In this Letter, we derive exponent inequalities relating the dynamic exponent z to the steady state exponent Γ for a general class of stochastically driven dynamical systems. We begin by deriving a general exact inequality, relating the response function and the correlation function, from which the various exponent inequalities emanate. We then distinguish between two classes of dynamical syste...

A conceptually simple method for derivation of lower bounds on the error exponent of specific families of block codes used on classical-quantum channels with arbitrary signal states over a finite Hilbert space is presented. It is shown that families of binary block codes with appropriately rescaled binomial multiplicity enumerators used on binary classical-quantum channels and decoded by the su...

All primitive trinomials over GF (2) with degree 859433 (which is the 33rd Mersenne exponent) are presented. They are X859433 +X288477 + 1 and its reciprocal. Also two examples of primitive pentanomials over GF (2) with degree 86243 (which is the 28th Mersenne exponent) are presented. The sieve used is briefly described.

We present the first exponentiation algorithm that uses the entropy of the source of the exponent to improve on existing exponentiation algorithms when the entropy is smaller than (1 + w(S)/l(S)), where w(S) is the Hamming weight of the exponent, and l(S) is its length. For entropy 1 it is comparable to the best-known general purpose exponentiation algorithms.

In this study we propose a bayesian approach to the estimation of the Hurst exponent in terms of linear mixed models. Even for unevenly sampled signals and signals with gaps, our method is applicable. We test our method by using artificial fractional brownian motion of different length and compare it with the detrended fluctuation analysis technique. The estimation of the Hurst exponent of a Ro...

Extensive simulations are performed to study the persistence behavior of a conserved lattice gas model exhibiting an absorbing phase transition from an active phase into an inactive phase. Both the global and the local persistence exponents are determined in two and higher dimensions. The local persistence exponent obeys a scaling relation involving the order parameter exponent of the absorbing...

Assume that each earthquake can produce a series of aftershock independently of its size according to its “local” Omori’s law with exponent 1+θ. Each aftershock can itself trigger other aftershocks and so on. The global observable Omori’s law is found to have two distinct power law regimes, the first one with exponent p− = 1− θ for time t < t ∗ ∼ κ−1/θ, where 0 < 1−κ < 1 measures the fraction o...

We have translated fractional Brownian motion (FBM) signals into a text based on two ”letters”, as if the signal fluctuations correspond to a constant stepsize random walk. We have applied the Zipf method to extract the ζ′ exponent relating the word frequency and its rank on a loglog plot. We have studied the variation of the Zipf exponent(s) giving the relationship between the frequency of occ...

In this work, we introduce the notion of the error exponent region for a multi-user channel. This region specifies the set of error-exponent vectors that are simultaneously achievable by all users in the multi-user channel. This is done by associating different probabilities of error for different users, contrary to the traditional approach where a single probability of system error is consider...