Two Novel Methods For The Determination Of The Number Of Components In Independent Components Analysis Models

Independent Components Analysis is a Blind Source Separation method that aims to find the pure source signals mixed together in unknown proportions in the observed signals under study. It does this by searching for factors which are mutually statistically independent. It can thus be classified among the latent-variable based methods. Like other methods based on latent variables, a careful investigation has to be carried out to find out which factors are significant and which are not. Therefore, it is important to dispose of a validation procedure to decide on the optimal number of independent components to include in the final model. This can be made complicated by the fact that two consecutive models may differ in the order and signs of similarly-indexed ICs. As well, the structure of the extracted sources can change as a function of the number of factors calculated. Two methods for determining the optimal number of ICs are proposed in this article and applied to simulated and real datasets to demonstrate their performance.

The Minimum Number of Points Taking Part in k-Sets in Sets of Unaligned Points

En este trabajo se da un ejemplo de un conjunto de n puntos situados en posición general, en el que se alcanza el mínimo número de puntos que pueden formar parte de algún k-set para todo k con 1menor que=kmenor quen/2. Se generaliza también, a puntos en posición no general, el resultado de Erdõs et al., 1973, sobre el mínimo número de puntos que pueden formar parte de algún k-set. The study of k- sets is a very relevant topic in the research area of computational geometry. The study of the maximum and minimum number of k-sets in sets of points of the plane in general position, specifically, has been developed at great length in the literature. With respect to the maximum number of k-sets, lower bounds for this maximum have been provided by Erdõs et al., Edelsbrunner and Welzl, and later by Toth. Dey also stated an upper bound for this maximum number of k-sets. With respect to the minimum number of k-set, this has been stated by Erdos el al. and, independently, by Lovasz et al. In this paper the authors give an example of a set of n points in the plane in general position (no three collinear), in which the minimum number of points that can take part in, at least, a k-set is attained for every k with 1 ≤ k < n/2. The authors also extend Erdos’s result about the minimum number of points in general position which can take part in a k-set to a set of n points not necessarily in general position. That is why this work complements the classic works we have mentioned before.

Relationship among research collaboration, number of documents and number of citations. A case study in Spanish computer science production in 2000-2009.

This paper analyzes the relationship among research collaboration, number of documents and number of citations of computer science research activity. It analyzes the number of documents and citations and how they vary by number of authors. They are also analyzed (according to author set cardinality) under different circumstances, that is, when documents are written in different types of collaboration, when documents are published in different document types, when documents are published in different computer science subdisciplines, and, finally, when documents are published by journals with different impact factor quartiles. To investigate the above relationships, this paper analyzes the publications listed in the Web of Science and produced by active Spanish university professors between 2000 and 2009, working in the computer science field. Analyzing all documents, we show that the highest percentage of documents are published by three authors, whereas single-authored documents account for the lowest percentage. By number of citations, there is no positive association between the author cardinality and citation impact. Statistical tests show that documents written by two authors receive more citations per document and year than documents published by more authors. In contrast, results do not show statistically significant differences between documents published by two authors and one author. The research findings suggest that international collaboration results on average in publications with higher citation rates than national and institutional collaborations. We also find differences regarding citation rates between journals and conferences, across different computer science subdisciplines and journal quartiles as expected. Finally, our impression is that the collaborative level (number of authors per document) will increase in the coming years, and documents published by three or four authors will be the trend in computer science literature.

Maximizing the number of polychronous groups in spiking networks

In this paper we investigate the effect of biasing the axonal connection delay values in the number of polychronous groups produced for a spiking neuron network model. We use an estimation of distribution algorithm (EDA) that learns tree models to search for optimal delay configurations. Our results indicate that the introduced approach can be used to considerably increase the number of such groups.

Gravitational actions upon a tether in a non-uniform gravity field with arbitrary number of zonal harmonics

We develop general closed-form expressions for the mutual gravitational potential, resultant and torque acting upon a rigid tethered system moving in a non-uniform gravity field produced by an attracting body with revolution symmetry, such that an arbitrary number of zonal harmonics is considered. The final expressions are series expansion in two small parameters related to the reference radius of the primary and the length of the tether, respectively, each of which are scaled by the mutual distance between their centers of mass. A few numerical experiments are performed to study the convergence behavior of the final expressions, and conclude that for high precision applications it might be necessary to take into account additional perturbation terms, which come from the mutual Two-Body interaction.

A simple mathematical model that describes the growth of the area and the number of total and viable cells in yeast colonies

We propose a model, based on the Gompertz equation, to describe the growth of yeasts colonies on agar medium. This model presents several advantages: (i) one equation describes the colony growth, which previously needed two separate ones (linear increase of radius and of the squared radius); (ii) a similar equation can be applied to total and viable cells, colony area or colony radius, because the number of total cells in mature colonies is proportional to their area; and (iii) its parameters estimate the cell yield, the cell concentration that triggers growth limitation and the effect of this limitation on the specific growth rate. To elaborate the model, area, total and viable cells of 600 colonies of Saccharomyces cerevisiae, Debaryomyces fabryi, Zygosaccharomyces rouxii and Rhodotorula glutinis have been measured. With low inocula, viable cells showed an initial short exponential phase when colonies were not visible. This phase was shortened with higher inocula. In visible or mature colonies, cell growth displayed Gompertz-type kinetics. It was concluded that the cells growth in colonies is similar to liquid cultures only during the first hours, the rest of the time they grow, with near-zero specific growth rates, at least for 3 weeks.

Plant protein-coding gene families: emerging bioinformatics approaches

Protein-coding gene families are sets of similar genes with a shared evolutionary origin and, generally, with similar biological functions. In plants, the size and role of gene families has been only partially addressed. However, suitable bioinformatics tools are being developed to cluster the enormous number of sequences currently available in databases. Specifically, comparative genomic databases promise to become powerful tools for gene family annotation in plant clades. In this review, I evaluate the data retrieved from various gene family databases, the ease with which they can be extracted and how useful the extracted information is.

Direct and Inverse Results on Row Sequences of Hermite-Pad, Approximants

We give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of simultaneous rational interpolants with a bounded number of poles. The conditions are expressed in terms of intrinsic properties of the system of functions used to build the approximants. Exact rates of convergence for these denominators and the simultaneous rational approximants are provided.