Related papers: Optimal algorithms for universal random number gen…

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…

Quantum coherence serves as a fundamental resource for generating intrinsic randomness, yet the quantification of randomness in quantum random number generators (QRNGs) based on spontaneous emission has remained largely phenomenological.…

Random Fourier Features (RFF) demonstrate wellappreciated performance in kernel approximation for largescale situations but restrict kernels to be stationary and positive definite. And for non-stationary kernels, the corresponding RFF could…

Recurrent neural network grammars (RNNG) are generative models of language which jointly model syntax and surface structure by incrementally generating a syntax tree and sentence in a top-down, left-to-right order. Supervised RNNGs achieve…

Random numbers play a crucial role in numerous scientific applications. Source-independent quantum random number generators (SI-QRNGs) can offer true randomness by leveraging the fundamental principles of quantum mechanics, eliminating the…

Emergence of stochastic simulations as an extensively used computational tool for scientific purposes intensified the need for more accurate ways of generating sufficiently long sequences of uncorrelated random numbers. Even though several…

The generation of pseudorandom elements over finite fields is fundamental to the time, space and randomness complexity of randomized algorithms and data structures. We consider the problem of generating $k$-independent random values over a…

We consider pairs of finite-length individual sequences that are realizations of unknown, finite alphabet, stationary sources in a clas M of sources with vanishing memory (e.g. stationary Markov sources). The task of a universal classifier…

Recurrent Neural Networks (RNNs) are becoming increasingly important for time series-related applications which require efficient and real-time implementations. The two major types are Long Short-Term Memory (LSTM) and Gated Recurrent Unit…

We present three simple algorithms to uniformly generate `Fibonacci words' (i.e., some words that are enumerated by Fibonacci numbers), Schr{\"o}der trees of size $n$ and Motzkin left factors of size $n$ and final height $h$. These…

We consider the problem of lossless compression of individual sequences using finite-state (FS) machines, from the perspective of the best achievable empirical cumulant generating function (CGF) of the code length, i.e., the normalized…

Currently, statistical tests for random number generators (RNGs) are widely used in practice, and some of them are even included in information security standards. But despite the popularity of RNGs, consistent tests are known only for…

We treat a random number generation from an i.i.d. probability distribution of $P$ to that of $Q$. When $Q$ or $P$ is a uniform distribution, the problems have been well-known as the uniform random number generation and the resolvability…

Recurrent Neural Networks (RNNs) are a class of machine learning algorithms used for applications with time-series and sequential data. Recently, there has been a strong interest in executing RNNs on embedded devices. However, difficulties…

Neural networks have been successfully employed in various domains such as classification, regression and clustering, etc. Generally, the back propagation (BP) based iterative approaches are used to train the neural networks, however, it…

Random Fourier features (RFF) represent one of the most popular and wide-spread techniques in machine learning to scale up kernel algorithms. Despite the numerous successful applications of RFFs, unfortunately, quite little is understood…

In this paper, we focus on analyzing the period distribution of the inversive pseudorandom number generators (IPRNGs) over finite field $({\rm Z}_{N},+,\times)$, where $N>3$ is a prime. The sequences generated by the IPRNGs are transformed…

Quantum random number generators (QRNGs) produce true random numbers, which are guaranteed by the fundamental principles of quantum physics. Miniaturization of QRNGs is crucial for a wide range of communication and cryptography…

Quantum random number generators (QRNGs) use the inherent unpredictability of quantum mechanics to generate true randomness, as opposed to classical random number generators. However, ensuring the authenticity of this randomness still…

Finite dimensional (FD) models, i.e., deterministic functions of time/space and finite sets of random variables, are constructed for target vector-valued random processes/fields. They are required to have two properties. First, standard…