Questions tagged [biology]
For questions regarding mathematical concepts with applications to Biology.
402
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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/...
- 351
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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 ...
- 430
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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 ...
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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 ...
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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/...
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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 $G$-...
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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 ...
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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 ...
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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 ...
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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
$$
\left\{
\begin{array}{l}
\frac{d c}{d t}=r_c c(1-c)-\frac{c h}{c+\theta_1} \\
\frac{...
- 11
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Recovery Time for Logistic model equation with harvesting
We are given a logistic growth model with constant harvesting as:
$\frac{dN}{dt} = rN(1-\frac{N}{K})-Y_0$
We are asked to show that the recovery time for harvesting a yield $Y_0$, $T_R(Y_0)$, ...
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persistence of SEIR epidemic model
We have the following stochastic SEIR model
$dS=\Lambda - \beta SI - \mu S - \sigma SI dB(t)$
$dE=\beta SI - (\lambda +\mu) E+\sigma SI dB(t)$
$dI=\lambda E-(\gamma +\alpha +\mu) I$
$dR=\gamma I-\mu R$...
- 15
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Showing an endemic steady state is stable
I need to show that the steady state of this non-dimensional model is stable using minimal algebra however I am not sure how to approach this without long lines of working.
The model is:
$$\frac{dS}{...
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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:
$$
\...
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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 ...
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