Mètodes algebraics i de teoria de la prova per a la formalització del raonament vague

Projecte de recerca elaborat a partir d’una estada a la Università degli studi di Siena, Italy , entre 2007 i 2009. El projecte ha consistit en un estudi de la formalització lògica del raonament en presència de vaguetat amb els mètodes de la Lògica Algebraica i de la Teoria de la Prova. S'ha treballat fonamental en quatre direccions complementàries. En primer lloc, s'ha proposat un nou plantejament, més abstracte que el paradigma dominant fins ara, per l'estudi dels sistemes de lògica borrosa. Fins ara en l'estudi d'aquests sistemes l'atenció havia recaigut essencialment en l'obtenció de semàntiques basades en tnormes contínues (o almenys contínues per l'esquerra). En primer nivell de major abstracció hem estudiat les propietats de completesa de les lògiques borroses (tant proposicionals com de primer ordre) respecte de semàntiques definides sobre qualsevol cadena de valors de veritat, no necessàriament només sobre l'interval unitat dels nombres reals. A continuació, en un nivell encara més abstracte, s’ha pres l'anomenada jerarquia de Leibniz de la Lògica Algebraica Abstracta que classifica tots els sistemes lògics amb un bon comportament algebraic i s'ha expandit a una nova jerarquia (que anomenem implicacional) que permet definir noves classes de lògiques borroses que contenen quasi totes les conegudes fins ara. En segon lloc, s’ha continuat una línia d'investigació iniciada els darrers anys consistent en l'estudi de la veritat parcial com a noció sintàctica (és a dir, com a constants de veritat explícites en els sistemes de prova de les lògiques borroses). Per primer cop, s’ha considerat la semàntica racional per les lògiques proposicionals i la semàntica real i racional per les lògiques de primer ordre expandides amb constants. En tercer lloc, s’ha tractat el problema més fonamental del significat i la utilitat de les lògiques borroses com a modelitzadores de (part de) els fenòmens de la vaguetat en un darrer article de caràcter més filosòfic i divulgatiu, i en un altre més tècnic en què defensem la necessitat i presentem l'estat de l'art de l'estudi de les estructures algèbriques associades a les lògiques borroses. Finalment, s’ha dedicat la darrera part del projecte a l'estudi de la complexitat aritmètica de les lògiques borroses de primer ordre.

Homologia de Lawson i descens

La meva recerca en els tres anys de gaudiment de beca s'ha centrat en l'estudi de teories semitopològiques definides a través d'espais de cicles algebraics, introduïts per Friedlander i Lawson. Hem estudiat propietats de descens d'aquestes teories i hem construït una successió espectral que calcula explícitament la cohomologia mòrfica d'una varietat tòrica. D'altra banda, estem treballant en l'estudi de propietats d'invariància homotòpica per la cohomologia mòrfica, així com en l'estructura algebraica dels grups d'homologia de Lawson.

Binary classification of dyslipidemia from the waist-to-hip ratio and body mass index: a comparison of linear, logistic, and CART models.

BACKGROUND: We sought to improve upon previously published statistical modeling strategies for binary classification of dyslipidemia for general population screening purposes based on the waist-to-hip circumference ratio and body mass index anthropometric measurements. METHODS: Study subjects were participants in WHO-MONICA population-based surveys conducted in two Swiss regions. Outcome variables were based on the total serum cholesterol to high density lipoprotein cholesterol ratio. The other potential predictor variables were gender, age, current cigarette smoking, and hypertension. The models investigated were: (i) linear regression; (ii) logistic classification; (iii) regression trees; (iv) classification trees (iii and iv are collectively known as "CART"). Binary classification performance of the region-specific models was externally validated by classifying the subjects from the other region. RESULTS: Waist-to-hip circumference ratio and body mass index remained modest predictors of dyslipidemia. Correct classification rates for all models were 60-80%, with marked gender differences. Gender-specific models provided only small gains in classification. The external validations provided assurance about the stability of the models. CONCLUSIONS: There were no striking differences between either the algebraic (i, ii) vs. non-algebraic (iii, iv), or the regression (i, iii) vs. classification (ii, iv) modeling approaches. Anticipated advantages of the CART vs. simple additive linear and logistic models were less than expected in this particular application with a relatively small set of predictor variables. CART models may be more useful when considering main effects and interactions between larger sets of predictor variables.

Alternative ways to estimate change points in multinomial sequences. An application to an authorship attribution problem

The statistical analysis of literary style is the part of stylometry that compares measurable characteristicsin a text that are rarely controlled by the author, with those in other texts. When thegoal is to settle authorship questions, these characteristics should relate to the author’s style andnot to the genre, epoch or editor, and they should be such that their variation between authors islarger than the variation within comparable texts from the same author.For an overview of the literature on stylometry and some of the techniques involved, see for exampleMosteller and Wallace (1964, 82), Herdan (1964), Morton (1978), Holmes (1985), Oakes (1998) orLebart, Salem and Berry (1998).Tirant lo Blanc, a chivalry book, is the main work in catalan literature and it was hailed to be“the best book of its kind in the world” by Cervantes in Don Quixote. Considered by writterslike Vargas Llosa or Damaso Alonso to be the first modern novel in Europe, it has been translatedseveral times into Spanish, Italian and French, with modern English translations by Rosenthal(1996) and La Fontaine (1993). The main body of this book was written between 1460 and 1465,but it was not printed until 1490.There is an intense and long lasting debate around its authorship sprouting from its first edition,where its introduction states that the whole book is the work of Martorell (1413?-1468), while atthe end it is stated that the last one fourth of the book is by Galba (?-1490), after the death ofMartorell. Some of the authors that support the theory of single authorship are Riquer (1990),Chiner (1993) and Badia (1993), while some of those supporting the double authorship are Riquer(1947), Coromines (1956) and Ferrando (1995). For an overview of this debate, see Riquer (1990).Neither of the two candidate authors left any text comparable to the one under study, and thereforediscriminant analysis can not be used to help classify chapters by author. By using sample textsencompassing about ten percent of the book, and looking at word length and at the use of 44conjunctions, prepositions and articles, Ginebra and Cabos (1998) detect heterogeneities that mightindicate the existence of two authors. By analyzing the diversity of the vocabulary, Riba andGinebra (2000) estimates that stylistic boundary to be near chapter 383.Following the lead of the extensive literature, this paper looks into word length, the use of the mostfrequent words and into the use of vowels in each chapter of the book. Given that the featuresselected are categorical, that leads to three contingency tables of ordered rows and therefore tothree sequences of multinomial observations.Section 2 explores these sequences graphically, observing a clear shift in their distribution. Section 3describes the problem of the estimation of a suden change-point in those sequences, in the followingsections we propose various ways to estimate change-points in multinomial sequences; the methodin section 4 involves fitting models for polytomous data, the one in Section 5 fits gamma modelsonto the sequence of Chi-square distances between each row profiles and the average profile, theone in Section 6 fits models onto the sequence of values taken by the first component of thecorrespondence analysis as well as onto sequences of other summary measures like the averageword length. In Section 7 we fit models onto the marginal binomial sequences to identify thefeatures that distinguish the chapters before and after that boundary. Most methods rely heavilyon the use of generalized linear models

Spectrum of some trianguled categories

In this paper, we compute the triangular spectrum (as de fined by P. Balmer) of two classes of tensor triangulated categories which are quite common in algebraic geometry. One of them is the derived category of G-equivariant sheaves on a smooth scheme X, for a fi nite group G. The other class is the derived category of split superschemes.

Monitoring procedures in environmental geochemistry and compositional data analysis theory

First discussion on compositional data analysis is attributable to Karl Pearson, in 1897. However, notwithstanding the recent developments on algebraic structure of the simplex, more than twenty years after Aitchison’s idea of log-transformations of closed data, scientific literature is again full of statistical treatments of this type of data by using traditional methodologies. This is particularly true in environmental geochemistry where besides the problem of the closure, the spatial structure (dependence) of the data have to be considered. In this work we propose the use of log-contrast values, obtained by asimplicial principal component analysis, as LQGLFDWRUV of given environmental conditions. The investigation of the log-constrast frequency distributions allows pointing out the statistical laws able togenerate the values and to govern their variability. The changes, if compared, for example, with the mean values of the random variables assumed as models, or other reference parameters, allow definingmonitors to be used to assess the extent of possible environmental contamination. Case study on running and ground waters from Chiavenna Valley (Northern Italy) by using Na+, K+, Ca2+, Mg2+, HCO3-, SO4 2- and Cl- concentrations will be illustrated

Avalanche dynamics of fiber bundle models

We present a detailed analytical and numerical study of the avalanche distributions of the continuous damage fiber bundle model CDFBM . Linearly elastic fibers undergo a series of partial failure events which give rise to a gradual degradation of their stiffness. We show that the model reproduces a wide range of mechanical behaviors. We find that macroscopic hardening and plastic responses are characterized by avalanche distributions, which exhibit an algebraic decay with exponents between 5/2 and 2 different from those observed in mean-field fiber bundle models. We also derive analytically the phase diagram of a family of CDFBM which covers a large variety of potential avalanche size distributions. Our results provide a unified view of the statistics of breaking avalanches in fiber bundle models

Effect of initial conditions on the speed of reaction-diffusion fronts

The effect of initial conditions on the speed of propagating fronts in reaction-diffusion equations is examined in the framework of the Hamilton-Jacobi theory. We study the transition between quenched and nonquenched fronts both analytically and numerically for parabolic and hyperbolic reaction diffusion. Nonhomogeneous media are also analyzed and the effect of algebraic initial conditions is also discussed

An Analysis of black-box optimization problems in reinsurance: evolutionary-based approaches

Black-box optimization problems (BBOP) are de ned as those optimization problems in which the objective function does not have an algebraic expression, but it is the output of a system (usually a computer program). This paper is focussed on BBOPs that arise in the eld of insurance, and more speci cally in reinsurance problems. In this area, the complexity of the models and assumptions considered to de ne the reinsurance rules and conditions produces hard black-box optimization problems, that must be solved in order to obtain the optimal output of the reinsurance. The application of traditional optimization approaches is not possible in BBOP, so new computational paradigms must be applied to solve these problems. In this paper we show the performance of two evolutionary-based techniques (Evolutionary Programming and Particle Swarm Optimization). We provide an analysis in three BBOP in reinsurance, where the evolutionary-based approaches exhibit an excellent behaviour, nding the optimal solution within a fraction of the computational cost used by inspection or enumeration methods.

Negative Fukui functions: new insights based on electronegativity equalization

The occurrence of negative values for Fukui functions was studied through the electronegativity equalization method. Using algebraic relations between Fukui functions and different other conceptual DFT quantities on the one hand and the hardness matrix on the other hand, expressions were obtained for Fukui functions for several archetypical small molecules. Based on EEM calculations for large molecular sets, no negative Fukui functions were found

A comparative analysis of two methods for the calculation of electric-field-induced perturbations to molecular vibration

Two common methods of accounting for electric-field-induced perturbations to molecular vibration are analyzed and compared. The first method is based on a perturbation-theoretic treatment and the second on a finite-field treatment. The relationship between the two, which is not immediately apparent, is made by developing an algebraic formalism for the latter. Some of the higher-order terms in this development are documented here for the first time. As well as considering vibrational dipole polarizabilities and hyperpolarizabilities, we also make mention of the vibrational Stark effec

Temporo-Parietal Junction encodes the Embodied Self: Neuro-Robotics, fMRI, and Lesion mapping.

Introduction: Neuroimaging of the self focused on high-level mechanisms such as language, memory or imagery of the self. Recent evidence suggests that low-level mechanisms of multisensory and sensorimotor integration may play a fundamental role in encoding self-location and the first-person perspective (Blanke and Metzinger, 2009). Neurological patients with out-of body experiences (OBE) suffer from abnormal self-location and the first-person perspective due to a damage in the temporo-parietal junction (Blanke et al., 2004). Although self-location and the first-person perspective can be studied experimentally (Lenggenhager et al., 2009), the neural underpinnings of self-location have yet to be investigated. To investigate the brain network involved in self-location and first-person perspective we used visuo-tactile multisensory conflict, magnetic resonance (MR)-compatible robotics, and fMRI in study 1, and lesion analysis in a sample of 9 patients with OBE due to focal brain damage in study 2. Methods: Twenty-two participants saw a video showing either a person's back or an empty room being stroked (visual stimuli) while the MR-compatible robotic device stroked their back (tactile stimulation). Direction and speed of the seen stroking could either correspond (synchronous) or not (asynchronous) to those of the seen stroking. Each run comprised the four conditions according to a 2x2 factorial design with Object (Body, No-Body) and Synchrony (Synchronous, Asynchronous) as main factors. Self-location was estimated using the mental ball dropping (MBD; Lenggenhager et al., 2009). After the fMRI session participants completed a 6-item adapted from the original questionnaire created by Botvinick and Cohen (1998) and based on questions and data obtained by Lenggenhager et al. (2007, 2009). They were also asked to complete a questionnaire to disclose the perspective they adopted during the illusion. Response times (RTs) for the MBD and fMRI data were analyzed with a 3-way mixed model ANOVA with the in-between factor Perspective (up, down) and the two with-in factors Object (body, no-body) and Stroking (synchronous, asynchronous). Quantitative lesion analysis was performed using MRIcron (Rorden et al., 2007). We compared the distributions of brain lesions confirmed by multimodality imaging (Knowlton, 2004) in patients with OBE with those showing complex visual hallucinations involving people or faces, but without any disturbance of self-location and first person perspective. Nine patients with OBE were investigated. The control group comprised 8 patients. Structural imaging data were available for normalization and co-registration in all the patients. Normalization of each patient's lesion into the common MNI (Montreal Neurological Institute) reference space permitted simple, voxel-wise, algebraic comparisons to be made. Results: Even if in the scanner all participants were lying on their back and were facing upwards, analysis of perspective showed that half of the participants had the impression to be looking down at the virtual human body below them, despite any cues about their body position (Down-group). The other participants had the impression to be looking up at the virtual body above them (Up-group). Analysis of Q3 ("How strong was the feeling that the body you saw was you?") indicated stronger self-identification with the virtual body during the synchronous stroking. RTs in the MBD task confirmed these subjective data (significant 3-way interaction between perspective, object and stroking). fMRI results showed eight cortical regions where the BOLD signal was significantly different during at least one of the conditions resulting from the combination of Object and Stroking, relative to baseline: right and left temporo-parietal junction, right EBA, left middle occipito-temporal gyrus, left postcentral gyrus, right medial parietal lobe, bilateral medial occipital lobe (Fig 1). The activation patterns in right and left temporo-parietal junction and right EBA reflected changes in self-location and perspective as revealed by statistical analysis that was performed on the percentage of BOLD change with respect to the baseline. Statistical lesion overlap comparison (using nonparametric voxel based lesion symptom mapping) with respect to the control group revealed the right temporo-parietal junction, centered at the angular gyrus (Talairach coordinates x = 54, y =-52, z = 26; p>0.05, FDR corrected). Conclusions: The present questionnaire and behavioural results show that - despite the noisy and constraining MR environment) our participants had predictable changes in self-location, self-identification, and first-person perspective when robotic tactile stroking was applied synchronously with the robotic visual stroking. fMRI data in healthy participants and lesion data in patients with abnormal self-location and first-person perspective jointly revealed that the temporo-parietal cortex especially in the right hemisphere encodes these conscious experiences. We argue that temporo-parietal activity reflects the experience of the conscious "I" as embodied and localized within bodily space.

What can spike train distances tell us about the neural code?

Time scale parametric spike train distances like the Victor and the van Rossum distancesare often applied to study the neural code based on neural stimuli discrimination.Different neural coding hypotheses, such as rate or coincidence coding,can be assessed by combining a time scale parametric spike train distance with aclassifier in order to obtain the optimal discrimination performance. The time scalefor which the responses to different stimuli are distinguished best is assumed to bethe discriminative precision of the neural code. The relevance of temporal codingis evaluated by comparing the optimal discrimination performance with the oneachieved when assuming a rate code.We here characterize the measures quantifying the discrimination performance,the discriminative precision, and the relevance of temporal coding. Furthermore,we evaluate the information these quantities provide about the neural code. Weshow that the discriminative precision is too unspecific to be interpreted in termsof the time scales relevant for encoding. Accordingly, the time scale parametricnature of the distances is mainly an advantage because it allows maximizing thediscrimination performance across a whole set of measures with different sensitivitiesdetermined by the time scale parameter, but not due to the possibility toexamine the temporal properties of the neural code.

Klassenkampf und Klassenkompromiss : Arbeit, Kapital und Staat in den Niederlanden und der Schweiz

Les Pays-Bas et la Suisse sont souvent décrits comme ayant des relations entre travail et capital similaires, marquées par des négociations et le compromis. La conviction est courante dans les deux pays qu'il y a une tendance constante au consensus et au compromis dans l'histoire nationale. Cette thèse livre une comparaison historique du développement des relations de classe dans la 1ers moitié du 20eme siècle. Une attention particulière est donnée aux confrontations sévères et partiellement violentes entre les classes qui ont eu lieu pendant et juste après la Première Guerre Mondiale. Dans la crise des années trente, les deux pays ont longtemps maintenu l'attachement à une politique de déflation, ce qui a mené à une nouvelle accentuation des tensions sociales. Dans ce contexte, loin d'être prêts à faire des concessions au mouvement ouvrier, d'importantes composantes du patronat néerlandais et suisse sympathisaient avec un corporatisme autoritaire comme il était prôné par les mouvements et régimes fascistes. Des alliances entre le mouvement ouvrier socialiste et des fractions importantes des classes moyennes étaient capables d'arrêter cette dérive autoritaire, sans avoir assez de force pour imposer leurs propres alternatives. C'est seulement après l'affaiblissement de la droite dure entre la deuxième moitié des années trente et l'immédiat après-guerre que des premiers fondements pour un compromis de classe stable ont été établis. Généralement, l'approche comparée de la thèse permet de mieux saisir les histoires nationales dans leur contexte européen et global et permet donc de dépasser une vue de l'histoire nationale comme «cas spécial».¦Die Beziehungen zwischen Arbeit und Kapital in Niederlande und die Schweiz werden oft als âhnlich und stark von Verhandlungen und von Kompromissen geprâgt beschrieben. In beiden Lândern ist die Auffassung weitverbreitet, dass es in der nationalen Geschichte eine konstante Tendenz zum Konsens und zum Kompromiss gebe. Diese Dissertation bietet einen historischen Vergleich der Entwicklung der Klassenbeziehungen in der ersten Hâlfte des 20. Jahrhunderts. Thematisiert werden insbesondere die ernsthaften und teilweise gewalttàtigen Zusammenstôsse zwischen den Klassen, die sich wàhrend und unmittelbar nach dem Ersten Weltkrieg ereigneten. In der Krise der Dreissigerjahre hielten beide Staaten lange an der Deflationspolitik fest, was erneut zu einer Verschârfung der sozialen Spannungen fïïhrte. Vor diesem Hintergrund lehnten weite Teile der schweizerischen und niederlândischen Grossunternehmer Konzessionen gegenuber der Arbeiterbewegung ab. Vielmehr sympathisierten sie mit einem autoritàren Korporatismus, wie er von den faschistischen Bewegungen und Regimes vertreten wurde. Allianzen zwischen der sozialistischen Arbeiterbewegung und Teilen der Mittelschichten gelang es zwar, diese autoritàren Tendenzen aufzuhalten, nicht aber ihre eigenen Alteraativkonzepte durchzusetzen. Erst nach der Schwâchung der radikalen Rechten in der Zeit zwischen der zweiten Hàlfte der 1930er Jahre und der unmittelbaren Nachkriegszeit nach dem Zweiten Weltkrieg fand sich eine¦Grundlage fur einen stabilen Klassenkompromiss. Generell ermôglicht es der vergleichende Ansatz der Dissertation, die nationale Geschichte in ihrem europâischen und globalen Kontext zu sehen und so eine Sicht auf die Geschichte eines einzelnen Landes als ,,Sonderfall" zu uberwinden.

A total order in [0,1] defined through a 'next' operator

A `next' operator, s, is built on the set R1=(0,1]-{ 1-1/e} defining a partial order that, with the help of the axiom of choice, can be extended to a total order in R1. Besides, the orbits {sn(a)}nare all dense in R1 and are constituted by elements of the samearithmetical character: if a is an algebraic irrational of degreek all the elements in a's orbit are algebraic of degree k; if a istranscendental, all are transcendental. Moreover, the asymptoticdistribution function of the sequence formed by the elements in anyof the half-orbits is a continuous, strictly increasing, singularfunction very similar to the well-known Minkowski's ?(×) function.