1
vote
0answers
83 views

Mean Capture time for the Rabbit-Hunter paper by Peres et al [closed]

I am a non-math student. I am trying to read the paper "Hunter, Cauchy Rabbit, and Optimal Kakeya Sets" by Yuval Peres et al. Link - http://arxiv.org/abs/1207.6389 In his video based on the paper - ...
15
votes
3answers
520 views

Which distributions can you sample if you can sample a Gaussian?

Explicitly: You have a computer that is able to pick a real number at random according to the normal distribution: $\mathcal{N}(0,1) = \frac{1}{\sqrt{2\pi}}e^{-x^2/2}$. Which distributions can this ...
13
votes
3answers
619 views

How do we express measurable spaces using type theory?

A measurable space $(X,\mathcal X)$ consists of a set $X$ equipped with a $\sigma$-algebra of subsets $\mathcal X$. I would like to write computer programs involving measurable spaces, but to the best ...
0
votes
0answers
192 views

An interesting version of the problem “balls into bins”

Consider n people, each has k identical balls. Each people choose k different bins from m bins, constrained by the condition that there are no two people choose exactly the same k bins. For instance, ...
18
votes
2answers
865 views

Expected edit distance

The edit or Levenshtein distance between two strings is the minimum number of single symbol insertions, deletions and substitutions to transform one string into another. For example ...
1
vote
0answers
129 views

Optimizing for a unique outcome of a probabilistic marriage problem

Let's say I have some number of individuals who are single, $(b_1, ..., b_N) \in B$, and for every possible pairing of two individuals, $b_i$ and $b_j$, I happen to know the exact probability that the ...
1
vote
3answers
347 views

Operator probability in a RPN string

Consider the set $S_n$ of all strings of length $n$ ($n$ integer, $n \geq 3$) representing an expression in RPN ( http://en.wikipedia.org/wiki/Reverse_Polish_notation. ) Assumptions (to simplify): ...
2
votes
2answers
228 views

Correcting bias in samples selected by a prediction

Here is the scenario: I'm trying to find as many golden tickets as I can, so that I can sell them to kids that want to go on a tour of Wonka's chocolate factory. Fortunately, I have a machine that ...
8
votes
0answers
1k views

Question on randomness extractors

Person A has a source $W$ with min-entropy($W$) = $k$. He also has an extra piece of information about the random source, denoted with $y$, such that min-entropy($W|y$) = $k/3$. The adversary doesn't ...
3
votes
2answers
1k views

finding numbers at k hamming distance

Guys, I have N < 2^n randomly generated n-bit numbers stored in a file the lookup for which is expensive. Given a number Y, I have to search for a number in the file that is at most k hamming ...
3
votes
4answers
1k views

Does an “efficient” random number generator exist?

Given some number $n$ and a seed number $s$<$n$, I want a random number generator (RNG) that will go through all integers `<$n$ before coming back to $s$. The resulting random number must be ...
9
votes
2answers
451 views

When can a freely moving sphere escape from a 'cage' defined by a set of impassible coordinates?

To ask this question in a (hopefully) more direct way: Please imagine that I take a freely moving ball in 3-space and create a 'cage' around it by defining a set of impassible coordinates, $S_c$ ...
4
votes
6answers
626 views

Reconstructing an ordering of a multiset from its consecutive submultisets

We have a multiset $S$ of size $t$ with $r$ distinct elements, where $t$ is much larger than $r$. We want to reconstruct an ordering $s_1, s_2, ... s_t$ of the elements of $S$ given the values of $t$ ...
2
votes
3answers
2k views

Counting lattice points on an n-simplex

Imagine an n-simplex, the solution set for the expression: $a_1$*$x_1$ + $a_2$*$x_2$ + ... + $a_n$*$x_n$ = S, where: $a_1$ through $a_n$ are positive bounded integers $x_1$ through $x_n$ are ...
13
votes
8answers
2k views

How Does Random Noise Typically Look?

How does random noise in the digital world typically look? Suppose you have a memory of n bits, and suppose that a "random noise" hits the memory in such a way that the probability of each bit being ...