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
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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
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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 ...
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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
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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 ...
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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 ...
- 19.8k
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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):
$$S'(t) = 0.31 S(t) \Big( 1 - \frac{S(...
user517860
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How to integrate an indicator function/constraint into the cost function of a linear program?
I have a mathematical model $P$ for which I optimize two cost functions say $F_1$ and $F_2$ subject to a set of constraints $C1$–$C10$.
In $F_2$, I want it to be included only when its expression ...
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Gaussian white noise model in application
I am interested in applications (to data) of non-parametric statistics, and my question concerned the Gaussian white noise model defined by,
$$
X_{t_1, \ldots, t_d}=f\left(t_1, \ldots, t_d\right) d ...
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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
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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 ...
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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 ...
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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
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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
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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
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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
\...
