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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special matrix in terms of its covariance matrix

How can we find a matrix $S\in \mathcal{M}_{n,n}$ and $Z\in \mathcal{M}_{n,m}$ whose $n$ entries of the $i^{th}$ column $Z_i$ are correlated $Z_i \sim \mathcal{N}(0,S)$ where $S \in \mathcal{M}_{n,n}$ ...
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334 views

How to classify equilibrium points

I have the two differential equations: $$\frac{dN_1}{dt} = N_1(2 - N_1 - 2N_2)$$ $$\frac{dN_2}{dt} = N_2(3 - N_2 - 3N_1).$$ I worked out the equilibrium points to be at $N_1 = 0, \frac{4}{5}$ and ...
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48 views

Solving a form of the logistic equation to arrive a given solution

I am writing my bachelor thesis on modelling of city growth and using the book Cities and Complexity by Michael Batty. On page 394, while modelling the growth as spatial epidemic, he writes: ...
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1answer
124 views

Shape of a Kite String

A kite is flown at some angle and elevation. Without wind, the string takes the shape of a catenary curve. But the wind is crucial. Is there a name for the shape of a kite string -- is it some ...
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80 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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2k views

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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3answers
816 views

I need a differentiable function whose plot is a plateau and the steepness and width can be varied arbitrarily and easily

I need to model the solar radiation incident on a solar panel. I tried using $$\tanh(b*(x-a))-\tanh(b*x)$$ but it does not give me a lot of flexibility with the characteristics of the curve, namely ...
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2k views

Calculating equilibrium point of non-linear ODE with free parameter

I have two ordinary differential equations equations: $$ \dot{x}=1+x^{2}y-(1+A)x $$ $$ \dot{y}=Ax-yx^{2} $$ I need to find the single equilibrium point in terms of $A$. So set $\dot{x}$ and ...
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62 views

Amount of information a hidden state can convey (HMM)

In this paper (Products of Hidden Markov Models, http://www.cs.toronto.edu/~hinton/absps/aistats_2001.pdf), the authors say that: The hidden state of a single HMM can only convey log K bits of ...
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43 views

Trouble understanding a part of the book Cities and Complexity

I am writing my bachelor thesis or whatever it is called about modelling of city growth, using a book called Cities and Complexity by Michael Batty. It is not that mathematical, to be honest, it has ...
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64 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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824 views

How to design a weighted formula with multiple inputs?

Apologies if this is the completely wrong verbiage for this sort of thing... kinda new to this. We're designing a social website, where users on the site have several statistics associated with them. ...
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2answers
343 views

Slide Puzzle logic??

say there is an image made into a slide puzzle in a grid of sections 4 wide and 6 high, the missing piece that is missing so you can slide the other pieces of the puzzle around is always the bottom ...
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1answer
103 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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25 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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80 views

Calculating the expected number of items shared by chance in a Venn Diagram

I have a Venn Diagram that looks like this: $$A) \, 213 \quad B) \, 160 \quad A\cap B) \, 100$$ The items from $A$ come from a population where their probability to be selected is ...
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103 views

how to estimate a variable's upper limit with 95% confidence level?

Suppose I have a variable, $S(t)$, for stock price. So always have $S(t) > 0$. $S(t)$ is a random variable, with some volatility $\sigma$ and trend. Now the requirement is to estimate $\hat ...
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78 views

Computing the length of a path

The rectangular grounds at Hillingham University is going to have a new path built which takes the curved shape of $y=2.2x^2$, starting from the south-west corner - (taken as the origin in a graph) ...
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2k 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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1answer
193 views

How large initial angular velocity is needed for pendulum to go completely around?

If a pendulum is initially at its unstable equilibrium position, how large an initial angular velocity is necessary for it to go completely around?
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132 views

Are there rigorous mathematical definitions for these waves?

My friend linked this .gif to me tonight, and asked me if I knew of any equations that might model these bottom two waves (the blue and green waves). Unfortunately, I am not far enough in my education ...
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54 views

a line perpendicular to a given line

I am confused now, I have a 2D line. If its equation is $r = x\cos(\theta) + y\sin(\theta)$, then what will be the line which is perpendicular to that line? Where $r, \theta$ is described ...
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438 views

Bookshelf problem

There is this thought problem I've been trying to solve, it goes as follows Imagine a bookshelf with a finite number of books in it, to which a finite number of people have access. Each person has a ...
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2answers
152 views
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1answer
251 views

Calculating Humidity, Wet Bulb Temp and Dew Point [closed]

I have been trying to simulate a climate system, but I have hit a wall. I am trying to calculate Humidity. But to calculate Humidity you need the Wet Bulb Temperature, but to calculate the Wet Bulb ...
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1answer
169 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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70 views

hopf bifurcation for an ode

I understand how to analyse a system of equations like $x'(t) = f(x,y)$ $y'(t) = g(x,y)$ set $x'$ and $y'$ to zero and find the fixed points etc, and find the stability. What Im am not sure of ...
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50 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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3answers
2k views

Is there a general solution for the “Spider and the Fly Problem”?

(I would be appreciative if somebody could give a more formal formulation of this problem.) The Spider and the Fly Problem is a problem in which the objective is to minimize the distance the spider ...
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1answer
500 views

Can the differentiating and squaring process in the cochlea explain a reported dichotic stimulation experiment?

On this math.stackexchange on url What is Octave Equivalence? in an answer on the related ( octave equivalence ) question is stated: Mathematically, this signifies that the mammalian cochlea ...
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1answer
127 views

Creating a model

Here's a seemingly simple pondering. If one item is more valuable the higher it is (i.e., $a=5$ is worth more than $a=2$) and another item is more valuable the lower it is (i.e., $b=2$ is worth more ...
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55 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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196 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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1answer
141 views

Could you help me to find a model for this curve?

I am very bad in mathematics and I'm not able to find by myself the model corresponding to this kind of curve. I wish to have a quick growth at the beginning, then it should increase slowly for a ...
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1answer
460 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
135 views

Iterative model fitting

I have a sequence of points $\{(x_k,y_k,z_k)\}$ and I need to fit some $2D$ model $P(x,y)$ that approximates $z$ in some sense. The $z_k$$'s$ are noisy samples of some $2D$ function $z_k = f(x,y) + ...
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1answer
45 views

How to solve these simultaneous equations:

$1 = 1/2y - bx,$ $1 = 1/2x - ay$ I need x,y it in terms of constants, but I can't figure it out!
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1answer
157 views

Actuarial / Modelling question - difference between RUN date and VAL date

My understanding is that RUN date is the date you do the RUN (eg in prophet / moses / igloo / whatever, the date on which you performed the calculations) Whereas VALuation date is the initial 'as at' ...
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145 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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25 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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1answer
446 views

Complex results in inverse Fourier transform for simulating ocean water

I don't understand the equation37 in simulate ocean water by Jerry Tessendorf.The result is all complex number, how to be the slope.Even if I compute the magnitude of it,the result is just positive ...
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0answers
105 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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1answer
104 views

Finding a logical expression (under some constrains) s.t. it is equivalent to another one

In this question, it was made clear, when $\bullet$ some statement $A$ is stronger than another statement $B$, namely if $A\Rightarrow B$ holds; and when the statement $A$ is weaker than another ...
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118 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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0answers
151 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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1answer
75 views

Inverse of itinerary function

Let $S^{-1}:\Sigma \to \Lambda$ be inverse of itinerary function. I showed that $S$ is continuous and bijective. How to show that $S^{-1}$ is continuous?
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418 views

Time-evolving probability distribution functions with an equation of motion

I came up with this question a while ago and haven't been able to gain any insight on it. You are playing baseball. As a batter with finite vision capabilities, the only information you have about ...
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1answer
281 views

a mathematical model for file system

We are supposed to come up with a mathematical model describing a file system and its operations. The file system stores metadata in a database, and retrieves it when necessary. How does one go about ...
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1answer
76 views

Which variable represents the predator and which the prey.

Just a quick question I have the following system: $$\frac{dx}{dt}=x\left(2-x-\frac{y}{1+x}\right),\qquad \frac{dy}{dt}=3y\left(\frac{x}{1+x}-4y\right)$$ It asks which variable represents the predator ...
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41 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 ...