Related papers: A recipe for an unpredictable random number genera…
Randomness is fundamental in quantum theory, with many philosophical and practical implications. In this paper we discuss the concept of algorithmic randomness, which provides a quantitative method to assess the Borel normality of a given…
Our aim is to experimentally study the possibility of distinguishing between quantum sources of randomness--recently proved to be theoretically incomputable--and some well-known computable sources of pseudo-randomness. Incomputability is a…
Transformers excel at discovering patterns in sequential data, yet their fundamental limitations and learning mechanisms remain crucial topics of investigation. In this paper, we study the ability of Transformers to learn pseudo-random…
Random graphs with prescribed degree sequences have been widely used as a model of complex networks. Comparing an observed network to an ensemble of such graphs allows one to detect deviations from randomness in network properties. Here we…
This paper is concerned with the development, analysis and numerical realization of a novel variational model for the regularization of inverse problems in imaging. The proposed model is inspired by the architecture of generative…
Measurement-based quantum computation (MBQC) offers a fundamentally unique paradigm to design quantum algorithms. Indeed, due to the inherent randomness of quantum measurements, the natural operations in MBQC are not deterministic and…
A process model of quantum mechanics utilizes a combinatorial game to generate a discrete and finite causal space upon which can be defined a self-consistent quantum mechanics. An emergent space-time M and continuous wave function arise…
$\mathbf F_2$-linear pseudorandom number generators are very popular due to their high speed, to the ease with which generators with a sizable state space can be created, and to their provable theoretical properties. However, they suffer…
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
Quantum mechanics offers a fundamentally unpredictable entropy source due to the intrinsic probabilistic nature of quantum measurements, making it attractive for secure random number generation. This paper explores the practicality of…
A systematic method for the design of linear residual generators for combined fault detection and estimation in nonlinear systems is developed. The proposed residual generator is a linear functional observer built for an extended system…
This article presents a new class of Pseudorandom Number Generators. The generators are based on traversing a n-cube where a Balanced Hamiltonian Cycle has been removed. The construction of such generators is automatic for small number of…
Designing a pseudorandom number generator (PRNG) is a difficult and complex task. Many recent works have considered chaotic functions as the basis of built PRNGs: the quality of the output would indeed be an obvious consequence of some…
Quantum physics can be exploited to generate true random numbers, which play important roles in many applications, especially in cryptography. Genuine randomness from the measurement of a quantum system reveals the inherent nature of…
We introduce the Romu family of pseudo-random number generators (PRNGs) which combines the nonlinear operation of rotation with the linear operations of multiplication and (optionally) addition. Compared to conventional linear-only PRNGs,…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful to the study of chaos since no analytical…
Neural networks are powerful tools for data-driven modeling of complex dynamical systems, enhancing predictive capability for control applications. However, their inherent nonlinearity and black-box nature challenge control designs that…
Random quantum circuits take an input quantum state and randomize it. This is a task with a growing number of identified uses in quantum information processing. We suggest a scheme to implement random circuits in a weighted graph state. The…
We propose a hybrid quantum-classical approach to model continuous classical probability distributions using a variational quantum circuit. The architecture of the variational circuit consists of two parts: a quantum circuit employed to…