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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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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281 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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293 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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138 views

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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253 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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374 views

Find The General Solution [closed]

Using separation of variables and partial fractions find the general solution: $$dP/dt = re^{-at}p(1-p)$$
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493 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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68 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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641 views

NDSolve simple matrix problem in mathematica

I have a problem with command NDSolve in mathematica. If we have simple second order differential equation, it is easy to write code in mathematica. But if we have matrix problem (for example 4 ...
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217 views

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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449 views

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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416 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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148 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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115 views

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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2answers
3k views

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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254 views

Legendre Polynomials

I was given a "generic" matrix that I was told was constructed using Legendre Polynomials. ...
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490 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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28 views

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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983 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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539 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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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 ...
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116 views

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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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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266 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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738 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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Deriving functions for empiracal distributions -very applied mathatics

First I am a new user of this site. Second my math background is very limited, although I do have a lot of experience in applied statistics. Component or piece part failures on high value parts($1000 ...
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Finding a good parametric form for a model

Hello I am trying to model the relationship between two variables, say x and y. I have a number of subjects - for each subjectm I have a number of x and corresponding y, both of which are always ...
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Preparing for the Mathematical Contest in Modeling

The Mathematical Contest in Modeling (MCM) is coming up in a couple of weeks. With the idea that the competition is ultimately about teaching students to become better at mathematical modeling, I was ...
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What sort of mathematical methods and models are used to model the brain

What sorts of mathematical tools, models and methods and theoretical frameworks do people use to simulate the function of the brain's neural networks? What mathematical properties do different brains ...
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147 views

Taylor Series. Reusing an approximation of a function

I have this function, $e^{-x}$ bounded between 0 and 1500 and I have an approximation by Taylor Series of the same function bounded between 0 and 0.5. I would like to express my function $e^{-x}$ ...
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167 views

Immunization and Sensitivity Analysis

Frequently a company wants to match its assets and liabilities. However, perfect matching is not practical due to fluctuations in interest rates. So they hedge their risk using immunization. This can ...
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2k views

How to start creating Mathematical models?

I know this is a quite general question , but I've always heard about creating mathematical models in economics, social sciences, engineering,... And I would want to know what are the starting points ...
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1answer
454 views

How do I calculate the instantaneous angular speed of a spindle given a spooled radius and required feed speed?

In an attempt to model the cassette tape spooling action, I'm hoping to solve this problem. Required feed speed 5cm/second. Two Spindles with starting radius of S1: 0.8cm (empty spool) S2: 1.8cm ...
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Probability in single-lane traffic flow: What are the odds of “choke points” being encountered?

Let's say you have a single-lane road (single in this case meaning single lane in each direction, or what you could also call two-lane). Let's say you have a random number of vehicles on a given ...