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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.

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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, ...
6
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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\...
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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 ...
2
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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 ...
3
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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 ...
2
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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 ...
5
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3answers
145 views

Removing outliers from circular average data

I'm trying to find the average from a set of circular data and am using the following which is doing what I'm expecting. $$a = \arctan\left(\frac{\sum\limits_{i=1}^N \sin(a_i)}{\sum\limits_{i=1}^N\...
2
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1answer
68 views

Simulating Fisher Equation (FKPP)

I'm researching about microbial growth (on 2D). I think that a microbial population can be modeled by the Fisher equation (any other suggestion is welcomed). My doubt is about how can I solve ...
1
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1answer
198 views

Math behind climate modeling.

Let me start with a purely mathematical question. What are the partial differential equations used in modeling our climate? I do mean the exact mathematical description. What are the initial ...
2
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0answers
121 views

Solve 4th order ODE with variable coefficients

I am trying to solve a 4th order boundary value problem with variable coefficients, namely the problem of a rotating cantilever beam: $u'''' - \frac{((1-x^2)u')'}{2\eta} - \frac{\alpha}{\eta}((1-x)u')...
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0answers
53 views

Ratio dependent predator prey model

In the article on Global qualitative analysis of a ratio-dependent predator–prey system- Kuang, 1998 The system is where a, K, c, m, f, d are positive constants that stand for prey intrinsic ...
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0answers
29 views

Latent Dirichlet Allocation on Contrived Data

I am doing a project that seems like it might be susceptible to Latent Dirichlet Allocation. However, my data is highly contrived (both in test cases and use cases) and my "words" don't come close to ...
2
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1answer
39 views

Purpose of using a saturable logistic like term

I would like to know what is the purpose of using the term $P\over (k+P)$ in the following. I found it when reading the article found here but it was commonly used in few other related articles . Is ...
6
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2answers
382 views

Need help with a model, Whatsapp data analysis

This is not actually a research question. It is more an exercise which I posed myself in mathematical/statistical modelling. I have some Whatsapp data of a chat with someone. I want to find a ...
-1
votes
1answer
297 views

Efficiency of the Baum-Welch Algorithm [closed]

One of our famous mathematicians, James Simons, used an extension of the Baum-Welch algorithm to 'crack' the wall street when he started trading on the stock market. Now, as Google, all informations ...
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0answers
60 views

If $(Φ^x)_{x∈ℝ}$ is a family of real-valued stochastic processes and $B$ is a Brownian motion, then $\int_0^tΦ^x_s\:dB_s=(\int_0^t\Phi_s\:dB_s)(x)$

Let $T>0$ $(\Omega,\mathcal A,\operatorname P)$ be a probability space $(\mathcal F_t)_{t\in[0,\:T]}$ be a complete filtration on $(\Omega,\mathcal A)$ $B$ be a (standard, real-valued) $\mathcal F$...
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0answers
110 views

In search for analytical solutions for sixth order nonlinear PDE

I am modelling the nonlinear behaviour of an bubble in hot water. I am trying to explain it's rotational, vibrational and translational motion in water with impurities and subject to varying ...
3
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2answers
1k views

Application for Differential Equation of higher order [closed]

We found some interesting insights in differential equations of the form $y^{(n)}(x)+F_\lambda(y(x),y'(x),...,y^{(n-1)}(x))=0$, i.e. for ordinary differential equations of $n$-th order with $n\geq2$....
2
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2answers
743 views

use of akaike information criterion with nonnested models

Would anybody be able to explain to me why the likelihood function $L$ can not be used to compare nonnested models whereas the AIC, which is a simple function of $L$ ($-2\log L+2k$ where $k$ is the ...
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0answers
131 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 ...
4
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0answers
566 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
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1answer
317 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 ...
26
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8answers
6k views

How is differential geometry used in immediate industrial applications and what are some sources to learn 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 ...
2
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2answers
316 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 \...
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0answers
490 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 ...
12
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3answers
1k 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 ...
8
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2answers
1k 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?
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0answers
97 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
2answers
758 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 ...
3
votes
0answers
290 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 ...
4
votes
1answer
233 views

SIRS Stability Analysis

I have set up the following ODE's for a SIRS model: $$\frac{dS}{dt} =-\alpha SI + \zeta R$$ $$\frac{dI}{dt} = \alpha SI - \beta I - \rho I$$ $$\frac{dR}{dt} = \beta I - \zeta R$$ $$\frac{dD}{...
5
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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. ...
1
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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-...
4
votes
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) ...
12
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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 ...
1
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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? ...
4
votes
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 ...
9
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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 ...
2
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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 ...
1
vote
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 ...
3
votes
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, ...
0
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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 ...
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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^...
14
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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 ...
4
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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 ...
25
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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 ...
6
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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 ...
6
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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/...
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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 ...
0
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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 ...