We study Voiculescu’s microstate free entropy for a single non–selfadjoint random variable. The main result is that certain additional constraints on eigenvalues of microstates do not change the free entropy. Our tool is the method of random regularization of Brown measure which was studied recently by Haagerup and the author. As a simple application we present an upper bound for the free entro...

We model Mandarin phrase break prediction as a classification problem with three level prosodic structures and apply conditional maximum entropy classification to this problem. We acquire multiple levels of linguistic knowledge from an annotated corpus to become well-integrated features for maximum entropy framework. Five kinds of features were used to represent various linguistic constraints i...

We derive a rst-order approximation of the density of maximum entropy for a continuous 1-D random variable, given a number of simple constraints. This results in a density expansion which is somewhat similar to the classical polynomial density expansions by Gram-Charlier and Edgeworth. Using this approximation of density, an approximation of 1-D diierential entropy is derived. The approximation...

In present communication, we have developed the suitable constraints for the given the mean codeword length and the measures of entropy. This development has proved that Renyi’s entropy gives the minimum value of the log of the harmonic mean and the log of power mean. We have also developed an important relation between best 1:1 code and the uniquely decipherable code by using different measure...

We derive a first-order approximation of the density of maximum entropy for a continuous 1-D random variable, given a number of simple constraints. This results in a density expansion which is somewhat similar to the classical polynomial density expansions by Gram-Charlier and Edgeworth. Using this approximation of density, an approximation of 1-D differential entropy is derived. The approximat...

Proteins fold from a highly disordered state into a highly ordered one. Traditionally, the folding problem has been stated as one of predicting "the" tertiary structure from sequential information. However, new evidence suggests that the ensemble of unfolded forms may not be as disordered as once believed, and that the native form of many proteins may not be described by a single conformation, ...

Experimental recordings of the collective activity of interacting spiking neurons exhibit 1 random behavior and memory effects, thus the stochastic process modeling the spiking activity 2 is expected to show some degree of time irreversibility. We use the thermodynamic formalism to 3 build a framework, in the context of spike train statistics, to quantify the degree of irreversibility 4 of any ...

These short notes cover the basic definitions and properties of entropy, with an emphasis on its use in dynamical systems. They are intended to show how the different notions of entropy that appear in probability, mathematical statistical physics can be modified for use in the study of measurable dynamical systems, culminating in one of the most striking such uses of entropy: the proof of Sinai...

We derive a rst-order approximation of the density of maximum entropy for a continuous 1-D random variable, given a number of simple constraints. This results in a density expansion which is somewhat similar to the classical polynomial density expansions by Gram-Charlier and Edgeworth. Using this approximation of density, an approximation of 1-D diierential entropy is derived. The approximation...

The minimum error entropy (MEE) criterion has been successfully used in fields such as parameter estimation, system identification and the supervised machine learning. There is in general no explicit expression for the optimal MEE estimate unless some constraints on the conditional distribution are imposed. A recent paper has proved that if the conditional density is conditionally symmetric and...