The mathematical-modeling tag has no usage guidance.

**34**

votes

**1**answer

1k views

### 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 ...

**24**

votes

**6**answers

3k views

### 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 ...

**24**

votes

**7**answers

2k views

### 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 ...

**12**

votes

**4**answers

2k views

### How is differential geometry used in immediate industrial applications and what are some source to know about it?

Intuitively it might be clear that differential geometry is a very applicable subject in engineering and industry. I'd like to know how some industries/companies use differential geometry. I'd guess ...

**12**

votes

**3**answers

646 views

### Models for graphs representing real-life networks

I am interested in basic models of graphs (stochastic or deterministic) that are offered for real-life networks (like social networks, the Internet, neuron networks).
I will be thankful for answers ...

**12**

votes

**0**answers

753 views

### 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 ...

**12**

votes

**0**answers

358 views

### 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 ...

**9**

votes

**1**answer

355 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 ...

**7**

votes

**2**answers

838 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, ...

**6**

votes

**2**answers

443 views

### 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 ...

**5**

votes

**3**answers

887 views

### 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 ...

**4**

votes

**5**answers

9k views

### 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 ...

**4**

votes

**1**answer

1k views

### 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 ...

**4**

votes

**2**answers

572 views

### 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 ...

**4**

votes

**1**answer

963 views

### How can I generate the simulated time series

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

**4**

votes

**1**answer

142 views

### 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. ...

**4**

votes

**1**answer

217 views

### 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) ...

**3**

votes

**3**answers

1k views

### 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? ...

**3**

votes

**2**answers

871 views

### What's the name of this geometric mathematical modeling problem?

There is a right angle corner with width 1 in both directions. One wants to find the largest area shape which can pass through this corner.
I know that this is a famous problem, but what is it called?
...

**3**

votes

**5**answers

2k views

### 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 ...

**3**

votes

**1**answer

134 views

### Good broad review of agent-based modeling? [closed]

Trying to find some good review of agent-based models and networks, specifically models that are defined by a graph of interacting nodes, that covers analysis of collective behavior based on model of ...

**3**

votes

**2**answers

1k views

### 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). ...

**3**

votes

**1**answer

138 views

### 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, ...

**3**

votes

**0**answers

97 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 ...

**3**

votes

**0**answers

164 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 ...

**3**

votes

**0**answers

107 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 ...

**2**

votes

**1**answer

570 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 ...

**2**

votes

**2**answers

289 views

### Suggestions for dealing with the “timed” balls-into-bins model

Definitions: Let $T$ (for "time") be a random variable $T \sim \text{Exp}(\lambda)$ and $\Delta t$ is a realization (or called an observed value) of $T$. Let $D$ (for "delay") be a random variable $D ...

**2**

votes

**1**answer

307 views

### 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, ...

**2**

votes

**0**answers

330 views

### Programming workbooks in C++ and Research Math [closed]

I know the basics of C++ by taking a few courses and going through "C++ Primer" by Lippman. As a math graduate student, I would love to get my hands on some programming-math exercises geared towards ...

**2**

votes

**0**answers

132 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

**2**answers

234 views

### Curves similarity metric [closed]

I am working on an optical character recognition algorithm that takes vector data (i.e. polylines) as input rather than raster picture. E.g., we have N polyline samples, and when certain polyline is ...

**1**

vote

**2**answers

1k views

### 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 ...

**1**

vote

**1**answer

110 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 ...

**1**

vote

**1**answer

116 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 ...

**1**

vote

**2**answers

4k views

### 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 ...

**1**

vote

**1**answer

840 views

### 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 ...

**1**

vote

**0**answers

89 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

86 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 ...

**1**

vote

**0**answers

65 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

98 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 ...

**1**

vote

**1**answer

70 views

### SIRS Stability Analysis

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

**0**

votes

**1**answer

153 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 ...

**0**

votes

**4**answers

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 ...

**0**

votes

**1**answer

183 views

### 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 ...

**0**

votes

**1**answer

210 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 ...

**0**

votes

**0**answers

470 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

289 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 ...

**0**

votes

**0**answers

230 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 ...