Justification of Logarithmic Loss via the Benefit of Side Information

We consider a natural measure of relevance: the reduction in optimal prediction risk in the presence of side information. For any given loss function, this relevance measure captures the benefit of side information for performing inference on a random variable under this loss function. When such a measure satisfies a natural data processing property, and the random variable of interest has alphabet size greater than two, we show that it is uniquely characterized by the mutual information, and the corresponding loss function coincides with logarithmic loss. In doing so, our work provides a new characterization of mutual information, and justifies its use as a measure of relevance. When the alphabet is binary, we characterize the only admissible forms the measure of relevance can assume while obeying the specified data processing property. Our results naturally extend to measuring causal influence between stochastic processes, where we unify different causal-inference measures in the literature as instantiations of directed information

An ERP study of low and high relevance semantic features

It is believed that the N400 elicited by concepts belonging to Living is larger than N400 to Non-living. This is considered as evidence that concepts are organized, in the brain, on the basis of categories. We conducted a feature-verification experiment where Living and Non-living concepts were matched for relevance of semantic features. Relevance is a measure of the contribution of semantic features to the “core” meaning of a concept. We found that when relevance is low the N400 is large. In addition, we found that when the two categories of Living and Non-living are equated for relevance the seemingly category effect at behavioral and neural level disappeared. In sum, N400 is sensitive, rather than to categories, to semantic features, thus showing that previously reported effects of semantic categories may arise as a consequence of the differing relevance of concepts belonging to Living and Non-living categories

The String Tension in Gauge Theories

A review article on string tension concept and their relevance as non-perturbative quantity on the study of quark confinement in lattice gauge theories. A detailed description of a variety of methods to measure the string tension on the lattice and an indication of the most promising developments is proposed.Comment: Postscript file, 46 pages and 14 figure

FEATURE TYPE EFFECTS IN SEMANTIC MEMORY: AN EVENT RELATED POTENTIALS STUDY

It is believed that the N400 elicited by concepts belonging to Living is larger than N400 to Objects. This is considered as evidence that concepts are organized, in the brain, on the basis of categories. Similarly, differential N400 to sensory and non-sensory semantic features was taken as evidence for a neural organisation of conceptual memory based on semantic features. We conducted a feature-verification experiment where Living and Non-Living concepts are described by sensory and non-sensory features were matched for age-of-acquisition, typicality and familiarity and for relevance of semantic features. Relevance is a measure of the contribution of semantic features to the “core” meaning of a concept. We found that when Relevance is low then N400 is larger. In addition, we found that when the two categories of Living and Non-Living concepts are matched for relevance the seemingly category effect at the neural level disappeared. Also no difference between sensory and non-sensory descriptions was detected when relevance was matched. In sum, N400 does not differ between categories or feature types. Previously reported effects of semantic categories and feature type may have arisen as a consequence of the differing Relevance of concepts belonging to Living and Non-Living categories

Feature selection for microarray gene expression data using simulated annealing guided by the multivariate joint entropy

In this work a new way to calculate the multivariate joint entropy is presented. This measure is the basis for a fast information-theoretic based evaluation of gene relevance in a Microarray Gene Expression data context. Its low complexity is based on the reuse of previous computations to calculate current feature relevance. The mu-TAFS algorithm --named as such to differentiate it from previous TAFS algorithms-- implements a simulated annealing technique specially designed for feature subset selection. The algorithm is applied to the maximization of gene subset relevance in several public-domain microarray data sets. The experimental results show a notoriously high classification performance and low size subsets formed by biologically meaningful genes.Postprint (published version

Applicability of Weyuker’s Properties on OO Metrics: Some Misunderstandings

Weyuker’s properties have been suggested as a guiding tool in identification of a good and comprehensive complexity measure by several researchers. Weyuker proposed nine properties to evaluate complexity measure for traditional programming. However, they are extensively used for evaluating object-oriented (OO) metrics, although the object-oriented features are entirely different in nature. In this paper, two recently reported OO metrics were evaluated and, based on it; the usefulness and relevance of these properties for evaluation purpose for object-oriented systems is discussed

Unique Continuation for the Magnetic Schr\"odinger Equation

The unique-continuation property from sets of positive measure is here proven for the many-body magnetic Schr\"odinger equation. This property guarantees that if a solution of the Schr\"odinger equation vanishes on a set of positive measure, then it is identically zero. We explicitly consider potentials written as sums of either one-body or two-body functions, typical for Hamiltonians in many-body quantum mechanics. As a special case, we are able to treat atomic and molecular Hamiltonians. The unique-continuation property plays an important role in density-functional theories, which underpins its relevance in quantum chemistry

Unique continuation for the magnetic Schrödinger equation

The unique‐continuation property from sets of positive measure is here proven for the many‐body magnetic Schrödinger equation. This property guarantees that if a solution of the Schrödinger equation vanishes on a set of positive measure, then it is identically zero. We explicitly consider potentials written as sums of either one‐body or two‐body functions, typical for Hamiltonians in many‐body quantum mechanics. As a special case, we are able to treat atomic and molecular Hamiltonians. The unique‐continuation property plays an important role in density‐functional theories, which underpins its relevance in quantum chemistry