Related papers: Arithmetic autocorrelation distribution of binary …
The discrete distribution of the length of longest increasing subsequences in random permutations of $n$ integers is deeply related to random matrix theory. In a seminal work, Baik, Deift and Johansson provided an asymptotics in terms of…
This paper presents a computationally efficient method for binary classification using Manski's (1975,1985) maximum score model when covariates are discretely distributed and parameters are partially but not point identified. We establish…
On time-series data, most causal discovery methods fit a new model whenever they encounter samples from a new underlying causal graph. However, these samples often share relevant information which is lost when following this approach.…
Extending the transfer matrix DMRG algorithm, we are able to calculate imaginary time spin autocorrelations with high accuracy (absolute error $<10^{-6}$) over a wide temperature range ($0<\beta J<20$). After analytic continuation using the…
We investigate the order of the variance of the optimal alignments score of two independent iid binary random words having the same length. The letters are equiprobable, but the scoring function is such that one letter has a larger score…
Boolean functions and binary sequences are main tools used in cryptography. In this work, we introduce a new bijection between the set of Boolean functions and the set of binary sequences with period a power of two. We establish a…
This work proves new results on the ability of binary Reed-Muller codes to decode from random errors and erasures. We obtain these results by proving improved bounds on the weight distribution of Reed-Muller codes of high degrees.…
Binary linear codes are constructed from graphs, in particular, by the generator matrix $[I_n|A]$ where $A$ is the adjacency matrix of a graph on $n$ vertices. A combinatorial interpretation of the minimum distance of such codes is given.…
Autocorrelation is a defining characteristic of time-series data, where each observation is statistically dependent on its predecessors. In the context of deep time-series forecasting, autocorrelation arises in both the input history and…
We consider finite Bernoulli convolutions with a parameter $1/2 < r < 1$ supported on a discrete point set, generically of size $2^N$. These sequences are uniformly distributed with respect to the infinite Bernoulli convolution measure…
The symmetry algebras of certain families of quantum spin chains are considered in detail. The simplest examples possess m states per site (m\geq2), with nearest-neighbor interactions with U(m) symmetry, under which the sites transform…
Sequences with a low correlation have very important applications in communications, cryptography, and compressed sensing. In the literature, many efforts have been made to construct good sequences with various lengths where binary…
Sine-skewed circular distributions are identifiable and have easily-computable trigonometric moments and a simple random number generation algorithm, whereas they are known to have relatively low levels of asymmetry. This study proposes a…
The concept of distance covariance/correlation was introduced recently to characterize dependence among vectors of random variables. We review some statistical aspects of distance covariance/correlation function and we demonstrate its…
We study the size of the largest biconnected components in sparse Erd\H{o}s-R\'enyi graphs with finite connectivity and Barab\'asi-Albert graphs with non-integer mean degree. Using a statistical-mechanics inspired Monte Carlo approach we…
Synchronizing clocks in a distributed system in which processes communicate through messages with uncertain delays is subject to inherent errors. Prior work has shown upper and lower bounds on the best synchronization achievable in a…
We evaluate the localization length of the wave solution of a random potential characterized by an arbitrary autocorrelation function. We go beyond the Born approximation to evaluate the localization length using a non-linear approximation…
The Binary Two-Up Sequence is the lexicographically earliest sequence of distinct nonnegative integers with the property that the binary expansion of the n-th term has no 1-bits in common with any of the previous floor(n/2) terms. We show…
Logistic regression is a commonly used method for binary classification. Researchers often have more than a single binary response variable and simultaneous analysis is beneficial because it provides insight into the dependencies among…
We propose a multiscale approach to time series autoregression, in which linear regressors for the process in question include features of its own path that live on multiple timescales. We take these multiscale features to be the recent…