For questions regarding mathematical concepts with applications to Biology.
Questions tagged [biology]
405 questions
39
votes
2 answers
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 are apparently a building block for living…
Ed Pegg
- 21,868
30
votes
5 answers
Can mathematics get from other sciences what it got from physics?
Throughout history, physics has been an unparalleled source of '' inspiration'' for discovering/inventing mathematical ideas, which is due to its ability to describe the physical world. But can this connection be made as profoundly with other fields…
17
votes
4 answers
Mathematics applied to biology
Can anyone suggest reference material on mathematics applied to biology, in particular the study of the behavior of say simple unicellular organisms or cells? Ideally the level of complexity should be aimed at a competent undergrad. Thank…
asker
- 171
14
votes
4 answers
PDEs in biology
I am student who mostly heard lectures on partial differential equations and homogenization. But I really like the idea of working in biology or with biologists - but (with my lack of overview) it seems to me it's either statistics or some ODE…
jkkk
- 141
10
votes
2 answers
Does the matrix exponential have this convexity property?
Let $A$ be a real matrix (not necessarily symmetric) whose off-diagonal elements are all non-negative, so that the elements of the matrix exponential $\exp(A)$ are all non-negative. Let $\mathbf x$ be a vector whose elements are all non-negative.…
N. Virgo
- 7,904
9
votes
1 answer
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 the most important challenges of Mathematical…
Euler_Salter
- 5,547
9
votes
1 answer
Learning roadmap for mathematical biology
Which courses (at an undergrad level or master's level) in mathematics or statistics should be taken by a student aiming for a PhD in mathematical biology?
The basics I imagine are calculus courses, linear algebra and probability.
But then I would…
Desmond
- 91
- 2
8
votes
5 answers
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) Linguistics and natural language processing (e.g. J.…
FWE
- 1,915
8
votes
4 answers
Hexagonal vs square tiling: comparing total length of edges
Today I saw this short video: Why do honeybees love hexagons?
The video explains that bees want to store their food (honey) in appropriately sized cells and that wax -the thing that makes the cells- is quite 'expensive' for bees to create. So the…
Thanassis
- 3,225
8
votes
1 answer
How can I model the number of insects in a house?
I really don't know if this question applies here or if it makes sense, but I'm curious as to whether these ideas are commonly used.
Imagine you are in a room, this room has holes, where bugs may enter or leave. At any given time number of bugs…
Apprentice
- 269
- 1
- 4
7
votes
2 answers
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 half-steps (i.e., adjacent keys). For example, the…
Chris Wilson
- 293
7
votes
0 answers
How Turing instability explains the patterns present on the animal skin?
Alan Turing in his original paper presents the following system of differential equations:
$\frac{\delta X_r}{\delta t} = f(X_r, Y_r) + \mu(X_{r+1} -2X_r + X_{r-1})$
$\frac{\delta Y_r}{\delta t} = g(X_r, Y_r) + v(Y_{r+1} - 2Y_r + Y_{r-1})$
for $r…
mercury0114
- 410
7
votes
4 answers
Is there any research in mathematical biology that isn't heavy in differential equations?
I'm near the end of my pure math undergrad trying to decide what sort of math I'm interested in for graduate school. I've always thought the idea of mathematical biology was cool, but it seems like a lot of it is steeped in differential equations,…
Samuel Reid
- 5,172
7
votes
2 answers
Coloring the pentagonal hexecontahedron
So, I'd like to color the pentagonal hexecontahedron in a way that is satisfying aesthetically and mathematically. For me this equates to, in order of priority -
1. No same-colored faces can share an edge
2. We must use as few colors as possible
3.…
Hamish Todd
- 321
6
votes
1 answer
Find the value of a function with definite integrals
I am trying to understand a paper of Maynard Smith (1974), that connects biology with game theory. I don't want to overwhelm you with useless stuff, but I have this definite integrals:
$$E(m)=\int_0^m (v-x)p(x) dx - \int_m^\infty mp(x) dx …
Vaaal88
- 468