Weighted Logratio Biplots, Correspondence Analysis and Spectral Maps

Starting with logratio biplots for compositional data, which are based on the principle of subcompositional coherence, and then adding weights, as in correspondence analysis, we rediscover Lewi's spectral map and many connections to analyses of two-way tables of non-negative data. Thanks to the weighting, the method also achieves the property of distributional equivalence

Holomorphic maps between moduli spaces

We prove that every non-constant holomorphic map&em&M&/em&&sub&g,p&/sub&→ &em&M&/em&&sub& g',p'&/sub& between moduli spaces of Riemann surfaces is a forgetful map, provided that g ≥ 6 and g' ≤ 2g-2.

Integración de Google Maps y TSP Solvers para la definición y resolución del TSP

Este trabajo final de carrera presenta la arquitectura e implementación de un entorno web para la descripción y visualización de instancias reales del TSP (Travelling Salesman Problem), a través de Google Maps, y su posterior resoluación mediante tècnicas de optimización combinatoria.

Using a Parameterization of a Radiative Transfer Model to Build High-Resolution Maps of Typical Clear-Sky UV Index in Catalonia, Spain

To perform a climatic analysis of the annual UV index (UVI) variations in Catalonia, Spain (northeast of the Iberian Peninsula), a new simple parameterization scheme is presented based on a multilayer radiative transfer model. The parameterization performs fast UVI calculations for a wide range of cloudless and snow-free situations and can be applied anywhere. The following parameters are considered: solar zenith angle, total ozone column, altitude, aerosol optical depth, and single-scattering albedo. A sensitivity analysis is presented to justify this choice with special attention to aerosol information. Comparisons with the base model show good agreement, most of all for the most common cases, giving an absolute error within 0.2 in the UVI for a wide range of cases considered. Two tests are done to show the performance of the parameterization against UVI measurements. One uses data from a high-quality spectroradiometer from Lauder, New Zealand [45.04°S, 169.684°E, 370 m above mean sea level (MSL)], where there is a low presence of aerosols. The other uses data from a Robertson–Berger-type meter from Girona, Spain (41.97°N, 2.82°E, 100 m MSL), where there is more aerosol load and where it has been possible to study the effect of aerosol information on the model versus measurement comparison. The parameterization is applied to a climatic analysis of the annual UVI variation in Catalonia, showing the contributions of solar zenith angle, ozone, and aerosols. High-resolution seasonal maps of typical UV index values in Catalonia are presented

Counterpoise-corrected geometries and harmonic frequencies of N-body clusters: application to (HF)n (n=3,4)

A study was conducted on the methods of basis set superposition error (BSSE)-free geometry optimization and frequency calculations in clusters larger than a dimer. In particular, three different counterpoise schemes were critically examined. It was shown that the counterpoise-corrected supermolecule energy can be easily obtained in all the cases by using the many-body partitioning of energy

Ratio maps and correspondence analysis

We compare two methods for visualising contingency tables and developa method called the ratio map which combines the good properties of both.The first is a biplot based on the logratio approach to compositional dataanalysis. This approach is founded on the principle of subcompositionalcoherence, which assures that results are invariant to considering subsetsof the composition. The second approach, correspondence analysis, isbased on the chi-square approach to contingency table analysis. Acornerstone of correspondence analysis is the principle of distributionalequivalence, which assures invariance in the results when rows or columnswith identical conditional proportions are merged. Both methods may bedescribed as singular value decompositions of appropriately transformedmatrices. Correspondence analysis includes a weighting of the rows andcolumns proportional to the margins of the table. If this idea of row andcolumn weights is introduced into the logratio biplot, we obtain a methodwhich obeys both principles of subcompositional coherence and distributionalequivalence.

Regions of rationality: Maps for bounded agents

An important problem in descriptive and prescriptive research in decision making is to identify regions of rationality, i.e., the areas for which heuristics are and are not effective. To map the contours of such regions, we derive probabilities that heuristics identify the best of m alternatives (m > 2) characterized by k attributes or cues (k > 1). The heuristics include a single variable (lexicographic), variations of elimination-by-aspects, equal weighting, hybrids of the preceding, and models exploiting dominance. We use twenty simulated and four empirical datasets for illustration. We further provide an overview by regressing heuristic performance on factors characterizing environments. Overall, sensible heuristics generally yield similar choices in many environments. However, selection of the appropriate heuristic can be important in some regions (e.g., if there is low inter-correlation among attributes/cues). Since our work assumes a hit or miss decision criterion, we conclude by outlining extensions for exploring the effects of different loss functions.

Extensions of maps defined on many fibres

Let S be a fibred surface. We prove that the existence of morphisms from non countably many fibres to curves implies, up to base change, the existence of a rational map from S to another surface fibred over the same base reflecting the properties of the original morphisms. Under some conditions of unicity base change is not needed and one recovers exactly the initial maps.

Gas identification with tin oxide sensor array and self-organizing maps: adaptive correction of sensor drifts

Low-cost tin oxide gas sensors are inherently nonspecific. In addition, they have several undesirable characteristics such as slow response, nonlinearities, and long-term drifts. This paper shows that the combination of a gas-sensor array together with self-organizing maps (SOM's) permit success in gas classification problems. The system is able to determine the gas present in an atmosphere with error rates lower than 3%. Correction of the sensor's drift with an adaptive SOM has also been investigated

Harmonic oscillators driven by colored noise: crossovers, resonances and spectra

We study second-order properties of linear oscillators driven by exponentially correlated noise. We focus our attention on dynamical exponents and crossovers and also on resonance phenomena that appear when the driving noise is dichotomous. We also obtain the power spectrum and show its different behaviors according to the color of the noise.

Strange nonchaotic attractors in Harper maps

We study the existence of strange nonchaotic attractors (SNA) in the family of Harper maps. We prove that for a set of parameters of positive measure, the map possesses a SNA. However, the set is nowhere dense. By changing the parameter arbitrarily small amounts, the attractor is a smooth curve and not a SNA.

Periodic points of holomorphic maps via Lefschetz numbers

In this paper we study the set of periods of holomorphic maps on compact manifolds, using the periodic Lefschetz numbers introduced by Dold and Llibre, which can be computed from the homology class of the map. We show that these numbers contain information about the existence of periodic points of a given period; and, if we assume the map to be transversal, then they give us the exact number of such periodic orbits. We apply this result to the complex projective space of dimension n and to some special type of Hopf surfaces, partially characterizing their set of periods. In the first case we also show that any holomorphic map of CP(n) of degree greater than one has infinitely many distinct periodic orbits, hence generalizing a theorem of Fornaess and Sibony. We then characterize the set of periods of a holomorphic map on the Riemann sphere, hence giving an alternative proof of Baker's theorem.