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.

Implications of governance structures on urban climate action: evidence from Italy and Spain

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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.

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.

Resveratrol: Anti-Obesity Mechanisms of Action

Resveratrol is a non-flavonoid polyphenol which belongs to the stilbenes group and is produced naturally in several plants in response to injury or fungal attack. Resveratrol has been recently reported as preventing obesity. The present review aims to compile the evidence concerning the potential mechanisms of action which underlie the anti-obesity effects of resveratrol, obtained either in cultured cells lines and animal models. Published studies demonstrate that resveratrol has an anti-adipogenic effect. A good consensus concerning the involvement of a down-regulation of C/EBPa and PPAR. in this effect has been reached. Also, in vitro studies have demonstrated that resveratrol can increase apoptosis in mature adipocytes. Furthermore, different metabolic pathways involved in triacylglycerol metabolism in white adipose tissue have been shown to be targets for resveratrol. Both the inhibition of de novo lipogenesis and adipose tissue fatty acid uptake mediated by lipoprotein lipase play a role in explaining the reduction in body fat which resveratrol induces. As far as lipolysis is concerned, although this compound per se seems to be unable to induce lipolysis, it increases lipid mobilization stimulated by beta-adrenergic agents. The increase in brown adipose tissue thermogenesis, and consequently the associated energy dissipation, can contribute to explaining the body-fat lowering effect of resveratrol. In addition to its effects on adipose tissue, resveratrol can also acts on other organs and tissues. Thus, it increases mitochondriogenesis and consequently fatty acid oxidation in skeletal muscle and liver. This effect can also contribute to the body-fat lowering effect of this molecule.

Physiological modules for generating discrete and rhythmic movements: action identification by a dynamic recurrent neural network

In this study we employed a dynamic recurrent neural network (DRNN) in a novel fashion to reveal characteristics of control modules underlying the generation of muscle activations when drawing figures with the outstretched arm. We asked healthy human subjects to perform four different figure-eight movements in each of two workspaces (frontal plane and sagittal plane). We then trained a DRNN to predict the movement of the wrist from information in the EMG signals from seven different muscles. We trained different instances of the same network on a single movement direction, on all four movement directions in a single movement plane, or on all eight possible movement patterns and looked at the ability of the DRNN to generalize and predict movements for trials that were not included in the training set. Within a single movement plane, a DRNN trained on one movement direction was not able to predict movements of the hand for trials in the other three directions, but a DRNN trained simultaneously on all four movement directions could generalize across movement directions within the same plane. Similarly, the DRNN was able to reproduce the kinematics of the hand for both movement planes, but only if it was trained on examples performed in each one. As we will discuss, these results indicate that there are important dynamical constraints on the mapping of EMG to hand movement that depend on both the time sequence of the movement and on the anatomical constraints of the musculoskeletal system. In a second step, we injected EMG signals constructed from different synergies derived by the PCA in order to identify the mechanical significance of each of these components. From these results, one can surmise that discrete-rhythmic movements may be constructed from three different fundamental modules, one regulating the co-activation of all muscles over the time span of the movement and two others elliciting patterns of reciprocal activation operating in orthogonal directions.

An update of the J48Consolidated WEKA’s class: CTC algorithm enhanced with the notion of coverage

This document aims to describe an update of the implementation of the J48Consolidated class within WEKA platform. The J48Consolidated class implements the CTC algorithm [2][3] which builds a unique decision tree based on a set of samples. The J48Consolidated class extends WEKA’s J48 class which implements the well-known C4.5 algorithm. This implementation was described in the technical report "J48Consolidated: An implementation of CTC algorithm for WEKA". The main, but not only, change in this update is the integration of the notion of coverage in order to determine the number of samples to be generated to build a consolidated tree. We define coverage as the percentage of examples of the training sample present in –or covered by– the set of generated subsamples. So, depending on the type of samples that we use, we will need more or less samples in order to achieve a specific value of coverage.

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.

Evaluación de la posible capacidad genotóxica de fármacos antihipertensivos: losartán e irbesartán

[es] La hipertensión arterial (AHT), estado patológico definido como la elevación persistente de la presión arterial, es considerada uno de los principales problemas de salud pública. El tratamiento de la patología se realiza preferentemente con fármacos antihipertensivos. Los pacientes se encuentran sometidos a una exposición larga e ininterrumpida a estos fármacos. Los fármacos antihipertensivos se clasifican en función del mecanismo de acción por el que logran su efecto. Una de las clases son los antagonistas de los receptores de angiotensina II (ARB). Los ARB son la última clase terapéutica incluida en la terapia antihipertensiva. En este Trabajo Fin de Grado, se ha evaluado la posible capacidad genotóxica in vitro, de dos tipos de fármacos ARB (losartán e irbesartán) mediante el empleo de uno de los métodos citogenéticos más utilizados, el ensayo de micronúcleos (MN). El índice de división nuclear (NDI) fue usado también como medida de genotoxicidad. El análisis se ha realizado en linfocitos de sangre periférica (PBL) de 10 individuos control mediante dos tipos de cultivo uno sin fármaco y otro añadiendo los fármacos a los cultivos en una concentración igual a la que se encuentra en el plasma de pacientes. Los resultados muestran un aumento estadísticamente significativo de la frecuencia de células binucleadas con micronúcleos (BNMN) pero no se observan diferencias estadísticamente significativas en el índice de división nuclear. Estos resultados sugieren un posible efecto genotóxico de los fármacos pero sería necesario llevar a cabo estudios en una población más amplia e in vivo con los mismos fármacos para confirmarlo.