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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What is distinction between Functional Linear Regression and Functional Linear Models?

Thanks in advance for the help. I want to make sure that I understand two concepts correctly. A functional linear model is a particular type of linear model while functional linear regression is the ...
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365 views

How do you go about formalizing a concept?

I am reading Godel Escher Bach. I love it. In the first few chapters, the author shows what a formal system is and gives examples that eventually lead to a typographical formal system of strings that ...
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297 views

Find the difference equation for {2, 4, 16, 256, …}

Write a difference equation to represent the change during the nth interval as a function of the previous term in the sequence. b. {2,4,16, 256,...} I know that an= 22n but I can't figure out how to ...
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40 views

Quantifiers and Mathematical Modelling

When we are in the context of pure mathematics, quantifiers are everywhere. When we are in the context of mathematical modelling, quantifiers usually disappear. For instance, in statistics we often ...
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405 views

Game theory: Bidding strategy during an auction in a card game

I'm trying to create a mathematical model for the auction process in a card game called Pitch. The specific question I'm interested in solving is: Let $p_i$ represent the probability of a specific ...
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1answer
353 views

Can we rotate a 3D lattice of deformed spheres?

EDIT by EricStucky: The full text of original post below for reference, but I have talked with the OP in chat and believe that this is the mathematical core of the question. Suppose that we have ...
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36 views

I need to model a population where every component have a fixed life span.

I have a certain population, which growth is function of a certain factor. I have already modeled the growth. Now I need to impose that every individual in the population have a fixed life length. Can ...
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1answer
216 views

How to represent R function dexp mathematically?

I need help representing this line of code mathematically. exp(sum(dexp(x,prop_theta,log=TRUE)) - sum(dexp(x,cur_theta,log=TRUE))) Thanks for your help in ...
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2answers
114 views

How do you formulate a vague notion into a mathematical expression?

I am a software engineer wanting to learn math. I also do a little bit of drawing. What I am wondering is, how do you formulate a vague notion of something you're trying to model into a mathematical ...
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112 views

How to model a real-world graphical structure into a mathematical formulation?

I am trying to learn how to model programming problems in a mathematical way. I am a software engineer, but have recently been running into road blocks where I can't solve some problems very ...
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2answers
418 views

How to determine new dimensionless variables when non-dimensionsionalizing a system of ODEs?

I am following this a research paper called "Evolution of Within-Host Antibiotic Resistance in Gonorrhea", which can be found here. I have one question regarding the method of non-dimensionalization. ...
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68 views

Find the expression of a function close to this drawing

I am trying to model mechanical response under constraint in materials, and I know that I need this kind of function if I want my model to be accurate. The point is, I have absolutely no idea about ...
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1answer
94 views

A question in application of derivatives and vectors

Consider a skier who is sliding without friction on the hill ${y = h(x)}$ in a two dimensional world. The skier is subject to two forces. One is gravity. The other acts perpendicularly to the hill. ...
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68 views

Computational compass-and-straightedge constructions

I recently came across Ancient Greek Geometry, a web toy by Nico Disseldorp, and it got me wondering: is there a way to exactly model the points generated by geometric constructions, starting from two ...
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1answer
370 views

Markov Chain with Memory

One of the defining characteristics of a Markov Chain is that it is memoryless: the next state depends only on the current state, and not on the set of preceding states. I'm looking for a ...
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18 views

Number of significant linear predictors if predictors are not independent?

I would like to determine which of a set of candidate predictors $\{x_1, x_2,\ldots, x_n\}$ are significantly relevant to the linear prediction of $y$. Typically, one can compare a full model ...
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50 views

Form of a function I can fit like a polynomial that has an asymptote on x-axis and is always positive

So I have a small list of pairs of the form $(\mathbb{R}, \mathbb{R}_{\geq 0})$ and I want to fit a function to this data. Additionally I know that as $x$ grows large in either direction $y$ tends to ...
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2answers
47 views

Rounding a real number w.r.t. a given amount of steps

Let $x$ be a real number, $x \in [0,1]$. Suppose a system can only provide a noisy signal about the value of $x$, given the granularity allowed by the system, $N \in \mathbb{N}^*$. I'm looking for an ...
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1answer
198 views

Start studying mathematical biology from basics

I am really passionate about theoretical and quantitative biology and I would like to build my future career around this topic. I've just got my bachelor's degree in biology (ecology) but scince ...
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1answer
134 views

Definition of “epidemic” when using SIR models

I haven't studied differential equations for a long time, but I have just started looking at material on the SIR model of epidemics. My problem is that the resources that I've looked at haven't given ...
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60 views

Finding the largest eigenvalue of a sparse matrix

I would like to find the largest eigenvalue of a sparse matrix by hand- this is part of analyzing a mathematical model for infectious diseases. The nonzero entries are very complicated - hence Maple ...
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1answer
232 views

Analytical Models for Hysteresis of Complicated Systems

I’ve been working with a system that exhibits hysteresis and I’ve found that the more common models do not work for me. I am wondering if anyone is aware of other models that might be out there for ...
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1answer
66 views

Finding a value that makes an expression negative

Background: I am working on the mathematical modeling of infectious diseases, namely HIV and TB. In the process of proving global asymptotic stability of the Disease-Free Equilibrium, I must ...
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2answers
112 views

Units of time in simple differential equation

Very simple question: There is a well-known model in epidemiology called SIR model. It describes the changes in the number of susceptible, infectious and recovered individuals in a population. It is ...
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1answer
64 views

How can I modelize a weekly menu and minimize the total number of ingredients it contains

Hi and many thanks for reading this question. I want to create an algorithm that will minimize the total number of ingredients that are in a weekly menu. A menu is made of several recipes, for ...
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2answers
130 views

Creating a mathematical formula to price a taxi booking

I've been asked to create a mathematical formula that will be used to price taxi bookings at a local taxi company. Current system used: A table is used as a reference Variables: x is the ...
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1answer
170 views

Estimate arrival time of a ship given the average of the ships in a day in a Poisson Distribution

I'm working in a simulation of a Port where ships come to specific stations of the port. I already know that the average amount of ships is given by a Poisson distribution and the service time (On ...
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1answer
94 views

Math Finance: Arbitragefree Pricing Q vs. P

I read that the Fundamental Theorem of Asset Pricing states, that a market is arbitrage-free if there exists a riskneutral equivalent martingale measure Q~P, under which the discounted asset price ...
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76 views

PDE modeling (heat conduction and flow)

The heat conduction is expressed by a classic heat equation like $p(x) u_t + div (A(x) u) = f(x,t) $. If I look at a porous medium like this (solid+gas) the heat equation should apply too (in a ...
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87 views

Simple differential equation modelling question.

The question is: A chemical dissolves in water at a rate equal to 10% of the amount of undissolved chemical per hour. At time $t$ hours the amount of undissolved chemicalis $x$ grams. Initially the ...
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167 views

Could the birthday paradox be interpreted also about deaths?

Is the probability from the birthday paradox also true about deaths? If so, why? Or why not? I would think that it is also true about deaths, but it doesn't say so.
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58 views

How can I find a tranformation matrix/Mathematical relation between two 5th degree polynomial curves in space?

I have the equation of two 5th degree polynomials which they don't intersect with each other. Each curve is made of 100 points and these two curves look similar but there are small differences. I am ...
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131 views

How can I find a tranformation matrix/Mathematical relation between two 5th degree polynomial curves in space?

I have the equation of two 5th degree polynomials which they don`t intersect with each other .Each curve is made of 100 points and these two curves looks similar but there are small differences .I am ...
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1answer
19 views

Multiplying a binary predictor variable with another predictor variable.

Is it completely valid, to have an equation with a certain amount of variables, where two of the variables multiply each other? For example, I want to have an equation $Y = B_0 + B_1X_1 + B_2X_2 ...
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37 views

System of $2$ nonlinear DEs

Please tell me if I'm on the right track for solving the following system: $$\frac{d{U}}{dt}=a - b U -\frac{\beta U V}{U+V} \\ \frac{d{V}}{dt}=\frac{\beta U V}{U+V}-(b+c+d)V $$ Steps: $1.$ I added ...
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1answer
58 views

How did they find this equilibrium condition?

I'm studying from a book titled "Mathematical Models in Population Biology and Epidemiology" and we're dealing with SIS models. In a chapter called "Infective Periods of Fixed Length", we get to this ...
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1answer
131 views

At what point discrepancy, in the NBA, does it make sense to milk the shot clock?

I am admittedly not great with probabilities, so I am soliciting the help of the community. I am watching game 3 of the NBA Finals and I am trying to work out when it makes sense to milk the shot ...
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1answer
134 views

Linear Optimization: Minimum Cost Network Flow Model

Consider the directed graph G=(V,A) where each directed arc (i,j) $\in A$ has associated with it a distance $d_{ij}$. Formulate a minimum cost network flow model that will identify the shortest paths ...
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1answer
34 views

Model going from Normal to Log-Normal

I'm getting in a real mess at the moment over something I think is very simple, as well as the wording/terminology. I have a model - $\ln(Y(x))=a+b\ln(x)+\epsilon, ...
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51 views

Distribution of phone calls during 24h

I would like to model the amount of phone calls at each time of the day. The phone calls should follow a poisson distribution and at 12:00 there should be the peak. So, semantically what I would like ...
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1answer
119 views

Carbon dioxide molecule model

A simple model of the carbon dioxide molecule can be modeled by a system of three masses and two springs. The oxygen atoms have mass M and carbon has mass m. The springs (bonds) have spring constant ...
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1answer
33 views

Bessell function of the first kind $J_v$ of the Bessel equation $x^2y''+xy'+(\lambda^2 x^2-v^2)y=0$

If we have an equation $x^2y''+xy'+(x^2-v^2)y=0$ then the solution of the first kind $J_v(x)=x^v\sum_{m=0}^{\infty}\frac{(-1)^mx^{2m}}{2^{2m+v}m!(m+v)!}$. Then how would you find the solution of ...
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106 views

Is it compulsory to make transformation to the econometric model in order to have only diagonal elements on variance-covariance matrix of errors?

I need some sharped and advanced advices for the following issue ... Model and its assumptions I'm working on the methodology of a two-way error component model. Here is the model: $y_{jis} = ...
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1answer
81 views

Does improving a model's accuracy directly improve the forecast?

Say I have a years worth of data on donut sales, and I use linear regression with variables such as daily occupancy, daily weather etc. because there is a good correlation between each variable and ...
2
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1answer
128 views

Function to predict processing service overload

We have a black box that for each input request a, it outputs a computed response b. The computation time for a given request varies in a stable way over time. Stable means here that it is still ...
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2answers
42 views

Playing audio files at lower % of regular speed - how long will they be? negative percentage / ratio calculation

I got a knot in my brain and can't think of this - I'm sure it's quite simple and I'll be like "duh!" once someone points it out to me... So the problem is as follows: An audio file is 30 seconds ...
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56 views

Elliptical Cone

I have a building design in the shape of an elliptical cone. To understand the elevation of the structure. I need to draw/unfold an elliptical cone. Can somebody explain the process for the same ?
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1answer
69 views

In math, what is a chessboard + pieces?

What mathematical concept would a chessboard + pieces be? Is there any matrix where the squares are kinda related, in the same way that for example a rock relates to all the column/row, where it is.
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1answer
79 views

Analyzing the stability of equilibria

There's a model with a condition $r>\mu$: $$\begin{align} S'&=r(S+I)-\beta SI-\mu S \\ I'&=\beta SI-(\mu +\alpha)I \end{align}$$ I can easily see that the equilibria of the second ...
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1answer
91 views

Express the new parameters in terms of the old parameters (SIQR model for mathematical epidemiology)

In the model considered here the population is divided into susceptibles (S), infectives (I), isolated or quarantined individuals (Q), and recovered individuals (R), for whom permanent immunity is ...