Riesz-Nágy singular functions revisited

In 1952 F. Riesz and Sz.Nágy published an example of a monotonic continuous function whose derivative is zero almost everywhere, that is to say, a singular function. Besides, the function was strictly increasing. Their example was built as the limit of a sequence of deformations of the identity function. As an easy consequence of the definition, the derivative, when it existed and was finite, was found to be zero. In this paper we revisit the Riesz-N´agy family of functions and we relate it to a system for real numberrepresentation which we call (t, t-1) expansions. With the help of these real number expansions we generalize the family. The singularity of the functions is proved through some metrical properties of the expansions used in their definition which also allows us to give a more precise way of determining when the derivative is 0 or infinity.

A new light on Minkowski's? $(x)$ function

The well--known Minkowski's? $(x)$ function is presented as the asymptotic distribution function of an enumeration of the rationals in (0,1] based on their continued fraction representation. Besides, the singularity of ?$(x)$ is clearly proved in two ways: by exhibiting a set of measure one in which ?ï$(x)$ = 0; and again by actually finding a set of measure one which is mapped onto a set of measure zero and viceversa. These sets are described by means of metrical properties of different systems for real number representation.

On p-beauty contest integer games

In this paper we provide a full characterization of the pure-strategyNash Equilibria for the p-Beauty Contest Game when we restrict player schoices to integer numbers. Opposed to the case of real number choices,equilibrium uniqueness may be lost depending on the value of p and thenumber of players: in particular, as p approaches 1 any symmetric profileconstitutes a Nash Equilibrium. We also show that any experimental p-BeautyContest Game can be associated to a game with the integer restriction andthus multiplicity of equilibria becomes an issue. Finally, we show thatin these games the iterated deletion of weakly dominated strategies maynot lead to a single outcome while the iterated best-reply process alwaysdoes (though the outcome obtained depends on the initial conditions).

Fractal dimension for Gaussian colored processes

The exact analytical expression for the Hausdorff dimension of free processes driven by Gaussian noise in n-dimensional space is obtained. The fractal dimension solely depends on the time behavior of the arbitrary correlation function of the noise, ranging from DX=1 for Orstein-Uhlenbeck input noise to any real number greater than 1 for fractional Brownian motions.

Analyzing aggregate real exchange rate persistence through the lens of sectoral data

In this paper we analyze the persistence of aggregate real exchange rates (RERs) for a group of EU-15 countries by using sectoral data. The tight relation between aggregate and sectoral persistence recently investigated by Mayoral (2008) allows us to decompose aggregate RER persistence into the persistence of its different subcomponents. We show that the distribution of sectoral persistence is highly heterogeneous and very skewed to the right, and that a limited number of sectors are responsible for the high levels of persistence observed at the aggregate level. We use quantile regression to investigate whether the traditional theories proposed to account for the slow reversion to parity (lack of arbitrage due to nontradibilities or imperfect competition and price stickiness) are able to explain the behavior of the upper quantiles of sectoral persistence. We conclude that pricing to market in the intermediate goods sector together with price stickiness have more explanatory power than variables related to the tradability of the goods or their inputs.

Biplots of fuzzy coded data

A biplot, which is the multivariate generalization of the two-variable scatterplot, can be used to visualize the results of many multivariate techniques, especially those that are based on the singular value decomposition. We consider data sets consisting of continuous-scale measurements, their fuzzy coding and the biplots that visualize them, using a fuzzy version of multiple correspondence analysis. Of special interest is the way quality of fit of the biplot is measured, since it is well-known that regular (i.e., crisp) multiple correspondence analysis seriously under-estimates this measure. We show how the results of fuzzy multiple correspondence analysis can be defuzzified to obtain estimated values of the original data, and prove that this implies an orthogonal decomposition of variance. This permits a measure of fit to be calculated in the familiar form of a percentage of explained variance, which is directly comparable to the corresponding fit measure used in principal component analysis of the original data. The approach is motivated initially by its application to a simulated data set, showing how the fuzzy approach can lead to diagnosing nonlinear relationships, and finally it is applied to a real set of meteorological data.

Identification by Real-time PCR of 13 mature microRNAs differentially expressed in colorectal cancer and non-tumoral tissues

MicroRNAs (miRNAs) are short non-coding RNA molecules playing regulatory roles by repressing translation or cleaving RNA transcripts. Although the number of verified human miRNA is still expanding, only few have been functionally described. However, emerging evidences suggest the potential involvement of altered regulation of miRNA in pathogenesis of cancers and these genes are thought to function as both tumours suppressor and oncogenes. In our study, we examined by Real-Time PCR the expression of 156 mature miRNA in colorectal cancer. The analysis by several bioinformatics algorithms of colorectal tumours and adjacent non-neoplastic tissues from patients and colorectal cancer cell lines allowed identifying a group of 13 miRNA whose expression is significantly altered in this tumor. The most significantly deregulated miRNA being miR-31, miR-96, miR-133b, miR-135b, miR-145, and miR-183. In addition, the expression level of miR-31 was correlated with the stage of CRC tumor. Our results suggest that miRNA expression profile could have relevance to the biological and clinical behavior of colorectal neoplasia.

Probe-specific mixed-model approach to detect copy number differences using multiplex ligation-dependent probe amplification (MLPA)

Background: MLPA method is a potentially useful semi-quantitative method to detect copy number alterations in targeted regions. In this paper, we propose a method for the normalization procedure based on a non-linear mixed-model, as well as a new approach for determining the statistical significance of altered probes based on linear mixed-model. This method establishes a threshold by using different tolerance intervals that accommodates the specific random error variability observed in each test sample.Results: Through simulation studies we have shown that our proposed method outperforms two existing methods that are based on simple threshold rules or iterative regression. We have illustrated the method using a controlled MLPA assay in which targeted regions are variable in copy number in individuals suffering from different disorders such as Prader-Willi, DiGeorge or Autism showing the best performace.Conclusion: Using the proposed mixed-model, we are able to determine thresholds to decide whether a region is altered. These threholds are specific for each individual, incorporating experimental variability, resulting in improved sensitivity and specificity as the examples with real data have revealed.

La figura del mediador intercultural a les institucions escolars catalanes: perfil real i ideal segons els propis actors

A Catalunya, en els darrers anys, han anat proliferant una sèrie de «professionals» que realitzen, amb més o menys adequació a la definició teòrica, la funció de mediadors inter-culturals. Primerament, es tractava de gitanos, però darrerament, fruit de l’increment de la presència d’infants d’origen immigrant a les escoles catalanes, s’ha vist créixer el nombre i el protagonisme dels estrangers pel reconeixement que se’ls ha donat des de l’Administració i des de les institucions. Els mediadors han intentat intervenir en qüestions com ara la participació dels pares d’origen minoritari, l’adaptació del currículum a la diversitat cultural, la negociació de conflictes culturals, la desescolarització, l’absentisme i l’abandonament escolar dels alumnes durant el període d’escolarització obligatòria, la traducció lingüística i la interpretació sociocultural, etc. Concretament, la nostra recerca ha consistit en vint-i-set entrevistes en profunditat a mediadors interculturals de tot Catalunya.

Integrating defeasible argumentation with fuzzy ART neural networks for pattern classification

Many classification systems rely on clustering techniques in which a collection of training examples is provided as an input, and a number of clusters c1,...cm modelling some concept C results as an output, such that every cluster ci is labelled as positive or negative. Given a new, unlabelled instance enew, the above classification is used to determine to which particular cluster ci this new instance belongs. In such a setting clusters can overlap, and a new unlabelled instance can be assigned to more than one cluster with conflicting labels. In the literature, such a case is usually solved non-deterministically by making a random choice. This paper presents a novel, hybrid approach to solve this situation by combining a neural network for classification along with a defeasible argumentation framework which models preference criteria for performing clustering.

Copy number variation in the porcine genome inferred from a 60 k SNP BeadChip

Background: Recent studies in pigs have detected copy number variants (CNVs) using the Comparative Genomic Hybridization technique in arrays designed to cover specific porcine chromosomes. The goal of this study was to identify CNV regions (CNVRs) in swine species based on whole genome SNP genotyping chips. Results: We used predictions from three different programs (cnvPartition, PennCNV and GADA) to analyze data from the Porcine SNP60 BeadChip. A total of 49 CNVRs were identified in 55 animals from an Iberian x Landrace cross (IBMAP) according to three criteria: detected in at least two animals, contained three or more consecutive SNPs and recalled by at least two programs. Mendelian inheritance of CNVRs was confirmed in animals belonging to several generations of the IBMAP cross. Subsequently, a segregation analysis of these CNVRs was performed in 372 additional animals from the IBMAP cross and its distribution was studied in 133 unrelated pig samples from different geographical origins. Five out of seven analyzed CNVRs were validated by real time quantitative PCR, some of which coincide with well known examples of CNVs conserved across mammalian species. Conclusions: Our results illustrate the usefulness of Porcine SNP60 BeadChip to detect CNVRs and show that structural variants can not be neglected when studying the genetic variability in this species.

Evaluating the impact of filming on the number of errors committed by nursing students to determine the efficacy of simulated clinical situations

Clinic simulation as a training and knowledge method allows people experiment a real event representation with the aim of acquiring knowledge, abilities and aptitudes. The filming of the staging represents a useful tool to review the decisions taken and the actions they did, with the purpose to highlight the strengths, weaknesses and the areas for improvement. The article describes a study carried out by a group of students in second course of nursing, and it tries to evaluate if there is any influence if somebody is filming you during the clinic simulation, does it make you do more errors or not?

A Case-based reasoning approach to validate grammatical gender and number agreement in Spanish language

Across Latin America 420 indigenous languages are spoken. Spanish is considered a second language in indigenous communities and is progressively introduced in education. However, most of the tools to support teaching processes of a second language have been developed for the most common languages such as English, French, German, Italian, etc. As a result, only a small amount of learning objects and authoring tools have been developed for indigenous people considering the specific needs of their population. This paper introduces Multilingual–Tiny as a web authoring tool to support the virtual experience of indigenous students and teachers when they are creating learning objects in indigenous languages or in Spanish language, in particular, when they have to deal with the grammatical structures of Spanish. Multilingual–Tiny has a module based on the Case-based Reasoning technique to provide recommendations in real time when teachers and students write texts in Spanish. An experiment was performed in order to compare some local similarity functions to retrieve cases from the case library taking into account the grammatical structures. As a result we found the similarity function with the best performance