A Bicategorical Model for Finite Nondeterminism

Finiteness spaces were introduced by Ehrhard as a refinement of the relational model of linear logic. A finiteness space is a set equipped with a class of finitary subsets which can be thought of being subsets that behave like finite sets. A morphism between finiteness spaces is a relation that preserves the finitary structure. This model provided a semantics for finite non-determism and it gave a semantical motivation for differential linear logic and the syntactic notion of Taylor expansion. In this paper, we present a bicategorical extension of this construction where the relational model is replaced with the model of generalized species of structures introduced by Fiore et al. and the finiteness property now relies on finite presentability

A Profunctorial Scott Semantics

In this paper, we study the bicategory of profunctors with the free finite coproduct pseudo-comonad and show that it constitutes a model of linear logic that generalizes the Scott model. We formalize the connection between the two models as a change of base for enriched categories which induces a pseudo-functor that preserves all the linear logic structure. We prove that morphisms in the co-Kleisli bicategory correspond to the concept of strongly finitary functors (sifted colimits preserving functors) between presheaf categories. We further show that this model provides solutions of recursive type equations which provides 2-dimensional models of the pure lambda calculus and we also exhibit a fixed point operator on terms

Stabilized profunctors and stable species of structures

We introduce a bicategorical model of linear logic which is a novel variation of the bicategory of groupoids, profunctors, and natural transformations. Our model is obtained by endowing groupoids with additional structure, called a kit, to stabilize the profunctors by controlling the freeness of the groupoid action on profunctor elements. The theory of generalized species of structures, based on profunctors, is refined to a new theory of \emph{stable species} of structures between groupoids with Boolean kits. Generalized species are in correspondence with analytic functors between presheaf categories; in our refined model, stable species are shown to be in correspondence with restrictions of analytic functors, which we characterize as being stable, to full subcategories of stabilized presheaves. Our motivating example is the class of finitary polynomial functors between categories of indexed sets, also known as normal functors, that arises from kits enforcing free actions. We show that the bicategory of groupoids with Boolean kits, stable species, and natural transformations is cartesian closed. This makes essential use of the logical structure of Boolean kits and explains the well-known failure of cartesian closure for the bicategory of finitary polynomial functors between categories of set-indexed families and cartesian natural transformations. The paper additionally develops the model of classical linear logic underlying the cartesian closed structure and clarifies the connection to stable domain theory.Comment: FSCD 2022 special issue of Logical Methods in Computer Science, minor changes (incorporated reviewers comments

X-linked agammaglobulinemia (XLA) : Phenotype, diagnosis, and therapeutic challenges around the world

Background: X-linked agammaglobulinemia is an inherited immunodeficiency recognized since 1952. In spite of seven decades of experience, there is still a limited understanding of regional differences in presentation and complications. This study was designed by the Primary Immunodeficiencies Committee of the World Allergy Organization to better understand regional needs, challenges and unique patient features. Methods: A survey instrument was designed by the Primary Immunodeficiencies Committee of the World Allergy Organization to collect both structured and semi-structured data on X-linked agammaglobulinemia. The survey was sent to 54 centers around the world chosen on the basis of World Allergy Organization participation and/or registration in the European Society for Immunodeficiencies. There were 40 centers that responded, comprising 32 countries. Results: This study reports on 783 patients from 40 centers around the world. Problems with diagnosis are highlighted by the reported delays in diagnosis>24 months in 34% of patients and the lack of genetic studies in 39% of centers Two infections exhibited regional variation. Vaccine-associated paralytic poliomyelitis was seen only in countries with live polio vaccination and two centers reported mycobacteria. High rates of morbidity were reported. Acute and chronic lung diseases accounted for 41% of the deaths. Unusual complications such as inflammatory bowel disease and large granular lymphocyte disease, among others were specifically enumerated, and while individually uncommon, they were collectively seen in 20.3% of patients. These data suggest that a broad range of both inflammatory, infectious, and autoimmune conditions can occur in patients. The breadth of complications and lack of data on management subsequently appeared as a significant challenge reported by centers. Survival above 20 years of age was lowest in Africa (22%) and reached above 70% in Australia, Europe and the Americas. Centers were asked to report their challenges and responses (n = 116) emphasized the difficulties in access to immunoglobulin products (16%) and reflected the ongoing need for education of both patients and referring physicians. Conclusions: This is the largest study of patients with X-linked agammaglobulinemia and emphasizes the continued morbidity and mortality of XLA despite progress in diagnosis and treatment. It presents a world view of the successes and challenges for patients and physicians alike. A pivotal finding is the need for education of physicians regarding typical symptoms suggesting a possible diagnosis of X-linked agammaglobulinemia and sharing of best practices for the less common complications.Peer reviewe

The evolving SARS-CoV-2 epidemic in Africa: Insights from rapidly expanding genomic surveillance

INTRODUCTION Investment in Africa over the past year with regard to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) sequencing has led to a massive increase in the number of sequences, which, to date, exceeds 100,000 sequences generated to track the pandemic on the continent. These sequences have profoundly affected how public health officials in Africa have navigated the COVID-19 pandemic. RATIONALE We demonstrate how the first 100,000 SARS-CoV-2 sequences from Africa have helped monitor the epidemic on the continent, how genomic surveillance expanded over the course of the pandemic, and how we adapted our sequencing methods to deal with an evolving virus. Finally, we also examine how viral lineages have spread across the continent in a phylogeographic framework to gain insights into the underlying temporal and spatial transmission dynamics for several variants of concern (VOCs). RESULTS Our results indicate that the number of countries in Africa that can sequence the virus within their own borders is growing and that this is coupled with a shorter turnaround time from the time of sampling to sequence submission. Ongoing evolution necessitated the continual updating of primer sets, and, as a result, eight primer sets were designed in tandem with viral evolution and used to ensure effective sequencing of the virus. The pandemic unfolded through multiple waves of infection that were each driven by distinct genetic lineages, with B.1-like ancestral strains associated with the first pandemic wave of infections in 2020. Successive waves on the continent were fueled by different VOCs, with Alpha and Beta cocirculating in distinct spatial patterns during the second wave and Delta and Omicron affecting the whole continent during the third and fourth waves, respectively. Phylogeographic reconstruction points toward distinct differences in viral importation and exportation patterns associated with the Alpha, Beta, Delta, and Omicron variants and subvariants, when considering both Africa versus the rest of the world and viral dissemination within the continent. Our epidemiological and phylogenetic inferences therefore underscore the heterogeneous nature of the pandemic on the continent and highlight key insights and challenges, for instance, recognizing the limitations of low testing proportions. We also highlight the early warning capacity that genomic surveillance in Africa has had for the rest of the world with the detection of new lineages and variants, the most recent being the characterization of various Omicron subvariants. CONCLUSION Sustained investment for diagnostics and genomic surveillance in Africa is needed as the virus continues to evolve. This is important not only to help combat SARS-CoV-2 on the continent but also because it can be used as a platform to help address the many emerging and reemerging infectious disease threats in Africa. In particular, capacity building for local sequencing within countries or within the continent should be prioritized because this is generally associated with shorter turnaround times, providing the most benefit to local public health authorities tasked with pandemic response and mitigation and allowing for the fastest reaction to localized outbreaks. These investments are crucial for pandemic preparedness and response and will serve the health of the continent well into the 21st century

Constructions d'orthogonalité bicatégoriques pour la logique linéaire

Cette thèse porte sur la sémantique bicatégorique de la logique linéaire. Elle s'incrit dans le cadre de catégorification des modèles de calculs où l'on remplace des sémantiques où les types sont interprétés par des ensembles ou des préordres par des structures catégoriques plus riches permettant d'obtenir des invariants mathématiques plus fins. Nous nous intéressons spécifiquement à la catégorification du modèle relationel de la logique linéaire par le modèle des espèces généralisées introduit par Fiore, Gambino, Hyland et Winskel ansi qu'à ses raffinements par des constructions d'orthogonalité. Nous présentons dans un premier temps une généralisation bicatégorique du modèle des espaces de finitude introduit par Ehrhard où nous introduisons une orthogonalité sur la bicatégorie des espèces nous permettant d'obtenir une bicatégorie où les interactions entre programmes et environnements sont finies. Toute la structure de logique linéaire du modèle des espèces peut alors être transposée dans cette nouvelle bicatégorie. Nous considérons ensuite la catégorification de la notion de stabilité des fonctions stables à la Berry vers les foncteurs stables. Nous combinons les espèces de structure avec la stabilité grâce à une orthogonalité sur les sous-groupes d'endomorphismes pour chaque objet d'un groupoïde. Cette orthogonalité peut aussi être traduite en une orthogonalité sur la catégorie de préfaiscaux d'un groupoïde nous permettant de restreindre les foncteurs analytiques associés aux espèces à des foncteurs stables et nous montrons qu'ils forment une bicatégorie cartésienne fermée. Nous étudions dernièrement la catégorification du modèle de Scott de la logique linéaire et son lien avec le modèle des espèces. Nous commençons par montrer que la bicatégorie des profoncteurs équipée de la pseudo-comonade des coproduits finis est un modèle de la logique linéaire catégorifiant le modèle de Scott. Nous introduisons ensuite une orthogonalité entre la bicatégorie de Scott obtenue et la bicatégorie des espèces et obtenons une nouvelle bicatégorie constituant une première étape afin de relier la substitution linéaire et non-linéaire dans ce contexte.This thesis is concerned with the bicategorical semantics of linear logic. We follow the line of research of categorifying models of linear logic by replacing semantics where types are sets or preorders with richer categorical structures providing finer mathematical invariants. In this thesis, we are interested in the categorification of the relational model of linear logic with the generalized species model introduced by Fiore, Gambino, Hyland and Winskel; and its refinements using orthogonality constructions. We first present a bicategorical generalization of the model of finiteness spaces introduced by Ehrhard where we introduce an orthogonality construction on the bicategory of profunctors based on finite presentability to obtain a new bicategory where all interactions between programs and environments are enforced to be finite. We show that all the linear logic structure in the bicategory of profunctors can be refined to this new bicategory. We then consider the categorication of the computational notion of stability from stable functions to stable functors. We bring together generalized species of structures and stability by refining the species model with an orthogonality on subgroups of endomorphisms for each object in a groupoid. We show that this orthogonality can also be translated to an orthogonality on the category of presheaves associated with a groupoid that allows us to restrict the analytic functors to stable functors and prove that they form a cartesian closed bicategory. We lastly study the categorification of the qualitative Scott model of linear logic and its connection with the quantitative species model of Fiore et al. We start by showing that the bicategory of profunctors with the finite coproduct pseudo-comonad is a model of linear logic that categorifies the Scott model. We then define an orthogonality between the Scott bicategory and the species bicategory that allows us to construct a new bicategory giving us a first step towards connecting linear and non-linear substitution in this setting

A combinatorial approach to higher-order structure for polynomial functors

Polynomial functors are categorical structures used in a variety of applications across theoretical computer science; for instance, in database theory, denotational semantics, functional programming, and type theory. A well-known problem is that the bicategory of finitary polynomial functors between categories of indexed sets is not cartesian closed, despite its success and influence on denotational models and linear logic. This paper introduces a formal bridge between the model of finitary polynomial functors and the combinatorial theory of generalised species of structures. Our approach consists in viewing finitary polynomial functors as free analytic functors, which correspond to free generalised species. In order to systematically consider finitary polynomial functors from this combinatorial perspective, we study a model of groupoids with additional logical structure; this is used to constrain the generalised species between them. The result is a new cartesian closed bicategory that embeds finitary polynomial functors.Research partially supported by EPSRC grant EP/V002309/1

Fixpoint constructions in focused orthogonality models of linear logic

Orthogonality is a notion based on the duality between programs and theirenvironments used to determine when they can be safely combined. For instance,it is a powerful tool to establish termination properties in classical formalsystems. It was given a general treatment with the concept of orthogonalitycategory, of which numerous models of linear logic are instances, by Hyland andSchalk. This paper considers the subclass of focused orthogonalities. Wedevelop a theory of fixpoint constructions in focused orthogonality categories.Central results are lifting theorems for initial algebras and final coalgebras.These crucially hinge on the insight that focused orthogonality categories arerelational fibrations. The theory provides an axiomatic categorical frameworkfor models of linear logic with least and greatest fixpoints of types. Wefurther investigate domain-theoretic settings, showing how to lift bifreealgebras, used to solve mixed-variance recursive type equations, to focusedorthogonality categories.Comment: 17 pages, MFPS 202

Pneumonia and Impaired T Cell Function in Children with Down's Syndrome: Double Strike

Abstract: Down's syndrome (DS) is the most common chromosomal abnormality in humans and is the most common known genetic cause of intellectual disability. DS is known for increased incidence of respiratory infections and autoimmune diseases, indicating impaired immunity. Subjects and methods: This study included sixty seven children; 49 preschool children with DS, with ages ranging from 2 to 6.5 years and 18 healthy, age-and gender-matched controls. Free T4, TSH, and thyroid autoantibodies (anti-thyroglobulin and anti-TSH receptor antibodies) were measured. Evaluation of total leucocytic count (TLC), lymphocytes, CD3+, CD4+, CD8+ and CD56+ cells was performed for each subject. Sputum specimens were collected from all DS subjects and controls for microscopic examination and culture. Results: Among 49 DS child 23 (46.9%) had signs and symptoms of respiratory tract infection, 11 of DS children (22.4%) were suffering from pneumonia. The culture results of sputum samples revealed that staphylococcus aurous was the most common organism; it represents 37.9% of the total bacterial pathogen isolates and 45.4% of the pneumonic patient's isolates. Nineteen DS subjects (38.78%) were hypothyroid according to the thyroid profile tests. Thyroid autoantibodies were detected in five (10.2%) of DS children, one euthyroid and four hypothyroid children. The values of TLC, lymphocyte, CD3+ and CD4+ cells (5772.2 ± 1861.1/mm 3 , 2234.2 ± 597.8, 1774.2 ± 396.5 and 760.9 ± 298.4 respectively), were lower in DS children than healthy controls (7908.0 ± 1464.8/mm 3 , 3158.9 ± 722.5, 2252.0 ± 636.8 and 1389.3 ± 379.4 respectively) and the differences were statistically significant. CD8+ and CD56+ cells were higher in DS children (979.4 ± 285.2 and 393.2 ± 102.9 respectively) than healthy controls (741.8 ± 170.6 and 175.5 ± 52.8 respectively) with significant statistical differences. CD4/CD8 ratio was reversed in DS children (0.78 ± 0.27). In conclusion, respiratory tract infection is very common in DS children and can easily complicate to pneumonia because of the complex impairment of T-lymphocytes which is one of the reasons of the defective immune responses among DS children