For questions regarding mathematical concepts with applications to Biology.

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13 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 ...
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0answers
13 views

How to calculate diffusion with different units

I need to find out the intial diffusion rate across membrane. I know the formula of J=DA(C1-C2) but i am confused about how to make the calculations I also know the following: 1) Na+ concentrations ...
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15 views

A rate model for sodium channels

I am studying by myself Human Physiology. I have encountered the following question: In the following given model of sodium channel with 3 states open closed blocked (which I assume means ...
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1answer
10 views

emmission probabilities in a hidden markov model with 2 states and an alphabet of 4 characters

I'm reading through a text that is describing how to use use hidden markov models to identify areas of biological sequences that correspond to specific biological features. It starts with a simple ...
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0answers
35 views

Mean time time until fixation in the Wright-Fisher model

I was reading these notes on mathematical population genetics, and they have a derivation of the mean time ($\tau$) until either of the alleles fix, in the Wright-Fisher model. They get, in page 12, ...
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2answers
40 views

Cool applications of reaction diffusion equations

I was thinking my undergrad thesis could be about reaction diffusion equations and their application to biology. For example, I know about pattern formation on the coat of animals, but I was told the ...
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1answer
28 views

Fixed points of $u'= u(1-u+ \alpha v)$, $v' = \rho v(1-v + \beta u)$

Hopefully a simple question however it has me stumped... I have the following system: $\frac{dN_1}{dt} = r_1N_1(1- \frac{N_1}{k_1} + b_{12} \frac{N_2}{k_1})$ $\frac{dN_2}{dt} = r_2N_2(1- ...
2
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1answer
27 views

How to model this recurrence?

I'm having some problems on how to model this situation correctly, using difference equations. Say there's a medicine that has a half-life of 12 hours (every 12 hours, the amount of it on your blood ...
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1answer
24 views

Important subjects for biological systems modelling

which subjects and tools are important for a person who wants to start modelling biological systems? For example, everyone knows that calculus is really important to step in any mathematical ...
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0answers
19 views

Genotype of siblings given IBD status (identity by descent status which can be $0, 1,$ or $2$)

I have a question regarding genotype of sibilings (specifically I am referring to the table on slide 19 here: http://ibgwww.colorado.edu/workshop2005/cdrom/ScriptsA/evans/IBDestimation/IBD--2005.pdf ...
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1answer
65 views

How to prove that the ellipse is a periodic orbit knowing that the orbital derivative of a function V is zero on there

The question is as follows: Show that the orbital derivative of the function $V=(1-x^2-2y^2)^2$ is zero on the ellipse $x^2+2y^2=1$, and explain why you can deduce that the ellipse is a periodic ...
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2answers
74 views

UnFlattening a 1/2 Triaxial Ellipsoid: Reconstructing a Squashed Tortoise

BACKSTORY: I have a flat tortoise. I need to figure out its original dimensions. I'm a paleontologist, and the site I'm working at has produced a [Hespertestudo crassiscutata], a giant tortoise ...
2
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2answers
79 views

Convergence of haplo-group

Every man inherits his haplo-type from his father, and thus the male lineage can be traced back. Given a population $n$ males, At each generation we uniformly sample $n$ males (with repetitions) to ...
1
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1answer
38 views

Interpretation of a reaction diffusion equation

I have a reaction-diffusion equation in 1-dimensions of the typical form: $$\frac{\partial }{\partial t} u(x,t)= \frac{\partial^2 }{\partial x^2} u(x,t)+ \alpha(x) u(x,t), \,\qquad (x,t)\in ...
2
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1answer
23 views

Turing criteria for Sel'kvo glycolysis model

I have the Sel'kov reaction diffusion model for glycolysis as follows: \begin{eqnarray} u_t=D_uu_{xx}-u+av+u^2v\\ v_t=D_vv_{xx}+b-av-u^2v \end{eqnarray} How can I obtain the values for $D_u$ and ...
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1answer
36 views

What does three bars and “def” mean in a partial derivate problem?

I'm reading the book "Mathematical Models in Biology" by Leah Edelstein-Keshet and in page 70 the following explanation appears. Here, F(x,y) is a function with P = F(X0 + Y0) and the idea is to ...
2
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0answers
38 views

Quasistationary distribution for the Moran model

The Moran model is a model for genetic drift. Basically, it is a finite Markov chain (more precisely, a birth-death chain) with state space $S:=\{0,...,N\}$ and the following transition probabilites: ...
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1answer
60 views

Calculating biological growth of doubling cells

For some kinds of experiments, biologists use isolated cells grown in culture. Cells differ significantly in their cell doubling times (one cell dividing into two cells). Plant cells ...
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0answers
60 views

Probability for a random k-mer to repeat at least $n$ times in a random $S$ characters long string

What is the probability for a random $k$ characters long string to be repeated $n$ times or more in a random $S$ characters long string, both made of a 4-symbols uniformely distributed alphabet? So ...
0
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1answer
56 views

How to reduce the chemical reaction system $A+B \rightleftharpoons^{k_+}_{k_-} C$ with transfer using the quasi steady state assumption

Suppose we have the reaction $$A+B \rightleftharpoons^{k_+}_{k_-} C$$ within some reaction $\Omega\subset\mathbb{R}^3$, we assume this region to be well mixed and we denote the concentration of $A$ as ...
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2answers
66 views

Theoretical justification of exponential growth differential equation

Consider a number of $x_0$ reproducing individuals and ignore death and limiting environmental factors. I've heard that the growth of such a population (of bacteria, insects, humans, etc...) can be ...
2
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1answer
45 views

Mathematical Epidemiology Reference Request

I'm looking for a good Textbook for learning Mathematical Epidemiology. Something that I could read through and use as a future reference book. Thanks for the advice!
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4answers
117 views

Relationship between Mathematics and Genetics [closed]

I was wondering how can we mathematically define the biological nature around us. How can we mathematically define a real plant or a tree, growing from being a 1 cell to a full grown plant with ...
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2answers
41 views

Population dynamics modelled by a wave function (Mathematical Biology)

The size of an insect population $N(x,t)$ is governed by the partial differential equation: $\frac {\partial N}{\partial t}=p(N) + \frac {\partial^2 N}{\partial x^2}$ for some function $p(N)$ . For ...
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1answer
46 views

Does this nonlinear differential equation have a closed form solution?

I have a differential equation inspired by a population dynamics problem and I'm don't know how to solve it. I wonder if anyone here can tell me if a closed form solution exists and how to find it. ...
2
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1answer
74 views

An algorithmic method to simplify the mathematical modeling of a reaction network using conservation laws

Consider the reaction scheme. where $S$ is the substrate, $E$ is the enzyme, $P$ is the product, $C_1$ and $C_2$ are enzyme substrate complexes. Let $[S] = s$, $[E] = e$, $[C_1] = c_1$, $[C_2] = ...
2
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1answer
77 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 ...
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1answer
106 views

Applications of Biology in Mathematics

I know that mathematics has applications in Biology, and in fact in everywhere, I am curious to know is it happened that a Biological concept comes to help math? I don't mean Biological names be ...
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0answers
45 views

How can I solve this ordinary differential equation? What are the Initial/Boundary Conditions used?

I am having trouble following the solution to this problem, I can understand how to obtain the general solution but cannot figure out the conditions used to obtain the particular solution with the ...
1
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1answer
92 views

Genetic probability problem(autosomal dominant,x-linked recessive)

Hemophilia is an X-linked recessive trait in humans. Huntington’s Disease is inherited with an autosomal dominant allele. a. Mr. Y is unaffected by either condition. He marries Ms. X, who is ...
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0answers
56 views

In the Glycolysys Sel'kov model, what are the meaning of “a” and “b” values?

In the Sel'kov model of glycolysis which I put on next $u'=-u+av+u^2v\\ v'=b-av-u^2v$ which have a limit cycle and have all sense because it is a glycolytic cycle. What are the ...
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0answers
29 views

How to determine the probability of seeing a time based event?

I am trying to figure out what the probability of capturing a time based event is. This is the situation. I'm observing a video of clusters of proteins in a cell with proteins tagged green and red ...
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2answers
43 views

Approximation of a negative exponential model?

I am trying to get an approximation of this model, it is a negative exponential model introduced by Olson in 1963 "Energy storage and the balance of producers and decomposers in ecological systems". ...
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0answers
29 views

How to make sense of this contour graph?

Recently, I have been studying the paper "Estimating the basic reproductive ratio for the Ebola outbreak in Liberia and Sierra Leone", published in Infectious Diseases of Poverty. I came across the ...
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0answers
49 views

How to model compartment chemical concentration with permeation through a membrane

Suppose we have one chemical species $V$ and two compartments in which $V$ can be, $A$ and $B$, with volumes $\Omega_A$ and $\Omega_B$ respectively, where $\Omega_A < \Omega_B$. Compartments $A$ ...
1
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1answer
38 views

How to write a covariance

Could somebody kindly explain how you can express something as a covariance? A paper I am reading contains this term: $$\sum_in_i(p_i-p)(b_a+\sum_t\sum_jr^t\frac {n_j} {n_i}b_c)$$ The author then ...
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1answer
43 views

Probability distribution of the number of heterozygous sites

We'll consider a stretch of DNA on a chromosome and we'll be looking at specific sites that are at certain distances on from the others. The distance between any two sites is express in centiMorgan ...
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0answers
67 views

testing significant difference on species richness

I measured the species richness (number species) in three different sites. Now, I want to test whether there is significant difference between each site in terms of species richness. The species ...
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0answers
40 views

A good book about quantitative analysis of movement in theoretical ecology?

Does anyone know a good book to start studying animal patterns of movement? I am interested in exploring different approaches, in particular models in stochastic settings. I have been checking ...
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0answers
40 views

Coalescent theory - Why are coalescent times independent?

I am reading from this book and I want to make sure I understand what is going on. What I get from the book Consider a population of $N$ individuals. The population size ($N$) is constant. select ...
0
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1answer
47 views

Equilibrium and Stability of Nonlinear Interactions

Examine the nonlinear model: $$\triangle x_t = rx_t(1-\frac{x_t}{K})-sx_ty_t$$ $$\triangle y_t = -dy_t+\epsilon x_ty_t$$ Find the equilibrium and their stability. Here all the parameters are ...
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0answers
98 views

How to define boundary conditions for a sphere to run reaction-diffusion equations on its surface?

I'm in a Biology lab, and we managed to simulate reaction-diffusion equations on a torus using periodic boundary conditions for a 2D matrix. We want to try doing the same on a sphere, but I'm a ...
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1answer
172 views

Conditions for Deriving $R_0$ for SIR Model Using Survival Function Method

I'm taking a look at the SIR model given by the system of differential equations \begin{align} \frac{dS}{dt} & = - \beta S I \\ \frac{dI}{dt} & = \beta S I - \gamma I \\ \frac{dR}{dt}& ...
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2answers
257 views

Finding Eigenvalues and Eigenvectors for Leslie Matrix

A Leslie Matrix is given by $$L =\begin{pmatrix}0 & (3/2)a^2 & (3/2)a^3\\1/2 & 0 & 0\\ 0 & 1/3 & 0\end{pmatrix}\cdot$$ Find the Eigenvalues and determine the dominant ...
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1answer
78 views

How to test if data follows a distribution?

Have been given some data and the question says to determine if the data follows any distribution. It says to compare the observed data vs expected graphically and to test further. The distributions ...
2
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1answer
48 views

Number of combinations in a string with n states

I have a problem in biology involving amino acids (think of them as a string of characters) that I want to formalise. Let assume we have a amino acid sequence of length 4, typical examples may be: ...
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0answers
48 views

Biological modelling math question?

I am trying to write a biological model that models protein interaction. I am having an issue with one aspect. Lets say protein A and protein B interact with eachother to form complex AB. Now every A ...
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1answer
59 views

How do find the general solution to this system of differential equations?

$$ \begin{align} \frac{dI_n}{dt} &= 2(1-p) I_n - I_n + 2(1-p) I_v \\ \frac{dI_v}{dt} &= 2p I_v - 3 I_v + 2p I_n \end{align} $$ I tried to find the eigenvalues and the eigenvectors for this ...
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2answers
70 views

What is math branch that studies general populations.

A population is a summation of all the organisms of the same group or species, which live in a particular geographical area, and have the capability of interbreeding so i would like to understand the ...
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0answers
26 views

Question about the cell cycle

A diploid cell in G1 has 6 chromosomes. How many chromosomes and how many chromatids are present in each of the following stages? Here is what I am guessing G1: 6 chromosomes ; 6 chromatids G2: 6 ...