Related papers: On the Variance of the Optimal Alignments Score fo…

This paper develops a framework for the design of scoring rules to optimally incentivize an agent to exert a multi-dimensional effort. This framework is a generalization to strategic agents of the classical knapsack problem (cf. Briest,…

Score matching is a recently developed parameter learning method that is particularly effective to complicated high dimensional density models with intractable partition functions. In this paper, we study two issues that have not been…

Fix two words over the binary alphabet $\{0,1\}$, and generate iid Bernoulli$(p)$ bits until one of the words occurs in sequence. This setup, commonly known as Penney's ante, was popularized by Conway, who found (in unpublished work) a…

We show that for n>2 the following equivalence problems are essentially the same: the equivalence problem for Lagrangians of order n with one dependent and one independent variable considered up to a contact transformation, a multiplication…

Consider the extreme value of a Bernoulli random walk on the one-dimensional integer lattice, with reflection at 0, over a finite discrete time interval. Only the asymmetric (biased) case is discussed. Asymptotic mean/variance results are…

We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…

When considering binary strings, it's natural to wonder how many distinct subsequences might exist in a given string. Given that there is an existing algorithm which provides a straightforward way to compute the number of distinct…

We define a new class of binary matrices by maximizing the peak-sidelobe distances in the aperiodic autocorrelations. These matrices can be used as robust position marks for in-plane spatial alignment. The optimal square matrices of…

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…

Unsupervised performance estimation, or evaluating how well models perform on unlabeled data is a difficult task. Recently, a method was proposed by Garg et al. [2022] which performs much better than previous methods. Their method relies on…

Variational and divergence symmetries are studied in this paper for the whole class of linear and nonlinear equations of maximal symmetry, and the associated first integrals are given in explicit form. All the main results obtained are…

We investigate the following problem: given a sample of classified strings, find a first-order sentence of minimal quantifier rank that is consistent with the sample. We represent strings as successor string structures, that is, finite…

Real world deployments of word alignment are almost certain to cover both high and low resource languages. However, the state-of-the-art for this task recommends a different model class depending on the availability of gold alignment…

Cross-lingual word embeddings aim to capture common linguistic regularities of different languages, which benefit various downstream tasks ranging from machine translation to transfer learning. Recently, it has been shown that these…

A key principle in assessing textual similarity is measuring the degree of semantic overlap between two texts by considering the word alignment. Such alignment-based approaches are intuitive and interpretable; however, they are empirically…

For words of length n, generated by independent geometric random variables, we consider the average value and the average position of the r-th left-to-right maximum, for fixed r and large n.

In this work, we introduce a framework to study the effect of random operations on the combinatorial list-decodability of a code. The operations we consider correspond to row and column operations on the matrix obtained from the code by…

We investigate the behavior of the periods and border lengths of random words over a fixed alphabet. We show that the asymptotic probability that a random word has a given maximal border length $k$ is a constant, depending only on $k$ and…

For high-dimensional classification, it is well known that naively performing the Fisher discriminant rule leads to poor results due to diverging spectra and noise accumulation. Therefore, researchers proposed independence rules to…

When flipping a fair coin, let $W = L_1L_2...L_N$ with $L_i\in\{H,T\}$ be a binary word of length $N=2$ or $N=3$. In this paper, we establish second- and third-order linear recurrence relations and their generating functions to discuss the…