The mathematical-modeling tag has no wiki summary.

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### SIRS Stability Analysis

I have set up the following ODE's for a SIRS model:
$$\frac{dS}{dt} =-\alpha SI + \zeta R$$
$$\frac{dI}{dt} = \alpha SI - \beta I - \rho I$$
$$\frac{dR}{dt} = \beta I - \zeta R$$
...

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### Non overlapping boxes with constraint modelling [closed]

I'm stucked with this problem for 2 days and i've finished the ideas. Any hint is appreciated.
Given a set of squares (2x2, 3x3, 4x4, 5x5), and a rectangular grid (9x7) place the squares on the grid ...

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### Interpretation for a condition in fluid dynamics

I have been working with some mathematical models in biology and fluid mechanics. My problem is about
the interpretation of a condition that I found for a vector
representing the velocity of a fluid. ...

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### convection/transport with different velocities

What is the prototypical model for convective transport of a quantity whose constituents move with constant but varying velocities?
In order to illustrate what a mean:
Suppose that a large number of ...

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**1**answer

97 views

### Solution of General Parametric Oscillator

I am wondering if there is a general solution for this ODE
$\ddot X +2\gamma \alpha \dot X + (\alpha+S(t)) X = \beta $
the dot represents time derivative, and $\gamma>1$, so it is in the ...

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### Concurrency related problems in $n$ independent, parallel $M/M/1$ queues

Queueing Model:
Consider $n$ independent, parallel $M/M/1$ queues with identical arrival rate $\lambda$ and service rate $\mu$. For each $M/M/1$ queue, we use the FCFS (First Come First Served) ...

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### Malaysia Airlines Flight 370? [closed]

News reports about Flight 370's disappearance have given a sketchy idea of how hourly pings to a satellite have helped build up a picture of where it went.
From a naive intuitive point of view, if ...

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### 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?
...

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374 views

### What are the uses of Limits and Colimits of Category Theory in every day problems? [closed]

I am interested in knowing how we can use the concepts of Limits and Colimits in modeling problems in every day life? Could anyone provide (Software) engineering examples, perhaps? Or describe ...

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314 views

### Coherence between different ranking methods of a graph's vertices

Given a (connected) graph $G$ it is natural to want to rank its vertices, with the more "central" vertices ranked higher.
Two natural ways of doing it are:
By the degrees.
By the entries in a ...

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### 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 ...

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**1**answer

107 views

### Modeling concurrent internet users

I'm feeling generous in the new year and want to open my Wifi connection to the public. I want to estimate the effect that $N$ additional users on my router would have on download times. In other ...

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**1**answer

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### The discrete theory of compressible fluids dynamics

I am working on the discrete theory of compressible fluids dynamics, i.e., numerically solving and simulating the compressible fluids , we are interested in the way using discrete exterior calculus, ...

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**1**answer

164 views

### How many ways we know to join two line segments with a smooth transitional function?

This topic was created to discuss how many ways we know to create piecewise linear functions with smooth transitions between the phases. An alternative is presents by Bacon & Watts (1971):
the ...

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### 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 ...

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### Which limit to take as a key applied math decision

The Borel-Kolmogorov paradox refers to situations where non-uniqueness in the notion of conditioning on a set of measure zero leads to apparent contradictions. As a formal matter, one requires ...

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### 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 ...

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### I know that you know…

A bit unsure if the following vague question has enough mathematical content to be suitable upon here. In the case, please feel free to close it.
In several circumstances of competition, a particular ...

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### Implications of a hypothetical blow-up of Navier-Stokes for the mathematical model

Let us suppose that there exists a (initially smooth) solution of NSE that blows up in finite time. Then, in particular, the corresponding velocity field becomes unbounded as time progresses. Which ...

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### Mathematical modeling of voting/rating (e.g. political elections, questions on MO, gadgets on amazon,…)

We need to make choices in our life and so we need to compare(=rate) things what is good what is bad. Question: are there some mathematical models which may capture features of some kind of ...

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342 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 ...

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352 views

### Recovering a function from a set of approximations

We assume that we have a finite set of agents with approximate knowledge about a certain function, and from this collection of approximations we want to recover the actual value of the function.
More ...

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**1**answer

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### Squared residuals versus just residuals?

In statistics (in particular time series analysis, like ARCH/GARCH models) I've noticed that residual diagnostics usually look at autocorrelation of residuals and squared residuals. Why both? What ...

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### Modeling question: how often does “the world's oldest person” die?

This story yesterday (no need to follow the link to understand the question!)
http://www.cnn.com/2011/US/02/01/texas.oldest.person.dies/index.html?hpt=T2
reminds me that I've often wondered about ...

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### Matlab book recommendation

Which book or books do you recommend that cover advanced engineering topics and problem solving using matlab?
I already finished a very good introductory book and i want something more advanced.
Do ...

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669 views

### How does a tournament's structure affect the likelihood that the best player will win?

Background
The origin of this question is a conversation I had with some friends a few years ago. At the time, Roger Federer and Tiger Woods were dominating professional tennis and golf, ...

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**1**answer

348 views

### How I can generate the simulated time series

I am curious how one can generate simulated time series data.I fount a list of simulated series here and a similar tool for stock market. What is best way to generate domain specific time series data ...

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### 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 ...

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### Physical Meaning of Constant Velocity Gradient

I'm interested in representing homogeneous elastic deformations using Lie groups/algebras. Homogeneous deformations are those with a deformation gradient F which depends only on time (not position). ...

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### 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 ...

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### Regular vs. Irregular Vertices in a Mesh

Hi everybody,
Reading about Geometry Processing, I have realized that people in this area are very interested in regular vertices(degree=6) rather than irregular ones.
Can anybody give me reasons ...

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### Resultant probability distribution when taking the cosine of gaussian distributed variable

I am trying to do a measurement uncertainty calculation. I have a gaussian distributed phase angle (theta) with a mean of 0 and standard deviation of 16.6666 micro radians. The variance is the ...

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### Mathematical means of studying large and complex but finite systems?

I want a list of the sort of mathematics/mathematical tools that are applied to the study of complex and probabilistic systems in order to make quantitative and qualitative observations about their ...

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### Which way is the right way to calculate auto correlation function

Fluorescence correlation spectroscopy (FCS) is a common technique used by physicists, chemists, and biologists to experimentally characterize the dynamics of fluorescent species.
The key of the ...

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### Modelling Construction

What would be the best way create a mathematical model of the construction of a large complex structure such as a high-rise building? It is preferable to model the 'people' rather than the actual ...

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### Switching function for Bang-Bang nagivation

I'm attempting to develop an equation to determine the "switching time" for a control system. I've managed to work out a specific solution for when starting and ending velocities are are the same, ...

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### Mathematical modeling - how to calculate the displacement at any point in a membrane

I'm trying to calculate the displacement of a wall at any point due to a point source of vibration. The vibration is considered to be directly perpendicular to the surface of the wall, for calculation ...

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150 views

### Introductions to Disease- and Price-Modeling

I'm looking for resources (anything from short articles to books) about building mathematical models or computer simulations of 'things that happen' in populations.
Specifically, I'm curious about ...

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### Does every ODE comes from something in physics?

Not sure if this is appropriate to Math Overflow, but I think there's some way to make this precise, even if I'm not sure how to do it myself.
Say I have a nasty ODE, nonlinear, maybe extremely ...

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### Mathematical definition of running [closed]

This will be a tad hard to explain, so bear with me. Taking into account only the legs what would be an accurate definition of the position of the upper legs, lower legs and feet with respect to time? ...