Episciences.org
Not a member yet
6707 research outputs found
Sort by
Computing subalgebras and -gradings of simple Lie algebras over finite fields
No full textThis paper introduces two new algorithms for Lie algebras over finite fieldsand applies them to the investigate the known simple Lie algebras of dimensionat most over the field with two elements. The firstalgorithm is a new approach towards the construction of -gradingsof a Lie algebra over a finite field of characteristic . Using this, weobserve that each of the known simple Lie algebras of dimension at most over has a -grading and we determine theassociated simple Lie superalgebras. The second algorithm allows us to computeall subalgebras of a Lie algebra over a finite field. We apply this to computethe subalgebras, the maximal subalgebras and the simple subquotients of theknown simple Lie algebras of dimension at most over (withthe exception of the -dimensional Zassenhaus algebra)
A characterization of finite \'etale morphisms in tensor triangular geometry
No full textWe provide a characterization of finite \'etale morphisms in tensortriangular geometry. They are precisely those functors which have aconservative right adjoint, satisfy Grothendieck--Neeman duality, and for whichthe relative dualizing object is trivial (via a canonically-defined map).Comment: 25 pages. Proposition 3.8 revised; added Remark 3.11--Example 3.12, Remark 4.10--Remark 4.25, and Corollary 5.1
The Theory of Universal Graphs for Infinite Duration Games
No full textWe introduce the notion of universal graphs as a tool for constructingalgorithms solving games of infinite duration such as parity games and meanpayoff games. In the first part we develop the theory of universal graphs, withtwo goals: showing an equivalence and normalisation result between differentrecently introduced related models, and constructing generic value iterationalgorithms for any positionally determined objective. In the second part wegive four applications: to parity games, to mean payoff games, to a disjunctionbetween a parity and a mean payoff objective, and to disjunctions of severalmean payoff objectives. For each of these four cases we construct algorithmsachieving or improving over the best known time and space complexity
La participation des patients : défis et enjeux de la co-innovation en santé connectée
No full textWith connected health and more particularly with the so-called "intelligent" technologies, the patient is faced with a real paradoxical injunction. On the one hand, the new solutions insistently solicit "patient work", making him not a simple user, but a true "co-creator of values" at the very heart of the system's operability. On the other hand, it is the opacity that is observed as the networks spread into the patients' living environments and as the solutions increase their computing power. While patient involvement is becoming an obvious necessity, I propose here to review some of the obstacles to participation in the specific field of current digital innovations. After having painted a sociological picture of the participating patient, I will also underline the interest of forging new categories in order to integrate the most ordinary digital and therapeutic competences and not only those of patient-experts. Finally, I intend to argue in favor of a dynamic and pragmatic framework of participation in co-innovation, a framework able to take into account the heterogeneity of experiential commitments and to resituate the patient's word within the interactional configurations of care (with the other parties involved) and of a shared quest for change.Avec la santé connectée et plus particulièrement celle ayant trait aux technologies dites « intelligentes », le malade se trouve face à une véritable injonction paradoxale. D’un côté, les nouvelles solutions sollicitent de manière insistante « le travail patient », faisant de lui, non pas un simple usager, mais un véritable « co-créateur de valeurs » au cœur même de l’opérativité du système. D’un autre côté, c’est l’opacité qui s’observe au fur et mesure que les réseaux se diffusent dans les environnements de vie des malades et que les solutions augmentent leur puissance de calcul. Alors que l’implication des patients s’impose de plus en plus comme une évidente nécessité, je propose ici de revenir sur quelques freins à la participation dans le domaine précis des innovations numériques actuelles. Après avoir brossé un tableau sociologique du patient participant, il sera par ailleurs souligné l’intérêt de forger de nouvelles catégories afin d’intégrer les compétences numériques et thérapeutiques les plus ordinaires et non plus seulement celles des patients-experts. Je compte enfin argumenter en faveur d’un cadre dynamique et pragmatique de participation en co-innovation, un cadre à même de prendre en compte l’hétérogénéité des engagements expérientiels et de resituer la parole patiente au sein des configurations interactionnelles du soin (avec les autres parties impliquées) et d’une quête partagée de changement
Categorical Data Structures for Technical Computing
No full textMany mathematical objects can be represented as functors fromfinitely-presented categories to . For instance,graphs are functors to from the category with two parallelarrows. Such functors are known informally as -sets. In this paper,we describe and implement an extension of -sets having dataattributes with fixed types, such as graphs with labeled vertices orreal-valued edge weights. We call such structures "acsets," short for"attributed -sets." Derived from previous work on algebraicdatabases, acsets are a joint generalization of graphs and data frames. Theyalso encompass more elaborate graph-like objects such as wiring diagrams andPetri nets with rate constants. We develop the mathematical theory of acsetsand then describe a generic implementation in the Julia programming language,which uses advanced language features to achieve performance comparable withspecialized data structures.Comment: 27 pages, 7 figure
Algebraic coherent confluence and higher globular Kleene algebras
No full textWe extend the formalisation of confluence results in Kleene algebras to aformalisation of coherent confluence proofs. For this, we introduce thestructure of higher globular Kleene algebra, a higher-dimensionalgeneralisation of modal and concurrent Kleene algebra. We calculate a coherentChurch-Rosser theorem and a coherent Newman's lemma in higher Kleene algebrasby equational reasoning. We instantiate these results in the context of higherrewriting systems modelled by polygraphs
Permutations avoiding 4321 and 3241 have an algebraic generating function
No full textWe show that permutations avoiding both of the (classical) patterns 4321 and3241 have the algebraic generating function conjectured by Vladimir Kruchinin.Comment: 11 pages, 6 figures, final version, to appear, Discrete Mathematics & Theoretical Computer Science (DMTCS
On commutativity of prime rings with skew derivations
No full textLet be a prime ring of Char and be a positive integer. If is a nonzero skew derivation with an associatedautomorphism of such that for all , then is commutative
Computing Parameterized Invariants of Parameterized Petri Nets
No full textA fundamental advantage of Petri net models is the possibility toautomatically compute useful system invariants from the syntax of the net.Classical techniques used for this are place invariants, P-components, siphonsor traps. Recently, Bozga et al. have presented a novel technique for the\emph{parameterized} verification of safety properties of systems with a ringor array architecture. They show that the statement \enquote{for every instanceof the parameterized Petri net, all markings satisfying the linear invariantsassociated to all the P-components, siphons and traps of the instance are safe}can be encoded in \acs{WS1S} and checked using tools like MONA. However, whilethe technique certifies that this infinite set of linear invariants extractedfrom P-components, siphons or traps are strong enough to prove safety, it doesnot return an explanation of this fact understandable by humans. We present aCEGAR loop that constructs a \emph{finite} set of \emph{parameterized}P-components, siphons or traps, whose infinitely many instances are strongenough to prove safety. For this we design parameterization procedures fordifferent architectures.Comment: Final version from edito
Photometric DIC: a unified framework for global Stereo Digital Image Correlation based on the construction of textured digital twins
No full textAn innovative approach allowing to rigorously address surface curvature and lighting effects in Digital Image Correlation (DIC) is proposed. We draw inspiration from the research work in Computer Vision (CV) regarding the physical modelling of a camera and adopt it to bring novel and significant capabilities for full-field measurements in experimental solid mechanics. It gives rise to a unified framework for global stereo DIC that we call Photometric DIC (PhDIC). It is based on the irradiance equation that relies on physical considerations and explicit assumptions, which stands for a clear breakthrough compared to the usual grey level conservation assumption. Most importantly, it allows to define a Digital Twin of the Region of Interest, which makes it possible to compare a model with different observations (real images taken from different viewpoints). This results in a consistent formalism throughout the framework, suitable for large-deformation and large-strain displacement measurements. The potential of PhDIC is illustrated on a real case. Multi-view images are first used to measure (or scan) the shape and albedo (sometimes called intrinsic texture) of an open-hole plate. The kinematic basis considered for the displacement measurement is associated to a Finite-Element mesh. Results for the shape and albedo measurement are compared for two completely different sets of pictures. Eventually, a large displacement of the structure is measured using a well-chosen single image