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Both sampling a time-varying signal, and its spectral analysis are activities subjected to theoretically compelling, such as Shannon's theorem and the objectively limiting of the frequency's resolution. Usually, the signals' spectra are…
We find a formula for the number of solutions of linear congruence systems, by using elementary methods.
The problem of optimal linear estimation of functionals depending on the unknown values of a random field $\zeta(t,x)$, which is mean-square continuous periodically correlated with respect to time argument $t\in\mathbb R$ and isotropic on…
The Coherent Multiplex is formalized and validated as a scalable, real-time system for identifying, analyzing, and visualizing coherence among multiple time series. Its architecture comprises a fast spectral similarity layer based on cosine…
We deal with the problem of optimal estimation of the linear functionals constructed from unobserved values of a continuous time stochastic process with periodically correlated increments based on past observations of this process. To solve…
We study the space requirements of a sorting algorithm where only items that at the end will be adjacent are kept together. This is equivalent to the following combinatorial problem: Consider a string of fixed length n that starts as a…
To assess whether there is some signal in a big database, aggregate tests for the global null hypothesis of no effect are routinely applied in practice before more specialized analysis is carried out. Although a plethora of aggregate tests…
For line spectrum estimation, we derive the maximum a posteriori probability estimator where prior knowledge of frequencies is modeled probabilistically. Since the spectrum is periodic, an appropriate distribution is the circular von Mises…
Linear temporal logic (LTL) is a specification language for finite sequences (called traces) widely used in program verification, motion planning in robotics, process mining, and many other areas. We consider the problem of learning LTL…
We address the problem of testing weak optimality of a given solution of a given interval linear program. The problem was recently wrongly stated to be polynomially solvable. We disprove it. We show that the problem is NP-hard in general.…
We investigate the behavior of optimal alignment paths for homologous (related) and independent random sequences. An alignment between two finite sequences is optimal if it corresponds to the longest common subsequence (LCS). We prove the…
The problem of constructing effective statistical tests for random number generators (RNG) is considered. Currently, statistical tests for RNGs are a mandatory part of cryptographic information protection systems, but their effectiveness is…
In this work a detailed spectral analysis of the time series of the 8B solar neutrino flux published by the Super-Kamiokande Collaboration is presented, performed through a likelihood scan approach. Preliminarily a careful review of the…
We develop, discuss, and compare several inference techniques to constrain theory parameters in collider experiments. By harnessing the latent-space structure of particle physics processes, we extract extra information from the simulator.…
We formulate nonparametric and semiparametric hypothesis testing of multivariate stationary linear time series in a unified fashion and propose new test statistics based on estimators of the spectral density matrix. The limiting…
A natural approach to software quality assurance consists in writing unit tests securing programmer-declared code invariants. Throughout the literature a great body of work has been devoted to tools and techniques automating this…
The nature of the alignment with gaps corresponding to a longest common subsequence (LCS) of two independent iid random sequences drawn from a finite alphabet is investigated. It is shown that such an optimal alignment typically matches…
In the era of big data, one of the key challenges is the development of novel optimization algorithms that can accommodate vast amounts of data while at the same time satisfying constraints and limitations of the problem under study. The…
Our model is a generalized linear programming relaxation of a much studied random K-SAT problem. Specifically, a set of linear constraints C on K variables is fixed. From a pool of n variables, K variables are chosen uniformly at random and…
Conformal prediction is a generic methodology for finite-sample valid distribution-free prediction. This technique has garnered a lot of attention in the literature partly because it can be applied with any machine learning algorithm that…