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.

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Understanding relation of 2 dependent, integral equations which are nested in a Bayesian Expectation

I'm trying hard to try understand the recursive nature between two equations in a recent macroeconomics paper, but my question mainly relates to how mathematically such recursive equations can depend ...
Justin Lee's user avatar
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0 answers
49 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 ...
GJC20's user avatar
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5 votes
0 answers
232 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 ...
domotorp's user avatar
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0 votes
1 answer
249 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(...
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1 answer
110 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 ...
LyLa's user avatar
  • 3
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0 answers
34 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 ...
BabaUtah's user avatar
0 votes
1 answer
221 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 $b$...
Quiet_waters's user avatar
1 vote
0 answers
84 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 ...
Youcef's user avatar
  • 19
5 votes
1 answer
204 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 ...
Rick's user avatar
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1 vote
0 answers
83 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 ...
Usual_Learner's user avatar
3 votes
0 answers
93 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 ...
Carlos Adir's user avatar
1 vote
2 answers
472 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 ...
Michael Hardy's user avatar
1 vote
0 answers
78 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 \...
Alberto Carraro's user avatar
2 votes
1 answer
151 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) ...
Carlos Adir's user avatar
3 votes
0 answers
166 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 ...
Carlos Adir's user avatar
2 votes
1 answer
346 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 ...
Medo's user avatar
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0 answers
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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 ...
User124356's user avatar
0 votes
0 answers
27 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 ...
User124356's user avatar
0 votes
3 answers
607 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, $y=1$?
A.R.S's user avatar
  • 25
1 vote
1 answer
82 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 ...
Gab Romero's user avatar
2 votes
1 answer
202 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 ...
mathemaniac's user avatar
2 votes
0 answers
101 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 ...
julien lagarde's user avatar
1 vote
0 answers
77 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 ...
Lateef's user avatar
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6 votes
1 answer
287 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 ...
Sam's user avatar
  • 261
2 votes
1 answer
135 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 ...
user avatar
1 vote
0 answers
73 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} ...
Pavan Sangha's user avatar
1 vote
0 answers
86 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 [...
TheMoreTheMerrier's user avatar
6 votes
1 answer
483 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 ...
Josiah Park's user avatar
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2 votes
1 answer
82 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. ...
Peter Strouvelle's user avatar
2 votes
1 answer
367 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\...
Bogdan's user avatar
  • 1,330
3 votes
1 answer
150 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,\...
Taras Banakh's user avatar
  • 40.7k
3 votes
0 answers
130 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 =...
Peeyush Kushwaha's user avatar
5 votes
1 answer
684 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 ...
Manuel Huppertz's user avatar
1 vote
0 answers
124 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}+...
Asrat  M. B.'s user avatar
6 votes
2 answers
292 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 '...
bambamfox's user avatar
  • 103
6 votes
1 answer
271 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 -...
Hans-Peter Stricker's user avatar
4 votes
1 answer
2k 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 ...
Paichu's user avatar
  • 513
4 votes
2 answers
259 views

Approximated solutions of SEIR models

Numerical solutions of the SEIR equations (describing the spreading of an epidemic disease) – or variations thereof – $\dot{S} = - N$ $\dot{E} = + N - E/\lambda$ $\dot{I} = + E/\lambda - I/\delta$ ...
Hans-Peter Stricker's user avatar
3 votes
0 answers
110 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,...
Elena Yudovina's user avatar
2 votes
0 answers
70 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 ...
IamWill's user avatar
  • 3,151
1 vote
1 answer
278 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 ...
Alexander Chervov's user avatar
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 ...
8 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
817 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}{\...
user151619's user avatar
30 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
4k 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
69 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. ...
zajer's user avatar
  • 111
0 votes
0 answers
105 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, ...
Paichu's user avatar
  • 513
7 votes
1 answer
428 views

How to study the global stability for this 3D system?

I am studying a biological system (HIV) and arrived at this simplified dynamical system: \begin{align} x_1' &= a_1 + a_2x_2 - a_1x_2 - a_4x_1 - a_5\frac{1+a_6x_3}{1+a_7x_3}x_1\\ x_2' &= a_5\...
Paichu's user avatar
  • 513
1 vote
0 answers
41 views

Mathematical modeling of multi-site reaction-diffusion

(I asked a similar question on Mathematics SE, but based on the Help section it might be better suited for this site, as it is focused on research-level mathematical modeling.) I am wondering if ...
Mowgli's user avatar
  • 111