Single-Instruction, Multiple-Data (SIMD) random number generators (RNGs) take advantage of vector units to offer significant performance gain over non-vectorized libraries, but they often rely on batch production of deviates from distributions with fixed parameters. In many statistical applications such as Gibbs sampling, parameters of sampled distributions change from one iteration to the next...

We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider (e.g., maximum relative to minimum) are such that the reference point from which the maximum is measured is itself a random quantity. We analytically calculate the limiting distributions ...

Uniform random sparse network architectures are ubiquitous in computational neuroscience, but the implicit hypothesis that they are a good representation of real neuronal networks has been met with skepticism. Here we used two experimental data sets, a study of triplet connectivity statistics and a data set measuring neuronal responses to channelrhodopsin stimuli, to evaluate the fidelity of th...

In this paper, we analyze the decision version of the NK landscape model from the perspective of threshold phenomena and phase transitions under two random distributions, the uniform probability model and the fixed ratio model. For the uniform probability model, we prove that the phase transition is easy in the sense that there is a polynomial algorithm that can solve a random instance of the p...

Random walks of two steps, with fixed sums of lengths of 1, taken into uniformly random directions in d-dimensional Euclidean spaces (d ≥ 2) are investigated to construct continuous step-length distributions which make them hyperuniform. The endpoint positions of hyperuniform walks are spread out in the unit ball as the projections in the walk space of points uniformly distributed on the surfac...

We have studied the presence of plateaus on the low-temperature magnetization of an antiferromagnetic spin-1 chain, as an external uniform magnetic field is varied. A crystal-field interaction is present in the model and the exchange constants follow a random quenched (Bernoulli or Gaussian) distribution. Using a transfer-matrix technique we calculate the largest Lyapunov exponent and, from it,...

In this paper, the largest and the smallest observations are considered, at the time when a new record of either kind (upper or lower) occurs based on a sequence of independent random variables with identical continuous distributions. We prove that sequences of the residual or past entropy of the current records characterizes F in the family of continuous distributions. The exponential and the ...

It is well known that the ratio of the number of clauses to the number of variables in a random k-SAT instance is highly correlated with the instance’s empirical hardness. We consider the problem of identifying such features of random SAT instances automatically using machine learning. We describe and analyze models for three SAT solvers—kcnfs, oksolver and satz—and for two different distributi...

We propose two random generation models for MaxSAT and Partial MaxSAT in order to produce instances more similar to the industrial benchmarks used in the MaxSAT evaluation. Following the work of [4] and [2], we analyze properties of industrial instances and use a non-uniform (powerlaw) distribution to select the variables. We also study empirically the optimum (minim number of unsatisfiable cla...