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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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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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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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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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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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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485 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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951 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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533 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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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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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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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 ...
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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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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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Is there a SoftMax distribution with confidence parameters?

This is a softmax probability distribution: $$P(i\mid w_1, w_2, \ldots, w_n) = \frac{\exp(w_i)}{\sum_{i=1}^n \exp(w_i)}.$$ It known also as Boltzmann distribution. It is used in generalized ...
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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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1k views

Simple math formula to calculate average

I am making a software that deals with employee trust. I am trying to make a math formula (no need to tell that I am bad in math :) ). Here is the scenario: ...
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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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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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100 views

Development of a specific hardware architecture for a particular algorithm. Modelling fuctions by Taylor sSeries.

I'm trying to develop a architecture hardware to make a implementation of an algorithm that can be descompose in terms of sums, multiplications, subtractions and exponential functions. I'm trying to ...
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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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449 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 ...