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2
votes
0answers
86 views

Comprehensive survey on mathematical modelling of neural networks: from the basic ideas to contemporary research topics

I am looking for a comprehensive survey (paper(s) or book(s)) on mathematical modelling of neural networks (both artificial and biological). It should start from the very basic concepts of modelling ...
-3
votes
0answers
27 views

Model of function of 2 random variables [closed]

In my model W = f(E, K). f is a complex function (several operations on E and K). for any W, infinity pairs of (E, K) exist that satisfy f. E and K are between [0, +oo] I have observations for W ...
0
votes
0answers
26 views

SIRS Stability Analysis

I have set up the following ODE's for a SIRS model: $$\frac{dS}{dt} =-\alpha SI + \zeta R$$ $$\frac{dI}{dt} = \alpha SI - \beta I - \rho I$$ $$\frac{dR}{dt} = \beta I - \zeta R$$ ...
1
vote
0answers
36 views

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 ...
1
vote
0answers
51 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. ...
0
votes
0answers
26 views

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 ...
1
vote
1answer
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 ...
4
votes
1answer
171 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) ...
12
votes
0answers
712 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 ...
1
vote
0answers
62 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? ...
2
votes
1answer
376 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 ...
9
votes
1answer
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 ...
2
votes
0answers
114 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
1answer
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 ...
3
votes
1answer
125 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, ...
0
votes
1answer
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 ...
1
vote
0answers
91 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 ...
11
votes
0answers
327 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 ...
3
votes
0answers
98 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 ...
24
votes
6answers
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 ...
6
votes
2answers
420 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 ...
4
votes
3answers
602 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 ...
0
votes
0answers
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 ...
0
votes
4answers
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 ...
4
votes
1answer
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 ...
33
votes
1answer
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 ...
2
votes
5answers
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 ...
7
votes
2answers
670 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, ...
3
votes
1answer
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 ...
0
votes
0answers
268 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 ...
3
votes
2answers
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). ...
0
votes
0answers
215 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 ...
1
vote
2answers
777 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 ...
3
votes
4answers
5k 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
2answers
544 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 ...
1
vote
1answer
3k 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 ...
0
votes
1answer
176 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 ...
2
votes
1answer
298 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, ...
1
vote
1answer
705 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 ...
0
votes
1answer
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 ...
24
votes
7answers
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 ...
3
votes
3answers
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? ...