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In this work, we consider the properties of the two-term Machin-like formula and develop an algorithm for computing digits of $\pi$ by using its rational approximation. In this approximation, both terms are constructed by using a…
We show that approximating the trace norm contraction coefficient of a quantum channel within a constant factor is NP-hard. Equivalently, this shows that determining the optimal success probability for encoding a bit in a quantum system…
Changes, planned or unexpected, are common during the execution of real-life processes. Detecting these changes is a must for optimizing the performance of organizations running such processes. Most of the algorithms present in the…
The Numerical Recipes series of books are a useful resource, but all the algorithms they contain cannot be used within open-source projects. In this paper we develop drop-in alternatives to the two algorithms they present for cubic spline…
We propose a novel modular debiasing technique applicable to any discrete random source, addressing the fundamental challenge of reliably extracting high-quality randomness from inherently imperfect physical processes. The method involves…
Computer programs often behave differently under different compilers or in different computing environments. Relative debugging is a collection of techniques by which these differences are analysed. Differences may arise because of…
Digital-analog is a universal quantum computing paradigm which employs the natural entangling Hamiltonian of the system and single-qubit gates as resources. Here, we study the stability of these protocols against Hamiltonian…
In a prior paper [14], along with P. Ellingsen, P. Felke and A. Tkachenko, we defined a new (output) multiplicative differential, and the corresponding c-differential uniformity, which has the potential of extending differential…
We consider nonconforming methods for symmetric elliptic problems and characterize their quasi-optimality in terms of suitable notions of stability and consistency. The quasi-optimality constant is determined and the possible impact of…
The convergence of a new general variable metric algorithm based on compositions of averaged operators is established. Applications to monotone operator splitting are presented.
A solution for Smale's 17th problem, for the case of systems with bounded degree was recently given. This solution, an algorithm computing approximate zeros of complex polynomial systems in average polynomial time, assumed infinite…
The Inverse Problem for the estimation of a point-wise approximation error occurring at the discretization and solving of the system of partial differential equations is addressed. The set of the differences between the numerical solutions…
We show that real-value approximations of Kolmogorov-Chaitin (K_m) using the algorithmic Coding theorem as calculated from the output frequency of a large set of small deterministic Turing machines with up to 5 states (and 2 symbols), is in…
In this paper, we study the classical problem of estimating the proportion of a finite population. First, we consider a fixed sample size method and derive an explicit sample size formula which ensures a mixed criterion of absolute and…
Internet supercomputing is an approach to solving partitionable, computation-intensive problems by harnessing the power of a vast number of interconnected computers. For the problem of using network supercomputing to perform a large…
We describe a practical algorithm to compute the (oriented) genus of a graph, give results of the program implementing this algorithm, and compare the performance to existing algorithms. The aim of this algorithm is to be fast enough for…
Anomaly detection has important applications in biosurveilance and environmental monitoring. When comparing measured data to data drawn from a baseline distribution, merely, finding clusters in the measured data may not actually represent…
Recent exact analytical results developed for the random number generators with taps are reported. These results are applicable to a wide class of algorithms, including random walks, cluster algorithms, Ising models. Practical…
Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…
Estimating consistently oriented normals for point clouds enables a number of important applications in computer graphics. While local normal estimation is possible with simple techniques like PCA, orienting them to be globally consistent…