The continuous wavelet transform as a maximum entropy solution of the corresponding inverse problem

The continuous wavelet transform is obtained as a maximumentropy solution of the corresponding inverse problem. It is well knownthat although a signal can be reconstructed from its wavelet transform,the expansion is not unique due to the redundancy of continuous wavelets.Hence, the inverse problem has no unique solution. If we want to recognizeone solution as "optimal", then an appropriate decision criterion hasto be adopted. We show here that the continuous wavelet transform is an"optimal" solution in a maximum entropy sense.

Second-order parameter estimation

This work provides a general framework for the design of second-order blind estimators without adopting anyapproximation about the observation statistics or the a prioridistribution of the parameters. The proposed solution is obtainedminimizing the estimator variance subject to some constraints onthe estimator bias. The resulting optimal estimator is found todepend on the observation fourth-order moments that can be calculatedanalytically from the known signal model. Unfortunately,in most cases, the performance of this estimator is severely limitedby the residual bias inherent to nonlinear estimation problems.To overcome this limitation, the second-order minimum varianceunbiased estimator is deduced from the general solution by assumingaccurate prior information on the vector of parameters.This small-error approximation is adopted to design iterativeestimators or trackers. It is shown that the associated varianceconstitutes the lower bound for the variance of any unbiasedestimator based on the sample covariance matrix.The paper formulation is then applied to track the angle-of-arrival(AoA) of multiple digitally-modulated sources by means ofa uniform linear array. The optimal second-order tracker is comparedwith the classical maximum likelihood (ML) blind methodsthat are shown to be quadratic in the observed data as well. Simulationshave confirmed that the discrete nature of the transmittedsymbols can be exploited to improve considerably the discriminationof near sources in medium-to-high SNR scenarios.

ML estimator and hybrid beamformer for multipath and interference mitigation in GNSS receivers

This paper addresses the estimation of the code-phase(pseudorange) and the carrier-phase of the direct signal received from a direct-sequence spread-spectrum satellite transmitter. Thesignal is received by an antenna array in a scenario with interferenceand multipath propagation. These two effects are generallythe limiting error sources in most high-precision positioning applications.A new estimator of the code- and carrier-phases is derivedby using a simplified signal model and the maximum likelihood(ML) principle. The simplified model consists essentially ofgathering all signals, except for the direct one, in a component withunknown spatial correlation. The estimator exploits the knowledgeof the direction-of-arrival of the direct signal and is much simplerthan other estimators derived under more detailed signal models.Moreover, we present an iterative algorithm, that is adequate for apractical implementation and explores an interesting link betweenthe ML estimator and a hybrid beamformer. The mean squarederror and bias of the new estimator are computed for a numberof scenarios and compared with those of other methods. The presentedestimator and the hybrid beamforming outperform the existingtechniques of comparable complexity and attains, in manysituations, the Cramér–Rao lower bound of the problem at hand.

NDA waveform estimation in the low-SNR regime

This correspondence addresses the problem of nondata-aidedwaveform estimation for digital communications. Based on the unconditionalmaximum likelihood criterion, the main contribution of this correspondenceis the derivation of a closed-form solution to the waveform estimationproblem in the low signal-to-noise ratio regime. The proposed estimationmethod is based on the second-order statistics of the received signaland a clear link is established between maximum likelihood estimation andcorrelation matching techniques. Compression with the signal-subspace isalso proposed to improve the robustness against the noise and to mitigatethe impact of abnormals or outliers.

On the q=1/2 non-extensive maximum entropy distribution

A detailed mathematical analysis on the q = 1/2 non-extensive maximum entropydistribution of Tsallis' is undertaken. The analysis is based upon the splitting of such adistribution into two orthogonal components. One of the components corresponds to theminimum norm solution of the problem posed by the fulfillment of the a priori conditionson the given expectation values. The remaining component takes care of the normalizationconstraint and is the projection of a constant onto the Null space of the "expectation-values-transformation"

A non-extensive maximum entropy based regulations method for bad conditioned inverse problems

A regularization method based on the non-extensive maximum entropy principle is devised. Special emphasis is given to the q=1/2 case. We show that, when the residual principle is considered as constraint, the q=1/2 generalized distribution of Tsallis yields a regularized solution for bad-conditioned problems. The so devised regularized distribution is endowed with a component which corresponds to the well known regularized solution of Tikhonov (1977).

Frames: a maximum entropy statistical estimate of the inverse problem

A maximum entropy statistical treatment of an inverse problem concerning frame theory is presented. The problem arises from the fact that a frame is an overcomplete set of vectors that defines a mapping with no unique inverse. Although any vector in the concomitant space can be expressed as a linear combination of frame elements, the coefficients of the expansion are not unique. Frame theory guarantees the existence of a set of coefficients which is “optimal” in a minimum norm sense. We show here that these coefficients are also “optimal” from a maximum entropy viewpoint.

PhylomeDB v4: zooming into the plurality of evolutionary histories of a genome

Phylogenetic trees representing the evolutionary relationships of homologous genes are the entry point for many evolutionary analyses. For instance, the use of a phylogenetic tree can aid in the inference of orthology and paralogy relationships, and in the detection of relevant evolutionary events such as gene family expansions and contractions, horizontal gene transfer, recombination or incomplete lineage sorting. Similarly, given the plurality of evolutionary histories among genes encoded in a given genome, there is a need for the combined analysis of genome-wide collections of phylogenetic trees (phylomes). Here, we introduce a new release of PhylomeDB (http://phylomedb.org), a public repository of phylomes. Currently, PhylomeDB hosts 120 public phylomes, comprising >1.5 million maximum likelihood trees and multiple sequence alignments. In the current release, phylogenetic trees are annotated with taxonomic, protein-domain arrangement, functional and evolutionary information. PhylomeDB is also a major source for phylogeny-based predictions of orthology and paralogy, covering >10 million proteins across 1059 sequenced species. Here we describe newly implemented PhylomeDB features, and discuss a benchmark of the orthology predictions provided by the database, the impact of proteome updates and the use of the phylome approach in the analysis of newly sequenced genomes and transcriptomes.

eggNOG v4.0: nested orthology inference across 3686 organisms

With the increasing availability of various 'omics data, high-quality orthology assignment is crucial for evolutionary and functional genomics studies. We here present the fourth version of the eggNOG database (available at http://eggnog.embl.de) that derives nonsupervised orthologous groups (NOGs) from complete genomes, and then applies a comprehensive characterization and analysis pipeline to the resulting gene families. Compared with the previous version, we have more than tripled the underlying species set to cover 3686 organisms, keeping track with genome project completions while prioritizing the inclusion of high-quality genomes to minimize error propagation from incomplete proteome sets. Major technological advances include (i) a robust and scalable procedure for the identification and inclusion of high-quality genomes, (ii) provision of orthologous groups for 107 different taxonomic levels compared with 41 in eggNOGv3, (iii) identification and annotation of particularly closely related orthologous groups, facilitating analysis of related gene families, (iv) improvements of the clustering and functional annotation approach, (v) adoption of a revised tree building procedure based on the multiple alignments generated during the process and (vi) implementation of quality control procedures throughout the entire pipeline. As in previous versions, eggNOGv4 provides multiple sequence alignments and maximum-likelihood trees, as well as broad functional annotation. Users can access the complete database of orthologous groups via a web interface, as well as through bulk download.

The maximum voltage drop in an on-chip power distribution network: analysis of square, triangular and hexagonal power pad arrangements

A mathematical model of the voltage drop which arises in on-chip power distribution networks is used to compare the maximum voltage drop in the case of different geometric arrangements of the pads supplying power to the chip. These include the square or Manhattan power pad arrangement, which currently predominates, as well as equilateral triangular and hexagonal arrangements. In agreement with the findings in the literature and with physical and SPICE models, the equilateral triangular power pad arrangement is found to minimize the maximum voltage drop. This headline finding is a consequence of relatively simple formulas for the voltage drop, with explicit error bounds, which are established using complex analysis techniques, and elliptic functions in particular.

Análisis de modelos de perfil del fuste y estudio de la cilindricidad para tres clones de chopo (Populus x euramericana) en Navarra

El presente trabajo tiene por objetivo principal analizar tres funciones de perfil del fuste sobre tres clones de Populus x euramericana (Canadá Blanco, I-214 y MC) en la Comunidad Foral de Navarra para elaborar una tarifa de cubicación con clasificación de volumen. Para minimizar el efecto de la autocorrelación entre los residuos se emplea una estructura de error continua autorregresiva de orden 2 o de orden 3 en función del clon analizado. Por otra parte, se compara el coeficiente local de forma de cada uno de los clones estudiados mediante dos metodologías: el análisis de la varianza de la estimación individual de dicho coeficiente y el contraste del estadístico de máxima verosimilitud entre ajustes, resultando ser el clon Canadá el más cónico de los tres. Los datos utilizados provienen de 143 chopos de plantaciones coetáneas y con mismo marco de plantación (marco real de 4,5 × 4,5 m).

Aplicación de imágenes radar de satélite a la cartografía de la vegetación en zonas boreales

El presente estudio se enmarca en el proyecto europeo SIBERIA. Trata de explorar el uso de imágenes radar de satélite (ERS y JERS) para la actualización de la cartografía de vegetación de zonas boreales. Se dispone de 8 imágenes de amplitud y coherencia tomadas en 1998, así como de un inventario de vegetación georreferenciado de dos pequeñas zonas. Se proponen tres tipos de clasificaciones supervisadas por el método de máxima verosimilitud. La primera con las imágenes de satélite, la segunda añadiendo algunas imágenes texturales, y la tercera utilizando sólo las imágenes de los componentes principales más significativos. Se siguen los criterios establecidos en el proyecto SIBERIA para la obtención de áreas de entrenamiento. Se propone una doble validación, por una parte vía matrices de confusión a partir de áreas de verdad-terreno obtenidas por el mismo método que las áreas de entrenamiento, y por otra parte contrastando y correlacionando las clasificaciones con los parámetros de inventario disponibles para dos pequeñas áreas de verdad-terreno. Los resultados indican una sensible mejora en la clasificación con la incorporación de imágenes texturales (la precisión aumenta de un 66% a un 75%), y señalan el parámetro biomasa como el mejor correlacionado con las clasificaciones derivadas (coeficiente de correlación r de hasta 0,49). Diferentes fuentes de error permiten augurar un margen de mejora para posteriores estudios.

Computational toolbox towards evolutionary domain mapping of membrane proteins

Membrane proteins account for about 20% to 30% of all proteins encoded in a typical genome. They play central roles in multiple cellular processes mediating the interaction of the cell with its surrounding. Over 60% of all drug targets contain a membrane domain. The experimental difficulties of obtaining a crystal structural severely limits our ability or understanding of membrane protein function. Computational evolutionary studies of proteins are crucial for the prediction of 3D structures. In this project, we construct a tool able to quantify the evolutionary positive selective pressure on each residue of membrane proteins through maximum likelihood phylogeny reconstruction. The conservation plot combined with a structural homology model is also a potent tool to predict those residues that have essentials roles in the structure and function of a membrane protein and can be very useful in the design of validation experiments.

Divergent evolution and purifying selection of the flaA gene sequences in Aeromonas

BACKGROUND: The bacterial flagellum is the most important organelle of motility in bacteria and plays a key role in many bacterial lifestyles, including virulence. The flagellum also provides a paradigm of how hierarchical gene regulation, intricate protein-protein interactions and controlled protein secretion can result in the assembly of a complex multi-protein structure tightly orchestrated in time and space. As if to stress its importance, plants and animals produce receptors specifically dedicated to the recognition of flagella. Aside from motility, the flagellum also moonlights as an adhesion and has been adapted by humans as a tool for peptide display. Flagellar sequence variation constitutes a marker with widespread potential uses for studies of population genetics and phylogeny of bacterial species. RESULTS: We sequenced the complete flagellin gene (flaA) in 18 different species and subspecies of Aeromonas. Sequences ranged in size from 870 (A. allosaccharophila) to 921 nucleotides (A. popoffii). The multiple alignment displayed 924 sites, 66 of which presented alignment gaps. The phylogenetic tree revealed the existence of two groups of species exhibiting different FlaA flagellins (FlaA1 and FlaA2). Maximum likelihood models of codon substitution were used to analyze flaA sequences. Likelihood ratio tests suggested a low variation in selective pressure among lineages, with an omega ratio of less than 1 indicating the presence of purifying selection in almost all cases. Only one site under potential diversifying selection was identified (isoleucine in position 179). However, 17 amino acid positions were inferred as sites that are likely to be under positive selection using the branch-site model. Ancestral reconstruction revealed that these 17 amino acids were among the amino acid changes detected in the ancestral sequence. CONCLUSION: The models applied to our set of sequences allowed us to determine the possible evolutionary pathway followed by the flaA gene in Aeromonas, suggesting that this gene have probably been evolving independently in the two groups of Aeromonas species since the divergence of a distant common ancestor after one or several episodes of positive selection. REVIEWERS: This article was reviewed by Alexey Kondrashov, John Logsdon and Olivier Tenaillon (nominated by Laurence D Hurst).

Pseudo-Próspero de Aquitania, Sobre la providencia de Dios. Introducción, texto latino revisado, traducción y comentario de Raúl Villegas Marín, Publicacions i edicions de la Universitat de Barcelona, Barcelona 2010, 346 pp. ISBN 9788447534869

El primer tercio del siglo V representó un momento muy convulso en la historia del Imperio Romano. Algunas zonas, como la Galia, se vieron inmersas en una crisis provocada principalmente por las devastaciones que poblaciones bárbaras estaban llevando a cabo, desde inicios de la centuria, en casi todo su territorio. El foedus pactado por el Imperio con los visigodos, por el cual éstos se establecían en Aquitania (418), lejos de representar una solución no hizo sino aumentar los problemas de convivencia entre galorromanos y germanos. El pesimismo cundió entre la población autóctona: la teología eusebiana que presentaba al Dios cristiano como garante de los bienes materiales a través de su culto ―siguiendo la tradicional ideología del do ut des― había fallado, y muchas conciencias cristianas se hundieron en la angustia al preg