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An efficient quantum algorithm is proposed to solve in polynomial time the parity problem, one of the hardest problems both in conventional quantum computation and in classical computation, on NMR quantum computers. It is based on the…
Certifying the positivity of trigonometric polynomials is of first importance for design problems in discrete-time signal processing. It is well known from the Riesz-Fej\'ez spectral factorization theorem that any trigonometric univariate…
Super-resolution (SR) is a promising tool for generating high-fidelity simulations of physical systems from low-resolution data, enabling fast and accurate predictions in engineering applications. However, existing deep-learning based SR…
The multi-resolution approximation (MRA) of Gaussian processes was recently proposed to conduct likelihood-based inference for massive spatial data sets. An advantage of the methodology is that it can be parallelized. We implemented the MRA…
Standard multiple testing procedures are designed to report a list of discoveries, or suspected false null hypotheses, given the hypotheses' p-values or test scores. Recently there has been a growing interest in enhancing such procedures by…
Many applications in scientific computing and data science require the computation of a rank-revealing factorization of a large matrix. In many of these instances the classical algorithms for computing the singular value decomposition are…
Mahler equations relate evaluations of the same function $f$ at iterated $b$th powers of the variable. They arise in particular in the study of automatic sequences and in the complexity analysis of divide-and-conquer algorithms. Recently,…
Several software systems are polyglot; that is, they comprise programs implemented in a combination of programming languages. Verifiers that directly run on mainstream programming languages are currently customized for single languages.…
We study the problem of the computation of Groebner basis for the ideal of linear recurring relations of a doubly periodic array. We find a set of indexes such that, along with some conditions, guarantees that the set of polynomials…
We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The…
The algorithms in the current sequential numerical linear algebra libraries (e.g. LAPACK) do not parallelize well on multicore architectures. A new family of algorithms, the tile algorithms, has recently been introduced. Previous research…
Probabilistic reasoning is an essential tool for robust decision-making systems because of its ability to explicitly handle real-world uncertainty, constraints and causal relations. Consequently, researchers are developing hybrid models by…
This paper explores methods for verifying the properties of Binary Neural Networks (BNNs), focusing on robustness against adversarial attacks. Despite their lower computational and memory needs, BNNs, like their full-precision counterparts,…
Programmable Logic Devices (PLDs) continue to grow in size and currently contain several millions of gates. At the same time, research effort is going into higher-level hardware synthesis methodologies for reconfigurable computing that can…
In latest years, several advancements have been made in symbolic-numerical eigenvalue techniques for solving polynomial systems. In this article, we add to this list. We design an algorithm which solves systems with isolated solutions…
We consider regular polynomial interpolation algorithms on recursively defined sets of interpolation points which approximate global solutions of arbitrary well-posed systems of linear partial differential equations. Convergence of the…
Two-sample hypothesis testing for network comparison presents many significant challenges, including: leveraging repeated network observations and known node registration, but without requiring them to operate; relaxing strong structural…
The most efficient way to calculate strong bisimilarity is by calculation the relational coarsest partition on a transition system. We provide the first linear time algorithm to calculate strong bisimulation using parallel random access…
We consider the problem of minimizing a polynomial $f$ over the binary hypercube. We show that, for a specific set of polynomials, their binary non-negativity can be checked in a polynomial time via minimum cut algorithms, and we construct…
Software realization of the complex spectra decomposition on unknown number of similarcomponents is proposed.The algorithm is based on non-linear minimizing the sum of squared residuals of the spectrum model. For the adequacy checking the…