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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How to find out a model function for two inputs?

I am doing a bit of machine learning for a control for an end user for a system. I am basically trying to figure out a delay number based on two inputs. Currently I collect a list of times (in ...
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1answer
30 views

Is there a formula for amalgamating speed and accuracy into a single variable?

I am performing a cognitive study in which I wish to examine the effect of an independent variable on an individual's computation accuracy and speed. Let's say the test is to have them solve a set of ...
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1answer
42 views

How to derive the error $e^{n}=M^{n}e^{0}$ from iteration $x^{n+1} = Mx^{n} + f$?

$x^{n+1} = Mx^{n} + f$ is fixed-point iteration for solving the equation $x = Mx + f$, i.e., $(I-M)x = f$. The error $e^{n} = x - x^{n}$ How does one get $e^{n}=M^{n}e^{0}$?
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24 views

Solve this area functional, area maximizing problem

Consider an airplane in motion in $R^3$ with velocity $v(t)$ in $R^3$ relative to surrounding steady air and ||$v(t)|| = v_0 > 0 $for $t$ in $[0,T]$. Assume that a wind blows with a fixed velocity $...
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1answer
40 views

a mathematic model for multi-factor rating system

I have to design a rating system for a eCommerce website. The rating with be like 1 - 5 or 1 - 100. There're multiple factors need to be considered to give the rating, like user feedback, customer ...
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32 views

Modeling Objective function using mixed integer programming formulation

I have the following objective function max 2x1 -2f(x2), where f(x2) = 3 if x2 = 0 and f(x2) = 2-5x2 if x2 > 0; can anyone help me formulate it using binary ...
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42 views

How to get mathematical model from a data set with MATLAB

I have some values imported from excel about the annual sell of a product, with 3 var, month, price, sold items I have seen how to plot a chart using curve fitting tool but I need to define a math ...
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1answer
63 views

ODE Modelling in Matlab

I need to model human hairs in Matlab by solving ODEs, but I'm struggling to understand what to do. Here is all of the provided information: I've been asked to write a function returning the $(x,y,...
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86 views

Group method of data handling (GMDH)

The task is to build mathematical model using GMDH (Wikipedia) and peform a forecast. There is initial data: x1 = 2; x2 = 2; x3 = 6; y = 18; The selection criterion to be used is the regularity ...
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13 views

bio heat equation modification

I have the bio heat equation as described .here And the solution to it is, But to this I am trying to include the effect from exercise intensity as well. So the modified bio heat equation is ...
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1answer
51 views

Tail driven inequality [closed]

In this empirical model, Lj is a measure of left-tail driven inequality and Rj a measure of right-tail driven inequality. It represents what in this article? What exactly is the meaning of ''left-tail ...
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1answer
35 views

Estimating how many spheres there are inside of a domain, only knowing one slide

Let $D$ be a domain, for example, a cylinder (like a glass of water) of height $H=500$, with circular base of radius $R=300$, which contains spheres (cells) with radius $r = 50\times 10^{-6}$ floating ...
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24 views

How to solve a system of diffusion equations (in $u,v$) in two regions with $u(x,t=0) = u_0$ and $v(x,t=0) = 0$

Let $u=u(x,t)$ be defined on $x\in[0,L/2]$ and $v=v(x,t)$ on $x\in[L/2,L]$. For $t>0$ we have the diffusion system $$\frac{\partial u}{\partial t}=D\frac{\partial^2 u}{\partial^2 x} \qquad \text{...
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1answer
33 views

A way to calculate the error of a model?

I am currently making a model for a set of raw data of sea levels from the NOAA data base. On the site, the sea level is recorded every 6 minutes. Because I wouldn't have time to copy data every 6 ...
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1answer
49 views

Predator and prey model: non-dimensionalization

I've been trying to non-dimensionalize the differential equations for the predator and prey model. I've written down the procedure below which I was using for non-dimensionalizing the differential ...
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3answers
55 views

Mixed Integer Linear Programming Conditional Constraints

I have a set of variables: $x_1,x_2,x_3,x_4$ $x_1$ is a binary integer variable while the rest are real numbers all between 0 and 1 I want a constraint such that: if $x_2+x_3+x_4$>0 then $x_1=1$ ...
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2answers
95 views

Product of two sinusoidal functions model

I'm trying to make a model of the rise and fall of sea levels. According to this explanation and image in the textbook, the product of two sinusoidal functions should look something like this: (...
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1answer
114 views

what are the practical uses of “game of life” or “langton's Ant”

A few questions: Besides looking really cool, what are the practical uses of "game of life" or "langton's Ant"? I understand how agent-based modeling itself is a potentially useful methodoly, not ...
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1answer
58 views

Bifurcation - first-order ODEs

Construct a first-order ODE with one critical point if $\left\lvert \mu \right\rvert \ge 1$ and three critical points if $\left\lvert \mu \right\rvert \lt 1$ and draw a bifurcation diagram. Having ...
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1answer
61 views

How to reduce the chemical reaction system $A+B \rightleftharpoons^{k_+}_{k_-} C$ with transfer using the quasi steady state assumption

Suppose we have the reaction $$A+B \rightleftharpoons^{k_+}_{k_-} C$$ within some reaction $\Omega\subset\mathbb{R}^3$, we assume this region to be well mixed and we denote the concentration of $A$ as ...
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18 views

Parametrize a sigmoid function given, $(0,a)$, $(b,a/2)$, $f'(b)=c$ and $\lim_{x \rightarrow \infty}f(x)=0$

I want to write a sigmoid function with the following properties $f(0)=a$, for some specified $a>0$ $f(b)=a/2$, for some specified $b>0$ $f'(b)=c$, for some specified $c<0$ $\lim_{x \...
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1answer
23 views

adding error terms to a mathematical model

I am reading a heuristic model of a herding activity of some animals. The mathematical (heuristic) model that was developed understandably includes an error term to account for a little randomness/non-...
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1answer
81 views

Advice on Mathematical Modeling with Differential Equations

I am on my fourth year studying in a bachelor program in applied mathematics and computer science and plan to write a term paper on mathematical modeling using differential equations. This will be the ...
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57 views

Finding bifurcation values of one-parameter families of first-order differential equations

Consider the following one-parameter families of first-order differential equations defined on the reals: $$ \dot x = \mu - x - e^{-x} $$ $$ \dot x = x(\mu + e^x) $$ $$ \dot x = x - \frac{\mu x}{...
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20 views

Mathematic modelisation of a gym members

i'm working on a business case, where i should run a gym (gym club/fitness club). I want to know if there's some well know mathematic modelisations ready made for that kind of cases. For instance, ...
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1answer
35 views

How do I compute a realization of h(x) given its PDF and covariance?

Desription of problem I've added a picture of what I want to compute. In the nomenclature of the picture, I want to compute a realization of y(x) given the known distributions and constants. Let's ...
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43 views

Population Growth; Differential Equations

The population of a certain community is known to increase at a rate proportional to the number of people present at time $t$. Suppose it is known that the population of the community is $10,000$ ...
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21 views

How to find mean and covariance for a multivariate Gaussian under a linear transformation W?

While there is a related question on here and it is very informative, my case has some additional conditions. We have a likelihood function and want to find its distribution, $$ p(Y|X,W) = \prod_{i=1}...
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10 views

Estimate function given PDF and covariance

Let's say $h(x)$, random variable, represents the height of a surface, with x being the usual x-axis. The probability distribution function is: $P(h) = Ke^{-\frac{h^2}{2s^2}}$ is Gaussian, where $K$ ...
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1answer
46 views

Bilaplacian - Explanation of the (Clamped) Plate Problem

I am studying the numerical aspects of fourth-order elliptic problems now, and I came across the plate problem: Let $\Omega\subset\mathbb{R}^n$ bounded domain with Lipschitz-Boundary. Find $u$ s.t. $\...
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2answers
71 views

Theoretical justification of exponential growth differential equation

Consider a number of $x_0$ reproducing individuals and ignore death and limiting environmental factors. I've heard that the growth of such a population (of bacteria, insects, humans, etc...) can be ...
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16 views

If then condition on mixed linear integer programming

My English is not as good as yours, sorry for that. I hope you understand me. Here is the question:
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1answer
46 views

Mathematical Epidemiology Reference Request

I'm looking for a good Textbook for learning Mathematical Epidemiology. Something that I could read through and use as a future reference book. Thanks for the advice!
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63 views

Evaluating integral with respect to brownian motion

I am attempting to integrate $$ \int _{0}^{t} \sin(s) dW_s $$ whereas $W_s$ is brownian motion, in some sense a normal random variable with mean 0 and variance $s$. I looked around in stack ...
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39 views

Conditional expectation and Variance

I have the interest rate model: $r(t)= x(t)+y(t)+\phi(t) $ $r(0)=0 $ $dx(t)⁼-ax(t)dt+\sigma dW_1(t) $ $x(0)=0$ $dy(t)⁼-bx(t)dt+\nu dW_2(t) $ $y(0)=0$ $(W_1,W_2) $Brownian (2 dimensions) 1-...
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29 views

Modify Nicholson-Bailey mdoel

Suppose that we modify the assumptions of the Nicholson-Bailey model in the following way: if a host has one encounter with parasitoid it gives rise to c parasitoid progeny, but if it has two or more ...
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1answer
21 views

Modeling Gaussian components with standard vs exact functions

I'm studying a paper on modeling DNA histograms. It presents two alternative formulas for modeling Gaussian components: Standard form: $G(x) = \frac{A}{\sqrt{2\pi}\sigma}e^{\frac{-(x-\mu)^2}{2\sigma^...
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17 views

Can sombody give me an ntuitive explanation about regression estimates as weighted averages?

I am trying to study weighted least square and found one article that sounds like it is explaining what I am trying to study. But I want to get some intuitive explanation about each calculation and ...
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0answers
47 views

Self learning complex systems modeling

I am currently a senior studying mathematics. My program is heavily focused on pure maths, however, my interests lie in the area of applied mathematics. Specifically, I am interested in the study of ...
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9 views

converting GA's fitnessfunction to mathematical expression

As part of my final report I have to explain my fitness function method using in mathematical form. However I am not very good at this. I have came up with something that I will share with you here. I ...
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27 views

Composite sinusoidal functions

Let' say you have a graph as such: !(http://blogs.scientificamerican.com/roots-of-unity/files/2014/12/sinxsin2x.jpg) ! (Black one) And you know that it's function is in the general form of cosx+...
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55 views

Formulation for solving puzzle game mathematically

I'm developing a solver for a simple constraint-based puzzle game. Here is an example of the puzzle: $$\begin{align} - \;6\; -\\ - - -\\ - \;3\; - \end{align} $$ The given 3$\times$3 grid of "clues" ...
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1answer
76 views

An algorithmic method to simplify the mathematical modeling of a reaction network using conservation laws

Consider the reaction scheme. where $S$ is the substrate, $E$ is the enzyme, $P$ is the product, $C_1$ and $C_2$ are enzyme substrate complexes. Let $[S] = s$, $[E] = e$, $[C_1] = c_1$, $[C_2] = ...
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1answer
70 views

When fitting a polynomial to data points, how to determine the reasonable degree to use?

I have wondered the following: Suppose that there is a set of data points $(x_i,y_i)$. Then I would like to know if it is more reasonable to assume if there is a polynomial relation of degree $m$ ...
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1answer
18 views

How to nondimenzionalize concerning the arc lenght

My question is a general one concerning mathematical modeling and the calculation of the arc lenght. There is a function $ f\colon [a, b]\to\mathbb {R} $, where $ f (x) $ includes a lot of parameters. ...
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58 views

what does it mean by this mathematical modeling

This is a mathematical model: $$ Z_{i} = \sum_{S \epsilon S'} P_{i} (S=S') $$ where set $$\ S'= \left\{ (X_0,X_1,..., X_{k-1}) | X_i \epsilon S, \forall 0≤i ≤k-1,X_i ≤X_j, \forall i ≤ j \right\...
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43 views

Natural Transformation Inductively defined?

So, I'm working on this project and I'm having some trouble with a definition. Maybe some more educated Category Theorists can help me. The context is actually not very relevant, as I just need to ...
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8 views

Distribute individuals to relevant mentors as evenly as possible

I'm working on a site that needs a matching feature, but I'm wondering if there's a mathematical model that already tackles what I'm trying to do. Users belong to Mentors, but they can choose their ...
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67 views

Mathematical Modeling

If the number of possible routes is less than 4, probability (a) will be used. All the routes will be considered and the travel time for each route will be calculated. However, if there are more or ...
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20 views

Determining relative weights of input variables

For $Q = f(a, b, c, d)$, what is a statistical test to determine the relative weight of how these variables contribute to $Q$? Better yet, how do I come up with a function for it? To put into context,...