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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…

Based on Restricted Boltzmann Machines (RBMs), an improved pseudo-stochastic sequential cipher generator is proposed. It is effective and efficient because of the two advantages: this generator includes a stochastic neural network that can…

In this paper, we consider the separable covariance model, which plays an important role in wireless communications and spatio-temporal statistics and describes a process where the time correlation does not depend on the spatial location…

Gaussian graphical models (GGMs) are widely used for statistical modeling, because of ease of inference and the ubiquitous use of the normal distribution in practical approximations. However, they are also known for their limited modeling…

For the additive Gaussian noise channel with average codeword power constraint, sparse superposition codes and adaptive successive decoding is developed. Codewords are linear combinations of subsets of vectors, with the message indexed by…

We demonstrate a quantum random number generator based on the random nature of the phase difference between two independent laser sources. The speed of random bit generation is determined by the photodetector bandwidth and the linewidth of…

Gravitational-wave parameter estimation for compact binary signals typically relies on sequential estimation of the properties of the detector Gaussian noise and of the binary parameters. This procedure assumes that the noise variance,…

A theoretical analysis, aimed at characterizing the degradation induced by the resampling and requantization processes applied to band-limited Gaussian signals with flat power spectrum, available through their digitized samples, is…

Diffusion models have achieved remarkable success in generating samples from unknown data distributions. Most popular stochastic differential equation-based diffusion models perturb the target distribution by adding Gaussian noise,…

We present the realization of a physical quantum random number generator based on the process of splitting a beam of photons on a beam splitter, a quantum mechanical source of true randomness. By utilizing either a beam splitter or a…

We prove several new results about bounded uniform and small-bias distributions. A main message is that, small-bias, even perturbed with noise, does not fool several classes of tests better than bounded uniformity. We prove this for…

The standard central limit theorem with a Gaussian attractor for the sum of independent random variables may lose its validity in presence of strong correlations between the added random contributions. Here, we study this problem for…

We present a new approach to constructing unconditional pseudorandom generators against classes of functions that involve computing a linear function of the inputs. We give an explicit construction of a pseudorandom generator that fools the…

We propose and demonstrate a technique for quantum random number generation based on the random population of the output spatial modes of a beam splitter when both inputs are simultaneously fed with indistinguishable weak coherent states.…

Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process…

While score-based generative models (SGMs) have achieved remarkable success in enormous image generation tasks, their mathematical foundations are still limited. In this paper, we analyze the approximation and generalization of SGMs in…

We investigate design and performance of communications over the bandlimited Gaussian channel with one-bit output quantization. A transceiver structure is proposed, which generates the channel input using a finite set of time-limited and…

We investigate the problem of jointly testing two hypotheses and estimating a random parameter based on data that is observed sequentially by sensors in a distributed network. In particular, we assume the data to be drawn from a Gaussian…

Within the Correlated Gaussian Method the parameters of the Gaussian basis functions are often chosen stochastically using pseudo-random sequences. We show that alternative low-discrepancy sequences, also known as quasi-random sequences,…

Correlation between microstructure noise and latent financial logarithmic returns is an empirically relevant phenomenon with sound theoretical justification. With few notable exceptions, all integrated variance estimators proposed in the…