Related papers: On the pseudorandomness of Parry--Bertrand automat…
The Thue--Morse sequence is a prototypical automatic sequence found in diverse areas of mathematics, and in computer science. We study occurrences of factors $w$ within this sequence, more precisely, the sequence of gaps between consecutive…
The merit factor of a $\{-1, 1\}$ binary sequence measures the collective smallness of its non-trivial aperiodic autocorrelations. Binary sequences with large merit factor are important in digital communications because they allow the…
Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…
The problem is sequence prediction in the following setting. A sequence $x_1,...,x_n,...$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, it is required…
An infinite binary sequence is deemed to be random if it has all definable properties that hold almost surely for the usual probability measure on the set of infinite binary sequences. There are only countably many such properties, so it…
A sequence $x_1,\dots,x_n,\dots$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, one is required to give conditional probabilities of the next…
For N=1,2,..., let S_N be a simple random sample of size n=n_N from a population A_N of size N, where 0<=n<=N. Then with f_N=n/N, the sampling fraction, and 1_A the inclusion indicator that A is in S_N, for any H a subset of A_N of size k>=…
Learning models have been shown to rely on spurious correlations between non-predictive features and the associated labels in the training data, with negative implications on robustness, bias and fairness. In this work, we provide a…
The proposal and study of dependent prior processes has been a major research focus in the recent Bayesian nonparametric literature. In this paper, we introduce a flexible class of dependent nonparametric priors, investigate their…
Given a real symmetric $n\times n$ matrix, the sepr-sequence $t_1\cdots t_n$ records information about the existence of principal minors of each order that are positive, negative, or zero. This paper extends the notion of the sepr-sequence…
The distribution of differences of consecutive members of sequences of primes is investigated. A quantitative measure for oscillations among these differences is the curvature of the sequence. If the sequence is not too sparse, then sharp…
A causal set is a countably infinite poset in which every element is above finitely many others; causal sets are exactly the posets that have a linear extension with the order-type of the natural numbers -- we call such a linear extension a…
We propose novel algorithms for sequence prediction based on ideas from stringology. These algorithms are time and space efficient and satisfy mistake bounds related to particular stringological complexity measures of the sequence. In this…
We discuss a general method to construct correlated binomial distributions by imposing several consistent relations on the joint probability function. We obtain self-consistency relations for the conditional correlations and conditional…
Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation,…
We consider random graphs with a given degree sequence and show, under weak technical conditions, asymptotic normality of the number of components isomorphic to a given tree, first for the random multigraph given by the configuration model…
Considering the optimal alignment of two i.i.d. random sequences of length $n$, we show that when the scoring function is chosen randomly, almost surely the empirical distribution of aligned letter pairs in all optimal alignments converges…
It is well known that the distribution of extreme values of strictly stationary sequences differ from those of independent and identically distributed sequences in that extremal clustering may occur. Here we consider non-stationary but…
In this paper, we study the sequences with (non-consecutive) two zero-symbols and ideal autocorrelation, which are also known as almost $m$-ary nearly perfect sequences. We show that these sequences are equivalent to $\ell$-partial direct…
In this paper, the defining properties of a valid measure of the dependence between two random variables are reviewed and complemented with two original ones, shown to be more fundamental than other usual postulates. While other popular…