Generalized diagonal crossed products and smash products for quasi-Hopf algebras. Applications

In this paper we introduce generalizations of diagonal crossed products, two-sided crossed products and two-sided smash products, for a quasi-Hopf algebra H. The results we obtain may be applied to H^*-Hopf bimodules and generalized Yetter-Drinfeld modules. The generality of our situation entails that the "generating matrix" formalism cannot be used, forcing us to use a different approach. This pays off because as an application we obtain an easy conceptual proof of an important but very technical result of Hausser and Nill concerning iterated two-sided crossed products.Comment: 41 pages, no figure

Collaborative Delivery with Energy-Constrained Mobile Robots

We consider the problem of collectively delivering some message from a specified source to a designated target location in a graph, using multiple mobile agents. Each agent has a limited energy which constrains the distance it can move. Hence multiple agents need to collaborate to move the message, each agent handing over the message to the next agent to carry it forward. Given the positions of the agents in the graph and their respective budgets, the problem of finding a feasible movement schedule for the agents can be challenging. We consider two variants of the problem: in non-returning delivery, the agents can stop anywhere; whereas in returning delivery, each agent needs to return to its starting location, a variant which has not been studied before. We first provide a polynomial-time algorithm for returning delivery on trees, which is in contrast to the known (weak) NP-hardness of the non-returning version. In addition, we give resource-augmented algorithms for returning delivery in general graphs. Finally, we give tight lower bounds on the required resource augmentation for both variants of the problem. In this sense, our results close the gap left by previous research.Comment: 19 pages. An extended abstract of this paper was published at the 23rd International Colloquium on Structural Information and Communication Complexity 2016, SIROCCO'1

On Iterated Twisted Tensor Products of Algebras

We introduce and study the definition, main properties and applications of iterated twisted tensor products of algebras, motivated by the problem of defining a suitable representative for the product of spaces in noncommutative geometry. We find conditions for constructing an iterated product of three factors, and prove that they are enough for building an iterated product of any number of factors. As an example of the geometrical aspects of our construction, we show how to construct differential forms and involutions on iterated products starting from the corresponding structures on the factors, and give some examples of algebras that can be described within our theory. We prove a certain result (called ``invariance under twisting'') for a twisted tensor product of two algebras, stating that the twisted tensor product does not change when we apply certain kind of deformation. Under certain conditions, this invariance can be iterated, containing as particular cases a number of independent and previously unrelated results from Hopf algebra theory.Comment: 44 pages, 21 figures. More minor typos corrections, one more example and some references adde

On the Power of Waiting when Exploring Public Transportation Systems

International audienceWe study the problem of exploration by a mobile entity (agent) of a class of dynamic networks, namely the periodically-varying graphs (the PV-graphs, modeling public transportation systems, among others). These are defined by a set of carriers following infinitely their prescribed route along the stations of the network. Flocchini, Mans, and Santoro (ISAAC 2009) studied this problem in the case when the agent must always travel on the carriers and thus cannot wait on a station. They described the necessary and sufficient conditions for the problem to be solvable and proved that the optimal number of steps (and thus of moves) to explore a n-node PV-graph of k carriers and maximal period p is in Theta(k p^2) in the general case. In this paper, we study the impact of the ability to wait at the stations. We exhibit the necessary and sufficient conditions for the problem to be solvable in this context, and we prove that waiting at the stations allows the agent to reduce the worst-case optimal number of moves by a multiplicative factor of at least Theta(p), while the time complexity is reduced to Theta(n p). (In any connected PV-graph, we have n < k p$.) We also show some complementary optimal results in specific cases (same period for all carriers, highly connected PV-graphs). Finally this new ability allows the agent to completely map the PV-graph, in addition to just explore it

More efficient periodic traversal in anonymous undirected graphs

We consider the problem of periodic graph exploration in which a mobile entity with constant memory, an agent, has to visit all n nodes of an arbitrary undirected graph G in a periodic manner. Graphs are supposed to be anonymous, that is, nodes are unlabeled. However, while visiting a node, the robot has to distinguish between edges incident to it. For each node v the endpoints of the edges incident to v are uniquely identified by different integer labels called port numbers. We are interested in minimisation of the length of the exploration period. This problem is unsolvable if the local port numbers are set arbitrarily. However, surprisingly small periods can be achieved when assigning carefully the local port numbers. Dobrev et al. described an algorithm for assigning port numbers, and an oblivious agent (i.e. agent with no memory) using it, such that the agent explores all graphs of size n within period 10n. Providing the agent with a constant number of memory bits, the optimal length of the period was previously proved to be no more than 3.75n (using a different assignment of the port numbers). In this paper, we improve both these bounds. More precisely, we show a period of length at most 4 1/3 n for oblivious agents, and a period of length at most 3.5n for agents with constant memory. Moreover, we give the first non-trivial lower bound, 2.8n, on the period length for the oblivious case

Mobile agent rendezvous: A survey

Abstract. Recent results on the problem of mobile agent rendezvous on distributed networks are surveyed with an emphasis on outlining the various approaches taken by researchers in the theoretical computer science community.

Collision-Free Network Exploration

International audienceA set of mobile agents is placed at different nodes of a $n$-node network. The agents synchronously move along the network edges in a {\em collision-free} way, i.e., in no round may two agents occupy the same node. In each round, an agent may choose to stay at its currently occupied node or to move to one of its neighbors. An agent has no knowledge of the number and initial positions of other agents. We are looking for the shortest possible time required to complete the collision-free {\em network exploration}, i.e., to reach a configuration in which each agent is guaranteed to have visited all network nodes and has returned to its starting location. We first consider the scenario when each mobile agent knows the map of the network, as well as its own initial position. We establish a connection between the number of rounds required for collision-free exploration and the degree of the minimum-degree spanning tree of the graph. We provide tight (up to a constant factor) lower and upper bounds on the collision-free exploration time in general graphs, and the exact value of this parameter for trees. For our second scenario, in which the network is unknown to the agents, we propose collision-free exploration strategies running in $O(n^2)$ rounds for tree networks and in $O(n^5\log n)$ rounds for general networks

The insulin polymorphism -23Hph increases the risk for type 1 diabetes mellitus in the Romanian population

The insulin -23Hph and IGF2 Apa polymorphisms were genotyped in Romanian patients with T1DM (n = 204), T2DM (n = 215) or obesity (n = 200) and normoponderal healthy subjects (n = 750). The genotypes of both polymorphisms were distributed in concordance with Hardy-Weinberg equilibrium in all groups. The -23Hph AA genotype increased the risk for T1DM (OR: 3.22, 95%CI: 2.09-4.98, p < 0,0001), especially in patients without macroalbuminuria (OR: 4.32, 95%CI: 2.54-7.45, p < 0,0001). No other significant association between the alleles or genotypes of insulin -23Hph and IGF2 Apa and diabetes or obesity was identified

Identification of the pathological alterations underlying respiratory failure in myotonic dystrophy transgenic mice

AbstractMyotonic dystrophy type 1 (DM1), also known as Steinert's disease, is an inherited autosomal dominant disease. DM1 is characterized by myotonia, muscular weakness and atrophy, but it has a multisystemic phenotype. The genetic basis of the disease is the abnormal expansion of CTG repeats in the 3' untranslated region of the DM protein kinase (DMPK) gene on chromosome 19. The size of the expansion correlates to the severity of the disease and the age of onset.Respiratory problems have long been recognized to be a major feature of the disease and are the main factor contributing to mortality ; however the mechanisms are only partly known. The aim of our study is to investigate whether respiratory failure results only from the involvement of the dystrophic process at the level of the respiratory muscles or comes also from abnormalities in the neuronal network that generates and controls the respiratory rhythm. The generation of valid transgenic mice displaying the human DM1 phenotype by the group of Dr. Gourdon provided us a useful tool to analyze the brain stem respiratory neurons, spinal phrenic motoneurons and phrenic nerves. We examined therefore these structures in transgenic mice carrying 350-500 CTGs and displaying a mild form of the disease (DM1 mice). The morphological and morphometric analysis of diaphragm muscle sections revealed a denervation of the end-plates (EPs), characterized by a decrease in size and shape complexity of EPs and a reduction in the density of acetylcholine receptors (AChRs). Also a strong and significant reduction in the number of phrenic unmyelinated fibers was detected, but not in the myelinated fibers. In addition, no pathological changes were detected in the cervical motoneurons and medullary respiratory centers (Panaite et al., 2008). These results suggest that the breathing rhythm is probably not affected in mice expressing a mild form of DM1, but rather the transmission of action potentials at the level of diaphragm NMJs is deficient.Because size of the mutation increases over generations, new transgenic mice were obtained from the mice with 350-500 CTGs, resulting from a large increase of CTG repeat in successive generations, these mice carry more than 1300 CTGs (DMSXL) and display a severe DM1 phenotype (Gomes-Pereira et al., 2007). Before we study the mechanism underlying the respiratory failure in DMSXL mice, we analyzed the peripheral nervous system (PNS) in these mice by electrophysiological, histological and morphometric methods. Our results provide strong evidence that DMSXL mice have motor neuropathy (Panaite et al., 2010, submitted). Therefore the DMSXL mice expressing severe DM1 features represent for us a good tool to investigate, in the future, the physiological, structural and molecular alterations underlying respiratory failure in DM1. Understanding the mechanism of respiratory deficiency will help to better target the therapy of these problems in DM1 patients. In addition our results may, in the future, orientate pharmaceutical and clinical research towards possible development of therapy against respiratory deficits associated with the DM1.RésuméLa dystrophic myotonique type 1 (DM1), aussi dénommée maladie de Steinert, est une maladie héréditaire autosomique dominante. Elle est caractérisée par une myotonie, une faiblesse musculaire avec atrophie et se manifeste aussi par un phénotype multisystémique. La base génétique de la maladie est une expansion anormale de répétitions CTG dans une région non traduite en 3' du gène de la DM protéine kinase (DMPK) sur le chromosome 19. La taille de l'expansion est corrélée avec la sévérité et l'âge d'apparition de DM1.Bien que les problèmes respiratoires soient reconnus depuis longtemps comme une complication de la maladie et soient le principal facteur contribuant à la mortalité, les mécanismes en sont partiellement connus. Le but de notre étude est d'examiner si l'insuffisance respiratoire de la DM1 est dû au processus dystrophique au niveau des muscles respiratoires ou si elle est entraînée aussi par des anomalies dans le réseau neuronal qui génère et contrôle le rythme respiratoire. La production par le groupe du Dr. Gourdon de souris transgéniques de DM1, manifestant le phénotype de DM1 humaine, nous a fourni un outil pour analyser les nerfs phréniques, les neurones des centres respiratoires du tronc cérébral et les motoneurones phréniques. Par conséquence, nous avons examiné ces structures chez des souris transgéniques portant 350-500 CTG et affichant une forme légère de la maladie (souris DM1). L'analyse morphologique et morphométrique des sections du diaphragme a révélé une dénervation des plaques motrices et une diminution de la taille et de la complexité de la membrane postsynaptîque, ainsi qu'une réduction de la densité des récepteurs à l'acétylcholine. Nous avons aussi détecté une réduction significative du nombre de fibres nerveuses non myélinisées mais pas des fibres myélinisées. Par ailleurs, aucun changement pathologique n'a été détecté pour les neurones moteurs médullaires cervicaux et centres respiratoires du tronc cérébral (Panaite et al., 2008). Ces résultats suggèrent que le iythme respiratoire n'est probablement pas affecté chez les souris manifestant une forme légère du DM1, mais plutôt que la transmission des potentiels d'action au niveau des plaques motrices du diaphragme est déficiente.Comme la taille du mutation augmente au fil des générations, de nouvelles souris transgéniques ont été générés par le groupe Gourdon; ces souris ont plus de 1300 CTG (DMSXL) et manifestent un phénotype sévère du DM1 (Gomes-Pereira et al., 2007). Avant d'étudier le mécanisme sous-jacent de l'insuffisance respiratoire chez les souris DMSXL, nous avons analysé le système nerveux périphérique chez ces souris par des méthodes électrophysiologiques, histologiques et morphométriques. Nos résultats fournissent des preuves solides que les souris DMSXL manifestent une neuropathie motrice (Panaite et al., 2010, soumis). Par conséquent, les souris DMSXL représentent pour nous un bon outil pour étudier, à l'avenir, les modifications physiologiques, morphologiques et moléculaires qui sous-tendent l'insuffisance respiratoire du DM1. La connaissance du mécanisme de déficience respiratoire en DM1 aidera à mieux cibler le traitement de ces problèmes aux patients. De plus, nos résultats pourront, à l'avenir, orienter la recherche pharmaceutique et clinique vers le développement de thérapie contre le déficit respiratoire associé à DM1