In this note, we establish the first variation formula of the adjusted log entropy functional Ya introduced by Ye in [14]. As a direct consequence, we also obtain the monotonicity of Ya along the Ricci flow. Various entropy functionals play crucial role in the singularity analysis of Ricci flow. Let (M, g(t)) be a smooth family of Riemannian metrics on a closed manifold M and suppose g(t) is a ...

Title of dissertation: ORDERS OF ACCUMULATION OF ENTROPY AND RANDOM SUBSHIFTS OF FINITE TYPE Kevin McGoff, Doctor of Philosophy, 2011 Dissertation directed by: Professor Mike Boyle Department of Mathematics The first portion of this dissertation concerns orders of accumulation of entropy. For a continuous map T of a compact metrizable space X with finite topological entropy, the order of accumu...

1 Introduction Kolmogorov-Sinai entropy (K-S entropy) is used to analyze radio wave intensity time series of quasars. K-S entropy measures the rate of change of probability with the change of dimension that trajectory points in the embedding space stay within a distance r [1]. The K-S entropy analysis method is a powerful formalism for describing dynamics of time series [1]. m-dimensional K-S e...

We shall show that a two-parameter extended entropy function is characterized by a functional equation. As a corollary of this result, we obtain that the Tsallis entropy function is characterized by a functional equation, which is a different form used in [1] i.e., in Proposition 2.1 in the present paper. We also give an interpretation of the functional equation giving the Tsallis entropy funct...

A problem of improving the accuracy of nonparametric entropy estimation for a stationary ergodic process is considered. New weak metrics are introduced and relations between metrics, measures, and entropy are discussed. Based on weak metrics, a new nearest-neighbor entropy estimator is constructed and has a parameter with which the estimator is optimized to reduce its bias. It is shown that est...

We show that maximum entropy models can be modeled with certain kinds of Hidden Markov Models (HMMs). This allows us to easily construct maximum entropy-style models with hidden variables, hidden state sequences, or other characteristics. The resulting models can be easily trained using standard algorithms with guaranteed locally, and in some cases globally, optimal parameter settings. We also ...

This paper studies the properties of a new class of demographic parameters for age-structured populations and analyzes the effect of natural selection on these parameters. Two new demographic variables are introduced: the entropy of a population and the reproductive potential. The entropy of a population measures the variability of the contribution of the different age classes to the stationary...

– In this Letter we investigate the density of states ΩN (E,M) of twoand threedimensional Ising models with N spins as a function of energy E and magnetization M . For a fixed energy lower than a critical value Ec,N the density of states exhibits two sharp maxima at M = ±Msp(E) which define the spontaneous magnetization. An analysis of the form Msp(E) ∝ (Ec,∞ − E) βε yields very good results fo...

[1] Boltzmann’s H function was evaluated using 10 years of 1-min distribution functions. These results were used to study the long-term averaged spatial distributions of four entropy parameters. The average entropy density sa(x), where a = i for ions and a = e for electrons, increased when moving Earthward or toward the flanks. The magnitudes of these entropy changes were similar for ions and e...

We consider the generation of entropy when particle pairs are created at a cosmological level. Making a reduction via the particle number basis, we compute the classical limit for the entropy generation due to the evolution of the matter field fluctuations (squeeze transformation), obtaining that it is linear in the squeeze parameter for a general class of initial states. We also discuss the de...