Let n be a positive integer and denote < n >= {1, ..., n}. We view < n > as an alphabet on n letters. Denote by < n > d the set of all mappings of Z to the set < n >. By extending the Hamming metric on < n > × < n > to < n >Zd one obtains that < n > d is a compact metric space. The group Z acts as a group of (translation) automorphisms on < n > d . A set S ⊂ Z which is closed and invariant unde...

Planar point location is among the most fundamental search problems in computational geometry. Although this problem has been heavily studied from the perspective of worst-case query time, there has been surprisingly little theoretical work on expected-case query time. We are given an n-vertex planar polygonal subdivision S satisfying some weak assumptions (satissed, for example, by all convex ...

Planar point location is among the most fundamental search problems in computational geometry. Although this problem has been heavily studied from the perspective of worst-case query time, there has been surprisingly little theoretical work on expected-case query time. We are given an n-vertex planar polygonal subdivision S satisfying some weak assumptions (satisfied, for example, by all convex...

A question that is currently highly debated is whether the microcanonical entropy should be expressed as the logarithm of the phase volume (volume entropy, also known as the Gibbs entropy) or as the logarithm of the density of states (surface entropy, also known as the Boltzmann entropy). Rather than postulating them and investigating the consequence of each definition, as is customary, here we...

Privacy ampliication allows two parties Alice and Bob knowing a partially secret string S to extract, by communication over a public channel, a shorter, highly secret string S 0. Bennett, Brassard, Cr epeau, and Maurer showed that the length of S 0 can be almost equal to the conditional R enyi entropy of S given an opponent Eve's knowledge. All previous results on privacy ampliication assumed t...

If the given problem instance is partially solved, we want to minimize our effort to solve the problem using that information. In this paper we introduce the measure of entropy H(S) for uncertainty in partially solved input data S(X) = (X1, ..., Xk), where X is the entire data set, and each Xi is already solved. We use the entropy measure to analyze three example problems, sorting, shortest pat...

Kolmogorov introduced a concept of ε-entropy to analyze information in classical continuous system. The fractal dimension of geometrical sets was introduced by Mandelbrot as a new criterion to analyze the complexity of these sets. The ε-entropy and the fractal dimension of a state in general quantum system were introduced by one of the present authors in order to characterize chaotic properties...

the second law of thermodynamic (entropy principle) is of special theo-philosophical importance. it seems that this law, which is renowned as “the death of software design” and despite the order in the world, is like an incompatible universal. this article examines the concept of entropy in the three temperature, statistic, and information applications and addresses the contradiction of the sec...

We show that if M is an oriented closed geometric four manifold the following notions are equivalent, (i) M has zero minimal entropy, h(M) = 0. (ii) M collapses with bounded curvature, VolK(M) = 0. (iii) The simplicial volume of M vanishes, ||M || = 0. (iv) M admits a T -structure. (v) M is modelled on one of the geometries S, CP , S × E, H × E, S̃L2 × E, Nil × E, Nil, Sol 1 , S × E, H × E, Sol ...