相关论文: Cyclotomy Primality Proofs and their Certificates

We give a large sieve type inequality for functions supported on primes. As application we prove a conjecture by Elliott, and give bounds for short character sums over primes. The proves uses a combination of the large sieve and the Selberg…

For rotationally invariant first passage percolation (FPP) on the plane, we use a multi-scale argument to prove stretched exponential concentration of the first passage times at the scale of the standard deviation. Our results are proved…

This paper presents two efficient primality tests that quickly and accurately test all integers up to $2^{64}$.

We study the asymptotic behaviour of the well-known Dykstra's algorithm through the lens of proof-theoretical techniques. We provide an elementary proof for the convergence of Dykstra's algorithm in which the standard argument is stripped…

The saddle-point problems (SPPs) with nonlinear coupling operators frequently arise in various control systems, such as dynamic programming optimization, H-infinity control, and Lyapunov stability analysis. However, traditional primal-dual…

This paper focuses on the algebraic theory underlying the study of the complexity and the algorithms for the Constraint Satisfaction Problem (CSP). We unify, simplify, and extend parts of the three approaches that have been developed to…

This paper investigates the admissibility of the substitution rule in cyclic-proof systems. The substitution rule complicates theoretical case analysis and increases computational cost in proof search since every sequent can be a conclusion…

A first proposal of a sparse and cellwise robust PCA method is presented. Robustness to single outlying cells in the data matrix is achieved by substituting the squared loss function for the approximation error by a robust version. The…

The purpose of this article is to introduce the concept of invariance and its properties. These properties can be used to check the primality of a number. Combining these properties with the Euler theorem, it is possible to generalize this…

We give a new sufficient condition which allows to test primality of Fermat's numbers. This characterization uses uniquely values at most equal to tested Fermat number. The robustness of this result is due to a strict use of elementary…

In 1982 Macdonald published his now famous constant term conjectures for classical root systems. This paper begins with the almost trivial observation that Macdonald's constant term identities admit an extra set of free parameters, thereby…

We call change-point problem (CPP) the identification of changes in the probabilistic behavior of a sequence of observations. Solving the CPP involves detecting the number and position of such changes. In genetics the study of how and what…

The study of near-factorizations of finite groups dates back to the 1950s. Recently, this topic has attracted renewed attention, and the concept has been extended to $\lambda$-fold near-factorizations, in which each non-identity group…

Dirichlet's proof of infinitely many primes in arithmetic progressions was published in 1837, introduced L-series for the first time, and it is said to have started rigorous analytic number theory. Dirichlet uses Euler's earlier work on the…

We consider the problem of late multi-modal fusion for discriminative learning. Motivated by noisy, multi-source domains that require understanding the reliability of each data source, we explore the notion of credibility in the context of…

DPPs were introduced by Macchi as a model in quantum optics the 1970s. Since then, they have been widely used as models and subsampling tools in statistics and computer science. Most applications require sampling from a DPP, and given their…

Wall published a paper in 1960 on the Fibonacci sequence where he derived many results concerning the period and prime power divisibility modulo m. His periodicity results have been generalized to second order linear recurrences. Here we…

On solving a convex-concave bilinear saddle-point problem (SPP), there have been many works studying the complexity results of first-order methods. These results are all about upper complexity bounds, which can determine at most how many…

In simulations of fluid motion time accuracy has proven to be elusive. We seek highly accurate methods with strong enough stability properties to deal with the richness of scales of many flows. These methods must also be easy to implement…

The Constant Degree Hypothesis was introduced by Barrington et. al. (1990) to study some extensions of $q$-groups by nilpotent groups and the power of these groups in a certain computational model. In its simplest formulation, it…