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 did Target figure out a teen girl was pregnant before her father did?

First of all I do not have a mathematics degree only a B.S. in finance so please take that into account when writing an answer. Generally what type of mathematics is involved here? And specifically ...
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158 views

Modelling a difference equation question?

Stuggling with this one: In a simple economic model, time t is set up as a discrete parameter (possibly referring to days or months), while demand $D_{t}$ and supply $S_t$ are described in terms of ...
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Mathematical model for my experiment?

I'm running a benchmark to find the efficiency of a my computer. There are $p$ control variables say, $x_1,x_2,...,x_p$ and one output variable $Y$. For example, every time I run an experiment I ...
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103 views

Equation model for project effort.

It is my first time here, so I hope I'm keeping on topic. I wanted to find an equation where I could use the variables which affect the amount of work, in a way that feeling it the variables, I'd ...
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249 views

Stochastic predator-prey

My system is a simple $P$ vs $I$ foxes- vs rabbits model given by: $$ \begin{cases} \frac{\mathrm{d}I}{\mathrm{d}t}=& \alpha_I+\lambda_IP- \gamma_II -\delta_IPI;\\ ...
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11th grade level exponential growth problem?

A certain strain of bacteria that is growing on your kitchen counter doubles every 5 minutes. Assuming you start with only one bacterium, how many bacteria could be present at the end of 96 ...
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Mathematical Modeling of Real-World Situations

I was considering how to model the following problem mathematically and was wondering what you thought the best way to do it is. "A takes 1 minute to cross a bridge, B takes 2 minutes, C takes 5 ...
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174 views

Von Mises width at half height

I'm fitting the following Von Mises type function to some data: $(A/2\pi)e^{k\cos(\theta)}+C$ where A and k are positive. I want to calculate the width at half height from the lowest point of the ...
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economic modelling asked for

I am putting together a proposal for a system of economic exchange which links a transaction of money through a period of time, and subjective relationship evaluation between two people. How can it be ...
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344 views

Heat Equation Derivation and Mean Value Theorem

Farlow book PDEs for Scientists and Engineers pg. 27 shows derivation for Heat Equation. It starts by stating Net change of heat inside $[x,x+\Delta x]$ = Net flux of heat across boundaries + Total ...
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118 views

Non-analytical equation

Suppose I have integrated a differential equation numerically using some time-interval $\delta t$. How might I determine the accuracy of the result? Does solving simultaneous equations reduce the ...
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449 views

Question Based On Mathematical Modeling [Applied Functions]

An example of a calulus book reads: A rectangular storage container with an open top has a volume of $10$ m . The length of its base is twice its width. Material for the base costs $10$ per ...
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How to change Hermite function to have a same shape with moving extremum point and zeros

If somebody has a experience with polynomials. How to set this Hermite function to have a general minimum where I want on $x$ axis, for example in $0.5$. Is it possible to be in analytic form ...
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315 views

Is there a mathematical function giving an approximation to human breathing over time?

I want to animate something with the same frequency that a human breathes in and out, something like the Apple Macbook power light when it is in sleep mode. So basically an ease in ease out function ...
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1answer
180 views

Help with recursion/difference equation manipulation

I'm trying to reproduce the analysis of a simple biological model from an old paper. The model describes the frequency of two organism types in a population as: $p_{t+1} = \frac{p_t ( s + (1 - ...
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4answers
588 views

Biological processes described by the exponential function

What are biological or biochemical processes that are described (stochastically or deterministically) by exponential function $f(x) = e^{ax}$? Edit: What about examples that are not related to the ...
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2answers
154 views

How to model multi-step cell differentiation

Can I better explain cell lineages using PDEs or stochastic?
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343 views

Conditional Expectation and the floor function

I have a piece of code the produces random integers. ...
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111 views

Is there a formal name for a mathematical model that has an overly sensitive parameter

I'm a software engineer with a bit of mathematics expertise working with an NGO that has developed mathematical models for ecosystem services. It turns out that one of these models is overly ...
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335 views

Population Dynamics model

I am currently searching for population dynamics models. Concerning animal population growth, I have found the following so far : Growth models for fish Predator-prey : Lotka-Voltera and ...
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256 views

Do Ambivalent Axioms have a place in Mathematics?

I can't think of any examples of ambivalent axioms in mathematics (two ideas are ambivalent if there are sometimes conflicts between them), so please let me humor you with a strange example. Suppose ...
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555 views

How to approach mathematical modeling of the human heart problem?

I have to create a mathematical model of the human heart but it was quite a time ago I finished University and I experience some difficulties with the math behind the subject. What is the necessary ...
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481 views

Simplify water salinity equations

I recently became interested in calculating water salinity from conductivity and temperature. I failed to find any theoretical model to how this is done, only empirical models derived from fitting to ...
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1answer
75 views

How to model a problem to validate/improve an attempt at solving computer programming problem

I have attempted a solution to a beginners programming question which produces what I think is unexpected output. I need a way to validate it and was hoping to do that mathematically. Problem ...
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364 views

What is a 4-8 mesh?

A paper I'm reading uses this classification for a mesh, but I'm not sure what the numbers 4 and 8 signify. Could someone clarify? Here's an image from the paper of a 4-8 mesh.
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Social network representation: graphs or sets?

for social network representation, what is better, sets or graphs ? What kind of feature the first gives that the second doesn't and viceversa?
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How to make simple iteration in Mathematica

How to make simple iteration in Mathematica for this three equations and save $q$ for each step. If we define $q'=dq/dx$, $q''=dq'/dx$ we have two equations (1) ...
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How to make iteration for Newmark method in Mathematica 8

How to make iteration method for solving differential equations by Newmark method? There are just three equations which describe the Newmark method. I need q for time step for example 0.01. Also, for ...
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How to model server load?

I want to model the server under load. I'm using following assumptions: The server serves only one request at a time, and all requests take him exactly 100ms to process. All requests that came ...
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494 views

Conserved Quantities in Dynamical Systems

A simple pendulum is modeled by the (nondimensionalized) differential equation $$\frac{d^{2}\theta}{dt^2} = -\sin(\theta)$$ With the auxiliary variable $w$, this is equivalent to the first-order ...
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Choosing set of best estimators for linear least squares

I have a measured experimental dataset which is well approximated by the sum of several basis functions in linear combinations. Linear least squares of course gives me the optimal weight for each ...
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154 views

Competition Models

Need help getting started on this homework problem and I am really lost. The notes given on this subject are really sparse and I haven't found anything online that was useful. Sorry about the lack of ...
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Modeling propositional formulas in integer programming

Say I have an binary integer programming problem: \begin{equation*} \begin{aligned} & \underset{\mathbf{x,y}}{\text{minimize}} & & f_0(\mathbf{x,y}) \\ & \text{subject to} & ...
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Operational research: group n items in x groups according to measure/constraints

I am searching for a consolidated model to group n items in x groups. Do you know how to find on the web some resources on the above subject? In my idea it can be something like: I have 4 persons and ...
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3answers
504 views

Dollar Cost Averaging and Gas Prices

Dollar cost averaging says the if you invest a set dollar amount at the fixed frequency, you will come out better than purchasing a set number of shares at the same frequency. While filling up the gas ...
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What is a “free parameter” in a computational model?

In many articles regarding computational models of some particular phenomenon, there seems to be a consensus: "the smaller the number of 'free parameters' in the model, the better". So, what is meant ...
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Legendre Polynomials

I was given a "generic" matrix that I was told was constructed using Legendre Polynomials. ...
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312 views

Is all acclimatization modeled by Newton’s Law of Cooling?

I have in mind things like language learning (native or foreign), and growth to adulthood. Is acclimatization the same thing as saturation? Can the logistic function be regarded as simply an ...
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754 views

How to calculate perceived value?

Is there a known formula to calculate perceived value? If I am auctioning some popular product that is worth $100 (shelf price), how much would people bid if they: Have a 1 in ...
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1answer
534 views

Automation of 3D Paper Modeling

I recently saw this creative paper contraption online this prior weekend and wanted to see if I could automate the process of creating all ~35 layers of an equation. Essentially what I would want the ...
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How can I learn to create and solve Rational Choice models?

I have some scenarios I would like to model using rational choice theory (i.e. utility maximizing agents). For example, a two population type (I suspect this means two representative agents), two ...
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2answers
1k views

How to 'minimize' correlation between series

Hi fellow mathemagicians, let's say that I have 3 series of numerical results (they represent 'drawdowns') : ...
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593 views

How do I fit a model with piecewise linear regression

I have a set of points in 3D (x,y,z). I ordered these points from the lowest to highest. So, I want to used linear regression to fit a line through these ordered points and then to find out a break ...
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How to formulate constrained optimization problems

For a constrained optimization problem, there can be different formulations. For example, consider the problem with the following formulation: $$\min_{x \in X \subseteq \mathbb{R}^n} \, f(x), $$ ...
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Transformation induced by a spherical mirror

This is at heart a mathematical problem, but is best motivated in physical terms. I'll introduce a very special case and move on to the general case later. Special case An object, taken for ...
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How to know if the Fourier Transform is surjective

I am studing if I could modell a function using LUTs (ROMs) for a electronic digital design. I have two functions, a FFT and other function, S. S function system recive as input the output of the FFT ...
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279 views

Modelling Traffic Congestion

I noticed that on a road, if the number of cars reaching a certain critical stage, all the cars would slow down immediately. Is there any theory/model that connects the number of cars $N$ with the ...
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1answer
791 views

Understanding the Pareto distribution as applied to wealth

The Pareto distribution is used to say, given a particular person X, what is the pdf of his wealth. I would like to explore the reciprocal question: Given the total amount of wealth in a population, ...
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Geometrical construction for Snell's law?

Snell's law from geometrical optics states that the ratio of the angles of incidence $\theta_1$ and of the angle of refraction $\theta_2$ as shown in figure1, is the same as the opposite ratio of the ...
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why does $\frac{b\partial a}{a \partial b} = \frac{\partial \log a}{\partial \log b}$?

I am doing some background research on sensitivity and elasticity analysis, and I came across the following definitions of elasticity: $$e_{ij}=\frac{a_{ij}\partial \lambda}{\lambda \partial ...