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Questions tagged [biology]

For questions regarding mathematical concepts with applications to Biology.

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Why does a lack of inversion symmetry in 2D pattern formation lead to hexagons?

In reaction diffusion based pattern formation (or other types of pattern formation too, really), it seems that the absence of an inversion symmetry (i.e., if the field $u(x,t)$ is a stable solution/...
SarthakC's user avatar
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Genomic and sum of geometric random variables

In their paper The Maximum of independent Geometric Random Variables as the Time for Genomic Evolutionthe authors noted that if to consider the genomic word of L letters, than the measure of the time ...
user124297's user avatar
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116 views

Family tree in Biology and Category theory

I thought about family tree as a way to understand category theory more easily. The family tree is a diagram that provides detailed information about which family members were born to whom. Like the ...
user1274233's user avatar
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Is there a mathematical notation that represents "up until" or "once reached"?

I am a biologist and I need some math help. I am writing a paper about how population density affects life-history traits of a snail. I want to list descriptive statistics of several life-history ...
bribina's user avatar
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90 views

Solving the PDE $\frac{\partial n}{\partial t} = -v \frac{\partial n}{\partial \alpha} - \mu n $ using a given ansatz

I'm working on exercise 25 of Chapter 10 in Mathematical Models in Biology by Edelstein-Keshet. In the exercise we analyze the following chemotherapy model which accounts for the process of cell aging/...
Leonidas's user avatar
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Given a social system in which people are supporters of either a $G$- or a $H$-orientation, calculate the probability to have a $G$-person elected.

In this paper, Majority rule, hierarchical structures, and democratic totalitarianism: A statistical approach, I read: A social system is considered in which people are supporters of either a $G$-...
Mark's user avatar
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1 vote
1 answer
53 views

Solving ODE describing negative autoregulation in systems biology

In the paper "Negative Autoregulation Speeds the Response Times of Transcription Networks" (see https://doi.org/10.1016/S0022-2836(02)00994-4) they present an ODE describing negative ...
PSLS's user avatar
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3 votes
1 answer
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Modeling the probability of $k$-mer collisions between DNA sequences

Let's imagine that I have a DNA sequence of known origin. Such a sequence can simply be thought of as a string of characters $(A|C|G|T)^l$ where $l$ is the length of the sequence. For purposes of this ...
Trevor Schneggenburger's user avatar
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60 views

Can the "escape" trajectory of a gazelle be considered random?

I was watching a video of a gazelle escaping from a cheetah and I wondered: may it's trajectory be considered random? Logically speaking, escaping in a random fashion would make almost impossible for ...
Edoardo's user avatar
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1 answer
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3 species Lotka–Volterra model. Limit cycle

Good day, I have 3 species Lotka–Volterra model. My goal is to determine if there is a limit cycle in the system $$ \left\{ \begin{array}{l} \frac{d c}{d t}=r_c c(1-c)-\frac{c h}{c+\theta_1} \\ \frac{...
tofffee's user avatar
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Recovery Time for Logistic model equation with harvesting

We are given a logistic growth model with constant harvesting as: $\frac{dN}{dt} = rN(1-\frac{N}{K})-Y_0$ We are asked to show that the recovery time for harvesting a yield $Y_0$, $T_R(Y_0)$, ...
Green Ideology's user avatar
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50 views

persistence of SEIR epidemic model

We have the following stochastic SEIR model $dS=\Lambda - \beta SI - \mu S - \sigma SI dB(t)$ $dE=\beta SI - (\lambda +\mu) E+\sigma SI dB(t)$ $dI=\lambda E-(\gamma +\alpha +\mu) I$ $dR=\gamma I-\mu R$...
Markiii's user avatar
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58 views

Showing an endemic steady state is stable

I need to show that the steady state of this non-dimensional model is stable using minimal algebra however I am not sure how to approach this without long lines of working. The model is: $$\frac{dS}{...
user00134857693's user avatar
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109 views

Finding the eigenvalue/vector of a Leslie Matrix and purpose of eigenvalue/vector

I am currently working on a population dynamics model, in which I have to model the population growth of an animal with the survival rate and fecundity rate. I have set-up a 6 x 6 Matrix below: $$ \...
User's user avatar
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48 views

An alternative to the popular Hutchinson population model

As an alternative to the popular Hutchinson population model, which introduces a delay in the per capita growth rate, one can introduce a delay solely in the growth contribution and consider a ...
Ri-Li's user avatar
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2 votes
1 answer
129 views

Epidemiology SEI disease model

I have the following model for simple endemic with susceptible (S), exposed (E), and infective (I), $$\frac{dS}{dt}=-\beta SI,$$ $$\frac{dE}{dt}=\beta SI-\delta E,$$ $$\frac{dI}{dt}=\delta E.$$ I have ...
user00134857693's user avatar
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75 views

Stability Analysis of DFE in terms of R0 Using Ruth-Hurwitz Criterion

I am working with an epidemiological model in the form of a dynamical system of seven ODEs and I am trying to show that the DFE is stable if R0<1. When applying the Routh-Hurwitz criterion, I see ...
Hew123's user avatar
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2 votes
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111 views

Biological meaning of "eigenvalue" in DDE-based population model

For example, consider a Verhulst model with delay $$ \boxed{\dot N(t) = r N(t) \left( 1 - \frac{N(t-T)}{K} \right)} $$ where $r$ gives the reproduction rate and $K$ means the carrying capacity of the ...
m1ssing's user avatar
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Probabilities of a biology experiment

So I was having a biology experiment about Mendel's law, and we are tasked to put 15 pairs of different beads with 4 different colors A, B, C, D (30 x 4 = 120 beads in total) for 2 different ...
MarioPrix's user avatar
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1 answer
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'Well defined' in a biological context

Question The following model is an approximation of the discrete logistic model $x_{t+1} = f(x_t)$ where $$ f(x) = \begin{cases} \mu x, & 0 \le x \le 1/2,\\ \mu(1-x), & 1/2 \le x \le 1. \...
murpw2011's user avatar
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Having two sigmoidal functions with different rate constant, how can I prove that one starts decreasing before the other?

I have two sigmoidal functions that I've fitted to some experimental data. The formula that I'm using to fit the function to my data is the following: $$ f(t) = \frac{A}{1+e^{k(t-t_0)}} $$ Where $k$ ...
Matheus Schultz's user avatar
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80 views

Probability of a bp sequence in a DNA

Question: DNA is composed of two strands carrying a sequence of nucleotides: adenine (A), cytosine (C), guanine (G) and thymine (T). Nucleotides along the two strands pair (bond) with one another: A ...
AvadaMouse's user avatar
2 votes
0 answers
29 views

strategies for looking at the phase space of a system with 6 dimensions

I have a system of odes where the state vector has 6 elements. The system is a population biology model, where I am tracking the evolution of some competing species over time. Now I was trying to ...
krishnab's user avatar
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5 votes
1 answer
123 views

Confusion About Physical Interpretation of Complex Numbers

Alan Turing's paper, Chemical Basis of Morphogenesis, is about how a symmetrical embryonic stage(like a blastula) can create an asymmetric organism or pattern. He creates differential equations to ...
MeltedStatementRecognizing's user avatar
2 votes
1 answer
85 views

Where to learn about whether a travelling wave solution to the reaction diffusion equation is a pushed or pulled wave?

I'm trying to understand pushed and pulled waves as seen in many biology articles such as: Gene Surfing in Expanding Populations by Hallatschek Spatial gene drives and pushed genetic waves by Tanaka ...
Yous's user avatar
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1 vote
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98 views

Can I non-dimensionalize this system of delay differential equations?

I am looking at an application from population dynamics in biology and trying to understand the dynamics of system of delay differential equations below. The model is for a single species with a multi-...
krishnab's user avatar
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1 vote
1 answer
42 views

How would we measure the non-randomness and compactness of this cubic lattice and corresponding graph?

The genetic code is decrypted into a 4x4x4 cubic lattice shown here: https://www.researchgate.net/publication/361073909_Decryption_and_Topology_of_the_Genetic_Code That cube was used to construct an ...
Youvan's user avatar
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4 votes
1 answer
149 views

Counting DNA sequences that contain all dinucleotides exactly once

I'm trying to figure out how many unique DNA sequences minimally contain every possible dinucleotide sequence. I'm convinced that this is likely a solved combinatorics question, but I don't have the ...
Ian Hamilton's user avatar
1 vote
2 answers
64 views

How is this ODE created?

So what I got was this but it doesn't match the answer sheet so not sure what went wrong
Balkaran Mali's user avatar
0 votes
1 answer
72 views

The French Newbie and the Lotka-Voltera Crazy Idea

I am back to talk with you and to have criticisms on ideas crossing my mind! I am currently working on a disease that is striking french vineyards really hard. I am currently using a model that is ...
8mo1's user avatar
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0 votes
1 answer
123 views

Bacteria and logarithms problem. [duplicate]

You are taking a biology class and you are growing a colony of bacteria starting with 5 bacteria. Suppose the colony of bacteria is grow exponentially and can be modeled using the following function: ...
marksawnson's user avatar
1 vote
0 answers
29 views

Solving chromosome mapping problem using linear algebra?

In biology, we were given a problem in which we had to use "distances" (recombination frequency) between genes in order to create a genetic map of how genes are located relative to each ...
Zack's user avatar
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0 votes
0 answers
212 views

Using Jury Conditions to Show Instability

If I want to force an equilibrium point of a discrete dynamical system to be unstable can I just violate one of the conditions for stability stated in the jury conditions $$|\mbox{Trace} (J)| < 1 + ...
kmw1985's user avatar
2 votes
0 answers
152 views

Converting one form of the Gompertz equation into another

Consider the Gompertz equation that models the dynamics of the population of a single-species $$\frac{dN}{dt}=r_0e^{-\alpha t}N$$ and convert it to the following form $$\frac{dN}{dt}=\alpha N\ln\left(\...
user5896534's user avatar
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0 answers
280 views

Comparing solutions of logistic equation and Gompertz equation

Considering the Gompertz equation, $\frac{dN}{dt}=r_oe^{-\alpha t}N$, and the logistic growth equation, $\frac{dN}{dt}=rN(1-\frac{N}{k})$. How is the carrying capacity from Gompertz equation differ ...
user5896534's user avatar
1 vote
1 answer
294 views

Question in population dynamics using exponential growth rate equation

Given population doubles in 20 minutes, what is intrinsic growth rate r? Attempt: Given population doubles, using exponential growth rate we have $\frac{dN}{dt}=2N$ so $N(t)=N_0e^{2t}$ therefore r=2, ...
user5896534's user avatar
4 votes
2 answers
126 views

Comparison of bird diet at two different nests

I have a list with the different prey types and quantities that birds at Nest $1$ gave to their fledglings. I also have the same information for another nest of the same bird species. Suppose I have <...
Stephen H. Anderson's user avatar
1 vote
0 answers
54 views

On the initial conditions for bacterial population growth

I want to prepare an example of a differential equation for bacetrial growth. We have $\frac{dy}{dt}=ry(t)$ Multiplying by dt and moving y(t) over to the other side we get $\frac{1}{y(t)}dy=rdt$, ...
Superunknown's user avatar
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0 votes
1 answer
77 views

How do you call this system?

Is there a specific name for a dynamical system that depends on the relative indexation $i\pm k$ for some $k$? For example, consider the following dynamical system defined on a ring of cells by $$ \...
sam wolfe's user avatar
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3 votes
1 answer
79 views

Turing's Symmetries

In Alan Turing's classic paper on the Chemical Basis of Morphogenesis, the following bilateral and left-right symmetries are defined as follows: Might be an misunderstanding of English from my side, ...
sam wolfe's user avatar
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1 vote
0 answers
30 views

Can I use the number of particles rather than concentration in biological differential equations?

(This question is not specific to biology, but I was just wondering about a common way that people view differential equations in biology.) Some simple biological differential equations take the form $...
Raymond Hancock's user avatar
0 votes
1 answer
90 views

Finding units for constants in ODE's

$$ \begin{array}{r c l} \frac{dN}{dt} & = & rN\left(1-\frac{N}{K}\right)-\alpha \frac{NP}{\beta P + \gamma N} \\ \frac{dP}{dt} & = & \epsilon \frac{NP}{\beta P + \gamma N} - \delta P \...
Michael Doherty's user avatar
0 votes
1 answer
112 views

How to solve simple differential equation (biology)

First of all, I am a biologist and I am not really knowledgeable in mathematics. Thus, I apologize if what I am asking is naive or not fully explained. I am trying to solve analytically a differential ...
locoric_polska's user avatar
-1 votes
1 answer
136 views

Predator-Prey Model [closed]

Can anyone explain the biological interpretation on the right hand side of these equations please? $$ \begin{array}{r c l} \frac{dN}{dt} & = & rN\left(1-\frac{N}{K}\right)-\alpha \frac{NP}{\...
Michael Doherty's user avatar
0 votes
0 answers
25 views

What is Iteration Number in modeling?

I am a biologist. Referring to mathematical modeling for biological data in the literature. Could someone explain what is the "Iteration Number" of modeling and the meaning of the up and ...
Dendrobium's user avatar
1 vote
0 answers
31 views

Non-trivial, time-independent solution at long times for a separable solution of an age-structured model

I'm taking an introductory course on mathematical modelling in biology and am completely at a loss with this question. We are considering the PDE for a population of cells $n$ with age $a$ over time $...
user3709's user avatar
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1 answer
212 views

Simplify the following differential equation by variable scaling

We have: $\frac{dx}{dt}=\frac{a}{x+b}, a>0,b>0$. We make substitutes: $x\to\alpha h, t\to\beta \tau$. Then the differential equation will be: $\frac{\alpha}{\beta}\frac{dx}{dt}=\frac{a}{x+b}$, ...
AndVld's user avatar
  • 172
1 vote
1 answer
44 views

Probability of having an all-heterogeneous genotype

Find the probability that the genotype of an offspring will be $\mathrm{AaBbCcDdEeFfGgHhIiJj}$ from the cross $\mathrm{AaBbCcDdEeFfGgHhIiJj \times AaBbCcDdEeFfGgHhIiJj}$. Making a Punnett square for ...
soupless's user avatar
  • 2,354
3 votes
1 answer
154 views

Can SIR models explain reduction in COVID case numbers in Florida and Texas, despite lack of restrictions?

This is a question about SIR or SEIR models and understanding the trajectory of the covid infections in Florida and Texas in September 2021. This is a genuinely academic question, and not meant to be ...
krishnab's user avatar
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1 vote
0 answers
28 views

Expected Value for distinct substrings of length $k$

Genomes consist of 4 nucleobases (A, C, G, T). If we take genome substrings of length $k$ (called $k$-mers), we have $4^k$ theoretically possible substrings. If we have a genome of length $l$ (meaning ...
Karl Heifisch's user avatar

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