# Tagged Questions

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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### Simple Non-Linear ODE - would like to find solution

In the modeling of the oscillation of a meniscus in a straw, the following non-linear ODE was derived. $$y'' = 1/y - 1$$ $y$ is a dimensionless displacement that is solely a function of time. The ...
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### Intuitive meaning of right and left eigenvector

I am trying to get an intuitive understanding of the meanings of right and left eigenvectors. I guess the best thing you can do is to provide examples of application. (Examples from the field of ...
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### What kind of stochastic model shall I build for x(t) if $stdev(dx)$ is linear to $dx$?

I'm building a stochastic model for a process $x(t)$. I notice that daily $dx$ and spot standard deviation of $dx$ seem not related. By spot standard deviation of $dx$ means i take 30 days $dx$ ...
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### What is the relative strength of each of the players in this game?

This is a real life problem. A group of people meet once a week to play a game between two teams. Each round 2 people are randomly appointed captains. Each captain takes turns picking people to be on ...
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### Enlightening Mathematical Models

What is your favourite Mathematical Model? What features make it intuitive or elegant? This question is largely inspired by an example and a desire to find other's like it. Suppose we have two ...
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### How to model a doubling process with errors

An original document is duplicated. With probability $p_{err}$ a mistake is made in the copy (we will dub the resulting document the "wrong" document.) Both the original and the copy (right, or wrong) ...
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### I'm trying to understand the solution to this simple mathematical modelling question

This is an example from Gary Chartrand's "Introductory Graph Theory" (Page 8, Example 1.5). He provides an answer without actually showing the steps or working, and I am unable to figure it out. The ...
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### Eigenvalue/eigenvector calculation for linearly changed matrices

I'm looking for a way to speed up my computation that involves solving a moderate size generalised eigenvalue problem (matrices 400x400) large number of times depending on the parameter $m$. The ...
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### Summation notation problem

Any help is greatly appreciated! Outline: Hermione has been thinking about the imminent return of the Dark Lord, so she has been busy packing her bag with all the items required for her survival. ...
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### Operations research - linear programming help appreciated.

George Weasley, the owner of Weasleys' Wizard Wheezes, recently found that his Skiving Snackboxes have become extremely popular amongst the students at Hogwarts School of Witchcraft and Wizardry, and ...
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### Why does my Barabasi Albert model implementation doesn't produce a scale free network

I'm trying to implement the Barabasi Albert model to generate some scale free network matching a power law distribution of degree. I'm using a value $m = 2$ for the main parameter of the algorithm, ...
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### Interpretation of Phase Portrait

I have the following system $x'=f(X)$ of ODES: \begin{align} x_1'=& -4x_1^3(x_2-2)^2 \\ x_2'=& 2x_1^4(2-x_2) \end{align} Solving for equilibria: I got $1$ at $(0, 2)$. I plotted this and I am ...
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### How to define a surface $z = f(x,y)$ with flat region at centre and sigmoidally tapering towards the edges?

How do we define a continuos function $f(x,y)$ within the bounded domain $x \in [a,b]$ and $y \in [c,d]$ so that $z=f(x,y)$ has a flat surface at the centre (flat means $f(x,y)= C$, $C$ being ...
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### Finding the jacobian of a differential system with a piecewise function

My system: $$\frac{\mathrm{dx} }{\mathrm{d} t}=-ax^2+y^2-\gamma z$$ $$\frac{\mathrm{dy} }{\mathrm{d} t}=- h(y)-\beta y$$ $$\frac{\mathrm{dz} }{\mathrm{d} t}=x+h(y)-\beta z$$ where $h$ is the ...
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### Invert this function $y=(1-x)e^{-x}$

Consider the fucntion $f:\mathcal{R}\rightarrow \mathcal{R}$ given by the rule $f(x)=(1-x)e^{-x}$ Now I want to invert this function(not just for fun but I have a data that seems to fit this ...
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### Given average network diameter, how many nodes are three hops away.

The University of Milan found in 2011 that everyone on the Internet was, on average, 4.74 steps away from anyone else.. is that information sufficient to answer this question: What proportion of ...
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### How to visualize a function to aid in optimization?

I am working on minimization of a function with more than two parameters. I want to see variations, local extremes, saddle points, etc. of this function to get some idea of how is this function in ...
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### Euler angle in ellipsoid rotation

I am modeling an ellipsoid tumbling in a flow field. I have derived an expression for the Euler angle $\phi(t)$ of the rotation in the $x$-$y$ plane as a function of time, but its range is only $\pi$, ...
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### Predicting time t given time t-n

..Hi, Everyone! I'm having a bit of trouble with a statistics/forecasting problem and I could use some help. I have temperature measurements for each hour of each day for the past 10 years. Given the ...
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### How to define an objective function that conveys the concept of selecting the best elements in a set

Consider a set of tasks $\mathcal{T} = \{t_1, \ldots, t_I\}$. Consider also a set of workers $\mathcal{W} = \{w^1, \ldots, w^J\}$, where each worker $w^j \in \mathcal{W}$ is associated with a value ...
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### Question regarding the projective models of the anti-de-Sitter spaces and good online references for learning them from the scratch? (Specifics below)

As my title says above, I am trying to find answers to and also good online reference where I can find complete description of projective models of hyperbolic space, de-Sitter space and anti-de-Sitter ...
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### Water Systems: When can I use buckets of water to simulate an ODE.

It is quite common to use physical systems to perform calculations (see here and here). This is for a number of reasons: sometimes the physical system is efficient, sometimes it helps us understand ...