相关论文: On the typical values of the cross-correlation mea…

Let $\tau_k$ be the $k$-fold divisor function. By constructing an approximant of $\tau_k$, denoted as $\tau_k^*$, which is a normalized truncation of the $k$-fold divisor function, we prove that when $\exp\left(C\log^{1/2}X(\log\log…

A set of sets is called a family. Two families $\mathcal{A}$ and $\mathcal{B}$ of sets are said to be cross-intersecting if each member of $\mathcal{A}$ intersects each member of $\mathcal{B}$. For any two integers $n$ and $k$ with $1 \leq…

Simultaneous statistical inference has been a cornerstone in the statistics methodology literature because of its fundamental theory and paramount applications. The mainstream multiple testing literature has traditionally considered two…

Family symmetries are possibly the most conservative extension of the Standard Model that attempt explanations of the pattern of fermion masses and mixings. The observed large mixing angles in the lepton sector may be the first signal for…

Comparing clusterings is central to evaluating unsupervised models, yet the many existing similarity measures can produce widely divergent, sometimes contradictory, evaluations. Clustering similarity measures are typically organized into…

Given a family $\mathcal{F}$ of subsets of $[n]$, we say two sets $A, B \in \mathcal{F}$ are comparable if $A \subset B$ or $B \subset A$. Sperner's celebrated theorem gives the size of the largest family without any comparable pairs. This…

As a generation of the classical percolation, clique percolation focuses on the connection of cliques in a graph, where the connection of two $k$-cliques means that they share at least $l<k$ vertices. In this paper, we develop a theoretical…

The connection between the commutativity of a family of $n\times n$ matrices and the generalized joint numerical ranges is studied. For instance, it is shown that ${\cal F}$ is a family of mutually commuting normal matrices if and only if…

When some treatments are ordered according to the categories of an ordinal categorical variable (e.g., extent of side effects) in a monotone order, one might be interested in knowing wether the treatments are equally effective or not. One…

We show that for a typical coordinate projection of a subgaussian class of functions, the infimum over signs $\inf_{(\epsilon_i)}{\sup_{f\in F}}|{\sum_{i=1}^k\epsilon_i}f(X_i)|$ is asymptotically smaller than the expectation over signs as a…

Given F:[a,b]^k\to [a,b] and a nonconstant X_0 with P(X_0\in [a,b])=1, define the hierarchical sequence of random variables {X_n}_{n\ge 0} by X_{n+1}=F(X_{n,1},...,X_{n,k}), where X_{n,i} are i.i.d. as X_n. Such sequences arise from…

The measurement of finite frequency noise cross-correlations represents an experimental challenge in mesoscopic physics. Here we propose a generalisation of the resonant LC circuit setup of Lesovik and Loosen which allow to probe directly…

We derandomize G. Valiant's [J. ACM 62 (2015) Art. 13] subquadratic-time algorithm for finding outlier correlations in binary data. Our derandomized algorithm gives deterministic subquadratic scaling essentially for the same parameter range…

In this paper, we use a new partial order, called the f-majorization order. The new order includes as special cases the majorization , the reciprocal majorization and the p-larger orders. We provide a comprehensive account of the…

In this paper we provide the asymptotic theory of the general of $\phi$-divergences measures, which includes the most common divergence measures : Renyi and Tsallis families and the Kullback-Leibler measure. Instead of using the Parzen…

A fractional fuzzy Potts measure is a probability distribution on spin configurations of a finite graph $G$ obtained in two steps: first a subgraph of $G$ is chosen according to a random cluster measure $\phi_{p,q}$, and then a spin…

A family of $k$-subsets $A_1, A_2, ..., A_d$ on $[n]=\{1,2,..., n\}$ is called a $(d, c)$-cluster if the union $A_1\cup A_2 \cup ... \cup A_d$ contains at most $ck$ elements with $c<d$. Let $\mathcal{F}$ be a family of $k$-subsets of an…

A function f : {0, 1}^n -> {0, 1} is said to be k-monotone if it flips between 0 and 1 at most k times on every ascending chain. Such functions represent a natural generalization of (1-)monotone functions, and have been recently studied in…

Simultaneously testing $K$ hypotheses while controlling the family-wise error rate is a fundamental problem in statistics. Existing procedures (Bonferroni, Holm, Hochberg, Hommel) provide valid control but sacrifice power, increasingly so…

Let $\{(A_i,B_i)\}_{i=1}^m$ be a set pair system. F\"{u}redi, Gy\'{a}rf\'{a}s and Kir\'{a}ly called it {\em $1$-cross intersecting} if $|A_i\cap B_j|$ is $1$ when $i\neq j$ and $0$ if $i=j$. They studied such systems and their…