Questions tagged [mathematical-modeling]
This tag is used to refer to mathematical/probabilistic/statistical modeling questions, usually this tag is used to ask about questions that are related with the mathematical formalism of the model instead of the correctness of a specific model in practice.
117 questions
1 vote
0 answers
183 views
Statistical interpretation of systolic geometry
Probability distributions on the two-dimensional torus are widely used to model phenomena in protein chemistry [1]. A prominent example is the family of bivariate von Mises distributions. When the ...
- 241
4 votes
1 answer
283 views
When is one dynamical system an approximation of another?
I've been thinking about the question of when a discrete time dynamical system $f : X \to X$ (or possibly other objects) can be said to approximately model another dynamical system. So far I've mostly ...
- 141
2 votes
1 answer
273 views
Construction of Scherk's surface using soap films
I am currently interested in the differential geometry of minimal surfaces, and I have a rather trivial question regarding Scherk's surface (the one which can be parametrised by the real function $(x,...
anon
0 votes
0 answers
81 views
Question on the modelling of (viscous) fluid in a bag with holes
Consider some fluid (as nice as possible) in a plastic bag with holes illustrated by the image below (of course no holes have been drawn in this picture) What is the corresponding PDE to model the ...
- 1,416
5 votes
0 answers
326 views
How to play golf in one dimension?
One-dimensional golf is a function $g$ on $\mathbb R$ such that $g(x)= 1+\min_\mu E[g(x+N(\mu,c\mu^2))]$ if $|x|>1$ and 0 if $|x|\le 1.$ Here $N$ is the normal distribution, whose mean $\mu$ you ...
- 19.7k
0 votes
1 answer
316 views
How to force my differential equations give a bounded solution?
I have modeled the interaction of two physical quantities, $S$ and $B$, by the following differential equations (the second one is a delay differential equation): $$S'(t) = 0.31 S(t) \Big( 1 - \frac{S(...
user517860
0 votes
1 answer
263 views
How to integrate an indicator function/constraint into the cost function of a linear program?
I have a mathematical model $P$ for which I optimize two cost functions say $F_1$ and $F_2$ subject to a set of constraints $C1$–$C10$. In $F_2$, I want it to be included only when its expression ...
- 3
0 votes
0 answers
95 views
Gaussian white noise model in application
I am interested in applications (to data) of non-parametric statistics, and my question concerned the Gaussian white noise model defined by, $$ X_{t_1, \ldots, t_d}=f\left(t_1, \ldots, t_d\right) d ...
- 93
0 votes
1 answer
383 views
Poisson Process x SIR model [closed]
Consider the simplest SIR model: $$S'=-a SI$$ $$I'=a SI - b I$$ $$R'=b I$$ It is known that the waiting time of an infeccious person in the compartment $I$ follows an exponential behavior with rate $b$...
- 123
1 vote
0 answers
124 views
How to smoothly interpolate gravitational field between trajectories in high dimension?
I'm looking for the adequate numerical interpolation technique to solve the following problem. This is probably trivial for physicists who study gravitational fields, but I didn't find clear answers ...
- 19
5 votes
1 answer
254 views
Equation in epidemic SIR model with the influence of vaccinations
I am currently preparing a presentation on different modifications of the SIR model. In my sources about the use of vaccines, I came across the following model for a specific rate at which the ...
- 51
1 vote
0 answers
117 views
Advice on constructing a Non-structural Flood Mitigation Model [closed]
I am not sure if this is the right site to post this. But I seek some valuable suggestions, and I believe I can get them here. At present, I am in the final semester of my BSMS Mathematics course. I ...
- 119
3 votes
0 answers
147 views
Mathematical formulation of beam: get stress/strain from forces and momentum
I'm working with static beams with Euler–Bernoulli model which ODE is $$ \dfrac{d^2}{dx^2} \left(EI \cdot \dfrac{d^2w}{dx^2}\right) = q(x). $$ With a beam along the $x$ axis, the solution consists of ...
- 273
1 vote
2 answers
605 views
Why should the logarithmic series distribution model the number of "Items" bought?
Suppose you're a shopkeeper in the business of selling Items. An "Item" is a thing whose only property is that the quantity that can be bought by a purchaser must be a positive integer; all ...
- 12.8k
3 votes
0 answers
127 views
Turing reaction diffusion equations and neural networks
Suppose you have a Turing-type reaction-diffusion system $$ \begin{cases} \partial_t \phi = & f(\phi, \psi) + D_\phi \nabla^2\phi \\ \partial_t \psi = & g(\phi, \psi) + D_\psi \nabla^2\psi \...
3 votes
1 answer
228 views
Mechanics: Model beam using differential vectorial formulation
At the Wikipedia there are the differential formulation for Euler-Bernoulli Beam \eqref{1} and Timoshenko Beam \eqref{2} $$ \begin{align} &\dfrac{d^2}{dx^2}\left(EI\dfrac{d^2w}{dx^2}\right) = q(x) ...
- 273
3 votes
0 answers
314 views
How to mix Lagrange mechanics + KKT conditions?
Question: How can I mix the concepts of Lagrange Mechanics and KKT conditions? I've learned that Lagrange Mechanics derivation comes from variational calculus, and in some formulations, we can add ...
- 273
2 votes
1 answer
425 views
Examples of ODEs with complex constant coefficients and applications to physics?
This question is asked on stackexchange: Are there examples for ODEs with complex coefficients with applications in physics? but received no answers. I am reposting it here on the hope that it catches ...
- 790
0 votes
0 answers
62 views
What is the meaning of column integrated fluxes?
I am solving an equation where one term $\bar{P}$ is given and is called the integrated column flux. In the equation, the term $P$ is the precipitation. I am doing this on the discrete domain. Anyone ...
- 101
0 votes
0 answers
45 views
How to define Mock Hadley Cell in mathematical modeling?
I am computing a force term in which one component is $F_{ext}$. To define this, the following content given in the paper. To capture the possible large-scale effects on precipitation clusters, we ...
- 101
0 votes
3 answers
1k views
Integer linear constraint(s) for y= x1 XOR x2 [closed]
Is there any way to convert $y=x_1~ \text{XOR} ~x_2$ to linear constraints? It means we write some linear relations with: if $x_1=x_2 =0$ or $x_1=x_2=1$ $\to$ $y=0$, else, $y=1$?
- 25
1 vote
1 answer
119 views
Resources/Reading Materials on PASA (optimal control theory)
I am currently working on my undergraduate thesis, and my adviser suggested that I look into a Polyhedral Active Set Algorithm (PASA) for my paper. I have been trying to find resources/materials on it ...
- 149
2 votes
1 answer
287 views
Literature on reaction diffusion equations
My research area is age structure modelling, basically when applied to reaction diffusion equations. We mainly discuss the existence of travelling wave solutions; I want to work on the stability of ...
- 21
2 votes
0 answers
134 views
How to quantify the non-commutativity of human body motion? [closed]
Some years ago, there was that question on this forum:"How to quantify noncommutativity?". I am asking that question in a context, human movement, which implies kinematic chains (like in ...
1 vote
0 answers
101 views
Real life applications of distributions through models or simulations [closed]
What are the areas we can apply distributions in classical harmonic analysis? I don't mean probability distributions but distributions that are continuous linear functionals on the space of test ...
- 91
6 votes
1 answer
382 views
Current status on Richardson's model (growth model)
A very simple stochastic growth model on a lattice is the Richardson's model (Actually originally defined by Murray Eden in the 60s). Each point of the lattice can be either occupied or vacant, once ...
- 304
2 votes
1 answer
169 views
Reference request: probabilistic models on climate (change)
I am looking for probabilistic models to address climate change. Are they known in the existing literature? I have found the post Math behind climate modeling. concerning PDE models. Many thanks for ...
user128095
1 vote
0 answers
105 views
Canonical representation of the a probability distribution for Hammersley Clifford Theorem
I'm reading the following paper http://www2.stat.duke.edu/~scs/Courses/Stat376/Papers/GibbsFieldEst/BesagJRSSB1974.pdf On page 7 they give the result that $$Q(\textbf{x}) = \sum_{1 \leq i \leq n} ...
- 913
1 vote
0 answers
116 views
Discrete-time model for spread of information when the probability of information transfer between each pair is known
[This question is cross-posted from MSE.] I'm interested in the behaviour of the following sort of system. We are given: a finite set $X$, a subset $A_0 \subset X$, and a function $f : X \times X \to [...
6 votes
1 answer
595 views
Graphs resembling the math genealogy graph must have concentration in a small number of families?
I was talking with a non-mathematician the other week at a workshop about the fact that many mathematicians, like myself, are indexed in the math genealogy database. We talked a little about how many ...
- 3,269
2 votes
1 answer
140 views
Introductory literature on the Voter Model
I am looking for a good introduction to the voter model appropriate for the Bachelor-Maths level (Europe). I need something that introduces the model on a low level, as a Glauber dynamics or similar. ...
- 121
2 votes
1 answer
507 views
Logistic sequence convergence
1) How can we prove that the logistic sequence $$x_{n+1}=rx_n(1-x_n),\ x_1=a\in (0,1)$$ converges to $\frac{r-1}{r}$, for $r\in [1,3]$? 2) Also I wonder how can we prove that the sequence $(x_n)_{n\in\...
- 2,029
3 votes
1 answer
188 views
What is the ideal form of an h-curve?
This question concerns mathematical modelling of the citation curve, well-known in the sciencemetry. The citation curve (or else the $h$-curve) of an individual researcher is the vector $(c_1,c_2,\...
- 44.2k
3 votes
0 answers
172 views
Notions of "completeness" and "sufficiency" of a mathematical model
I'm modelling a real-world problem as having instances $i$ in a set $P$. As a very simple artificial example, consider the problem of choosing a meeting room given a certain number of people. Then $i =...
- 139
5 votes
1 answer
1k views
Generalized linear models: What's the benefit of the underlying theory?
I was recently trying to understand generalized linear models (GLMs) and after investing quite a few days, it still hasn't dawned on me what the fundamental benefit of the framework is. Normally, I am ...
- 161
1 vote
0 answers
150 views
Next-generation matrix of infectious disease
If the population is classified into $\mathbf{S}$, $\mathbf{E}$, $\mathbf{I}$ and $\mathbf{R}$ compartments such that \begin{equation} \label{eq4} \begin{aligned} \mathbf{S} &=\dfrac{S_{1}N_{1}+...
6 votes
2 answers
348 views
Searching for an early, highly theoretical, even philosophical, math paper on models or small-world networks
All I can remember is that it was very high-level / abstact and kind of philosophical, explaining (the discovery or interdependence of) small world networks. I assume that it was +50 years old and '...
- 103
6 votes
1 answer
364 views
Time of peak of an SIR epidemic
I've learned some classical results on the peak and the attack rate of an idealized epidemic which evolves according to a SIR model $\dot{s} = -\beta\cdot i \cdot s$ $\dot{i} = +\beta\cdot i \cdot s -...
- 9,934
4 votes
1 answer
3k views
How to mathematically characterize a feedback loop in ODEs?
I have a biological system that exhibits a feedback type of behavior. The diagram is a schematic of the system of ODEs. In this system, the total amount of $x_1, x_2, x_3$ is conserved; however, there ...
- 513
4 votes
2 answers
371 views
Approximated solutions of SEIR models
Numerical solutions of the SEIR equations (describing the spreading of an epidemic disease) – or variations thereof – $\dot{S} = - N$ $\dot{E} = + N - E/\lambda$ $\dot{I} = + E/\lambda - I/\delta$ ...
- 9,934
3 votes
0 answers
126 views
Image restoration quality general lower bounds
A typical image restoration model posits that, starting from a true image $f = f(x,y)$, we observe $$ \tilde f = f \star h + n $$ where $\star$ is convolution, $h$ is the point spread function (caused,...
- 1,069
2 votes
0 answers
97 views
SIR model constraint [closed]
During these past months, I've heard a lot about some pandemic modelling techniques, specially the so-called SIR model. Before I begin, I'd like to stress that my interest and question are just a ...
- 3,645
1 vote
1 answer
311 views
How many persons pass your 1.5 meter neighbourhood during 1 week ? If the distribution is power law what is the exponent?
Consider a graph with vertices being people (in some region), and make an edge if one person pass another closer than say 1.5 meter during say one week. (Such a graph might be thought a kind of ...
- 26.3k
12 votes
6 answers
1k views
Suggestions for reducing the transmission rate?
What are suggestions for reducing the transmission rate of the current epidemics? In summary, my best one so far is (once we are down to the stay home rule) to discretize time, i.e., to introduce the ...
9 votes
4 answers
1k views
Virus community spread mathematical modeling [closed]
What is the basic math behind the Virus community spread mathematical modeling,and how the time variable;(in these models),interacts with knowledge (data)?. I am not asking about how the virus is ...
0 votes
1 answer
1k views
Reflecting Boundary conditions for advection-diffusion equations
I am trying to model the dynamics of phytoplankton in a water column using one-dimensional advection-diffusion partial differential equations. $$\frac{\partial P}{\partial t}= D\frac{\partial^2 P}{\...
31 votes
7 answers
6k views
Applications of mathematics in clinical setting
What are some examples of successful mathematical attempts in clinical setting, specifically at the patient-disease-drug level? To clarify, by patient-disease-drug level, I mean the mathematical work ...
29 votes
15 answers
5k views
Unconventional examples of mathematical modelling
I'll soon be teaching a (basic) course on mathematical control theory. The first part of the course will focus on mathematical modelling of dynamical systems. More precisely, I will present examples ...
1 vote
0 answers
94 views
A mathematical area capable of describing nonstationary game-like problem [closed]
Here is my definition of the problem that I am trying to model: Let's have two agents and an environment. Each agent can do two types of actions. They are either supporting the environment or don't. ...
- 111
0 votes
0 answers
158 views
Global stability question for system with a unique locally-asymptotically-stable steady state
I have an ordinary differential system of dimension 3 that contains a locally-asymptotically-stable unique fixed point. Additionally, the system is strictly-positively invariant and bounded. Now, ...
- 513