We study the effect of a random perturbation on a one-parameter family of dynamical systems whose behavior in the absence of perturbation is ill understood. We provide conditions under which the perturbed system is ergodic and admits a positive Lyapunov exponent, with an explicit lower bound, for a large and controlled set of parameter values. Acknowledgements. The authors are indebted to Lai-S...

We’ll use a statistical model of the problem to motivate a prediction strategy, as well as to evaluate the quality of various strategies. In this model, the outcome of the coin toss is random; it is “heads” with some probability, say, p; and it is “tails” with the remaining probability 1− p. This number p is a parameter of the model; the possible values it can taken on, namely the interval [0, ...

We devise a message passing algorithm for probabilistic inference in composite systems, consisting of a large number of variables, that exhibit weak random interactions among all variables and strong interactions with a small subset of randomly chosen variables; the relative strength of the two interactions is controlled by a free parameter. We examine the performance of the algorithm numerical...

Jittery clock signals produced in oscillators, particularly in ring oscillators are commonly used as a source of randomness in true random number generators (TRNG). The robustness of the generators, and hence their security, is closely linked to the entropy of the generated bit stream, which depends on the size of the jitter. Known jitter size can be used as an input parameter in a stochastic m...

In a probabilistic graphical model, each node represents a random variable, and the links express probabilistic relationships between these variables. The structure that graphical models exploit is the independence properties that exist in many real-world phenomena. The graph then captures the way in which the joint distribution over all of the random variables can be decomposed into a product ...

We report results from large-scale experiments in satisfiability testing. As has been observed by others, testing the satisfiability of random formulas often appears surprisingly easy. Here we show that by using the right distribution of instances, and appropriate parameter values, it is possible to generate random formulas that are hard, that is, for which satisfiability testing is quite diffi...

We report results from large-scale experiments in satis-ability testing. As has been observed by others, testing the satissability of random formulas often appears surprisingly easy. Here we show that by using the right distribution of instances, and appropriate parameter values, it is possible to generate random formulas that are hard, that is, for which satissability testing is quite diicult....

We report results from large-scale experiments in satissability testing. As has been observed by others, testing the satissability of random formulas often appears surprisingly easy. Here we show that by using the right distribution of instances, and appropriate parameter values, it is possible to generate random formulas that are hard, that is, for which satissability testing is quite diicult....

The luminescence spectra of milk containing rhodamine 6G are shown to exhibit typical signatures of random lasing when excited with 532 nm laser pulses. Experiments carried out on whole and skim forms of two commercial brands of UHT milk, with fat volume concentrations ranging from 0 to 4%, presented lasing threshold values dependent on the fat concentration, suggesting that a random laser tech...

the problem of steady magnetohydrodynamic boundary layer flow of an electrically conducting nanofluid due to an exponentially permeable stretching sheet with heat source/sink in presence of thermal radiation is numerically investigated. the effect of transverse brownian motion and thermophoresis on heat transfer and nano particle volume fraction considered. the governing partial differential eq...