Relational Graph Models at Work

We study the relational graph models that constitute a natural subclass of relational models of lambda-calculus. We prove that among the lambda-theories induced by such models there exists a minimal one, and that the corresponding relational graph model is very natural and easy to construct. We then study relational graph models that are fully abstract, in the sense that they capture some observational equivalence between lambda-terms. We focus on the two main observational equivalences in the lambda-calculus, the theory H+ generated by taking as observables the beta-normal forms, and H* generated by considering as observables the head normal forms. On the one hand we introduce a notion of lambda-K\"onig model and prove that a relational graph model is fully abstract for H+ if and only if it is extensional and lambda-K\"onig. On the other hand we show that the dual notion of hyperimmune model, together with extensionality, captures the full abstraction for H*

Variables influencing executive functioning in preschool hearing-impaired children implanted within 24 months of age: an observational cohort study

Executive Functions (EFs) are fundamental to every aspect of life. The present study was implemented to evaluate factors influencing their development in a group of preschools orally educated profoundly deaf children of hearing parents, who received CI within two years of age. Methods Twenty-five preschool CI children were tested using the Battery for Assessment of Executive Functions (BAFE) to assess their flexibility, inhibition and non-verbal visuo-spatial working memory skills. The percentage of children performing in normal range was reported for each of the EF subtests. Mann-Whitney and Kruskal-Wallis were performed to assess differences between gender, listening mode and degree of parents’ education subgroups. The Spearman Rank Correlation Coefficient was calculated to investigate the relationship between EF scores audiological and linguistic variables. Results Percentages ranging from 76% to 92% of the children reached adequate EF scores at BAFE. Significant relations (p<0.05) were found between EFs and early intervention, listening and linguistic skills. Further, CI children from families with higher education level performed better at the response shifting, inhibitory control and attention flexibility tasks. Economic income correlated significantly with flexibility and inhibitory skills. Females performed better than males only in the attention flexibility task. Conclusions The present study is one of the first to focus attention on the development of EFs in preschool CI children, providing an initial understanding of the characteristics of EFs at the age when these skills emerge. Clinical practice must pay increasing attention to these aspects which are becoming the new emerging challenge of rehabilitation programs

Modèles de Graphe Relationnels et Observabilité à la Morris : recherches sémantiques sensibles aux ressources sur le λ-calcul non typé

This thesis is a contribution to the study of Church’s untyped λ-calculus, a term rewritingsystem having the β-reduction (the formal counterpart of the idea of execution of programs) asmain rule. The focus is on denotational semantics, namely the investigation of mathematical models of the λ-calculus giving the same denotation to β-convertible λ-terms. We investigate relational semantics, a resource-sensitive semantics interpreting λ-terms as relations,with their inputs grouped together in multisets. We define a large class of relational models,called relational graph models (rgm’s), and we study them in a type/proof-theoretical way, using some non-idempotent intersection type systems. Firstly, we find the minimal and maximal λ-theories (equational theories extending -conversion) represented by the class.Then we use rgm’s to solve the full abstraction problem for Morris’s observational λ-theory,the contextual equivalence of programs that one gets by taking the β-normal forms asobservable outputs. We solve the problem in different ways. Through a type-theoretical characterization of β-normalizability, we find infinitely many fully abstract rgm’s, that wecall uniformly bottomless.We then give an exhaustive answer to the problem, by showing thatan rgm is fully abstract for Morris’s observability if and only if it is extensional (a model of ŋ-conversion) and λ-König. Intuitively an rgm is λ-König when every infinite computable tree has an infinite branch witnessed by some type of the model, where the witnessing is a property of non-well-foundedness on the type.La thèse contribue à l’étude du λ-calcul non-typé de Church, un système de réécriture dont la règle principale est la β-réduction (formalisant l’exécution d’un programme). Nous nous concentrons sur la sémantique dénotationnelle, l’étude de modèles du λ-calcul interprétant de la même façon les λ-termes β-convertibles. On examine la sémantique relationnelle, une sémantique sensible aux ressources qui interprète les λ-termes comme des relations avec les entrées regroupées en multi-ensembles. Nous définissons une classe de modèles relationnels, les modèles de graphe relationnels (rgm’s), que nous étudions avec une approche issue de la théorie des types et de la démonstration, par le biais de certains systèmes de types avec intersection non-idémpotente. D’abord, nous découvrons la plus petite et la plus grande λ–théorie (théorie équationnelle étendant la β-conversion) représentées dans la classe. Ensuite, nous utilisons les rgm’s afin de résoudre le problème de l’adéquation complète pour la λ–théorie observationnelle de Morris, à savoir l’équivalence contextuelle de programmes que l’on obtient lorsqu’on prend les β-formes normales comme sorties observables. On résoudre le problème de différentes façons. En caractérisant la β-normalisabilité avec les types, nous découvrons une infinité de rgm’s complètement adéquats, que nous appelons uniformément sans fond. Puis, nous résolvons le problème de façon exhaustive, en prouvant qu’un rgm est complètement adéquat pour l’observabilité de Morris si et seulement si il est extensionnel (il modèle l’ŋ-conversion) et λ-König. Moralement un rgm est λ-König si tout arbre récursif infini a une branche infinie témoignée par un type non-bien-fond

New Results on Morris's Observational Theory: the benefits of separating the inseparable

International audienceWorking in the untyped lambda calculus, we study Morris's λ-theory H +. Introduced in 1968, this is the original extensional theory of contextual equivalence. On the syntactic side, we show that this λ-theory validates the ω-rule, thus settling a long-standing open problem. On the semantic side, we provide sufficient and necessary conditions for relational graph models to be fully abstract for H +. We show that a relational graph model captures Morris's observational preorder exactly when it is extensional and λ-König. Intuitively, a model is λ-König when every λ-definable tree has an infinite path which is witnessed by some element of the model. Both results follows from a weak separability property enjoyed by terms differing only because of some infinite η-expansion, which is proved through a refined version of the Böhm-out technique

Relational Graph Models, Taylor Expansion and Extensionality

International audienceWe define the class of relational graph models and study the induced order-and equational-theories. Using the Taylor expansion, we show that all λ-terms with the same Böhm tree are equated in any relational graph model. If the model is moreover extensional and satisfies a technical condition, then its order-theory coincides with Morris's observational pre-order. Finally, we introduce an extensional version of the Taylor expansion, then prove that two λ-terms have the same extensional Taylor expansion exactly when they are equivalent in Morris's sense

Listening comprehension in profoundly deaf children with cochlear implants: the role of auditory perception and foundational linguistic and cognitive skills

Purpose: The aim of the study was to investigate the listening comprehension (LC) skills in deaf and hard of hearing children (DHH) using cochlear implants (CI). Besides, personal and audiological variables that could influence the levels of competence reached were analyzed. Methods: Thirty-four children using CI were enrolled. LC skills were assessed through the standardized Italian test "Comprensione Orale-Test e Trattamento" (CO-TT). A univariate analysis was conducted to compare LC with gender, listening mode (unilateral or bilateral), maternal level of education and family income. A bivariate analysis was performed to search possible connections between children's performances and their individual characteristics, audiological conditions, and language levels. Finally, a multivariate analysis was performed using a stepwise hierarchical linear regression model which included all variables whose p value resulted ≤ 0.05. Results: Twenty-one children using CI (61.8%) showed adequate performances in terms of chronological age, while 13 (38.2%) showed difficulties in LC. Maternal level of education, age at diagnosis and non-verbal cognitive level accounted for 43% of the observed variance. Auditory attention skills explained an additional 15% of variance. Morphosyntactic comprehension added a further 12% of variance. Conclusion: CI can really help many DHH children to reach adequate LC skills, but in some cases difficulties remain. Factors influencing LC need to be early investigated and considered when planning an appropriate rehabilitative intervention

A new case of M/SCHAD deficiency: The contribution of metabolic findings in directing the definitive genetic diagnosis for an optimal management

ongenital hyperinsulinemic hypoglycemia (CHH) is a rare metabolic disease (prevalence <1/1,000,000) characterized by persistent hypoglycemia and inappropriate secretion of insulin often in neonatal period and infancy. Early diagnosis and management of patients with CHH are important to avoid brain damage. Recent advances in genetics have showed that CHH is due to mutations in twelve genes: ABCC8, KCNJ11, GCK, GLUD1, HADH, SLC16A1, UCP2, HNF1A, HNF4A, HK1, PGM1 and CACNA1D. The HADH gene codifies the medium and short chain 3-hydroxyacyl-CoA dehydrogenase (M./SCHAD), a mitochondrial matrix enzyme which catalyzes the penultimate reaction in the beta-oxidation of medium and short-chain fatty acids, specifically the conversion of medium- and short-chain L-3-hydroxyacyl-CoA to corresponding 3-ketoacyl-CoA. Mutations in this gene result in a recessive form of CHH, with a good diazoxide responsivity and, occasionally, an abnormal urinary organic acid and plasma acylcarnitine's profile. Herein, we describe a new case of CHH due to M/SCHAD deficiency, highlighting the importance of metabolic findings to lead genetic testing and clinical management

The influence of auditory selective attention on linguistic outcomes in deaf and hard of hearing children with cochlear implants

Purpose Auditory Selective Attention (ASA) is crucial to focus on significant auditory stimuli without being distracted by irrelevant auditory signals and has an important role on language development. The present study aimed to investigate the unique contribution of ASA on the linguistic levels reached by a group of cochlear implanted (CI) children. Methods Thirty-four CI children with a median age of 10.05 years were tested using both the “Batteria per la Valutazione dell’Attenzione Uditiva e della Memoria di Lavoro Fonologica nell’età evolutiva-VAUM-ELF”, to assess their ASA skills, and two Italian standardized tests, to measure lexical and morphosyntactic skills. A regression analysis, including also demographic and audiological variables, was conducted to assess the unique contribution of ASA on language skills. Results The percentages of CI children with adequate ASA performances ranged from 50% to 29.4%. Bilateral CI children performed better than their monolateral peers did. ASA skills revealed to give an independent contribute to linguistic skills, accounting alone for the 25% of the observed variance. Conclusions The present findings are clinically relevant as they highlight the importance to assess ASA skills as early as possible, due to their important role in language development. Using simple clinical instruments, ASA skills could be studied at early developmental stages. This may provide us additional information to traditional auditory testing and may allow us to implement specific training programs that could positively contribute to the development of neural mechanisms of ASA and, consequently, induce improvements in language skills