Fixed Points of Closed and Compact Composite Sequences of Operators and Projectors in a Class of Banach Spaces

Some results on fixed points related to the contractive compositions of bounded operators in a class of complete metric spaces which can be also considered as Banach's spaces are discussed through the paper. The class of composite operators under study can include, in particular, sequences of projection operators under, in general, oblique projective operators. In this paper we are concerned with composite operators which include sequences of pairs of contractive operators involving, in general, oblique projection operators. The results are generalized to sequences of, in general, nonconstant bounded closed operators which can have bounded, closed, and compact limit operators, such that the relevant composite sequences are also compact operators. It is proven that in both cases, Banach contraction principle guarantees the existence of unique fixed points under contractive conditions.

On a Class of Self-Adjoint Compact Operators in Hilbert Spaces and Their Relations with Their Finite-Range Truncations

This paper investigates a class of self-adjoint compact operators in Hilbert spaces related to their truncated versions with finite-dimensional ranges. The comparisons are established in terms of worst-case norm errors of the composite operators generated from iterated computations. Some boundedness properties of the worst-case norms of the errors in their respective fixed points in which they exist are also given. The iterated sequences are expanded in separable Hilbert spaces through the use of numerable orthonormal bases.

Asymptotic Hyperstability of a Class of Linear Systems under Impulsive Controls Subject to an Integral Popovian Constraint

This paper is focused on the study of the important property of the asymptotic hyperstability of a class of continuous-time dynamic systems. The presence of a parallel connection of a strictly stable subsystem to an asymptotically hyperstable one in the feed-forward loop is allowed while it has also admitted the generation of a finite or infinite number of impulsive control actions which can be combined with a general form of nonimpulsive controls. The asymptotic hyperstability property is guaranteed under a set of sufficiency-type conditions for the impulsive controls.

Properties of convergence of a class of iterative processes generated by sequences of self-mappings with applications to switched dynamic systems

This article investigates the convergence properties of iterative processes involving sequences of self-mappings of metric or Banach spaces. Such sequences are built from a set of primary self-mappings which are either expansive or non-expansive self-mappings and some of the non-expansive ones can be contractive including the case of strict contractions. The sequences are built subject to switching laws which select each active self-mapping on a certain activation interval in such a way that essential properties of boundedness and convergence of distances and iterated sequences are guaranteed. Applications to the important problem of stability of dynamic switched systems are also given.

Advantages and Versatility of Fluorescence-Based Methodology to Characterize the Functionality of LDLR and Class Mutation Assignment

Familial hypercholesterolemia (FH) is a common autosomal codominant disease with a frequency of 1:500 individuals in its heterozygous form. The genetic basis of FH is most commonly mutations within the LDLR gene. Assessing the pathogenicity of LDLR variants is particularly important to give a patient a definitive diagnosis of FH. Current studies of LDLR activity ex vivo are based on the analysis of I-125-labeled lipoproteins (reference method) or fluorescent-labelled LDL. The main purpose of this study was to compare the effectiveness of these two methods to assess LDLR functionality in order to validate a functional assay to analyse LDLR mutations. LDLR activity of different variants has been studied by flow cytometry using FITC-labelled LDL and compared with studies performed previously with I-125-labeled lipoproteins. Flow cytometry results are in full agreement with the data obtained by the I-125 methodology. Additionally confocal microscopy allowed the assignment of different class mutation to the variants assayed. Use of fluorescence yielded similar results than I-125-labeled lipoproteins concerning LDLR activity determination, and also allows class mutation classification. The use of FITC-labelled LDL is easier in handling and disposal, cheaper than radioactivity and can be routinely performed by any group doing LDLR functional validations.

Towards Application of One-Class Classification Methods to Medical Data

In the problem of one-class classification (OCC) one of the classes, the target class, has to be distinguished from all other possible objects, considered as nontargets. In many biomedical problems this situation arises, for example, in diagnosis, image based tumor recognition or analysis of electrocardiogram data. In this paper an approach to OCC based on a typicality test is experimentally compared with reference state-of-the-art OCC techniques-Gaussian, mixture of Gaussians, naive Parzen, Parzen, and support vector data description-using biomedical data sets. We evaluate the ability of the procedures using twelve experimental data sets with not necessarily continuous data. As there are few benchmark data sets for one-class classification, all data sets considered in the evaluation have multiple classes. Each class in turn is considered as the target class and the units in the other classes are considered as new units to be classified. The results of the comparison show the good performance of the typicality approach, which is available for high dimensional data; it is worth mentioning that it can be used for any kind of data (continuous, discrete, or nominal), whereas state-of-the-art approaches application is not straightforward when nominal variables are present.

About the Stabilization of a Nonlinear Perturbed Difference Equation

This paper investigates the local asymptotic stabilization of a very general class of instable autonomous nonlinear difference equations which are subject to perturbed dynamics which can have a different order than that of the nominal difference equation. In the general case, the controller consists of two combined parts, namely, the feedback nominal controller which stabilizes the nominal (i.e., perturbation-free) difference equation plus an incremental controller which completes the stabilization in the presence of perturbed or unmodeled dynamics in the uncontrolled difference equation. A stabilization variant consists of using a single controller to stabilize both the nominal difference equation and also the perturbed one under a small-type characterization of the perturbed dynamics. The study is based on Banach fixed point principle, and it is also valid with slight modification for the stabilization of unstable oscillatory solutions.

On Best Proximity Point Theorems and Fixed Point Theorems for p-Cyclic Hybrid Self-Mappings in Banach Spaces

This paper relies on the study of fixed points and best proximity points of a class of so-called generalized point-dependent (K-Lambda)hybrid p-cyclic self-mappings relative to a Bregman distance Df, associated with a Gâteaux differentiable proper strictly convex function f in a smooth Banach space, where the real functions Lambda and K quantify the point-to-point hybrid and nonexpansive (or contractive) characteristics of the Bregman distance for points associated with the iterations through the cyclic self-mapping.Weak convergence results to weak cluster points are obtained for certain average sequences constructed with the iterates of the cyclic hybrid self-mappings.

Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings: Applications to Impulsive Differential and Difference Equations

This paper is devoted to the study of convergence properties of distances between points and the existence and uniqueness of best proximity and fixed points of the so-called semicyclic impulsive self-mappings on the union of a number of nonempty subsets in metric spaces. The convergences of distances between consecutive iterated points are studied in metric spaces, while those associated with convergence to best proximity points are set in uniformly convex Banach spaces which are simultaneously complete metric spaces. The concept of semicyclic self-mappings generalizes the well-known one of cyclic ones in the sense that the iterated sequences built through such mappings are allowed to have images located in the same subset as their pre-image. The self-mappings under study might be in the most general case impulsive in the sense that they are composite mappings consisting of two self-mappings, and one of them is eventually discontinuous. Thus, the developed formalism can be applied to the study of stability of a class of impulsive differential equations and that of their discrete counterparts. Some application examples to impulsive differential equations are also given.

Inoculation of Triatoma Virus (Dicistroviridae: Cripavirus) elicits a non-infective immune response in mice

Background: Dicistroviridae is a new family of small, non-enveloped, +ssRNA viruses pathogenic to both beneficial arthropods and insect pests. Little is known about the dicistrovirus replication mechanism or gene function, and any knowledge on these subjects comes mainly from comparisons with mammalian viruses from the Picornaviridae family. Due to its peculiar genome organization and characteristics of the per os viral transmission route, dicistroviruses make good candidates for use as biopesticides. Triatoma virus (TrV) is a pathogen of Triatoma infestans (Hemiptera: Reduviidae), one of the main vectors of the human trypanosomiasis disease called Chagas disease. TrV was postulated as a potential control agent against Chagas' vectors. Although there is no evidence that TrV nor other dicistroviruses replicate in species outside the Insecta class, the innocuousness of these viruses in humans and animals needs to be ascertained. Methods: In this study, RT-PCR and ELISA were used to detect the infectivity of this virus in Mus musculus BALB/c mice. Results: In this study we have observed that there is no significant difference in the ratio IgG2a/IgG1 in sera from animals inoculated with TrV when compared with non-inoculated animals or mice inoculated only with non-infective TrV protein capsids. Conclusions: We conclude that, under our experimental conditions, TrV is unable to replicate inmice. This study constitutes the first test to evaluate the infectivity of a dicistrovirus in a vertebrate animal model.

Classification of neocortical interneurons using affinity propagation

In spite of over a century of research on cortical circuits, it is still unknown how many classes of cortical neurons exist. Neuronal classification has been a difficult problem because it is unclear what a neuronal cell class actually is and what are the best characteristics are to define them. Recently, unsupervised classifications using cluster analysis based on morphological, physiological or molecular characteristics, when applied to selected datasets, have provided quantitative and unbiased identification of distinct neuronal subtypes. However, better and more robust classification methods are needed for increasingly complex and larger datasets. We explored the use of affinity propagation, a recently developed unsupervised classification algorithm imported from machine learning, which gives a representative example or exemplar for each cluster. As a case study, we applied affinity propagation to a test dataset of 337 interneurons belonging to four subtypes, previously identified based on morphological and physiological characteristics. We found that affinity propagation correctly classified most of the neurons in a blind, non-supervised manner. In fact, using a combined anatomical/physiological dataset, our algorithm differentiated parvalbumin from somatostatin interneurons in 49 out of 50 cases. Affinity propagation could therefore be used in future studies to validly classify neurons, as a first step to help reverse engineer neural circuits.

El clima de aula. Un factor decisivo en el aprendizaje de lenguas

[spa] Se ha propuesto una guía didáctica para realizar en sesiones de euskera que profundice en el conocimiento mutuo entre los alumnos para que se fomente así la creación de vinculos interpersonales basados en el diálogo, la negociación y la comprensión. Todo ello supone la generación de un ambiente de aula cálido en el que todos los alumnos (gitanos y no gitanos) se sientan respetados, reconocidos y valorados, lo que garantiza el desarrollo óptimo y el acercamiento de los alumnos a la segunda lengua

Zientzien irakaskuntza: Argumentazio gaitasuna eta datuen erabilera sustatzeko esku-hartze proposamen berritzailea

Gaur egun, konpetentzia zientifikoen garapena Lehen Hezkuntzako eskolan gutxi garatuta eta eztabaidagarria den gaia da. Ikasleek kultura zientifikoan murgiltzeko forma aurkitu eta, bereziki, argumentazio gaitasuna garatzen laguntzea, zientziak hitz egiteko aukerak emanez, ez da batere arrunta gure eskoletan. Esku-hartze berritzaile hau egoera honi aurre egiteko eta arazoari irtenbide bat bilatzeko diseinatuta izan da. Honen bidez, Lehen Hezkuntzan zientzienganako interesa sustatzen saiatzen da, zientziako klaseetan datuen erabilerari eta argumentazioari lehentasuna emanez. Ekimena 2013-2014ko martxoan jarri da martxan.

San Francisco : a city reinvented by creative innovation

The aim of this paper is to analyse the recent evolution of the city of San Francisco to outline the major features that have made it possible this continuing process of creative innovation in the city. In order to meet this objective, the project is framed around answering two key research questions: (1) what are the main economic and social elements that characterise urban change in the city of San Francisco and (2) which is the role of public strategies in the continuing economic success of San Francisco. The paper concludes that the successful performance of San Francisco is the result of the actions taken by many agents in the city, but the role of public authorities, especially the City and County, must be stressed, both through direct intervention and by coordinating, fostering and supporting the private and non-profit sectors. This is especially relevant in a country like the US where private initiative has been seen in many occasions as the greatest driver of economic and social success. Yet, the performance of San Francisco City cannot be explained without the role played by the public sector, in coordination with the civil society

On the optimal usage of labelled examples in semi-supervised multi-class classification problems

In recent years, the performance of semi-supervised learning has been theoretically investigated. However, most of this theoretical development has focussed on binary classification problems. In this paper, we take it a step further by extending the work of Castelli and Cover [1] [2] to the multi-class paradigm. Particularly, we consider the key problem in semi-supervised learning of classifying an unseen instance x into one of K different classes, using a training dataset sampled from a mixture density distribution and composed of l labelled records and u unlabelled examples. Even under the assumption of identifiability of the mixture and having infinite unlabelled examples, labelled records are needed to determine the K decision regions. Therefore, in this paper, we first investigate the minimum number of labelled examples needed to accomplish that task. Then, we propose an optimal multi-class learning algorithm which is a generalisation of the optimal procedure proposed in the literature for binary problems. Finally, we make use of this generalisation to study the probability of error when the binary class constraint is relaxed.