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Questions tagged [biology]

For questions regarding mathematical concepts with applications to Biology.

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1answer
30 views

Stability matrix - order of elements

I have two equations: $$\frac{dx}{dt} = v(k-ux) - \delta x, \hspace{3mm} \frac{dv}{dt} = v(r-px)$$ I want to calculate the Jacobean so I can analyse the stability of the fixed points. Does it ...
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0answers
30 views

genetical distance of one's parent and sibling to him/her self

here Josh-D. Davis says: On average, you share 50% with each. In reality, you share 45–55% with a parent, and 32–49% with a sibling. ( to question "How similar is one's DNA to their parents and ...
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1answer
46 views

Modelling cancer with ordinary differential equations

How can I model cancer spread and cancer treatment using first order differential equations? I will be investigating this topic in my high school math paper, but am unsure of where to begin.
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1answer
41 views

Model for population growth and finding the equilibrium solutions

A model for population growth is given by: $$\frac{dN}{dt} = f(N) = r N \left( 1-\frac{N}{K} \right) \left( \frac{N}{U}-1 \right) $$ where $r,\ U,$ and $K$ are positive parameters and $U < K$. (a)...
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1answer
24 views

Maths Bio - small gene circuits/law of mass action

As a summary, I'm looking at this binding reaction: $$O_0 + X_2 \rightleftharpoons O_1 $$ where $O_0$ is a state of unbound promoter and $O_1$ is a state of bound promoter. The forward and ...
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0answers
44 views

Approximating $\max \big\{\frac{x_\tau}{x}\big\}$ as $x$ and $x_\tau \rightarrow 0^+$

I have the following delay system: $$x'(t) = g(t,\tau,x,x_\tau)$$ Given that $g(\cdot)$ is smooth and bounded, $x(t)$ is bounded in a non-negative region. What are some possible ways to obtain an ...
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1answer
49 views

Matrix algebra needed to derive tricky equation… Trophic levels and networks!

Imagine a food web (a directed, acyclic network) where the nodes are species and the edges represent predator-prey relationships. Prey nodes have an edge directed to the predators that eat them. ...
2
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1answer
26 views

Drawing graphs of parametric equations

the SIR model is an epidemiological model which sorts the whole population into three subclasses. x(t)(susceptibles), y(t)(infected), z(t)(recovered), with initial populations $x(0)= N_{1},y(0) = N_{2}...
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0answers
68 views

Biological/chemical mathematical modeling - two partners with multiple binding site interactions

I am wondering if there is any reported attempt to mathematically model the interaction of two multiple-sites molecules? I know that there is a lot of literature on how to mathematically model the ...
0
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1answer
22 views

Making different time scales and limit situation rigorous

There is a splitting of time scales which I don't understand; it is described below: We have the following system: $$ {\dot {\textbf x}=A({\textbf x})\textbf c\atop\dot {\textbf c}=B({\textbf x})\...
2
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1answer
66 views

Simple Statistics/Probability Problem

I have used a python script to identify target sequences in a DNA sequence file. There are two classes of sequence: coding and non-coding. I have identified $728$ sequences of interest. $597$ of ...
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2answers
78 views

Improved model of a fishery: $\dot N=rN(1-\frac{N}{K})-H\frac{N}{A+N}$

Strogatz exercise $3.7.4.a:$ An improved model of a fishery is: $$\dot N=rN\left(1-\frac{N}{K}\right)-H\frac{N}{A+N}.$$ a) Give a biological interpretation of the parameter $A$; what does it ...
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0answers
13 views

Defining a system in MatCont where a parameter depends on other parameter value

I'm trying to define a biological system in MatCont but I'm facing the following problem. A parameter $UU$ depends on another parameter $T_S$ in the following way ...
3
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1answer
78 views

Asymptotic behaviour of recurrence

In DNA chain, there are four types of bases: A, C, G, T. Let $g(n)$ be the number of configurations of a DNA chain of length $n$, in which the sequences TT and TG never appear. Write a recurrence for $...
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0answers
10 views

Modeling Cellular Motility Using Data

How would I model cellular motility from this format This is what my data looks like. t=48; % total time elapsed in hours C = [89.1 98.6 41.3751 124 54]; % cell density in cells/mm^2 C0= 12 * 10^...
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0answers
51 views

Setting up a predator-prey model with diffusion

I'm trying to set up a predator-prey model, where the predator affects the distribution of the prey. Effectively, over time the prey has moved from areas of high concentration of the predator to areas ...
1
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1answer
20 views

Evolutionary tree metric

I met a student at the JMM poster session last year who was showing a project studying the distance between organisms, using the tree metric on the evolutionary tree. He had shown some statistical ...
1
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1answer
112 views

Modelling a system of differential equations with dirac delta function using Matlab

I have a system similar to the model in here. This is a simplified version with only two states, bacteria ($P$) and antibiotic ($C$). After 3 days have passed (the system is run from day 0) antibiotic ...
0
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0answers
29 views

Validity of Index Notation

I have the following questions on my biomechanics homework (we're finally getting to multidimensional spaces). However, we haven't gone over it yet and won't have class again until after it's due. I'...
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2answers
55 views

Why is the degree of freedom not 5?

So we got out homework back and along with it the answers to the questions. I understood that the degree of freedom Can be obtained with N-1. So we have 6 sets of data then N =6. So df =5. But here it ...
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0answers
21 views

What are the Applications of Scoring Matrix in Bioinformatics

I've been doing some research through the internet, I can't really determine exactly the Applications of Scoring matrix in Bioinformatics. I'm thinking one of them ...
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0answers
34 views

Homogeneous ODEs of degree one

Consider a homogeneous ODE of degree one, i.e. $x'=f(x) \quad$ s.t. $\quad f(\alpha x)=\alpha f(x) \quad$ for $\alpha>0$ and $x\in \mathbb R^n$. Let $T_\alpha$ be the operator that multiplies a ...
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0answers
29 views

If sample size is 20 and I want to know the probability of 2 or less.

Am I making harder then it is based on this question: See my answer below. F2 population of a plant species (which is a diploid) resulted from a cross between a plant with red flowers and a plant ...
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0answers
22 views

Formulating a linear difference equation model and some MatLab tips

I've been trying to learn about population models, and have been having some problems when it comes to actually solving problems. The reading and looking at formulas and models is easy enough, perhaps ...
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4answers
404 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) ...
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1answer
45 views

Probability that two events will occur consecutively

Hi we are trying to determine the statistical significance of our summer water quality survey. 72 water samples were taken in two consecutive summer seasons. That is three sampling sites per week and ...
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0answers
51 views

Harvesting fish model in mathematical biology

Consider a lake where fishing occurs at a constant rate. $N_i$ is population of fish at time point $i$ and discrete model is written in the following format: $N_{i+1} = N_i + BN_i -DN_i^2-Y$ Since it ...
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1answer
28 views

What is the expected value and standard deviation of a weighted binomial distribution?

I'm working on a genetics problem and am using binary representation of the genes i.e. they can be 0 or 1. With 20 genes, I have an expected additive genetic value (i.e. mean) of 10 with standard ...
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0answers
38 views

Deciding the parameter value in a ODE system

I am working with a system that includes pharmacokinetic and pharmacodynamic elements. To model the antibiotic effect on bacteria I am using a commonly used Hill type function as,${(\phi_{max} - \phi ...
2
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1answer
45 views

modelling a differential equation system

I have a system of ODEs with a pathogen population $(P)$ being modelled as a logistic growth as, ${dP\over dt}=rP(1-{P\over k})$, where $r$ is the replication rate and $k$ is the carrying capacity ...
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0answers
34 views

How to write a specific user-defined exponential function?

I'm trying to write a function that replicates the output of an exponential function in a paper. It's equation A3 in the S1 supplementary material of this paper with the figure shown in figure A. ...
4
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1answer
49 views

Assumption on traveling wave solutions of Fisher's equation

I have a question about Fisher's equation in a biology context. For example, in Fisher's equation $u_{t} = Du_{xx} + u(1-u)$, where $u$ is a density of cell, the logistic term explains that the ...
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0answers
25 views

In Depth Treatment of 1-D Adaptive Mesh Refinement Analytics and Implementation

I am looking for a good resource for implementing adaptive mesh refinement (AMR) on a 1-D PDE and an analytical treatment. Pretty much everything I've found on AMR use 1-D as a toy example to show the ...
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2answers
13k 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 ...
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3answers
151 views

Difference between Population Growth Models (Differential Equations)

I'm currently studying population growth models in Math class right now and is presented with different equations for different models. I think I understand that we use $dP/dt = rP$ (where $r$ is the ...
1
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1answer
346 views

Half saturation constant

What is the meaning of the half saturation constant in the following system, describing the interaction between a population of predators of size $y$ and a population of preys of size $x$? $$\dot x=x(...
0
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1answer
46 views

Question regarding global lyapunov function of a biological system? [closed]

Suppose I have the following Lyapunov function that is often used in biological model: $V(x) = x - \ln x$, how is this bounded below since as $x \rightarrow -\infty$, $V(x) \rightarrow -\infty$? My ...
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0answers
38 views

Modelling Spatial Diffusion, MATLAB

I'm due to begin work on a project soon meant to build upon a pre-existing biological model. I'm an undergrad that's most experienced with Python, but I'll be working with MATLAB. The model that ...
1
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1answer
44 views

How to calculate this limit for a biological model?

This is from a mathematical biology exam: I’ve answered parts $a)$ to $f)$ absolutely fine but I’m struggling with what I presume is the final mark of part $f)$. I’ve solved the equation directly to ...
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1answer
31 views

How to sketch the discrete time graph?

In order to sketch following question what I have done so far: $ lim_{Nt->0} F(N_{t})= 0 $ and $ lim_{Nt->\infty} F(N_{t})=r$ (For the case of s=0). Now since this a discrete time graph I am not ...
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1answer
18 views

Why is the higlighted equivalence true?

I am not able to see why the equivalence highlighted is true? Is it possible to move the u from the right hand side of A on to the left hand side? Any help would be much appreciated!
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2answers
65 views

Why is u=0 always an unstable fixed point?

In the following analysis, I cannot see why $u$ is always an unstable fixed point. Calculating $f'(u)= 2R_{0}u-R_{0}-\ln(u)-1 $ at $ u=0 : -R_{0}-1 $ and this in fact suggests that u is a stable fixed ...
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0answers
30 views

Something about an “index of consecutiveness”

I'm no expert in the field of number theory, if this is the exact field, and I just hope my question is not ill-posed. I was reasoning about this: is there something like "an index of consecutiveness"...
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1answer
44 views

How to get from the the matrix to the constant?

A is a symmetric matrix such that $ Av=\lambda v$. I am not sure how to get from the first highlighted part to the second. The first one is a matrix whereas the second one is a number. At first I ...
2
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1answer
26 views

Extending a model

I'm going through a question on my maths biology course, and I'm confused at one part. you are given the formulas for a tumour and the drug that effects it. They are shown below: I've also non-...
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2answers
31 views

How to factor in the 'immediately prior to the administration of the next dose' statement in this question?

For part b I have found that the stationary state is $a_{n}=d/k$. For part $d)$ however I am not sure on how to take into account the statement 'immediately prior to the administration of the next ...
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1answer
37 views

What is the meaning of the parameter d in the model $ a_{n+1}=a_{n}-ka_{n}+d $?

In the following model I am having difficulty understanding the meaning of the parameter d in the context. I think it is a constant it terms of the dimension but I am not sure what it represents. ...
3
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1answer
87 views

Equality at equilibrium of a ODE system arising in immunology

Consider the following system of ODE's [1]: \begin{align} \dot x & = \lambda - d_1 x - \frac{k_1 x v}{x + v}\\ \dot y & = \frac{k_1 x v}{x + v} - d_2 y - k_2 y \\ \dot s &= k_2 y - d_3s \\ ...
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2answers
848 views

How to find the third eigenvector of a 3x3 matrix given the other two eigenvectors?

In the following question, I believe that there is a way to find the third eigenvector without computing everything explicitly i.e. a way to find the third eigenvector given two eigenvectors. I am not ...
2
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1answer
41 views

How to analyse u as s evolves across different values?

For part (d) of the following question should I look at the integrated version of the equation in part (a) in order to look at how $u$ evolves i.e. take limits of $s$ or does it make sense to just ...