KAM theory for conformally symplectic systems

We present a KAM theory for some dissipative systems (geometrically, these are conformally symplectic systems, i.e. systems that transform a symplectic form into a multiple of itself). For systems with n degrees of freedom depending on n parameters we show that it is possible to find solutions with n-dimensional (Diophantine) frequencies by adjusting the parameters. We do not assume that the system is close to integrable, but we use an a-posteriori format. Our unknowns are a parameterization of the solution and a parameter. We show that if there is a sufficiently approximate solution of the invariance equation, which also satisfies some explicit non–degeneracy conditions, then there is a true solution nearby. We present results both in Sobolev norms and in analytic norms. The a–posteriori format has several consequences: A) smooth dependence on the parameters, including the singular limit of zero dissipation; B) estimates on the measure of parameters covered by quasi–periodic solutions; C) convergence of perturbative expansions in analytic systems; D) bootstrap of regularity (i.e., that all tori which are smooth enough are analytic if the map is analytic); E) a numerically efficient criterion for the break–down of the quasi–periodic solutions. The proof is based on an iterative quadratically convergent method and on suitable estimates on the (analytical and Sobolev) norms of the approximate solution. The iterative step takes advantage of some geometric identities, which give a very useful coordinate system in the neighborhood of invariant (or approximately invariant) tori. This system of coordinates has several other uses: A) it shows that for dissipative conformally symplectic systems the quasi–periodic solutions are attractors, B) it leads to efficient algorithms, which have been implemented elsewhere. Details of the proof are given mainly for maps, but we also explain the slight modifications needed for flows and we devote the appendix to present explicit algorithms for flows.

Theory of mind and cognitive processes in aging and Alzheimer type dementia: a systematic review.

OBJECTIVES: Theory of mind (ToM) performance in aging and dementia of the Alzheimer type (DAT) has been a growing interest of researchers and recently, theoretical trends in ToM development have led to a focus on determining the cognitive skills involved in ToM performance. The aim of the present review is to answer three main questions: How is ToM assessed in aging and DAT? How does ToM performance evolve in aging and DAT? Do cognitive processes influence ToM performance in aging and DAT? METHOD: A systematic review was conducted to provide a targeted overview of recent studies relating ToM performance with cognitive processes in aging and DAT. RESULTS: RESULTS suggest a decrease in ToM performance, more pronounced in complex ToM tasks. Moreover, the review points up the strong involvement of executive functions, especially inhibition, and reasoning skills in ToM task achievement. CONCLUSION: Current data suggest that the structure of ToM tasks itself could lead to poor performance, especially in populations with reduced cognitive abilities.

Theory of mind and social functioning in first episode psychosis

There is evidence of associations between social functioning and theory of mind performance and between social functioning and negative symptoms in chronic psychosis. This study investigates these associations in those with first episode psychosis who are unaffected by factors related to long-term mental illness. Our first hypothesis states that there is an association between theory of mind and social functioning. The second hypothesis states that there is no association between symptoms of psychosis and social functioning. Methods. Fifty-two individuals with first episode psychosis were assessed for social functioning, theory of mind ability (using the Hinting test with verbal stimuli and the Visual Cartoon test with pictorial stimuli), and symptoms of psychosis. Multivariable logistic regression was used to examine associations. Results. Social functioning and theory of mind were associated when measured by the Hinting test (OR 1.70, 95% CI 1.08, 2.66), but not with the Visual Cartoon test (ToM jokes OR 0.61, 95% CI 0.15, 2.53). There was no association between social functioning and symptoms (psychotic symptoms; OR 0.95, 95% CI 0.81, 1.12; selected negative symptoms; OR 1.33, 95% CI 0.78, 2.25). Conclusions. Theory of mind assessed by verbal stimuli is associated with social functioning in a population with first episode psychosis. These findings may be related to language disorders in psychosis.

Luck and the control theory of knowledge

The dissertation accomplishes two aims: 1) to diagnose what prevents true beliefs from being knowledge; 2) to give an positive account of knowledge. Concerning the first aim, it offers an account of the notion of luck. It defends the view that luck is a form of risk and distinguishes two types of luck. Then, it applies the account to the problem of epistemic luck and distinguishes, accordingly, two types of epistemic luck. It is argued that these two types of epistemic luck explain the whole range of cases of not-known true belief. Concerning the second aim, the dissertation advances an account of knowledge in terms of the notion of cognitive control that deals with the two forms of epistemic luck distinguished.

Discovering similarities in the time use patterns of the Spanish Autonomous Communities by Fuzzy techniques

In 2000 the European Statistical Office published the guidelines for developing theHarmonized European Time Use Surveys system. Under such a unified framework,the first Time Use Survey of national scope was conducted in Spain during 2002–03. The aim of these surveys is to understand human behavior and the lifestyle ofpeople. Time allocation data are of compositional nature in origin, that is, they aresubject to non-negativity and constant-sum constraints. Thus, standard multivariatetechniques cannot be directly applied to analyze them. The goal of this work is toidentify homogeneous Spanish Autonomous Communities with regard to the typicalactivity pattern of their respective populations. To this end, fuzzy clustering approachis followed. Rather than the hard partitioning of classical clustering, where objects areallocated to only a single group, fuzzy method identify overlapping groups of objectsby allowing them to belong to more than one group. Concretely, the probabilistic fuzzyc-means algorithm is conveniently adapted to deal with the Spanish Time Use Surveymicrodata. As a result, a map distinguishing Autonomous Communities with similaractivity pattern is drawn.Key words: Time use data, Fuzzy clustering; FCM; simplex space; Aitchison distance

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

Ciclo de vida organizacional pautado no modelo de Lester, Parnell e Carraher (2003) e na lógica fuzzy: classificação de empresas de um segmento industrial de Santa Catarina

Neste estudo, objetiva-se identificar os estágios do ciclo de vida organizacional pautados no modelo de Lester, Parnell e Carraher (2003) das empresas do segmento industrial de máquinas, aparelhos e materiais elétricos do estado de Santa Catarina. Pesquisa descritiva, com abordagem quantitativa, foi realizada por meio de levantamento com aplicação de questionário aos gestores das empresas. A população constituiu-se das 264 empresas desse segmento econômico, listadas na Secretaria da Fazenda do Estado de Santa Catarina, e a amostra não aleatória das 40 empresas que responderam a pesquisa. As variáveis de identificação dos estágios de ciclo de vida utilizadas no questionário foram extraídas de Lester, Parnell e Carraher (2003). Os dados da pesquisa foram submetidos à técnica estatística denominada lógica fuzzy. Os resultados da pesquisa demonstraram que 57,5% das empresas foram classificadas no estágio do nascimento, 15% do, 7,5% da Maturidade, 10% do rejuvenescimento e 10% do declínio. Concluiu-se que determinados estágios do ciclo de vida organizacional estão próximos uns dos outros e que não se pode perceber claramente uma progressão determinista nas fases do ciclo de vida, como uma sequência única, definitiva e irreversível, no sentido tradicional biológico.

Advances in Sequence Analysis: Theory, Methods, Applications

This book gives a general view of sequence analysis, the statistical study of successions of states or events. It includes innovative contributions on life course studies, transitions into and out of employment, contemporaneous and historical careers, and political trajectories. The approach presented in this book is now central to the life-course perspective and the study of social processes more generally. This volume promotes the dialogue between approaches to sequence analysis that developed separately, within traditions contrasted in space and disciplines. It includes the latest developments in sequential concepts, coding, atypical datasets and time patterns, optimal matching and alternative algorithms, survey optimization, and visualization. Field studies include original sequential material related to parenting in 19th-century Belgium, higher education and work in Finland and Italy, family formation before and after German reunification, French Jews persecuted in occupied France, long-term trends in electoral participation, and regime democratization. Overall the book reassesses the classical uses of sequences and it promotes new ways of collecting, formatting, representing and processing them. The introduction provides basic sequential concepts and tools, as well as a history of the method. Chapters are presented in a way that is both accessible to the beginner and informative to the expert.

War Signals: A Theory of Trade, Trust and Conflict

We construct a dynamic theory of civil conflict hinging on inter-ethnic trust and trade. The model economy is inhabitated by two ethnic groups. Inter-ethnic trade requires imperfectly observed bilateral investments and one group has to form beliefs on the average propensity to trade of the other group. Since conflict disrupts trade, the onset of a conflict signals that the aggressor has a low propensity to trade. Agents observe the history of conflicts and update their beliefs over time, transmitting them to the next generation. The theory bears a set of testable predictions. First, war is a stochastic process whose frequency depends on the state of endogenous beliefs. Second, the probability of future conflicts increases after each conflict episode. Third, "accidental" conflicts that do not reflect economic fundamentals can lead to a permanent breakdown of trust, plunging a society into a vicious cycle of recurrent conflicts (a war trap). The incidence of conflict can be reduced by policies abating cultural barriers, fostering inter-ethnic trade and human capital, and shifting beliefs. Coercive peace policies such as peacekeeping forces or externally imposed regime changes have instead no persistent effects.