Let (M, g) be a time-oriented Lorentzian manifold and d the Lorentzian distance on M . The function τ(q) := supp<q d(p, q) is the cosmological time function of M , where as usual p < q means that p is in the causal past of q. This function is called regular iff τ(q) <∞ for all q and also τ → 0 along every past inextendible causal curve. If the cosmological time function τ of a spacetime (M, g) ...

We analyse the data for the proton structure function F2 over the entire Q 2 domain, including especially low Q 2 , in terms of perturbative and non-perturbative QCD contributions. The small distance configurations are given by perturbative QCD, while the large distance contributions are given by the vector dominance model and, for the higher mass qq states, by the additive quark approach.

Bounds for the bracketing entropy of the classes of bounded k-monotone functions on [0, A] are obtained under both the Hellinger distance and the L(p)(Q) distance, where 1 ≤ p < ∞ and Q is a probability measure on [0, A]. The result is then applied to obtain the rate of convergence of the maximum likelihood estimator of a k-monotone density.

Preprocess: a set D of points in R d Query: given a new point q, report a point pD with the smallest distance to q q p Motivation

In this paper, we determine the parameters of Z q-MacDonald Code of dimension k for any positive integer q ≥ 2. Further, we have obtained the weight distribution of Z q-MacDonald code of dimension 3 and furthermore, we have given the weight distribution of Z q-Simplex code of dimension 3 for any positive integer q ≥ 2. and Minimum Hamming distance.

Article history: Received 14 December 2007 Revised 9 September 2008 Accepted 11 September 2008 Available online 25 September 2008 Communicated by Naoki Saito We present a condition on the matrix of an underdetermined linear system which guarantees that the solution of the system with minimal q-quasinorm is also the sparsest one. This generalizes, and slightly improves, a similar result for the ...

In general, to understand hadronic uncertainties we need a separation of short p ∼ Q and long p ∼ ΛQCD distance fluctuations. For processes in QCD with momentum transfers Q ≫ ΛQCD, the short distance part is calculable in terms of Wilson coefficients or hard scattering functions. The long distance contributions can be arranged into universal non-perturbative matrix elements which can be extract...

We currently know the following four bounds on rate as a function of relative distance, three of them upper bounds (which tell us what rate-distance combinations are impossible), and one lower bound (which tells us what rate-distance combinations we can achieve). In the following, R is the rate and δ the relative distance of a code. For example, a (n, k, d) code has R = k/n and δ = d/n. Hq(x) i...

In this paper, we address an under-represented class of learning algorithms in the study of connectionism: reinforcement learning. We first introduce these classic methods in a new formalism which highlights the particularities of implementations such as Q-Learning, QLearning with Hamming distance, Q-Learning with statistical clustering and Dyna-Q. We then present in this formalism a neural imp...

Let GF(q) be the finite field of q = pa elements, where p is a prime. Let V be the vector space (GF(q))< The minimum distance drain of a set C _C V is defined as the smallest Hamming distance between different vectors of C. The greatest integer ~ 1, a set C _C V is called an e-error-correcting q-ary code, if ] C I, the cardinality of C, is />2 and e = [(dmin 1)/2]....