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Let $E/\mathbb{Q}$ be an elliptic curve with full rational 2-torsion. As d varies over squarefree integers, we study the behaviour of the quadratic twists $E_d$ over a fixed quadratic extension $K/\mathbb{Q}$. We prove that for 100% of twists the dimension of the 2-Selmer group over K is given by an explicit local formula, and use this to show that this dimension follows an Erd\H{o}s--Kac type distribution. This is in stark contrast to the distribution of the dimension of the corresponding 2-Selmer groups over $\mathbb{Q}$, and this discrepancy allows us to determine the distribution of the 2-torsion in the Shafarevich--Tate groups of the $E_d$ over K also. As a consequence of our methods we prove that, for 100% of twists d, the action of $\operatorname{Gal}(K/\mathbb{Q})$ on the 2-Selmer group of $E_d$ over K is trivial, and the Mordell--Weil group $E_d(K)$ splits integrally as a direct sum of its invariants and anti-invariants. On the other hand, we give examples of thin families of quadratic twists in which a positive proportion of the 2-Selmer groups over K have non-trivial $\operatorname{Gal}(K/\mathbb{Q})$-action, illustrating that the previous results are genuinely statistical phenomena., Comment: Added additional hypothesis to the statement of Corollary 6.7. Other minor corrections following referee report

The face of neurology in clinical practice is changing. Neurology is no longer primarily a diagnostic specialty. As more therapeutic treatments become available in all fields from epilepsy to multiple sclerosis, early and accurate diagnosis is increasingly required so that patients can benefit from early treatment aiming to reduce the lifelong burden of neuro­logical disease. Diagnosis of neurological disorders is often considered by junior doc­tors to be highly complex and, as such, is responsible for a great deal of anxiety. One of the most difficult challenges can be determining the loca­tion of the lesion. A helpful approach to this is by analysis of the patterns that each lesion produces. Table 8.1 describes some of the common patterns seen in clinical practice, and the questions in this chapter will attempt to highlight some of the other specific presentations needed in assessing the neurology patient.

Nested datatypes generalise regular datatypes in much the same way that context-free languages generalise regular ones. Although the categorical semantics of nested types turns out to be similar to the regular case, the fold functions are more limited because they can only describe natural transformations. Practical considerations therefore dictate the introduction of a generalised fold function in which this limitation can be overcome. In the paper we show how to construct generalised folds systematically for each nested datatype, and show that they possess a uniqueness property analogous to that of ordinary folds. As a consequence, generalised folds satisfy fusion properties similar to those developed for regular datatypes. Such properties form the core of an effective calculational theory of inductive datatypes.

This paper is an exploration of the parallel graph reduction approach to parallel functional programming, illustrated by a particular example: pipelined, dynamically-scheduled implementation of search, updates and read-modify-write transactions on an in-store binary search tree. We use program transformation, execution-driven simulation and analytical modelling to expose the maximum potential parallelism, the minimum communication and synchronisation overheads, and to control the overall space requirement. We begin with a lazy functional program specifying a series of transactions on a binary tree, each involving several searches and updates, in a side-effect-free fashion. Transformation of the source code produces a formulation of the program with greater locality and larger grain size than can be achieved using naive parallelization methods, and we show that, with care, these tasks can be scheduled effectively. Even with a workload using random keys, significant spatial locality is found, and we evaluate a modified cache coherency protocol which avoids false sharing so that large cache lines can be used to minimise the number of messages required. As expected with a pipeline, the application should reach a steady state as soon as the first transaction is completed. However, if the network latency is too large, the rate of completion lags behind the rate at which work is admitted, and internal queues grow without bound. We determine the conditions under which this occurs, and show how it can be avoided while maximising speedup.

“I have no data yet. It is a capital mistake to theorise before one has data.” Sir Arthur Conan Doyle The Adventures of Sherlock Holmesde Bruijn notation is a coding of lambda terms in which each occurrence of a bound variable x is replaced by a natural number, indicating the ‘distance’ from the occurrence to the abstraction that introduced x. One might suppose that in any datatype for representing de Bruijn terms, the distance restriction on numbers would have to be maintained as an explicit datatype invariant. However, by using a nested (or non-regular) datatype, we can define a representation in which all terms are well-formed, so that the invariant is enforced automatically by the type system. Programming with nested types is only a little more difficult than programming with regular types, provided we stick to well-established structuring techniques. These involve expressing inductively defined functions in terms of an appropriate fold function for the type, and using fusion laws to establish their properties. In particular, the definition of lambda abstraction and beta reduction is particularly simple, and the proof of their associated properties is entirely mechanical.

Reynolds' abstraction theorem (Reynolds, J. C. (1983) Types, abstraction and parametric polymorphism,Inf. Process.83(1), 513–523) shows how a typing judgement in System F can be translated into a relational statement (in second-order predicate logic) about inhabitants of the type. We obtain a similar result for pure type systems (PTSs): for any PTS used as a programming language, there is a PTS that can be used as a logic for parametricity. Types in the source PTS are translated to relations (expressed as types) in the target. Similarly, values of a given type are translated to proofs that the values satisfy the relational interpretation. We extend the result to inductive families. We also show that the assumption that every term satisfies the parametricity condition generated by its type is consistent with the generated logic.

Reynolds' abstraction theorem shows how a typing judgement in System F can be translated into a relational statement (in second order predicate logic) about inhabitants of the type. We (in second order predicate logic) about inhabitants of the type. We obtain a similar result for a single lambda calculus (a pure type system), in which terms, types and their relations are expressed. Working within a single system dispenses with the need for an interpretation layer, allowing for an unusually simple presentation. While the unification puts some constraints on the type system (which we spell out), the result applies to many interesting cases, including dependently-typed ones.

This study examines the financing of housing production and consumption in five early twentieth-century Toronto suburbs. The study areas range in status from upper-middle class to working class.Research findings include the persistence of a traditional pattern of finance characterized by high levels of cash transactions and private financing. Institutional lenders, while influential in financing high-status housing played a relatively minor role in the overall provision of mortgage funding.The study adds to our understanding of the role of housing finance during this formative period when the major element of modern suburbanization, including the emergence of a corporate land development industry, were being established., Cette étude se penche sur le financement de la production et de la consommation des logements dans cinq subdivisions de Toronto au début du 20e siècle. Elle examine principalement les diverses sources de financement du logement à l’intérieur des villes. Cette étude révèle la persistance d’une formule traditionnelle de financement du logement, caractérisée par une abondance d’argent comptant et de financement privé. Les établissements de prêts jouèrent un rôle relativement mineur dans le financement des hypothèques, quoique leur importance ait été significative dans le financement des logements de luxe. La prépondérance d’argent comptant, de financement privé et de prêts hypothécaires consentis par les vendeurs montre que Toronto a une aptitude remarquable à financer le développement de ses logements.

In this article, we introduce Applicative functors – an abstract characterisation of an applicative style of effectful programming, weaker than Monads and hence more widespread. Indeed, it is the ubiquity of this programming pattern that drew us to the abstraction. We retrace our steps in this article, introducing the applicative pattern by diverse examples, then abstracting it to define the Applicative type class and introducing a bracket notation that interprets the normal application syntax in the idiom of an Applicative functor. Furthermore, we develop the properties of applicative functors and the generic operations they support. We close by identifying the categorical structure of applicative functors and examining their relationship both with Monads and with Arrow.

Transaction processing can be formulated as a simple functional program operating on a stream of transaction requests and a tree-structured database. In this paper we use algebraic transformation of the initial program to yield an optimistic implementation in which unnecessary synchronization is eliminated, thereby allowing concurrent processing of transactions. A detailed simulation is used to study the program's behaviour and to assess scheduling policies based on the characteristics of the target architecture. Our results show that good speedups can be achieved, and that transformation can be used to derive a highly concurrent program with better locality and grain size. >

Darwin is a configuration language for distributed and parallel programs, providing a hierarchical structure of components with dynamic binding. To specify precisely the behavior of Darwin programs, the authors sketch a translation of the features of the language into the pi -calculus, a formalism for modeling concurrent processes. The match between underlying models for Darwin and pi -calculus is good. An example to demonstrate each language is developed. This is followed by a formal semantics of Darwin in the calculus. >

SUMMARYAn indirect fluorescent antibody test was used to detect the presence ofStreptococcus suistype 2 in nasal and pharyngeal swabs taken from pigs in Papua New Guinea. The rate of carriage for the two sites in domesticated indigenous village pigs was 0·5 and 2·5% respectively, compared to 39 and 43% for intensively reared pigs. These findings were supported by the results of a serological survey, using an enzyme linked immunosorbent assay, in which 87% of intensively reared pigs but only 8% of village pigs were seropositive toS. suistype 2.It is proposed that in intensive piggeriesS. suistype 2 is continually cycled between pigs. In village pigs, the low population density and harsh environmental conditions prevents this cycle of infection.

The non-deterministic lambda-calculus is a tiny core language in terms of which all the declaratively understood constructs of constraint functional languages may be defined. This paper describes a denotational semantics based on lower powerdomains, and a polymorphic type system. The calculus has a confluent operational semantics, which may be formulated in several ways—an extension of de Bruijn’s calculus is used here.

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L’article traite de planification suburbaine à partir d’un examen des activités de la Home Smith and Company, et en particulier du développement et de la construction de Kingsway Park, une des premières subdivisions de cette compagnie. De plus, l’étude montre que la période de l’entre-deux-guerres constitue une période charnière dans l’élaboration du processus de construction du milieu urbain, servant ainsi de transition entre le système fragmenté utilisé durant la période victorienne pour la construction des banlieues et l’actuel processus, fortement intégré, de développement du territoire., An examination of planned suburbanisation is provided in this study through a discussion of the activities of the Home Smith and Company, and in particular, by an examination of the development and building of one of the Company's premier subdivisions, Kingsway Park. The study presents further evidence that the inter-war period encompassed a pivotal period in the evolving city-building process, bridging the transition between the fragmentary system employed in building the Victorian suburbs and the highly integrated land development process in place today.