements in order to meet the criteria for a good hypothesis.

In this article, we will learn about what distinguishes a weak hypothesis from a strong one. We will also learn how to phrase your thesis question and frame your variables so that you are able to write a strong hypothesis statement and great thesis.

What is a hypothesis?

A hypothesis statement posits, or considers, a relationship between two variables.

As we mentioned above, a hypothesis statement posits or considers a relationship between two variables. In our hypothesis statement example above, the two variables are wildfires and tornadoes, and our assumed relationship between the two is a causal one (wildfires cause tornadoes). It is clear from our example above what we will be investigating: the relationship between wildfires and tornadoes.

A strong hypothesis statement should be:

A prediction of the relationship between two or more variables

A hypothesis is not just a blind guess. It should build upon existing theories and knowledge . Tornadoes are often observed near wildfires once the fires reach a certain size. In addition, tornadoes are not a normal weather event in many areas; they have been spotted together with wildfires. This existing knowledge has informed the formulation of our hypothesis.

Depending on the thesis question, your research paper might have multiple hypothesis statements. What is important is that your hypothesis statement or statements are testable through data analysis, observation, experiments, or other methodologies.

Formulating your hypothesis

One of the best ways to form a hypothesis is to think about “if...then” statements.

Now that we know what a hypothesis statement is, let’s walk through how to formulate a strong one. First, you will need a thesis question. Your thesis question should be narrow in scope, answerable, and focused. Once you have your thesis question, it is time to start thinking about your hypothesis statement. You will need to clearly identify the variables involved before you can begin thinking about their relationship.

One of the best ways to form a hypothesis is to think about “if...then” statements . This can also help you easily identify the variables you are working with and refine your hypothesis statement. Let’s take a few examples.

If teenagers are given comprehensive sex education, there will be fewer teen pregnancies .

In this example, the independent variable is whether or not teenagers receive comprehensive sex education (the cause), and the dependent variable is the number of teen pregnancies (the effect).

If a cat is fed a vegan diet, it will die .

Here, our independent variable is the diet of the cat (the cause), and the dependent variable is the cat’s health (the thing impacted by the cause).

If children drink 8oz of milk per day, they will grow taller than children who do not drink any milk .

What are the variables in this hypothesis? If you identified drinking milk as the independent variable and growth as the dependent variable, you are correct. This is because we are guessing that drinking milk causes increased growth in the height of children.

Refining your hypothesis

Do not be afraid to refine your hypothesis throughout the process of formulation.

Do not be afraid to refine your hypothesis throughout the process of formulation. A strong hypothesis statement is clear, testable, and involves a prediction. While “testable” means verifiable or falsifiable, it also means that you are able to perform the necessary experiments without violating any ethical standards. Perhaps once you think about the ethics of possibly harming some cats by testing a vegan diet on them you might abandon the idea of that experiment altogether. However, if you think it is really important to research the relationship between a cat’s diet and a cat’s health, perhaps you could refine your hypothesis to something like this:

If 50% of a cat’s meals are vegan, the cat will not be able to meet its nutritional needs .

Another feature of a strong hypothesis statement is that it can easily be tested with the resources that you have readily available. While it might not be feasible to measure the growth of a cohort of children throughout their whole lives, you may be able to do so for a year. Then, you can adjust your hypothesis to something like this:

I f children aged 8 drink 8oz of milk per day for one year, they will grow taller during that year than children who do not drink any milk .

As you work to narrow down and refine your hypothesis to reflect a realistic potential research scope, don’t be afraid to talk to your supervisor about any concerns or questions you might have about what is truly possible to research.

What makes a hypothesis weak?

We noted above that a strong hypothesis statement is clear, is a prediction of a relationship between two or more variables, and is testable. We also clarified that statements, which are too general or specific are not strong hypotheses. We have looked at some examples of hypotheses that meet the criteria for a strong hypothesis, but before we go any further, let’s look at weak or bad hypothesis statement examples so that you can really see the difference.

Bad hypothesis 1: Diabetes is caused by witchcraft .

While this is fun to think about, it cannot be tested or proven one way or the other with clear evidence, data analysis, or experiments. This bad hypothesis fails to meet the testability requirement.

Bad hypothesis 2: If I change the amount of food I eat, my energy levels will change .

This is quite vague. Am I increasing or decreasing my food intake? What do I expect exactly will happen to my energy levels and why? How am I defining energy level? This bad hypothesis statement fails the clarity requirement.

Bad hypothesis 3: Japanese food is disgusting because Japanese people don’t like tourists .

This hypothesis is unclear about the posited relationship between variables. Are we positing the relationship between the deliciousness of Japanese food and the desire for tourists to visit? or the relationship between the deliciousness of Japanese food and the amount that Japanese people like tourists? There is also the problematic subjectivity of the assessment that Japanese food is “disgusting.” The problems are numerous.

The null hypothesis and the alternative hypothesis

The null hypothesis, quite simply, posits that there is no relationship between the variables.

What is the null hypothesis?

The hypothesis posits a relationship between two or more variables. The null hypothesis, quite simply, posits that there is no relationship between the variables. It is often indicated as H 0 , which is read as “h-oh” or “h-null.” The alternative hypothesis is the opposite of the null hypothesis as it posits that there is some relationship between the variables. The alternative hypothesis is written as H a or H 1 .

Let’s take our previous hypothesis statement examples discussed at the start and look at their corresponding null hypothesis.

H a : If teenagers are given comprehensive sex education, there will be fewer teen pregnancies .

H 0 : If teenagers are given comprehensive sex education, there will be no change in the number of teen pregnancies .

The null hypothesis assumes that comprehensive sex education will not affect how many teenagers get pregnant. It should be carefully noted that the null hypothesis is not always the opposite of the alternative hypothesis. For example:

If teenagers are given comprehensive sex education, there will be more teen pregnancies .

These are opposing statements that assume an opposite relationship between the variables: comprehensive sex education increases or decreases the number of teen pregnancies. In fact, these are both alternative hypotheses. This is because they both still assume that there is a relationship between the variables . In other words, both hypothesis statements assume that there is some kind of relationship between sex education and teen pregnancy rates. The alternative hypothesis is also the researcher’s actual predicted outcome, which is why calling it “alternative” can be confusing! However, you can think of it this way: our default assumption is the null hypothesis, and so any possible relationship is an alternative to the default.

Step-by-step sample hypothesis statements

Now that we’ve covered what makes a hypothesis statement strong, how to go about formulating a hypothesis statement, refining your hypothesis statement, and the null hypothesis, let’s put it all together with some examples. The table below shows a breakdown of how we can take a thesis question, identify the variables, create a null hypothesis, and finally create a strong alternative hypothesis.

Once you have formulated a solid thesis question and written a strong hypothesis statement, you are ready to begin your thesis in earnest. Check out our site for more tips on writing a great thesis and information on thesis proofreading and editing services.

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Start with a clear thesis question

Think about “if-then” statements to identify your variables and the relationship between them

Create a null hypothesis

Formulate an alternative hypothesis using the variables you have identified

Make sure your hypothesis clearly posits a relationship between variables

Make sure your hypothesis is testable considering your available time and resources

What makes a hypothesis strong? +

A hypothesis is strong when it is testable, clear, and identifies a potential relationship between two or more variables.

What makes a hypothesis weak? +

A hypothesis is weak when it is too specific or too general, or does not identify a clear relationship between two or more variables.

What is the null hypothesis? +

The null hypothesis posits that the variables you have identified have no relationship.

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Market Efficiency

There are generally two theories to assist pricing. The Efficient Market Hypothesis (EFM) and the Behavioural Finance Theory. Understanding the limitations of each of the theories is critical. Read the three concepts on this page to have a comprehensive understanding of EFM. What are the limitations of the EMH?

Implications and Limitations of the Efficient Market Hypothesis

Weak, semi-strong, and strong.

The efficient-market hypothesis emerged as a prominent theory in the mid-1960's. Paul Samuelson had begun to circulate Bachelier's work among economists. In 1964 Bachelier's dissertation along with the empirical studies mentioned above were published in an anthology edited by Paul Cootner. In 1965 Eugene Fama published his dissertation arguing for the random walk hypothesis, and Samuelson published a proof for a version of the efficient-market hypothesis. In 1970 Fama published a review of both the theory and the evidence for the hypothesis. The paper extended and refined the theory, included the definitions for three forms of financial market efficiency: weak, semi-strong, and strong.

It has been argued that the stock market is "micro efficient," but not "macro inefficient. " The main proponent of this view was Samuelson, who asserted that the EMH is much better suited for individual stocks than it is for the aggregate stock market. Research based on regression and scatter diagrams has strongly supported Samuelson's dictum.

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The Weak, Strong and Semi-Strong Efficient Market Hypotheses

Though the efficient market hypothesis as a whole theorizes that the market is generally efficient, the theory is offered in three different versions: weak, semi-strong and strong.

The basic efficient market hypothesis posits that the market cannot be beaten because it incorporates all important determinative information into current share prices . Therefore, stocks trade at the fairest value, meaning that they can't be purchased undervalued or sold overvalued . The theory determines that the only opportunity investors have to gain higher returns on their investments is through purely speculative investments that pose substantial risk.

The three versions of the efficient market hypothesis are varying degrees of the same basic theory. The weak form suggests that today’s stock prices reflect all the data of past prices and that no form of technical analysis can be effectively utilized to aid investors in making trading decisions. Advocates for the weak form efficiency theory believe that if fundamental analysis is used, undervalued and overvalued stocks can be determined, and investors can research companies' financial statements to increase their chances of making higher-than-market-average profits.

Semi-Strong Form

The semi-strong form efficiency theory follows the belief that because all information that is public is used in the calculation of a stock's current price , investors cannot utilize either technical or fundamental analysis to gain higher returns in the market. Those who subscribe to this version of the theory believe that only information that is not readily available to the public can help investors boost their returns to a performance level above that of the general market.

Strong Form

The strong form version of the efficient market hypothesis states that all information – both the information available to the public and any information not publicly known – is completely accounted for in current stock prices, and there is no type of information that can give an investor an advantage on the market. Advocates for this degree of the theory suggest that investors cannot make returns on investments that exceed normal market returns, regardless of information retrieved or research conducted.

There are anomalies that the efficient market theory cannot explain and that may even flatly contradict the theory. For example, the price/earnings (P/E) ratio shows that firms trading at lower P/E multiples are often responsible for generating higher returns. The neglected firm effect suggests that companies that are not covered extensively by market analysts are sometimes priced incorrectly in relation to their true value and offer investors the opportunity to pick stocks with hidden potential. The January effect shows historical evidence that stock prices – especially smaller cap stocks – tend to experience an upsurge in January.

Though the efficient market hypothesis is an important pillar of modern financial theories and has a large backing, primarily in the academic community, it also has a large number of critics. The theory remains controversial, and investors continue attempting to outperform market averages with their stock selections.

Has the efficient market hypothesis been proven correct or incorrect, is the stock market efficient, what does the efficient market hypothesis have to say about fundamental analysis, what is the efficient market hypothesis, why does the efficient market hypothesis state that technical analysis is bunk, top 7 market anomalies investors should know.

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Efficient Markets Hypothesis (EMH)

EMH Definition and Forms

What Is Efficient Market Hypothesis?

What are the types of emh, emh and investing strategies, the bottom line, frequently asked questions (faqs).

The Efficient Market Hypothesis (EMH) is one of the main reasons some investors may choose a passive investing strategy. It helps to explain the valid rationale of buying these passive mutual funds and exchange-traded funds (ETFs).

The Efficient Market Hypothesis (EMH) essentially says that all known information about investment securities, such as stocks, is already factored into the prices of those securities. If that is true, no amount of analysis can give you an edge over "the market."

EMH does not require that investors be rational; it says that individual investors will act randomly. But as a whole, the market is always "right." In simple terms, "efficient" implies "normal."

For example, an unusual reaction to unusual information is normal. If a crowd suddenly starts running in one direction, it's normal for you to run that way as well, even if there isn't a rational reason for doing so.

There are three forms of EMH: weak, semi-strong, and strong. Here's what each says about the market.

Weak Form EMH: Weak form EMH suggests that all past information is priced into securities. Fundamental analysis of securities can provide you with information to produce returns above market averages in the short term. But no "patterns" exist. Therefore, fundamental analysis does not provide a long-term advantage, and technical analysis will not work.
Semi-Strong Form EMH: Semi-strong form EMH implies that neither fundamental analysis nor technical analysis can provide you with an advantage. It also suggests that new information is instantly priced into securities.
Strong Form EMH: Strong form EMH says that all information, both public and private, is priced into stocks; therefore, no investor can gain advantage over the market as a whole. Strong form EMH does not say it's impossible to get an abnormally high return. That's because there are always outliers included in the averages.

EMH does not say that you can never outperform the market . It says that there are outliers who can beat the market averages. But there are also outliers who lose big to the market. The majority is closer to the median. Those who "win" are lucky; those who "lose" are unlucky.

Proponents of EMH, even in its weak form, often invest in index funds or certain ETFs. That is because those funds are passively managed and simply attempt to match, not beat, overall market returns.

Index investors might say they are going along with this common saying: "If you can't beat 'em, join 'em." Instead of trying to beat the market, they will buy an index fund that invests in the same securities as the benchmark index.

Some investors will still try to beat the market, believing that the movement of stock prices can be predicted, at least to some degree. For that reason, EMH does not align with a day trading strategy. Traders study short-term trends and patterns. Then, they attempt to figure out when to buy and sell based on these patterns. Day traders would reject the strong form of EMH.

For more on EMH, including arguments against it, check out the EMH paper from economist Burton G. Malkiel. Malkiel is also the author of the investing book "A Random Walk Down Main Street." The random walk theory says that movements in stock prices are random.

If you believe that you can't predict the stock market, you would most often support the EMH. But a short-term trader might reject the ideas put forth by EMH, because they believe that they are able to predict changes in stock prices.

For most investors, a passive, buy-and-hold , long-term strategy is useful. Capital markets are mostly unpredictable with random up and down movements in price.

When did the Efficient Market Hypothesis first emerge?

At the core of EMH is the theory that, in general, even professional traders are unable to beat the market in the long term with fundamental or technical analysis . That idea has roots in the 19th century and the "random walk" stock theory. EMH as a specific title is sometimes attributed to Eugene Fama's 1970 paper "Efficient Capital Markets: A Review of Theory and Empirical Work."

How is the Efficient Market Hypothesis used in the real world?

Investors who utilize EMH in their real-world portfolios are likely to make fewer decisions than investors who use fundamental or technical analysis. They are more likely to simply invest in broad market products, such as S&P 500 and total market funds.

Corporate Finance Institute. " Efficient Markets Hypothesis ."

IG.com. " Random Walk Theory Definition ."

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Strong Induction

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Strong induction is a variant of induction, in which we assume that the statement holds for all values preceding $k$. This provides us with more information to use when trying to prove the statement.

Proof of Strong Induction

Additional problems.

Now that we know how standard induction works, it's time to look at a variant of it, strong induction. In many ways, strong induction is similar to normal induction. There is, however, a difference in the inductive hypothesis. Normally, when using induction, we assume that $P(k)$ is true to prove $P(k+1)$. In strong induction, we assume that all of $P(1), P(2), . . . , P(k)$ are true to prove $P(k + 1)$.

Why would we need to do that? Let's go back to our domino analogy. Say that you have infinitely many dominoes arranged in a line. But this time, the weight of the $k^\text{th}$ domino isn't enough to knock down the $(k+1)^\text{th}$ domino. Knocking down the $(k+1)^\text{th}$ domino requires the weight of all the dominoes before it. Even now, if you are able to knock down the first domino, you can prove that all the dominoes will eventually fall.

The reason why this is called "strong induction" is that we use more statements in the inductive hypothesis. Let's write what we've learned till now a bit more formally.

Proof by strong induction Step 1. Demonstrate the base case: This is where you verify that $P(k_0)$ is true. In most cases, $k_0=1.$ Step 2. Prove the inductive step: This is where you assume that all of $P(k_0)$, $P(k_0+1), P(k_0+2), \ldots, P(k)$ are true (our inductive hypothesis). Then you show that $P(k+1)$ is true.

The proof of why this works is similar to that of standard induction.

The Fibonacci sequence is defined by $ F_{n+2} = F_{n+1} + F_n $ for integers $ n \geq 0 $, with starting values $ F_1 = F_ 2 = 1 $. Show that \[ F_n = \frac{ 1}{ \sqrt{5} } \left [ \left ( \frac{1 + \sqrt{5} } { 2} \right)^n - \left ( \frac{1 - \sqrt{5} } { 2} \right)^n \right]. \] Base case: For $ n = 1 $, we have $ LHS: F_1 =1 $ and $ RHS: \frac{ 1}{ \sqrt{5} } \left [ \left ( \frac{1 + \sqrt{5} } { 2} \right)^1 - \left ( \frac{1 - \sqrt{5} } { 2} \right)^1 \right] = \frac{ 1 } { \sqrt{5} } \left[ \frac{ 2 \sqrt{5} } { 2} \right] = 1 $. For $ n = 2 $, we have $ LHS: F_2 = 1 $ and $ RHS: \frac{ 1}{ \sqrt{5} } \left [ \left ( \frac{1 + \sqrt{5} } { 2} \right)^2 - \left ( \frac{1 - \sqrt{5} } { 2} \right)^2 \right] = \frac{ 1 } { \sqrt{5} } \left[ \frac{ 4 \sqrt{5} } { 4} \right] = 1 $. Induction step: Suppose that the statement is true for $ n = k-1 $ and $ k $. Then, we have \[\begin{align} F_{n+1} & = F_n + F_{n-1} \\\\ & = \frac{ 1}{ \sqrt{5} } \left [ \left ( \frac{1 + \sqrt{5} } { 2} \right)^n - \left ( \frac{1 - \sqrt{5} } { 2} \right)^n \right] + \frac{ 1}{ \sqrt{5} } \left [ \left ( \frac{1 + \sqrt{5} } { 2} \right)^{n-1} - \left ( \frac{1 - \sqrt{5} } { 2} \right)^{n-1} \right] \\\\ & = \frac{ 1}{ \sqrt{5} } \left [ \left ( \frac{1 + \sqrt{5} } { 2} \right)^n + \left ( \frac{1 + \sqrt{5} } { 2} \right)^{n-1} \right] - \frac{ 1}{ \sqrt{5} } \left [ \left ( \frac{1 - \sqrt{5} } { 2} \right)^n + \left ( \frac{1 - \sqrt{5} } { 2} \right)^{n-1} \right] \\\\ & = \frac{ 1}{ \sqrt{5} } \left [ \left ( \frac{1 + \sqrt{5} } { 2} \right)^{n+1} - \left ( \frac{1 - \sqrt{5} } { 2} \right)^{n+1} \right]. \end{align} \] Hence, the proposition is true. $_\square$

Note that, in this case, we did not need to use all of prior statements, but just the previous 2.

A chocolate bar consists of unit squares arranged in an $ n \times m $ rectangular grid. You may split the bar into individual unit squares, by breaking along the lines. What is the number of breaks required? We will show that the number of breaks needed is $ nm - 1 $. Base Case: For a $ 1 \times 1 $ square, we are already done, so no steps are needed. $ 1 \times 1 - 1 = 0 $, so the base case is true. Induction Step: Let $ P(n,m) $ denote the number of breaks needed to split up an $ n \times m $ square. WLOG, we may assume that the first break is along a row, and we get an $ n_1 \times m $ and an $ n_2 \times m $ bar, where $ n_1 + n_2 = n $. By the induction hypothesis, the number of further breaks that we need is $ n_1 \times m - 1 $ and $ n_2 \times m - 1 $. Hence, the total number of breaks that we need is \[ 1 + ( n_1 \times m -1 ) + ( n_2 \times m - 1 ) = (n_1 + n_2) \times m - 1 = n \times m - 1.\ _\square \]

Note: This problem can also be approached using Invariance principle .

A country has $n$ cities. Any two cities are connected by a one-way road. Show that there is a route that passes through every city. If you have already read the wiki on standard induction , this problem may seem familiar. Yes, we did prove this in that article (if you haven't read that wiki, now would be a good time to do that). We'll see how stronger induction produces a shorter and cleaner solution. As we've already seen, our base case for this is true. Now we make the "strong hypothesis." We assume that our statement is true for any set of $k$ or fewer cities. Now, for a set of $(k+1)$ cities, take out the $(k+1)^\text{th}$ city $C_{k+1}$ and split the rest of them into two sets $A$ and $B$. $A$ will contain all the cities that lead to $C_{k+1}$ and $B$ will contain all the cities $C_{k+1}$ leads to. Since $A$ has $k$ or fewer cities in it, by the inductive hypothesis, there is a route that passes through every city in $A$. The same argument holds for $B$. Now start with the route that passes through every city in $A$. Then go to $C_{k+1}$. You can do that because all the cities in $A$ lead to $C_{k+1}$. After that, go to the route that passes through every city in $B$. Again, you can do that because $C_{k+1}$ leads to every city in $B$. And just like that, our proof is complete! $_\square$

This proof is almost identical to the proof of standard induction . Can you spot the differences?

Let $S$ be a set of positive integers with the following properties: The integer 1 belongs to the set. Whenever the integers $1, 2, 3, \ldots, k$ are in $S$, the next integer $k+1$ must also be in $S$. Then $S$ is the set of all positive integers.

We will prove this theorem by contradiction. Let $T$ be the set of all positive integers not in $S$. By assumption, $T$ is non-empty. Hence it must contain a smallest element, which we will denote by $\alpha$. By (1), $0 < \alpha-1 < \alpha$. Since $ \alpha$ is the smallest integer in $T$, this implies that $ 1, 2, \ldots, \alpha - 1 \not \in T \implies 1, 2, \ldots, \alpha -1 \in S $. By (2), $S$ must also contain $ (\alpha-1)+1=\alpha$. This contradicts the assumption that $\alpha\subset$ $T$. Hence set $T$ is empty, and set $S$ contains all positive integers. $_\square $

Show that every integer $N \neq 0$ can be written in the form $N=2^k l$, where $k$ is a non-negative integer and $l$ is an odd integer.

[APMO '99] Let $\{a_i\}$ be a sequence of real numbers that satisfy $ a_{i+j} \leq a_i + a_j$ $\forall i, j$. Prove that \[\frac{ a_1}{1} + \frac {a_2}{2} + \cdots+ \frac {a_n}{n} \geq a_n. \]

Prove that every positive integer $n$ has a binary expression. Namely, that there exists integers $ c_i \in \{ 0, 1 \} $ such that \[ n = c_r 2^r + c_{r-1} 2^{r-1} + \cdots + c_2 2^2 + c_1 2^1 + c_0 2^ 0. \]

Consider the sequence defined as $ d_1 = 1, d_2 = 2, d_3 = 3, $ and $ d_{n+3} = d_{n+2} + d_{n+1} + d_n $ for all positive integers $n$. Show that $ d_n < 2 ^ n $.

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Supplement to Philosophy of Linguistics

Whorfianism.

Emergentists tend to follow Edward Sapir in taking an interest in interlinguistic and intralinguistic variation. Linguistic anthropologists have explicitly taken up the task of defending a famous claim associated with Sapir that connects linguistic variation to differences in thinking and cognition more generally. The claim is very often referred to as the Sapir-Whorf Hypothesis (though this is a largely infelicitous label, as we shall see).

This topic is closely related to various forms of relativism—epistemological, ontological, conceptual, and moral—and its general outlines are discussed elsewhere in this encyclopedia; see the section on language in the Summer 2015 archived version of the entry on relativism (§3.1). Cultural versions of moral relativism suggest that, given how much cultures differ, what is moral for you might depend on the culture you were brought up in. A somewhat analogous view would suggest that, given how much language structures differ, what is thinkable for you might depend on the language you use. (This is actually a kind of conceptual relativism, but it is generally called linguistic relativism, and we will continue that practice.)

Even a brief skim of the vast literature on the topic is not remotely plausible in this article; and the primary literature is in any case more often polemical than enlightening. It certainly holds no general answer to what science has discovered about the influences of language on thought. Here we offer just a limited discussion of the alleged hypothesis and the rhetoric used in discussing it, the vapid and not so vapid forms it takes, and the prospects for actually devising testable scientific hypotheses about the influence of language on thought.

Whorf himself did not offer a hypothesis. He presented his “new principle of linguistic relativity” (Whorf 1956: 214) as a fact discovered by linguistic analysis:

When linguists became able to examine critically and scientifically a large number of languages of widely different patterns, their base of reference was expanded; they experienced an interruption of phenomena hitherto held universal, and a whole new order of significances came into their ken. It was found that the background linguistic system (in other words, the grammar) of each language is not merely a reproducing instrument for voicing ideas but rather is itself the shaper of ideas, the program and guide for the individual’s mental activity, for his analysis of impressions, for his synthesis of his mental stock in trade. Formulation of ideas is not an independent process, strictly rational in the old sense, but is part of a particular grammar, and differs, from slightly to greatly, between different grammars. We dissect nature along lines laid down by our native languages. The categories and types that we isolate from the world of phenomena we do not find there because they stare every observer in the face; on the contrary, the world is presented in a kaleidoscopic flux of impressions which has to be organized by our minds—and this means largely by the linguistic systems in our minds. We cut nature up, organize it into concepts, and ascribe significances as we do, largely because we are parties to an agreement to organize it in this way—an agreement that holds throughout our speech community and is codified in the patterns of our language. The agreement is, of course, an implicit and unstated one, but its terms are absolutely obligatory ; we cannot talk at all except by subscribing to the organization and classification of data which the agreement decrees. (Whorf 1956: 212–214; emphasis in original)

Later, Whorf’s speculations about the “sensuously and operationally different” character of different snow types for “an Eskimo” (Whorf 1956: 216) developed into a familiar journalistic meme about the Inuit having dozens or scores or hundreds of words for snow; but few who repeat that urban legend recall Whorf’s emphasis on its being grammar, rather than lexicon, that cuts up and organizes nature for us.

In an article written in 1937, posthumously published in an academic journal (Whorf 1956: 87–101), Whorf clarifies what is most important about the effects of language on thought and world-view. He distinguishes ‘phenotypes’, which are overt grammatical categories typically indicated by morphemic markers, from what he called ‘cryptotypes’, which are covert grammatical categories, marked only implicitly by distributional patterns in a language that are not immediately apparent. In English, the past tense would be an example of a phenotype (it is marked by the - ed suffix in all regular verbs). Gender in personal names and common nouns would be an example of a cryptotype, not systematically marked by anything. In a cryptotype, “class membership of the word is not apparent until there is a question of using it or referring to it in one of these special types of sentence, and then we find that this word belongs to a class requiring some sort of distinctive treatment, which may even be the negative treatment of excluding that type of sentence” (p. 89).

Whorf’s point is the familiar one that linguistic structure is comprised, in part, of distributional patterns in language use that are not explicitly marked. What follows from this, according to Whorf, is not that the existing lexemes in a language (like its words for snow) comprise covert linguistic structure, but that patterns shared by word classes constitute linguistic structure. In ‘Language, mind, and reality’ (1942; published posthumously in Theosophist , a magazine published in India for the followers of the 19th-century spiritualist Helena Blavatsky) he wrote:

Because of the systematic, configurative nature of higher mind, the “patternment” aspect of language always overrides and controls the “lexation”…or name-giving aspect. Hence the meanings of specific words are less important than we fondly fancy. Sentences, not words, are the essence of speech, just as equations and functions, and not bare numbers, are the real meat of mathematics. We are all mistaken in our common belief that any word has an “exact meaning.” We have seen that the higher mind deals in symbols that have no fixed reference to anything, but are like blank checks, to be filled in as required, that stand for “any value” of a given variable, like …the x , y , z of algebra. (Whorf 1942: 258)

Whorf apparently thought that only personal and proper names have an exact meaning or reference (Whorf 1956: 259).

For Whorf, it was an unquestionable fact that language influences thought to some degree:

Actually, thinking is most mysterious, and by far the greatest light upon it that we have is thrown by the study of language. This study shows that the forms of a person’s thoughts are controlled by inexorable laws of pattern of which he is unconscious. These patterns are the unperceived intricate systematizations of his own language—shown readily enough by a candid comparison and contrast with other languages, especially those of a different linguistic family. His thinking itself is in a language—in English, in Sanskrit, in Chinese. [footnote omitted] And every language is a vast pattern-system, different from others, in which are culturally ordained the forms and categories by which the personality not only communicates, but analyzes nature, notices or neglects types of relationship and phenomena, channels his reasoning, and builds the house of his consciousness. (Whorf 1956: 252)

He seems to regard it as necessarily true that language affects thought, given

the fact that language must be used in order to think, and
the facts about language structure that linguistic analysis discovers.

He also seems to presume that the only structure and logic that thought has is grammatical structure. These views are not the ones that after Whorf’s death came to be known as ‘the Sapir-Whorf Hypothesis’ (a sobriquet due to Hoijer 1954). Nor are they what was called the ‘Whorf thesis’ by Brown and Lenneberg (1954) which was concerned with the relation of obligatory lexical distinctions and thought. Brown and Lenneberg (1954) investigated this question by looking at the relation of color terminology in a language and the classificatory abilities of the speakers of that language. The issue of the relation between obligatory lexical distinctions and thought is at the heart of what is now called ‘the Sapir-Whorf Hypothesis’ or ‘the Whorf Hypothesis’ or ‘Whorfianism’.

1. Banal Whorfianism

No one is going to be impressed with a claim that some aspect of your language may affect how you think in some way or other; that is neither a philosophical thesis nor a psychological hypothesis. So it is appropriate to set aside entirely the kind of so-called hypotheses that Steven Pinker presents in The Stuff of Thought (2007: 126–128) as “five banal versions of the Whorfian hypothesis”:

“Language affects thought because we get much of our knowledge through reading and conversation.”
“A sentence can frame an event, affecting the way people construe it.”
“The stock of words in a language reflects the kinds of things its speakers deal with in their lives and hence think about.”
“[I]f one uses the word language in a loose way to refer to meanings,… then language is thought.”
“When people think about an entity, among the many attributes they can think about is its name.”

These are just truisms, unrelated to any serious issue about linguistic relativism.

We should also set aside some methodological versions of linguistic relativism discussed in anthropology. It may be excellent advice to a budding anthropologist to be aware of linguistic diversity, and to be on the lookout for ways in which your language may affect your judgment of other cultures; but such advice does not constitute a hypothesis.

2. The so-called Sapir-Whorf hypothesis

The term “Sapir-Whorf Hypothesis” was coined by Harry Hoijer in his contribution (Hoijer 1954) to a conference on the work of Benjamin Lee Whorf in 1953. But anyone looking in Hoijer’s paper for a clear statement of the hypothesis will look in vain. Curiously, despite his stated intent “to review and clarify the Sapir-Whorf hypothesis” (1954: 93), Hoijer did not even attempt to state it. The closest he came was this:

The central idea of the Sapir-Whorf hypothesis is that language functions, not simply as a device for reporting experience, but also, and more significantly, as a way of defining experience for its speakers.

The claim that “language functions…as a way of defining experience” appears to be offered as a kind of vague metaphysical insight rather than either a statement of linguistic relativism or a testable hypothesis.

And if Hoijer seriously meant that what qualitative experiences a speaker can have are constituted by that speaker’s language, then surely the claim is false. There is no reason to doubt that non-linguistic sentient creatures like cats can experience (for example) pain or heat or hunger, so having a language is not a necessary condition for having experiences. And it is surely not sufficient either: a robot with a sophisticated natural language processing capacity could be designed without the capacity for conscious experience.

In short, it is a mystery what Hoijer meant by his “central idea”.

Vague remarks of the same loosely metaphysical sort have continued to be a feature of the literature down to the present. The statements made in some recent papers, even in respected refereed journals, contain non-sequiturs echoing some of the remarks of Sapir, Whorf, and Hoijer. And they come from both sides of the debate.

3. Anti-Whorfian rhetoric

Lila Gleitman is an Essentialist on the other side of the contemporary debate: she is against linguistic relativism, and against the broadly Whorfian work of Stephen Levinson’s group at the Max Planck Institute for Psycholinguistics. In the context of criticizing a particular research design, Li and Gleitman (2002) quote Whorf’s claim that “language is the factor that limits free plasticity and rigidifies channels of development”. But in the claim cited, Whorf seems to be talking about the psychological topic that holds universally of human conceptual development, not claiming that linguistic relativism is true.

Li and Gleitman then claim (p. 266) that such (Whorfian) views “have diminished considerably in academic favor” in part because of “the universalist position of Chomskian linguistics, with its potential for explaining the striking similarity of language learning in children all over the world.” But there is no clear conflict or even a conceptual connection between Whorf’s views about language placing limits on developmental plasticity, and Chomsky’s thesis of an innate universal architecture for syntax. In short, there is no reason why Chomsky’s I-languages could not be innately constrained, but (once acquired) cognitively and developmentally constraining.

For example, the supposedly deep linguistic universal of ‘recursion’ (Hauser et al. 2002) is surely quite independent of whether the inventory of colour-name lexemes in your language influences the speed with which you can discriminate between color chips. And conversely, universal tendencies in color naming across languages (Kay and Regier 2006) do not show that color-naming differences among languages are without effect on categorical perception (Thierry et al. 2009).

4. Strong and weak Whorfianism

One of the first linguists to defend a general form of universalism against linguistic relativism, thus presupposing that they conflict, was Julia Penn (1972). She was also an early popularizer of the distinction between ‘strong’ and ‘weak’ formulations of the Sapir-Whorf Hypothesis (and an opponent of the ‘strong’ version).

‘Weak’ versions of Whorfianism state that language influences or defeasibly shapes thought. ‘Strong’ versions state that language determines thought, or fixes it in some way. The weak versions are commonly dismissed as banal (because of course there must be some influence), and the stronger versions as implausible.

The weak versions are considered banal because they are not adequately formulated as testable hypotheses that could conflict with relevant evidence about language and thought.

Why would the strong versions be thought implausible? For a language to make us think in a particular way, it might seem that it must at least temporarily prevent us from thinking in other ways, and thus make some thoughts not only inexpressible but unthinkable. If this were true, then strong Whorfianism would conflict with the Katzian effability claim. There would be thoughts that a person couldn’t think because of the language(s) they speak.

Some are fascinated by the idea that there are inaccessible thoughts; and the notion that learning a new language gives access to entirely new thoughts and concepts seems to be a staple of popular writing about the virtues of learning languages. But many scientists and philosophers intuitively rebel against violations of effability: thinking about concepts that no one has yet named is part of their job description.

The resolution lies in seeing that the language could affect certain aspects of our cognitive functioning without making certain thoughts unthinkable for us .

For example, Greek has separate terms for what we call light blue and dark blue, and no word meaning what ‘blue’ means in English: Greek forces a choice on this distinction. Experiments have shown (Thierry et al. 2009) that native speakers of Greek react faster when categorizing light blue and dark blue color chips—apparently a genuine effect of language on thought. But that does not make English speakers blind to the distinction, or imply that Greek speakers cannot grasp the idea of a hue falling somewhere between green and violet in the spectrum.

There is no general or global ineffability problem. There is, though, a peculiar aspect of strong Whorfian claims, giving them a local analog of ineffability: the content of such a claim cannot be expressed in any language it is true of . This does not make the claims self-undermining (as with the standard objections to relativism); it doesn’t even mean that they are untestable. They are somewhat anomalous, but nothing follows concerning the speakers of the language in question (except that they cannot state the hypothesis using the basic vocabulary and grammar that they ordinarily use).

If there were a true hypothesis about the limits that basic English vocabulary and constructions puts on what English speakers can think, the hypothesis would turn out to be inexpressible in English, using basic vocabulary and the usual repertoire of constructions. That might mean it would be hard for us to discuss it in an article in English unless we used terminological innovations or syntactic workarounds. But that doesn’t imply anything about English speakers’ ability to grasp concepts, or to develop new ways of expressing them by coining new words or elaborated syntax.

5. Constructing and evaluating Whorfian hypotheses

A number of considerations are relevant to formulating, testing, and evaluating Whorfian hypotheses.

Genuine hypotheses about the effects of language on thought will always have a duality: there will be a linguistic part and a non-linguistic one. The linguistic part will involve a claim that some feature is present in one language but absent in another.

Whorf himself saw that it was only obligatory features of languages that established “mental patterns” or “habitual thought” (Whorf 1956: 139), since if it were optional then the speaker could optionally do it one way or do it the other way. And so this would not be a case of “constraining the conceptual structure”. So we will likewise restrict our attention to obligatory features here.

Examples of relevant obligatory features would include lexical distinctions like the light vs. dark blue forced choice in Greek, or the forced choice between “in (fitting tightly)” vs. “in (fitting loosely)” in Korean. They also include grammatical distinctions like the forced choice in Spanish 2nd-person pronouns between informal/intimate and formal/distant (informal tú vs. formal usted in the singular; informal vosotros vs. formal ustedes in the plural), or the forced choice in Tamil 1st-person plural pronouns between inclusive (“we = me and you and perhaps others”) and exclusive (“we = me and others not including you”).

The non-linguistic part of a Whorfian hypothesis will contrast the psychological effects that habitually using the two languages has on their speakers. For example, one might conjecture that the habitual use of Spanish induces its speakers to be sensitive to the formal and informal character of the speaker’s relationship with their interlocutor while habitually using English does not.

So testing Whorfian hypotheses requires testing two independent hypotheses with the appropriate kinds of data. In consequence, evaluating them requires the expertise of both linguistics and psychology, and is a multidisciplinary enterprise. Clearly, the linguistic hypothesis may hold up where the psychological hypothesis does not, or conversely.

In addition, if linguists discovered that some linguistic feature was optional in two different languages, then even if psychological experiments showed differences between the two populations of speakers, this would not show linguistic determination or influence. The cognitive differences might depend on (say) cultural differences.

A further important consideration concerns the strength of the inducement relationship that a Whorfian hypothesis posits between a speaker’s language and their non-linguistic capacities. The claim that your language shapes or influences your cognition is quite different from the claim that your language makes certain kinds of cognition impossible (or obligatory) for you. The strength of any Whorfian hypothesis will vary depending on the kind of relationship being claimed, and the ease of revisability of that relation.

A testable Whorfian hypothesis will have a schematic form something like this:

Linguistic part : Feature F is obligatory in L 1 but optional in L 2 .
Psychological part : Speaking a language with obligatory feature F bears relation R to the cognitive effect C .

The relation R might in principle be causation or determination, but it is important to see that it might merely be correlation, or slight favoring; and the non-linguistic cognitive effect C might be readily suppressible or revisable.

Dan Slobin (1996) presents a view that competes with Whorfian hypotheses as standardly understood. He hypothesizes that when the speakers are using their cognitive abilities in the service of a linguistic ability (speaking, writing, translating, etc.), the language they are planning to use to express their thought will have a temporary online effect on how they express their thought. The claim is that as long as language users are thinking in order to frame their speech or writing or translation in some language, the mandatory features of that language will influence the way they think.

On Slobin’s view, these effects quickly attenuate as soon as the activity of thinking for speaking ends. For example, if a speaker is thinking for writing in Spanish, then Slobin’s hypothesis would predict that given the obligatory formal/informal 2nd-person pronoun distinction they would pay greater attention to the formal/informal character of their social relationships with their audience than if they were writing in English. But this effect is not permanent. As soon as they stop thinking for speaking, the effect of Spanish on their thought ends.

Slobin’s non-Whorfian linguistic relativist hypothesis raises the importance of psychological research on bilinguals or people who currently use two or more languages with a native or near-native facility. This is because one clear way to test Slobin-like hypotheses relative to Whorfian hypotheses would be to find out whether language correlated non-linguistic cognitive differences between speakers hold for bilinguals only when are thinking for speaking in one language, but not when they are thinking for speaking in some other language. If the relevant cognitive differences appeared and disappeared depending on which language speakers were planning to express themselves in, it would go some way to vindicate Slobin-like hypotheses over more traditional Whorfian Hypotheses. Of course, one could alternately accept a broadening of Whorfian hypotheses to include Slobin-like evanescent effects. Either way, attention must be paid to the persistence and revisability of the linguistic effects.

Kousta et al. (2008) shows that “for bilinguals there is intraspeaker relativity in semantic representations and, therefore, [grammatical] gender does not have a conceptual, non-linguistic effect” (843). Grammatical gender is obligatory in the languages in which it occurs and has been claimed by Whorfians to have persistent and enduring non-linguistic effects on representations of objects (Boroditsky et al. 2003). However, Kousta et al. supports the claim that bilinguals’ semantic representations vary depending on which language they are using, and thus have transient effects. This suggests that although some semantic representations of objects may vary from language to language, their non-linguistic cognitive effects are transitory.

Some advocates of Whorfianism have held that if Whorfian hypotheses were true, then meaning would be globally and radically indeterminate. Thus, the truth of Whorfian hypotheses is equated with global linguistic relativism—a well known self-undermining form of relativism. But as we have seen, not all Whorfian hypotheses are global hypotheses: they are about what is induced by particular linguistic features. And the associated non-linguistic perceptual and cognitive differences can be quite small, perhaps insignificant. For example, Thierry et al. (2009) provides evidence that an obligatory lexical distinction between light and dark blue affects Greek speakers’ color perception in the left hemisphere only. And the question of the degree to which this affects sensuous experience is not addressed.

The fact that Whorfian hypotheses need not be global linguistic relativist hypotheses means that they do not conflict with the claim that there are language universals. Structuralists of the first half of the 20th century tended to disfavor the idea of universals: Martin Joos’s characterization of structuralist linguistics as claiming that “languages can differ without limit as to either extent or direction” (Joos 1966, 228) has been much quoted in this connection. If the claim that languages can vary without limit were conjoined with the claim that languages have significant and permanent effects on the concepts and worldview of their speakers, a truly profound global linguistic relativism would result. But neither conjunct should be accepted. Joos’s remark is regarded by nearly all linguists today as overstated (and merely a caricature of the structuralists), and Whorfian hypotheses do not have to take a global or deterministic form.

John Lucy, a conscientious and conservative researcher of Whorfian hypotheses, has remarked:

We still know little about the connections between particular language patterns and mental life—let alone how they operate or how significant they are…a mere handful of empirical studies address the linguistic relativity proposal directly and nearly all are conceptually flawed. (Lucy 1996, 37)

Although further empirical studies on Whorfian hypotheses have been completed since Lucy published his 1996 review article, it is hard to find any that have satisfied the criteria of:

adequately utilizing both the relevant linguistic and psychological research,
focusing on obligatory rather than optional linguistic features,
stating hypotheses in a clear testable way, and
ruling out relevant competing Slobin-like hypotheses.

There is much important work yet to be done on testing the range of Whorfian hypotheses and other forms of linguistic conceptual relativism, and on understanding the significance of any Whorfian hypotheses that turn out to be well supported.

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Sapir–Whorf hypothesis (Linguistic Relativity Hypothesis)

Mia Belle Frothingham

Author, Researcher, Science Communicator

BA with minors in Psychology and Biology, MRes University of Edinburgh

Mia Belle Frothingham is a Harvard University graduate with a Bachelor of Arts in Sciences with minors in biology and psychology

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Saul Mcleod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

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There are about seven thousand languages heard around the world – they all have different sounds, vocabularies, and structures. As you know, language plays a significant role in our lives.

But one intriguing question is – can it actually affect how we think?

Collection of talking people. Men and women with speech bubbles. Communication and interaction. Friends, students or colleagues. Cartoon flat vector illustrations isolated on white background

It is widely thought that reality and how one perceives the world is expressed in spoken words and are precisely the same as reality.

That is, perception and expression are understood to be synonymous, and it is assumed that speech is based on thoughts. This idea believes that what one says depends on how the world is encoded and decoded in the mind.

However, many believe the opposite.

In that, what one perceives is dependent on the spoken word. Basically, that thought depends on language, not the other way around.

What Is The Sapir-Whorf Hypothesis?

Twentieth-century linguists Edward Sapir and Benjamin Lee Whorf are known for this very principle and its popularization. Their joint theory, known as the Sapir-Whorf Hypothesis or, more commonly, the Theory of Linguistic Relativity, holds great significance in all scopes of communication theories.

The Sapir-Whorf hypothesis states that the grammatical and verbal structure of a person’s language influences how they perceive the world. It emphasizes that language either determines or influences one’s thoughts.

The Sapir-Whorf hypothesis states that people experience the world based on the structure of their language, and that linguistic categories shape and limit cognitive processes. It proposes that differences in language affect thought, perception, and behavior, so speakers of different languages think and act differently.

For example, different words mean various things in other languages. Not every word in all languages has an exact one-to-one translation in a foreign language.

Because of these small but crucial differences, using the wrong word within a particular language can have significant consequences.

The Sapir-Whorf hypothesis is sometimes called “linguistic relativity” or the “principle of linguistic relativity.” So while they have slightly different names, they refer to the same basic proposal about the relationship between language and thought.

How Language Influences Culture

Culture is defined by the values, norms, and beliefs of a society. Our culture can be considered a lens through which we undergo the world and develop a shared meaning of what occurs around us.

The language that we create and use is in response to the cultural and societal needs that arose. In other words, there is an apparent relationship between how we talk and how we perceive the world.

One crucial question that many intellectuals have asked is how our society’s language influences its culture.

Linguist and anthropologist Edward Sapir and his then-student Benjamin Whorf were interested in answering this question.

Together, they created the Sapir-Whorf hypothesis, which states that our thought processes predominantly determine how we look at the world.

Our language restricts our thought processes – our language shapes our reality. Simply, the language that we use shapes the way we think and how we see the world.

Since the Sapir-Whorf hypothesis theorizes that our language use shapes our perspective of the world, people who speak different languages have different views of the world.

In the 1920s, Benjamin Whorf was a Yale University graduate student studying with linguist Edward Sapir, who was considered the father of American linguistic anthropology.

Sapir was responsible for documenting and recording the cultures and languages of many Native American tribes disappearing at an alarming rate. He and his predecessors were well aware of the close relationship between language and culture.

Anthropologists like Sapir need to learn the language of the culture they are studying to understand the worldview of its speakers truly. Whorf believed that the opposite is also true, that language affects culture by influencing how its speakers think.

His hypothesis proposed that the words and structures of a language influence how its speaker behaves and feels about the world and, ultimately, the culture itself.

Simply put, Whorf believed that you see the world differently from another person who speaks another language due to the specific language you speak.

Human beings do not live in the matter-of-fact world alone, nor solitary in the world of social action as traditionally understood, but are very much at the pardon of the certain language which has become the medium of communication and expression for their society.

To a large extent, the real world is unconsciously built on habits in regard to the language of the group. We hear and see and otherwise experience broadly as we do because the language habits of our community predispose choices of interpretation.

Studies & Examples

The lexicon, or vocabulary, is the inventory of the articles a culture speaks about and has classified to understand the world around them and deal with it effectively.

For example, our modern life is dictated for many by the need to travel by some vehicle – cars, buses, trucks, SUVs, trains, etc. We, therefore, have thousands of words to talk about and mention, including types of models, vehicles, parts, or brands.

The most influential aspects of each culture are similarly reflected in the dictionary of its language. Among the societies living on the islands in the Pacific, fish have significant economic and cultural importance.

Therefore, this is reflected in the rich vocabulary that describes all aspects of the fish and the environments that islanders depend on for survival.

For example, there are over 1,000 fish species in Palau, and Palauan fishers knew, even long before biologists existed, details about the anatomy, behavior, growth patterns, and habitat of most of them – far more than modern biologists know today.

Whorf’s studies at Yale involved working with many Native American languages, including Hopi. He discovered that the Hopi language is quite different from English in many ways, especially regarding time.

Western cultures and languages view times as a flowing river that carries us continuously through the present, away from the past, and to the future.

Our grammar and system of verbs reflect this concept with particular tenses for past, present, and future.

We perceive this concept of time as universal in that all humans see it in the same way.

Although a speaker of Hopi has very different ideas, their language’s structure both reflects and shapes the way they think about time. Seemingly, the Hopi language has no present, past, or future tense; instead, they divide the world into manifested and unmanifest domains.

The manifested domain consists of the physical universe, including the present, the immediate past, and the future; the unmanifest domain consists of the remote past and the future and the world of dreams, thoughts, desires, and life forces.

Also, there are no words for minutes, minutes, or days of the week. Native Hopi speakers often had great difficulty adapting to life in the English-speaking world when it came to being on time for their job or other affairs.

It is due to the simple fact that this was not how they had been conditioned to behave concerning time in their Hopi world, which followed the phases of the moon and the movements of the sun.

Today, it is widely believed that some aspects of perception are affected by language.

One big problem with the original Sapir-Whorf hypothesis derives from the idea that if a person’s language has no word for a specific concept, then that person would not understand that concept.

Honestly, the idea that a mother tongue can restrict one’s understanding has been largely unaccepted. For example, in German, there is a term that means to take pleasure in another person’s unhappiness.

While there is no translatable equivalent in English, it just would not be accurate to say that English speakers have never experienced or would not be able to comprehend this emotion.

Just because there is no word for this in the English language does not mean English speakers are less equipped to feel or experience the meaning of the word.

Not to mention a “chicken and egg” problem with the theory.

Of course, languages are human creations, very much tools we invented and honed to suit our needs. Merely showing that speakers of diverse languages think differently does not tell us whether it is the language that shapes belief or the other way around.

Supporting Evidence

On the other hand, there is hard evidence that the language-associated habits we acquire play a role in how we view the world. And indeed, this is especially true for languages that attach genders to inanimate objects.

There was a study done that looked at how German and Spanish speakers view different things based on their given gender association in each respective language.

The results demonstrated that in describing things that are referred to as masculine in Spanish, speakers of the language marked them as having more male characteristics like “strong” and “long.” Similarly, these same items, which use feminine phrasings in German, were noted by German speakers as effeminate, like “beautiful” and “elegant.”

The findings imply that speakers of each language have developed preconceived notions of something being feminine or masculine, not due to the objects” characteristics or appearances but because of how they are categorized in their native language.

It is important to remember that the Theory of Linguistic Relativity (Sapir-Whorf Hypothesis) also successfully achieves openness. The theory is shown as a window where we view the cognitive process, not as an absolute.

It is set forth to look at a phenomenon differently than one usually would. Furthermore, the Sapir-Whorf Hypothesis is very simple and logically sound. Understandably, one’s atmosphere and culture will affect decoding.

Likewise, in studies done by the authors of the theory, many Native American tribes do not have a word for particular things because they do not exist in their lives. The logical simplism of this idea of relativism provides parsimony.

Truly, the Sapir-Whorf Hypothesis makes sense. It can be utilized in describing great numerous misunderstandings in everyday life. When a Pennsylvanian says “yuns,” it does not make any sense to a Californian, but when examined, it is just another word for “you all.”

The Linguistic Relativity Theory addresses this and suggests that it is all relative. This concept of relativity passes outside dialect boundaries and delves into the world of language – from different countries and, consequently, from mind to mind.

Is language reality honestly because of thought, or is it thought which occurs because of language? The Sapir-Whorf Hypothesis very transparently presents a view of reality being expressed in language and thus forming in thought.

The principles rehashed in it show a reasonable and even simple idea of how one perceives the world, but the question is still arguable: thought then language or language then thought?

Modern Relevance

Regardless of its age, the Sapir-Whorf hypothesis, or the Linguistic Relativity Theory, has continued to force itself into linguistic conversations, even including pop culture.

The idea was just recently revisited in the movie “Arrival,” – a science fiction film that engagingly explores the ways in which an alien language can affect and alter human thinking.

And even if some of the most drastic claims of the theory have been debunked or argued against, the idea has continued its relevance, and that does say something about its importance.

Hypotheses, thoughts, and intellectual musings do not need to be totally accurate to remain in the public eye as long as they make us think and question the world – and the Sapir-Whorf Hypothesis does precisely that.

The theory does not only make us question linguistic theory and our own language but also our very existence and how our perceptions might shape what exists in this world.

There are generalities that we can expect every person to encounter in their day-to-day life – in relationships, love, work, sadness, and so on. But thinking about the more granular disparities experienced by those in diverse circumstances, linguistic or otherwise, helps us realize that there is more to the story than ours.

And beautifully, at the same time, the Sapir-Whorf Hypothesis reiterates the fact that we are more alike than we are different, regardless of the language we speak.

Isn’t it just amazing that linguistic diversity just reveals to us how ingenious and flexible the human mind is – human minds have invented not one cognitive universe but, indeed, seven thousand!

Kay, P., & Kempton, W. (1984). What is the Sapir‐Whorf hypothesis?. American anthropologist, 86(1), 65-79.

Whorf, B. L. (1952). Language, mind, and reality. ETC: A review of general semantics, 167-188.

Whorf, B. L. (1997). The relation of habitual thought and behavior to language. In Sociolinguistics (pp. 443-463). Palgrave, London.

Whorf, B. L. (2012). Language, thought, and reality: Selected writings of Benjamin Lee Whorf. MIT press.

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What Makes a Strong Hypothesis for Scientific Research?

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Adam Becker

Author and astrophysicist, weak forms and strong forms.

For Cameron Neylon, because he kept asking me for this…

The Sapir-Whorf hypothesis 1 states that language affects thought — how we speak influences how we think. Or, at least, that’s one form of the hypothesis, the weak form. The strong form of Sapir-Whorf says that language determines thought, that how we speak forms a hard boundary on how and what we think. The weak form of Sapir-Whorf says that we drive an ATV across the terrain of thought; language can smooth the path in some areas and create rocks and roadblocks in others, but it doesn’t fundamentally limit where we can go. The strong form, in contrast, says we drive a steam train of thought, and language lays down the rails. There’s an intricate maze of forks and switchbacks spanning the continent, but at the end of the day we can only go where the rails will take us — we can’t lay down new track, no matter how we might try.

Most linguists today accept that some form of the weak Sapir-Whorf hypothesis must be true: the language(s) we speak definitely affect how we think and act. But most linguists also accept that the strong Sapir-Whorf hypothesis can’t be true, just as a matter of empirical fact. New words are developed, new concepts formed, new trails blazed on the terrain of thought. Some tasks may be easier or harder depending on whether your language is particularly suited for them — though even this is in dispute . But it’s simply not the case that we can’t think about things if we don’t have the words for them, nor that language actually determines our thought. In short, while the weak form of Sapir-Whorf is probably correct, the strong form is wrong. And this makes some sense: it certainly seems like language affects our thoughts, but it doesn’t seem like language wholly determines our thoughts.

But the Sapir-Whorf hypothesis isn’t the only theory with strong and weak forms — in fact, there’s a whole pattern of theories like this, and associated rhetorical dangers that go along with them. The pattern looks like this:

Start with a general theoretical statement about the world, where…
…there are two forms, a weak form and a strong form, and…
…the weak form is obviously true — how could it not be? — and…
…the strong form is obviously false, or at least much more controversial. Then, the rhetorical danger rears its head, and…
…arguments for the (true) weak form are appropriated, unmodified or nearly so, as arguments for the strong form by the proponents of the latter. (You also sometimes see this in reverse: people who are eager to deny the strong form rejecting valid arguments for the weak form.)

I don’t know why (5) happens, but I suspect (with little to no proof) that this confusion stems from rejection of a naive view of the world. Say you start with a cartoonishly simple picture of some phenomenon — for example, say you believe that thought isn’t affected by language in any way at all. Then you hear (good!) arguments for the weak form of the Sapir-Whorf hypothesis, which shows this cartoon picture is too simple to capture reality. With your anchor line to your old idea cut, you veer to the strong form of Sapir-Whorf. Then, later, when arguing for your new view, you use the same arguments that convinced you your old naive idea was false — namely, arguments for the weak form. (This also suggests that when (5) happens in reverse, this is founded in the same basic confusion: people defend themselves from the strong form by attacking the weak form because they would feel unmoored from their (naive) views if the weak form were true.) But why this happens is all speculation on my part. All I know for sure is that it does happen.

Cultural relativism about scientific truth is another good example. The two forms look something like this:

Weak form : Human factors like culture, history, and economics influence the practice of science, and thereby the content of our scientific theories.

Strong form : Human factors like culture, history, and economics wholly determine the content of our scientific theories.

It’s hard to see how the weak form could be wrong. Science is a human activity, and like any human activity, it’s affected by culture, economics, history, and other human factors. But the strong form claims that science is totally disconnected from anything like a “real world,” is simply manufactured by a variety of cultural and social forces, and has no special claim to truth. This is just not true. In her excellent book Brain Storm — itself about how the weak form of this thesis has played out in the spurious science of innate gender differences in the development of the human brain — Rebecca Jordan-Young forcefully rejects the strong form of relativism about science, and addresses both directions of the rhetorical confusion that arises from confounding the weak form with the strong:

The fact that science is not, and can never be, a simple mirror of the world also does not imply that science is simply “made up” and is not constrained by material phenomena that actually exist—the material world “pushes back” and exerts its own effects in science, even if we accept the postmodern premise that we humans have no hope of a direct access to that world that is unmediated by our own practices and culturally determined cognitive and linguistic structures. There is no need to dogmatically insist (against all evidence) that science really is objective in order to believe in science as a good and worthwhile endeavor, and even to believe in science as a particularly useful and trustworthy way of learning about the world. 2

Successful scientific theories, in general, must bear some resemblance to the world at large. Indeed, the success of scientific theories in predicting phenomena in the world would be nothing short of a miracle if there were absolutely no resemblance between the content of those theories and the content of the world. 3 That’s not to say that our theories are perfect representations of the world, nor that they are totally unaffected by cultural and political factors: far from it. I’m writing a book right now that’s (partly) about the cultural and historical factors influencing the debate on the foundations of quantum physics. But the content of our scientific theories is certainly not solely determined by human factors. Science is our best attempt to learn about the nature of the world. It’s not perfect. That’s OK.

There are many people, working largely in Continental philosophy and critical theory of various stripes, who advocate the strong form of relativism about science. 4 Yet most of their arguments which are ostensibly in favor of this strong form are actually arguments for the weak form: that culture plays some role in determining the content of our best scientific theories. 5 And that’s simply not the same thing.

Another, much more popular example of a strong and weak form problem is the set of claims around the “power of positive thinking.” The weak form suggests that being more confident and positive can make you happier, healthier, and more successful. This is usually true, and it’s hard to see how it couldn’t be usually true — though there are many specific counterexamples. For example, positive thinking can’t keep your house from being destroyed by a hurricane. Yet the strong form of positive-thinking claims — known as “the law of attraction,” and popularized by The Secret — suggests exactly that. This states that positive thinking, and positive thinking alone, can literally change the world around you for the better, preventing and reversing all bad luck and hardship. 6 Not only is this manifestly untrue, but the logical implications are morally repugnant: if bad things do happen to you, it must be a result of not thinking positively enough . For example, if you have cancer, and it’s resistant to treatment, that must be your fault . While this kind of neo-Calvinist victim-blaming is bad enough, it becomes truly monstrous — and the flaw in the reasoning particularly apparent — when extended from unfortunate individual circumstances to systematically disadvantaged groups. The ultimate responsibility for slavery, colonialism, genocide, and institutionalized bigotry quite obviously does not lie with the victims’ purported inability to wish hard enough for a better world.

In short, easily-confused strong and weak forms of a theory abound. I’m not claiming that this is anything like an original idea. All I’m saying is that some theories come in strong and weak forms, that sometimes the weak forms are obviously true and the strong obviously false, and that in those cases, it’s easy to take rhetorical advantage (deliberately or not) of this confusion. You could argue that the weak form directly implies the strong form in some cases, and maybe it does. But that’s not generally true, and you have to do a lot of work to make that argument — work that often isn’t done.

Again, I strongly suspect other people have come up with this idea. When I’ve talked with people about this, they’ve generally picked it up very quickly and come up with examples I didn’t think of. This seems to be floating around. If someone has a good citation for it, I’d be immensely grateful.

Image credit: Zink Dawg at English Wikipedia , CC-BY 3.0. I was strongly tempted to use this image instead.

This is apparently a historical misnomer, but we’ll ignore that for now. [ ↩ ]
Rebecca M. Jordan-Young, in Brain Storm: The Flaws in the Science of Sex Differences, Harvard University Press, 2011, pp. 299-300. Emphasis in the original. [ ↩ ]
See J.J.C. Smart, Philosophy and Scientific Realism , and Hilary Putnam, Mathematics, Matter, and Method . [ ↩ ]
Bruno Latour is the first name that comes to mind. [ ↩ ]
See, for example, Kuhn, who even seems to have confused himself about whether he was advocating the strong or the weak version. [ ↩ ]
The “arguments” in favor of this kind of nonsense take advantage of more than just the confusion between the strong and weak forms of the thesis about positive thinking. They also rely on profound misunderstandings about quantum physics and other perversions of science. But let’s put that aside for now. [ ↩ ]

Preference Hypothesis and Strong Ordering (Explained With Diagram)

Samuelson’s revealed preference theory has preference hypothesis as a basis of his theory of demand.

According to this hypothesis, when a consumer is observed to choose a combination A out of various alternative combinations open to him, then he ‘reveals’, his preference for A over all other alternative combinations which he could have purchased.

In other words, when a consumer chooses a combination A, it means he considers all other alternative combinations which he could have purchased to be inferior to A. That is, he rejects all other alternative combinations open to him in favour of the chosen combination A. Thus, according to Samuelson, choice reveals preference. Choice of the combination A reveals his definite preference for A over all other rejected combinations.

From the hypothesis of ‘choice reveals preference’ we can obtain definite information about the preferences of a consumer from the observations of his behaviour in the market. By comparing preferences of a consumer revealed in different price-income situations we can obtain certain information about his preference scale.

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Let us graphically explain the preference hypothesis. Given the prices of two commodities X and Y and the income of the consumer, price line PL is drawn in Fig. 12.1. The price line PL represents a given price-income situation. Given the price-income situation as represented by PL, the consumer can buy or choose any combination lying within or on the triangle OPL.

In other words, all combinations lying on the line PL such as A, B, C and lying below the line PL such as D, E, F and G are alternative combinations open to him, from among which he has to choose any combination. If our consumer chooses combination A out of all those open to him in the given price-income situation, it means he reveals his preference for A over all other combinations such as B, C, D, E and F which are rejected by him. As is evident from Fig. 12.1, in his observed chosen combination A, the consumer is buying OM quantity of commodity X and ON quantity of commodity Y.

Besides, we can infer more from consumer’s observed choice. As it is assumed that a rational consumer prefers more of both the goods to less of them or prefers more of at least one good, the amount of the other good remaining the same, we can infer that all combinations lying in the rectangular shaded area drawn above and to the right of chosen combination A are superior to A.

Since in the rectangular shaded area there lie those combinations (baskets) of two goods which contain either more of both the goods or at least more of one good, the amount of the other remaining the same, this means that the consumer would prefer all combinations in the rectangular shaded area to the chosen combination A. In other words, all combinations in the shaded area MAN are superior to the chosen combination A.

As seen above, all other combinations lying in the budget-space OPL are attainable or affordable but are rejected in favour of A and are therefore revealed to be inferior to it. It should be carefully noted that Samuelson’s revealed preference theory is based upon the strong form of preference hypothesis.

In other words, in revealed preference theory, strong- ordering preference hypothesis has been applied. Strong ordering implies that there is definite ordering of various combinations in consumer’s scale of preferences and therefore the choice of a combination by a consumer reveals his definite preference for that over all other alternatives open to him.

Thus, under strong ordering, relation of indifference between various alternative combinations is ruled out. When in Fig. 12.1a consumer chooses a combination A out of various alternative combinations open to him, it means he has a definite preference for A over all others; the possibility of the chosen combination A being indifferent to any other possible combination is ruled out by strong ordering hypothesis.

J. R. Hicks in his “A Revision of Demand Theory’ does not consider the assumption of strong ordering as satisfactory and instead employs weak ordering hypothesis. Under weak ordering hypothesis (with an additional assumption that the consumer will always prefer a larger amount of a good to a smaller amount of it), the chosen combination A is preferred over all positions that lie within the triangle OPL and further that the chosen position A will be either preferred to or indifferent to the other positions on the price-income line PL.

“The difference between the consequences of strong and weak ordering, so interpreted amounts to no more than this that under strong ordering the chosen position is shown to be preferred to all other positions in and on the triangle, while under weak ordering it is preferred to all positions within the triangle, but may be indifferent to other positions on the same boundary as itself.”

The revealed preference theory rests upon a basic assumption which has been called the ‘consistency postulate’. In fact, the consistency postulate is implied in the strong ordering hypothesis. The consistency postulate can be stated thus: ‘no two observations of choice behaviour are made which provide conflicting evidence to the individual’s preference.”

In other words, consistency postulate asserts that if an individual chooses A rather than B in one particular instance, then he cannot choose B rather than A in any other instance when both are available to the consumer. If he chooses A rather than B in one instance and chooses B rather than A in another when A and B are present in both the instances, then he is not behaving consistently.

Thus, consistency postulate requires that if once A is revealed to be preferred to B by an individual, then B cannot be revealed to be preferred to A by him at any other time when A and B are present in both the cases. Since comparison here is between the two situations consistency involved in this has been called ‘ two term consistency by J.R. Hicks.

Weak Axiom of Revealed Preference (WARP):

If a person chooses combination A rather than combination B which he could purchase with the given budget constraint, then it cannot happen that he would choose (i.e. prefer) B over A in some other situation in which he could have bought A if he so wished. This means his choices or preferences must be consistent.

This is called revealed preference axiom. We illustrate, revealed preference axiom in Figure 12.2. Suppose with the given prices of two goods X and Y and given his money income to spend on the two goods, PL is the budget line facing a consumer. In this budgetary situation PL, the consumer chooses A when he could have purchased B (note that combination B would have even cost him less than A). Thus, his choice of A over B means he prefers the combination A to the combination B of the two goods.

Now suppose that price of good X falls, and with some income and price adjustments, budget line changes to P’L’. Budget line P’L’ is flatter than PL reflecting relatively lower price of X as compared to the budget line PL. With this new budget line P ‘U, if the consumer chooses combination B when he can purchase the combination A (as A lies below the budget line P’L’ in Fig. 12.2), then the consumer will be inconsistent in his preferences, that is, he will be violating the axiom of revealed preference.

Such inconsistent consumer’s behaviour is ruled out in revealed preference theory based on strong ordering. This axiom of revealed preference according to which consumer’s choices are consistent is also called ‘ Weak Axiom of Revealed Preference or simply WARP. To sum up, according to the weak axiom of revealed preference.

“If combination A is directly revealed preferred to another combination B, then in any other situation, the combination B cannot be revealed preferred to combination A by the consumer when combination A is also affordable”.

Now consider Figure 12.3 where to start with a consumer is facing budget line PL where he chooses combination A of two goods X and Y. Thus, consumer prefers combination A to all other combinations within and on the triangle OPL. Now suppose that budget constraint changes to P ‘L’ and consumer purchases combination B on it.

As combination B lies outside the budget line PL it was not affordable when combination A was chosen. Therefore, choice of combination B with the budget line P ‘L’ is consistent with his earlier choice A with the budget constraint PL and is in accordance with the weak axiom of revealed preference.

Transitivity Assumption of Revealed Preference :

The axiom of revealed preference described above provides us a consistency condition that must be satisfied by a rational consumer who makes an optimum choice. Apart from the axiom of revealed preference, revealed preference theory also assumes that revealed preferences are transitive.

According to this, if an optimising consumer prefers combination A to combination B of the goods and combination B to combination C of the goods, then he will also prefer combination A to combination C of the goods. To put it briefly, assumption of transitivity of preferences requires that if A> B and B> C, then A > C.

In this way we say that combination A is indirectly revealed to be preferred to combination C. Thus, if a combination A is either directly or indirectly revealed preferred to another combination we say that combination A is revealed to be preferred to the other combination. Consider Figure 12.4 where with budget constraint PL, the consumer chooses A and therefore reveals his preference for A over combination B which he could have purchased as combination B is affordable in budget constraint PL.

Now suppose budget constraint facing the consumer changes to P’L’, he chooses B when he could have purchased C. Thus, the consumer prefers B to C. From the transitivity assumption it follows that the consumer will prefer combination A to combination C. Thus, combination A is indirectly revealed to be preferred to combination C. We therefore conclude that the consumer prefers A either directly or indirectly to all those combinations of the two goods lying in the shaded regions in Figure 12.4.

It is thus evident from above that concept of revealed preference is a very significant and powerful tool which provides a lot of information about consumer’s preferences who behave in an optimising and consistent manner. By merely looking at the consumer’s choices in different price-income situations we can get a lot of information about consumer’s preferences.

It may be noted that the consistency postulate of revealed preference theory is the counterpart of the utility maximisation assumption in both Marshallian utility theory and Hicks- Allen indifference curve theory. The assumption that the consumer maximises utility or satisfaction is known as rationality assumption. It has been said that a rational consumer will try to maximise utility or satisfaction.

Recently, some economists have challenged this assumption. They assert that consumers in actual practice do not maximise utility. The revealed theory has the advantage that its rationality assumption can be easily realised in actual practice. The rationality on the part of the consumer in revealed preference theory only requires that he should behave in a ‘consistent’ manner.

Consistency of choice is a less restrictive assumption than the utility maximisation assumption. This is one of the improvements of Samuelson’s theory over the Marshallian cardinal utility and Hicks-Allen indifference curve theories of demand.

It is important to note that Samuelson’s revealed preference is not a statistical concept. If it were a statistical concept, then the preference of an individual for a combination A would have been inferred from giving him opportunity to exercise his choice several times in the same circumstances.

If the individual from among the various alternative combinations open to him chooses a particular combination more frequently than any other, only then the individual’s preference for A would have been statistically revealed. But in Samuelson’s revealed preference theory preference is said to be revealed from a single act of choice.

It is obvious that no single act of choice on the part of the consumer can prove his indifference between the two situations. Unless the individual is given the chance to exercise his choice several times in the given circumstances, he has no way of revealing his indifference between various combinations.

Thus, because Samuelson infers preference from a single act of choice the relation of indifference is inadmissible to his theory. Therefore, the rejection of indifference relation by Samuelson follows from his methodology. “The rejection of indifference in Samuelson theory is, therefore, not a matter of convenience but dictated by the requirements of his methodology.”

Choice of Revealed Preference (With Diagram)
Hick’s Logical Theory of Demand: Preference Hypothesis and Logic of Ordering
The Revealed Preference Hypothesis (With Diagram)
Consumption Theory on Revealed Preference Approach

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Published: 24 March 2022

Scientific success from the perspective of the strength of weak ties

Agata Fronczak 1 ,
Maciej J. Mrowinski 1 &
Piotr Fronczak 1

Scientific Reports volume 12 , Article number: 5074 ( 2022 ) Cite this article

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Complex networks
Computational science

We present the first complete verification of Granovetter’s theory of social networks using a massive dataset, i.e. DBLP computer science bibliography database. For this purpose, we study a coauthorship network, which is considered one of the most important examples that contradicts the universality of this theory. We achieve this goal by rejecting the assumption of the symmetry of social ties. Our approach is grounded in well-established heterogeneous (degree-based) mean-field theory commonly used to study dynamical processes on complex networks. Granovetter’s theory is based on two hypotheses that assign different roles to interpersonal, information-carrying connections. The first hypothesis states that strong ties carrying the majority of interaction events are located mainly within densely connected groups of people. The second hypothesis maintains that these groups are connected by sparse weak ties that are of vital importance for the diffusion of information—individuals who have access to weak ties have an advantage over those who do not. Given the scientific collaboration network, with strength of directed ties measured by the asymmetric fraction of joint publications, we show that scientific success is strongly correlated with the structure of a scientist’s collaboration network. First, among two scientists, with analogous achievements, the one with weaker ties tends to have the higher h-index, and second, teams connected by such ties create more cited publications.

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Social networks (SN), representing patterns of human interactions, have been the subject of both empirical and theoretical research since at least the middle of the last century 1 . At the beginning of the twenty-first century, there was a breakthrough in social network analysis (SNA) 2 , 3 . With the era of widespread digitization, which provided access to huge electronic databases, new empirical methods of SNA have emerged and replaced traditional approaches based on questionnaires and interviews. These new methods, rooted in big data mining, finally allowed for the verification of many well-established theoretical SN ideas, in some cases confirming their validity and in others failing to do so 4 . In this regard, the present status of Granovetter’s weak-tie theory 5 , 6 of SN, one of the oldest and most influential theories in sociology, is still vague. There are convincing studies that show the validity of its selected aspects (e.g., 7 , 8 , 9 , 10 ), but there are also many that question it (e.g., 11 , 12 , 13 ). Our analysis presented in this paper is unique because, using a massive dataset, not only do we confirm Granovetter’s weak tie theory in its full spectrum but also indicate a possible source of problems related to research questioning its validity.

Granovetter’s theory is based on two hypotheses. The first pertains to the structure of social networks and the second to their dynamics (the way in which the afore-mentioned structure influences the flow of information in the network). It is significant that although most empirical studies have focused on the first hypothesis, far less research has been undertaken to verify the second. One possible reason is that the second hypothesis involves notions relative to the nature and importance of information that are hard to quantify and measure. In this study, we clearly confirm both hypotheses—and Granovetter’s theory in its entirety—in the context of a scientific collaboration network.

The scientific collaboration network 14 , 15 , 16 , 17 , 18 is particularly well suited to the overarching goal of this paper (i.e., complete confirmation of Granovetter’s theory) because: (i) connections (ties) between network nodes (scientists) are well defined, and their weight 19 (strength of ties) is easy to measure (e.g., through joint publications); (ii) scientific publications themselves are also a specific proxy of information flow in the studied network (diffusion of innovations 20 ); and (iii) the number of citations is an obvious measure of their significance. Easy access to large datasets is also important, making our conclusions statistically reliable.

The network we investigated has all the features of a complex network 21 . In particular, it shows the scale-free node degree distribution $P(k)\propto k^{-\gamma }$ with the characteristic exponent $\gamma \simeq 2.3$ . In the theory of complex networks, this value of $\gamma $ is alarming in the sense that it indicates that the network requires special treatment, including methods of results averaging different to the ones used in homogeneous systems. In relation to Granovetter’s theory, this means that in such networks, basic concepts, such as tie strength and neighbourhood overlap, should be defined in a more careful manner than in homogeneous networks. Their incorrect definition may, instead of confirming the theory, result in its contradiction. In all known empirical studies on Granovetter’s theory, interpersonal ties are assumed to be positive and symmetric. However, it is obvious that social relations do not usually follow this assumption (see, for example, the theory of social balance 22 , 23 or the concept of multirelational organization of SN 24 , 25 ). For example, the scientific collaboration between a young scientist and an established one can hardly be called symmetric.

In his original paper 5 , Granovetter treated ties as if they were positive and symmetric, but he also noted that “the comprehensive theory might require discussion of negative and/or asymmetric ties”. We follow this suggestion in this study and reject the assumption about the symmetry of social ties, which is omnipresent in the literature on the subject. The validity of this approach can be explained by intuition trained in the field of complex networks. Granovetter argued that “the degree of overlap of two individuals’ friendship networks varies directly with the strength of their tie to one another”. However, from the theory of complex networks, we know that in social networks with a high degree of heterogeneity (e.g., due to scale-free node degree distribution), the sizes of ego-networks of two connected nodes may differ drastically. Therefore, their common neighbours can be a significant part of the neighbourhood of one node and an insignificant part of the neighbourhood of the other, resulting in a completely different perception of the strength of the link on both ends.

In what follows, we show that the above reasoning, which assumes the asymmetry of tie strength, allows for a quantitative validation of Granovetter’s theory in scientific collaboration networks, that have resisted such verification so far. We use the DBLP Computer Science Bibliography dataset, which includes information on nearly five million computer science papers (i.e., their publication dates, lists of authors and citation records) authored by over four million scientists (see “ Data availability ” section for more details).

In the standard approach to scientific collaboration networks, the nodes represent authors, and an undirected internode connection occurs when two authors have published at least one paper together. When considered as binary networks—without any additional features assigned to nodes and connections—these networks show numerous structural similarities to other SNs (e.g. high clustering, small-world effect, skewed degree distribution and clear community structure; Fig. 1 a,b,c) 14 , 15 , 16 , 17 . However, when edges are assigned weights representing, for example, the number of joint publications, then, although macroscopic characteristics of scientific collaboration networks (e.g., distributions of connection weights and node strengths; Fig. 1 d) still correspond to those observed in typical SNs 7 , 26 , their microscopic structure related to the location of strong and weak ties is completely different. Dense, local neighbourhoods of nodes consist of weak ties, while strong ties act as bridges between local research groups. The atypical properties of scientific collaboration networks have been confirmed in several independent studies 9 , 11 , 27 .

Basic structural properties of the real coauthorship network constructed using the DBLP computer science bibliography. ( a ) Visualization of the giant component of the network using Graphia application 28 . For better visibility only nodes with degree larger than 50 are shown resulting in the core network of almost seventy thousand nodes. The network is organized as a large number of communities. Each community was assigned a color according to the partitions identified by the Louvain algorithm 29 . ( b , c , d ) Logarithmically binned: node degree distribution P ( k ), community size distribution P ( c ), and link weight distribution P ( w ). The values $\gamma =2.3$ and $\beta =3.3$ shown in the graphs ( b ) and ( d ) correspond to the scaling exponents obtained by fitting power-law distributions to the relevant empirical data: $P(k)\propto k^{-\gamma }$ and $P(w)\propto w^{-\beta }$ .

Specifically, as shown in Ref. 11 , these unusual weight-topology correlations can be seen by analysing the relationship between the tie strength, $w_{ij}$ , of two scientists i and j , and the overlap, $O_{ij}$ , of their ego-networks. As indicated by Onnela et al. 7 , the overlap of two connected individuals is the ratio of the number of their common neighbours, $n_{ij}$ , to the number of all their neighbours:

where $k_i$ and $k_{j}$ represent degrees of the considered individuals. In typical SNs 30 , 31 , 32 , 33 , the above-defined overlap is an increasing function of the tie strength, $w_{ij}$ , while analyses of scientific collaboration networks show something completely different. As can be seen in Fig. 2 a, in the studied network of computer scientists, with $w_{ij}$ standing for the number of joint publications 34 , for the vast majority of connections ( $98\%$ ), the overlap decreases with connection weight. This relationship indicates that weak ties mainly reside inside dense network neighbourhoods, whereas strong ties act as connectors between them. It has been hypothesized that this counterintuitive observation could be attributed to different driving mechanisms of tie formation and reinforcement in scientific collaboration networks in comparison to other social networks 11 . In what follows, we argue that the observation is related to the definitions of the tie strength and neighbourhood overlap that are not properly suited to the structure of the studied network.

Dependence of neighbourhood overlap on tie strength in: ( a ) undirected, weighted DBLP scientific collaboration network, in which tie strength $w_{ij}$ corresponds to the number of joint publications (i.e. the number of times that co-authorship has been repeated) and the symmetric neighbourhood overlap $O_{ij}$ is given by the standard formula, Eq. ( 1 ); ( b ) directed, weighted projection of the same network with asymmetric tie strength $v_{ij}$ and asymmetric overlap $Q_{ij}$ , obtained from Eqs. ( 3 ) and ( 2 ). In both graphs, circles indicate averages of overlaps (in intervals of logarithmically increasing width in the main panel and of constant width in the inset, respectively), while bars represent the number of samples from which the averages were calculated. Empirical relationships, similar to the one from the left graph ( a ), showing the decreasing character of $O_{ij}(w_{ij})$ , have so far been the basic argument against validity of the Granovetter’s theory in scientific collaboration networks. The graph on the right ( b ) shows that the necessary condition to confirm the Granovetter’s theory in the studied networks is to reject the assumption about the symmetry of social ties.

First, let us deal with the definition of the overlap ( 1 ) (referred to as symmetric overlap ). In Fig. 3 a, this local measure is shown in the case of a link connecting nodes with significantly different degrees. In such cases, for $k_i\ll k_j$ , Eq. ( 1 ) can be simplified to $O_{ij}\simeq n_{ij}/k_j$ , which shows that it is strongly biased towards nodes with high degrees, distorting the image of the common neighbourhood as seen from the perspective of nodes with small degrees. This drawback of symmetric overlap gains importance in networks with highly skewed, fat-tailed node degree distributions P ( k ). In such networks, as brilliantly exploited by the degree-based mean-field theory of complex networks 35 , 36 , 37 , node degree distributions for nearest neighbours are even more fat-tailed than the original distributions P ( k ). As a result, the number of edges in such networks connecting nodes with high and low degrees can be very high, leading to an unintended overrepresentation of strongly connected nodes by Eq. ( 1 ).

Illustration of the difference between symmetric and asymmetric neighbourhood overlap. In the figure, to highlight the benefits of analysing asymmetric overlaps, the corresponding values of: ( a ) symmetric $O_{ij}$ ( 1 ) and ( b , c ) asymmetric $Q_{ij}\ne Q_{ji}$ ( 2 ) overlaps have been calculated for the same network configuration, in which interconnected nodes differ in the size of their ego-networks. In such cases, which are typical for complex networks with underlying fat-tailed distributions, a common scenario is that for $k_i\ll k_j$ one has $Q_{ij}\gg Q_{ji}\simeq O_{ij}$ . This explains why introducing tie direction is necessary for reliable verification of the Granowetter’s theory in scientific collaboration networks.

To overcome problems with symmetric overlap, we introduce the concept of asymmetric overlap :

This can be used to describe the overlap between the neighbourhoods of two connected nodes from the perspective of each node separately. In the context of complex networks, this new definition is free from the shortcomings of the previous one. In particular, it copes well with connected nodes (collaborating scientists) whose degrees (ego-networks) differ significantly—that is, when their common neighbours (if any) are a significant part of the neighbourhood of one node and an insignificant part of the neighbourhood of the other. In such cases, the values of $Q_{ij}$ and $Q_{ji}$ corresponding to the same tie are different (see Fig. 3 b,c). The value of $Q_{ij}$ that is close to 1 means that almost all neighbours of i are also neighbours of j . The value of $Q_{ji}$ close to 0 means that only a small part of the neighbourhood of j belongs to the neighbourhood of i .

The concept of asymmetric overlap naturally leads to the idea of directed networks and justifies the introduction of asymmetric tie strength :

where $p_i$ stands for the number of all publications of the i -th scientist 38 . The intuitive rationale behind Eq. ( 3 ) is as follows: For a young scientist, with a small number of publications, each publication makes a significant contribution to his or her publication output, just as each co-author is an important part of his or her research environment (cf. Eqs. ( 2 ) and ( 3 )). However, the importance of each publication and collaboration from the perspective of an established scientist with a large number of publications and an extensive network of collaborators is completely different. Depending on the circumstances, a given number of joint publications (e.g., $w_{ij}=1$ ) may have a completely different meaning.

In Fig. 2 b, the dependence of asymmetric overlap on asymmetric tie strength for the considered network of computer scientists is shown. Contrary to what can be seen in Fig. 2 a, the relationship $Q_{ij}(v_{ij})$ is increasing in the entire range of variability of its parameters. The result indicates that, from the point of view of a single scientist (ego-network approach), strong ties mainly constitute dense local clusters, whereas weak ties connect these clusters or play the role of intermediary ties 10 . The observation clearly confirms the validity of Granovetter’s first hypothesis in scientific collaboration networks.

Now, using the concept of asymmetric tie strength, we will discuss Granovetter’s second hypothesis, which postulates that although weak ties do not carry as much communication as strong ties do, they often act as bridges, providing novel, non-redundant information, which guarantees weakly connected nodes generally understood social success.

In scientific collaboration networks, the validity of Granovetter’s second hypothesis has never been tested. Nevertheless, it is widely believed (see 39 and references therein) that information and expertise at the disposal of tightly connected research groups are often redundant, resulting in less creative collaborations and less innovative publications, while intergroup collaborations that bridge the so-called structural holes 40 , 41 , 42 can provide access to information and resources beyond those available in densely connected communities, thus leading to novel ideas and valuable publications. To quantitatively address these issues, we check whether the bibliometric indexes of scientists and publications are correlated with the tie strength of the scientific collaboration network. Specifically, we focus on two questions: (i) How does the researcher’s h-index depend on the structure of his/her local collaboration network? (ii) How does the strength of the ties between scientists influence the success of their joint publication?

To answer the first question, we examined how the h-index 43 , 44 of a scientist depends on his or her average asymmetric tie strength (see Fig. 4 ):

Average asymmetric tie strength of a scientist. The figure presents ego-networks of three different scientists (egos) with the same number of co-authors $k_i=3$ and publications $p_i=3$ , but with different patterns of collaboration. On the left scheme ( a ), each of the three publications has only two authors; on the central scheme ( b ), two publications were written by a team of three and one by a team of two; in the scheme on the right ( c ), all publications involved the entire ego-network of a scientist. In each of the presented cases, the ego’s average asymmetric tie strength is different. Its value increases from the left diagram to the right, exactly in the same way as the intuitively understood social role of collaborators, on which depends not only the ego’s productivity but also integrity of his/her research group.

Equation ( 4 ) quantitatively measures the tendency of scientists to keep collaborating with the same people (cf. the concept of social inertia 45 , 46 ). Figure 5 a shows that the averaged (over all scientists who have a similar average tie strength) h-index decreases with $\langle v_i\rangle $ . It means that successful (double-digit h-index) scientists have significantly weaker ties than less successful (single-digit h-index) researchers. The result is consistent with Granovetter’s general understanding of the role of weak and strong ties. However, since some doubts may arise from the fact that the data presented in Fig. 5 a are averaged over many different scientists (having a small and large number of all publications, with a small and very extensive network of collaborators), in Fig. 6 , we demonstrate that the decreasing nature of the relationship between the h-index and tie strength is independent of the choice of a group of scientists. That is, it still decreases, even in very homogeneous (in terms of scientific achievements) groups of researchers. In particular, as one can see in the small graphs accompanying the colour histogram that represents the available scientists’ samples, of any two researchers who have the same number of publications and/or co-authors, the one with weaker ties tends to have the higher h-index. In a way, this suggests that being a good manager and skilfully planning one’s network of scientific contacts ensures success 47 . This conclusion, however alarming as it may seem, finds its basis in the theory of social networks—the already mentioned concept of Burt’s structural holes and social capital 40 , 41 .

The role of tie configuration on scientific success of researchers and publications. ( a ) The mean h-index of scientists characterized by a given average asymmetric tie strength $\langle v_i\rangle $ , Eq. ( 4 ). ( b ) The average number of citations obtained by papers created in teams with a given average asymmetric tie strength. The decreasing nature of both empirical relationships ( a , b ) clearly indicates that scientific collaboration based on weak ties is more appreciated in terms of the number of citations. Moreover, since the number of citations is often correlated with the quality of research, the above results also show that weak ties usually result in more creative (in terms of knowledge production) scientific collaborations.

Scientists’ h-index versus tie strength. In this figure, we present a more detailed analysis of the relationship from Fig. 5 a, which shows the data averaged over all scientists in the studied collaboration network, regardless of the stage of their scientific career. Here we divide scientists into groups in which everyone has the same number of total publications and the same number of co-authors (see the colour map in the figure). The more homogeneous conditions thus established allow us to clearly confirm earlier findings. In particular, as one can see in the small graphs on the right side of the colour map, regardless of the choice of the homogeneous group of scientists their h-index always decreases with increasing average asymmetric tie strength.

The role of weak ties in scientific success is even more apparent in relation to scientific publications. Figure 5 b shows how the number of citations of a scientific paper depends on the asymmetric tie strength (averaged over all co-authors of each article). The decreasing nature of this relationship indicates that publications created by teams of scientists linked by weak ties are better cited than those that arise in teams with strong ties. In Fig. 7 , by analysing more homogeneous samples of publications (published in the same year and/or by the same number of co-authors), we clearly confirm the validity of the above finding. Furthermore, although the number of citations does not always translate into the quality of the research presented, it is undoubtedly a measure of the commercial success of a publication and a specific measure of the knowledge diffusion in scientific collaboration networks.

Citations of publications versus tie strength. In this figure, we present a more detailed analysis of the relationship from Fig. 5 b. To this aim, all publications available in the analysed database are divided into groups according to the year of publication and the number of authors (see the colour map in the figure). Given homogeneous sample of publications thus established, we found that the number of their citations always decreases with increasing average asymmetric tie strength between their authors. To clarify, the average tie strength was determined at the time of paper’s publication, and the number of citations refers to the time of the last update of the analysed database.

Discussion and concluding remarks

The purpose of this work is to thoroughly verify Granovetter’s weak-tie theory of social networks. As clearly stated in the abstract and in the introduction: Granovetter’s theory is based on two hypotheses that assign different roles to interpersonal, information-carrying connections . Not all those who deal with the Granovetter’s theory pay attention to this distinction, which is undoubtedly crucial. The first hypothesis states that strong ties carrying the majority of interaction events usually correspond to intra-group connections. The second hypothesis maintains that weak inter-group ties, although less active, are of particular importance for the exchange of relevant information. A review of the literature reveals a striking disproportion between the research on the two hypotheses. In fact, the vast majority of empirical research to date has dealt with the first hypothesis, completely ignoring and sometimes not fully correctly interpreting the second one. In this respect our work is unique, because we confirm Granovetter’s weak tie theory in its full spectrum . And although in the absence of other studies, the analysis of the second hypothesis may seem to be the most important result of this work, our research on the verification of the first hypothesis also deserves attention as it highlights some important (and sometimes questionable or not entirely correct) threads in previous studies.

In particular, using massive datasets, clear empirical evidence for the first hypothesis, supported by the positive correlation between the symmetric overlap and tie strength, $O_{ij}(w_{ij})$ , were reported in: mobile communication networks 7 , 30 , multiplayer online games 31 , 32 , and dialogues-based online SN 33 . On the other hand, the above mentioned methodology, exploiting symmetric network measures, failed in the analysis of scientific collaboration networks 9 , 11 , 27 , incorrectly classifying them as contradicting Granovetter’s theory. In this paper, we identify the reason why scientific collaboration networks behave differently than other SN. We argue that the U-shaped relation between $w_{ij}$ and $O_{ij}$ observed in coauthorship networks (see Fig. 2 a) is related to the definitions of tie strength $w_{ij}$ and neighbourhood overlap $O_{ij}$ that are not properly suited to networks with scale-free node degree distributions. In any of the networks that were considered in Refs. 7 , 30 , 31 , 32 , 33 this problem did not exist, because these networks were not truly scale-free (e.g. in mobile communication networks $P(k)\sim k^{-\gamma }$ , with $\gamma =8.4$ ).

In this paper, to overcome the aforementioned issue, we have paid attention to the role of asymmetry in social ties. We have introduced new measures: asymmetric overlap $Q_{ij}$ and asymmetric tie strength $v_{ij}$ , which not only allowed the successful verification of the first Granovetter’s hypothesis in scientific collaboration networks (see Fig. 2 b), but have also opened the possibility to verify the second hypothesis. Moreover, as for the second hypothesis, which involves concepts related to the nature and importance of information, coauthorship networks have proved to be an extremely accurate choice, because: (i) connections (ties) between network nodes (scientists) are well defined, and their weight (strength of ties) is easy to measure (e.g., through joint publications); (ii) scientific publications themselves are also a specific proxy of information flow in the studied network (diffusion of innovations); and (iii) the number of citations is an obvious measure of their significance.

To be concrete, with regard to the second Granovetter’s hypothesis our results quantify what most scientists know very well: Scientific success is strongly correlated with the structure of a scientist’s collaboration network. We have explicitly shown that publications created by teams of scientists with weak ties are better cited than those that arise in teams with strong ties. And although this result was to be expected, it may be surprising that the differences in the number of citations of works created by weakly tied research groups compared to strongly tied groups amount not to a few or a dozen, but several hundred percent (see Fig. 7 ). Of course, when looking at these results quantitatively, one should bear in mind the limitations of the DBLP database used for the study. The database covers publications from computer science and includes publications from hybrid fields, where they are considered pertinent to computer science research. Papers from other disciplines are present there only occasionally. It means that super weak inter-domain ties are not covered by our analysis and the differences presented in Figs. 6 and 7 may be underestimated. On the other hand, computer science is quite heterogeneous due to the presence of many subfields, with very different norms in terms of team size and citation standards. Therefore, the results presented in Figs. 6 and 7 are aggregated over different subfields. Keeping above in mind, using more comprehensive database (e.g. Scopus or Web of Science), for the analysis reported in this study, can act as a double-edged sword. It would solve the first problem, but aggravate the second one. In this sense, our choice of the source of data seems to be a golden middle way.

Finally, an important research direction that was not undertaken in this paper, although it directly refers results reported here, is the issue of two recently discovered empirical scaling laws for social networks which relate link weight $w_{ij}$ , symmetric overlap $O_{ij}$ , and link betweenness centrality 48 $b_{ij}$ in a non-linear way: $O_{ij}\propto \root 3 \of {w_{ij}}$ and $O_{ij}\propto 1/\sqrt{b_{ij}}$ . Several studies (see e.g. 31 , 32 , 33 ) have confirmed universality of these “social laws”. As we have already shown (cf. Fig. 2 a and the corresponding figures in 9 , 11 , 27 ), the first of these scaling laws—relating tie strength to the cube of the symmetric overlap—is not fulfilled in coauthorship networks. We have also checked that the same conclusion holds true for the second relation—expressing edge betweenness centrality as the inverse square of the overlap. In our case, the relationship $O_{ij}(b_{ij})$ is non-monotonic (non-increasing for small and intermediate values of betweenness and increasing for its large values, see Fig. S1 in Supplementary Information). Along these lines, we have also checked whether there is a clear correlation between tie strength and betweenness centrality and we have found no apparent dependency (see Fig. S2 in SI).

The additional analysis mentioned above provoke interesting research questions. The most controversial is whether the correlation between link betweenness centrality and symmetric overlap brings any relevant information about dynamical properties of social networks. In particular, whether the negative correlation between these measures provides quantitative evidence for the Granovetter’s theory. A kind of argument that supports these objections is that if we shuffle edge weights in a social network without changing the structure of its binary connections, then the weak ties hypothesis will surely cease to work, although the mentioned correlations will remain unchanged. Perhaps this argument could be refuted by using a kind of weighted/directed edge betweenness centrality, which, in combination with the asymmetric overlap $Q_{ij}$ introduced in this work, would allow for the formulation of more general laws of social dynamics than those formulated in 31 . An interesting way to overcome this problem has been proposed in 49 , where the authors pointed out that classical betweenness centrality is not useful to measure the influence of a team that is composed of more than two people 50 . Instead of this, a weighted hypergraph representation of the coauthorship network with higher-order interactions has been introduced and betweenness centrality measure has been adequately adapted to this new structure. In order to pursue studies on the role of weak ties in this direction, a new kind of overlap measure in hypergraphs has to be devised which itself seems to be challenging. The above considerations can be a starting point for interesting, new research on social networks.

Data availability

The research presented in this paper is based on the publicly and freely available Citation Network Dataset 51 . We used the 12th version of the dataset (DBLP-Citation-network V12) which contains detailed information (i.e., year of publication, journal, number of citations, references, list of authors) and approximately 5 million articles published mostly during the last 20 years.

It is important to note that our analysis is limited to the largest connected component (LCC) in the co-authorship network, which can be recreated using the dataset. LCC comprises of close to three million nodes (authors), which means it spans 65% of the entire network. These nodes are connected by more than 13 million bi-directional co-authorship edges.

While the dataset provides exhaustive information about published papers, it does not directly contain any bibliometric information about authors. However, it is possible to calculate various bibliometric indicators either by recreating the network of citations or by directly using article metadata available in the dataset for each article (such as the number of citations). In order to calculate the h-index for all authors in the LCC, we decided to rely on the latter method and use article metadata to determine the number of citations. Considering that the citation network recreated from the dataset is only a sample of the full citation network, this method is more reliable. The number of citations calculated by counting links in the citation network is, in general, underestimated when compared with the number of citations available in the article’s metadata.

Code availability

The code that supports the findings of this study is available from the corresponding author upon request.

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Research was funded by (POB Cybersecurity and Data Science) of Warsaw University of Technology within the Excellence Initiative: Research University (IDUB) programme.

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Fronczak, A., Mrowinski, M.J. & Fronczak, P. Scientific success from the perspective of the strength of weak ties. Sci Rep 12 , 5074 (2022). https://doi.org/10.1038/s41598-022-09118-8

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Article Contents

Introduction, acknowledgements, data availability, author biographies.

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CPPLS-MLP: a method for constructing cell–cell communication networks and identifying related highly variable genes based on single-cell sequencing and spatial transcriptomics data

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Tianjiao Zhang, Zhenao Wu, Liangyu Li, Jixiang Ren, Ziheng Zhang, Guohua Wang, CPPLS-MLP: a method for constructing cell–cell communication networks and identifying related highly variable genes based on single-cell sequencing and spatial transcriptomics data, Briefings in Bioinformatics , Volume 25, Issue 3, May 2024, bbae198, https://doi.org/10.1093/bib/bbae198

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In the growth and development of multicellular organisms, the immune processes of the immune system and the maintenance of the organism’s internal environment, cell communication plays a crucial role. It exerts a significant influence on regulating internal cellular states such as gene expression and cell functionality. Currently, the mainstream methods for studying intercellular communication are focused on exploring the ligand–receptor–transcription factor and ligand–receptor–subunit scales. However, there is relatively limited research on the association between intercellular communication and highly variable genes (HVGs). As some HVGs are closely related to cell communication, accurately identifying these HVGs can enhance the accuracy of constructing cell communication networks. The rapid development of single-cell sequencing (scRNA-seq) and spatial transcriptomics technologies provides a data foundation for exploring the relationship between intercellular communication and HVGs. Therefore, we propose CPPLS-MLP, which can identify HVGs closely related to intercellular communication and further analyze the impact of Multiple Input Multiple Output cellular communication on the differential expression of these HVGs. By comparing with the commonly used method CCPLS for constructing intercellular communication networks, we validated the superior performance of our method in identifying cell-type-specific HVGs and effectively analyzing the influence of neighboring cell types on HVG expression regulation. Source codes for the CPPLS_MLP R, python packages and the related scripts are available at ‘CPPLS_MLP Github [ https://github.com/wuzhenao/CPPLS-MLP ]’.

Cell communication plays a pivotal role in multicellular organisms, driving cell differentiation, orchestrating the harmonious functioning of tissues and organs and regulating both beneficial and detrimental immune responses in diseases [ 1 ]. The rise of single-cell and transcriptomic technologies has provided crucial technical support and foundational data for comprehending the diverse cellular landscape within tissues and organs [ 2 ]. These advancements have also empowered detailed exploration of molecular interactions and information exchange at the molecular level among distinct cell populations. In the realm of tumor research, the expression of programmed cell death-Ligand 1 (PD-L1) protein within tumor cells, binding with programmed death 1 (PD-1) protein on T cells, modulates T-cell gene expression patterns, attenuating the immune response against tumor growth [ 3 ]. Disrupting this intercellular communication via PD-1 pathway inhibitors effectively curtails tumor cell proliferation. To unravel and manage intricate multicellular systems, dissecting intercellular information exchange stands as a potent approach for uncovering the regulatory mechanisms governing gene expression [ 4–6 ].

In recent years, significant advancements have been made in methodologies to predict ligand–receptor interactions (LRIs) in single-cell RNA sequencing (scRNA-seq) and spatial transcriptomics (ST) data [ 7–9 ]. These approaches have shed light on the intricate communication processes between cells. Notably, Ramilowski and colleagues pioneered the construction of a meticulously curated dataset comprising 2422 LRIs [ 10 ]. This dataset has become a cornerstone in studying intercellular information exchange. Advances in databases and statistical tools have enhanced our ability to infer communication mechanisms between diverse cell types. Current strategies primarily revolve around two approaches. The first leverages highly co-expressed ligands and receptors as potential mediators of cell communication. Integration of extensive ligand and receptor information enables signaling inference from signal senders to receivers, exemplified by tools like CellphoneDB [ 11–13 ]. The second approach focuses on downstream targets activated in receptors due to LRIs. This strategy enriches and assesses ligand–receptor–downstream target signaling networks and is implemented in methods such as NicheNet and Cellchat [ 7–9 , 14 ]. Despite these advancements, our understanding of the relationship between HVGs and intercellular communication remains limited.

scRNA-seq and ST technologies have been extensively applied to delve into the complexities of multicellular systems. These methods have unveiled highly variable gene expression within the same cell types, a variation crucial for normal growth, development and disease states [ 11 , 15–18 ].

A comprehensive understanding of the relationship between HVGs and intercellular communication holds significant implications for unraveling the intricate mechanisms underlying cellular interactions and exploring disease progression [ 19 ]. Yet, research on HVG expression has predominantly focused on computational tools utilizing scRNA-seq data to infer potential cell–cell communications. These tools typically deduce intercellular signaling by comparing the expression levels of ligand and receptor genes across different cell types [ 20–22 ]. However, these methods come with inherent limitations, including incomplete knowledge of ligand–receptor pairs, potential crosstalk between ligands and receptors and the challenge of capturing cellular spatial contexts.

Gene expression in cells is influenced by the spatial arrangement and configuration of neighboring cells, akin to an MIMO system [ 23 , 24 ]. Recently, several methods have emerged to decipher the spatial communication mechanisms between cells, with some taking into account the MIMO framework. For instance, Giotto utilizes the concept of ‘preferred cell neighbors’ among different cell types in single-cell ST datasets. It employs enrichment testing to assess the likelihood of specific cell–cell interactions in adjacent co-expressing cells, thereby inferring spatial communication modes between cells [ 25 ]. CCPLS, on the other hand, applies single-cell and ST datasets. It utilizes Partial Least Squares (PLS) regression to model the linear relationship between HVG intercellular differential expression and cell spatial coordinates. This approach deduces the impact of intercellular communication among different cell types on HVG expression [ 26 ]. However, Giotto and CCPLS are limited to inferring the possibility of proximal co-expression in single-cell and ST data (rather than the entire cellular environment) and the linear relationship between individual gene expression and cell coordinates. Moreover, these methods focus on multiple inputs (MIs) rather than multiple outputs (MIMO) of intercellular communication. Notably, these methods lack a standardized classification criterion to determine whether a gene is associated with cell communication. To date, there is still a significant challenge in establishing metrics to gauge whether genes are related to cell communication. Furthermore, the challenge extends to fitting continuous, discrete and combined signals, representing multiple dependent and independent variables, in constructing MIMO networks for intercellular communication. These challenges pose significant hurdles in decoding the spatial cellular dynamics of potential disease pathologies.

To address this challenge, we propose CPPLS-MLP, a method that integrates Constrained Partial Least Squares (CPPLS) [ 27 , 28 ] and Multilayer Perceptron (MLP) [ 29 , 30 ] techniques, for the construction of MIMO cell communication networks and gene classification. CPPLS-MLP combines gene expression data and cell spatial coordinates, modeling the impact of intercellular communication among multiple cell types on HVGs. It introduces a novel criterion for genes associated with cell communication and utilizes MLP for gene classification under this criterion. CPPLS-MLP demonstrates superior stability in the selection of HVGs from the dataset compared to other methods. The kernel functions employed in CPPLS-MLP highlight the uniqueness of HVGs within each cell type, surpassing other methodologies. Applied to Seq-scope and seqFISH+ datasets, CPPLS-MLP unveils the regulatory role of intercellular communication across various cell types on HVG expression. Furthermore, it classifies these HVGs according to the new criteria. These results underscore CPPLS-MLP as a novel approach to comprehend how spatial intercellular communication within tissues impacts HVG expression. Importantly, it proves valuable in unraveling cell–cell communication at single-cell and ST resolutions, showcasing its practical utility in this domain.

Constrained Partial Least Squares introduces additional constraints on top of PLS to control model properties and behaviors. Apart from minimizing the residual sum of squares, it imposes extra constraints such as regularization on regression coefficients and relationships among regression coefficients. Multilayer Perceptron is a feedforward neural network model consisting of multiple neurons, including input layers, multiple hidden layers and output layers. Each neuron connects with all neurons from the previous layer via weights, and through learning these weights, it approximates the output of a function, achieving complex mappings from inputs to outputs.

The nonlinear modeling capability of MLP enables it to capture complex interactions in gene expression data and genetic networks, revealing hidden patterns and relationships. Its multi-layer structure allows for the extraction of advanced features layer by layer, uncovering deeper biological insights. In contrast, the CNN and other graph network methods are better suited for data with grid-like structures, such as images, while the high-dimensional and unstructured nature of gene expression data may limit their effectiveness in feature extraction.

Cell communication network construction

To process single-cell and spatial transcriptomic data, let W represent the number of genes, Z denote the number of cells and A indicate the number of cell types. The gene expression matrix U∈ |${V}^{Z\ast W}$| contains each cell c (1 ≤ c ≤ Z) and the expression values |${u}_{c,w}$| for each gene [ 31 , 32 ]. The coordinate matrix O∈ |${V}^{Z\ast 2}$| includes the two-dimensional spatial coordinates |$({O}_{c,1}$|⁠ , |${O}_{c,2})$| (1 ≤ c ≤ Z ) for each cell. The cell type label vector D = { |${d}_c$| | |${d}_c$| ∈ {1, …, A }} consists of A unique cell type labels |${d}_c$|⁠ . We assume the presence of specific HVGs, denoted as |${h}^a$| within each cell type a , which includes the expression matrix |${U}^a$| for cells c(1 ≤ c≤ |${Z}^a$|⁠ ) of cell type a. Based on this data, a linear model is established:

Here, h∈ |${h}^a$|⁠ , |${w}_{b,h}^{(a)}$| denotes the coefficient, |${f}_{c,b}^{(a)}$| represents the score of neighboring cell type and |${\varepsilon}_{c,h}$| is the residual term. CPPLS-MLP assumes that for each HVG, neighboring cell type b acts uniquely on cell type a . Therefore, its objective is to estimate the direction and magnitude of cell–cell communication regulation using the coefficients |${w}_{b,h}^{(a)}$|⁠ .

The coefficient represented by W signifies the relationship between genes and adjacent cells after the input data passes through the model. The magnitude of the coefficient reflects the degree of regulation exerted by adjacent cells on this HVG. On the other hand, f denotes the regulatory direction of adjacent cells on this HVG. Its value can be positive or negative, where positive indicates upregulation and negative signifies downregulation of expression.

Here, |${u}_{c,h}^{(a)}$| ( h = 1, …, H ) represents the preprocessed expression values of HVGs, ‘H’ represents processed HVGs represented by a number from 1 to H . CPPLS-MLP divides the gene expression matrix U into A matrices, each corresponding to a specific cell type. |${U}^{\prime (a)}$| ∈ U represents the expression values within cell type a , where genes with zero expression across all cells of cell type a are removed, and the remaining genes’ z-scores are normalized. CPPLS-MLP identifies specific HVG |${h}^a$| within cell type a .

In the equation, |${f}_{c,b}^{(a)}$| represents the calculated score for adjacent cell types for each type a . CPPLS-MLP computes the raw adjacent cell type scores |${f}_{c,b}^{\prime (a)}$| from the input coordinate matrix O and cell type label vector D.

where |${s}_{n,b,m}$| represents a binary value determining whether cell n belonging to cell type label |${d}_n$| is also of cell type b (1 ≤ b ≤ Z ， m ≠ n ), |${dist}_{m,n}$| represents the Euclidean distance calculation between cells m and n based on their coordinates and |$\mathrm{d} ist0$| is set as the minimum Euclidean distance among all pairwise cell combinations in the coordinate matrix O. Finally, z-score transformation is applied to the raw adjacent cell type scores calculated for each cell type b , resulting in the matrix |${U}^a$| of adjacent cell type scores.

CPPLS-MLP regression modeling

For each cell type a , CPPLS-MLP performs CPPLS regression modeling. CPPLS-MLP leverages CPPLS regression with two major advantages: (1) its capability to handle the ‘small N, large P’ problem, a characteristic of ST [ 33 , 34 ] and (2) its ability to handle continuous, discrete and combinatorial data, reflecting the cooperative maintenance of all genes and cells within the internal environment homeostasis.

Firstly, we can consider the initial step as a process composed of the evolution of external relationships (measured by F and U). These two data matrices are decomposed into latent variables and residual matrices. These submatrices can be represented as products of scores and loadings, which are then recombined into separate matrices, as illustrated below:

Here, X∈ |${R}^{Z\ast C}$| and Y∈ |${R}^{Z\ast C}$| represent the score matrices of F and U matrices, respectively. |${P}^{D\ast C}$| and |${Q}^{D\ast C}$| are the loading matrices of F and U matrices, where C denotes the number of components in the CPPLS regression. The matrices I∈ |${R}^{Z\ast D}$| and J∈ |${R}^{Z\ast H}$| correspond to the residuals of the CPPLS regression model.

The second step is to calculate the supplementary score matrix ,

X ′ and Y′ in the formula represent the supplementary score matrices of F and U , respectively.

The third step is to fit the intrinsic linear relationship between X and Y ,

In this equation, K ∈ |${R}^{C\ast C}$| represents a diagonal matrix, and H ∈ |${R}^{Z\ast C}$| represents the residual matrix. Finally, the result of the CPPLS regression model can be expressed as follows:

W∈ |${R}^{D\ast H}$| in the formula represents the coefficient matrix,

G∈ |${R}^{Z\ast H}$| is the residual matrix.

For each cell type a , after performing CPPLS regression modeling, CPPLS-MLP obtains a matrix |${W}^{(a)}$| composed of coefficients |${w}_{b,h}^{(a)}$| (1 ≤ b ≤ A, h∈ |$\left\{{h}^{(a)}\right\}$|⁠ ). Each coefficient |${w}_{b,h}^{(a)}$| is the sum of all genes |${w}_{b,h}^{(a)}={\sum}_c{w}_{b,h,c}^{(a)}$| in the corresponding block c . Finally, the direction and magnitude of cell–cell communication regulation are estimated based on the coefficient matrix [ 35 ]. To prevent our model from developing a preference for certain data, we input gene expression data and spatial coordinate information into the model and divide these data into 10 subsets of approximately equal size. By repeatedly using different subsets as the test set and the remaining nine as the training set, we can reduce bias introduced by unreasonable dataset division. In each round of cross-validation, the model is trained and validated on different subsets of data, effectively preventing the model from overfitting.

Filtering of coefficients

CPPLS-MLP filters the coefficient |${w}_{b,h}^{(a)}$| twice. The first filtering step involves performing a t -test on the factor loadings |${w}_{b,h,c}^{(a)}$| from each block c obtained in the CPPLS regression modeling. This test is applied to derive the P -values corresponding to the Pearson correlation coefficients [ 36 ]. In constructing our MIMO system, the base of the exponent in the edge weight decay function was derived by considering the median of scores for all cell types generated by the model. Using a model-trained value could potentially lead to significant variations in the interaction values between every pair of cell types. Hence, to prevent excessive elimination of edges for any particular cell type, we opted for a fixed value that is moderate and applicable across all cell types.

In the equation, corr () and var () calculate the Pearson correlation coefficient and variance, respectively. |${f}_b^{(a)}$| and |${u}_{\mathrm{h}}^{(a)}$| represent the preprocessed scores of neighboring cell type b and the preprocessed expression values of HVG h in cell type a , while |${t}_c^{(a)}$| and |${l}_c^{(a)}$| are the scores of the c -th block obtained during CPPLS regression modeling. These P -values are adjusted using the Benjamini–Hochberg (BH) method [ 37 ] to obtain the false discovery rate (FDR)–adjusted values |${s}_{b,c}^{(a)}$| and |${s}_{h,c}^{(a)}$|⁠ . A parameter δ is set, and if δ is greater than or equal to 0.05, the coefficients |${w}_{b,h}^{\prime (a)}=\sum_c{w}_{b,h,c}^{\prime (a)}$| are returned:

The second filtering step involves CPPLS calculating the P -values |${s}_{h,c}^{\prime \prime (a)}$| for the genes that were not filtered out in the first step but lack statistical significance using the BH method. For coefficients |${w}_{b,h}^{\prime (a)}$| of each cell type a , if δ is greater than or equal to 0.05, the coefficients |${w}_{b,h}^{\prime \prime (a)}=\sum_c{w}_{b,h,c}^{\prime (a)}$| are returned:

Clustering of HVGs

Before clustering, all the HVGs with coefficients equal to 0 are filtered out. For each cell type a , CPPLS-MLP employs the k -means method to cluster the filtered coefficients of HVGs [ 38 ]. The optimal number of clusters k is determined using the Silhouette method. k ranges from the minimum integer value 2 to the maximum integer value 15. we utilize Silhouette analysis to determine the number of clusters for each cell type clustering, ranging from 2 to 15. Silhouette analysis assesses the quality of clustering results by considering both the compactness and separation of clusters. For each data point, a Silhouette coefficient is computed, ranging from −1 to 1, with values closer to 1 indicating better clustering results. By trying different values of k and calculating the average Silhouette coefficient for each k value, we can identify the optimal range of k values.

The construction of MIMO graph

CPPLS-MLP will summarize the two-point diagram obtained in the previous step:

In the equation, |${w}_{a,b}$| represents the square root of the coefficients of gene clusters within neighboring cell type b for cell type a . The aggregated coefficient matrix W is summarized by calculating its mean. Values below the mean are set to 0, and the remaining values are visualized in the form of a directed graph, illustrating the MIMO interactions between cells. In constructing the MIMO system from bipartite graphs, we ensure that the number of gene clusters within each cell type does not influence the final decision by standardizing the gene cluster counts across all cell types to their minimum value.

To align with the principle that the homeostasis within the tissue is collectively maintained by all cells, and considering that communication weakens as the distance between cells increases, CPPLS-MLP assumes pathways such as A → B, A → C → B, A → C → D → B (where A, B, C and D represent distinct cell types). Moreover, CPPLS-MLP acknowledges that the strength of communication exponentially decreases as the number of intermediate cells along the path increases. Therefore, based on the obtained coefficient matrix W, CPPLS-MLP calculates pathways from cell type a to all other cell types and applies attenuation to each path k :

j , i represent the first side and the last side of the departure from a → b , respectively. The path of the final a → b is:

Getting the path matric matrix R of all cell types can be visually displayed in the form of chord diagram.

Identification and classification of genes involved in cell communication

CPPLS-MLP initially filters the top 2000 HVGs using the FindVariableFeatures() method [ 39 ]. In addition to this, CPPLS-MLP employs three other methods, namely, variance [ 40 ], scranpy [ 41 ] and M3drop [ 42 ], to select 16 000 HVGs across both datasets. These 16 000 HVGs are categorized into two classes based on predefined labels from databases such as GeneCards and Gene Ontology (GO). In our single-cell transcriptomics analysis, we selected the top 2000 HVGs related to cell communication as our analysis threshold because the default threshold of the FindVariableFeatures() method is 2000, and we did not alter it. Moreover, limiting the number of variable genes significantly enhances computational efficiency when processing large datasets, thereby avoiding unnecessary resource consumption. Therefore, adopting the top 2000 HVGs as our threshold is a result of our comprehensive consideration of multiple factors, aimed at improving the efficiency of constructing cell communication networks.

(i) Strong correlation(strong_com): ‘receptor’, ‘ligand’, ‘receptors’, ‘ligands’, ‘cell–cell adhesion’, ‘intercellular interaction’.

(ii) Weak correlation(weak_com): ‘surfaces of many cells and extracellular matrices’, ‘Participates in cellular’, ‘Pathway’, ‘regulation’, ‘signal transduction’.

During manual querying, genes are assessed for their relevance to cell communication. A strong correlation is used as the criterion: genes with a label are assigned a value of 1, while those without are given 0.

In the process of cell communication, interactions often occur in conjunction with LRIs. Therefore, prior to tagging, we reviewed information recorded in the GeneCards and GO databases for 16 000 HVGs, extracting a total of 11 tags including ‘receptor’, ‘ligand’, ‘receptors’, ‘ligands’, ‘cell–cell adhesion’ and ‘intercellular interaction’, among others. We considered these tags directly related to the cell communication process as strongly relevant. For other tags that describe gene functions related to cell communication, we categorized them as weakly relevant. The MLP possesses powerful non-linear mapping capabilities and has been widely applied in bioinformatics for classification tasks [ 43 , 44 ]. Therefore, CPPLS-MLP utilizes the genes selected through FindVariableFeatures() from both datasets and employs the MLP neural network model to classify these genes.

Overview of the CPPLS-MLP method

Figure 1 provides an overview of the workflow developed and tested for CPPLS-MLP, primarily comprising two main components: (1) construction of cell–cell communication networks based on single-cell and spatial transcriptomic data, including gene expression matrices and spatial coordinate matrices, and (2) identification and classification of gene clusters involved in network construction. In the first part, utilizing single-cell gene expression matrices, spatial coordinate matrices from ST data and cell type label data, a linear model (CPPLS) is employed to capture the multi-response (continuous, discrete and combined) relationship between intercellular communication and HVGs expression ( Figure 1A ). This step constructs the cell communication network, wherein edge weights are attenuated based on the number of nodes along the paths, yielding the final communication strength between two cell types ( Figure 1B ). By integrating the BH method and Silhouette method, the model utilizes 10-fold cross-validation to obtain average metrics, generating a coefficient matrix representing the direction and degree of regulation for each HVG’s expression by adjacent cell types.

Workflow of the CPPLS-MLP method and visualization. ( A ) CPPLS-MLP processes gene expression and spatial information from single-cell and ST datasets. Subsequently, the data are modeled using the CPPLS model for subsequent analysis. ( B ) Cell–cell communication strength is influenced by proximity. In the MIMO system, all paths between each pair of nodes in the graph are extracted. Edge weights are attenuated based on the number of nodes along the paths. This process yields the optimal weights and bipartite graphs between the two cell types, visualized as directed graphs and heat maps. ( C ) Gene clusters involved in constructing the cell communication network are analyzed. Strong relevant labels are extracted from GeneCards and GO databases. Using the neural network model MLP, these clusters are classified based on their association with cell communication.

The second component of CPPLS-MLP involves labeling and categorizing HVGs that contribute to constructing the cell communication network ( Figure 1C ). Utilizing four methods, FindVariableFeatures(), variance, scannpy and M3drop, 16 000 HVGs were selected through manual queries in official databases like Genecard and GO. Strong relevant labels, identified as strong_com, were extracted. These labels were used to tag the HVGs involved in CPPLS-MLP modeling. Subsequently, a neural network model, MLP, was employed to classify these genes.

CPPLS-MLP is also employed for visualizing cell–cell communication networks and assessing the extent and direction of HVG expression modulation by intercellular communication ( Figure 1B ). For example, in single-cell datasets, it evaluates relationships between gene clusters and neighboring cells, as well as interactions among different cell types. This analysis and visualization utilize two distinct spatial techniques and their corresponding datasets: the seqFISH+ mouse cortex dataset and the Seq-Scope mouse colon dataset.

Performance comparison of CPPLS-MLP with other methods

The construction of the cell–cell communication network by CPPLS-MLP serves as the foundation for subsequent analyses. To evaluate its performance, two single-cell and ST datasets from mouse cortex and mouse colon were utilized. CPPLS-MLP demonstrated its ability to identify known HVGs whose expression is influenced by intercellular communication in spatial contexts, as shown in cases based on the seqFISH+ mouse cortex and Seq-Scope mouse colon datasets. Although the number of predicted HVGs regulated by cell–cell communication varied across methods, a significant overlap was observed between CPPLS-MLP and other approaches. This suggests the reproducibility of inferences made by these methods.

Therefore, we proceeded to conduct a horizontal comparison, evaluating CPPLS-MLP’s performance in inferring HVGs expression regulated by intercellular communication. Additionally, we compared its gene classification capabilities with those of existing methods. CPPLS-MLP consistently outperformed these methods across the benchmark datasets, securing the top position. Illustrative examples from the seqFISH+ dataset, depicting interactions between neural layers, indicated that CPPLS-MLP might be more effective in single-cell and ST datasets characterized by higher the uniqueness of HVG among different cell types.

Because CPPLS-MLP is not limited to estimating cell–cell communication solely based on LRIs for regulating HVGs in intercellular differential expression, we conducted a comparative analysis with other existing methods, specifically CCPLS, which estimate the degree and direction of HVG regulation through intercellular communication. We ensured uniformity in cell types across the comparison datasets. In both Seq-Scope and seqFISH+ datasets, we categorized the HVGs involved in cell communication networks into communication-related genes (Y HVGs) and non-related genes (N HVGs) based on strong and weak correlation labels. After calculating the percentage of Y HVGs within each cell type cluster in relation to the total genes obtained, we determined the overlap rate of Y HVGs between different cell types. As depicted in Figure 2A and B , on the Seq-Scope dataset, CPPLS-MLP demonstrated higher uniqueness of HVGs in only two cell types, Macrophage and Paneth_like, compared to CCPLS under strong correlation labels. Additionally, under weak correlation labels, CPPLS-MLP showed slightly lower uniqueness than CCPLS specifically in macrophage cells. In the seqFISH+ dataset, under strong correlation labels, HVGs in L6.eNeuron cells exhibited slightly higher uniqueness with CPPLS-MLP compared to CCPLS. This difference was due to the fact that CCPLS identified only three genes as Y HVGs in this specific cell type. Under weak correlation labels, CPPLS-MLP achieved a Y HVGs overlap rate of 0 in these two cell types. This result provides evidence that the HVGs identified by CPPLS-MLP in constructing cell communication networks are more representative for each specific cell type.

Superior performance of CPPLS-MLP compared to existing methods. ( A ) Comparison of the uniqueness of Y HVGs in each cell type based on strong and weak correlation labels between CPPLS-MLP and existing methods estimating intercellular communication-regulated HVG expression (CCPLS) in the SeqScope dataset. ( B ) Comparison of the uniqueness of Y HVGs in each cell type based on strong and weak correlation labels between CPPLS-MLP and CCPLS in the seqFISH+ dataset. ( C ) Performance comparison of CPPLS-MLP with some existing classification methods (LightGBM, Single Tree and Random Forest) on the Seq-Scope and seqFISH+ datasets.

Subsequently, when labeling HVGs based on strong correlation labels, we compared the performance of CPPLS-MLP with existing classification methods. We posited that genes associated with cell communication follow specific expression patterns, enabling their classification through methods trained on labeled data. As illustrated in Figure 2C , CPPLS-MLP exhibited superior performance on both datasets, outperforming several existing classification methods. In summary, these results indicate that CPPLS-MLP is a relatively accurate and effective approach for deducing the regulation of intercellular communication on HVGs’ intercellular differential expression and for classifying HVGs based on cell communication labels.

We compared our method with popular approaches like cellphoneDB and Cellchat by considering the top 50% of their predicted results and evaluated the number of genes related to cell communication identified by each method based on strong correlation labels. In the seqFISH+ mouse brain dataset and the Seqscope human colon dataset, our CPPLS-MLP method identified 354 and 345 genes related to cell communication, respectively. In contrast, cellphoneDB identified 284 and 104 genes, respectively, for the seqFISH+ and Seqscope datasets, while Cellchat identified 388 and 142 genes, respectively.

Identification of signals between fibroblasts and B.cell_IgA cells

First, we applied CPPLS-MLP to the single-cell and ST dataset, Seq-Scope mouse colon dataset ( Figure 3A left). This dataset encompasses 10 806 genes and nine distinct cell types: B immature cells, DCSC, IgA B cells, macrophages, smooth muscle cells, stem cells, Paneth-like cells, fibroblasts and IgG B cells. Before utilizing CPPLS-MLP, we examined the HVGs extracted among the nine cell types in the real Seq-Scope dataset. The experimental findings revealed that the average overlap ratio of HVGs between these cell types was 0.31 ( Figure 3B left). Specifically, most highly variable genes differed across different cell types, indicating unique characteristics for HVGs in each cell type. Next, we clustered the HVGs within each cell type to infer their relationships with other cell types. Visualization was performed using heat maps and bipartite graphs ( Figure 3C and D left; Supplementary Figures S1 and S2 ). Additionally, we conducted GO enrichment analysis on the detected gene clusters ( Figure 3E left; Supplementary Figure S3 ).

Single-cell and ST real data sets Seq-Scope and seqFISH+ are applied to CPPLS-MLP. ( A ) seq-scope and seqfish+dataset schematic diagram. ( B ) The overlap rate of HVGs between different cell types is at two real data concentrations. ( C ) A heat map was generated to display the relationship coefficients between HVG clusters within fibroblast cells and other cell types in the Seq-Scope real dataset experiment, as well as between HVG clusters within L5.eNeuron cells and other cell types in the seqFISH+ real dataset experiment. ( D ) Bipartite graph showing the relationship between gene clusters and adjacent cell types in B_immature cells and L5.eNeuron cells. ( E ) GO enrichment of genes in B.cell_lgA cells and L5.eNeuron cells.

CPPLS-MLP was employed to assess the impact of intercellular communication on HVG expression by comparing the detected genes with the average expression levels in the mouse and human genome annotation packages ( Figure 4A and B ). Further exploration focused on the communication between immature B cells and fibroblasts. Fibroblasts, known as cancer-associated fibroblasts (CAFs), constitute a major stromal component in cancer and play a crucial role in maintaining tissue homeostasis by interacting with molecules within the extracellular matrix (ECM). B.cell_IgA cells, on the other hand, have vital roles in the immune system. These two cell types influence each other’s states and functions through molecular interactions in the ECM, contributing to the stability of colonic tissue. Both B cells and fibroblasts secrete cytokines such as IL-6, IL-8 and IL-10, which regulate immune responses [ 45 ]. Notably, fibroblasts not only serve as microenvironmental regulators of intestinal stem cells but also modulate lymphatic endothelial cells, blood endothelial cells and immune cells in the intestine. Through signaling interactions with different signal molecules and cell types, fibroblasts play crucial roles in intestinal development, homeostasis and diseases [ 46 ]. In cases of intestinal diseases, abnormal ECM secretion by fibroblasts may disrupt the regulation of epithelial cells, leading to pathological fibrosis. Hence, fibroblasts secrete ECM to interact with immune cells, regulating inflammation and immune responses to help control tissue inflammation processes.

Identification of signals between fibroblasts and B.cell_IgA cells. ( A ) Upregulated genes detected by CPPLS-MLP in the Seq-Scope dataset. ( B ) Downregulated genes detected by CPPLS-MLP in the Seq-Scope dataset. ( C , D ) The two-dimensional distribution diagrams of gene GPX1 expression in cell types B.cell_IgA and fibroblast, respectively.

Taking the gene GPX1 as an example, the protein encoded by this gene belongs to the glutathione peroxidase family, catalyzing the reduction of organic hydroperoxides and hydrogen peroxide by glutathione [ 47 ]. It exerts antioxidative effects in fibroblasts, reducing the impact of oxygen radicals. In communication with B.cell_IgA cells, GPX1 mitigates oxidative stress on B.cell_IgA cells through its antioxidative properties. We further plotted the positions of cells in a two-dimensional space and visualized the expression levels of the GPX1 gene in B.cell_IgA cells and fibroblasts ( Figure 4C and D ). It is noteworthy that the GPX1 gene is known to be associated with colitis, indicating its involvement in the regulation of inflammatory signaling pathways. Additionally, in GO analysis, the GPX1 gene is annotated with ‘epithelial cell development’. Notably, at the boundary between B.cell_IgA cells and fibroblasts, B.cell_IgA cells exhibited high expression of the GPX1 gene. These findings suggest that the epithelial cell development in B.cell_IgA cells occurs through their interactions with fibroblasts. The MIMO interactions in the Seq-Scope real data set are illustrated in a directional graph ( Supplementary Figure S8A ).

Finally, CPLS-MLP adopts the neural network model MLP to classify the top 2000 HVGs with the largest expression differences between cells, which are extracted using the FindVariableFeatures() method and labeled according to the strong correlation labels selected from the dataset.

Recognition of preference communication in the fifth and sixth layers of mouse brain neurons

Next, CPPLS-MLP was applied to study and visualize intercellular communication within the mouse cortex dataset from the single-cell and ST dataset, seqFISH+. This dataset comprised data from 10 000 sequenced genes, covering 12 cell types, including Adarb2 iNeuron, astrocytes, endothelial cells, L2/3 eNeuron, L4 eNeuron, L5 eNeuron, L6 eNeuron, Lhx6 iNeuron, microglia, mural cells, oligodendrocytes (Olig) and oligodendrocyte progenitor cells (OPCs) ( Figure 3A right). Before applying CPPLS-MLP, we examined HVGs extracted from interactions between these 12 cell types in the seqFISH+ real dataset. In our experiments, the average overlap ratio of HVGs between these cell types was 0.25 ( Figure 3B right), indicating the uniqueness of cell-type-specific sets of highly variable genes across different cell types. Subsequently, HVGs from each cell type were clustered to infer their relationships with other cell types. The relationships were visualized using heat maps and bipartite graphs ( Figure 3C and D right; Supplementary Figures S4 and S5 ). Additionally, the detected gene clusters were subjected to GO enrichment analysis ( Figure 3E right; Supplementary Figure S6 ).

CPPLS-MLP initially examined the impact of intercellular communication on the expression of HVGs in the seqFISH+ dataset ( Supplementary Figure S7A ). It identified communication between cells L5 eNeuron and L6 eNeuron, both belonging to the pyramidal neurons of the mouse brain’s fifth and sixth cortical layers, respectively. Neurons of this type typically transmit information in neural networks [ 48 ]. Experimental evidence has shown that in the visual and somatosensory cortex, the intracortical axons of L6 CT neurons primarily target L5a. When activated, L6 CT neurons trigger action potentials in L5a pyramidal neurons. Additionally, the activation of L6 CT neurons inhibits the excitatory neurons in L4 [ 49 ]. This interaction pattern plays a crucial role in visual and somatosensory processing.

For example, CPLX1 in L5 eNeuron belongs to the synaptic protein gene family, encoding a protein involved in synaptic vesicle exocytosis. Its protein product binds to the SNAP receptor complex and disrupts it, allowing neurotransmitter release. These processes play a crucial role in communication between the neurons in the brain’s neural cortex and regulate bodily movements [ 50 ]. CPPLS-MLP further plotted a two-dimensional spatial distribution of L5 eNeuron and L6 eNeuron. It was observed that the closer L5 eNeuron is to L6 eNeuron, the higher the expression level of CPLX1 in L5 eNeuron, indicating that the communication between L5 eNeuron and L6 eNeuron influences the expression of HVGs within the cells ( Supplementary Figure S7B ). The directional graph illustrating the MIMO in the seqFISH+ real dataset is provided in Supplementary Figure S8B .

Finally, CPPLS-MLP employed the neural network model MLP to classify the top 2000 HVGs exhibiting the most significant intercellular expression differences, as determined by the Find VariableFeatures() method and based on strong correlation labels, within this dataset.

We have demonstrated the impact of cell–cell communication on HVGs expression and its accurate classification using CPPLS-MLP in two single-cell and ST datasets, Seq-scope and seqFISH+. These datasets encompass single-cell and ST data generated by Seq-Scope and seqFISH+ methods.

When applying the Seqscope dataset, we aimed to predict communication between immature B cells and fibroblasts. Communication between these two cell types occurs via the extracellular matrix and plays a crucial role in maintaining the homeostasis of colon tissue. To validate our predictions, we visualized the expression levels of the GPX1 gene in both cell types and its spatial distribution. This visualization confirmed the accuracy of our predictions. When applying the seqFISH+ dataset, we aimed to predict communication between L5 eNeurons and L6 eNeurons. These two cell types communicate via neurons and play a crucial role in maintaining visual and somatosensory processing. To confirm our predictions, we visualized the expression levels of the CPLX1 gene and its spatial distribution in these two cell types. This visualization confirmed the accuracy of our predictions.

For assessing model performance, we indeed selected two single-cell and ST datasets, namely, from the mouse cortex and human colon. Despite the limited number of datasets, we chose these due to their representativeness, covering various organs and cell types. Additionally, we believe these two datasets align well with the application scenario of our model, as cellular communication in tissues like the cortex and colon is crucial for understanding their biological functions. There are two principles explaining how cell–cell communication impacts the expression of HVGs and allows for classification: adjacent cells can communicate through extracellular signaling molecules (such as growth factors, cytokines, hormones, etc.), which can influence the gene expression patterns of HVGs cells, leading to differential expression; genes from two interacting cells have similarities in their expression profiles. This hypothesis is grounded in several theoretical and empirical studies, such as the Correlation AnalyzeR, a method for functional gene prediction based on the analysis of gene co-expression correlations. Existing scRNA-seq technologies, which identify cell subpopulations associated with specific phenotypes based on single-cell data, have been widely applied to determine cell types and states, revealing significant differences in gene expression profiles across different cell types. However, we have also observed that within similar biological environments, such as the same tissue type or neighboring cell groups, there can be a degree of similarity in gene expression profiles between cells. This similarity may reflect interactions and communication between cells, including the interaction of cytokines and the activation of signaling pathways. Therefore, ST data are particularly suitable for inferring cell–cell communication-regulated differential expression of HVGs based on these principles and can be classified using specific strategies. In this context, our proposed method CPPLS-MLP combines the cell–cell communication network and labels genes in a known database to filter out HVGs that are not involved in cell communication. Then, it utilizes the multivariate linear regression properties of CPPLS to model the spatial coordinates of cells and gene expression information. Finally, it classifies genes based on strong correlation labels. Thus, on benchmark ST datasets, the uniqueness and accuracy of classification for the HVGs involved in CPPLS-MLP modeling surpass existing methods, demonstrating the applicability of these principles in decoding cell–cell cross-talk. This approach is especially suited for deciphering the regulation of cell–cell communication on HVGs expression.

Furthermore, CPPLS-MLP infers that interacting cells exhibit similarity in their gene expression profiles, indicating that genes within interacting cells are governed by specific expression patterns. By manually querying genes in databases like Genecard and GO and extracting labels, CPPLS-MLP offers novel insights into assessing whether genes are associated with cellular communication. Currently, analyzing and visualizing ligand–receptor pairs in scRNA-seq data at single-cell resolution is challenging. CPPLS-MLP, on the other hand, analyzes the relevance of genes to cell communication based on gene expression patterns and labels. If certain genes within ligands and receptors exhibit similar expression patterns, the cells harboring these genes are likely engaging in communication. CPPLS-MLP integrates spatial coordinates, gene expression data and extracted strong and weak correlation labels, offering a new perspective on evaluating intercellular communication.

In the inference of cell–cell communication, incorporating spatial information and gene categorization is crucial for spatial analysis of intercellular communication. Utilizing prior knowledge to classify genes as relevant or irrelevant to cellular communication aids in computational inference of intercellular communication. Furthermore, in studying spatially regulated cell–cell communication, integrating different omics data and multimodal datasets such as 10x Multiome and Digital Spatial Profiling provides more comprehensive, multidimensional information. We propose utilizing image processing techniques to extract precise cell location information from tissue slice images in ST data. This location data will provide us with accurate information about cell positions within tissues, enriching the data foundation for our research. By integrating this spatial information, we can overcome the challenge of analyzing data when only gene expression is available. This enhancement will not only make CPPLS-MLP compatible with current multimodal data but also improve our ability to explore biologically meaningful cell–cell interactions. This approach enhances our understanding of cell interactions and regulatory mechanisms. In this context, reliable computational models are needed to accurately integrate multimodal data and perform inference.

We developed an innovative model integrating neural networks and multiple linear regression functions, called CPPLS_MLP. This model uses coordinate information in spatial transcriptomic data and gene expression information in single-cell sequencing data to accurately construct a cell communication network and classify HVGs in the network based on existing database information.

CPPLS_MLP exhibits excellent accuracy and robustness, making it suitable for various experimental designs, single-cell sequencing presumably derived from different organs and cell communication of ST data.

CPPLS_MLP is provided in an open-source format and can be directly used to predict cell communication in different tissues and classify genes in their communication networks.

The authors thank the anonymous reviewers for their constructive suggestions.

This work was supported by the National Key R and D Program of China [2022YFF1202100], National Natural Science Foundation of China [62172087, 62072095] and Project supported by the National Science Foundation for Distinguished Young Scholars of China [62225109].

For seqFISH+，the single-cell ST data of the mouse somatosensory cortex dataset was retrieved from the “Github repository [ https://rubd.github.io/Giotto_site/articles/mouse_seqFISH_cortex_200914 ]” [ 25 ].For Seq-Scope, the single-cell ST data of the human colon dataset was downloaded from “Deep Blue Data[Data Set | Seq-Scope processed datasets for liver and colon results (RDS) and H&E images | ID: 9c67wn05f | Deep Blue Data (umich.edu)]” [ 51 ]. Source codes for the CPPLS_MLP R, python packages and the related scripts are available at “CPPLS_MLP Github [ https://github.com/wuzhenao/CPPLS-MLP ]”.

Tianjiao Zhang is an associate professor of College of Computer and Control Engineering at Northeast Forestry University of China. His research interests include bioinformatics.

Zhenao Wu is a master candidate of College of Computer and Control Engineering at Northeast Forestry University of China. His research interests include bioinformatics.

Liangyu Li is a master candidate of College of Computer and Control Engineering at Northeast Forestry University of China. His research interests include bioinformatics.

Jixiang Ren is a master candidate of College of Computer and Control Engineering at Northeast Forestry University of China. His research interests include bioinformatics.

Ziheng Zhang is a master candidate of College of Computer and Control Engineering at Northeast Forestry University of China. His research interests include bioinformatics.

Guohua Wang is a professor of College of Computer and Control Engineering at Northeast Forestry University of China. He is also professor of Faculty of Computing at Harbin Institute of Technology of China. His research interests are bioinformatics, machine learning and algorithm.

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Strong, Semi-Strong, and Weak Efficient Market Hypothesis
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Efficient market hypothesis: Weak, semi strong and strong market
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The Weak, Strong, and Semi-Strong Efficient Market Hypotheses
The weak form of the theory is the most lenient and concedes that there are circumstance when fundamental analysis can help investors find value. The strong form of the theory is the least lenient ...
Efficient-market hypothesis
2.1 Weak, semi-strong, and strong-form tests. 3 Historical background. 4 Criticism. Toggle Criticism subsection. 4.1 Behavioral psychology. ... The efficient-market hypothesis (EMH) is a hypothesis in financial economics that states that asset prices reflect all available information. A direct implication is that it is impossible to "beat the ...
Efficient Market Hypothesis (EMH)
What are the 3 Forms of Efficient Market Hypothesis? Weak Form, Semi-Strong, and Strong Form Market Efficiency. Eugene Fama classified market efficiency into three distinct forms: Weak Form EMH: All past information like historical trading prices and volume data is reflected in the market prices.
The 20% Statistician: Strong versus Weak Hypothesis Tests
Strong versus Weak Hypothesis Tests. The goal of a hypothesis test is to carefully examine whether predictions that are derived from a scientific theory hold up under scrutiny. Not all predictions we can test are equally exciting. For example, if a researcher asks two groups to report their mood on a scale from 1 to 7, and then predicts the ...
Efficient Market Hypothesis (EMH)
The hypothesis argues that since all relevant information is already reflected in stock prices, it is not possible to gain an advantage and generate abnormal returns through stock picking or market timing. The EMH comes in three forms: weak, semi-strong, and strong, each representing different levels of market efficiency.
Efficient Market Hypothesis: Strong, Semi-Strong, and Weak
Weak Efficient Market Hypothesis. The weak form of EMH says that you cannot predict future stock prices on the basis of past stock prices. Weak-form EMH is a shot aimed directly at technical analysis. If past stock prices don't help to predict future prices, there's no point in looking at them — no point in trying to discern patterns in ...
What Is the Efficient Market Hypothesis?
The Semi-Strong Form of the Efficient Market Hypothesis This form takes the same assertions of weak form, and includes the assumption that all new public information is instantly priced into the ...
Writing a Strong Hypothesis Statement
Make sure your hypothesis clearly posits a relationship between variables. Make sure your hypothesis is testable considering your available time and resources. Before writing a thesis, it is important to create a strong hypothesis statement. This statement is a prediction of what you think will happen in your research study.
Market Efficiency: Weak, Semi-strong, and Strong
In 1970 Fama published a review of both the theory and the evidence for the hypothesis. The paper extended and refined the theory, included the definitions for three forms of financial market efficiency: weak, semi-strong, and strong. It has been argued that the stock market is "micro efficient," but not "macro inefficient.
The Weak, Strong and Semi-Strong Efficient Market Hypotheses
The three versions of the efficient market hypothesis are varying degrees of the same basic theory. The weak form suggests that today's stock prices reflect all the data of past prices and that no form of technical analysis can be effectively utilized to aid investors in making trading decisions. Advocates for the weak form efficiency theory believe that if fundamental analysis is used ...
Efficient Markets Hypothesis—EMH Definition and Forms
Weak Form EMH: Weak form EMH suggests that all past information is priced into securities.Fundamental analysis of securities can provide you with information to produce returns above market averages in the short term. But no "patterns" exist. Therefore, fundamental analysis does not provide a long-term advantage, and technical analysis will not work.
Strong Induction
The reason why this is called "strong induction" is that we use more statements in the inductive hypothesis. Let's write what we've learned till now a bit more formally. Proof by strong induction. Step 1. Demonstrate the base case: This is where you verify that $P(k_0)$ is true. In most cases, $k_0=1.$ Step 2. Prove the inductive step:
What exactly is the difference between weak and strong induction?
Kenneth Rosen remark in Discrete Mathematics and Its Applications Study Guide: Understanding and constructing proofs by mathematical induction are extremely difficult tasks for most students. Do not be discouraged, and do not give up, because, without doubt, this proof technique is the most important one there is in mathematics and computer science.
Whorfianism
Strong and weak Whorfianism One of the first linguists to defend a general form of universalism against linguistic relativism, thus presupposing that they conflict, was Julia Penn (1972). She was also an early popularizer of the distinction between 'strong' and 'weak' formulations of the Sapir-Whorf Hypothesis (and an opponent of the ...
What Is Weak Form Efficiency and How Is It Used?
Weak form efficiency is one of the three different degrees of efficient market hypothesis (EMH) ; it claims that past price movements and volume data do not affect stock prices. As weak form ...
How to Write a Strong Hypothesis
5. Phrase your hypothesis in three ways. To identify the variables, you can write a simple prediction in if…then form. The first part of the sentence states the independent variable and the second part states the dependent variable. If a first-year student starts attending more lectures, then their exam scores will improve.
Sapir-Whorf hypothesis (Linguistic Relativity Hypothesis)
The Sapir-Whorf hypothesis states that people experience the world based on the structure of their language, and that linguistic categories shape and limit cognitive processes. It proposes that differences in language affect thought, perception, and behavior, so speakers of different languages think and act differently.
What Makes a Strong Hypothesis for Scientific Research?
A strong hypothesis is concise, clear, and defines an expected relationship between the dependent and independent variables. This relationship should be stated as explicitly as possible and must be testable. Having a concise hypothesis makes it obvious to the reader when you transition from background information to a research question without ...
Weak Forms and Strong Forms
For Cameron Neylon, because he kept asking me for this… The Sapir-Whorf hypothesis 1 states that language affects thought — how we speak influences how we think. Or, at least, that's one form of the hypothesis, the weak form. The strong form of Sapir-Whorf says that language determines thought, that how we speak forms a hard boundary on how and what we think.
Preference Hypothesis and Strong Ordering (Explained With Diagram)
J. R. Hicks in his "A Revision of Demand Theory' does not consider the assumption of strong ordering as satisfactory and instead employs weak ordering hypothesis. Under weak ordering hypothesis (with an additional assumption that the consumer will always prefer a larger amount of a good to a smaller amount of it), the chosen combination A ...
Strong and weak sampling
Strong and weak sampling are two sampling approach in Statistics, and are popular in computational cognitive science and language learning. In strong sampling, it is assumed that the data are intentionally generated as positive examples of a concept, [3] while in weak sampling, it is assumed that the data are generated without any restrictions.
Cosmic censorship hypothesis
Cosmic censorship hypothesis. The weak and the strong cosmic censorship hypotheses are two mathematical conjectures about the structure of gravitational singularities arising in general relativity . Singularities that arise in the solutions of Einstein's equations are typically hidden within event horizons, and therefore cannot be observed from ...
Scientific success from the perspective of the strength of weak ties
Now, using the concept of asymmetric tie strength, we will discuss Granovetter's second hypothesis, which postulates that although weak ties do not carry as much communication as strong ties do ...
Gravity is Really Weak?
Sounds like we are right back to the start of this lesson again. Let's put some real numbers on this. The "weak" nuclear force is 10 to the 25th power stronger than Gravity. That's 100,000,000,000,000,000,000,000,000 times stronger! Electromagnetism - the force we know best - is 10 to the 36th power stronger than Gravity.
CPPLS-MLP: a method for constructing cell-cell communication networks
This hypothesis is grounded in several theoretical and empirical studies, such as the Correlation AnalyzeR, a method for functional gene prediction based on the analysis of gene co-expression correlations. ... CPPLS-MLP integrates spatial coordinates, gene expression data and extracted strong and weak correlation labels, offering a new ...