Related papers: Synchronization of Bernoulli sequences on shared l…
Synchronization of networked oscillators is known to depend fundamentally on the interplay between the dynamics of the graph's units and the microscopic arrangement of the network's structure. For non identical elements, the lack of…
Many natural language processing applications use language models to generate text. These models are typically trained to predict the next word in a sequence, given the previous words and some context such as an image. However, at test time…
We address the problem of detecting deviations of binary sequence from randomness,which is very important for random number (RNG) and pseudorandom number generators (PRNG). Namely, we consider a null hypothesis $H_0$ that a given bit…
Standard sequential generation methods assume a pre-specified generation order, such as text generation methods which generate words from left to right. In this work, we propose a framework for training models of text generation that…
We determine the distributions of lengths of runs in random sequences of elements from a totally ordered set (total order) or partially ordered set (partial order). In particular, we produce novel formulae for the expected value, variance,…
Uniform sampling of simple graphs having a given degree sequence is a known problem with exponential complexity in the square of the mean degree. For undirected graphs, randomised approximation algorithms have nonetheless been shown to…
Learning to read words aloud is a major step towards becoming a reader. Many children struggle with the task because of the inconsistencies of English spelling-sound correspondences. Curricula vary enormously in how these patterns are…
Reflecting boundary conditions cause two one-dimensional random walks to synchronize if a common direction is chosen in each step. The mean synchronization time and its standard deviation are calculated analytically. Both quantities are…
We investigate classes of systems based on different interaction patterns with the aim of achieving distributability. As our system model we use Petri nets. In Petri nets, an inherent concept of simultaneity is built in, since when a…
A novel compression scheme for compressing the outcome of $n$ independent Bernoulli trials is introduced and analysed. The resulting algorithm, BernoulliZip, is a fast and near-optimal method to produce prefix codes for a Bernoulli process.…
Synchronous systems provide a basic model of embedded systems and industrial systems are modeled as Simulink diagrams and/or Lustre programs. Although the test generation problem is critical in the development of safe systems, it often…
In this paper, we consider the multivariate Bernoulli distribution as a model to estimate the structure of graphs with binary nodes. This distribution is discussed in the framework of the exponential family, and its statistical properties…
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…
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…
The distributions of the number of occurrences of words (the distributions of words for short) play key roles in information theory, statistics, probability theory, ergodic theory, computer science, and DNA analysis. Bassino et al. 2010 and…
The power of natural language generation models has provoked a flurry of interest in automatic methods to detect if a piece of text is human or machine-authored. The problem so far has been framed in a standard supervised way and consists…
A very simple event frequency approximation algorithm that is sensitive to event timeliness is suggested. The algorithm iteratively updates categorical click-distribution, producing (path of) a random walk on a standard $n$-dimensional…
The rate of convergence of the distribution of the length of the longest increasing subsequence, toward the maximal eigenvalue of certain matrix ensembles, is investigated. For finite-alphabet uniform and nonuniform i.i.d. sources, a rate…
We investigate the linear statistics of random matrices with purely imaginary Bernoulli entries of the form $H_{pq} = \overline{H}_{qp} = \pm i$, that are either independently distributed or exhibit global correlations imposed by the…
We investigate a population of binary mistake sequences that result from learning with parametric models of different order. We obtain estimates of their error, algorithmic complexity and divergence from a purely random Bernoulli sequence.…