# 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/...
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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 ...
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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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### 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 $k$ ...
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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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-...
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### 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 ...
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### 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 ...
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1 vote
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### 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
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### 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 ...
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### 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: ...
1 vote
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### 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 ...
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### 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 ...
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### 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, ...
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### 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 <...
1 vote
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 $\frac{1}{y(t)}dy=rdt$, ...
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### 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 ...
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### 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}{\...