Difference between revisions of "AMS Student Chapter Seminar"

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The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.
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The AMS Student Chapter Seminar (aka Donut Seminar) is an informal, graduate student seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.
  
* '''When:''' Wednesdays, 3:00 PM – 3:30 PM
+
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM
* '''Where:''' Van Vleck, 9th floor lounge
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* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)
* '''Organizers:''' Laura Cladek, Ryan Julian, Xianghong Chen, Daniel Hast
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* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu], Carrie Chen
  
Everyone is welcome to give a talk. To sign up, please contact the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.
+
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 25 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.
  
==Spring 2015==
+
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].
  
===January 28, Moisés Herradón===
+
== Spring 2020 ==
  
Title: Winning games and taking names
+
=== February 5, Alex Mine===
  
Abstract: So let’s say we’re already amazing at playing one game (any game!) at a time and we now we need to play several games at once, to keep it challenging. We will see that doing this results in us being able to define an addition on the collection of all games, and that it actually turns this collection into a Group. I will talk about some of the wonders that lie within the group. Maybe lions? Maybe a field containing both the real numbers and the ordinals? For sure it has to be one of these two!
+
Title: Khinchin's Constant
  
===February 11, Becky Eastham===
+
Abstract: I'll talk about a really weird fact about continued fractions.
  
Title: A generalization of van der Waerden numbers: (a, b) triples and (a_1, a_2, ..., a_n) (n + 1)-tuples
+
=== February 12, Xiao Shen===
  
Abstract: Van der Waerden defined w(k; r) to be the least positive integer such that for every r-coloring of the integers from 1 to w(k; r), there is a monochromatic arithmetic progression of length k.  He proved that w(k; r) exists for all positive k, r.  I will discuss the case where r = 2.  These numbers are notoriously hard to calculate: the first 6 of these are 1, 3, 9, 35, 178, and 1132, but no others are known.  I will discuss properties of a generalization of these numbers, (a_1, a_2, ..., a_n) (n + 1)-tuples, which are sets of the form {d, a_1x + d, a_2x + 2d, ..., a_nx + nd}, for d, x positive natural numbers.
+
Title: Coalescence estimates for the corner growth model with exponential weights
  
===February 18, Solly Parenti===
+
Abstract: (Joint with Timo Seppalainen) I will talk about estimates for the coalescence time of semi-infinite directed geodesics in the planar corner growth model. Not much probability background is needed.
  
Title: Chebyshev's Bias
+
=== February 19, Hyun Jong Kim===
  
Abstract: Euclid told us that there are infinitely many primes.  Dirichlet answered the question of how primes are distributed among residue classes.  This talk addresses the question of "Ya, but really, how are the primes distributed among residue classes?"  Chebyshev noted in 1853 that there seems to be more primes congruent to 3 mod 4 than their are primes congruent to 1 mod 4.  It turns out, he was right, wrong, and everything in between.  No analytic number theory is presumed for this talk, as none is known by the speaker.
+
Title: Orbifolds for Music
  
===February 25, DJ Bruce===
+
Abstract: In the first-ever music theory article published by the journal ''Science'', Dmitri Tymoczko uses orbifolds to describe a general framework for thinking about musical tonality. I am going to introduce the musical terms and ideas needed to describe how such orbifolds arise so that we can see an example of Tymoczko's geometric analysis of chord progressions.
  
Title: TBA
+
=== February 26, Solly Parenti===
  
Abstract: TBA
+
Title: Mathematical Measuring
  
==Fall 2014==
+
Abstract: What's the best way to measure things? Come find out!
  
===September 25, Vladimir Sotirov===
+
=== March 4, ===
  
Title: [[Media:Compact-openTalk.pdf|The compact open topology: what is it really?]]
+
Title: TBD
  
Abstract: The compact-open topology on the space C(X,Y) of continuous functions from X to Y is mysteriously generated by declaring that for each compact subset K of X and each open subset V of Y, the continous functions f: X->Y conducting K inside V constitute an open set. In this talk, I will explain the universal property that uniquely determines the compact-open topology, and sketch a pretty constellation of little-known but elementary facts from domain theory that dispell the mystery of the compact-open topology's definition.
+
Abstract: TBD
  
===October 8, David Bruce===
+
=== March 11, Ivan Aidun===
  
Title: Hex on the Beach
+
Title: The Notorious CRT
  
Abstract: The game of Hex is a two player game played on a hexagonal grid attributed in part to John Nash. (This is the game he is playing in /A Beautiful Mind./) Despite being relatively easy to pick up, and pretty hard to master, this game has surprising connections to some interesting mathematics. This talk will introduce the game of Hex, and then explore some of these connections. *As it is a lot more fun once you've actually played Hex feel free to join me at 3:00pm on the 9th floor to actually play a few games of Hex!*
+
Abstract: You're walking up Bascomb hill when a troll suddenly appears and says he'll kill you unless you compute the determinant of
 +
:<math> \begin{bmatrix}0 & -7 & -17 & -5 & -13\\8 & -14 & 14 & 11 & 15\\-5 & -17 & 10 & 2 & 10\\17 & 3 & -16 & -13 & 7\\-1 & 2 & -13 & -11 & 10\end{bmatrix}</math>
 +
by hand. wdyd?
  
===October 22, Eva Elduque===
+
=== March 24 - Visit Day===
  
Title: The fold and one cut problem
+
==== Brandon Boggess, Time TBD====
  
Abstract: What shapes can we get by folding flat a piece of paper and making (only) one complete straight cut? The answer is surprising: We can cut out any shape drawn with straight line segments. In the talk, we will discuss the two methods of approaching this problem, focusing on the straight skeleton method, the most intuitive of the two.
+
Title: TBD
  
===November 5, Megan Maguire===
+
Abstract: TBD
  
Title: Train tracks on surfaces
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==== Yandi Wu, Time TBD====
  
Abstract: What is a train track, mathematically speaking? Are they interesting? Why are they interesting? Come find out!
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Title: TBD
  
===November 19, Adrian Tovar-Lopez===
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Abstract: TBD
  
Title:  Hodgkin and Huxley equations of a single neuron
+
==== Maya Banks, Time TBD====
  
===December 3, Zachary Charles===
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Title: TBD
  
Abstract: An addition chain is a sequence of numbers starting at one, such that every number is the sum of two previous numbers. What is the shortest chain ending at a number n? While this is already difficult, we will talk about how addition chains answer life's difficult questions, including: How do we compute 2^4? What can the Ancient Egyptians teach us about elliptic curve cryptography? What about subtraction?
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Abstract: TBD
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==== TBD, Time TBD====
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Title: TBD
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==== TBD, Time TBD====
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==== TBD, Time TBD====
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Title: TBD
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==== TBD, Time TBD====
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Title: TBD
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Abstract: TBD
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==== TBD, Time TBD====
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Title: TBD
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Abstract: TBD
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==== TBD, Time TBD====
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Title: TBD
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Abstract: TBD
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=== April 1, Ying Li===
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 +
Title: TBD
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 +
Abstract: TBD
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=== April 8, TBD===
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 +
Title: TBD
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Abstract: TBD
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=== April 15, Owen Goff===
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 +
Title: TBD
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Abstract: TBD
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=== April 22, TBD===
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Title: TBD
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Abstract: TBD
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== Fall 2019 ==
 +
 
 +
=== October 9, Brandon Boggess===
 +
 
 +
Title: An Application of Elliptic Curves to the Theory of Internet Memes
 +
 
 +
Abstract: Solve polynomial equations with this one weird trick! Math teachers hate him!!!
 +
 
 +
[[File:Thumbnail fruit meme.png]]
 +
 
 +
=== October 16, Jiaxin Jin===
 +
 
 +
Title: Persistence and global stability for biochemical reaction-diffusion systems
 +
 
 +
Abstract: The investigation of the dynamics of solutions of nonlinear reaction-diffusion PDE systems generated by biochemical networks is a great challenge; in general, even the existence of classical solutions is difficult to establish. On the other hand, these kinds of problems appear very often in biological applications, e.g., when trying to understand the role of spatial inhomogeneities in living cells. We discuss the persistence and global stability properties of special classes of such systems, under additional assumptions such as: low number of species, complex balance or weak reversibility.
 +
 
 +
=== October 23, Erika Pirnes===
 +
 
 +
(special edition: carrot seminar)
 +
 
 +
Title: Why do ice hockey players fall in love with mathematicians? (Behavior of certain number string sequences)
 +
 
 +
Abstract: Starting with some string of digits 0-9, add the adjacent numbers pairwise to obtain a new string. Whenever the sum is 10 or greater, separate its digits. For example, 26621 would become 81283 and then 931011. Repeating this process with different inputs gives varying behavior. In some cases the process terminates (becomes a single digit), or ends up in a loop, like 999, 1818, 999... The length of the strings can also start growing very fast. I'll discuss some data and conjectures about classifying the behavior.
 +
 
 +
=== October 30, Yunbai Cao===
 +
 
 +
Title: Kinetic theory in bounded domains
 +
 
 +
Abstract: In 1900, David Hilbert outlined 23 important problems in the International Congress of Mathematics. One of them is the Hilbert's sixth problem which asks the mathematical linkage between the mechanics from microscopic view and the macroscopic view. A relative new mesoscopic point of view at that time which is "kinetic theory" was highlighted by Hilbert as the bridge to link the two. In this talk, I will talk about the history and basic elements of kinetic theory and Boltzmann equation, and the role boundary plays for such a system, as well as briefly mention some recent progress.
 +
 
 +
=== November 6, Tung Nguyen===
 +
 
 +
Title: Introduction to Chemical Reaction Network
 +
 
 +
Abstract: Reaction network models are often used to investigate the dynamics of different species from various branches of chemistry, biology and ecology. The study of reaction network has grown significantly and involves a wide range of mathematics and applications. In this talk, I aim to show a big picture of what is happening in reaction network theory. I will first introduce the basic dynamical models for reaction network: the deterministic and stochastic models. Then, I will mention some big questions of interest, and the mathematical tools that are used by people in the field. Finally, I will make connection between reaction network and other branches of mathematics such as PDE, control theory, and random graph theory.
 +
 
 +
=== November 13, Jane Davis===
 +
 
 +
Title: Brownian Minions
 +
 
 +
Abstract: Having lots of small minions help you perform a task is often very effective. For example, if you need to grade a large stack of calculus problems, it is effective to have several TAs grade parts of the pile for you. We'll talk about how we can use random motions as minions to help us perform mathematical tasks. Typically, this mathematical task would be optimization, but we'll reframe a little bit and focus on art and beauty instead. We'll also try to talk about the so-called "storytelling metric," which is relevant here. There will be pictures and animations! 🎉
 +
 
 +
Sneak preview: some modern art generated with MATLAB.
 +
 
 +
[[File:Picpic.jpg]]
 +
 
 +
=== November 20, Colin Crowley===
 +
 
 +
Title: Matroid Bingo
 +
 
 +
Abstract: Matroids are combinatorial objects that generalize graphs and matrices. The famous combinatorialist Gian Carlo Rota once said that "anyone who has worked with matroids has come away with the conviction that matroids are one of the richest and most useful ideas of our day." Although his day was in the 60s and 70s, matroids remain an active area of current research with connections to areas such as algebraic geometry, tropical geometry, and parts of computer science. Since this is a doughnut talk, I will introduce matroids in a cute way that involves playing bingo, and then I'll show you some cool examples.
 +
 
 +
=== December 4, Xiaocheng Li===
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 +
Title: The method of stationary phase and Duistermaat-Heckman formula
 +
 
 +
Abstract: The oscillatory integral $\int_X e^{itf(x)}\mu=:I(t), t\in \mathbb{R}$ is a fundamental object in analysis. In general, $I(t)$ seldom has an explicit expression as Fourier transform is usually inexplicit. In practice, we are interested in the asymptotic behavior of $I(t)$, that is, for $|t|$ very large. A classical tool of getting an approximation is the method of stationary phase which gives the leading term of $I(t)$. Furthermore, there are rare instances for which the approximation coincides with the exact value of $I(t)$. One example is the Duistermaat-Heckman formula in which the Hamiltonian action and the momentum map are addressed. In the talk, I will start with basic facts in Fourier analysis, then discuss the method of stationary phase and the Duistermaat-Heckman formula.
 +
 
 +
=== December 11, Chaojie Yuan===
 +
 
 +
Title: Coupling and its application in stochastic chemical reaction network
 +
 
 +
Abstract: Stochastic models for chemical reaction networks have become increasingly popular in the past few decades. When the molecules are present in low numbers, the chemical system always displays randomness in their dynamics, and the randomness cannot be ignored as it can have a significant effect on the overall properties of the dynamics. In this talk, I will introduce the stochastic models utilized in the context of biological interaction network. Then I will discuss coupling in this context, and illustrate through examples how coupling methods can be utilized for numerical simulations. Specifically, I will introduce two biological models, which attempts to address the behavior of interesting real-world phenomenon.

Revision as of 22:19, 25 February 2020

The AMS Student Chapter Seminar (aka Donut Seminar) is an informal, graduate student seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.

Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 25 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.

The schedule of talks from past semesters can be found here.

Spring 2020

February 5, Alex Mine

Title: Khinchin's Constant

Abstract: I'll talk about a really weird fact about continued fractions.

February 12, Xiao Shen

Title: Coalescence estimates for the corner growth model with exponential weights

Abstract: (Joint with Timo Seppalainen) I will talk about estimates for the coalescence time of semi-infinite directed geodesics in the planar corner growth model. Not much probability background is needed.

February 19, Hyun Jong Kim

Title: Orbifolds for Music

Abstract: In the first-ever music theory article published by the journal Science, Dmitri Tymoczko uses orbifolds to describe a general framework for thinking about musical tonality. I am going to introduce the musical terms and ideas needed to describe how such orbifolds arise so that we can see an example of Tymoczko's geometric analysis of chord progressions.

February 26, Solly Parenti

Title: Mathematical Measuring

Abstract: What's the best way to measure things? Come find out!

March 4,

Title: TBD

Abstract: TBD

March 11, Ivan Aidun

Title: The Notorious CRT

Abstract: You're walking up Bascomb hill when a troll suddenly appears and says he'll kill you unless you compute the determinant of

[math] \begin{bmatrix}0 & -7 & -17 & -5 & -13\\8 & -14 & 14 & 11 & 15\\-5 & -17 & 10 & 2 & 10\\17 & 3 & -16 & -13 & 7\\-1 & 2 & -13 & -11 & 10\end{bmatrix}[/math]

by hand. wdyd?

March 24 - Visit Day

Brandon Boggess, Time TBD

Title: TBD

Abstract: TBD

Yandi Wu, Time TBD

Title: TBD

Abstract: TBD

Maya Banks, Time TBD

Title: TBD

Abstract: TBD

TBD, Time TBD

Title: TBD

Abstract: TBD

TBD, Time TBD

Title: TBD

Abstract: TBD

TBD, Time TBD

Title: TBD

Abstract: TBD

TBD, Time TBD

Title: TBD

Abstract: TBD

TBD, Time TBD

Title: TBD

Abstract: TBD

TBD, Time TBD

Title: TBD

Abstract: TBD

April 1, Ying Li

Title: TBD

Abstract: TBD

April 8, TBD

Title: TBD

Abstract: TBD

April 15, Owen Goff

Title: TBD

Abstract: TBD

April 22, TBD

Title: TBD

Abstract: TBD

Fall 2019

October 9, Brandon Boggess

Title: An Application of Elliptic Curves to the Theory of Internet Memes

Abstract: Solve polynomial equations with this one weird trick! Math teachers hate him!!!

Thumbnail fruit meme.png

October 16, Jiaxin Jin

Title: Persistence and global stability for biochemical reaction-diffusion systems

Abstract: The investigation of the dynamics of solutions of nonlinear reaction-diffusion PDE systems generated by biochemical networks is a great challenge; in general, even the existence of classical solutions is difficult to establish. On the other hand, these kinds of problems appear very often in biological applications, e.g., when trying to understand the role of spatial inhomogeneities in living cells. We discuss the persistence and global stability properties of special classes of such systems, under additional assumptions such as: low number of species, complex balance or weak reversibility.

October 23, Erika Pirnes

(special edition: carrot seminar)

Title: Why do ice hockey players fall in love with mathematicians? (Behavior of certain number string sequences)

Abstract: Starting with some string of digits 0-9, add the adjacent numbers pairwise to obtain a new string. Whenever the sum is 10 or greater, separate its digits. For example, 26621 would become 81283 and then 931011. Repeating this process with different inputs gives varying behavior. In some cases the process terminates (becomes a single digit), or ends up in a loop, like 999, 1818, 999... The length of the strings can also start growing very fast. I'll discuss some data and conjectures about classifying the behavior.

October 30, Yunbai Cao

Title: Kinetic theory in bounded domains

Abstract: In 1900, David Hilbert outlined 23 important problems in the International Congress of Mathematics. One of them is the Hilbert's sixth problem which asks the mathematical linkage between the mechanics from microscopic view and the macroscopic view. A relative new mesoscopic point of view at that time which is "kinetic theory" was highlighted by Hilbert as the bridge to link the two. In this talk, I will talk about the history and basic elements of kinetic theory and Boltzmann equation, and the role boundary plays for such a system, as well as briefly mention some recent progress.

November 6, Tung Nguyen

Title: Introduction to Chemical Reaction Network

Abstract: Reaction network models are often used to investigate the dynamics of different species from various branches of chemistry, biology and ecology. The study of reaction network has grown significantly and involves a wide range of mathematics and applications. In this talk, I aim to show a big picture of what is happening in reaction network theory. I will first introduce the basic dynamical models for reaction network: the deterministic and stochastic models. Then, I will mention some big questions of interest, and the mathematical tools that are used by people in the field. Finally, I will make connection between reaction network and other branches of mathematics such as PDE, control theory, and random graph theory.

November 13, Jane Davis

Title: Brownian Minions

Abstract: Having lots of small minions help you perform a task is often very effective. For example, if you need to grade a large stack of calculus problems, it is effective to have several TAs grade parts of the pile for you. We'll talk about how we can use random motions as minions to help us perform mathematical tasks. Typically, this mathematical task would be optimization, but we'll reframe a little bit and focus on art and beauty instead. We'll also try to talk about the so-called "storytelling metric," which is relevant here. There will be pictures and animations! 🎉

Sneak preview: some modern art generated with MATLAB.

Picpic.jpg

November 20, Colin Crowley

Title: Matroid Bingo

Abstract: Matroids are combinatorial objects that generalize graphs and matrices. The famous combinatorialist Gian Carlo Rota once said that "anyone who has worked with matroids has come away with the conviction that matroids are one of the richest and most useful ideas of our day." Although his day was in the 60s and 70s, matroids remain an active area of current research with connections to areas such as algebraic geometry, tropical geometry, and parts of computer science. Since this is a doughnut talk, I will introduce matroids in a cute way that involves playing bingo, and then I'll show you some cool examples.

December 4, Xiaocheng Li

Title: The method of stationary phase and Duistermaat-Heckman formula

Abstract: The oscillatory integral $\int_X e^{itf(x)}\mu=:I(t), t\in \mathbb{R}$ is a fundamental object in analysis. In general, $I(t)$ seldom has an explicit expression as Fourier transform is usually inexplicit. In practice, we are interested in the asymptotic behavior of $I(t)$, that is, for $|t|$ very large. A classical tool of getting an approximation is the method of stationary phase which gives the leading term of $I(t)$. Furthermore, there are rare instances for which the approximation coincides with the exact value of $I(t)$. One example is the Duistermaat-Heckman formula in which the Hamiltonian action and the momentum map are addressed. In the talk, I will start with basic facts in Fourier analysis, then discuss the method of stationary phase and the Duistermaat-Heckman formula.

December 11, Chaojie Yuan

Title: Coupling and its application in stochastic chemical reaction network

Abstract: Stochastic models for chemical reaction networks have become increasingly popular in the past few decades. When the molecules are present in low numbers, the chemical system always displays randomness in their dynamics, and the randomness cannot be ignored as it can have a significant effect on the overall properties of the dynamics. In this talk, I will introduce the stochastic models utilized in the context of biological interaction network. Then I will discuss coupling in this context, and illustrate through examples how coupling methods can be utilized for numerical simulations. Specifically, I will introduce two biological models, which attempts to address the behavior of interesting real-world phenomenon.