For questions regarding mathematical concepts with applications to Biology.

learn more… | top users | synonyms

0
votes
1answer
12 views

Line spacing for scaffold porosity calculations

I'm trying to calculate the correct distance to achieve a certain porosity in a 3D printed scaffold. The scaffold is circular with fixed distances between lines of printed material, with alternating ...
0
votes
1answer
24 views

Biostatistics Sampling Distributions

I am so confused, can someone please help? The activity of a certain enzyme is measured by counting emissions from a radioactively labeled molecule. For a given tissue specimen, the counts in ...
-3
votes
0answers
63 views

How to calculate the monodromy matrix of the following ODE system (Compensation for answer)

I have the following equation: $$ \frac{dw}{dt} = (-V(t)+\frac{1}{\lambda}F(t)) w, $$ with $t>0$ and parameter $\lambda>0$ The matrices $F(t)$ and $V(t)$ take the form $$ F(t)= \left( \begin{...
0
votes
1answer
38 views

Books on mathematical biology

Can someone recommend good books on mathematical biology for self study. Especially to understand SIR models and stochastic models such as branching process. For SIR models I want more of beginner ...
1
vote
0answers
18 views

SIR model parameter notation

I am reading on SIR models and I found this article In the article it has three groups as one without vaccination, one with only whole cell(wP) vaccination, and one with only acelluar(aP) vaccination....
0
votes
0answers
48 views

Interpreting $\log_2\left(\frac{1}{0}\right)$ and $\log_2\left(\frac{0}{0}\right)$

I'm hoping someone can confirm what I've done is correct. I am working with biological datasets ... about 100 RNA-Seq datasets and I'm trying to analyze the relative up or down regulation of genes. ...
0
votes
0answers
21 views

Estimation of suitable significance level for high numbers of experiments

I am a scientist and work with high numbers of experiments. For example: I have tested $ 1000 $ different parameters between $2$ groups. I found $10 $ parameters, which are significantly different ...
0
votes
0answers
9 views

Using coefficient of variation vs standard deviation to understand trial-to-trial variability

The basic model I have is as follows: I'm studying the response time of a neuron that's affected by two sources of noise: intrinsic noise and synaptic noise (i.e. random fluctuations in the voltage ...
1
vote
0answers
32 views

Show that $\big(k+D(b-c)\big)D-pg(1-pu)\Big(k+(b-c)\big(2D-pg(1-pu)\big)\Big)$ equals $\Big(k+(b-c)\big(D-pg(1-pu)\big)\Big)\big(D-pg(1-pu)\big)$ [closed]

So, I'm having a doubt here. I would like to transform this:$$ \big(k + D(b-c)\big)D - pg(1-pu)\Big(k + (b-c)\big(2D-pg(1-pu)\big)\Big)$$ into this: $$\Big(k+(b-c)\big(D-pg(1-pu)\big)\Big)\big(D-pg(...
0
votes
0answers
13 views

Using partial derivatives to optimise an animal foraging model in R

I'm developing a foraging model for a bird and want to determine what aspects of its foraging behaviour would be most beneficial for it to optimise in order to increase its time at sea. I think ...
0
votes
0answers
30 views

Linear Algebra and Biology

Would it make more sense for a biology student to study two semesters of calculus during first year (dealing with derivatives in the first semester and integrals in the second) or to study one unit of ...
1
vote
0answers
25 views

FitzHugh–Nagumo system with diffusion

I was studying the FitzHugh-Nagumo model with diffusion and I quite do not understand the meaning of it. If we consider the system without diffusion, \begin{equation}\label{FHN}\begin{cases} \dot{u}=...
1
vote
0answers
52 views

Genetic algebras; what should a mathematician know about them?

I recently learned that genetic algebras are a thing, which means there is a link between abstract algebra and genetics. Question: What should I (wearing my mathematician's hat) know about them? ...
2
votes
2answers
26 views

Programming Bifurcation analysis

Next year I'm going to do my final project for graduation. I've been assigned to search and study some biomathematical models with bifurcation theory and numerical bifurcation analysis. I'm thinking ...
2
votes
1answer
24 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 ...
0
votes
0answers
14 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 ...
0
votes
0answers
16 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 inactivated)...
0
votes
1answer
13 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 ...
1
vote
0answers
36 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, ...
0
votes
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 ...
0
votes
1answer
30 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- \frac{N_2}{...
2
votes
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 ...
0
votes
1answer
25 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 ...
0
votes
1answer
33 views

Genotype of siblings given identity by descent status

I have a question regarding genotype of siblings (specifically I am referring to the table on slide 19 here: http://ibgwww.colorado.edu/workshop2005/cdrom/ScriptsA/evans/IBDestimation/IBD--2005.pdf ) ...
0
votes
1answer
68 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 ...
0
votes
2answers
77 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
votes
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
vote
1answer
40 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 (0,1)\...
2
votes
1answer
27 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 $...
0
votes
1answer
39 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
votes
0answers
41 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: ...
0
votes
1answer
62 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 can ...
0
votes
0answers
61 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
votes
1answer
61 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 ...
1
vote
2answers
71 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
votes
1answer
46 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!
1
vote
4answers
124 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 ...
0
votes
2answers
42 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 ...
-2
votes
1answer
48 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
votes
1answer
76 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
votes
1answer
79 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 ...
3
votes
1answer
109 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 ...
0
votes
0answers
46 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
vote
1answer
104 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 ...
2
votes
0answers
62 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 biological-medical-...
0
votes
0answers
31 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
50 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
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 ...
0
votes
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
vote
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 ...