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.
35
questions with no upvoted or accepted answers
5
votes
0
answers
234
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 ...
4
votes
0
answers
579
views
Models used for the Zika virus?
I am currently teaching an ordinary differential equations course, and am thinking about doing a module on infectious disease models, e.g. SIR/SIRS. I thought, if possible, it would be nice to ...
4
votes
0
answers
149
views
The Damworld model of Hamilton and Henderson
I've been reading some of the literature around Lovelock and Watson's famous Daisyworld earth-system model. It is a simple non-linear system of ODEs that illustrates various interesting principles in ...
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 ...
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 ...
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 =...
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,...
3
votes
0
answers
368
views
How to promote a blog?
Math behind might be interesting.
Quite recent bloggingg activity might have interesting math model.
The point is that bloggers compete for subscribers and at the same time
cooperate gaining ...
3
votes
0
answers
319
views
What mathematical models can analyze and optimize systems based on gossip?
I look for a mathematical model that can accommodate, analyze and suggest optimizations for a system that can be humanly described as people gossiping about stuff.
System description:
We have a ...
2
votes
0
answers
51
views
Finding a queuing model for waste accumulation
I've been tasked with modeling the accumulation of solid waste in an urban setting. In particular, the objective is to find the steady state distribution describing the amount of waste in a given ...
2
votes
0
answers
162
views
Solve 4th order ODE with variable coefficients
I am trying to solve a 4th order boundary value problem with variable coefficients, namely the problem of a rotating cantilever beam:
$u'''' - \frac{((1-x^2)u')'}{2\eta} - \frac{\alpha}{\eta}((1-x)u')...
2
votes
0
answers
143
views
Optimization over Spectral Laplacian in cycles and trees
Is there any idea on how one can deal with an optimization problem of sum of k largest eigenvalues(min) of Laplacian matrix of a simple cycle or tree?
I would like to use semidefinite programming for ...
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 ...
1
vote
0
answers
78
views
Turing reaction diffusion equations and neural networks
Suppose you have a Turing-type reaction-diffusion system
$$
\begin{cases}
\partial_t \phi = & f(\phi, \psi) + D_\phi \nabla^2\phi \\
\partial_t \psi = & g(\phi, \psi) + D_\psi \nabla^2\psi
\...
1
vote
0
answers
73
views
Canonical representation of the a probability distribution for Hammersley Clifford Theorem
I'm reading the following paper
http://www2.stat.duke.edu/~scs/Courses/Stat376/Papers/GibbsFieldEst/BesagJRSSB1974.pdf
On page 7 they give the result that
$$Q(\textbf{x}) = \sum_{1 \leq i \leq n} ...
1
vote
0
answers
87
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 [...
1
vote
0
answers
125
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}+...
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 ...
1
vote
0
answers
81
views
Ratio dependent predator prey model
In the article on Global qualitative analysis of a ratio-dependent predator–prey system- Kuang, 1998
The system is
where a, K, c, m, f, d
are positive constants that stand for prey intrinsic ...
1
vote
0
answers
40
views
Latent Dirichlet Allocation on Contrived Data
I am doing a project that seems like it might be susceptible to Latent Dirichlet Allocation. However, my data is highly contrived (both in test cases and use cases) and my "words" don't come close to ...
1
vote
0
answers
123
views
In search for analytical solutions for sixth order nonlinear PDE
I am modelling the nonlinear behaviour of an bubble in hot water. I am trying to explain it's rotational, vibrational and translational motion in water with impurities and subject to varying ...
1
vote
0
answers
165
views
A mathematical biology reference request
Is there any mathematical articles that describe the differential equation modelling of locomotion of amoeba using pseduopodia? I am looking for physics based models of pressure difference modeling of ...
1
vote
0
answers
111
views
Notions of consistency / heterogeneity in sets of vector values?
The problem
Let us consider a row vector u of size $n\in\mathbb{N}$, containing only binary values (0,1):
$$u=(u_1 \cdots u_n), n\in\mathbb{N}$$
$$\forall i \in \{1\ldots n\}, u_i \in\{0,1\}$$
I would ...
1
vote
0
answers
75
views
Are there any known bounds on the value of solutions of linear integer programming?
Given a linear objective function and a system of linear constraints; are there any known bounds on the values of (positive) integral solutions in terms of the coefficient matrix of the constraints?
...
1
vote
0
answers
118
views
Influence of parameter variations on the solution of an ODE system
Hello community,
suppose we are given a system of ODEs
\begin{align}
x'(t) &=f(x(t),p) \newline
x(0) &= x_0
\end{align}
where $f\in C^1(U,\mathbb{R}^n)$, $U\subseteq \mathbb{R}_{+}^n\times R^...
1
vote
0
answers
284
views
Use Lie Sub-Groups of GL(3, R) for elastic deformation ?
I'm interested in representing elastic deformations (e.g. stretching) using Lie groups. There are a few references to using $GL(3,\mathbf{R})$ but I'm wondering if possible to use subgroups of $GL(3,\...
0
votes
0
answers
12
views
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 ...
0
votes
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 ...
0
votes
0
answers
35
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 ...
0
votes
0
answers
36
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 ...
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 ...
0
votes
0
answers
106
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, ...
0
votes
0
answers
70
views
If $(Φ^x)_{x∈ℝ}$ is a family of real-valued stochastic processes and $B$ is a Brownian motion, then $\int_0^tΦ^x_s\:dB_s=(\int_0^t\Phi_s\:dB_s)(x)$
Let
$T>0$
$(\Omega,\mathcal A,\operatorname P)$ be a probability space
$(\mathcal F_t)_{t\in[0,\:T]}$ be a complete filtration on $(\Omega,\mathcal A)$
$B$ be a (standard, real-valued) $\mathcal F$...
0
votes
0
answers
1k
views
Covariance matrix/kriging interpolation
I have a covariance matrix that I am trying to interpolate using kriging interpolation. The point of the kriging is to statistically predict any unknown point in-between know points. For example if I ...
0
votes
0
answers
582
views
Orthogonal Projections in Lie Theory
I have been studying a finite element method where rigid & elastic spatial motions are separated using an orthogonal projection (actually two: one for translations/stretches, the other for ...