assignment root meaning

assignment (n.)

late 14c., "an order, request, directive," from Old French assignement "(legal) assignment (of dower, etc.)," from Late Latin assignamentum , noun of action from past-participle stem of Latin assignare / adsignare "to allot, assign, award" (see assign ). The meaning "appointment to office" is mid-15c.; that of "a task assigned (to someone), commission" is by 1848.

Entries linking to assignment

c. 1300, "to transfer, convey, bequeath (property); appoint (to someone a task to be done); order, direct (someone to do something); fix, settle, determine; appoint or set (a time); indicate, point out," from Old French assigner "assign, set (a date, etc.); appoint legally; allot" (13c.), from Latin assignare / adsignare "to mark out, to allot by sign, assign, award," from ad "to" (see ad- ) + signare "make a sign," from signum "identifying mark, sign" (see sign (n.)). Its original use was in legal transfers of personal property. Related: Assigned ; assigning .

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Dictionary entries near assignment

assignation

assimilable

assimilation

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Definition of assignment

task , duty , job , chore , stint , assignment mean a piece of work to be done.

task implies work imposed by a person in authority or an employer or by circumstance.

duty implies an obligation to perform or responsibility for performance.

job applies to a piece of work voluntarily performed; it may sometimes suggest difficulty or importance.

chore implies a minor routine activity necessary for maintaining a household or farm.

stint implies a carefully allotted or measured quantity of assigned work or service.

assignment implies a definite limited task assigned by one in authority.

Examples of assignment in a Sentence

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'assignment.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Word History

see assign entry 1

14th century, in the meaning defined at sense 1

Phrases Containing assignment

• self - assignment

Dictionary Entries Near assignment

Cite this entry.

“Assignment.” Merriam-Webster.com Dictionary , Merriam-Webster, https://www.merriam-webster.com/dictionary/assignment. Accessed 4 Apr. 2024.

Legal Definition

Legal definition of assignment, more from merriam-webster on assignment.

Nglish: Translation of assignment for Spanish Speakers

Britannica English: Translation of assignment for Arabic Speakers

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Definition of assign verb from the Oxford Advanced Learner's Dictionary

• assign something (to somebody) The teacher assigned a different task to each of the children.
• The two large classrooms have been assigned to us.
• assign somebody something We have been assigned the two large classrooms.
• The teacher assigned each of the children a different task.

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Find out which words work together and produce more natural-sounding English with the Oxford Collocations Dictionary app. Try it for free as part of the Oxford Advanced Learner’s Dictionary app.

Definition of 'assignment'

Video: pronunciation of assignment

assignment in British English

Assignment in american english, examples of 'assignment' in a sentence assignment, cobuild collocations assignment, trends of assignment.

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something assigned, as a particular task or duty: She completed the assignment and went on to other jobs.

a position of responsibility, post of duty, or the like, to which one is appointed: He left for his assignment in the Middle East.

an act of assigning; appointment.

the transference of a right, interest, or title, or the instrument of transfer.

a transference of property to assignees for the benefit of creditors.

Origin of assignment

Synonym study for assignment, other words for assignment, other words from assignment.

• mis·as·sign·ment, noun
• non·as·sign·ment, noun
• re·as·sign·ment, noun

Words that may be confused with assignment

• assignment , assignation

Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2024

How to use assignment in a sentence

He traveled to China, India, Russia, and Africa for fashion-related assignments.

Among his previous assignments were stints in war zones like Afghanistan and the Congo.

He also had a reputation for not sticking to the brief of his assignments.

His writing assignments were filled with “a disturbing level” of mayhem, war, and death.

The first faux-Fleming assignments went to writers such as Kingsley Amis (writing as “Robert Markham”) and John Gardner.

Toward the end of the campaign his assignments increased until all his time was taken.

Assignments came to be made of one acre to a family, near the palisaded hamlet for convenience and better security.

For a short time he had no assignments that taxed his abilities in either direction.

If you make as good time as you have made on some other assignments, you can get back here before 10:30.

Not a lot of business-reporting assignments involved spending time with half-naked, sun-baked dudes in remote southern junkyards.

British Dictionary definitions for assignment

/ ( əˈsaɪnmənt ) /

something that has been assigned, such as a mission or task

a position or post to which a person is assigned

the act of assigning or state of being assigned

the transfer to another of a right, interest, or title to property, esp personal property : assignment of a lease

the document effecting such a transfer

the right, interest, or property transferred

law (formerly) the transfer, esp by an insolvent debtor, of property in trust for the benefit of his creditors

logic a function that associates specific values with each variable in a formal expression

Australian history a system (1789–1841) whereby a convict could become the unpaid servant of a freeman

Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

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Mathematics > Group Theory

Title: root graded groups.

Abstract: We define and study root graded groups, that is, groups graded by finite root systems. This notion generalises several existing concepts in the literature, including in particular Jacques Tits' notion of RGD-systems. The most prominent examples of root graded groups are Chevalley groups over commutative associative rings. Our main result is that every root graded group of rank at least 3 is coordinatised by some algebraic structure satisfying a variation of the Chevalley commutator formula. This result can be regarded as a generalisation of Tits' classification of thick irreducible spherical buildings of rank at least 3 to the case of non-division algebraic structures. All coordinatisation results in this book are proven in a characteristic-free way. This is made possible by a new computational method that we call the blueprint technique.

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• Square Roots

Square Root

Square root of a number is a value, which on multiplication by itself, gives the original number. The square root is an inverse method of squaring a number. Hence, squares and square roots are related concepts. 

Suppose x is the square root of y, then it is represented as x=√y, or we can express the same equation as x 2 = y. Here, ‘√’ is the radical symbol used to represent the root of numbers. The positive number, when multiplied by itself, represents the square of the number . The square root of the square of a positive number gives the original number.

For example, the square of 3 is 9, 3 2 = 9 and the square root of 9, √9 = 3. Since 9 is a perfect square, hence it is easy to find the square root. But for an imperfect square like 3, 7, 5, etc., we have to use different methods to find the square root. Learn square roots from 1 to 25   with some shortcut tricks here.

Square Roots Definition

The square root of any number is equal to a number, which when squared gives the original number. Let us say m is a positive integer, such that  √ (m.m) = √(m 2 ) = m

In mathematics, a square root function is defined as a one-to-one function that takes a positive number as an input and returns the square root of the given input number.

For example, if x=4, then the function returns the output value as 2.

Note: The square root of a negative number represents a complex number .

Suppose √-n = i√n, where i is the imaginary number.

Square Root Symbol

The square root symbol is usually denoted as ‘ √’ . It is called a radical symbol. To represent a number ‘x’ as a square root using this symbol can be written as: ‘ √x ‘

where x is the number. The number under the radical symbol is called the radicand . For example, the square root of 6 is also represented as radical of 6. Both represent the same value.

Square Root Formula

The formula to find the square root is:

Since, y.y = y 2  = a; where ‘a’ is the square of a number ‘y’.

Properties of Square root

Some of the important properties of the square root are as follows:

• If a number is a perfect square number, then there exists a perfect square root.
• If a number ends with an even number of zeros (0’s), then it can have a square root.
• The two square root values can be multiplied. For example, √3 can be multiplied by √2, then the result should be √6.
• When two same square roots are multiplied, then the result should be a radical number. It means that the result is a non-square root number. For instance, when √7 is multiplied by √7, the result obtained is 7.
• The square root of any negative numbers is not defined because the perfect square cannot be negative.
• If a number ends with 2, 3, 7 or 8 (in the unit digit), then the perfect square root does not exist.
• If a number ends with 1, 4, 5, 6 or 9 in the unit digit, then the number may have a perfect square root.

How do Find Square Root of Numbers?

To find the square root of any number, we need to figure out whether the given number is a perfect square or an imperfect square. If the number is a perfect square, such as 4, 9, 16, etc., then we can factorize the number by prime factorisation method. If the number is an imperfect square, such as 2, 3, 5, etc., then we have to use a long division method to find the root.

Hence, the methods to find the square root of numbers are:

• Square Root by Prime Factorisation
• Square Root by Repeated Subtraction Method
• Square Root by Long Division Method
• Square Root by Estimation Method

Let us learn each method of square root with examples.

Square root By Prime Factorization

The square root of a perfect square number is easy to calculate using the prime factorization method. Let us solve some of the examples here:

Finding Square Roots by Repeated Subtraction Method

As per the repeated subtraction method, if a number is a perfect square, then we can determine its square root by:

• Repeatedly subtracting consecutive odd numbers from it
• Subtract till the difference is zero
• Number of times we subtract is the required square root

For example, let us find the square root of 25.

• 25 – 1 = 24
• 24 – 3 = 21
• 21 – 5 = 16
• 16 – 7 = 9
• 9 – 9 = 0

Since, the subtraction is done for 5 times, hence the square root of 25 is 5.

Finding Square Roots by Long Division Method

Finding square roots for the imperfect numbers is a bit difficult but we can calculate using a long division method. This can be understood with the help of the example given below. Consider an example of finding the square root of 436.

Thus, the square root of 436 is 20.880 (rounding to 3 decimals).

Square root by Estimation Method

This method is used as an approximation method, to find the square root by guessing the values.

For example, the square root of 4 is 2 and the square root of 9 is 3, thus, we can guess the square root of 5 will lie between 2 and 3.

But, we need to check the value of √5 is nearer to 2 or 3. Let us find the square of 2.2 and 2.8.

• 2.2 2 = 4.84
• 2.8 2 = 7.84

Since the square of 2.2 gives an approximate value of 5, thus we can estimate the square root of 5 is equal to 2.2 approximately.

How to Find Square Roots Without Calculator?

This is quite an interesting way to figure out the square root of a given number. The procedure is completely based on the method called “guess and check”. Guess your answer, and verify. Repeat the procedure until you have the desired accurate result. We can also use the long division method to find the square root of a number.

Square Root of Perfect squares

Below are the numbers which are perfect squares and then finding the square roots of such numbers is easy.

• 1 2 = 1  ⇔ √1 = 1
• 2 2 = 4  ⇔ √4 = 2
• 3 2 = 9  ⇔ √9 = 3
• 4 2 = 16  ⇔ √16 = 4
• 5 2 = 25  ⇔ √25 = 5
• 6 2 = 36  ⇔ √36 = 6
• 7 2 = 49  ⇔ √49 = 7
• 8 2 = 64  ⇔ √64 = 8
• 9 2 = 81  ⇔ √81 = 9
• 10 2 = 100  ⇔ √100 = 10

Hence, 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100 are the perfect squares here. Check square roots of some numbers here:

Square Root Table (1 to 50)

Here is the list of the square root of numbers from 1 to 50.

Square Root of Decimal

A decimal value will have a dot (.) such as 3.8, 5.2, 6.33, etc. For a whole number, we have understood how to derive the square root but let us see how to get the square root of a decimal.

Square Root of Negative Number

The square root of a negative number is not a real number but a complex number. It is because the square of any integer is a positive value. The square root of a negative number, say, -y,  is: √(-y)= i√y, where ‘i’ is the square root of -1.

Square root of Complex Numbers

To find the square root of complex numbers is a little complicated. We can find the square root of a+ib using the below formula:

\(\begin{array}{l}\sqrt{a+b i}=\pm(\sqrt{\frac{\sqrt{a^{2}+b^{2}+a}}{2}}+i \sqrt{\frac{\sqrt{a^{2}+b^{2}-a}}{2}})\end{array} \) where a+ib is a complex number.

How to Solve the Square Root Equation?

A square root equation is such an equation that has a variable in the radicand of the root. It is also called the radical equation.

To solve the radical equation, we need to follow the below steps:

• Isolate the square root to one of the sides (L.H.S or R.H.S). 
• Square both the sides of the given equation 
• Now solve the rest equation.

Let us understand the steps with examples.

Condition 1: If the equation has more than one radical or square root.

If the radical equation has more than one root then repeat the above given steps for each square root.

Squaring a Number

To find the square of a number, we need to multiply the number by itself.

For example, 2 multiplied by 2 is equal to 4

Below is a 2 by 2 table that shows, a total of four blocks.

Similarly, 

square of 5 is: 5 multiplied by 5 = 5 x 5 = 5 2 = 25

Square of 9 = 9 2 = 9 x 9 = 81

Square of 15 = 15 2 = 15 x 15 = 225

Applications of Square Roots

The square root formula is an important section of mathematics that deals with many practical applications of mathematics and it also has its applications in other fields such as computing. Some of the applications are:

• Quadratic equations

List of Square Roots of Numbers

Video lessons on square roots, visualising square roots.

Finding Square roots

Solved Examples on Square Roots

Let us understand this concept with the help of an example:

Example 1: Solve √10 to 2 decimal places.

Step 1:  Select any two perfect square roots that you feel your number may fall in between.

We know that 2 2 = 4; 3 2 = 9, 4 2 = 16 and 5 2 = 25

Now, choose 3 and 4 (as √ 10 lies between these two numbers)

Step 2: Divide the given number by one of those selected square roots.

Divide 10 by 3.

=> 10/3 = 3.33 (round off answer at 2 places)

Step 3: Find the average of root and the result from the above step i.e.

(3 + 3.33)/2 = 3.1667

Verify: 3.1667 x 3.1667 = 10.0279 (Not required)

Repeat step 2 and step 3

Now 10/3.1667 = 3.1579

Average of 3.1667 and 3.1579.

(3.1667+3.1579)/2 = 3.1623

Verify: 3.1623 x 3.1623 = 10.0001 (more accurate)

Stop the process.

Example 2 : Find the square roots of whole numbers which are perfect squares from 1 to 100.

Solution: The perfect squares from 1 to 100: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100

Example 3 : What is:

• The square root of 2
• The square root of 3
• The square root of 4
• The square root of 5

Solution : Use square root list, we have

• value of root 2 i.e. √2 = 1.4142
• value of root 3 i.e. √3 = 1.7321
• value of root 4 i.e. √4 = 2
• value of root 5 i.e. √5 = 2.2361

Example 4 : Is square Root of a Negative Number a whole number?

Solution : No, As per the square root definition, negative numbers shouldn’t have a square root. This is because if we

multiply two negative numbers, the result will always be a positive number.  Square roots of negative numbers expressed

as multiples of i (imaginary numbers).

Example 5: Solve the equation: √(x+2) = 4

Solution: Given,

Squaring both the sides, we get;

x = ±4 – 2

x = 2 or x = -6

Practice Questions on Square roots

• What is square root of 64?
• Simplify √142
• Find the square root of 250
• What is the square root of 10000?
• Find the value of √12.
• Are √155, √121 and √139 perfect squares?

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Watch CBS News

What caused the Dali to slam into Baltimore's Francis Scott Key Bridge? What we know about what led up to the collapse

By Kerry Breen

Updated on: March 27, 2024 / 7:43 PM EDT / CBS News

Shocking video showed the moment a massive cargo ship collided with Baltimore's Francis Scott Key Bridge early Tuesday morning, sending parts of the decades-old suspension bridge, along with people and vehicles, into the Patapsco River. 

Six people who were on the bridge are missing and presumed dead , officials said late Tuesday. Two others were rescued from the water. All eight were construction workers who were repairing potholes on the bridge, officials said. There were 22 Indian nationals, including two pilots, aboard the cargo ship. 

Investigators and officials are now crafting a timeline of events, including what caused the Singapore-owned vessel , called the Dali, to hit the bridge just minutes after leaving port . Here's what we know so far. 

What caused the Dali to slam into the Francis Scott Key Bridge? 

The Dali, which was chartered by shipping giant Maersk and operated by Synergy Marine Group, hit the Francis Scott Key Bridge shortly after leaving the Port of Baltimore. 

An unclassified memo issued by CISA, the Cybersecurity and Infrastructure Security Agency, said the ship reported losing propulsion . Maryland Gov. Wes Moore said the ship's crew reported a "power issue." A spokesperson for the National Transportation Safety Board, which is investigating the crash, said the agency still needs to verify that the Dali lost power before striking the bridge column. 

Two U.S. officials told CBS News multiple alarms rang out on the ship, alerting pilots and crew to an issue on board. The crew ran several system tests to attempt to remedy the loss of propulsion from the motor, but the tests proved unsuccessful. At that point, the ship's pilots alerted the Maryland Department of Transportation and the Maryland Transit Authority. 

That alert allowed local officials to stop traffic on the bridge and likely saved lives , officials said. 

The ship's crew tried to deploy the anchor, though it remains unclear how much progress was made, multiple officials said. The massive ship is over 900 feet long and was moving at about 8 knots, or just over 9 miles per hour. Authorities said that speed is considered "very rapid." 

Captain Michael Burns, executive director of the Massachusetts Maritime Academy's Maritime Center for Responsible Energy, told CBS Boston  that stopping a cargo ship is difficult, especially in such a short time. 

"It's extremely challenging, and takes years of experience and training in order to be able to do this safely," he said. "It can take up to a mile for some of these ships to get stopped, depending on the circumstances, so we really need to think well out, miles ahead of the ship."

Why did the Dali lose propulsion? 

It's not clear what caused the vessel to lose propulsion, officials said. 

A spokesperson for the NTSB told CBS Baltimore that it had collected the ship's data recorder, and would review and analyze the material there to determine what happened aboard the vessel in the moments before the collision. 

That data recorder will also be used to establish a timeline of events. 

What happens when a ship loses propulsion? 

James Mercante, the president of the New York Board of Pilot Commissioners, told CBS News that a ship that has lost steering and power is essentially "a dead ship just being carried by the current or its own momentum." 

He highlighted a moment in the video of the crash that appears to show a "big, big puff of black, real dark black smoke" which might indicate that the vessel's power was "restored at the last minute" and that the pilot was "attempting to make an emergency maneuver" to avoid hitting the bridge. However, he emphasized that it would be difficult to stop the massive cargo ship, especially in such a short time. 

"It would take quite a while — probably the length of five [or] six football fields — to bring that ship to a stop, even after dropping the anchors, because of its power and momentum," said Mercante. "This is a behemoth." 

• Francis Scott Key Bridge
• Bridge Collapse

Kerry Breen is a reporter and news editor at CBSNews.com. A graduate of New York University's Arthur L. Carter School of Journalism, she previously worked at NBC News' TODAY Digital. She covers current events, breaking news and issues including substance use.

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Watch: Authorities rescue injured dog stuck on railroad tracks for 3 days

• Cambridge Dictionary +Plus

Meaning of assign in English

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assign verb [T] ( CHOOSE )

• Every available officer will be assigned to the investigation .
• The textbooks were assigned by the course director .
• Part of the group were assigned to clear land mines .
• Each trainee is assigned a mentor who will help them learn more about the job .
• We were assigned an interpreter for the duration of our stay .
• accommodate
• accommodate someone with something
• administration
• arm someone with something
• hand something back
• hand something down
• hand something in
• hand something out
• re-equipment
• reassignment

You can also find related words, phrases, and synonyms in the topics:

assign verb [T] ( SEND )

• She was assigned to the Paris office .
• All the team were assigned to Poland.
• advertisement
• employment agency
• equality, diversity and inclusion
• reinstatement
• relocation expenses
• testimonial

assign verb [T] ( COMPUTING )

• 3-D printing
• adaptive learning
• additive manufacturing
• hexadecimal
• hill climbing
• telerobotics
• word processing

assign verb [T] ( GIVE LEGALLY )

Phrasal verb, assign | american dictionary, assign | business english, examples of assign, translations of assign.

Get a quick, free translation!

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• Methodology
• Open access
• Published: 01 April 2024

A system for the study of roots 3D kinematics in hydroponic culture: a study on the oscillatory features of root tip

• Valentina Simonetti 1 ,
• Laura Ravazzolo 2 ,
• Benedetto Ruperti 2 ,
• Silvia Quaggiotti 2 &
• Umberto Castiello 1  

Plant Methods volume  20 , Article number:  50 ( 2024 ) Cite this article

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The root of a plant is a fundamental organ for the multisensory perception of the environment. Investigating root growth dynamics as a mean of their interaction with the environment is of key importance for improving knowledge in plant behaviour, plant biology and agriculture. To date, it is difficult to study roots movements from a dynamic perspective given that available technologies for root imaging focus mostly on static characterizations, lacking temporal and three-dimensional (3D) spatial information. This paper describes a new system based on time-lapse for the 3D reconstruction and analysis of roots growing in hydroponics.

The system is based on infrared stereo-cameras acquiring time-lapse images of the roots for 3D reconstruction. The acquisition protocol guarantees the root growth in complete dark while the upper part of the plant grows in normal light conditions. The system extracts the 3D trajectory of the root tip and a set of descriptive features in both the temporal and frequency domains. The system has been used on Zea mays L. (B73) during the first week of growth and shows good inter-reliability between operators with an Intra Class Correlation Coefficient (ICC) > 0.9 for all features extracted. It also showed measurement accuracy with a median difference of < 1 mm between computed and manually measured root length.

Conclusions

The system and the protocol presented in this study enable accurate 3D analysis of primary root growth in hydroponics. It can serve as a valuable tool for analysing real-time root responses to environmental stimuli thus improving knowledge on the processes contributing to roots physiological and phenotypic plasticity.

Plants are able to sense environmental changes and accomplish adequate problem-solving physiological and developmental responses [ 1 , 2 , 3 , 4 , 5 ]. The root is the plant organ devoted to water and nutrients uptake, meanwhile providing anchorage to the plant [ 6 ]. The root apex is involved in the perception of many environmental stimuli [ 7 ], such as gravity [ 8 , 9 ], light [ 10 , 11 ], electric fields [ 12 ], moisture gradient [ 13 , 14 ] and nitrate [ 15 , 16 , 17 , 18 ]. Further, it has been hypothesized that the root apex exhibits computational features related to sensory integration [ 2 , 19 ].

Investigating root growth dynamics as a mean of their interaction with the environment is of key importance for improving knowledge in plant behaviour, biology and agriculture. Roots movements represent an instance of active behaviour [ 20 ] calling for an effective kinematical investigation of the circumnutating movement of primary roots, a key component of exploratory behaviour and substrate penetration [ 6 , 21 , 22 , 23 , 24 , 25 , 26 , 27 ]. What is needed is the implementation of specific and repeatable protocols for in vivo measurements on a short time scale enabling the investigation of how plants cope with frequent and unexpected environmental changes that drive readjustments of root growth and development [ 7 ].

A variety of studies underline the importance of implementing tools for high throughput analysis of roots features [ 28 , 29 ]. To date, it is difficult to study roots movements from a dynamic point of view given that available technologies for root imaging focus mostly on static characterizations, lacking temporal and three-dimensional (3D) spatial information.

Root features are usually evaluated only at the time the root system is extracted from the soil (e.g., Liu et al. [ 30 ]) or without considering repeated imaging of the roots as for tomography scans (e.g., Zeng et al. [ 31 ]). Time-lapse techniques, able to capture dynamical changes in root growth, may help to a better characterization of roots movements but, to date, they are chiefly based on two-dimensional (2D) approaches [ 32 ]. Tomography scans and Magnetic Resonance Imaging (MRI) have been used recently in studies involving repeated imaging and 3D time-lapse reconstruction: an example for tomographic scans is described in the study by Keyes et al. [ 33 ] while an example for MRI is the work by Popova et al. [ 34 ]. These technologies, however, face limitations related to imaging sampling rate which can take from few minutes to hours. Additionally, the acquisition setup typically involves the movement of the plant inside the scanner, constrained by specific dimensions and limited field of view. Despite these aspects, tomography scans and MRI remain a valuable choice for conducting in vivo measurements for appropriate experimental setups. Another method for achieving 3D time-lapse reconstruction is described in the work by Clark et al. [ 35 ]. In this study, the authors set up a system based on a custom rotating mechatronic platform that captures images of the roots from different angles enabling in this way 3D reconstruction. However, the system may result difficult to use and to adapt to different experimental configurations. Light-sheet microscopy for root imaging [ 36 ] has not been considered here because of its small field of view (from tens of micrometres to few millimetres) but it might be a valuable choice to achieve 3D imaging of root when a smaller field of view is acceptable.

In the present paper, we describe a fairly simple and affordable system with high time resolution that enables the 3D reconstruction and analysis of roots growing in hydroponics. Hydroponics is frequently used in studies requiring the control of nutrients and allow accessibility to the root system, since it is appropriate for cultivation of the plants throughout their entire life cycle and allows to perform independent experiments in reproducible root-environment conditions [ 37 ].

Materials and methods

Experimental set up.

We developed a system enabling effective dynamic 3D imaging of maize root tip in hydroponic culture, which could be adapted to any configuration using transparent substrates (e.g. agar). The system is based on a pair of infrared stereo-cameras (RGB-IR stereo cameras: IP 2.1 Mpx outdoor varifocal IR 1080 P.) to acquire time-lapse images of the roots [ 38 ]. Acquired stereo images are then used for 3D reconstruction compensating for water distortion. The cameras are kept inside a box to maintain the roots in complete dark while the upper part of the plant grows in normal light conditions. The system has been tested on 19 Zea mays L. (B73) seedlings. Seeds were germinated on filter paper with the same seed orientation with the extremity where the root emerges facing down and they were kept in the dark at a constant temperature of 25 °C. 4-days-old seedlings were measured positioning the seedling on a horizontal surface and measuring the root from the lower tip of the seed to the root tip. Seedlings with a root length of approx. 3–4 cm were selected and placed in an acrylic glass container filled with a nutrient solution (modified Hoagland nutrient solution [ 39 ]) with a day/night cycle of 14/10 h. To stabilize the seedling, the seed was placed in a 1 cm thick foam rubber support with the root inside the solution and the upper part outside. To maximize the gas exchange with the atmosphere, four symmetrical holes of 7 mm diameter have been made in the foam rubber support. Measurements started right after the placement. Images for each plant were acquired for 7 days. The primary root of each plant was manually measured at the beginning and at the end of the acquisition using a measurement tape and placing the plant on a horizontal surface. Figure  1 shows the system configuration and the materials used.

System configuration and materials. Top panel: system configuration allowing for root imaging acquisition in complete dark for the entire time of the experiment. The root grows in a transparent acrylic glass container filled with nutrient solution while a pair of stereo cameras take a picture every 3 min. Both the acrylic glass container and the stereo cameras are placed inside a box that guarantees that roots grow in a complete dark condition. The whole system is placed inside a growing chamber in controlled condition of light with a day/night cycle of 14/10. Bottom panel: components of the system. ( a ) Containing box: cardboard box 60cmX40cmX40cm. ( b ) Acrylic glass water container (PLEXX, Piazzola sul Brenta PD): acrylic glass container 10cmX10cmX30cm filled with nutrient solution (modified Hoagland nutrient solution [ 39 ], all chemicals were purchased from Sigma Chemicals (Sigma, St Louis, MO, USA) unless otherwise stated). ( c ) Foam rubber: punched foam rubber rectangle (11cmX11cmX1,5 cm) used to host and stabilize the seed. ( d ) RGB-IR stereo cameras: IP 2.1 Mpx outdoor varifocal IR 1080 P. Each camera is wired with Ethernet cables to a router. ( e ) Router: D-link Dsr-250n connected via Wi-Fi to a PC. ( f ) Maize: Zea mays L. (B73)

Protocol for calibration, images acquisition and 3D trajectory extraction

The protocol implemented to obtain 3D root tip trajectories from time-lapses of the stereo-cameras consisted of the following steps:

System calibration - Each camera was calibrated to estimate its intrinsic and extrinsic parameters. This process was performed only once for each camera and the calibration pattern used was a 10 × 7 chessboard with square size of 8 mm printed on a Forex® plate. The second step was the stereo-cameras system calibration to extract relative position between the two cameras. This step was performed only once (because the relative position between the two cameras does not change in the design setup) using the same calibration pattern. The stereo-cameras system must also handle the distortion introduced by water due to refraction and the impossibility of using the pinhole camera model for calibration. We used starting assumptions as in Dolerait et al. [ 40 ] assuming that, in stereovision calibrated systems acquiring underwater objects, the virtual object point is always located above the real object point on the perpendicular of the flat refractive interface, meaning that the distortion effect is on the z (depth) axis. We implemented a water calibration process that used the same chessboard calibration pattern used for the previous calibration steps. The calibration pattern was positioned in the water container rotated around the vertical axis, tilted around 30° on the z axis and it was acquired by the stereo-cameras system. Reconstructed calibration pattern showed the effect of water distortion on the z axis. Computing the difference between the expected size of the calibration pattern and its reconstructed size on the z axis we extracted the linear approximation of water distortion. Applying the resulting linear function for water distortion compensation to the reconstructed points we obtained corrected 3D points coordinates.

Time-lapse acquisition – Each camera acquired an image with a time interval of 3 min. Studies adopting a similar approach on root imaging report a chosen time interval between 2 and 4 min [ 32 , 41 ]. Popova et al. [ 41 ] reports circumnutation periods for maize root tip that range between 30 and 120 min, so our choice for a 3 min interval between pictures guarantees that these movements are captured. The system supports also lower time intervals (up to few seconds) that may be used for other experiments exploring faster root tip movements. A C + + script handled the images acquisition from the cameras: it implemented a time counter set to the specified time interval and, when the counter reached the threshold value, it accessed the IP of the camera which was connected to the local network through a router (using the same approach as in Simonetti et al. [ 38 ]). This process guaranteed the synchronization of the two cameras acquisitions. Possible time shift between cameras acquisition due to network connection and threads execution are less than 1 s.

Video processing – Acquired time-lapses were processed using SPROUTS software (Ab.Acus srl Milan, Italy; [ 35 ]). The software is a standalone desktop application that allows to select and perform semi-automatic tracking of specific key points in the video. The outcome of this step is the extraction of 2D trajectories from the time-lapses of both the left and the right camera.

3D trajectory extraction – 3D trajectory of the selected points was extracted triangulating the 2D trajectories extracted from the left and right camera. The process was implemented in a Python script using OpenCV library. First, the script computed the projection matrices by multiplying the camera matrix by the rotation and translation matrix obtained during the calibration step. The projection matrices were then used to triangulate the 2D trajectories implementing a direct linear transformation. Finally, the 3D points obtained were compensated for water distortion using the linear function for water distortion compensation extracted in step 1.

All the protocol steps are summarized in Fig.  2 . Figure  3 shows examples of 3D trajectory reconstruction.

Acquisition and processing protocols used to extract the 3D trajectory of root growth for each plant. The first step of system calibration is performed only once and consists of a standard single camera calibration for lens distortion using a chessboard pattern followed by stereo cameras calibration for extrinsic parameters extraction (to enable stereo vision 3D reconstruction). The system calibration includes the calibration for the distortion introduced by water. Water distortion calibration is performed using the chessboard pattern to model (linear modelling) the distortion introduced in the depth component. The time-lapse acquisition step consists of a simultaneous acquisition of pictures by the two cameras every 3 min. The obtained time-lapse video is processed in the video processing step using a semi-automatic tracking software [ 38 ]. The 2D trajectories obtained by each camera are then triangulated using the calibration parameters to extract the 3D trajectory of the root growth

Outcomes of the root tip 3D trajectory reconstruction. ( a ) Example of trajectory reconstruction for 6 days acquisition on the xy plane. ( b ) Zoom on part of the 3D trajectory of the same root as in point ( a ) focusing on the circumnutation movement reconstruction

Features extraction

The system extracts the 3D trajectory of the root tip and a set of descriptive features.

Extracted features are 3D versions of 2D features found in available literature [ 25 , 41 , 42 , 43 ]:

Preliminary processing – root growth main component extraction

3D root tip trajectory was pre-processed to enable the calculation of other features. The pre-processing step computes the main component of root growth to correctly handle and differentiate it from the oscillatory movements performed by the root tip. The main component of root growth was computed performing a moving average on the 3D trajectory coordinates with a centered window of N samples, where N was equal to the number of samples acquired in 4 h. The 4 h time window should guarantee that the root main component of growth extracted is not affected by the circumnutation movements (considering circumnutation periods in the range 30–120 min as reported by Popova et al. [ 41 ] while taking into accont the drifts of the root that are slower than 120 min). In our case, with an acquisition period of 3 min, we applied a 80-samples moving average. An example of the extraction of the root main component of growth is shown in Fig.  4 where the root tip trajectory extracted from the triangulation process is plotted in black while the root main component of growth is plotted in red. In the figure, the oscillatory movements of the root tip are clearly visible.

Example of the root main component of growth. Root trajectory as extracted from the triangulation step are represented in black while the root main component of growth is represented in red

Overall primary root length

The overall primary root length was computed as the discrete sum of the 3D euclidean distances between samples of the root main component of growth:

N = number of samples along the root main component of growth.

p = sample of the root main component of growth.

Primary root growth rate

Root growth rate is computed both as absolute and relative root growth rate. Absolute growth rate is calculated as the discrete sum of the 3D euclidean distances between samples of the root main component of growth in a specified time interval. Relative growth rate is calculated as the discrete sum of the 3D euclidean distances between samples of the root main component of growth in a specified time interval divided by the root main component of growth length at the end of the specified time interval.

a = First sample of the selected time interval.

d = Number of samples for the selected time interval.

p = Sample of the root main component of growth.

In our case, both absolute and relative growth rate were calculated over 1-day time intervals along the whole acquisition time. In this way we obtained growth rate arrays where each element of the array represented the growth rate value for the specific day.

Average tip velocity

Average tip velocity was calculated as the average distance travelled by the root tip per hour. First we computed the hourly tip velocity every N minutes of the whole movement (in our case every 15 min), then we computed the average for all the values obtained.

Maximum nutation amplitude

To compute the maximum nutation amplitude we first computed the array of euclidean distances on the XY plane between each sample on the root tip trajectory and the root main component of growth, then the maximum nutation amplitude was calculated as the maximum value of the array.

Frequency spectrum and main period of nutation

First we computed the array of euclidean distances on the XY plane between each sample on the root tip trajectory and the root main component of growth to obtain a time series like the one shown in Fig.  5 a. The time series obtained was then used to calculate its Discrete Fourier Transform (DFT) by means of the Fast Fourier Transform (FFT) algoritm. The main period of nutation was computed as the period corresponding to the frequency in the power spectrum obtined with the FFT where the maximum amplitude value was detected (as shown in Fig.  5 b).

Time series of the distance of the root tip from the root main component of growth obtained computing the euclidean distance between the trajectory and the main root component of growth on the xy plane along time. Root main component of growth is computed applying a 3D moving average on the trajectory with 80 samples window. Red line represents the light/dark cycle (day = 1, night = 0). ( b ) Frequency spectrum of the signal shown in ( a ) obtained computing the one-dimensional Discrete Fast Fourier Transform using Python Numpy package. Red arrow shows the frequency with highest amplitude in the spectrum, corresponding, in this case, to a period of around 1 h

Results and discussion

The system showed good inter-reliability between operators with an Intra Class Correlation Coefficient (ICC) > 0.9 for all features extracted. ICC was computed comparing the results obtained from 2 different operators on 4 plants (see Table  1 ). The ICC has been computed using the absolute agreement of the two-way random effect model following [ 44 ].

The system showed good measurement accuracy: comparing manual measurement of the overall primary root length acquired at the end of the experiment versus the overall primary root length computed by the system, we obtained an absolute mean difference of 0.54, an absolute median difference of 0.68 mm and a distribution of values that is below an absolute value of 5 mm within the 25th and the 75th percentile (see boxplot in Fig.  6 a). The average root length measured at the end of the experiment was 20.2 cm, so the estimated mean error is 2.7% of the overall root length.

Figure  6 shows the boxplots for the distributions of the features calculated. Values obtained are in line with expected values when considering similar experiments on maize [ 26 , 41 , 43 ].

( a ) Boxplot of the distribution of the difference (in mm) between overall root length value measured manually at the end of the experiment and overall root length value as computed by the system. Red line represents the median value. ( b ) Boxplots of the distributions of daily growth rates (%) for each of the first 6 days of the experiment. Red line represent the median values. ( c ) Boxplot of the distribution of average relative growth rate (%/day). Red line represents the median value. ( d ) Boxplot of the distribution of maximum circumnutation amplitude values computed as maximum distance from the root main component of growth. Red line represents the median value. ( e ) Boxplot of the distribution of average tip velocity (mm/h). Red line represents the median value

We extracted the frequency spectrum of root tip movements for all the plants as described in section “Materials and methods – Features extraction”. Analysing the frequency spectra for different plants, we identified a similar frequency amplitude distribution across plants, with two main peaks (see examples of spectra in Fig.  7 ). To quantitatively evaluate this trend on the whole population, we performed a frequency-based average of all power spectra extracted from all the acquired plants. For each frequency value we performed the average of the spectrum amplitude corresponding to that frequency for all the plants obtaining an average spectrum. The resulting average spectrum is shown in Fig.  8 . The average spectrum clearly showed 2 peaks in the frequency amplitude. The first peak corresponded to a frequency of 0.000062 Hz and a time period of 4.5 h, while the second peak corresponded to a frequency of 0.00027 Hz and a time period of 1.02 h. The value obtained for the second peak, which was around 60 min period, is perfectly in line with the findings of Popova et al. [ 41 ] where they obtained that, in the majority of cases, circumnutations show 40–80 min periods.

Frequency spectra for 6 sample plants. In grey, the raw data, while in black the spectrum after an 8-samples moving average

Average frequency spectrum obtained as the average of all the spectra extracted for each plant acquired. In grey, the raw data, while in black the spectrum after an 8-samples moving average

The system and protocol presented in this study enable accurate 3D analysis of primary root growth in hydroponic culture. Comparing the overall root length computed by the system and the manually measured root length we obtained a median difference which is less than 1 mm. The approach is easy to adopt and has the potential to become a standard for time-dependent 3D root imaging. The system has been used on maize roots to investigate their kinematic and oscillatory features during the first 7 days of growth. It resulted reliable across operators (with ICC values > 0.9 for all the features extracted as shown in Table  1 ) and accurate in the values obtained. Statistics extracted from the maize plants analysed showed a clear oscillatory content in the root tip movement that is the combination of two main periodic signals, one with a period of around 4 h and a second one with a period of around 1 h. In the future it would be interesting to analyse the variation of the frequency spectrum along the time of the experiment, applying, for example, a wavelet analysis approach.

Our system may become a useful tool to analyse real-time motor root responses to environmental stimuli, thus improving knowledge on processes contributing to roots physiological and phenotypic plasticity.

Data availability

Data describing 3D trajectories used in this paper are available here: https://zenodo.org/record/8422242 . Software and scripts are available for research purposes upon request through the email address: [email protected].

Abbreviations

Two dimensional

Three dimensional

Discrete Fourier Transform

Fast Fourier Transform

Intra Class Correlation Coefficient

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Acknowledgements

We thank G. Simonetti for the support in the tracking process and S. Massaccesi for the technical support in setting up the system. We also thank S. Guerra and B. Bonato for the help given in controlling the acquisitions.

Funded by the European Union (ERC, ROOMors, Grant Number 101096728) to U.C. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them. This work was also funded by a MUR grant (prot. n. 20227ZYLH9) to U.C. and grant prot. BIRD211752- 2021 to L.R. and a grant DOR 2022-23 to S.Q.

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All authors contributed to the design of the research. V.S. and L.R. built the experimental setup. V.S. worked on the technical aspects. L.R., S.Q. and B.R. studied the physiological aspects related to root growth in hydroponic. U.C and V.S. evaluated the behavioural aspects of the study and its implications. V.S. implemented the software and performed the data analysis. All authors discussed the results reviewed and edited the manuscript and contributed to the revision of the final manuscript.

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Simonetti, V., Ravazzolo, L., Ruperti, B. et al. A system for the study of roots 3D kinematics in hydroponic culture: a study on the oscillatory features of root tip. Plant Methods 20 , 50 (2024). https://doi.org/10.1186/s13007-024-01178-3

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DOI : https://doi.org/10.1186/s13007-024-01178-3

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Brogdon will lose his spot on Philadelphia's 40-man roster one day after surrendering four runs (three earned) over just two-thirds of an inning Monday against the Reds. The 29-year-old righty holds a 3.88 ERA and 1.26 WHIP in his MLB career and may attract interest from other teams in need of bullpen depth. Ricardo Pinto was selected from Triple-A Lehigh Valley in a corresponding move.

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Phillies' connor brogdon: optioned to triple-a, phillies' connor brogdon: opening monday's game, phillies' connor brogdon: picks up second save, phillies' connor brogdon: notches first save of 2022, phillies' connor brogdon: reinstated from covid list, our latest fantasy baseball stories.

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