For questions regarding mathematical concepts with applications to Biology.

learn more… | top users | synonyms

2
votes
0answers
23 views

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

In the Sel'kov model of glycolysis wich I put on next $u'=-u+av+u^2v\\ v'=b-av-u^2v$ wich have a limit cycle and have all sense because it is a glycolytic cicle. What are the ...
0
votes
0answers
21 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 ...
0
votes
2answers
17 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". ...
0
votes
0answers
16 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 ...
0
votes
0answers
33 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
vote
1answer
25 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 ...
1
vote
1answer
34 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 ...
0
votes
0answers
19 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 ...
0
votes
0answers
24 views

A good book about theoretical ecology (Quantitative analysis of movement)

I would like to ask if anyone knows 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 ...
0
votes
0answers
34 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
votes
1answer
41 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 ...
1
vote
0answers
43 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 ...
1
vote
1answer
69 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}& ...
1
vote
2answers
79 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 ...
0
votes
1answer
38 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
votes
1answer
40 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: ...
0
votes
0answers
38 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 ...
0
votes
1answer
50 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 ...
0
votes
0answers
36 views

Discrete Population Model Crashing

Consider the discrete population model $$U_{t+1} = au_t^2/(b^2+u_t^2)$$ Where $a >0$ If $a^2 > 4b^2$ show that the population may be driven to extinction if it becomes less than a critical ...
0
votes
0answers
70 views

PDE reaction diffusion equilibrium solutions reaction diffusion cauchy (R-D-C)

where H1 is: f is lipschitz continuous on any closed bounded interval and H2 is: f(0)=0 I am unsure on how to start this question to show that f satisfies H1, and how to show that R-D-C cauchy has ...
-1
votes
1answer
67 views

Consider a species of animal which only breeds during the spring. Suppose that all adults die before the next…

Consider a species of animal which only breeds during the spring. Suppose that all adults die before the next breeding season. However, assume that every female produces (on average) $R$ female ...
0
votes
2answers
58 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 ...
2
votes
0answers
20 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 ...
1
vote
1answer
52 views

Keeping an exponentially decaying system steady.

To give a bit of background: I am trying to figure out what amount of substance X to continuously add over a time interval in order to keep it constant in a system where substance X has the half-life ...
1
vote
0answers
43 views

How do I interpret this density function

I'm currently freshing up on math for my computational biology seminar. Now I have a question concerning the following density function that is used to calculate the signaling time in a signaling ...
4
votes
1answer
86 views

Opportunities for Mathematicians to Work in Biological/Disease Areas

Yesterday, I was reading some of the question Can I Use My Powers for Good? and it got me thinking. It's quite an old question (3 years), so I don't want to resurrect it and also my own question's ...
-1
votes
1answer
68 views

Differential Equation with biology!

I am working on a growth model for bacteria as a function of a nutrient, and I am stuck. So the differential equation I am supposed to be solving is $\frac{dN}{\ DT} = k(C_0 -\alpha N(T)) N$ The ...
1
vote
1answer
38 views

Calculate migration probability matrix from distances matrix

Imagine the world-wide human populations as a series of interconnecting populations. The distances between any two populations is given by the following kind of matrix $$ \begin{matrix} ...
0
votes
1answer
40 views

Fish Eggs, Calculus, and Optimization

The survival of a fish egg through its critical period is a function of its mass, $x$. The larger the egg, the more nutrients are present and the more likely it is to hatch successfully. This ...
26
votes
5answers
2k views

Can mathematics get from other sciences what it got from physics?

Throughout history, physics has been an unparalleled source of '' inspiration'' for discovering/inventing mathematical ideas, which is due to its ability to describe the physical world. But can this ...
1
vote
1answer
66 views

Neural networks and mathematical modelling

Could you point out some reference books [accessible to an undergrad math student] that deal with the mathematical modelling aspect of neural networks?
6
votes
1answer
121 views

How can I model the number of insects in a house?

I really don't know if this question applies here or if it makes sense, but I'm curious as to whether these ideas are commonly used. Imagine you are in a room, this room has holes, where bugs may ...
1
vote
1answer
39 views

Sigmoidal function

Can someone explain what a sigmoidal function is? I have "$S(x)$ is a sigmoidal function with $S'(x)\ge0$ and $\lim_{x\rightarrow-\infty}S(x)=0$ but I really don't understand what $S(x)$ is I found ...
0
votes
1answer
14 views

serial dilution

If $0.01$ is $10$ to the negative 2nd power then what is $0.2$? I am having trouble making all the test tubes a number that can be added together. Test tube A is $.01 = 10$ to the negative 2nd ...
1
vote
1answer
56 views

How to find the basic reproductive number of a discrete SIS epidemic model

I have been following a textbook called Mathematical Models in Population Biology and Epidemiology. The SIS model is given by the system \begin{aligned} S_{n+1} &= \Lambda + S_n e^{-\mu} ...
0
votes
1answer
79 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 ...
1
vote
1answer
74 views

How to connect the deterministic and probabilistic descriptions of the SIR model

I am a 17 year old student and I was reading up on epidemic modelling for a math project, specifically the SIR model and I came across this: "This" refers to the assumptions to which the Markov Chain ...
1
vote
1answer
70 views

sum of exponential series in population growth model

I am a biology student who has recently started studying population dynamics. I've recently found a model of population growth where the number of organisms at an age class (N) is calculated by: ...
0
votes
1answer
126 views

The variance of Lincoln-Peterson estimator

Capture-recapture is a method commonly used in ecology to estimate an animal population's size. Let $N$ = Number of animals in the population; $K$ = Number of animals marked on the first visit; $n$ ...
1
vote
1answer
41 views

Is there an introductory book on Genetic Sequencing Theory for mathematicians?

I am interested in Genetic Sequencing Theory (see the wikipedia link over here), and I was wondering whether there is some introduction to this field for someone with a mathematics background and ...
0
votes
1answer
106 views

physical meaning of heat equation

consider the heat equation $u_t=a(t)u_{xx}+f(x,t)$, $0<x<L$, $0<t<T$ subject to the initial condition $u(x,0)=g(x)$ and boundary conditions $u(1,t)=0,$ $u_x(0,t)+hu(0,t)=0$ where ...
0
votes
2answers
37 views

Patlak equation

For solute flux across microvessel wall, these two equations are supposed to be equivalent: $$ \begin{align} J_s &= J_v(1-\sigma_f)\frac{C_i - C_Le^{\mathrm{Pe}}}{1 - e^{\mathrm{Pe}}} \\ J_s ...
0
votes
0answers
274 views

Topology of biological compartments

In the field of cell biology, there is a general sub-field concerned with the topology of organelle membranes, and a key focus remains on how these dynamic membranes deform and interact with cellular ...
0
votes
0answers
102 views

Implementing formula correctly in matlab for neuroscience: total soma membrane potential?

Please help me to understand: am I correctly implementing a total soma membrane potential (TSMP) equation in Matlab? Due to being a new member I need to use this list link to refer to the links ...
3
votes
1answer
160 views

Start studying mathematical biology from basics

I am really passionate about theoretical and quantitative biology and I would like to build my future career around this topic. I've just got my bachelor's degree in biology (ecology) but scince ...
1
vote
0answers
70 views

For starting the studies in Mathematical-Biology

I will take an undergraduate course in Mathematical Biologylearn themes like: population dynamics; the emergence of patterns of Philotaxia; TuringĀ“s bifurcation; Genetics; Chaos; Neural networks; ...
5
votes
2answers
171 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 ...
2
votes
1answer
117 views

What paradigm of automated theorem proving is appropriate for Principia Mathematica-style formalization?

I am in possession of a book, which, inspired by Russell's Principia Mathematica (PM) and logical positivism, attempts to formalize a specific domain by determining axioms and deducing theorems from ...
0
votes
1answer
26 views

Reaction-Diffusion question

Can somebody help me with this question,I don't have a clue really. Q: I The spread of an impulse from one end of a one-dimensional nerve fibre is modelled by the partial differential equation ...
0
votes
1answer
81 views

Biology Discrete Population model

I'm stuck on a particular part of a long question, so I will post the entire question and tell you guys where I'm stuck. Q: The size of a locust population in each year is given in terms of the ...