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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Undergraduate thesis advice
I am presently in my senior year and I am considering fluid mechanics for my thesis. What area of research of fluid mechanics or models of transport mechanism in Biological systems which is purely ...
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89 views
Looking for a Lyapunov function for the next system
I am really stuck looking for a Lypaunov candidate for the next system (which in simulation is stable).
$$ \dot{x} = -(A+A^T)x + Ay \\
\dot{y} = K(x-y)
$$
where x and y are vectors in R^3, A is a ...
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540 views
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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26 views
Regression model for a shearing process
30 Widgets are randomly assigned to a shearing process.
There are 3 such processes, each getting 10 widgets.
The lengths of each widget are recorded before undergoing the shearing.
The amount that ...
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61 views
How to model bending, folding of 2D figures?
2D shape can be folded in various ways. For example, trapezoid can have its sides (with the acute angles) folded, so that it will effectively become rectangle – with the difference, that part of the ...
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316 views
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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25 views
Differential Equations & Sinusoidal Funtions
I am developing a model for sales forecasting and I came up with an ODE:-
The basic premise of the model is that the rate of change of sales is proportional to the no of possible buyers.
...
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45 views
What kinds of sets are reasonable to place on the continuum?
Warning: I don't know anything about set theory so I wouldn't really know how to spot an existing answer if it were around.
Suppose I want to model some economic good or product. I would like to ...
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48 views
Boltzmann machines - motivation for the energy function
I've been studying Boltzmann machines lately and was wondering if anyone could give me a "high-level" explanation or motivation for the energy function used:
$$E = -\sum_{i<j} w_{ij} \, s_i \, s_j ...
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74 views
Considering the predator prey model to find the range of values to be a spiral
I have the following problem:
Consider the predator-prey model: $$\frac{du}{dt}=u(1-\alpha(u)-v), \frac{dv}{dt}=\rho(-1-\alpha(v)+u),$$
where $\rho$ and $\alpha$ are positive parameters with ...
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46 views
Measuring Model Bias
If given the choice between two statistical models (for argument's sake, let's say Model 1 is $y = \beta_0 + \beta_1 x_1 + \epsilon$ and Model 2 is $y = \beta_0 + \beta_1 x^2_1 + \epsilon$), is there ...
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83 views
Modelling randomized cup stacking, animal behaviour
This question has no scientific relevance for me whatsoever, but is a real life question which left me puzzled for a while. Even though I am not going anywere with this, maybe there is still somebody ...
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188 views
Finding a model for multiple non-linear regression
I want to implement a regression analysis, but I have problems with finding a model for the given data. There are $149$ $(x,y,z)$-values. $y$ values are all positive, $x$ is between $[-10, 10]$ and ...
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96 views
Check my solution - Modelling of a spring with Differential Equation
I am doing some work with differential equations. I have solved the following problem but am uncertain if I'm doing it correctly. Could someone look over it for me and check if I'm doing something ...
2
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38 views
Need some help on petri nets?
Here's the question:
$\qquad$
How do we go about doing this ? I have very little knowledge on petri nets. Can someone answer it for me ? (And regarding the program part , just give me an idea on ...
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110 views
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 ...
2
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184 views
Legendre Polynomials
I was given a "generic" matrix that I was told was constructed using Legendre Polynomials.
...
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91 views
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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43 views
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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24 views
How do you set up a system of ODE's for this problem?
The problem is as follows:
Black and White balls are being created inside an arbitrary volume at rates of $Q_{B}$ and $Q_{W}$. They also disappear from the volume at rates $\lambda_{B}$ and ...
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63 views
How to calculate probability with sigmoid output in feedforward neural network?
first of all I'm sorry for my not very skilled English, but I will do my best to explain my problem.
I'm trying to create a feedforward neural network with one hidden layer (with probably arctan ...
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46 views
Can any axiom of a first order mathematical theory be written as a definition?
I have seen different axiomatizations of PA. I some, equality is defined in others is an axiom. The same can be said of addition and multiplication. So it is not clear to me why and when axioms are ...
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32 views
Tensor compact/matrix form.
I have got this tensor $S_{ij} = \frac{1}{2}(\frac{\partial u_i}{\partial x_j} + \frac{\partial u_j}{\partial x_i})$
Anyway I solve it for my problem and get
$$ S_{ij} =
\left( \begin{array}{ccc}
0 ...
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33 views
Curvature of surface
So lets say I have a mesh and for each face I have the position of its $3$ vertices and the area of the face.
So let's say I have a point $p$ on this face and a vector $v$ that goes from $p$ to the ...
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15 views
Is there a trade model which takes in account credulity?
I have to admit I'm not to familiar with mathematical economics but, as a student in mathematics, I was trying to play a bit with a toy trade model I'm try to build over a finite population.
My ...
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34 views
How to model a system with multiple probability distributions, each for a part of the system?
I need to build a complex probability model to describe some "real world" scenarios. The system consists of several types of objects, and the contraints upon these objects and their interactions are ...
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39 views
Transport problem wth time management
Are there general methods for solving the transportation problem with additional conditions:
Time management (transportation from point A to point B is so much)
Transportation of more than one ...
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101 views
How to parametrize a function such that it approaches $f(0)=0$ and $f(1)=1$ with different speed
I need a function (polynome) that values $0$ at $0$ and $1$ at $1$ and has these values as local maxima and minima. So far so easy the straight solution is:
$$f(x) = -x^4+2x^2$$
Now I want to ...
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52 views
Should I get the absolute value of the result of the inverse discrete fourier transform？
The result of equation 36 can be positive and negative.And if I don't get the absolute value of it,the ocean surface tend to be very regular.But according to the paper,the author never get the ...
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20 views
Model to reward adaptative communication
I'm currently working in different simulations focused on the study of artificial evolution of communications in robots, and I have stumbled against the problem of its mathematic formulation.
The ...
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0answers
40 views
Best way to statistically compare two polynomial models?
I'm working on modeling and comparing data sets, and I need a good way to see if there is a significant difference between the data from the 2 models. An example of the models are here.
I initially ...
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29 views
using a scientific paper to model the temperature of pools in an irrigation system
Quite a general question...
I am referring to a scientific paper :
http://www.springerlink.com/content/41p817v1584q1850/
I am trying to model water temperature over a year.
I have the initial ...
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132 views
Phase Plane Analysis
Classify the fixed point at the origin and sketch an accurate phase portrait for the following system:
$$dx/dt = 36x-16y$$
$$dy/dx = -3x+28y$$
Am I correct in thinking that I need to write these two ...
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125 views
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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286 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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278 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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129 views
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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101 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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21 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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104 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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176 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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88 views
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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121 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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21 views
Mathematical Modelling Question
I am just wondering is there any ways you could find out the functions with the use of MATLAB .. to create 3 unknown quadratic functions in the form of :
"a(x-b)^2+c" and use MATLAB or other programs ...
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15 views
mathematical equations that represent the equilibrium model for CO2 absorption.
I want to mathematically model a carbon dioxide absorption column using the equilibrium model (not rate based or dynamic) but I am having trouble finding the same number of numerical equations as I ...
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34 views
Pursuit curves and arc length question
I am studying pursuit curves where a fast pirate ship which pursues a heavily
laden treasure ship which tracks along a straight line. The ratio of the speeds of the
ships is r > 1 (which is fixed) and ...
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32 views
How many ways we know to join two line segments?
This topic was created to discuss how many ways we know to create piecewise linear functions with smooth transitions between the phases. An alternative is presents by Bacon & Watts (1971):
the ...
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18 views
is there a Kalman filter for distribution function?
The standard Kalman filter uses a series of measurements observed over time, to decomposite the signal and noise.
However, when I'm modeling the distribution (pdf or cdf) of a variant, is there a ...
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19 views
Location based Simulations
I wasn't sure if I should ask this on CrossValidated stack, but since this is a math/programming problem for me I figured I'd ask here first. I am data mining user locations via schedules - so I know ...
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179 views
Experiment with a Fourier series with missing fundamental. Mathematical explanation?
On this math.stackexchange
on url Can the differentiating and squaring process in the cochlea explain a reported dichotic stimulation experiment?
I asked the question: Can the differentiating and ...
