A vast area which includes generating results from computer models.

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31 views

What platform is best for simulating a stochastic process on a graph/network?

I'm simulating a dynamic process which was so far done only on a lattice, and Matlab was quite sufficient for that. However, I can't seem to find a convenient way to model such a process on a graph ...
1
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1answer
48 views

Permutation algorithm for simulating random variables $X,Y,Z \in [0,1]: X+Y+Z = 1$ and $X,Y,Z \sim U(0,1)$

Edit: Sorry, I tend to jump back and forth between math notation and computer science notation....often to the chagrin of my more rigorous colleagues (and Math.SE folks ;-) Also, I accidentally ...
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1answer
45 views

Looking for Method to evaluate the optimal node rate vs number of simulation rate in a Monte Carlo simulation

I am currently working on evaluating an American Option using a Monte Carlo simulation, and I am getting answers but they vary quite a bit. The two variables that I can alter are number of simulations ...
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1answer
52 views

uniqueness of svd decomposition and its role in statistical analysis

let us consider following model according to following link http://www4.ncsu.edu/~ipsen/REU09/chapter4.pdf it says that : The singular values are unique, but the singular vector matrices are ...
2
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2answers
105 views

Probability that winner of tournament is best player

There are $2^n$ players with skills $1, 2, \ldots, 2^n$ where the probability of Player A winning any game (against B) is $\text{skill}(A)/(\text{skill}(A)+\text{skill}(B))$. Set up a tournament of ...
3
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1answer
42 views

Simulating elastic collision

I wrote a simple program where i can move around some objects. Every object has a bounding box and I use hooke's law to apply forces to the colliding objects. On every tick, I calculate the forces, ...
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1answer
34 views

Tissue Deformation Simulation using FEM

I need to simulate tissue deformation using FEM. Is it advisable to represent the object as a triangle mesh or a ...
4
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1answer
94 views

Applying MCMC Metropolis algorithm

I'm interested in all possible paths (on the grid $\mathbb{N}^2 $) that goes from $ (0,0) $ to $ (n, n) $. At each step there are two possibilities: go right or go up. The path is a sequence $ ...
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2answers
220 views

Calculating a Cardgame

I was send here from stackoverflow because they thought maybe you can help me. Here my original post: http://stackoverflow.com/questions/26799476/a-faster-way-then-doing-14-for-loops What I want: ...
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1answer
140 views

Incomplete Cholesky decomposition conjugate gradient method in Matlab

I have a problem in finding the numerical material that describing in detail for incomplete Cholesky combined with conjugate gradient method by using Matlab. Someone can help me? Many thank in ...
0
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1answer
46 views

Angular momentum superposition

I am doing a space simulation. I have a spaceship and this spaceship has engines that don't push the spaceship through its center of gravity. These engines can therefore give the spaceship angular ...
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1answer
52 views

Generate a random chain with cauchy distribution using C language

Here is my question: I want to simulate a random variable using cauchy distribution with C language. Scale and position must be setted manually. I fuond the GSL library wich contain the function: ...
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0answers
84 views

Uniform Sampling over Convex Polytope (not full-dimensional)

I want to simulate a uniform distribution on a convex polytope that is not full-dimensional for optimization purposes (to generate random points on the set I want to minimize over). The polytope is ...
3
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1answer
58 views

Hypercomputation & Higher Dimensional Variants of Conway's Game of Life

Conway's Game of Life is a simple and important mathematical game with some rules of evolution in a two dimensional space. It appears in many subjects in mathematics, artificial intelligence and ...
2
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0answers
33 views

Are these two approaches to calculating return rate mathematically consistent?

I have coded two C# programs, which use two different approaches to evaluate the outcome of a certain casino-style game (casino-style in the sense that the user pays points to take a turn, and ...
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0answers
125 views

Backward Euler method with a cross-product.

I want to solve the following differential equation with the backward Euler method ...
0
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1answer
46 views

Conditional probability problem and Alias Method

I hopefully someone can help me with this problem of conditional probability: "A disk server receives requests from many client machines and requires 10 milliseconds to respond to each request. The ...
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0answers
88 views

Expected Probability of a Random Agent and a Probabilistic Agent

I'm running simulations on two agents: random agent and probabilistic agent. The world they are running in is the Wumpus World where the agent is dropped in a 4x4 grid where each cell has a 20% chance ...
2
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0answers
22 views

orderstatistics of uniform distributions on different ranges

During a simulation I discovered an interesting phenomenon: Given you have 3 agents. 2 are uniformly distributed between [0,1] and one between [0,2]. The question is how often do the smaller agents ...
0
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1answer
42 views

Simulating a controlled dynamical system

I am try to simulate a controlled dynamical system of the form $$\dot{x}=f(x,\phi(x)),$$ where $\phi$ is the controller. To do so, I am using Octave (an open source version of Matlab). My commands ...
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1answer
45 views

Approximation and Monte Carlo simulation.

I am a bit up over my head here, I will present an argument and then I hope you guys will say if my reasoning is correct or what should be changed, ultimately I am hoping to say something qualified ...
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1answer
182 views

Simple Monte Carlo simulation/approximation of 2 pair in a 5 card poker hand

I am very curious about simulation of an event where an estimating/sampling technique is used. In this example, the goal is to simulate a subset of all the roughly $2.6$ million $5$ card poker hands ...
0
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1answer
78 views

Distribution of hitting position of line by brownian motion.

What is known about the distribution of the hitting position of a line by a 2d brownian motion? I've tried to make some simulations of a 2d brownian motion where every computational step has a ...
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2answers
279 views

How to calculate the direction (of velocity of a ball) after collision with another ball?

Say I have two balls of same radius, in the 2-D Plane. So like a pool (billiard) game. I have the cue ball, moving with the velocity vector V, the magnitude is not important, so we only need an angle ...
3
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0answers
69 views

Maximize or find an upper bound of the function $kx^{k-1}\exp(-\mu(x^k-x))$

I was programming some random variable simulation using the acceptance-rejection method and I encounter with the Weibull$(k,\lambda)$ distribution. This random variable is posible to simulate with ...
0
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1answer
68 views

Simulate simple non-homogeneous Poisson proces

Consider a Poisson process whose conditional intensity is $$\lambda(t) = \alpha e^{-t}$$ starting at time $t=0$ for some parameter $\alpha>0$. I would like to simulate arrival/event/failure ...
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1answer
49 views

How to simulate from a simple point process

Define a point process by the conditional intensity function $$\lambda^*(t) = \mu + \alpha \sum_{t_i < t} e^{-(t-t_i)}$$ where $\mu$ and $\alpha$ are positive parameters. I would like to ...
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0answers
20 views

Stability of simulation of brownian noise

As I understand, Brownian noise can be simulated by the process $$x_{n+1}=x_n+R_n$$ where $R\sim U[-a,a]$. The expected value for $x_n$ is then $x_0$. But $\text{Var} x_n\to\infty$ as $n\to\infty$ ...
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1answer
139 views

Estimate arrival time of a ship given the average of the ships in a day in a Poisson Distribution

I'm working in a simulation of a Port where ships come to specific stations of the port. I already know that the average amount of ships is given by a Poisson distribution and the service time (On ...
1
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1answer
37 views

Simulation of orbiting bodies

I am writing a computer program to simulate orbiting bodies such as planets and stars. I wish to have a starting point in which a number of bodies are randomly scattered around a central heavy body. ...
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0answers
48 views

Distribution of phone calls during 24h

I would like to model the amount of phone calls at each time of the day. The phone calls should follow a poisson distribution and at 12:00 there should be the peak. So, semantically what I would like ...
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votes
2answers
64 views

Operations on distributions

Say we have two r.v X and Y which are independent and differently distributed ( for e.g X follows a bell curve and Y follows an exponential distribution with parameter $\lambda > 0$ What are the ...
0
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1answer
36 views

Simulation from cdf

Give a method for simulating from $$F(x) =\left\{\matrix{ \frac{(1-e^{-2x}+2x)}{3},& 0 < x < 1\cr \frac{3-e^{-2x}}{3}, & 1 < x < ∞}\right.$$ (Work out the pdf, and try to ...
0
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1answer
52 views

Calculate expectation under risk neutral measure: $\mathbb{E_Q}(\max(S-1,0))$

I am busy with a numerical simulation and I want the calculate the following expectation under the risk neutral measure: $\mathbb{E_Q}(\max(S-1,0))$. $S$ is some variable that I calculated using ...
1
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1answer
28 views

Proportion expected in a simulation

X and Y are independent random variables uniform taking values ​​in the sets {1, 2, 3} and {1, 2}, respectively. As can know by simulating the expected ratio for the pair $(X, Y)$ such that $X > ...
2
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1answer
61 views

Mean Value Function and CDF of Nonhomogeneous Poisson

Consider a nonhomogeneous Poisson process on $[0, T]$ with mean value function $m(t)$ for $t \in [0, T]$. Let $X_1$ denote the time of the first arrival. Show that $(X_1\,|\,N(T) = 1)$ has the ...
0
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1answer
38 views

Standard deviation shouldn't reduce?

I need to do a algorithm to calculate an integral via Monte Carlo Method, and for a purpose of simulation, I need to calculate the standard deviation of a sample generated in my program. My problem is ...
0
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1answer
176 views

Simulation - Find the maximum of a function with exponential decay

I need to run a program to calculate the integral of the following function with exponential decay $$t(x) = \exp(-Lx)(a\sin(bx) + d\cos(ex))$$ and for a simulation purpose, I need to find maximum of ...
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0answers
63 views

Forest fire simulation; analytically constructing a function for tree residual after fire

Consider a Cellular Automaton with an $n \times n$ grid, where each cell corresponds either to a tree or dirt. We assign a tree to cell $(i,j)$ by probability $p$. Next, we initiate a fire in some ...
3
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1answer
154 views

Proving that Markov Chain Monte Carlo converges

I am trying to understand how the very basic Markov Chain Monte Carlo approach works: We try to approximately calculate the expected value $E_{\pi(x)}[X]$ by drawing sequential samples from a Markov ...
1
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1answer
24 views

How to know when samples tend toward lowest number?

I am working on a computer simulation. In a perfect world, I only want to know what the minimum result value is from the simulation. (I have no a-priori knowledge about the range of numbers or their ...
2
votes
2answers
215 views

Calculate maximal island of ones in a matrix

I have came up with a problem involving matlab and matrices with entries 1 or zero. The matrix represents people in a footballstadium, doing a wave. If a person does the wave, he has a one in the ...
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0answers
104 views

Kalman Filter application to non-linear system.

I want to use the Kalman filter to have a better estimate of the state of a system which I know its equations of motion: ...
7
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1answer
121 views

Distribution of time spent above $0$ by a Brownian Bridge.

Let's say I have a Brownian motion, such that I know its value at time 0 (0) and time T (also 0). I am trying to evaluate the time spent above 0 between time 0 and T. Obviously I know that the ...
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0answers
71 views

simulate hitting time of Brownian motion

let's say I have a brownian motion $W_t$, and I know the value of $W_1$. Is there a way to simulate the hitting time of $W_t$ and a given function $f(t)$ ? For instance I know that if $f(t)$ is a ...
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0answers
50 views

Random graphs simulation

Reading the article "Emergence of scaling in random network, by Barabasi and Albert" I faced a lot of results obtained by simulations of the A-B random graph model. I always wanted to do such ...
0
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1answer
27 views

Determining simulation threshold

Let's suppose we have some sort of game (for instance tic-tac-toe) with a limited amount of moves. I want to simulate that game, and with that I will use a random number generator (RNG) to calculate ...
0
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1answer
852 views

R - generate sample that follows a geometric distribution

I'm having trouble coming up with an algorithm that generates a sample (X1,...,Xn) of size n, considering several values for n, where the random variable Xi – “number of trials until the first success ...
2
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4answers
2k views

How do I simulate a simple pendulum?

I have the equation of motion of a simple pendulum as $$\frac{d^2\theta}{dt^2} + \frac{g}{l}\sin \theta = 0$$ It's a second order equation. I am trying to simulate it using a SDL library in C++. I ...
2
votes
2answers
61 views

Analytic methods vs Monte Carlo (terminology)

What's the correct terminology to say "We can calculate the probability exactly using pure math, as opposed to Monte Carlo simulation"? Analytically sounds like we need Calculus, which we may not ...