Related papers: Advances in Tabulating Carmichael Numbers

We study the minimization problem for Conjunctive Regular Path Queries (CRPQs) and unions of CRPQs (UCRPQs). This is the problem of checking, given a query and a number $k$, whether the query is equivalent to one of size at most $k$. For…

This paper proposes a new approach for approximate evaluation of #P-hard queries with probabilistic databases. In our approach, every query is evaluated entirely in the database engine by evaluating a fixed number of query plans, each…

In this paper we extend the rank-reduced coupled-cluster formalism to the calculation of non-iterative energy corrections due to quadruple excitations. There are two major components of the proposed formalism. The first is an approximate…

Let a polytope $P$ be defined by a system $A x \leq b$. We consider the problem of counting the number of integer points inside $P$, assuming that $P$ is $\Delta$-modular, where the polytope $P$ is called $\Delta$-modular if all the rank…

We describe two new algorithms for the efficient and rigorous computation of Dirichlet L-functions and their use to verify the Generalised Riemann Hypothesis for all such L-functions associated with primitive characters of modulus…

In settings where only a budgeted amount of labeled data can be afforded, active learning seeks to devise query strategies for selecting the most informative data points to be labeled, aiming to enhance learning algorithms' efficiency and…

Iteration of the modular l-th power function f(x) = x^l (mod n) provides a common pseudorandom number generator (known as the Blum-Blum-Shub generator when l=2). The period of this pseudorandom number generator is closely related to…

Weird numbers are abundant numbers that are not pseudoperfect. Since their introduction, the existence of odd weird numbers has been an open problem. In this work, we describe our computational effort to search for odd weird numbers, which…

Given a graph $G$, a cost function on the non-edges of $G$, and an integer $d$, the problem of finding a cheapest globally rigid supergraph of $G$ in $\mathbb{R}^d$ is NP-hard for $d\geq 1$. For this problem, which is a common…

An adaptive regularization algorithm using high-order models is proposed for partially separable convexly constrained nonlinear optimization problems whose objective function contains non-Lipschitzian $\ell_q$-norm regularization terms for…

The $k$-cut problem asks, given a connected graph $G$ and a positive integer $k$, to find a minimum-weight set of edges whose removal splits $G$ into $k$ connected components. We give the first polynomial-time algorithm with approximation…

We consider the problem of minimizing a convex objective which is the sum of a smooth part, with Lipschitz continuous gradient, and a nonsmooth part. Inspired by various applications, we focus on the case when the nonsmooth part is a…

Topological data analysis has emerged as a powerful tool for analyzing large-scale data. An abstract simplicial complex, in principle, can be built from data points, and by using tools from homology, topological features could be…

The Boolean product $R = P \cdot Q$ of two $\{ 0, 1\} \; m \times m \; $ matrices is $$R(j,k) = 1 \; \mathrm{\ IF\ for\ some\ } \; t \; \,P(j, t) = Q(t, k) = 1\; \; \mathrm{ELSE\ } \, R(j, k) = 0. $$ The near-optimal design reduces the…

In this work, we give several new upper and lower bounds on Ramsey numbers for books and wheels, including a tight upper bound establishing $R(W_5, W_7) = 15$, matching upper and lower bounds giving $R(W_5, W_9) = 18$, $R(B_2, B_8) = 21$,…

The development of randomized algorithms for numerical linear algebra, e.g. for computing approximate QR and SVD factorizations, has recently become an intense area of research. This paper studies one of the most frequently discussed…

In this paper, we study the problem of approximating the minimum cut in a distributed message-passing model, the CONGEST model. The minimum cut problem has been well-studied in the context of centralized algorithms. However, there were no…

In this paper, we study the fundamental open question of finding the optimal high-order algorithm for solving smooth convex minimization problems. Arjevani et al. (2019) established the lower bound $\Omega\left(\epsilon^{-2/(3p+1)}\right)$…

We generalise a formula of Shou-Wu Zhang, which describes local arithmetic intersection numbers of three Cartier divisors with support in the special fibre on a a self-product of a semi-stable arithmetic surface using elementary analysis.…

Let $ACC \circ THR$ be the class of constant-depth circuits comprised of AND, OR, and MOD$m$ gates (for some constant $m > 1$), with a bottom layer of gates computing arbitrary linear threshold functions. This class of circuits can be seen…