A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modelling.

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Online resources for Mathematical Modeling

I'm taking mathematical modeling this semester in college and usually there are resources online to read examples and see another point of view but I'm not able to find it for this class. Can anyone ...
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Calculate migration probability matrix from distances matrix

Imagine the world-wide human populations as a series of interconnecting populations. The distances between any two populations is given by the following kind of matrix $$ \begin{matrix} ...
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How many additional crews should be brought in to minimize the cost of an oil spill?

An oil spill has fouled $200$ miles of Pacific shoreline. The oil company responsible has been given $14$ days to clean up, after which a fine will be $10000$ \$/day. The local cleanup crew cleans $5$ ...
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Linear algebra of state space representation won't be linear (superposition theorem)…

After answering a question about calculating the state space representation of a circuit with 3 sources in it (the circuit is there), I had a doubt - while checking, it became clear there is something ...
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What is the correct term for the equations which comprise a mathematical model?

I have a mathematical model constructed by myself and my supervisor. In writing my report do I refer to the equations that make up this model as "constitutive equations", or is there another term ...
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20 views

Modeling predator/prey pursuit behavior?

I want to program a model of predator/prey pursuit behavior on a 2D topographical map (not predator/prey diff. eq. model!), primarily for fun, but I'd love to know if there's any literature or ...
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How can i Plot Laguerre-Gaussian mode vortex by Mathematica? [closed]

I've been using Mathematica for a few years. I couldn't plot the Laguerre-Gaussian vortex vawefron by using the Mathematica. I know i should use the Laguerre-Gaussian function in coding, but i ...
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21 views

Modeling Forced Oscillations Resonance Given from Second Order Differential Equation (2.13-3)

My answer to this problem does not agree with the text's answer: $y=sin(t)-3cos(t)$ Problem to solve is to find the steady state oscillations of the vibrating system governed by the following ...
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24 views

Maximum Likelihood Method, finding a minimum

I know that to find the minimum of a function i have to calculate its derivative. It's fine with me, i can do it but.. what is that o_O? OK, after going through my textbook, The Maximum Likelihood ...
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18 views

Saturation Modeling in ODE45

I have a machine with an arm that can move in a linear one dimensional way. There are 3 limits on the arm: The arm has boundary for its location $(x_{min},x_{max})$ The arm has limit on its velocity ...
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Linearizing the sum of product of a binary and a continuous variable

Now suppose we have this expression $z = \sum_jA[j] * x[j]$, where $A[j]$ is a continuous variable and $x[j]$ is binary variable. $A[j]$ is bounded below by zero and above by $AM[j]$ , so I know how ...
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Math theories in Game Theory

What are all the mathematical theories in Game Theory? I have taken Mathematical Modelling, including: application of linear systems, matrix operations, inverse of matrix, leontif input-output model, ...
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Positivity of compartments in epidemiological model

Given the following dynamical model (system of ODEs): \begin{array} $ \frac{dA}{dt}=\Lambda-\mu A-\beta(C+D+E+F)\frac{A}{N}-\tau(B+D)\frac{A}{N} \\ ...
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31 views

Arrange soccer fixtures with correct home - away alternation for each team

I am trying to do as the title says. I have 10 teams in the same group. Every team must play the rest once each but each of them will always alternate home and away. This means that if they play at ...
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19 views

Matrix representation from a linear function

I'm studying an opinion formation model [1] where the main rule is: $p^{(t)}_i = \frac{p^{(0)}_i + \sum_{j \in N(i)} w_{i,j} p^{(t-1)}_j}{1 + \sum_{j \in N(i)} w_{i,j}}$ Now, I'd like to represent ...
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MLGetFigure for copy Matlab figures into Excel spreadsheet [migrated]

For to copy several error histogram () figures (by a loop) into an Excel spreadsheet, I try use MLGetFigure; but I get "Undefined function ('MLGetFigure') for input arguments of type 'double' ". ...
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35 views

Help me find the function behind this data?

I have a function $f(x, y)$ and I have another (non-mathematical) algorithm capable of inefficiently generating the exact same results as in in a 'brute force' manner. Since I have been able to find ...
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Applications (“in everyday life”) of graph theory

EDIT another idea someone gave me was to consider flows in a network that would not only depend on the node at the beginning and at the end of a vertice but also about the vertice itself, like a ...
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Problem in game theory related to traffic networks

I have learnt game theory for a short period of time and I am not familiar with multi-player non-zero sum games. Here is a problem from my book which I am stuck: In this road network below each of ...
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20 views

A prove for information restoration with 2 schedules that delete information

What kind of mathematics or technique do I need to use the following? Just pointing me in the right direction is also helpful as I love mathematics but I am not so good at it. It's a problem I have ...
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30 views

Understanding mathematical syntax in SO(3) - Part II

In a paper I found in internet there is a relation about mapping a matrix into a vector and viceversa. One question has been already kindly answered here, but since I'm new to this kind of syntax I ...
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32 views

Help for understanding a vectorial equation found in a paper.

Trying to implement a code for the algorithm described in this paper I found something not very clear to me that leads me to misunderstand the whole concept. To calculate the vector $\vec{b_{3d}}$ ...
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45 views

Understanding mathematical syntax in SO(3)

In this paper, pp. 2, I found the following differential equation system and a statement: There are two things not clear to me: the hat map symbol seems to make mathematical symbolics shorter and ...
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36 views

Neural networks and mathematical modelling

Could you point out some reference books [accessible to an undergrad math student] that deal with the mathematical modelling aspect of neural networks?
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time varing Gaussian distribution

does there exist time varing Gaussian model? To be sepecific, a 2-D Gaussian model whose mean and covariance matrix is varing with another parameter called time. The $\mu$ (mean) and $\sigma$ ...
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linear programming problem - how much additional resources should I buy?

I have the following linear optimization problem: Maximize $$\sum_{i=1}^{n}x_{i}B_{i}$$ subject to the constraints $$a_{11}x_1+a_{12}x_2+\cdots+a_{1n}x_n \le l_1$$ $$...$$ ...
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How can I model the number of insects in a house?

I really don't know if this question applies here or if it makes sense, but I'm curious as to whether these ideas are commonly used. Imagine you are in a room, this room has holes, where bugs may ...
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20 views

How to model function with unknown exponents?

I know the Cobb-Douglass function which describes the production quantity: $$Q(K, L) = A \cdot K^\alpha \cdot L^\beta$$ Also I do know multiple assignments of K ...
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45 views

Smooth function to model a well or pit

In order to solve a Physics problem, I have to model an axisymmetric well or pit on a plane. I am looking for a function $f(x)$ that is smooth and monotonic in the domain $(0,1)$, where the origin ...
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52 views

Rayleigh-Bénard convection

I have a nondimensionalized linear perturbation system relevant to the appropriate pure conduction solution for Rayleigh-Bénard convection in upper planetary atmospheres under the compressible gas ...
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50 views

Assistance with Bayesian Random Effects and Mixed Effects Models

I am looking to build either a random effects or mixed effects model for a project I am working on, but have had trouble finding good sources and understanding the general structure of the model. ...
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12 views

Has anyone come across a non-constant population SIR model with infected birth?

I've come up with a seemingly new type of SIR model for one of my classes which allows for non-constant population and infected members to birth more infected members (such as is the case for many ...
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Estimating number of slaves imported before 1790

I have a statistics problem I am having a hard time figuring out how to model mathematically. The 1790 US Census counted 697,681 slaves and 59,196 free Africans in the United States. (A) assume ...
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28 views

Establishing a stable state withing a discrete dynamic model

Given the following discrete dynamic model: $P_0=360$ and $R_0=80$ and $t[0,200]$ $P_t=1,18*P_{t-1}-0,002*R_{t-1}*P_{t-1}$and $R_t=0,86*R_{t-1}+0,0004*P_{t-1}*R_{t-1}$ One can rewrite the ...
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Mathematical model for MILP optimisation problem- power scheduling

I am having trouble trying to formulate a mathematical model for the problem below to solve later as an MILP problem using different optimization software. I want to formulate the model so as to ...
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85 views

fantasy basketball model

i'm creating a fantasy basketball model (could be used in other games too) where we can project how well a player will do against another team even when the player hasn't played against a certain team ...
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Interperate Jacobian Determinant - Stability of Equilibriums

In my SIR model, I have the following Jacobian Matrix \begin{align*} J =\begin{bmatrix} -\alpha I & -\alpha S & \zeta & 0 \\ \alpha I & \alpha S - \beta - \rho & 0 & 0 \\ 0 ...
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37 views

What does this determinant mean?

I have the following Jacobian matrix for an equilibrium of an SIR model $$J=\left( \begin{array}{cccc} -\text{$\alpha $N} & 0 & \zeta & 0 \\ \text{$\alpha $N} & -\beta -\rho & ...
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107 views

Is this probabilistic balls-and-bins problem well-defined and is my solution correct?

Problem definition: There are $n$ bins, labeled with $1, 2, \ldots, n$. Let $X_i$ be a random variable denoting the number of balls contained in the $i$-th bin. The collection of random variables ...
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Split cab fare proportional to saving made across the board

Interesting dilemma. I've figured out how to split a cab fare 3 ways (proportional to time, mileage and equally) but I've found that when the cab fare is split proportional to time and mileage, the ...
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How to find the basic reproductive number of a discrete SIS epidemic model

I have been following a textbook called Mathematical Models in Population Biology and Epidemiology. The SIS model is given by the system \begin{aligned} S_{n+1} &= \Lambda + S_n e^{-\mu} ...
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Split a cab fare proportional to the time everyone has spent in taxi

How would you split a cab fare proportional to the time everyone has spent in the taxi? Total journey time = 19 min Fare = $17.25 ...
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mathematical model of an assignment/scheduling problem

I am solving a scheduling problem and I am able to abstract it into an assignment problem of assigning 45 machines to 42 jobs. the assignment problem was given as having 14 jobs, each with 3 tasks and ...
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53 views

Anyone know about definition of weak dictator?

I am trying to prove arrow's impossibility theorem in case which ties are allowed in individual preference lists and so is social preference list. It says that if $p$ is a weak dictator, then we can ...
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Questions about arrow's impossibility theorem.

If we had chosen to work in a context where ties are allowed in the individual preference lists, then Arrow’s Theorem no longer holds with the conclusion that there is a person whose list is always ...
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Analyzing/Modeling DynamoDB Usage

I'm seeking the correct mathematical tools to analyze/model a real world process for the purpose of optimizing resource allocation. I want to analyze consumed throughput of a AWS DynamoDB table and ...
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Which Probabilistic model to apply for this problem

I am a little confused about which probabilistic model to apply to this. Say I have an intern who is entering data on a daily basis. I have a clerk who at the end of the week pulls out a random ...
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How to connect the deterministic and probabilistic descriptions of the SIR model

I am a 17 year old student and I was reading up on epidemic modelling for a math project, specifically the SIR model and I came across this: "This" refers to the assumptions to which the Markov Chain ...
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Classifying growth as percent increase.

So I have been thinking about resource consumption a lot after watching the most important video you will ever see. It is pretty long so I will summarize it as follows, the professor makes a strong ...
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How to plot a phase potrait of a system of ODEs (in Mathematica)

I am asked to use mathematica to plot the fixed-points of the following system $$ \frac{dN}{dt} = -\gamma N \left( 1 - \left( \beta M + N\right) \right) $$ $$\frac{dM}{dt} = M \left( 1 - \left( ...