# 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.

68 questions
0answers
36 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, ...
1answer
208 views

### How to study the global stability for this 3D system?

I am studying a biological system (HIV) and arrived at this simplified dynamical system: \begin{align} x_1' &= a_1 + a_2x_2 - a_1x_2 - a_4x_1 - a_5\frac{1+a_6x_3}{1+a_7x_3}x_1\\ x_2' &= a_5\...
0answers
26 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 ...
0answers
28 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 ...
1answer
54 views

### How to value the extent of separation or mixing of point sets in plane?

As the image presented below, the reddish point set is totally separated from the blueish one and the greenish one, while the blueish point set is quite mixed with the greenish one. A number of ...
0answers
239 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 ...
3answers
145 views

1answer
178 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. ...
1answer
120 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 over-...
1answer
307 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) ...
0answers
778 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 ...
0answers
73 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? ...
1answer
818 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 ...
1answer
376 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 Perron ...
0answers
140 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 ...
1answer
143 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 ...
1answer
160 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, ...
1answer
658 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 ...
0answers
108 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^...
1answer
531 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 ...
0answers
124 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 ...
6answers
4k 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 ...
2answers
484 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 ...
3answers
1k 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 voting/...
0answers
731 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 ...
4answers
368 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 ...