Junction conditions for finite horizon optimal control problems on multi-domains with continuous and discontinuous solutions

This paper deals with junction conditions for Hamilton-Jacobi-Bellman (HJB) equations for finite horizon control problems on multi-domains. We consider two different cases where the final cost is continuous or lower semi-continuous. In the continuous case we extend the results of "Hamilton-Jacobi-Bellman equations on multi-domains" by the second and third authors in a more general framework with switching running costs and weaker controllability assumptions. The comparison principle has been established to guarantee the uniqueness and the stability results for the HJB system on such multi-domains. In the lower semi-continuous case, we characterize the value function as the unique lower semi-continuous viscosity solution of the HJB system, under a local controllability assumption

La séparation entre Essence et Existence et son influence sur la logique chez Ibn Al-Nafīs

The separation of Avicenna between Essence and Existence influenced logic and Arab and Muslim logicians in the Middle Ages among them Ibn al-Nafīs (1208-1288). Under this influence he contributed to the development of logic and especially the theory of the universal term. By means of the consequences of this analysis: -It has become possible to make a distinction between abstract concepts and formal concepts independent of any sensible reality, and hence the questioning of Aristotelian categories, that is to say the ability to conceive for Ibn al-Nafīs like Avicenna, subjects and predicates which are not necessarily words expressing or belonging to one of the Aristotelian categories. -The analysis of the universal proposition as a conditional proposition, which made easier the distinction between absolute proposition which has no existential implication, and the other which differ from the first by an affirmation of explicit existence. La séparation d’Avicenne entre « essence » et ««existence » a influencé la logique et les logiciens arabo-musulmans au Moyen-âge, dont Ibn al-Nafīs (1208-1288). Enthousiasmé par cette conception, celui-ci a contribué au développement de la logique et à l’élaboration d’une théorie du terme (universel). Parmi les conséquences de cette analyse, notons : -La possibilité de concevoir, à côté des concepts abstraits, des concepts formels indépendants de toute réalité sensible, et de là, la remise en cause des catégories « imprédicables » aristotéliciennes, c’est-à-dire la possibilité de concevoir, pour Ibn al Nafīs comme pour Avicenne, des sujets et des prédicats qui ne sont pas nécessairement des termes exprimant ou appartenant à l’une des catégories Aristotéliciennes ; -L’analyse de la proposition universelle, qui prend la forme d’une conditionnelle, ce qui a facilité la distinction entre deux types de propositions universelles, la proposition absolue, qui n’a aucune portée existentielle, et l’autre, qui se distingue de la première par son affirmation d’existence explicite

Wi-Fi Security Analysis

AbstractIn recent years, a significant increasing in development of Wireless networks is noticed; they become an entire part of the Internet and demonstrate effectiveness in handling communication for reduced public LAN and military applications. This is mainly due to their mobility and low cost solutions; nevertheless, they are also prone to several attacks related to data integrity, Deni of Service and eavesdropping. This paper discusses wireless security protocols, their limitations and weakness. We present also an overview of the FMS (Fluhrer, Mantin, Shamir), a recovery key attack and demonstrate its effectiveness in reducing the average number of intercept packets based on a well choice of IV (initialization vectors). Some comparative experiments on ciphertext-only attacks were performed in order to study the efficiency of such technique and underline encountered difficulties

Level-set approach for Reachability Analysis of Hybrid Systems under Lag Constraints

International audienceThis study aims at characterizing a reachable set of a hybrid dynamical system with a lag constraint in the switch control. The setting does not consider any controllability assumptions and uses a level-set approach. The approach consists in the introduction of on adequate hybrid optimal control problem with lag constraints on the switch control whose value function allows a characterization of the reachable set. The value function is in turn characterized by a system of quasi-variational inequalities (SQVI). We prove a comparison principle for the SQVI which shows uniqueness of its solution. A class of numerical finite differences schemes for solving the system of inequalities is proposed and the convergence of the numerical solution towards the value function is studied using the comparison principle. Some numerical examples illustrating the method are presented. Our study is motivated by an industrial application, namely, that of range extender electric vehicles. This class of electric vehicles uses an additional module -- the range extender -- as an extra source of energy in addition to its main source -- a high voltage battery. The reachability study of this system is used to establish the maximum range of a simple vehicle model

Memes and the Spread of Misinformation: Establishing the Importance of Media Literacy in the Era of Information Disorder

Sulafa Zidani and Rachel E. Moran in “Memes and the Spread of Misinformation: Establishing the Importance of Media Literacy in the Era of Information Disorder” aim to equip students with the skills to tackle misinformation and participate in online conversations critically and ethically. The lesson does so through introducing core concepts in media literacy and participatory culture, such as “user-generated content,” “memes,” and “information disorder,” and facilitated student activities to examine their everyday social media consumption. Students will learn to identify the characteristics of culture and technology, connect user-generated content with the spread of dis/misinformation, and apply learned theories by remaking a meme or a different form of user-generated content to serve a different informational purpose

Transfinite interpolation for well-definition in error analysis in solid modelling

An overall approach to the problem of error analysis in the context of solid modelling, analogous to the standard forward/backward error analysis of Numerical Analysis, was described in a recent paper by Hoffmann and Stewart. An important subproblem within this overall approach is the well-definition of the sets specified by inconsistent data. These inconsistencies may come from the use of finite-precision real-number arithmetic, from the use of low-degree curves to approximate boundaries, or from terminating an infinite convergent (subdivision) process after only a finite number of steps. An earlier paper, by Andersson and the present authors, showed how to resolve this problem of well-definition, in the context of standard trimmed-NURBS representations, by using the Whitney Extension Theorem. In this paper we will show how an analogous approach can be used in the context of trimmed surfaces based on combined-subdivision representations, such as those proposed by Litke, Levin and Schröder. A further component of the problem of well-definition is ensuring that adjacent patches in a representation do not have extraneous intersections. (Here, "extraneous intersections" refers to intersections, between two patches forming part of the boundary, other than prescribed intersections along a common edge or at a common vertex.) The paper also describes the derivation of a bound for normal vectors that can be used for this purpose. This bound is relevant both in the case of trimmed-NURBS representations, and in the case of combined subdivision with trimming