相关论文: Fast normal random number generators on vector pro…

Randomized sampling has recently been demonstrated to be an efficient technique for computing approximate low-rank factorizations of matrices for which fast methods for computing matrix vector products are available. This paper describes an…

We propose a simple and all-optical method for fast random number generation based on the laser mode hopping. Through periodically restarting a two-mode laser operating in the bistable state, a random number stream can be generated due to…

Diagrammatic expansions are a paradigmatic and powerful tool of quantum many-body theory. Their evaluation to high order, e.g., by the Diagrammatic Monte Carlo technique, can provide unbiased results in strongly correlated and challenging…

This paper deals with circulant matrices. It is shown that a circulant matrix can be multiplied by a vector in time O(n log(n)) in a ring with roots of unity without making use of an FFT algorithm. With our algorithm we achieve a speedup of…

We introduce an error resilient distributed computing method based on an extension of the channel polarization phenomenon to distributed algorithms. The method leverages an algorithmic split operation that transforms two identical compute…

This paper presents a sequential randomized lowrank matrix factorization approach for incrementally predicting values of an unknown function at test points using the Gaussian Processes framework. It is well-known that in the Gaussian…

The support vector clustering algorithm is a well-known clustering algorithm based on support vector machines using Gaussian or polynomial kernels. The classical support vector clustering algorithm works well in general, but its performance…

Computation in the past decades has been driven by deterministic computers based on classical deterministic bits. Recently, alternative computing paradigms and domain-based computing like quantum computing and probabilistic computing have…

Sequence generators obtained by linear recursions over the two-element field $\mathbb{F}_2$, i.e., $\mathbb{F}_2$-linear generators, are widely used as pseudorandom number generators. For example, the Mersenne Twister MT19937 is one of the…

We perform forward error analysis for a large class of recursive matrix multiplication algorithms in the spirit of [D. Bini and G. Lotti, Stability of fast algorithms for matrix multiplication, Numer. Math. 36 (1980), 63--72]. As a…

We describe new families of random fractals, referred to as "V-variable", which are intermediate between the notions of deterministic and of standard random fractals. The parameter V describes the degree of "variability" : at each…

In 1952, von Neumann introduced the rejection method for random variate generation. We revisit this algorithm when we have a source of perfect bits at our disposal. In this random bit model, there are universal lower bounds for generating a…

Hjort and Glad (1995) present a method for semiparametric density estimation. Relative to the ordinary kernel density estimator, this technique performs much better when a parametric vehicle distribution fits the data, and otherwise…

In order to find the outcome probabilities of quantum mechanical systems like the optical networks underlying Boson sampling, it is necessary to be able to compute the permanents of unitary matrices, a computationally hard task. Here we…

The asymptotic analysis of high exceedance probabilities for Gaussian processes and fields has been a blooming research area since J. Pickands introduced the now-standard techniques in the late 60's. The \textit{vector-valued} processes,…

Quantum pseudorandomness, also known as unitary designs, comprise a powerful resource for quantum computation and quantum engineering. While it is known in theory that pseudorandom unitary operators can be constructed efficiently, realizing…

A technique for controlling errors in the functioning of nodes for the formation of $q$-valued pseudo-random sequences (PRS) operating under both random errors and errors generated through intentional attack by an attacker is provided, in…

The spectral test of random number generators (R.R. Coveyou and R.D. McPherson, 1967) is generalized. The sequence of random numbers is analyzed explicitly, not just via their n-tupel distributions. We find that the mixed multiplicative…

There is an ongoing effort to find quantum speedups for learning problems. Recently, [Y. Liu et al., Nat. Phys. $\textbf{17}$, 1013--1017 (2021)] have proven an exponential speedup for quantum support vector machines by leveraging the…

A Monte Carlo method for computing the action of a matrix exponential for a certain class of matrices on a vector is proposed. The method is based on generating random paths, which evolve through the indices of the matrix, governed by a…