Permutative conversions in intuitionistic multiary sequent calculi with cuts

This work presents an extension with cuts of Schwichtenberg's multiary sequent calculus. We identify a set of permutative conversions on it, prove their termination and confluence and establish the permutability theorem. We present our sequent calculus as the typing system of the {\em generalised multiary $\lambda$-calculus} lambda-Jm, a new calculus introduced in this work. Lambda-Jm corresponds to an extension of $\lambda$-calculus with a notion of {\em generalised multiary application}, which may be seen as a function applied to a list of arguments and then explicitly substituted in another term. Proof-theoretically the corresponding typing rule encompasses, in a modular way, generalised eliminations of von Plato and Herbelin's head cuts.Fundação para a Ciência e a Tecnologia (FCT)

A calculus of multiary sequent terms

Multiary sequent terms were originally introduced as a tool for proving termination of permutative conversions in cut-free sequent calculus. This work develops the language of multiary sequent terms into a term calculus for the computational (Curry-Howard) interpretation of a fragment of sequent calculus with cuts and cut-elimination rules. The system, named generalised multiary lambda-calculus, is a rich extension of the lambda-calculus where the computational content of the sequent calculus format is explained through an enlarged form of the application constructor. Such constructor exhibits the features of multiarity (the ability of forming lists of arguments) and generality (the ability of prescribing a kind of continuation). The system integrates in a modular way the multiary lambda-calculus and an isomorphic copy of the lambda-calculus with generalised application LambdaJ (in particular, natural deduction is captured internally up to isomorphism). In addition, the system: (i) comes with permutative conversion rules, whose role is to eliminate the new features of application; (ii) is equipped with reduction rules --- either the mu-rule, typical of the multiary setting, or rules for cut-elimination, which enlarge the ordinary beta-rule. This paper establishes the meta-theory of the system, with emphasis on the role of the mu-rule, and including a study of the interaction of reduction and permutative conversions.Fundação para a Ciência e a Tecnologia (FCT

Characterising strongly normalising intuitionistic sequent terms

This paper gives a characterisation, via intersection types, of the strongly normalising terms of an intuitionistic sequent calculus (where LJ easily embeds). The soundness of the typing system is reduced to that of a well known typing system with intersection types for the ordinary lambda-calculus. The completeness of the typing system is obtained from subject expansion at root position. This paper's sequent term calculus integrates smoothly the lambda-terms with generalised application or explicit substitution. Strong normalisability of these terms as sequent terms characterises their typeability in certain "natural'' typing systems with intersection types. The latter are in the natural deduction format, like systems previously studied by Matthes and Lengrand et al., except that they do not contain any extra, exceptional rules for typing generalised applications or substitution

Refocusing generalised normalisation

When defined with general elimination/application rules, natural deduction and $\lambda$-calculus become closer to sequent calculus. In order to get real isomorphism, normalisation has to be defined in a ``multiary'' variant, in which reduction rules are necessarily non-local (reason: nomalisation, like cut-elimination, acts at the \emph{head} of applicative terms, but natural deduction focuses at the \emph{tail} of such terms). Non-local rules are bad, for instance, for the mechanization of the system. A solution is to extend natural deduction even further to a \emph{unified calculus} based on the unification of cut and general elimination. In the unified calculus, a sequent term behaves like in the sequent calculus, whereas the reduction steps of a natural deduction term are interleaved with explicit steps for bringing heads to focus. A variant of the calculus has the symmetric role of improving sequent calculus in dealing with tail-active permutative conversions

Questions and Answers in Extreme Energy Cosmic Rays – a guide to explore the data set of the Pierre Auger Observatory

The Pierre Auger Observatory is the largest extensive air shower detector, covering 3000 km 2 in Argentina. The Observatory makes available, for educational and outreach purposes, 1% of its cosmic ray data set, corresponding after 10 years of running to more than 35 000 cosmic ray events. Several different proposals of educational activities have been developed within the collaboration and are available. We will focus on the activity guide we developed with the aim of exploring the rich education and outreach potential of cosmic rays with Portuguese high school students. In this guide we use the Auger public data set as a starting point to introduce open questions on the origin, nature and spectrum of high energy cosmic rays. To address them, the students learn about the air-shower cascade development, data reconstruction and its statistical analysis. The guide has been used both in the context of student summer internships at research labs and directly in schools, under the supervision of trained teachers and in close collaboration with Auger researchers. It is now available in Portuguese, English and Spanish.Peer Reviewe

Permutability in proof terms for intuitionistic sequent calculus with cuts

This paper gives a comprehensive and coherent view on permutability in the intuitionistic sequent calculus with cuts. Specifically we show that, once permutability is packaged into appropriate global reduction procedures, it organizes the internal structure of the system and determines fragments with computational interest, both for the computation-as-proof-normalization and the computation-as-proof-search paradigms. The vehicle of the study is a lambda-calculus of multiary proof terms with generalized application, previously developed by the authors (the paper argues this system represents the simplest fragment of ordinary sequent calculus that does not fall into mere natural deduction). We start by adapting to our setting the concept of normal proof, developed by Mints, Dyckhoff, and Pinto, and by defining natural proofs, so that a proof is normal iff it is natural and cut-free. Natural proofs form a subsystem with a transparent Curry-Howard interpretation (a kind of formal vector notation for lambda-terms with vectors consisting of lists of lists of arguments), while searching for normal proofs corresponds to a slight relaxation of focusing (in the sense of LJT). Next, we define a process of permutative conversion to natural form, and show that its combination with cut elimination gives a concept of normalization for the sequent calculus. We derive a systematic picture of the full system comprehending a rich set of reduction procedures (cut elimination, flattening, permutative conversion, normalization, focalization), organizing the relevant subsystems and the important subclasses of cut-free, normal, and focused proofs.Partially financed by FCT through project UID/MAT/00013/2013, and by COST action CA15123 EUTYPES. The first and the last authors were partially financed by Fundação para a Ciência e a Tecnologia (FCT) through project UID/MAT/00013/2013. The first author got financial support by the COST action CA15123 EUTYPES.info:eu-repo/semantics/publishedVersio

Kaposi’s sarcoma, case report

O Sarcoma de Kaposi (SK) é um distúrbio angioproliferativo descrito como doença benigna de pessoas idosas. Divide- se em 4 tipos: O Clássico, epidémico, endêmico e iatrogénico. Os autores descrevem o caso de um homem caucasiano de 50 anos, português, que iniciou a sintomatologia 6 anos antes do internamento com lesões urticariformes na perna direita e perda ponderal de 10 kg em 6 meses. Por agravamento das lesões e aparecimento de púrpura nos membros inferiores recorreu ao hospital. O exame objetivo era normal à exceção de púrpuras dispersas com relevo, descamativas e violáceas na região plantar e restante membros inferiores, membros superiores e tronco. As serologias para o HIV 1 e 2 foram negativas a serologia viral para o Herpes virus humano 8 IGG foi positivo, PCR H8 positivo, a biópsia das lesões com histologia foi compatível com Sarcoma de Kaposi. Iniciou o 1º ciclo de Doxorrubicina lipossómica peguilhada e manteve seguimento em Hospital dia de Oncologia.info:eu-repo/semantics/publishedVersio

Doação e transplantes de órgãos: Contribuições dos profissionais sobre o trabalho interprofissional nos programas

Objective: This study aimed to identify the contributions for improvement in the interprofessional working relationship pointed out by professionals involved in organ and tissue procurement and transplantation programs. Method: exploratory study with a quantiqualitative approach conducted over a period of 21 months, with the participation of health professionals invited to complete an online questionnaire on the Google form platform. After collection, the quantitative data were organized and analyzed descriptively, and the qualitative data were categorized and submitted to content analysis. Results: 130 health professionals participated in the study, 84% were female, of which 64% said they were white, between 41-59 years old, and 31% had worked for more than 15 years in the programs. The categories identified were: working conditions; appreciation of non-medical professionals; psychological support to professionals and funding for training of professionals pointed out as improvements in the work relationship in the programs. Conclusion: the study identified that working conditions and greater valorization of the interprofessional team allied to offering psychological support to professionals are necessary and important strategies, and may bring impacts on the satisfaction of professionals, on mental health, in addition to improvements in work processes, impacting transplantation rates.Objetivo: Com este estudo, objetivou-se identificar as contribuições de melhoria na relação de trabalho interprofissional apontadas por profissionais envolvidos nos programas de procura e de transplantação de órgãos e tecidos. Método: estudo exploratório com abordagem quanti-qualitativo realizado no período de 21 meses, com a participação de profissionais da área da saúde convidados a preencher um questionário online da plataforma de formulários do Google. Após a coleta, organizaram-se os dados quantitativos, analisando-os de maneira descritiva e, em categorias, os dados qualitativos, submetendo-os à análise de conteúdo. Resultados:participaram do estudo 130 profissionais de saúde, sendo 84% do gênero feminino, dos quais 64% se declararam de cor de pele branca; de faixa etária entre 41–59 anos, sendo que (31%) trabalhavam há mais de quinze anos nos programas. As categorias identificadas foram: condições de trabalho; valorização dos profissionais não médicos; suporte psicológico e financiamento para capacitação dos profissionais apontadas como melhorias na relação de trabalho nos programas. Conclusão: o estudo possibilitou identificar que na relação de trabalho as condições laborais e maior valorização da equipe interprofissional aliadas ao oferecimento de suporte psicológico aos profissionais são estratégias necessárias, podendo trazer impactos na satisfação dos profissionais, na saúde mental, além de melhorias nos processos de trabalho, impactando as taxas de transplantes.info:eu-repo/semantics/publishedVersio