# Questions tagged [biology]

For questions regarding mathematical concepts with applications to Biology.

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### Travelling Wave Solution For Fisher Equation

I am working with the Fisher equation which I have non-dimensionalised as $$\frac{\partial u}{\partial t} = \frac{\partial^2 u}{\partial x^2} +u(1-u)$$ I am looking for ...
1 vote
54 views

### 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/...
1k views

### Model for population growth and finding the equilibrium solutions

A model for population growth is given by: $$\frac{dN}{dt} = f(N) = r N \left( 1-\frac{N}{K} \right) \left( \frac{N}{U}-1 \right)$$ where $r,\ U,$ and $K$ are positive parameters and $U < K$. (a)...
26 views

### 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 ...
113 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 ...
756 views

### Simulating a continuous-time Markov branching process

For my MMath dissertation I am exploring the medicinal applications of branching processes, including the Galton-Watson process, Bellman-Harris process ETC. I would like a way for these processes to ...
54 views

### 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 ...
505 views

### Hopf bifurcation and limit cycles

$$dV/dt=10(V-\frac{V^3}{3}-R+I_{input})$$ $$dR/dt=0.8(-R+1.25V+1.5)$$ Use $I_{input}$ as the relative parameter to prove that there these equations undergo 2 hopf bifurcations and indicate whether ...
87 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/...
52 views

### 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 $G$-...
1 vote
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 ...
147 views

### Coalescent theory - Why are coalescent times independent?

I am reading from this book and I want to make sure I understand what is going on. What I get from the book Consider a population of $N$ individuals. The population size ($N$) is constant. select ...
14k views

### The Scutoid, a new shape

The scutoid (Nature, Gizmodo, New Scientist, eurekalert) is a newly defined shape found in epithelial cells. It's a 5-prism with a truncated vertex. The g6 format of the graph is KsP`?_HCoW?T . They ...
59 views

### 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 ...
638 views

### Most Important Challenges in Mathematical Biology

This question is to everyone, but especially to whoever is doing a PhD in Mathematical Biology, to who is teaching Mathematical Biology and finally to who works or researches in this area. What are ...
67 views

### Interpreting replicator dynamic for simplest population model

Suppose the simplest population model where we track the size $y$ of a population: $$\frac{dy}{dt} = ry$$ for a positive constant $r$ and some $y$ such that $y(0) > 0$. For this population model ...
2k views

### Category Theory & Biology

Category theory is becoming more and more used in the following fields (besides others) (1) Quantum physics (e.g. C. Isham and B. Coecke et al) (2) General relativity (e.g. A.K. Guts et al) (3) ...
1 vote
82 views

2k views

### Measuring the Shannon entropy of an ordered sequence

I have 927 unique sequences of the numbers 1, 2 and 3, all of which sum to 12 and represent every possible one-octave scale on the piano, with the numbers representing the intervals between notes in ...
1 vote
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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 $k$ ...
72 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 ...
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 ...
121 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 ...
81 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 ...
1 vote
210 views

### Derivation R0 in a Next-generation Matrix

Following a couple of textbooks for an example, Brauer 2019 Models in Epidemiology, and in whichever paper i read regarding Next-generation-matrices they have defined, R0 as the spectral radius of the ...
1 vote
94 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-...
641 views

### SIR infection induced mortality

I am reading the book Modelling Infectious Diseases in Humans and Animals by Matt J Keeling and Pejman Rohani. In it the SIR model is given as, $\frac{dS}{dt} =\mu-\beta{S}I-\mu S$ \$\frac{dI}{...
1 vote
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 ...
146 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 ...
1 vote
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
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 ...
1 vote
2k views

### How to test if data follows a distribution?

Have been given some data and the question says to determine if the data follows any distribution. It says to compare the observed data vs expected graphically and to test further. The distributions ...
3k views

### biology models which uses a system of differential equations

I am trying to find mathematical models used in Biology that uses a system of differential equations. I found the lotka-volterra model and Michaelis-Menten kinetics but I would like to know more than ...
1 vote
642 views

### Calculate ssgsea score by hand

I hope this is the right place for this question, if not, feel free to suggest more suitable sites. I would like to calculate a single sample gene set enrichment analysis (ssGSEA) score step by step ...
9k views

### What are differences between Geometric, Logarithmic and Exponential Growth?

At past I have read in some ecology text that geometrical, logarithmic and exponential growths are not exactly the same thing; and there were various equations for them. (The book is not available to ...
119 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: ...
1 vote