Diagnostic potential of structural neuroimaging for depression from a multi-ethnic community sample

Background At present, we do not have any biological tests which can contribute towards a diagnosis of depression. Neuroimaging measures have shown some potential as biomarkers for diagnosis. However, participants have generally been from the same ethnic background while the applicability of a biomarker would require replication in individuals of diverse ethnicities. Aims We sought to examine the diagnostic potential of the structural neuroanatomy of depression in a sample of a wide ethnic diversity. Method Structural magnetic resonance imaging (MRI) scans were obtained from 23 patients with major depressive disorder in an acute depressive episode (mean age: 39.8 years) and 20 matched healthy volunteers (mean age: 38.8 years). Participants were of Asian, African and Caucasian ethnicity recruited from the general community. Results Structural neuroanatomy combining white and grey matter distinguished patients from controls at the highest accuracy of 81% with the most stable pattern being at around 70%. A widespread network encompassing frontal, parietal, occipital and cerebellar regions contributed towards diagnostic classification. Conclusions These findings provide an important step in the development of potential neuroimaging-based tools for diagnosis as they demonstrate that the identification of depression is feasible within a multi-ethnic group from the community. Declaration of interests C.H.Y.F. has held recent research grants from Eli Lilly and Company and GlaxoSmithKline. L.M. is a former employee and stockholder of Eli Lilly and Company.

Shear, shear stress and shearing

New simpler formulae are derived for the shear of a pair of material elements within the context of infinitesimal strain and finite strain. Also, new formulae are derived for shear stress based on the (symmetric) Cauchy stress and for the rate of shear of a pair of material elements within the rate of strain theory. These formulae are exploited to obtain results and to derive new simpler proofs of familiar classical results. In particular, a very simple short derivation is presented of the classical result of Coulomb and Hopkins on the maximum orthogonal shear stress. © 1992.

A Tutorial on the Universality and Expressiveness of Fold

In functional programming, fold is a standard operator that encapsulates a simple pattern of recursion for processing lists. This article is a tutorial on two key aspects of the fold operator for lists. First of all, we emphasize the use of the universal property of fold both as a proof principle that avoids the need for inductive proofs, and as a definition principle that guides the transformation of recursive functions into definitions using fold. Secondly, we show that even though the pattern of recursion encapsulated by fold is simple, in a language with tuples and functions as first-class values the fold operator has greater expressive power than might first be expected.

Proof methods for structured corecursive programs

Corecursive programs produce values of greatest fixpoint types, in contrast to recursive programs, which consume values of least fixpoint types. There are a number of widely used methods for proving properties of corecursive programs, including fixpoint induction, the take lemma, and coinduction. However, these methods are all rather low level, in that they do not exploit the common structure that is often present in corecursive definitions. We argue for a more structured approach to proving properties of corecursive programs. In particular, we show that by writing corecursive programs using a simple operator that encapsulates a common pattern of corecursive definition, we can then use high-level algebraic properties of this operator to conduct proofs in a purely calculational style that avoids the use of inductive or coinductive methods.

The Use of Proof Planning Critics to Diagnose Errors in the Base Cases of Recursive Programs

This paper reports the use of proof planning to diagnose errors in program code. In particular it looks at the errors that arise in the base cases of recursive programs produced by undergraduates. It describes two classes of error that arise in this situation. The use of test cases would catch these errors but would fail to distinguish between them. The system adapts proof critics, commonly used to patch faulty proofs, to diagnose such errors and distinguish between the two classes. It has been implemented in Lambda-clam, a proof planning system, and applied successfully to a small set of examples.

A Comparison of two Proof Critics: Power vs. Robustness

Proof critics are a technology from the proof planning paradigm. They examine failed proof attempts in order to extract information which can be used to generate a patch which will allow the proof to go through. We consider the proof of the $quot;whisky problem$quot;, a challenge problem from the domain of temporal logic. The proof requires a generalisation of the original conjecture and we examine two proof critics which can be used to create this generalisation. Using these critics we believe we have produced the first automatic proofs of this challenge problem. We use this example to motivate a comparison of the two critics and propose that there is a place for specialist critics as well as powerful general critics. In particular we advocate the development of critics that do not use meta-variables.

Inductive Theorem Proving and Computer Algebra in the Mathweb Software Bus

Reasoning systems have reached a high degree of maturity in the last decade. However, even the most successful systems are usually not general purpose problem solvers but are typically specialised on problems in a certain domain. The MathWeb SOftware Bus (Mathweb-SB) is a system for combining reasoning specialists via a common osftware bus. We described the integration of the lambda-clam systems, a reasoning specialist for proofs by induction, into the MathWeb-SB. Due to this integration, lambda-clam now offers its theorem proving expertise to other systems in the MathWeb-SB. On the other hand, lambda-clam can use the services of any reasoning specialist already integrated. We focus on the latter and describe first experimnents on proving theorems by induction using the computational power of the MAPLE system within lambda-clam.

Ordinal Arithmetic: A Case Study for Rippling in a Higher Order Domain

This paper reports a case study in the use of proof planning in the context of higher order syntax. Rippling is a heuristic for guiding rewriting steps in induction that has been used successfully in proof planning inductive proofs using first order representations. Ordinal arithmetic provides a natural set of higher order examples on which transfinite induction may be attempted using rippling. Previously Boyer-Moore style automation could not be applied to such domains. We demonstrate that a higher-order extension of the rippling heuristic is sufficient to plan such proofs automatically. Accordingly, ordinal arithmetic has been implemented in lambda-clam, a higher order proof planning system for induction, and standard undergraduate text book problems have been successfully planned. We show the synthesis of a fixpoint for normal ordinal functions which demonstrates how our automation could be extended to produce more interesting results than the textbook examples tried so far.

The Productive use of Failure to Generate Witnesses from Divergent Proof Attempts for Coinduction

Coinduction is a proof rule. It is the dual of induction. It allows reasoning about non--well--founded structures such as lazy lists or streams and is of particular use for reasoning about equivalences. A central difficulty in the automation of coinductive proof is the choice of a relation (called a bisimulation). We present an automation of coinductive theorem proving. This automation is based on the idea of proof planning. Proof planning constructs the higher level steps in a proof, using knowledge of the general structure of a family of proofs and exploiting this knowledge to control the proof search. Part of proof planning involves the use of failure information to modify the plan by the use of a proof critic which exploits the information gained from the failed proof attempt. Our approach to the problem was to develop a strategy that makes an initial simple guess at a bisimulation and then uses generalisation techniques, motivated by a critic, to refine this guess, so that a larger class of coinductive problems can be automatically verified. The implementation of this strategy has focused on the use of coinduction to prove the equivalence of programs in a small lazy functional language which is similar to Haskell. We have developed a proof plan for coinduction and a critic associated with this proof plan. These have been implemented in CoClam, an extended version of Clam with encouraging results. The planner has been successfully tested on a number of theorems.

The Real-Quaternionic Indicator of Irreducible Self-Conjugate Representations of Real Reductive Algebraic Groups and A Comment on the Local Langlands Correspondence of GL(2, F )

The real-quaternionic indicator, also called the $\delta$ indicator, indicates if a self-conjugate representation is of real or quaternionic type. It is closely related to the Frobenius-Schur indicator, which we call the $\varepsilon$ indicator. The Frobenius-Schur indicator $\varepsilon(\pi)$ is known to be given by a particular value of the central character. We would like a similar result for the $\delta$ indicator. When $G$ is compact, $\delta(\pi)$ and $\varepsilon(\pi)$ coincide. In general, they are not necessarily the same. In this thesis, we will give a relation between the two indicators when $G$ is a real reductive algebraic group. This relation also leads to a formula for $\delta(\pi)$ in terms of the central character. For the second part, we consider the construction of the local Langlands correspondence of $GL(2,F)$ when $F$ is a non-Archimedean local field with odd residual characteristics. By re-examining the construction, we provide new proofs to some important properties of the correspondence. Namely, the construction is independent of the choice of additive character in the theta correspondence.

A aprendizagem da leitura : Concepções sobre a funcionalidade da linguagem escrita e o sucesso na leitura no final do 1º ano de escolaridade

A Aprendizagem da Leitura é um desafio para as crianças que iniciam o primeiro ano de escolaridade tomando-se, para algumas, difícil de alcançar e influenciando negativamente todo o seu percurso escolar. O objectivo deste estudo é procurar perceber qual a relação entre os conhecimentos/concepções que as crianças do primeiro ano de escolaridade possuem, no início do ensino básico, sobre os objectivos/funções da leitura e o sucesso na sua aprendizagem no final do ano lectivo. A amostra foi constituída por 59 crianças, de nacionalidade portuguesa, que no ano lectivo 2006/2007 frequentaram pela primeira vez o primeiro ano de escolaridade, nas Escolas Básicas do 1o Ciclo do Agrupamento de Escolas de Arraiolos e que ainda não saibam ler no início do ano lectivo. A recolha de dados foi feita em dois momentos: no início e no final do ano lectivo. No primeiro momento, em Setembro e Outubro de 2006, foi feita às crianças uma entrevista individual semi-directiva (Alves Martins, 2000), que permitiu conhecer as suas concepções funcionais da leitura e foi também aplicada a Prova de Linguagem Técnica da Leitura/Escrita (Alves Martins, Mata, Peixoto & Monteiro, 2000), para avaliar os conhecimentos de linguagem técnica das crianças; no segundo momento, em Junho de 2007, foi aplicada uma Prova de Leitura (Alves Martins, 2000), para avaliar o desempenho em leitura no final do ano lectivo. Para o tratamento dos dados, a metodologia que utilizámos combinou a análise qualitativa e a análise quantitativa Relativamente à entrevista recorremos à análise qualitativa - análise de conteúdo, quanto à Prova de Linguagem Técnica da Leitura/Escrita e à Prova de Leitura foi feita uma análise quantitativa, seguindo o tratamento estatístico a metodologia proposta pelos autores das provas. ABSTRACT; The Learning of the Reading is a challenge to children who begin the first school year, becoming, for some of them, difficult to achieve and influencing in a negative way their entire school itinerary. The purpose of this study is to try to understand what the relation is between the knowledge/conceptions children in the first school year possess, at the beginning of the elementary education, about the purposes/functions of reading and the success of their learning at the end of the school year. The sample was constituted by 59 children, of Portuguese nationality, that in the school year of 2006/2007 attended for the first time the first school year, in the Elementary Schools of the 1st Cycle of the Assemblage of Schools of Arraiolos and that could not read in the beginning of the school year. The joining of data was made in two moments: in the beginning and in the end of the school year. ln the first moment, in September and October 2006, an individual semi­directive interview (Alves Martins, 2000) was made to the children, which allowed to know their functional conceptions of reading and was also made the Proof of Technical Language of Reading/Writing (Alves Martins, Mata, Peixoto & Monteiro, 2000), in order to evaluate the children's knowledge of technical language; in the second moment, in June 2007, a Proof of Reading (Alves Martins, 2000) was made, to evaluate the performance in reading at the end of the school year. For data treatment, the method we used combined the qualitative analysis and the quantitative analysis. About the interview, we used the qualitative analysis-content analysis, about the Proof of Technical Language of Reading/Writing and the Proof of Reading was made a quantitative analysis, having the statistic treatment followed the method proposed by the authors of the proofs.

Demonstração de fórmulas matemáticas no ensino médio

The objective of this study is to analyze the validity of working with proofs in the classroom and to present a partial list of proofs of mathematical formulae of the Brazilian secondary/high school curriculum. The adaptation of the proofs into the knowledge and abilities of a secondary school student should also be considered. How the teaching of proofs is treated in official publications in Brazil and other countries is also described. Working with proofs provides a number of benefits to the students, including: the development of logical reasoning, argumentative capacity, analytical skills on a daily basis, as well as motivation and a better understanding of mathematics as a science. The convenience of including the teaching of proofs in Brazilian secondary school curriculum and the need of a balance between the abstraction of proofs and contextualization of the school programmes is discussed. The approach of the proof teaching in the classroom can become a motivating factor or, conversely, a discouraging one. The conclusion is that it would be very useful to create a reference list covering the mathematical expressions of school programmes with their respective proofs that can be understood by secondary school students.

A distributed, compact routing protocol for the Internet

The Internet has grown in size at rapid rates since BGP records began, and continues to do so. This has raised concerns about the scalability of the current BGP routing system, as the routing state at each router in a shortest-path routing protocol will grow at a supra-linearly rate as the network grows. The concerns are that the memory capacity of routers will not be able to keep up with demands, and that the growth of the Internet will become ever more cramped as more and more of the world seeks the benefits of being connected. Compact routing schemes, where the routing state grows only sub-linearly relative to the growth of the network, could solve this problem and ensure that router memory would not be a bottleneck to Internet growth. These schemes trade away shortest-path routing for scalable memory state, by allowing some paths to have a certain amount of bounded “stretch”. The most promising such scheme is Cowen Routing, which can provide scalable, compact routing state for Internet routing, while still providing shortest-path routing to nearly all other nodes, with only slightly stretched paths to a very small subset of the network. Currently, there is no fully distributed form of Cowen Routing that would be practical for the Internet. This dissertation describes a fully distributed and compact protocol for Cowen routing, using the k-core graph decomposition. Previous compact routing work showed the k-core graph decomposition is useful for Cowen Routing on the Internet, but no distributed form existed. This dissertation gives a distributed k-core algorithm optimised to be efficient on dynamic graphs, along with with proofs of its correctness. The performance and efficiency of this distributed k-core algorithm is evaluated on large, Internet AS graphs, with excellent results. This dissertation then goes on to describe a fully distributed and compact Cowen Routing protocol. This protocol being comprised of a landmark selection process for Cowen Routing using the k-core algorithm, with mechanisms to ensure compact state at all times, including at bootstrap; a local cluster routing process, with mechanisms for policy application and control of cluster sizes, ensuring again that state can remain compact at all times; and a landmark routing process is described with a prioritisation mechanism for announcements that ensures compact state at all times.

Przestrzenne formy upamiętniania Zagłady

This book is a synthesizing reflection on the Holocaust commemoration, in which space becomes a starting point for discussion. The author understands space primarily as an amalgam of physical and social components, where various commemorative processes may occur. The first part of the book draws attention to the material aspect of space, which determines its character and function. Material culture has been a long ignored and depreciated dimension of human culture in the humanities and social sciences, because it was perceived as passive and fully controlled by human will, and therefore insignificant in the course of social and historical processes. An example of the Nazi system perfectly illustrates how important were the restrictions and prohibitions on the usage of mundane objects, and in general, the whole material culture in relation to macro and micro space management — the state, cities, neighborhoods and houses, but also parks and swimming pools, factories and offices or shops and theaters. The importance of things and space was also clearly visible in exploitative policies present in overcrowded ghettos and concentration and death camps. For this very reason, when we study spatial forms of Holocaust commemoration, it should be acknowledged that the first traces, proofs and mementoes of the murdered were their things. The first "monuments" showing the enormity of the destruction are thus primarily gigantic piles of objects — shoes, glasses, toys, clothes, suitcases, toothbrushes, etc., which together with the extensive camps’ space try to recall the scale of a crime impossible to understand or imagine. The first chapter shows the importance of introducing the material dimension in thinking about space and commemoration, and it ends with a question about one of the key concepts for the book, a monument, which can be understood as both object (singular or plural) and architecture (sculptures, buildings, highways). However, the term monument tends to be used rather in a later and traditional sense, as an architectural, figurative form commemorating the heroic deeds, carved in stone or cast in bronze. Therefore, the next chapter reconstructs this narrower line of thinking, together with a discussion about what form a monument commemorating a subject as delicate and sensitive as the Holocaust should take on. This leads to an idea of the counter-monument, the concept which was supposed to be the answer to the mentioned representational dilemma on the one hand, and which would disassociate it from the Nazi’s traditional monuments on the other hand. This chapter clarifies the counter-monument definition and explains the misunderstandings and confusions generated on the basis of this concept by following the dynamics of the new commemorative form and by investigating monuments from the ‘80s and ‘90s erected in Germany. In the next chapter, I examine various forms of the Holocaust commemoration in Berlin, a city famous for its bold, monumental, and even controversial projects. We find among them the entire spectrum of memorials – big, monumental, and abstract forms, like Peter Eisenman’s Memorial to the Murdered Jews of Europe or Daniel Liebeskind’s Jewish Museum Berlin; flat, invisible, and employing the idea of emptiness, like Christian Boltanski’s Missing House or Micha Ullman’s Book Burning Memorial; the dispersed and decentralized, like Renata Stih and Frieder Schnock’s Memory Places or Gunter Demnig’s Stumbling Blocks. I enrich descriptions of the monuments by signaling at this point their second, extended life, which manifests itself in the alternative modes of (mis)use, consisting of various social activities or artistic performances. The formal wealth of the outlined projects creates a wide panorama of possible solutions to the Holocaust commemoration problems. However, the discussions accompanying the building of monuments and their "future life" after realization emphasize the importance of the social component that permeates the biography of the monument, and therefore significantly influences its foreseen design. The book also addresses the relationship of space, place and memory in a specific situation, when commemoration is performed secretly or remains as unrealized potential. Although place is the most common space associated with memory, today the nature of this relationship changes, and is what indicates popularity and employment of such terms as Marc Augé’s non-places or Pierre Nora’s site of memory. I include and develop these concepts about space and memory in my reflections to describe qualitatively different phenomena occurring in Central and Eastern European countries. These are unsettling places in rural areas like glades or parking lots, markets and playgrounds in urban settings. I link them to the post-war time and modernization processes and call them sites of non-memory and non-sites of memory. Another part of the book deals with a completely different form of commemoration called Mystery of memory. Grodzka Gate - NN Theatre in Lublin initiated it in 2000 and as a form it situates itself closer to the art of theater than architecture. Real spaces and places of everyday interactions become a stage for these performances, such as the “Jewish town” in Lublin or the Majdanek concentration camp. The minimalist scenography modifies space and reveals its previously unseen dimensions, while the actors — residents and people especially related to places like survivors and Righteous Among the Nations — are involved in the course of the show thanks to various rituals and symbolic gestures. The performance should be distinguished from social actions, because it incorporates tools known from religious rituals and art, which together saturate the mystery of memory with an aura of uniqueness. The last discussed commemoration mode takes the form of exposition space. I examine an exhibition concerning the fate of the incarcerated children presented in one of the barracks of the Majdanek State Museum in Lublin. The Primer – Children in Majdanek Camp is unique for several reasons. First, because even though it is exhibited in the camp barrack, it uses a completely different filter to tell the story of the camp in comparison to the exhibitions in the rest of the barracks. For this reason, one experiences immersing oneself in all subsequent levels of space and narrative accompanying them – at first, in a general narrative about the camp, and later in a specifically arranged space marked by children’s experiences, their language and thinking, and hence formed in a way more accessible for younger visitors. Second, the exhibition resigns from didacticism and distancing descriptions, and takes an advantage of eyewitnesses and survivors’ testimonies instead. Third, the exhibition space evokes an aura of strangeness similar to a fairy tale or a dream. It is accomplished thanks to the arrangement of various, usually highly symbolic material objects, and by favoring the fragrance and phonic sensations, movement, while belittling visual stimulations. The exhibition creates an impression of a place open to thinking and experiencing, and functions as an asylum, a radically different form to its camp surrounding characterized by a more overwhelming and austere space.

GeoGebraTUTOR : développement d’un système tutoriel autonome pour l’accompagnement d’élèves en situation de résolution de problèmes de démonstration en géométrie plane et genèse d’un espace de travail géométrique idoine

Travaux d'études doctorales réalisées conjointement avec les travaux de recherches doctorales de Nicolas Leduc, étudiant au doctorat en génie informatique à l'École Polytechnique de Montréal.