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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2
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0answers
47 views

SIR model constraint [closed]

During these past months, I've heard a lot about some pandemic modelling techniques, specially the so-called SIR model. Before I begin, I'd like to stress that my interest and question are just a ...
2
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1answer
170 views

How many persons pass your 1.5 meter neighbourhood during 1 week ? If the distribution is power law what is the exponent?

Consider a graph with vertices being people (in some region), and make an edge if one person pass another closer than say 1.5 meter during say one week. (Such a graph might be thought a kind of ...
12
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6answers
983 views

Suggestions for reducing the transmission rate?

What are suggestions for reducing the transmission rate of the current epidemics? In summary, my best one so far is (once we are down to the stay home rule) to discretize time, i.e., to introduce the ...
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4answers
1k views

Virus community spread mathematical modeling [closed]

What is the basic math behind the Virus community spread mathematical modeling,and how the time variable;(in these models),interacts with knowledge (data)?. I am not asking about how the virus is ...
0
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1answer
81 views

Reflecting Boundary conditions for advection-diffusion equations

I am trying to model the dynamics of phytoplankton in a water column using one-dimensional advection-diffusion partial differential equations. $$\frac{\partial P}{\partial t}= D\frac{\partial^2 P}{\...
28
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7answers
3k views

Applications of mathematics in clinical setting

What are some examples of successful mathematical attempts in clinical setting, specifically at the patient-disease-drug level? To clarify, by patient-disease-drug level, I mean the mathematical work ...
27
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15answers
4k views

Unconventional examples of mathematical modelling

I'll soon be teaching a (basic) course on mathematical control theory. The first part of the course will focus on mathematical modelling of dynamical systems. More precisely, I will present examples ...
1
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0answers
68 views

A mathematical area capable of describing nonstationary game-like problem [closed]

Here is my definition of the problem that I am trying to model: Let's have two agents and an environment. Each agent can do two types of actions. They are either supporting the environment or don't. ...
0
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0answers
56 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, ...
7
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1answer
271 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
32 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
36 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
72 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
247 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
182 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
98 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
242 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
135 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')...
1
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0answers
61 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
35 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
49 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
415 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
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1answer
478 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
67 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
113 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 $n\geq2$....
3
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2answers
917 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
146 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
576 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
353 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 ...
28
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8answers
8k 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
327 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 \...
3
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0answers
506 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
101 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 would ...
2
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2answers
1k 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
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0answers
308 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
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1answer
252 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
184 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
124 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
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1answer
317 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
785 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
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1answer
841 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
382 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
141 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
150 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
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1answer
165 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
779 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 ...