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Questions tagged [mathematical-modeling]

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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Hankel singular values of Discrete time system and its inverse.

An $n$ dimensional discrete-time system $\Sigma$ is describe by the ewuations $$x^{+}=Ax+Bu, \quad y=Cx+Du $$ and has the property that $D$ is invertib;e. Its inverse system $\Sigma^{-1}$ is ...
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Balanced truncation of given state space system.

The following balanced truncation question is from an exam of the course Model Reduction. The transfer function $G(s)$ is realized by the state space equations $$\dot{x}(t)=\begin{bmatrix} -\frac{9}{...
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Deriving a mathematical model for a fluid system.Help.

ive been trying to derive a mathematical model for the system shown in the image The case is a pump, pumps water into a Column. The drain of the column is blocked. Thus there is only flow in. i know ...
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Algebraic structure of sound

I was wondering if there is an algebraic structure that describes sound in a similar way we can describe images. Especially when viewed as a spectrogram. Heard a talk about how an image has the same ...
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Is there a generative network model for arbitrary distributions that guarantees an edge count?

So what I am trying to do is rewire a random directed graph (specifically a boolean network) so the out-degree distribution is scale-free. However I need a generative model that will allow me to ...
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Modeling problems using graphs

I was wondering how can I learn how to model problems using some classical models in graph theory (graph coloring, vertex cover, matching, maximum cliques, independent sets and so on) For example, I ...
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Modeling $t \in [a,b] \; \Rightarrow y_{[a,b] }=1$, asking for alternatives if any

Suppose you have a variable $t\ge 0 $, I want to model the following statement : $$ t \in [a_i,b_i] \; \Rightarrow y_i =1 $$ I am assuming $t$ belongs to a unique interval among the ones proposed. I ...
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Simulation Geometric Brownian Motion and C++ Implementation [on hold]

I am a student and have some exercises to do. Could you please help me with these? Any contribution highly appreciated! Thank you for yout time! enter image description here
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Hankel norm and H infinity norm model reduction exam question.

Shown below is a question from a model reduction exam. I'm not sure how to answer the questions and I'm wondering if my approach is correct. A continuous time system relates the inputs $u_1$ and $u_2$...
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1answer
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I have one question about mathematical modeling

My school does Orienteering in PE, and basically the grades are from 0 to 20, the is the best,0 is the worst and 10 is 50%, well my teacher calculates the grades this way, if you do the task in 5 ...
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What are the best books to study Neural Networks from a purely mathematical perspective?

I am looking for a book that goes through the mathematical aspects of neural networks, from simple forward passage of multilayer perceptron in matrix form or differentiation of activation functions, ...
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How to reformulate (or model differently) the sum of fractions in the objective of integer program?

I have the following (integer) program: $ \max \sum_{i\in I} \frac{a_i}{b_i + \sum_{j\in J} c_{ij} x_{ij}} $ s.t. $ x \in X $ $ x_{ij}\in \{0,1\}, \quad\forall i\in I \wedge j\in J $, where $ a_i ...
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1answer
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Selection of jobs based on queue priority

I have a set of workers $P$ and a set of jobs $I$. I'm evaluating the queue priority at every time interval $T$ and the worker will take the job with the highest priority. The priority is calculated ...
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1answer
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Open Travelling Salesman Problem

I am trying to find a linear program for the open Travelling Salesman Problem, where the salesman does not need to return to the starting point. More precisely, I have to do this with multiple ...
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Population linear model

I have a dataset with 15 people. For each person I have the age and a blood measurement. The relation between the age and the blood measurement is linear. The plot between the two variables looks ...
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Akaike Information Criterion Interpretation

It is commonly known that the lower the AIC is, the better fit the model is. Is AIC on a scale where it means that the closer the number is to 0 the better it is? Thanks.
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why output values of linear transformation are wrong?

I am going to fit my data using an equation, Y=a*(1-e^(-bx))^c equation. a & c are the intercept and slope, b is given. Here are the steps I did: ...
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1answer
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Non-dimensionalising an equation containing an exponent

I am being asked to write the non-dimensional version of the equation $ae^{bx}+c=x^2$. I understand the process that one would use to non-dimensionalise an equation, but in this case it was the ...
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Name of this Markov model, and how to estimate?

I came across a paper by Rodda (2004), who simulates interest rates with a Markov sequence. To simulate changes in the interest rates, they used the historical transition probabilities. Their ...
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Modelling alcohol concentration in the blood.

Me and my partner are working on a modelling project where we study the concentration levels of alcohol in the stomach $(C_s)$, blood $(C_b)$ and brain $(C_h)$. The system of differential equations ...
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1answer
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Galerkin projection model reduction exam question.

The following question is from an exam for the course Model Reduction. There are no answers and I don't really know what steps to take. Looking for an expert that can show me how it's done. The ...
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Chess Tournament Probability Problem Explanation

I am reading the book Introduction to Probability by Dimitri Bertsekas and John Tsitsiklis Athena Scientific 2nd edition 2008 and I stumbled upon a probabilistic model problem and I can't seem to ...
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1answer
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Fourier series of non-periodic function $f(x)=e^{-\frac{ax}{L}}$

The definition of Fourier series states that It decomposes any periodic function or periodic signal into the weighted sum of a (possibly infinite) set of simple oscillating functions, namely sines ...
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1answer
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How to know how many points I need to fit a model?

I need to do viscosity measurements at different temperatures in order to fit a model of the form (Flucher equation): $$\log_{10}{\eta}=A+\frac{B}{T-T_0}$$ Where $T_0$ is constant and known, $T$ is ...
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Algorithms (millions of solid random intersections)

I am looking for a numerical method to calculate the volume of the intersection of more than two cylinders in any angle (not just 90° (Steinmetz Solid)). There is an old Hubbell paper (1965) but it ...
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1answer
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how to reduce the summation value of binary variable to 1 , Integer Linear Programming

I have a binary set of variable Viu whose value can be either 0 or 1 , There can be multiple time when(ith value of Viu) V_1_A is assigned value 1 There is another integer Variable Xi which holds ...
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Modelling 1-D expanding-accelerating space

I am writing physics engine in C++ and I am stuck on advanced math problem. I need equation that allows me update the position of a moving point in 1-D expanding and accelerating space. Just good ...
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1answer
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Writing integer programming math statements

I am currently in a linear programming class, and we are on the topic of integer programming. I am asked to write certain relationships in "integer mathematical formulation" with binary ($y_i$), ...
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2answers
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Deduction for joining two non linear equations

I have, as dummy in math, to make the deduction for joining two nonlinear equations. I have one equation $$Y_v = 0.0000464 + x_1^{1.61} + x_2^{1.24}$$ that expresses $Y_v$ as a function of $x_1$ and $...
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Is this a correct approach to weighting algorithm in a math equation?

I have a list of products and each product is connected to another. Each connection strength_level ranges from 1 to 10. ...
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1answer
302 views

Two fluids flowing perpendicular in thermal contact with a Wall [Help to mathematically model]

I will try to describe briefly how I am modelling the problem. (Please bear with the length). The governing equation describing temperature for a block at steady state is $$\nabla^2 T = 0$$ where $\...
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1answer
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Finding population growth rate given initial population and average pubs per female reproduction

I am new to mathematical modeling and having trouble modelling the following population growth scenario: Starting population: $100$ individuals Average age: $7$ years Assumption: population equally ...
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How do we plot a domain wall between two strings?

Intuitively, an angular vector field $\theta(x)$ such as the following would describe a domain wall between two vortices/strings of opposite winding number. I would like to draw this on a computer ...
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Is this physical model exactly solvable?

There exists a popular model in the Physics of heavy quark bound systems, called the Cornell potential model, in which the inter-quark potential is modeled to vary with radial distance $r$ as $$V(r) ...
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Connectionism and AGI

Marvin Minsky and Papert prove that the XOR function($\newcommand{\xor}{\oplus} x \oplus y$) cannot be implemented by a single layer perceptron and ended connectionism research for some time. My ...
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Modeling distributed densities or is it?

Lets say that I am counting pixels over time. Each pixel is either the color red or blue. Let's say that I make up some threshold for the number of red pixels that I count and that when I reach this ...
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I need to get mathematical model for such matrices

I have a question similar to another question I've asked here, but it's with more parameters. The question is, need to find the mathematical model for the relationship between number of columns and ...
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1answer
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First-order logic from computational linguistics - implication

I am reading Natural Language Understanding by James Allen. It has the following sentence That John is rich implies that he is happy. And first-order logic ...
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1answer
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What's the mathematical model for this matrix.

I need to find the mathematical model for the relationship between number of columns and all possible number of combinations when including two elements, one is not repeating and the other repeats ...
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dct modelling of a scalar field

I have been reading this paper on MRI and I could not understand the following model: The displacement field (i.e. d) is modelled as a linear combination of basis warps i.e., $$ \mathbf d=[\mathbf ...
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Social Force Model for Pedestrian Dynamics by Euler Method

The social force model is a model using newtonian forces to describe the movement of individuals. As seens here : page 1 Each individual feel the following forces : ->a driving force towards the ...
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1answer
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how to model if else statement in mixed integer program

I am trying to model a if-then condition for a MIP. The MIP looks like Maximize $\sum\limits_i H_i - C$ s.t. $\sum\limits_j x_{ij} \le D_i$ and $\sum\limits_i x_{ij} \le S_i$, where $H_i = 1$ if $\...
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Big M Equality Constraints Question

I am a newcomer to mixed integer linear programming, and I am having some trouble using the Big M method to linearize some constraints, and was wondering if I implementing it incorrectly. Here is ...
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1answer
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Determine the values of a,b,c, and d, so that the following function is a cubic spline

Determine the values of a,b,c, and d, so that the following function s(x) is a cubic spline satisfying $s''(3)=0$. $s(x)= \Big\{^{x^3-4x^2+7 x \in [-1,1]}_{ax^3+bx^2+cx+d x \in [1,3]}$ To use the ...
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1answer
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Linear Programming Model with Strict Inequality and Negative Constraint

I just want to know if it is possible to convert this LP model into a standard LP model: $\max Z = 2x_1+4x_2$ subject to $-2x_1+3x_2<3$ $4x_1+5x_2>10$ $x_1 \leq 0$ $x_1<4$ $x_2$ ...
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2answers
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Definition: what is the difference between generating a random variable versus generating a random number?

Can someone clarify to me the difference between: generating a random variable (according to a certain distribution) versus generating a random number (according to a certain distribution)? I am ...
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problem in input/putput and decision variable of RL? Could we consider input and output on the decision variables on a feedback problemsuch as RL

Could we consider input and output on the decision variables on a feedback problem such as RL? Could we consider "state" as "input" instead of "input from environment:D"? Could we consider "state" ...
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A mathematical model to get a probability of finding players at a particular location on the map in the game PUBG

I assume you are aware about the game PUBG (see the Wikipedia entry), where 100 players are dropped on island, and last team/individual to survive wins. I was thinking about a mathematical model/...
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2answers
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How to justify this general Taylor series argument given by physicists?

I'm a 3rd year Physics and Mathematics student, an in this 3 year, I always faced with arguments like this; Let $f(t)$ be a function of $t$. Then, for small $\delta >0$, we can expand $f$ ...
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2answers
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Partial differential equations that involve an infinite “continuum” of variables: “Each point in space contributes additional degrees of freedom”?

Page 11, Nonlinear Dynamics and Chaos, by Strogatz, says the following: This is the domain of classical applied mathematics and mathematical physics where the linear partial differential equations ...