A Coding Theoretic Study on MLL proof nets

Coding theory is very useful for real world applications. A notable example is digital television. Basically, coding theory is to study a way of detecting and/or correcting data that may be true or false. Moreover coding theory is an area of mathematics, in which there is an interplay between many branches of mathematics, e.g., abstract algebra, combinatorics, discrete geometry, information theory, etc. In this paper we propose a novel approach for analyzing proof nets of Multiplicative Linear Logic (MLL) by coding theory. We define families of proof structures and introduce a metric space for each family. In each family, 1. an MLL proof net is a true code element; 2. a proof structure that is not an MLL proof net is a false (or corrupted) code element. The definition of our metrics reflects the duality of the multiplicative connectives elegantly. In this paper we show that in the framework one error-detecting is possible but one error-correcting not. Our proof of the impossibility of one error-correcting is interesting in the sense that a proof theoretical property is proved using a graph theoretical argument. In addition, we show that affine logic and MLL + MIX are not appropriate for this framework. That explains why MLL is better than such similar logics.Comment: minor modification

Unifying type systems for mobile processes

We present a unifying framework for type systems for process calculi. The core of the system provides an accurate correspondence between essentially functional processes and linear logic proofs; fragments of this system correspond to previously known connections between proofs and processes. We show how the addition of extra logical axioms can widen the class of typeable processes in exchange for the loss of some computational properties like lock-freeness or termination, allowing us to see various well studied systems (like i/o types, linearity, control) as instances of a general pattern. This suggests unified methods for extending existing type systems with new features while staying in a well structured environment and constitutes a step towards the study of denotational semantics of processes using proof-theoretical methods

Hybrid Type-Logical Grammars, First-Order Linear Logic and the Descriptive Inadequacy of Lambda Grammars

In this article we show that hybrid type-logical grammars are a fragment of first-order linear logic. This embedding result has several important consequences: it not only provides a simple new proof theory for the calculus, thereby clarifying the proof-theoretic foundations of hybrid type-logical grammars, but, since the translation is simple and direct, it also provides several new parsing strategies for hybrid type-logical grammars. Second, NP-completeness of hybrid type-logical grammars follows immediately. The main embedding result also sheds new light on problems with lambda grammars/abstract categorial grammars and shows lambda grammars/abstract categorial grammars suffer from problems of over-generation and from problems at the syntax-semantics interface unlike any other categorial grammar

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 22nd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 29 papers presented in this volume were carefully reviewed and selected from 85 submissions. They deal with foundational research with a clear significance for software science

Étude des signatures géniques dans un contexte d’expériences de RNA- Seq

Le principal intérêt des expériences de séquençage d’ARN (RNA-Seq) est qu’elles consti- tuent une vue d’ensemble sur les procédés géniques intrinsèques de la cellule. L’état malade différe de l’état sain de par son usage génique et de nombreux efforts ont été canalisés dans les dernières années en bioinformatique, pour affiner ces signatures gé- niques, notamment dans la classification de leucémies et le typage de cancers du sein. Tous ces modèles voient, cependant, leur performance détériorée par un grand nombre de dimensions d’entrée et la plupart des auteurs choisissent d’imposer un seuil d’exclusion de gènes. J’ai voulu déterminer la nature d’une signature génique et sa taille optimale, en nombre de gènes. Pour déterminer la taille d’une signature génique j’ai appliqué des algorithmes de co-partitionnements à un sous-ensemble de données transcriptomiques afin d’en extraire la signature génique. Mes résultats indiquent que la signature génique ne peut être extraite en entier et l’utilisation de seuils d’exclusions de gènes est le prin- cipal problème. J’ai exploré une méthode d’extraction de la signature génique avec un réseau de neurones artificiels (ANN) en calculant le plus petit ajustement en expression génique nécessaire pour passer d’un phénotype à un autre. La signature génique extraite indique que presque la totalité des gènes sont affectés pour un phénotype donné. Consé- quemment, il est inapproprié de considérer des méthodes avec seuil d’exclusion de gènes et je propose que les signatures géniques sont des phénomènes omnigéniques. Afin de pallier à l’inconvénient dû à la nécessité d’inclure tous les gènes dans l’analyse, j’ai élaboré une méthode d’apprentissage machine par ANN qui gère simultanément deux espaces : l’espace des gènes et l’espace des échantillons. Les coordonnées des gènes et des échantillons dans leur espaces respectifs sont arrangés de manière à ce qu’ils pré- disent l’expression génique. Ma contribution est donc un modèle qui apprend de manière simultanée les interactions entre les gènes et les interactions entre les échantillons. Ma méthode permet également d’inclure dans l’analyse de jeux de données partiellement manquantes, faisant le lien vers l’intégration de données et l’analyses d’échantillons de séquençage de cellule unique (scRNA-Seq).The main appeal of RNA sequencing experiments is that they offer a general view of all cell’s intrinsic genetic processes. Diseased state differs from healthy by it’s gene usage and many efforts have been channeled in bioinformatics these last few years to purify these gene signatures, in particular in the classification of leukemia and breast cancer subtyping. However, these models see their performance hindered by a large size of input dimensions and most authors chose to impose a threshold of gene exclusion. I wanted to determine what is a gene signature and how many genes it truly contains. To determine it’s size, I applied co-clustering algorithms to a subset of transcriptomic data, to extract it’s gene signature. My results indicate that the gene signature cannot be extracted entirely and the use of exclusion thresholds is the main problem. I then explored a gene signature extraction method using an artificial neural net (ANN), by calculating the smallest adjustment in gene expression necessary to go from one phe- notypic class to another. The extracted gene signature indicated that almost all genes are affected for the given phenotype. Consequently, it seems inappropriate to consider threshold-based methods and I, therefore, propose that gene signatures are omnigenic phenomena. To level the disadvantage of having to include all genes in gene expres- sion analyses, I designed a ANN method that simultaneously manages two spaces: the gene and the sample space. The coordinates for genes and samples in their respective space are arranged to predict the gene expression. My contribution is a model that learns simultaneously about genes and samples. My method allows the analysis of datasets with missing data, making the integration of heterogenous data integration as well as the analysis of single-cell RNA-Seq experiments