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Questions tagged [biology]

For questions regarding mathematical concepts with applications to Biology.

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Lyapunov function for predator-prey system

I'm feeling stuck with this problem, It was taken from the book: Dinamical models in biology - Miklos Farkas: Consider the Lotka-Volterra system, so the equations are and the fixed points are the ...
ChuckTesta's user avatar
2 votes
0 answers
154 views

Case study in population biology. Sequences and series, find general solution.

Think about a population of individuals which all have two set of chromosomes (as human do). There is one gene that codes for a helping behaviour. This gene has two alleles (an allele is a variant of ...
Remi.b's user avatar
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38 votes
2 answers
14k views

The Scutoid, a new shape

The scutoid (Nature, Gizmodo, New Scientist, eurekalert) is a newly defined shape found in epithelial cells. It's a 5-prism with a truncated vertex. The g6 format of the graph is KsP`?_HCoW?T . They ...
Ed Pegg's user avatar
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17 votes
4 answers
2k views

Mathematics applied to biology

Can anyone suggest reference material on mathematics applied to biology, in particular the study of the behavior of say simple unicellular organisms or cells? Ideally the level of complexity should be ...
asker's user avatar
  • 171
8 votes
5 answers
2k views

Category Theory & Biology

Category theory is becoming more and more used in the following fields (besides others) (1) Quantum physics (e.g. C. Isham and B. Coecke et al) (2) General relativity (e.g. A.K. Guts et al) (3) ...
FWE's user avatar
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7 votes
4 answers
886 views

Is there any research in mathematical biology that isn't heavy in differential equations?

I'm near the end of my pure math undergrad trying to decide what sort of math I'm interested in for graduate school. I've always thought the idea of mathematical biology was cool, but it seems like a ...
Samuel Reid's user avatar
  • 5,092
6 votes
5 answers
3k views

What is Octave Equivalence?

This is an updated copy of a question I asked on Physics Stack Exchange not too long ago. Since I work primarily in mathematics, I thought it would be a good idea to ask it here as well (especially ...
Alexander Sibelius's user avatar
6 votes
2 answers
2k views

Measuring the Shannon entropy of an ordered sequence

I have 927 unique sequences of the numbers 1, 2 and 3, all of which sum to 12 and represent every possible one-octave scale on the piano, with the numbers representing the intervals between notes in ...
Chris Wilson's user avatar
5 votes
1 answer
317 views

Fibonacci and the spreading of viruses

I tried to understand better the spreading of a virus on a case-by-case basis, not by differential or difference equations as in SIR and SEIR models with possibly non-integer rates and time constants. ...
Hans-Peter Stricker's user avatar
5 votes
2 answers
9k views

What are differences between Geometric, Logarithmic and Exponential Growth?

At past I have read in some ecology text that geometrical, logarithmic and exponential growths are not exactly the same thing; and there were various equations for them. (The book is not available to ...
user avatar
5 votes
2 answers
1k views

Biology: How to find the probability of randomly generating multiple, sequentially identical sets

If I randomly generate a substring (example "ATGCAGC") with equal probability (1/X where X=4) for each digit with length (L) digits: What is the formula for finding the probability (P) of randomly ...
12345678910111213's user avatar
5 votes
1 answer
384 views

Does COVID-19 fit into the Caspar-Klug (Quasi-Equivalence) Theory for virus architecture?

The following is compiled largely from my "Applications of Group Theory to Virology" module I took at The University of York as an undergraduate back in 2012. The icosahedral group $I$ with ...
Shaun's user avatar
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4 votes
1 answer
397 views

Building a hidden markov model with an absorbing state.

I'm working on trying to implement a hidden markov model to model the affect of a specific protein that can cut an RNA when the ribosome is translating the RNA slowly. Some brief background: The ...
lstbl's user avatar
  • 571
4 votes
2 answers
2k views

Biology: Wright-Fisher model of genetic drift

In evolutionary biology (in population genetics to be more accurate) exists the concept of genetic drift. It describes how an allele (gene variant) (that has no advantage or disadvantage in terms of ...
Remi.b's user avatar
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3 votes
1 answer
153 views

Can SIR models explain reduction in COVID case numbers in Florida and Texas, despite lack of restrictions?

This is a question about SIR or SEIR models and understanding the trajectory of the covid infections in Florida and Texas in September 2021. This is a genuinely academic question, and not meant to be ...
krishnab's user avatar
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3 votes
1 answer
215 views

How does the reproduction number depend on characteristics of the physical contact graph of a population?

Related question at Biology SE: How to model social structure in SIR models Preliminaries Let me start with the definition of the reproduction number of an airborne virus, e.g. as given here, only ...
Hans-Peter Stricker's user avatar
2 votes
1 answer
506 views

Hopf bifurcation and limit cycles

$$dV/dt=10(V-\frac{V^3}{3}-R+I_{input})$$ $$dR/dt=0.8(-R+1.25V+1.5)$$ Use $I_{input}$ as the relative parameter to prove that there these equations undergo 2 hopf bifurcations and indicate whether ...
Math Major's user avatar
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2 votes
1 answer
3k views

Any application of vector spaces in Biology or Biotechnology?

I would like to know any application of vector spaces in Biology or Bitechnology, if you got an example i would be very glad to know it. But basically just what tool or what operations of vector ...
Luis's user avatar
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2 votes
1 answer
67 views

An unexpected pair of almost-Fibonacci and Tribonacci series

I use a modification of the SEIR model of epidemic spread which yields - for me totally out of the blue - for special parameters an astoninglishly good approximation of the Fibonacci series with a ...
Hans-Peter Stricker's user avatar
2 votes
2 answers
140 views

Using MATLAB to solve a system of two PDEs encountered in Mathematical Biology

I am in an undergraduate summer project and am studying a paper, I hope I could solve the following two PDEs with two boundary conditions for $y_1(t,a)$ and $y_2(t,a)$ using MATLAB. $$\frac{\partial ...
mzhsy034's user avatar
2 votes
1 answer
180 views

An easy reference for genetic algorithm

My field is Coding Theory and my background is Algebraic, there are many applications of Genetic Algorithm in Coding Theory, I would to know the easiest and the most elementary and introductory note ...
toress's user avatar
  • 169
1 vote
1 answer
327 views

Leslie Matrix for Population of Plants and Seeds

I am asked to onsider a population of annual plants with the following life cycle: Seeds are produced at the end of summer, after which all adult plants die. A proportion of the seeds survives winter ...
Monya Feldman's user avatar
1 vote
0 answers
106 views

SIS model with vaccination

For the simple SIS model $$ \begin{aligned} \mathsf{S}′ &= \Lambda − \beta \mathsf{SI} − \mu \mathsf{S} + \gamma \mathsf{I} \\ \mathsf{I}′ &= \beta \mathsf{SI} −(\mu+\gamma)\mathsf{I} \...
Brenda's user avatar
  • 155
0 votes
1 answer
88 views

Finding units for constants in ODE's

$$ \begin{array}{r c l} \frac{dN}{dt} & = & rN\left(1-\frac{N}{K}\right)-\alpha \frac{NP}{\beta P + \gamma N} \\ \frac{dP}{dt} & = & \epsilon \frac{NP}{\beta P + \gamma N} - \delta P \...
Michael Doherty's user avatar
0 votes
1 answer
77 views

How do you call this system?

Is there a specific name for a dynamical system that depends on the relative indexation $i\pm k$ for some $k$? For example, consider the following dynamical system defined on a ring of cells by $$ \...
sam wolfe's user avatar
  • 3,417
0 votes
0 answers
114 views

Biological model of integrate-and-fire neurons

I need help in solving a set of equations. Background: I'd like to model the firing rate of an integrate-and-fire neuron depending on the supply of usable energy that is available. (I don't know how ...
Hans-Peter Stricker's user avatar