Related papers: Increasing Randomness Using Permutations on Blocks
A general method to produce uniformly distributed pseudorandom numbers with extended precision by combining two pseudorandom numbers with lower precision is proposed. In particular, this method can be used for pseudorandom number generation…
Adversarial robustness refers to a model's ability to resist perturbation of inputs, while distribution robustness evaluates the performance of the model under data shifts. Although both aim to ensure reliable performance, prior work has…
In this work I look at the distribution of primes by calculation of an infinite number of intersections. For this I use the set of all numbers which are not elements of a certain times table in each case. I am able to show that it exists a…
We consider the problem of evaluating designs for a two-arm randomized experiment with the criterion being the power of the randomization test for the one-sided null hypothesis. Our evaluation assumes a response that is linear in one…
Ultrafast physical random bit generation at hundreds of Gb/s rates, with verified randomness, is a crucial ingredient in secure communication and have recently emerged using optics based physical systems. Here we examine the inverse problem…
We review a recent development at the interface between discrete mathematics on one hand and probability theory and statistics on the other, specifically the use of Markov chains and their boundary theory in connection with the asymptotics…
The ever-increasing need for random numbers is clear in many areas of computer science, from neural networks to optimization. As such, most common programming language provide easy access to Pseudorandom Number Generators. However, these…
We introduce a new, elementary method for studying random differences in arithmetic progressions and convergence phenomena along random sequences of integers. We apply our method to obtain significant improvements on previously known…
We examine the number of cycles of length k in a permutation, as a function on the symmetric group. We write it explicitly as a combination of characters of irreducible representations. This allows to study formation of long cycles in the…
Cryptographic primitives have been used for various non-cryptographic objectives, such as eliminating or reducing randomness and interaction. We show how to use cryptography to improve the time complexity of solving computational problems.…
In this paper, we numerically investigate the robustness of cooperation clusters in prisoner's dilemma played on scale-free networks, where the network topologies change by continuous removal and addition of nodes. Each removal and addition…
In [4] we describe a variation of the classical permutation decoding algorithm that can be applied to any binary affine-invariant code; in particular, it can be applied to first-order Reed-Muller codes successfully. In this paper we study…
A refinement of the multinomial distribution is presented where the number of inversions in the sequence of outcomes is tallied. This refinement of the multinomial distribution is its joint distribution with the number of inversions in the…
Considering two optimally aligned random sequences, we investigate the effect on the alignment score caused by changing a random letter in one of the two sequences. Using this idea in conjunction with large deviations theory, we show that…
We investigate the probability that a random odd composite number passes a random Fermat primality test, improving on earlier estimates in moderate ranges. For example, with random numbers to $2^{200}$, our results improve on prior…
We investigate the effect of unidirectional regular and random couplings of units in a network on stochastic resonance. For simplicity we choose the units as Bellows map with bistability. In a regular network we apply a weak periodic signal…
Speculative decoding is an effective method for lossless acceleration of large language models during inference. It uses a fast model to draft a block of tokens which are then verified in parallel by the target model, and provides a…
We investigate how robust the results of committee elections are to small changes in the input preference orders, depending on the voting rules used. We find that for typical rules the effect of making a single swap of adjacent candidates…
In the paper, a theoretical work is done for investigating effects of splitting data sequence into packs of data set. We proved that a partitioning of data sequence is possible to find such that the entropy rate at each subsequence is lower…
In the context of the genome rearrangement problem, we analyze two well known models, namely the block transposition and the prefix block transposition models, by exploiting the connection with the notion of permutation pattern. More…