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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
70 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
52 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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0answers
28 views

which statistics to use? [migrated]

I have a medical research in which i have two set of data 1) control group [ people who have no ailment] 2) study group [ people who have some particular ailment] Within each category there are ...
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1answer
16 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
48 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
12 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
76 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
35 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
32 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 ...
0
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2answers
67 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 ...
1
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1answer
35 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
36 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
136 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 ...
2
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0answers
28 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
83 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
28 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
14 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
20 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
23 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
34 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
55 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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0answers
27 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
64 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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0answers
32 views

Formula for residence time/turnover rate with unsteady state

I'm not sure this is the correct place to ask my question... but maybe someone could still help me. I'm looking for a way to calculate the residence time/turnover rate. I have the production and ...
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2answers
247 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
167 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 ...
1
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1answer
23 views

Expectation and variance of occurrences of patterns in a random text

I'm not sure how to complete the following problem from the book An Introduction to Bioinformatics Algorithms: Problem 9.1 Derive the expectation and the variance of the number of occurrences ...
0
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1answer
64 views

Square brackets in derivatives

I have two equations that (attempt to) describe biological systems. (1) vgen = d[s]/dt (2) vdec = -d[s]/dt When (1) = (2) then we have homeostasis When (1) > (2) then we have growth When (1) ...
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4answers
53 views

Can a sampling based method estimate how many species exist?

I've got in to a bit of a debate online and I'm hoping some people here can help clear it up. The position I'm arguing against is "It's impossible even come up with a ballpark estimate for how many ...
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0answers
82 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 ...
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0answers
31 views

Asynchronous reproduction allows us to use continuous exponential growth?

Assume that in a population, every $T$ time units, each individual reproduces then dies, the effect of which is that it is replaced by $m$ offspring. Further assume that the initial population $x_0$ ...
2
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0answers
61 views

Are Navier-Stokes equations used in molecular biology research?

I am wondering whether Navier-Stokes equations have been used in some molecular biology research papers in the past. A quick Google search revealed that such papers exist but I want to know if there ...
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0answers
43 views

Simplifying a chain rule in a model.

I was reading a paper (Taylor and Frank, 1996). There is a chain rule of a function $W(y,z)$ thus: $$\frac{dW}{dx}=\frac{\partial W}{\partial y}\cdot\frac{dy}{dx}+\frac{\partial W}{\partial ...
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1answer
79 views

How to learn biomathematics?

I'm currently an undergraduate math student and researching on the internet I discover that exists an area called "biomathematics". Looks so interesting. They use the graph theory and topology to ...
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4answers
253 views

PDEs in biology

I am student who mostly heard lectures on partial differential equations and homogenization. But I really like the idea of working in biology or with biologists - but (with my lack of overview) it ...
0
votes
1answer
172 views

steady states and stability mathematical biology

could anyone help on how to do this please? find the steady states of $$F(N)=\frac{rN}{1+N}.$$ do you differentiate and set it equal to zero and find $N$? many thanks in advance.
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0answers
39 views

Caclulating limits of Hassell Model to show under/over compensation

For this question, you will need the following definition: For a discrete time model of intraspecific competition $N_{t+1} = F(N_t)$, if the limit $F_{\infty} = \lim_{N \to \infty} F(N)$ exists, ...
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0answers
73 views

van der pol and liapunov

i have attempted this question and done as much as i possibly could, any help regarding this question would be very helpful and appreciated. a) show that the second-order differential equation for ...
1
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2answers
366 views

steady states and stability

im just checking to see if im doing this right? $$\frac{du}{d\tau}=u(1-u)-h $$ show this equations has 2 steady states and check their linear stability. this is what i have done: $u=0$ and ...
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1answer
116 views

Find the value of a function with definite integrals

I am trying to understand a paper of Maynard Smith (1974), that connects biology with game theory. I don't want to overwhelm you with useless stuff, but I have this definite integrals: ...
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2answers
32 views

Working out the interval in which the algae becomes extinct (how to get the interval)

I have a birth rate that is $$b(p) = \frac{p^2}{p^2 + 3}$$ and a death rate that is $$d(p) = \frac{p}{4}.$$ I therefore have a reproduction rate as $r = b - d$. In order for my algae to become ...
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1answer
121 views

How can I count clockwise vs counterclockwise cycles in a series of (modular) integers?

I'm working with a Markov process that has a state and transition diagram like in the picture: The transition probabilities are not listed, but they are always positive, but not necessarily ...
0
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1answer
83 views

Entrainment of linear and non-linear systems

I'm trying to understand this paper: http://arxiv.org/abs/1301.2440 They use the Van der Pol oscillator model which gives oscillatory behaviour both sides of the bifurcation point: a limit cycle ...
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2answers
57 views

Find the micro-organism growth after a certain amount of minutes

For an experiment, I put in a cell growing medium, 1 bacterium of type A and 3 bacteria of type B and every minute I add 1 bacterium of type A and 3 bacteria of type B. So, after 1 minute it means ...
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2answers
278 views

The human brain — what kind of graph would it be?

I've read an article about a comparison between human brain and artificial neural networks. It's said that human brain contains $\approx 10^{11}$ neurons and each neuron is connected to $\approx 10^4$ ...
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0answers
110 views

What's the “average diversity” of a population?

The formal problem is as follows: Given a collection of $m$ natural numbers, each of which has an equal probability of being from $1$ to $n$ ($m > n$), what is the expected "effective number of ...
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0answers
41 views

Calculating the variance of the a regular expression assuming position dependent

Hello I am having trouble with a slightly biological problem I am given a regular expression $- [RK]-[LV]-[DE]-x(2)-Y$ this expression means that there is a string with the first position being an ...
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4answers
250 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 ...
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4answers
1k 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 ...