Perineuronal nets protect fast-spiking interneurons against oxidative stress.

A hallmark of schizophrenia pathophysiology is the dysfunction of cortical inhibitory GABA neurons expressing parvalbumin, which are essential for coordinating neuronal synchrony during various sensory and cognitive tasks. The high metabolic requirements of these fast-spiking cells may render them susceptible to redox dysregulation and oxidative stress. Using mice carrying a genetic redox imbalance, we demonstrate that extracellular perineuronal nets, which constitute a specialized polyanionic matrix enwrapping most of these interneurons as they mature, play a critical role in the protection against oxidative stress. These nets limit the effect of genetically impaired antioxidant systems and/or excessive reactive oxygen species produced by severe environmental insults. We observe an inverse relationship between the robustness of the perineuronal nets around parvalbumin cells and the degree of intracellular oxidative stress they display. Enzymatic degradation of the perineuronal nets renders mature parvalbumin cells and fast rhythmic neuronal synchrony more susceptible to oxidative stress. In parallel, parvalbumin cells enwrapped with mature perineuronal nets are better protected than immature parvalbumin cells surrounded by less-condensed perineuronal nets. Although the perineuronal nets act as a protective shield, they are also themselves sensitive to excess oxidative stress. The protection might therefore reflect a balance between the oxidative burden on perineuronal net degradation and the capacity of the system to maintain the nets. Abnormal perineuronal nets, as observed in the postmortem patient brain, may thus underlie the vulnerability and functional impairment of pivotal inhibitory circuits in schizophrenia.

Effective atomic orbitals for fuzzy atoms

The method of extracting effective atomic orbitals and effective minimal basis sets from molecular wave function characterizing the state of an atom in a molecule is developed in the framework of the "fuzzy" atoms. In all cases studied, there were as many effective orbitals that have considerable occupation numbers as orbitals in the classical minimal basis. That is considered to be of high conceptual importance

Energy partitioning for "fuzzy" atoms

The total energy of molecule in terms of 'fuzzy atoms' presented as sum of one- and two-atomic energy components is described. The divisions of three-dimensional physical space into atomic regions exhibit continuous transition from one to another. The energy components are on chemical energy scale according to proper definitions. The Becke's integration scheme and weight function determines realization of method which permits effective numerical integrations

Student modeling based on fuzzy inference mechanisms

The paper presents a competence-based instructional design system and a way to provide a personalization of navigation in the course content. The navigation aid tool builds on the competence graph and the student model, which includes the elements of uncertainty in the assessment of students. An individualized navigation graph is constructed for each student, suggesting the competences the student is more prepared to study. We use fuzzy set theory for dealing with uncertainty. The marks of the assessment tests are transformed into linguistic terms and used for assigning values to linguistic variables. For each competence, the level of difficulty and the level of knowing its prerequisites are calculated based on the assessment marks. Using these linguistic variables and approximate reasoning (fuzzy IF-THEN rules), a crisp category is assigned to each competence regarding its level of recommendation.

Proposta de reconhecimento de padrão de conforto em clientes com pênfigo vulgar utilizando a Lógica Fuzzy

Propuesta de reconocimiento del estándar de comodidad en clientes con pénfigo vulgar utilizando la Lógica FuzzyO objetivo é propor a Lógica Fuzzy para reconhecimento de padrões de conforto de pessoas submetidas a uma tecnologia de cuidar em Enfermagem por apresentarem pênfigo vulgar, uma doença cutâneo-mucosa rara que acomete principalmente adultos. A proposta aplicável em métodos experimentais com sujeitos submetidos à comparação quali-quantitativa (taxonomia/pertinência) do padrão de conforto antes e depois da intervenção. Requer o registro em escala cromática correspondente à intensidade de cada atributo: dor; mobilidade e comprometimento da autoimagem. As regras Fuzzy estabelecidas pela máquina de inferência definem o padrão de conforto em desconforto máximo, mediano e mínimo, traduzindo a eficácia dos cuidados de Enfermagem. Apesar de pouco utilizada na área de Enfermagem, essa lógica viabiliza pesquisas sem dimensionamento a priori do número de sujeitos em função da estimação de parâmetros populacionais. Espera-se avaliação do padrão de conforto do cliente com pênfigo diante da tecnologia aplicada de forma personalizada, conduzindo a avaliação global.

Measures of fit in multiple correspondence analysis of crisp and fuzzy coded data

When continuous data are coded to categorical variables, two types of coding are possible: crisp coding in the form of indicator, or dummy, variables with values either 0 or 1; or fuzzy coding where each observation is transformed to a set of "degrees of membership" between 0 and 1, using co-called membership functions. It is well known that the correspondence analysis of crisp coded data, namely multiple correspondence analysis, yields principal inertias (eigenvalues) that considerably underestimate the quality of the solution in a low-dimensional space. Since the crisp data only code the categories to which each individual case belongs, an alternative measure of fit is simply to count how well these categories are predicted by the solution. Another approach is to consider multiple correspondence analysis equivalently as the analysis of the Burt matrix (i.e., the matrix of all two-way cross-tabulations of the categorical variables), and then perform a joint correspondence analysis to fit just the off-diagonal tables of the Burt matrix - the measure of fit is then computed as the quality of explaining these tables only. The correspondence analysis of fuzzy coded data, called "fuzzy multiple correspondence analysis", suffers from the same problem, albeit attenuated. Again, one can count how many correct predictions are made of the categories which have highest degree of membership. But here one can also defuzzify the results of the analysis to obtain estimated values of the original data, and then calculate a measure of fit in the familiar percentage form, thanks to the resultant orthogonal decomposition of variance. Furthermore, if one thinks of fuzzy multiple correspondence analysis as explaining the two-way associations between variables, a fuzzy Burt matrix can be computed and the same strategy as in the crisp case can be applied to analyse the off-diagonal part of this matrix. In this paper these alternative measures of fit are defined and applied to a data set of continuous meteorological variables, which are coded crisply and fuzzily into three categories. Measuring the fit is further discussed when the data set consists of a mixture of discrete and continuous variables.

An Automatic Approach for Learning and Tuning Gaussian Interval Type-2 Fuzzy Membership Functions Applied to Lung CAD Classification System

The potential of type-2 fuzzy sets for managing high levels of uncertainty in the subjective knowledge of experts or of numerical information has focused on control and pattern classification systems in recent years. One of the main challenges in designing a type-2 fuzzy logic system is how to estimate the parameters of type-2 fuzzy membership function (T2MF) and the Footprint of Uncertainty (FOU) from imperfect and noisy datasets. This paper presents an automatic approach for learning and tuning Gaussian interval type-2 membership functions (IT2MFs) with application to multi-dimensional pattern classification problems. T2MFs and their FOUs are tuned according to the uncertainties in the training dataset by a combination of genetic algorithm (GA) and crossvalidation techniques. In our GA-based approach, the structure of the chromosome has fewer genes than other GA methods and chromosome initialization is more precise. The proposed approach addresses the application of the interval type-2 fuzzy logic system (IT2FLS) for the problem of nodule classification in a lung Computer Aided Detection (CAD) system. The designed IT2FLS is compared with its type-1 fuzzy logic system (T1FLS) counterpart. The results demonstrate that the IT2FLS outperforms the T1FLS by more than 30% in terms of classification accuracy.

Fuzzy coding in constrained ordinations

Canonical correspondence analysis and redundancy analysis are two methods of constrained ordination regularly used in the analysis of ecological data when several response variables (for example, species abundances) are related linearly to several explanatory variables (for example, environmental variables, spatial positions of samples). In this report I demonstrate the advantages of the fuzzy coding of explanatory variables: first, nonlinear relationships can be diagnosed; second, more variance in the responses can be explained; and third, in the presence of categorical explanatory variables (for example, years, regions) the interpretation of the resulting triplot ordination is unified because all explanatory variables are measured at a categorical level.

Transfers, social safety nets and economic growth

The role of social safety nets in the form of redistributional transfersand wage subsidies is analyzed using a simple model of criminal behavior. Itis argued that public welfare programs act as a crime--preventing ordisruption--preventing devices because they tend to increase the opportunitycost of engaging in crime or disruptive activities. It is shown that, in thepresence of a leisure choice, wage subsidies may be better than pure transfers. Using a simple growth model, it is shown that it is not optimal for the governmentto try to fully eliminate crime. The optimal size of the public welfare programis found and it is argued that public welfare should be financed with income(not lump--sum) taxes, despite the fact that income taxes are distortionary.The intuition for this result is that income taxes act as a user fee oncongested public goods and transfers can be thought of as {\it productive}public goods {\it subject to congestion}. Finally, using a cross-section of 75 countries, the partial correlation betweentransfers and growth is shown to be significantly positive.

On circuit functionality in boolean networks.

It has been proved, for several classes of continuous and discrete dynamical systems, that the presence of a positive (resp. negative) circuit in the interaction graph of a system is a necessary condition for the presence of multiple stable states (resp. a cyclic attractor). A positive (resp. negative) circuit is said to be functional when it "generates" several stable states (resp. a cyclic attractor). However, there are no definite mathematical frameworks translating the underlying meaning of "generates." Focusing on Boolean networks, we recall and propose some definitions concerning the notion of functionality along with associated mathematical results.

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.

Nets: Network estimation for time series

This work proposes novel network analysis techniques for multivariate time series.We define the network of a multivariate time series as a graph where verticesdenote the components of the process and edges denote non zero long run partialcorrelations. We then introduce a two step LASSO procedure, called NETS, toestimate high dimensional sparse Long Run Partial Correlation networks. This approachis based on a VAR approximation of the process and allows to decomposethe long run linkages into the contribution of the dynamic and contemporaneousdependence relations of the system. The large sample properties of the estimatorare analysed and we establish conditions for consistent selection and estimation ofthe non zero long run partial correlations. The methodology is illustrated with anapplication to a panel of U.S. bluechips.