Non-semi-regular quantum groups coming from number theory

In this paper, we study C*-algebraic quantum groups obtained through the bicrossed product construction. Examples using groups of adeles are given and they provide the first examples of locally compact quantum groups which are not semi-regular: the crossed product of the quantum group acting on itself by translations does not contain any compact operator. We describe all corepresentations of these quantum groups and the associated universal C*-algebras. On the way, we provide several remarks on C*-algebraic properties of quantum groups and their actions.Comment: 25 pages LaTe

Managing Price Uncertainty in Prosumer-Centric Energy Trading: A Prospect-Theoretic Stackelberg Game Approach

In this paper, the problem of energy trading between smart grid prosumers, who can simultaneously consume and produce energy, and a grid power company is studied. The problem is formulated as a single-leader, multiple-follower Stackelberg game between the power company and multiple prosumers. In this game, the power company acts as a leader who determines the pricing strategy that maximizes its profits, while the prosumers act as followers who react by choosing the amount of energy to buy or sell so as to optimize their current and future profits. The proposed game accounts for each prosumer's subjective decision when faced with the uncertainty of profits, induced by the random future price. In particular, the framing effect, from the framework of prospect theory (PT), is used to account for each prosumer's valuation of its gains and losses with respect to an individual utility reference point. The reference point changes between prosumers and stems from their past experience and future aspirations of profits. The followers' noncooperative game is shown to admit a unique pure-strategy Nash equilibrium (NE) under classical game theory (CGT) which is obtained using a fully distributed algorithm. The results are extended to account for the case of PT using algorithmic solutions that can achieve an NE under certain conditions. Simulation results show that the total grid load varies significantly with the prosumers' reference point and their loss-aversion level. In addition, it is shown that the power company's profits considerably decrease when it fails to account for the prosumers' subjective perceptions under PT

Unitaires multiplicatifs en dimension finie et leurs sous-objets

A pre-subgroup of a multiplicative unitary $V$ on a finite dimensionnal Hilbert space $H$ is a vector line $L$ in $H$ such that $V(L\otimes L)=L\otimes L$. We show that there are finitely many pre-subgroups, give a Lagrange theorem and generalize the construction of a `bi-crossed product'. Moreover, we establish bijections between pre-subgroups and coideal subalgebras of the Hopf algebra associated with $V$, and therefore with the intermediate subfactors of the associated (depth two) inclusions. Finally, we show that the pre-subgroups classify the subobjects of $(H,V)$.Comment: 34 page

Estudio documental sobre la viabilidad de la seguridad electrónica para la protección de estudiantes y docentes en instituciones educativas de básica primaria y media vocacional en Bogotá

En Colombia, específicamente en Bogotá, uno de cada dos estudiantes ha sido víctima de robo en el colegio, asimismo uno de cada tres ha sido agredido a golpes y expuesto a maltrato físico por parte de sus compañeros, un alto porcentaje de los agredidos requirió atención médica por esta causa y un alto porcentaje de los agredidos fue amenazado con arma de fuego, corto-punzante y contundente, todo esto asociado a la realidad del país, la cual está marcada por un conflicto armado prolongado, afecta de manera manifiesta la dinámica educativa e influye en las conductas agresivas de los estudiantes de cada región. Durante el 2007, y aún en años anteriores, se ha podido ver en diferentes partes del país manifestaciones de violencia en las instituciones educativas. La pobreza, el pandillismo, las drogas, la violencia intrafamiliar, los medios de comunicación, el conflicto armado y otros factores, se suman a las causas que liberan la violencia en las aulas clases. Por eso se hace necesario saber cómo es el estado del arte acerca de la implementación de tecnologías de vigilancia en escuelas de la ciudad de Bogotá, para lo cual se realizo una búsqueda bibliográfica y su posterior tabulación y análisis estadístico encontrando que el 52.9% de la información hallada es de procedencia colombiana, 54.5% de la información encontrada se hayo por medio del buscador Google y el 52.9% del fue escrito en formato de publicación de articulo de internetPregrad

Performance Limits of a Deep Learning-Enabled Text Semantic Communication under Interference

A deep learning (DL)-enabled semantic communication (SemCom) has emerged as a 6G enabler while promising to minimize power usage, bandwidth consumption, and transmission delay by minimizing irrelevant information transmission. However, the benefits of such a semantic-centric design can be limited by radio frequency interference (RFI) that causes substantial semantic noise. The impact of semantic noise due to interference can be alleviated using an interference-resistant and robust (IR$^2$) SemCom design. Nevertheless, no such design exists yet. To shed light on this knowledge gap and stimulate fundamental research on IR$^2$ SemCom, the performance limits of a text SemCom system named DeepSC are studied in the presence of (multi-interferer) RFI. By introducing a principled probabilistic framework for SemCom, we show that DeepSC produces semantically irrelevant sentences as the power of (multi-interferer) RFI gets very large. We also derive DeepSC's practical limits and a lower bound on its outage probability under multi-interferer RFI. Toward a fundamental 6G design for an IR$^2$ SemCom, moreover, we propose a generic lifelong DL-based IR$^2$ SemCom system. Eventually, we corroborate the derived performance limits with Monte Carlo simulations and computer experiments, which also affirm the vulnerability of DeepSC and DL-enabled text SemCom to a wireless attack using RFI

Étude du décalage en cisaillement dans les assemblages soudés de poutres à treillis en acier

Le travail porte sur les effets du décalage en cisaillement sur la résistance en traction des membrures d'âmes des poutres à treillis métalliques. Étant donné qu'une seule partie de la section des membrures est raccordée à la membrure principale, la distribution des contraintes est non uniforme réduisant ainsi la résistance à la traction de ces membrures. Une recherche bibliographique a été effectuée afin de préciser le sujet de recherche et de permettre au lecteur de situer le travail dans l'ensemble de la recherche faite à ce jour. Par la suite, une approche rationnelle a été développée afin de visualiser et de comprendre la distribution des contraintes au voisinage des assemblages. Cette approche a été validée par un modèle mathématique et appuyée par des résultats expérimentaux. Enfin, une analyse par éléments finis a ensuite été effectuée. Elle a permis d'appuyer la forme des diagrammes des contraintes obtenus par la méthode rationnelle

Gastric Pouch Gastrointestinal Stromal Tumour Post-Roux-en-Y Gastric Bypass: A First Reported Case

Gastric gastrointestinal stromal tumour is an extremely rare condition to occur after bariatric surgery. To the authors’ knowledge, only two cases of gastric gastrointestinal stromal tumours after Roux-en-Y gastric bypass have been reported in the medical literature, both occurring in the excluded gastric remnant. Herein, the authors report the third case of gastric gastrointestinal stromal tumour post-Roux-en-Y gastric bypass, and the first case to occur in the gastric pouch, which was managed surgically by laparoscopic resection. From here, combining the observations of clinicians treating and following up patients post-bariatric surgery in an international database will be beneficial to patients, and aid in development of surveillance guidelines