This paper studies the fundamental limits of the minimum average length of variable-length compression when a nonzero error probability ǫ is tolerated. We give non-asymptotic bounds on the minimum average length in terms of Erokhin’s rate-distortion function and we use those bounds to obtain a Gaussian approximation on the speed of approach to the limit which is quite accurate for all but small...

We make the hypothesis that molecular cloud fragments are triaxial bodies with a large scale magnetic field oriented along the short axis. While consistent with theoretical expectations, this idea is supported by magnetic field strength data, which show strong evidence for flattening along the direction of the mean magnetic field. It is also consistent with early submillimeter polarization data...

This paper addresses the control of a team of autonomous agents pursuing a smart evader in a nonaccurately mapped terrain. By describing this problem as a partial information Markov game, we are able to integrate map-learning and pursuit. We propose receding horizon control policies, in which the pursuers and the evader try to respectively maximize and minimize the probability of capture at the...

In this paper we consider the problem of computing on a local memory machine the product y = Ax, where A is a random n n sparse matrix with (n) nonzero elements. To study the average case communication cost of this problem, we introduce four different probability measures on the set of sparse matrices. We prove that on most local memory machines with p processors, this computation requires ((n=...

We propose new empirical tests for pseudorandom numbers based on random walks on Zm. The tests focus on the distribution of arrival time at zero starting from a nonzero fixed point x. The exact probability density of the arrival time is obtained by the Fourier analysis on finite groups. This kind of test based on the probability density for a random walk on a finite group is done for the first ...

We argue that significant probability of protons with momenta above their Fermi surface leads for proton concentrations p/n ≥ 1/8 to the enhancement of termally excited direct and modified URCA processes within a cold neutron star, and to a nonzero probability of direct URCA processes for small proton concentrations (p/n ≤ 1/8). We evaluate high momentum tails of neutron, proton and electrons d...

A module $M$ is said to be coretractable if there exists a nonzero homomorphism of every nonzero factor of $M$ into $M$. We prove that all right (left) modules over a ring are coretractable if and only if the ring is Morita equivalent to a finite product of local right and left perfect rings.

The annihilating-ideal graph of a commutative ring $R$ is denoted by $AG(R)$, whose vertices are all nonzero ideals of $R$ with nonzero annihilators and two distinct vertices $I$ and $J$ are adjacent if and only if $IJ=0$. In this article, we completely characterize rings $R$ when $gr(AG(R))neq 3$.

The unicity distance, U, of a secret-key cipher is defined by Shannon as the minimum amount of intercepted ciphertext symbols needed, in principle, to uniquely determine the secret key and, therefore, break the cipher. Accordingly, for a ciphertext of size N symbols less than U, the estimated key will have a nonzero probability of error. Of interest is knowing the chance or probability that an ...

In this paper, we consider new and general models for imperfect sources of randomness, and show how to obtain quasi-random sequences from such sources. Intuitively, quasi-random sequences are sequences of almost unbiased elements over a finite set. Our model is as follows: Let A be a finite set whose number of elements is a power of 2. Let 1/|A| ≤ δ < 1 be a constant. The source outputs an elem...