Related papers: Constructions for Clumps Statistics
Several classical results on boundary crossing probabilities of Brownian motion and random walks are extended to asymptotically Gaussian random fields, which include sums of i.i.d. random variables with multidimensional indices,…
For analysing text algorithms, for computing superstrings, or for testing random number generators, one needs to compute all overlaps between any pairs of words in a given set. The positions of overlaps of a word onto itself, or of two…
Quasirandomness is a general mathematical concept meant to encapsulate several characteristics usually satisfied by random combinatorial objects, and which we regard as describing when a given object 'looks random'. In this survey we…
We use a cluster ensemble to determine the number of clusters, k, in a group of data. A consensus similarity matrix is formed from the ensemble using multiple algorithms and several values for k. A random walk is induced on the graph…
Word matches are often used in sequence comparison methods, either as a measure of sequence similarity or in the first search steps of algorithms such as BLAST or BLAT. The D2 statistic is the number of matches of words of k letters between…
Aggregation patterns are often visually detected in sets of location data. These clusters may be the result of interesting dynamics or the effect of pure randomness. We build an asymptotically Gaussian test for the hypothesis of randomness…
Gibbs-type exchangeable random partitions, which is a class of multiplicative measures on the set of positive integer partitions, appear in various contexts, including Bayesian statistics, random combinatorial structures, and stochastic…
With rapidly increasing data, clustering algorithms are important tools for data analytics in modern research. They have been successfully applied to a wide range of domains; for instance, bioinformatics, speech recognition, and financial…
The word-frequency distribution provides the fundamental building blocks that generate discourse in language. It is well known, from empirical evidence, that the word-frequency distribution of almost any text is described by Zipf's law, at…
We obtain quenched hitting distributions to be compound Poissonian for a certain class of random dynamical systems. The theory is general and designed to accommodate non-uniformly expanding behavior and targets that do not overlap much with…
Let $\pi_n$ be a uniformly chosen random permutation on $[n]$. Using an analysis of the probability that two overlapping consecutive $k$-permutations are order isomorphic, the authors of a recent paper showed that the expected number of…
Existing statistical approaches to natural language problems are very coarse approximations to the true complexity of language processing. As such, no single technique will be best for all problem instances. Many researchers are examining…
We use a probabilistic method to produce some combinatorial inequalities by considering pattern containment in permutations and words.
When approximating the joint distribution of the component counts of a decomposable combinatorial structure that is `almost' in the logarithmic class, but nonetheless has irregular structure, it is useful to be able first to establish that…
In this article we survey properties of mixed Poisson distributions and probabilistic aspects of the Stirling transform: given a non-negative random variable $X$ with moment sequence $(\mu_s)_{s\in\mathbb{N}}$ we determine a discrete random…
The paper describes clustering problems from the combinatorial viewpoint. A brief systemic survey is presented including the following: (i) basic clustering problems (e.g., classification, clustering, sorting, clustering with an order over…
Although many successful ensemble clustering approaches have been developed in recent years, there are still two limitations to most of the existing approaches. First, they mostly overlook the issue of uncertain links, which may mislead the…
We study pairs and m--tuples of compositions of a positive integer n with parts restricted to a subset P of positive integers. We obtain some exact enumeration results for the number of tuples of such compositions having the same number of…
Let $n\geq 1$ and $X_{n}$ be the random variable representing the size of the smallest component of a random combinatorial object made of $n$ elements. A combinatorial object could be a permutation, a monic polynomial over a finite field, a…
Clustering is an unsupervised machine learning methodology where unlabeled elements/objects are grouped together aiming to the construction of well-established clusters that their elements are classified according to their similarity. The…