# All Questions

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### Hypergraph clustering conductance Formula

Consider the Hypergraph $H=(V,E)$, with $V$ being the vertices and $E$ being the hyperedges. What is the formula of conductance $\Phi(S)$ for hypergraphs, with $S$ being a set of vertices (cluster ...
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### On the notion of conelike stratified (cs-) space

The notion of cs-stratification of a topological space is apparently due to Siebenmann, see also the paper by N. Habegger and L. Saper in the paper "Intersection cohomology of cs-spaces and Zeeman's ...
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### Uniform mean-square-error estimates

Consider a standard statistical estimation problem with iid real observations $\{X_i\}_{i=1}^N$. For a collection of real functions $\mathcal{F}$, I want to get an estimate of the uniform rate of ...
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### How to flip a graph over the x-axis but retain the original equation [on hold]

I know this question seems really very basic for this forum, but after about an hour of trying to work it out for myself, I decided to look here for help. The premise I'm trying to create the graph ...
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### Proving that a complex expression of integrals is increasing in a given parameter

Let $f$ and $F$ denote the respective pdf and cdf of a probability distribution on $\mathbb{R}$. Consider any natural $n\geq3$ and any real $c$ such that $c\geq0$, and $\rho\geq0$. We want to prove ...
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### When is a finite $R$-algebra isomorphic to $R$?

Let $R$ be a $\bar{k}$-algebra (of finite type or complete) reduced (and maybe integral, if needed), let $A$ be an $R$-algebra, finite as an $R$-module, reduced and connected and such that there ...
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### Intuitional feeling of harmonic measure on one-third Cantor set

It is known that the harmonic measure on classical one-third Cantor set has Hausdorff dimension strictly less than $\frac{\log 2}{\log 3}$. Even harmonic measure has a close relation with brownian ...
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### I need to know the most active research topic which depend on Real analysis and functional analysis? [on hold]

I need to know the most current topic in pure math with depend mainly on real analysis and functional analysis and not need a good knowledge in algebra and geomtry ? is delay differntial equations is ...
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### Unique Stationary Distribution of A Markov Chain

I have a Markov Chain like $Y_i=\sum_n\pi_{n,i}(Y)Y_n$, i=1,2,3...N. So the Markov chain has N states and the transition matrix depends on the vector $\textbf{Y}$. Moreover, $Y_i$ is continuous and ...
### Randomly put $k$ balls in $2n$ circular boxes, pick $n$ consecutive boxes such that the number of balls is minimum!
You are given $2n$ boxes that are arranged circular (you can imagine all boxes are on the edge of a circular table). Then randomly, you put $k$ balls in the boxes such that each box is containing ...