Factorization and escorting in the game-theoretical approach to non-extensive entropy measures

The game-theoretical approach to non-extensive entropy measures of statistical physics is based on an abstract measure of complexity from which the entropy measure is derived in a natural way. A wide class of possible complexity measures is considered and a property of factorization investigated. The property reflects a separation between the system being observed and the observer. Apparently, the property is also related to escorting. It is shown that only those complexity measures which are connected with Tsallis entropy have the factorization property.Comment: 7 pages, revtex4. For NEXT2005 proceeding

Paradigms of Cognition

An abstract, quantitative theory which connects elements of information —key ingredients in the cognitive proces—is developed. Seemingly unrelated results are thereby unified. As an indication of this, consider results in classical probabilistic information theory involving information projections and so-called Pythagorean inequalities. This has a certain resemblance to classical results in geometry bearing Pythagoras’ name. By appealing to the abstract theory presented here, you have a common point of reference for these results. In fact, the new theory provides a general framework for the treatment of a multitude of global optimization problems across a range of disciplines such as geometry, statistics and statistical physics. Several applications are given, among them an “explanation” of Tsallis entropy is suggested. For this, as well as for the general development of the abstract underlying theory, emphasis is placed on interpretations and associated philosophical considerations. Technically, game theory is the key tool

In Situ Detection of Active Edge Sites in Single-Layer MoS2_2 Catalysts

MoS2 nanoparticles are proven catalysts for processes such as hydrodesulphurization and hydrogen evolution, but unravelling their atomic-scale structure under catalytic working conditions has remained significantly challenging. Ambient pressure X-ray Photoelectron Spectroscopy (AP-XPS) allows us to follow in-situ the formation of the catalytically relevant MoS2 edge sites in their active state. The XPS fingerprint is described by independent contributions to the Mo3d core level spectrum whose relative intensity is sensitive to the thermodynamic conditions. Density Functional Theory (DFT) is used to model the triangular MoS2 particles on Au(111) and identify the particular sulphidation state of the edge sites. A consistent picture emerges in which the core level shifts for the edge Mo atoms evolve counter-intuitively towards higher binding energies when the active edges are reduced. The shift is explained by a surprising alteration in the metallic character of the edge sites, which is a distinct spectroscopic signature of the MoS2 edges under working conditions

Exact Prediction and Universal Coding for Trees

Abstract — No closed formula for the optimal predictor (estimator) exists for the model of order preserving distributions on a finite tree. We present an algorithm of low complexity for a large class of trees. Let T = (T, ≤) be a finite rooted tree and consider the model P of all distributions over the nodes of T which respect the ordering (P ∈ P means P (a) ≤ P (b) whenever a ≤ b – hence the root has minimal, the leaves maximal probability). For the unique optimal predictor P ∗ ∈ P, sup P ∈P D(P ‖P ∗) is minimal among all distributions in P. It is our goal to determine P ∗ exactly. Presently, results in this direction (exact rather than numerical or asymptotic results) are somewhat sporadic. The starting point of exact results of the type here considered is Ryabko [1]. The author, jointly with Peter Harremoës, ha

Two General Games of Information

The Maximum Entropy Principle (MaxEnt) as well as the Minimum Information Divergence Principle (MinDiv) and other optimization principles of information theory and its applications to physics, statistics, economy and other fields are here discussed from the standpoint of two-person zero-sum games. 1

Bounds for Entropy and Divergence for Distributions over a Two-element Set

ABSTRACT. Three results dealing with probability distributions (p, q) over a two-element set are presented. The first two give bounds for the entropy function H(p, q) and are referred to as the logarithmic and the power-type bounds, respectively. The last result is a refinement of well known Pinsker-type inequalities for information divergence. The refinement readily extends to general distributions, but the key case to consider involves distributions on a two-element set. The discussion points to some elementary, yet non-trivial problems concerning seemingly simple concrete functions. Key words and phrases: Entropy, divergence, Pinsker’s inequality. 2000 Mathematics Subject Classification. 94A17, 26D15. 1