Related papers: On the Variance of the Optimal Alignments Score fo…
Distribution matching is the process of invertibly mapping a uniformly distributed input sequence onto sequences that approximate the output of a desired discrete memoryless source. The special case of a binary output alphabet and…
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…
We consider the problem of estimating the probability of an observed string drawn i.i.d. from an unknown distribution. The key feature of our study is that the length of the observed string is assumed to be of the same order as the size of…
Researchers are often interested in drawing inferences regarding the order between two experimental groups on the basis of multivariate response data. Since standard multivariate methods are designed for two-sided alternatives, they may not…
Comparison and evaluation of graph-based representations of sentence meaning is a challenge because competing representations of the same sentence may have different number of nodes, and it is not obvious which nodes should be compared to…
In this paper we consider lossless source coding for a class of sources specified by the total variational distance ball centred at a fixed nominal probability distribution. The objective is to find a minimax average length source code,…
We calculate the large deviations for the length of the longest alternating subsequence and for the length of the longest increasing subsequence in a uniformly random permutation that avoids a pattern of length three. We treat all six…
Consider infinite random words over a finite alphabet where the letters occur as an i.i.d. sequence according to some arbitrary distribution on the alphabet. The expectation and the variance of the waiting time for the first completed…
The study of linear codes over a finite field of odd cardinality, derived from determinantal varieties obtained from symmetric matrices of bounded rank, was initiated in a recent paper by the authors. There, one found the minimum distance…
Sequence comparison is a prerequisite to virtually all comparative genomic analyses. It is often realised by sequence alignment techniques, which are computationally expensive. This has led to increased research into alignment-free…
The size and complexity of software and hardware systems have significantly increased in the past years. As a result, it is harder to guarantee their correct behavior. One of the most successful methods for automated verification of…
The analysis of strings of $n$ random variables with geometric distribution has recently attracted renewed interest: Archibald et al. consider the number of distinct adjacent pairs in geometrically distributed words. They obtain the…
The problem is considered of arranging symbols around a cycle, in such a way that distances between different instances of a same symbol be as uniformly distributed as possible. A sequence of moments is defined for cycles, similarly to the…
Sequential word order is important when processing text. Currently, neural networks (NNs) address this by modeling word position using position embeddings. The problem is that position embeddings capture the position of individual words,…
We explore the role of group symmetries in binary classification tasks, presenting a novel framework that leverages the principles of Neyman-Pearson optimality. Contrary to the common intuition that larger symmetry groups lead to improved…
We study a binary distributed hypothesis testing problem where two agents observe correlated binary vectors and communicate compressed information at the same rate to a central decision maker. In particular, we study linear compression…
In automatic speech recognition, many studies have shown performance improvements using language models (LMs). Recent studies have tried to use bidirectional LMs (biLMs) instead of conventional unidirectional LMs (uniLMs) for rescoring the…
This paper considers the problem of variable-length intrinsic randomness. We propose the average variational distance as the performance criterion from the viewpoint of a dual relationship with the problem formulation of variable-length…
Algorithms to find optimal alignments among strings, or to find a parsimonious summary of a collection of strings, are well studied in a variety of contexts, addressing a wide range of interesting applications. In this paper, we consider…
In this note we put forward a conjecture on the average optimal length for bipartite matching with a finite number of elements where the different lengths are independent one from the others and have an exponential distribution.