C*-algebras nearly contained in type I algebras

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Dynamical systems of type (m,n) and their C*-algebras

Given positive integers n and m, we consider dynamical systems in which n copies of a topological space is homeomorphic to m copies of that same space. The universal such system is shown to arise naturally from the study of a C*-algebra we denote by Om;n, which in turn is obtained as a quotient of the well known Leavitt C*-algebra Lm;n, a process meant to transform the generating set of partial isometries of Lm;n into a tame set. Describing Om;n as the crossed-product of the universal (m; n) -dynamical system by a partial action of the free group Fm+n, we show that Om;n is not exact when n and m are both greater than or equal to 2, but the corresponding reduced crossed-product, denoted Or m;n, is shown to be exact and non-nuclear. Still under the assumption that m; n &= 2, we prove that the partial action of Fm+n is topologically free and that Or m;n satisfies property (SP) (small projections). We also show that Or m;n admits no finite dimensional representations. The techniques developed to treat this system include several new results pertaining to the theory of Fell bundles over discrete groups.

Chebyshev-type quadrature formulas for new weight classes

We give Chebyshev-type quadrature formulas for certain new weight classes. These formulas are of highest possible degree when the number of nodes is a power of 2. We also describe the nodes in a constructive way, which is important for applications. One of our motivations to consider these type of problems is the Faraday cage phenomenon for discrete charges as discussed by J. Korevaar and his colleagues.

Wellposedness of a nonlinear, logarithmic Schrödinger equation of Doebner-Goldin type modeling quantum dissipation

This paper is concerned with the modeling and analysis of quantum dissipation phenomena in the Schrödinger picture. More precisely, we do investigate in detail a dissipative, nonlinear Schrödinger equation somehow accounting for quantum Fokker–Planck effects, and how it is drastically reduced to a simpler logarithmic equation via a nonlinear gauge transformation in such a way that the physics underlying both problems keeps unaltered. From a mathematical viewpoint, this allows for a more achievable analysis regarding the local wellposedness of the initial–boundary value problem. This simplification requires the performance of the polar (modulus–argument) decomposition of the wavefunction, which is rigorously attained (for the first time to the best of our knowledge) under quite reasonable assumptions.

Inference of distributional parameters from compositional samples containing nondetects

Low concentrations of elements in geochemical analyses have the peculiarity of beingcompositional data and, for a given level of significance, are likely to be beyond thecapabilities of laboratories to distinguish between minute concentrations and completeabsence, thus preventing laboratories from reporting extremely low concentrations of theanalyte. Instead, what is reported is the detection limit, which is the minimumconcentration that conclusively differentiates between presence and absence of theelement. A spatially distributed exhaustive sample is employed in this study to generateunbiased sub-samples, which are further censored to observe the effect that differentdetection limits and sample sizes have on the inference of population distributionsstarting from geochemical analyses having specimens below detection limit (nondetects).The isometric logratio transformation is used to convert the compositional data in thesimplex to samples in real space, thus allowing the practitioner to properly borrow fromthe large source of statistical techniques valid only in real space. The bootstrap method isused to numerically investigate the reliability of inferring several distributionalparameters employing different forms of imputation for the censored data. The casestudy illustrates that, in general, best results are obtained when imputations are madeusing the distribution best fitting the readings above detection limit and exposes theproblems of other more widely used practices. When the sample is spatially correlated, itis necessary to combine the bootstrap with stochastic simulation

Monitoring switch-type sensors and powering autonomous sensors via inductive coupling: application to removable seats in vehicles

Aquesta tesi explora la possibilitat de fer servir enllaços inductius per a una aplicació de l’automòbil on el cablejat entre la centraleta (ECU) i els sensors o detectors és difícil o impossible. S’han proposat dos mètodes: 1) el monitoratge de sensors commutats (dos possibles estats) via acoblament inductiu i 2) la transmissió mitjançant el mateix principi físic de la potència necessària per alimentar els sensors autònoms remots. La detecció d'ocupació i del cinturó de seguretat per a seients desmuntables pot ser implementada amb sistemes sense fils passius basats en circuits ressonants de tipus LC on l'estat dels sensors determina el valor del condensador i, per tant, la freqüència de ressonància. Els canvis en la freqüència són detectats per una bobina situada en el terra del vehicle. S’ha conseguit provar el sistema en un marge entre 0.5 cm i 3 cm. Els experiments s’han dut a terme fent servir un analitzador d’impedàncies connectat a una bobina primària i sensors comercials connectats a un circuit remot. La segona proposta consisteix en transmetre remotament la potència des d’una bobina situada en el terra del vehicle cap a un dispositiu autònom situat en el seient. Aquest dispositiu monitorarà l'estat dels detectors (d'ocupació i de cinturó) i transmetrà les dades mitjançant un transceptor comercial de radiofreqüència o pel mateix enllaç inductiu. S’han avaluat les bobines necessàries per a una freqüència de treball inferior a 150 kHz i s’ha estudiat quin és el regulador de tensió més apropiat per tal d’aconseguir una eficiència global màxima. Quatre tipus de reguladors de tensió s’han analitzat i comparat des del punt de vista de l’eficiència de potència. Els reguladors de tensió de tipus lineal shunt proporcionen una eficiència de potència millor que les altres alternatives, els lineals sèrie i els commutats buck o boost. Les eficiències aconseguides han estat al voltant del 40%, 25% i 10% per les bobines a distàncies 1cm, 1.5cm, i 2cm. Les proves experimentals han mostrat que els sensors autònoms han estat correctament alimentats fins a distàncies de 2.5cm.

Kuranishi type Moduli Spaces for proper CR submersions fibering over the circle

Kuranishi's fundamental result (1962) associates to any compact complex manifold X&sub&0&/sub& a finite-dimensional analytic space which has to be thought of as a local moduli space of complex structures close to X&sub&0&/sub&. In this paper, we give an analogous statement for Levi-flat CR manifolds fibering properly over the circle by describing explicitely an infinite-dimensional Kuranishi type local moduli space of Levi-flat CR structures. We interpret this result in terms of Kodaira-Spencer deformation theory making clear the likenesses as well as the differences with the classical case. The article ends with applications and examples.

Human synthetic lethal inference as potential anti-cancer target gene detection

Background: Two genes are called synthetic lethal (SL) if mutation of either alone is not lethal, but mutation of both leads to death or a significant decrease in organism's fitness. The detection of SL gene pairs constitutes a promising alternative for anti-cancer therapy. As cancer cells exhibit a large number of mutations, the identification of these mutated genes' SL partners may provide specific anti-cancer drug candidates, with minor perturbations to the healthy cells. Since existent SL data is mainly restricted to yeast screenings, the road towards human SL candidates is limited to inference methods. Results: In the present work, we use phylogenetic analysis and database manipulation (BioGRID for interactions, Ensembl and NCBI for homology, Gene Ontology for GO attributes) in order to reconstruct the phylogenetically-inferred SL gene network for human. In addition, available data on cancer mutated genes (COSMIC and Cancer Gene Census databases) as well as on existent approved drugs (DrugBank database) supports our selection of cancer-therapy candidates.Conclusions: Our work provides a complementary alternative to the current methods for drug discovering and gene target identification in anti-cancer research. Novel SL screening analysis and the use of highly curated databases would contribute to improve the results of this methodology.

Vitamin E but not 17B-estradiol protect against vascular toxicity induced by B-amyloid wild type and the Dutch amyploid variant

Amyloid β-peptide (Aβ) fibril deposition on cerebral vessels produces cerebral amyloid angiopathy that appears in the majority of Alzheimer's disease patients. An early onset of a cerebral amyloid angiopathy variant called hereditary cerebral hemorrhage with amyloidosis of the Dutch type is caused by a point mutation in Aβ yielding AβGlu22→Gln. The present study addresses the effect of amyloid fibrils from both wild-type and mutated Aβ on vascular cells, as well as the putative protective role of antioxidants on amyloid angiopathy. For this purpose, we studied the cytotoxicity induced by Aβ1–40 Glu22→Gln and Aβ1–40 wild-type fibrils on human venule endothelial cells and rat aorta smooth muscle cells. We observed that AβGlu22→Gln fibrils are more toxic for vascular cells than the wild-type fibrils. We also evaluated the cytotoxicity of Aβ fibrils bound with acetylcholinesterase (AChE), a common component of amyloid deposits. Aβ1–40 wild-type–AChE fibrillar complexes, similar to neuronal cells, resulted in an increased toxicity on vascular cells. Previous reports showing that antioxidants are able to reduce the toxicity of Aβ fibrils on neuronal cells prompted us to test the effect of vitamin E, vitamin C, and 17β-estradiol on vascular damage induced by Aβwild-type and AβGlu22→Gln. Our data indicate that vitamin E attenuated significantly the Aβ-mediated cytotoxicity on vascular cells, although 17β-estradiol and vitamin C failed to inhibit the cytotoxicity induced by Aβ fibrils.

Impairment of mossy fiber long-term potentiation and associative learning in pituitary adenylate cyclase activating polypeptide type I receptor-deficient Mice

The pituitary adenylate cyclase activating polypeptide (PACAP) type I receptor (PAC1) is a G-protein-coupled receptor binding the strongly conserved neuropeptide PACAP with 1000-fold higher affinity than the related peptide vasoactive intestinal peptide. PAC1-mediated signaling has been implicated in neuronal differentiation and synaptic plasticity. To gain further insight into the biological significance of PAC1-mediated signaling in vivo, we generated two different mutant mouse strains, harboring either a complete or a forebrain-specific inactivation of PAC1. Mutants from both strains show a deficit in contextual fear conditioning, a hippocampus-dependent associative learning paradigm. In sharp contrast, amygdala-dependent cued fear conditioning remains intact. Interestingly, no deficits in other hippocampus-dependent tasks modeling declarative learning such as the Morris water maze or the social transmission of food preference are observed. At the cellular level, the deficit in hippocampus-dependent associative learning is accompanied by an impairment of mossy fiber long-term potentiation (LTP). Because the hippocampal expression of PAC1 is restricted to mossy fiber terminals, we conclude that presynaptic PAC1-mediated signaling at the mossy fiber synapse is involved in both LTP and hippocampus-dependent associative learning.

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.

A mathematical excursion: From the three-door problem to a Cantor-type perfect set

We start with a generalization of the well-known three-door problem:the n-door problem. The solution of this new problem leads us toa beautiful representation system for real numbers in (0,1] as alternated series, known in the literature as Pierce expansions. A closer look to Pierce expansions will take us to some metrical properties of sets defined through the Pierce expansions of its elements. Finally, these metrical properties will enable us to present 'strange' sets, similar to the classical Cantor set.

A generalization of histogram type estimators

We introduce simple nonparametric density estimators that generalize theclassical histogram and frequency polygon. The new estimators are expressed as linear combination of density functions that are piecewisepolynomials, where the coefficients are optimally chosen in order to minimize the integrated square error of the estimator. We establish the asymptotic behaviour of the proposed estimators, and study theirperformance in a simulation study.

Inference with the lognormal distribution

Several estimators of the expectation, median and mode of the lognormal distribution are derived. They aim to be approximately unbiased, efficient, or have a minimax property in the class of estimators we introduce. The small-sample properties of these estimators are assessed by simulations and, when possible, analytically. Some of these estimators of the expectation are far more efficient than the maximum likelihood or the minimum-variance unbiased estimator, even for substantial samplesizes.

Subsampling inference in threshold autoregressive models

This paper discusses inference in self exciting threshold autoregressive (SETAR)models. Of main interest is inference for the threshold parameter. It iswell-known that the asymptotics of the corresponding estimator depend uponwhether the SETAR model is continuous or not. In the continuous case, thelimiting distribution is normal and standard inference is possible. Inthe discontinuous case, the limiting distribution is non-normal and cannotbe estimated consistently. We show valid inference can be drawn by theuse of the subsampling method. Moreover, the method can even be extendedto situations where the (dis)continuity of the model is unknown. In thiscase, also the inference for the regression parameters of the modelbecomes difficult and subsampling can be used advantageously there aswell. In addition, we consider an hypothesis test for the continuity ofthe SETAR model. A simulation study examines small sample performance.