A fine-grained computational interpretation of Girard’s intuitionistic proof-nets

This paper introduces a functional term calculus, called pn, that captures the essence of the operational semantics of Intuitionistic Linear Logic Proof-Nets with a faithful degree of granularity, both statically and dynamically. On the static side, we identify an equivalence relation on pn-terms which is sound and complete with respect to the classical notion of structural equivalence for proof-nets. On the dynamic side, we show that every single (exponential) step in the term calculus translates to a different single (exponential) step in the graphical formalism, thus capturing the original Girard’s granularity of proof-nets but on the level of terms. We also show some fundamental properties of the calculus such as confluence, strong normalization, preservation of β-strong normalization and the existence of a strong bisimulation that captures pairs of pn-terms having the same graph reduction.

Miofrenuloplasty for Full Functional Tongue Release in Ankyloglossia in Adults and Adolescents—Preliminary Report and Step-by-Step Technique Showcase

Background and Objectives: Ankyloglossia is a functional term describing limitations of motor activity of the tongue due to the embryological malformation of the lingual frenulum. The lingual frenulum has a complex, three-dimensional structure, it is not only a mucosal fold, which connects the ventral surface of the tongue and the floor of the mouth. Such knowledge forced us to develop more advanced techniques for tongue release in ankyloglossia. The aim of this study is to describe a novel, precise surgical technique for tongue release. Materials and Methods: Miofrenuloplasty was performed in six patients with impaired tongue movements due to anatomical limitations. All of them were prepared for surgery and evaluated after the procedure by a speech therapist. Results: The healing process was uneventful in all patients. We did not observe any major complications. Tongue mobility and neck muscle tension improved significantly in all cases. In one case, the speech improvement was minor. Conclusions: Miofrenuloplasty is an advanced, but effective and highly predictable procedure for full functional tongue release in cases caused by MFGG complex. It should be done by experienced surgeon.

Boundary value problems associated with singular strongly nonlinear equations with functional terms

We study boundary value problems associated with singular, strongly nonlinear differential equations with functional terms of type $$\big({\it \Phi}(k(t)\,x'(t))\big)' + f(t,{{\mathcal{G}}}_x(t))\,\rho(t, x'(t)) = 0,$$ on a compact interval [a, b]. These equations are quite general due to the presence of a strictly increasing homeomorphism Φ, the so-called Φ-Laplace operator, of a non-negative function k, which may vanish on a set of null measure, and moreover of a functional term Gx. We look for solutions, in a suitable weak sense, which belong to the Sobolev space W1,1([a, b]). Under the assumptions of the existence of a well-ordered pair of upper and lower solutions and of a suitable Nagumo-type growth condition, we prove an existence result by means of fixed point arguments.

A Reconsideration of Grammatical Categorization in English: The Clause

Various models for categorizing grammatical units exist in the literature. Particularly nebulous, however, are terminologies for conceptualizing categories at the level of the clause. For example, the term complement has been used, confusingly sometimes, as both a functional term and, on some occasions, as a structural term. In this study, a model of categorization is proposed, which keeps functional classification separate from structural classification, in order that concepts used in grammatical analysis can be clearly understood and be applied more easily in text analysis. Accordingly, the specific aim of this study is to examine some already ‘accepted’ subcategories of the dependent clause and, in the process, propose a new approach for the analysis of this clause type. This approach, it is hoped, will remove (a) semantic considerations from the analysis of these grammatical units and (b) the confusion between the notional and syntactic description of the units. In the end, this work involves a reconsideration of some traditional ways of doing grammatical categorization with the hope that it will ease identification of grammatical categories. The overall goal is to offer a more consistent and structured approach to the grammatical analysis of the clause in English.

Solutions to an advanced functional partial differential equation of the pantograph type

A model for cells structured by size undergoing growth and division leads to an initial boundary value problem that involves a first-order linear partial differential equation with a functional term. Here, size can be interpreted as DNA content or mass. It has been observed experimentally and shown analytically that solutions for arbitrary initial cell distributions are asymptotic as time goes to infinity to a certain solution called the steady size distribution. The full solution to the problem for arbitrary initial distributions, however, is elusive owing to the presence of the functional term and the paucity of solution techniques for such problems. In this paper, we derive a solution to the problem for arbitrary initial cell distributions. The method employed exploits the hyperbolic character of the underlying differential operator, and the advanced nature of the functional argument to reduce the problem to a sequence of simple Cauchy problems. The existence of solutions for arbitrary initial distributions is established along with uniqueness. The asymptotic relationship with the steady size distribution is established, and because the solution is known explicitly, higher-order terms in the asymptotics can be readily obtained.

English as a Lingua Franca in Flanders

This article reports on a study that examines the attitudes of 69 Flemish university students towards the emerging conceptualization of English as a lingua franca (ELF) on the basis of a questionnaire survey. Built on the notion of ELF as a functional term theorized on sociolinguistic grounds, this study seeks to understand the relation between ELF as a theoretical construct and ELF as a reality in the life of these language students through their experiences of engagement with English, both within and outside the academic community. The results show that the students have embraced some ideas of the ELF phenomenon on a macro level, but retain a strong belief in the native standard norm on a micro level.

Continuation-based compilation of functional languages for parallel machines

We tackle the problems of correctness and efficiency of paralled implementations of functional languages. We present a compilation technique described in terms of program transformations in the functional framework. The original functional expression is transformed into a functional term, which can be seen as traditional machine code. The main feature of the parallel implementation is the use of continuations. We introduce a parallel abstract machine describing lazy task creation in terms of exportation of continuations. The advantages of the approach are twofold: (1)correetness proofs are made simpler and (2) the implementation is efficient because the use of continuations reduces the task management overhead.