Author: ignougroup

Problem Detail: I’m reading a paper that refers to the limit as n goes to infinity of Rényi entropy. It defines it as ${{H}_{n}}left( X right)=dfrac{1}{1-n} log_2 left( sumlimits_{i=1}^{N}{p_{i}^{n}} right)$. It then says that the limit as $nto infty $ is Read More …

Problem Detail: I was watching the lecture by Jim Weirich, titled ‘Adventures in Functional Programming‘. In this lecture, he introduces the concept of Y-combinators, which essentially finds the fixed point for higher order functions. One of the motivations, as he mentions Read More …

Problem Detail: Suppose we’re receiving numbers in a stream. After each number is received, a weighted sum of the last $N$ numbers needs to be calculated, where the weights are always the same, but arbitrary. How efficiently can this done if Read More …

Problem Detail: Given – A center(lat=x,lng=y) ‘C’ from which a delivery boy makes a round trip. A delivery boy has a bag which may contain at the most 10 boxes to deliver. A set of points Di (lat=xi,lng=yi) around ‘C’ where Read More …

Problem Detail: Let $text{NOT-SELF} = {langle M rangle : M text{ is a TM that does not accept } langle M rangle }$. How do you prove the following claim? If $Q$ is a TM so that $L(Q) subseteq text{NOT-SELF}$, prove Read More …

Problem Detail: I want to study theory of computation on my own, so I am looking for books. What set of books would you recommend for the equivalent of a one-semester course that introduces theory of computation? Please post answers that Read More …

Problem Detail: I want to express the following constraint, in an integer linear program: $$y = begin{cases} 0 &text{if } x=0 1 &text{if } xne 0. end{cases}$$ I already have the integer variables $x,y$ and I’m promised that $-100 le x Read More …

Problem Detail: So say we have a bipartite graph G=(X,Y,E). Let’s make a game out of it. I go first. I pick a node in X. You go next. You pick a node in Y that is connected by an edge Read More …

Problem Detail: I have an undirected unweighted graph $G$ and I want to select $k$ nodes from $G$ such that they are pairwise as far as possible from each other, in terms of geodesic distance. In other words they have to Read More …

Problem Detail: I’ve been reading some formal language theory papers, and I’ve come across a term that I don’t understand. The paper will often refer to a set being “effectively closed under intersection” or other operations. What does “effectively” mean here? Read More …