We investigate the asymptotic behavior of the maxmin values of repeated two-person zero-sum games with a bound on the strategic entropy of the maximizer’s strategies while the other player is unrestricted. We will show that if the Ž . bound h n , a function of the number of repetitions n, satisfies the condition Ž . Ž . nŽ Ž .. Ž .Ž . h n rn a g n a ` , then the maxmin value W h n converges to ...

Our paper analyzes some new lines to advance on an evolving concept, the so-called Entropy. We need to model this measure by adequate conditions, departing from vague pieces of information. For this, it will be very necessary to analyze the relationship between some such measures, which may be of di¤erent types, with their very interesting applications, as Graph Entropy, Metric Entropy, Algorit...

We investigate the complexity of computing entropy of various Markovian models including Markov Chains (MCs), Interval Markov Chains (IMCs) and Markov Decision Processes (MDPs). We consider both entropy and entropy rate for general MCs, and study two algorithmic questions, i.e., entropy approximation problem and entropy threshold problem. The former asks for an approximation of the entropy/entr...

-Let C = {5(t), 0 5 t I T} be a process with covariance function K(s,t ) and E jf t'(t) dt < co. It is proved that for every E > 0 the E-entropy H,(T) satisfies where & is a Gaussian process with the covarhmce K&t) and &‘;,(T) is the entropy of the measure induced by c (in function space) with respect to that induced by &,. It is also shown that if ze,(T) < co, then, as E + 0 Furthermore, if th...

The entropy of an ergodic finite-alphabet process can be computed from a single typical sample path x1 using the entropy of the k-block empirical probability and letting k grow with n roughly like logn. We further assume that the distribution of the process is a g-measure. We prove large deviation principles for conditional, non-conditional and relative k(n)-block empirical entropies.

I review some recent work (done in collaboration with G. Veneziano) which clarifies the existence of a correspondence between self-gravitating fundamental string states and Schwarzschild black holes. The main result is a detailed calculation showing that selfgravity causes a typical string state of mass M to shrink, as the string coupling g increases, down to a compact string state whose mass, ...

Let G be a sofic group, and let Σ “ pσnqně1 be a sofic approximation to it. For a probability-preserving G-system, a variant of the sofic entropy relative to Σ has recently been defined in terms of sequences of measures on its model spaces that ‘converge’ to the system in a certain sense. Here we prove that, in order to study this notion, one may restrict attention to those sequences that have ...

The scale of environmental impacts associated with the manufacture of microchips is characterized through analysis of material and energy inputs into processes in the production chain. The total weight of secondary fossil fuel and chemical inputs to produce and use a single 2-gram 32MB DRAM chip are estimated at 1600 g and 72 g, respectively. Use of water and elemental gases (mainly N2) in the ...

| We describe an algorithm to eeciently compute maximum entropy densities, i.e. densities maximizing the Shannon entropy ? R p(x) log p(x)dx under a set of constraints Eg i (x)] = c i , i = 1;: : : ; n: Our method is based on an algorithm by Zellner and Highheld, which has been found not to converge under a variety of circumstances. To demonstrate that our method overcomes these diiculties, we ...