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Reconstruction of Convex Sets from One or Two X-rays
No full textWe consider a class of problems of Discrete Tomography which has been deeplyinvestigated in the past: the reconstruction of convex lattice sets from theirhorizontal and/or vertical X-rays, i.e. from the number of points in a sequenceof consecutive horizontal and vertical lines. The reconstruction of theHV-convex polyominoes works usually in two steps, first the filling stepconsisting in filling operations, second the convex aggregation of theswitching components. We prove three results about the convex aggregation step:(1) The convex aggregation step used for the reconstruction of HV-convexpolyominoes does not always provide a solution. The example yielding to thisresult is called \textit{the bad guy} and disproves a conjecture of the domain.(2) The reconstruction of a digital convex lattice set from only one X-ray canbe performed in polynomial time. We prove it by encoding the convex aggregationproblem in a Directed Acyclic Graph. (3) With the same strategy, we prove thatthe reconstruction of fat digital convex sets from their horizontal andvertical X-rays can be solved in polynomial time. Fatness is a property of thedigital convex sets regarding the relative position of the left, right, top andbottom points of the set. The complexity of the reconstruction of the latticesets which are not fat remains an open question.Comment: 31 pages, 24 figure
Rigidity of projective symmetric manifolds of Picard number 1 associated to composition algebras
No full textTo each complex composition algebra , there associates aprojective symmetric manifold of Picard number one, which isjust a smooth hyperplane section of the following varieties In this paper, it is proven that thesevarieties are rigid, namely for any smooth family of projective manifolds overa connected base, if one fiber is isomorphic to , then everyfiber is isomorphic to
A data science and machine learning approach to continuous analysis of Shakespeare's plays
No full textThe availability of quantitative text analysis methods has provided new waysof analyzing literature in a manner that was not available in thepre-information era. Here we apply comprehensive machine learning analysis tothe work of William Shakespeare. The analysis shows clear changes in the styleof writing over time, with the most significant changes in the sentence length,frequency of adjectives and adverbs, and the sentiments expressed in the text.Applying machine learning to make a stylometric prediction of the year of theplay shows a Pearson correlation of 0.71 between the actual and predicted year,indicating that Shakespeare's writing style as reflected by the quantitativemeasurements changed over time. Additionally, it shows that the stylometrics ofsome of the plays is more similar to plays written either before or after theyear they were written. For instance, Romeo and Juliet is dated 1596, but ismore similar in stylometrics to plays written by Shakespeare after 1600. Thesource code for the analysis is available for free download.Comment: Journal of Data Mining and Digital Humanities, accepte
Les modèles LSAWfP non récursifs sont des workflows structurés
No full textÉditeurs: Mathieu Roche, Nabil Gmati, Amel Ben Abda, Marcellin NkenlifackWorkflow languages are a key component of the Business Process Management (BPM) discipline: they are used to model business processes in order to facilitate their automatic management by means of BPM systems. There are numerous workflow languages addressing various issues (expressiveness, formal analysis, etc.). In the last decade, some workflow languages based on context-free grammars (having then formal semantics) and offering new perspectives to process modelling, have emerged: LSAWfP (a Language for the Specification of Administrative Workflow Processes) is one of them. LSAWfP has many advantages over other existing languages, but it is its expressiveness (which has been very little addressed in previous works) that is studied in this paper. Indeed, the work in this paper aims to demonstrate that any non-recursive LSAWfP model is a structured workflow. Knowing that the majority of commercial BPM systems only implement structured workflows, the result of this study establishes that, although LSAWfP is still much more theoretical, it is a language with commercial potential.Les langages de workflow occupent une place importante dans la discipline du Business Process Management (BPM) : ils sont utilisés pour modéliser les processus opérationnels afin de faciliter leur gestion automatique à l'aide de systèmes BPM. Il existe de nombreux langages de workflow qui traitent de divers aspects (expressivité, analyse formelle, etc.). Au cours de la dernière décennie, certains langages de workflow basés sur des grammaires algébriques (ayant alors une sémantique formelle) et offrant de nouvelles perspectives à la modélisation des processus ont vu le jour : LSAWfP (a Language for the Specification of Administrative Workflow Processes) est l'un d'entre eux. LSAWfP présente de nombreux avantages par rapport aux langages existants, mais c'est son expressivité (qui a été très peu abordée dans les travaux antérieurs) qui est étudiée dans le présent document. En effet, les travaux présentés dans ce document visent à démontrer que tout modèle LSAWfP non récursif est un workflow structuré. Sachant que la majorité des systèmes BPM commerciaux ne gèrent que des workflows structurés, le résultat de cette étude montre que, bien que LSAWfP soit encore très théorique, il est un langage au potentiel économique certain
Combiner Scrum et l'Architecture Dirigée par les modèles pour le développement d'un système de surveillance épidémiologique
No full textEpidemiological surveillance systems evolve with time, depending on the context and the data already collected. Then, the software used must evolve in order to meet requirements. However, introducing new requirements in order to update the software takes time, is expensive and may lead to the problem of software regression. The problem of failed software developed for epidemiological surveillance are often the result of an unsystematic transfer of business requirements to the implementation. This problem can be avoided if the system is established using a well-defined framework/architecture permitting the rapid development/update of the surveillance software. Empirical research shows on the one hand that Model Driven Techniques such as Model Driven Architecture (MDA) are more effective than code-centric approaches for the development and the maintenance of software. On the other hand, Agile Processes such as Scrum are more effective than Structured Processes when requirements are subject to frequent change. Researchers demonstrated that developers of medical software such as epidemiological surveillance software are experiencing difficulties when following Structured Processes and code-centric approaches. The main goal of this empirical study was to apply the combination of Scrum and Model Driven Architecture for the development of epidemiological surveillance of tuberculosis. During this research, we found the approach ease of use and very useful when the MDA tool can generate the complete source code. It has had positive effects on programmer productivity and satisfaction, cost-effectiveness, timelines and customer satisfaction. In addition, we learned that to involve non-informatic experts in the development/update, the modeling user interface must be as simple as possible.Les systèmes de surveillance épidémiologiques évoluent avec le temps, en tenant compte du contexte et des données collectées. Ainsi, les logiciels utilisés doivent aussi évoluer pour pouvoir répondre aux besoins. Cependant, de nouvelles exigences des clients peuvent prendre du temps pour être implémentées, coûter plus cher (dans le cas où il faut recruter des programmeurs) et causer des problèmes comme le problème de régression logiciel. Ainsi, le logiciel peut devenir défaillant. Ceci est dû à un mauvais transfert des exigences des clients vers la mise en œuvre. Ce problème peut être évité si le système est développé en utilisant un framework et une architecture permettant le développement/la mise à jour rapide des logiciels de surveillance. La recherche empirique d'une part montre que l'Ingénierie Dirigée par les Modèles (par exemple, Architecture Dirigée par les Modèles ou Model-Driven Architecture - MDA) est plus efficace que les approches basées sur le code pour le développement et la maintenance de certains logiciels. D'autre part, les processus agiles tels que Scrum sont plus efficaces que les processus structurés lorsque les exigences sont sujettes aux changements fréquents. Il a été démontré que le développement des logiciels de santé comme les logiciels de surveillance épidémiologique en utilisant les processus structurés ou les approches de développement centrées sur le code n'est pas évident car ces logiciels sont sujettes aux changements fréquents. Dans ce travail, nous étudions la combinaison de Scrum avec MDA pour le développement du système de surveillance épidémiologique de la tuberculose. A son terme, nous avons trouvé la combinaison de Scrum et MDA simple, très utile lorsque l'outil sous-jacent peut générer tout le code source. La combinaison de Scrum et MDA a eu des effets positifs sur la productivité et la satisfaction des programmeurs et des clients. En plus, nous avons constaté que pour impliquer les non-informaticiens dans le développement ou la mise à jour, l'interface de modélisation doit être aussi simple que possible
Mélanger des concepts de biologie et d'informatique pour concevoir des lacs de données résilients
No full textData lakes appeared a few years ago, introduced in particular to meet the challenges of storing and exploiting IoT data. They were first considered as a new technical and commercial tool, sold by the main database software editors. More recently, they have become the subject of research, in particular to define what a data lake should be, what it should provide in terms of services, and how it should be built. In this work, we have tried to return to the origins of data lakes, starting from the name “lake”. We present here how we worked, between biologists and computer scientists, to understand the links between natural and data lakes. In this article, we first explore the links between the disciplines of biology and computer science before declining these links for the particular theme of lakes. This could appear as a work of transferring knowledge from biology to computer science, and a “simple” application of the concepts. However, we had to interact and understand each other’s concepts and issues to align a possible comparison between the disciplines, for example to determine at what scale to establish the biological comparison, from DNA to the more macro system of the animal and plant ecosystem present in a natural lake. For this reason, we are inspired by a hybrid method based on ecological and logistical network topology to propose the resilient structure for the data lake. Thus, we use the Ecological Network Analysis (ENA) as a bio-inspired method and Graph theory as a logistical-inspired framework to study the interdisciplinary resilience strategies for the data lake network
Flexible Correct-by-Construction Programming
No full textCorrectness-by-Construction (CbC) is an incremental program constructionprocess to construct functionally correct programs. The programs areconstructed stepwise along with a specification that is inherently guaranteedto be satisfied. CbC is complex to use without specialized tool support, sinceit needs a set of predefined refinement rules of fixed granularity which areadditional rules on top of the programming language. Each refinement ruleintroduces a specific programming statement and developers cannot depart fromthese rules to construct programs. CbC allows to develop software in astructured and incremental way to ensure correctness, but the limitedflexibility is a disadvantage of CbC. In this work, we compare classic CbC withCbC-Block and TraitCbC. Both approaches CbC-Block and TraitCbC, are related toCbC, but they have new language constructs that enable a more flexible softwareconstruction approach. We provide for both approaches a programming guideline,which similar to CbC, leads to well-structured programs. CbC-Block extends CbCby adding a refinement rule to insert any block of statements. Therefore, weintroduce CbC-Block as an extension of CbC. TraitCbC implementscorrectness-by-construction on the basis of traits with specified methods. Weformally introduce TraitCbC and prove soundness of the construction strategy.All three development approaches are qualitatively compared regarding theirprogramming constructs, tool support, and usability to assess which is bestsuited for certain tasks and developers.Comment: arXiv admin note: text overlap with arXiv:2204.0564
Affine Subspace Concentration Conditions
No full textWe define a new notion of affine subspace concentration conditions forlattice polytopes, and prove that they hold for smooth and reflexive polytopeswith barycenter at the origin. Our proof involves considering the slopestability of the canonical extension of the tangent bundle by the trivial linebundle and with the extension class on Fano toricvarieties.Comment: 14 pages, v2: published version, revisions following referee's comments, major changes in Lemma 3.2 and its proof, to appear in EPIG
Amenability problem for Thompson's group : state of the art
No full textThis is a survey of our recent results on the amenability problem forThompson's group . They mostly concern esimating the density of finitesubgraphs in Cayley graphs of for various systems of generators, and alsoequations in the group ring of . We also discuss possible approaches tosolve the problem in both directions.Comment: 24 pages, 1 figure. Published in journal of Groups, Complexity, Cryptology. arXiv admin note: text overlap with arXiv:2112.09812, arXiv:2210.1230
Bounds On Broadcast Domination of -Dimensional Grids
No full textIn this paper, we study a variant of graph domination known as broadcast domination, first defined in Blessing, Insko, Johnson, and Mauretourin 2015. In this variant, each broadcast provides reception to eachvertex a distance from the broadcast. If then no reception isprovided. A vertex is considered dominated if it receives total receptionfrom all broadcasts. Our main results provide some upper and lower bounds onthe density of a dominating pattern of an infinite grid, as well asmethods of computing them. Also, when we describe a family ofcounterexamples to a generalization of Vizing's Conjecture to broadcastdomination.Comment: 13 pages, 4 figure