An Introduction to Hyperbolic Barycentric Coordinates and their Applications

Barycentric coordinates are commonly used in Euclidean geometry. The adaptation of barycentric coordinates for use in hyperbolic geometry gives rise to hyperbolic barycentric coordinates, known as gyrobarycentric coordinates. The aim of this article is to present the road from Einstein's velocity addition law of relativistically admissible velocities to hyperbolic barycentric coordinates along with applications.Comment: 66 pages, 3 figure

Ultrafast spin dynamics in II-VI diluted magnetic semiconductors with spin-orbit interaction

We study theoretically the ultrafast spin dynamics of II-VI diluted magnetic semiconductors in the presence of spin-orbit interaction. Our goal is to explore the interplay or competition between the exchange $sd$-coupling and the spin-orbit interaction in both bulk and quantum well systems. For bulk materials we concentrate on Zn$_{1-x}$Mn$_x$Se and take into account the Dresselhaus interaction, while for quantum wells we examine Hg$_{1-x-y}$Mn$_x$Cd$_y$Te systems with a strong Rashba coupling. Our calculations were performed with a recently developed formalism which incorporates electronic correlations beyond mean-field theory originated from the exchange $sd$-coupling. For both bulk and quasi-two-dimensional systems we find that, by varying the system parameters within realistic ranges, both interactions can be chosen to play a dominant role or to compete on an equal footing with each other. The most notable effect of the spin-orbit interaction in both types of systems is the appearance of strong oscillations where the exchange $sd$-coupling by itself only causes an exponential decay of the mean electronic spin components. The mean-field approximation is also studied and it is interpreted analytically why it shows a strong suppression of the spin-orbit-induced dephasing of the spin component parallel to the Mn magnetic field.Comment: 9 pages, 5 figure

\u3ci\u3eA\u3c/i\u3e-Optimality for Active Learning of Logistic Regression Classifiers

Over the last decade there has been growing interest in pool-based active learning techniques, where instead of receiving an i.i.d. sample from a pool of unlabeled data, a learner may take an active role in selecting examples from the pool. Queries to an oracle (a human annotator in most applications) provide label information for the selected observations, but at a cost. The challenge is to end up with a model that provides the best possible generalization error at the least cost. Popular methods such as uncertainty sampling often work well, but sometimes fail badly. We take the A-optimality criterion used in optimal experimental design, and extend it so that it can be used for pool-based active learning of logistic regression classifiers. A-optimality has attractive theoretical properties, and empirical evaluation confirms that it offers a more robust approach to active learning for logistic regression than alternatives

PennAspect: Two-Way Aspect Model Implementation

The two-way aspect model is a latent class statistical mixture model for performing soft clustering of co-occurrence data observations. It acts on data such as document/word pairs (words occurring in documents) or movie/people pairs (people see certain movies) to produce their joint distribution estimate. This document describes our software immplementation of the aspect model available under GNU Public License (included with the distribution). We call this package PennAspect. The distribution is packaged as Java source and class files. The software comes with no guarantees of any kind. We welcome user feedback and comments. To download PennAspect, visit: http://www.cis.upenn.edu/datamining/software_dist/PennAspect/index.html

Bayesian Example Selection Using BaBiES

Active learning is widely used to select which examples from a pool should be labeled to give best results when learning predictive models. It is, however, sometimes desirable to choose examples before any labeling or machine learning has occurred. The optimal experimental design literature has many theoretically attractive optimality criteria for example selection, but most are intractable when working with large numbers of predictive features. We present the BaBiES criterion, an approximation of Bayesian A-optimal design for linear regression using binary predictors, which is both simple and extremely fast. Empirical evaluations demonstrate that, in spite of selecting all examples prior to learning, BaBiES is competitive with standard active learning methods for a variety of document classification tasks

Los arenales costeros del litoral catalán (la bahía de Rosas)

[ES] Se distinguen dos fuentes para los minerales pesados que se encuentran en las playas de la bahía de Rosas: los basaltos de Olot, para la augita, olivino e hiperstena y las rocas metamórficas del macizo de los Alberes y Cabo de Creus de donde proceden la andalucita, silimanita y distena. La distribución de los minerales, se explica por el transporte efectuado por las corrientes de deriva, los temporales y el viento. Las anomaiías en la distribucidn de algunas especies se deben a los accicentes del terreno y a las condiciones dinámicas muy activas de la bahía, que afectan a la seleccidn de minerales.[EN] The heavy minerals of Gulf of Rosas coastal sand have two different sources. The more frequent heavy minerals are augite and olivine which come from Olot basalts. The metamorfic association is presented by andalusite, siliimanite and kyanite and they come from the metamorfic rocks of the Pyrenees and Cap of Creus massif. Homblende can have two origins: the metamorfic and the granitic rocks of river Muga basin.Peer reviewe