Entropy maximization

About: Entropy maximization is a research topic. Over the lifetime, 1068 publications have been published within this topic receiving 20730 citations.

Entropy optimization principles with applications

Abstract: Entropy optimization principles Jaynes' maximum entropy principle applications of Jaynes' maximum entropy principle Kullback's minimum cross-entropy principle further applications of MaxEnt and MinEnt new entropy optimization principles generalized principles of maximum entropy the four inverse maximum entropy principles.

Submodular Function Maximization

Abstract: In this chapter we will introduce submodularity and some of its generalizations, illustrate how it arises in various applications, and discuss algorithms for optimizing submodular functions. Submodularity is a property of set functions with deep theoretical consequences and far-reaching applications. At first glance it seems very similar to concavity, in other ways it resembles convexity. It appears in a wide variety of applications: in Computer Science it has recently been identified and utilized in domains such as viral marketing [39], information gathering [44], image segmentation [10, 40, 36], document summarization [56], and speeding up satisfiability solvers [73]. Our emphasis in this chapter is on maximization; there are many important results and applications related to minimizing submodular functions that we do not cover. As a concrete running example, we will consider the problem of deploying sensors in a drinking water distribution network (see Figure 3.1) in order to detect contamination. In this domain, we may have a model of how contaminants, accidentally or maliciously introduced into the network, spread over time. Such a model then allows to quantify the benefit f(A) of deploying sensors at a particular set A of locations (junctions or pipes in the network) in terms of the detection performance (such as average time to detection). Based on this notion of utility, we then wish to find an optimal subset A ⊆ V of locations maximizing the utility, max A f(A) , subject to some constraints (such as bounded cost). This application requires solving a difficult real-world optimization problem, that can be handled with the techniques discussed in this chapter (Krause et al. [49] show in detail how submodular optimization can be applied in this domain.)

Thermodynamical aspects of gravity: new insights

Abstract: The fact that one can associate thermodynamic properties with horizons brings together principles of quantum theory, gravitation and thermodynamics and possibly offers a window to the nature of quantum geometry. This review discusses certain aspects of this topic, concentrating on new insights gained from some recent work. After a brief introduction of the overall perspective, sections 2 and 3 provide the pedagogical background on the geometrical features of bifurcation horizons, path integral derivation of horizon temperature, black hole evaporation, structure of Lanczos-Lovelock models, the concept of Noether charge and its relation to horizon entropy. Section 4 discusses several conceptual issues introduced by the existence of temperature and entropy of the horizons. In section 5 we take up the connection between horizon thermodynamics and gravitational dynamics and describe several peculiar features which have no simple interpretation in the conventional approach. The next two sections describe the recent progress achieved in an alternative perspective of gravity. In section 6 we provide a thermodynamic interpretation of the field equations of gravity in any diffeomorphism invariant theory and in section 7 we obtain the field equations of gravity from an entropy maximization principle. The last section provides a summary.