For questions regarding mathematical concepts with applications to Biology.

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1answer
38 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 ...
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1answer
18 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} ...
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0answers
11 views

Scaling linear constraints to give increased weight to values closer to 0

I am working on devising a integer linear programming model for a gene copy number problem. The general gist of it is that a ILP variable is created for each window for which we have data values. ...
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1answer
31 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 ...
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31 views

Branching Processes

I would like to have some hints about the following problem: Imagine a descendant tree. We assume that each species can give birth to a new specie in a constant rate $\lambda$. (This rate is called ...
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0answers
27 views

Stability of 2-periodic solution

I'm studying the following discrete system (Ricker model): $u_{t+1}=\alpha u_t e^{-u_t}$. By the direct calculation I showed that for $\alpha > e^2$ exist 2-periodic solution. Now, my professor ...
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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 ...
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1answer
37 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?
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1answer
102 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 ...
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1answer
29 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 ...
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0answers
20 views

Ion channels in math

I am taking a mathematical biology course and this question is about Na and K channels So I have two functions, one describes the change in voltage $dV/dt$ and the other describes the change in ...
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0answers
24 views

Verbal explanation of meaning of biological equation

Now replacing each variable with its meaning looks like this: Can anyone explain to me in "layman's terms" how to verbally state what the left side of this inequality means? In context: I have ...
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1answer
11 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 ...
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1answer
30 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} ...
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1answer
57 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 ...
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1answer
44 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 ...
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1answer
29 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: ...
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1answer
50 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; $n$ ...
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0answers
13 views

Biostatistics book

Do you know a book in biostatistics that fits very well to these topics: Analysis of counts: estimating probabilities, re-expression probabilities as ratios, odds, logits, probits, etc., comparing ...
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1answer
38 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 ...
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1answer
40 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 ...
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2answers
27 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 ...
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0answers
94 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 ...
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0answers
68 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 ...
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1answer
94 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 ...
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0answers
56 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; Turing´s bifurcation; Genetics; Chaos; Neural networks; ...
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2answers
96 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 ...
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1answer
93 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 ...
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1answer
20 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 ...
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1answer
74 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 ...
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0answers
20 views

Which cut-off for collapsing this tree?

I have a Newick tree that is built by comparing similarity (euclidean distance) of Position Weight Matrices (PWMs or PSSMs) of DNA regulatory motifs that are ~5-9 bp long sequences. An interactive ...
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1answer
620 views

Gompertz growth model problem

The growth of tumor cells is characterized with Gompertz model. $N'=-aNln(bN),$ where N(t) is proportional to the number of cells in the tumor, while a and b denote positive parameters. ...
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0answers
40 views

Which in graph theory book do you recommend for a Biologist?

I need a book in Graph Theory for my Thesis project in Biology (6 months from now). I have reasonable mathematical knowledge. The book must be strict but not as complicated as an advanced book. The ...
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0answers
51 views

Relationship between Reproductive Ratio and Jacobian in Population Model

In class we defined the Reproductive Ratio, $R_0$ of a population modelled by SIR, SEIR,... as the average number of secondary infections caused by an average infected individual in an average ...
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2answers
72 views

mathematical biology1

Consider the infectious disease model defined by \begin{equation} \frac{dS_3}{dt}= -\rho I_3S_3+\gamma I_3+\mu-\mu S_3\tag 1 \end{equation} \begin{equation} \frac{dI_3}{dt}=\rho I_3S_3-\gamma ...
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1answer
36 views

Why is chemotaxis considered an emergent behavior?

this is an applied math question. I could have posted this under a biological stackexchange, but the idea of emergent behavior or emergent properties of a system seems more appropriate to an applied ...
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0answers
39 views

Quantitatively comparing event trains of different lengths for Poissonness

I have a parameterized, effectively black box process that generates a series of events (simulated action potentials). Different parameter values often lead to different numbers of events. How can I ...
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2answers
138 views

Computing $\langle\sin(\gamma_i)\rangle= \int_{(S^2)^N} \sin(\gamma_i)p(\Theta)dS$

I'm trying to evaluate the following integral, which I know must be zero, $$\langle\sin(\gamma_i)\rangle= \int_{(S^2)^N} \sin(\gamma_i)p(\Gamma)dS$$ Where, $$\langle ...
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0answers
39 views

Normalizing multiple different features from unknown distributions

I'm doing some "exploratory" data analysis over a large set of classes/proteins, with a few hundred different features (I.E. Continuous variables) extracted from the data. The features are calculated ...
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1answer
130 views

Mathematical Biology and modelling

Consider the two species competition model given by $$ \frac{da}{dt }= \frac {λ_1 a} {a+K_1} - r_{ab}\cdot ab - da, \ \ \ \ \ \ \ \ \ \ (1)$$ $$\frac{db}{dt }= λ_2 b (1-\frac{b}{K_2}) - ...
2
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1answer
39 views

Trouble finding equilibrium points

I'm working on a nonlinear predator prey model and am struggling finding my equilibrium points. I've done this three times and gotten three different answers. I'd appreciate if someone could check ...
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1answer
18 views

Time-Scale Decomposition: The slow variable only has a single unstable steady state?

I'm completing a time-scale decomposition of a set of equations. The original set of two equations is $$ S'= 3k_1S^3E_T + (3k_{-1}-3k_1S^3)E_1 $$ $$ E_1'=-k_1S^3E_T+(k_{-1}+k_2+k_1S^3)E_1 $$ I was ...
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1answer
28 views

How to interpret this summation equation

I'm a computational biologist trying to interpret this equation correctly. $$CI(x)= 1- \frac{2}{(N(N-1))} \sum_i^N\sum_j^N [ S(x_i,x_j) / \sqrt{S(x_i,x_i)S(x_j,x_j)}\ ] $$ i=1 ; j=i+1 I'm confused ...
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1answer
27 views

Indirect Way of Standarizing Sample means: Is this possible?

I'm an undergrad working on a biochemistry experiment where I take a bunch of fish fin samples (each of which is composed of n individual cut fins) and run the samples through a mass spec. It is ...
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1answer
51 views

Equilibrium analysis of a Holling Type II differential Equation

I'm working on a problem which I am to determine what value of parameter $a$ will make a population become extinct. However, I am struggling in getting to the equilibrium points, which is necessary. ...
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1answer
66 views

Understanding a derivative in a biology article

From this biology article (5th page, right column) They have... $$1-P_t ≈ 1-(1+s)P_{t+1}+\frac{p_{t+1}^2}{2}$$ and they conclude that... $$\frac{dP}{dt} ≈ -sP + \frac{P^2}{2}$$ I don't really ...
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33 views

What fundamental assumption is taken here?

In biology, the following is often used for collecting data from a population: if we have data from $n$ people, over $m$ years, then we have $nm$ years of data for one person (to simplify). To give a ...
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1answer
113 views

Fitting Vogel's formula for phyllotaxis to an actual plant.

A simple model for the arrangement of florets in a sunflower was given by Vogel: $r = c\sqrt{n}$ $\theta = 137.508 n$ Where $r$ and $\theta$ are polar coordinates, $c$ is some constant and $n$ is ...
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2answers
407 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 ...
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2answers
374 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 ...