Continuity of set-valued maps revisited in the light of tame geometry

Continuity of set-valued maps is hereby revisited: after recalling some basic concepts of variational analysis and a short description of the State-of-the-Art, we obtain as by-product two Sard type results concerning local minima of scalar and vector valued functions. Our main result though, is inscribed in the framework of tame geometry, stating that a closed-valued semialgebraic set-valued map is almost everywhere continuous (in both topological and measure-theoretic sense). The result –depending on stratification techniques– holds true in a more general setting of o-minimal (or tame) set-valued maps. Some applications are briefly discussed at the end.

Condensation of polyhedric structures onto soap films

We study the existence of solutions to general measure-minimization problems over topological classes that are stable under localized Lipschitz homotopy, including the standard Plateau problem without the need for restrictive assumptions such as orientability or even rectifiability of surfaces. In case of problems over an open and bounded domain we establish the existence of a “minimal candidate”, obtained as the limit for the local Hausdorff convergence of a minimizing sequence for which the measure is lower-semicontinuous. Although we do not give a way to control the topological constraint when taking limit yet— except for some examples of topological classes preserving local separation or for periodic two-dimensional sets — we prove that this candidate is an Almgren-minimal set. Thus, using regularity results such as Jean Taylor’s theorem, this could be a way to find solutions to the above minimization problems under a generic setup in arbitrary dimension and codimension.

Geometry and physics of knots

KNOTS are usually categorized in terms of topological properties that are invariant under changes in a knot's spatial configuration(1-4). Here we approach knot identification from a different angle, by considering the properties of particular geometrical forms which we define as 'ideal'. For a knot with a given topology and assembled from a tube of uniform diameter, the ideal form is the geometrical configuration having the highest ratio of volume to surface area. Practically, this is equivalent to determining the shortest piece of tube that can be closed to form the knot. Because the notion of an ideal form is independent of absolute spatial scale, the length-to-diameter ratio of a tube providing an ideal representation is constant, irrespective of the tube's actual dimensions. We report the results of computer simulations which show that these ideal representations of knots have surprisingly simple geometrical properties. In particular, there is a simple linear relationship between the length-to-diameter ratio and the crossing number-the number of intersections in a two-dimensional projection of the knot averaged over all directions. We have also found that the average shape of knotted polymeric chains in thermal equilibrium is closely related to the ideal representation of the corresponding knot type. Our observations provide a link between ideal geometrical objects and the behaviour of seemingly disordered systems, and allow the prediction of properties of knotted polymers such as their electrophoretic mobility(5).

Homotopy Batalin-Vilkovisky algebras

This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution we extend the theory of Koszul duality to operads and properads that are defined by quadratic and linear relations. The operad encoding Batalin-Vilkovisky algebras is shown to be Koszul in this sense. This allows us to prove a Poincaré-Birkhoff-Witt Theorem for such an operad and to give an explicit small quasi-free resolution for it. This particular resolution enables us to describe the deformation theory and homotopy theory of BV-algebras and of homotopy BV-algebras. We show that any topological conformal field theory carries a homotopy BV-algebra structure which lifts the BV-algebra structure on homology. The same result is proved for the singular chain complex of the double loop space of a topological space endowed with an action of the circle. We also prove the cyclic Deligne conjecture with this cofibrant resolution of the operad BV. We develop the general obstruction theory for algebras over the Koszul resolution of a properad and apply it to extend a conjecture of Lian-Zuckerman, showing that certain vertex algebras have an explicit homotopy BV-algebra structure.

Generador de compiladores basado en analizadores ascendentes

El objetivo fundamental de este proyecto consiste en crear un generador de compilador, basado en analizadores ascendentes. Como base para hacer este analizador se usará el lenguaje Cosel y el módulo Com, que es un generador de compiladores basado en analizadores descendentes y que actualmente se está utilizando en las prácticas de la asignatura de Compiladores I. El nuevo generador, que tiene como entrada una gramática, ha de comprobar si es una gramática ascendente LALR (1) y analizar una cadena de entrada de símbolos usando dicha gramática.

Interactive Epistemology and Reasoning: On the Foundations of Game Theory

Game theory describes and analyzes strategic interaction. It is usually distinguished between static games, which are strategic situations in which the players choose only once as well as simultaneously, and dynamic games, which are strategic situations involving sequential choices. In addition, dynamic games can be further classified according to perfect and imperfect information. Indeed, a dynamic game is said to exhibit perfect information, whenever at any point of the game every player has full informational access to all choices that have been conducted so far. However, in the case of imperfect information some players are not fully informed about some choices. Game-theoretic analysis proceeds in two steps. Firstly, games are modelled by so-called form structures which extract and formalize the significant parts of the underlying strategic interaction. The basic and most commonly used models of games are the normal form, which rather sparsely describes a game merely in terms of the players' strategy sets and utilities, and the extensive form, which models a game in a more detailed way as a tree. In fact, it is standard to formalize static games with the normal form and dynamic games with the extensive form. Secondly, solution concepts are developed to solve models of games in the sense of identifying the choices that should be taken by rational players. Indeed, the ultimate objective of the classical approach to game theory, which is of normative character, is the development of a solution concept that is capable of identifying a unique choice for every player in an arbitrary game. However, given the large variety of games, it is not at all certain whether it is possible to device a solution concept with such universal capability. Alternatively, interactive epistemology provides an epistemic approach to game theory of descriptive character. This rather recent discipline analyzes the relation between knowledge, belief and choice of game-playing agents in an epistemic framework. The description of the players' choices in a given game relative to various epistemic assumptions constitutes the fundamental problem addressed by an epistemic approach to game theory. In a general sense, the objective of interactive epistemology consists in characterizing existing game-theoretic solution concepts in terms of epistemic assumptions as well as in proposing novel solution concepts by studying the game-theoretic implications of refined or new epistemic hypotheses. Intuitively, an epistemic model of a game can be interpreted as representing the reasoning of the players. Indeed, before making a decision in a game, the players reason about the game and their respective opponents, given their knowledge and beliefs. Precisely these epistemic mental states on which players base their decisions are explicitly expressible in an epistemic framework. In this PhD thesis, we consider an epistemic approach to game theory from a foundational point of view. In Chapter 1, basic game-theoretic notions as well as Aumann's epistemic framework for games are expounded and illustrated. Also, Aumann's sufficient conditions for backward induction are presented and his conceptual views discussed. In Chapter 2, Aumann's interactive epistemology is conceptually analyzed. In Chapter 3, which is based on joint work with Conrad Heilmann, a three-stage account for dynamic games is introduced and a type-based epistemic model is extended with a notion of agent connectedness. Then, sufficient conditions for backward induction are derived. In Chapter 4, which is based on joint work with Jérémie Cabessa, a topological approach to interactive epistemology is initiated. In particular, the epistemic-topological operator limit knowledge is defined and some implications for games considered. In Chapter 5, which is based on joint work with Jérémie Cabessa and Andrés Perea, Aumann's impossibility theorem on agreeing to disagree is revisited and weakened in the sense that possible contexts are provided in which agents can indeed agree to disagree.

Bioinformática: identificar genes en una interfaz gráfica vía web para la comparación de genomas

Este trabajo desarrolla el proceso de diseño e implementación de una interfaz web que permite la exploración en detalle de las relaciones entre genomas completos. La interfaz permite la comparación simultánea de nueve genomas, representando en cada gráfica las relaciones entre cada par de genomas junto los genes identificados de cada uno de ellos. Es capaz de trabajar con genomas del dominio Eukaryota y se adapta a la capacidad de cómputo de la máquina cliente. La información representada son MUMs (Maximal Unique Matching, secuencia máxima y única encontrada en ambos genomas) y SuperMUMs (agrupación de MUMs mediante Approximate String Matching). Los datos son previamente calculados y accesibles desde un servidor web.

Evaluación de un nuevo método de sutura para la cirugía endoscopica transluminal a través de orificios naturales en un modelo animal

Natural Orifice Transluminal Endoscopic Surgery (NOTES) is a novel, potentially less invasive alternative to laparoscopic surgery. However, the problems of transluminal access and closure represent significant obstacles to its successful introduction in humans. Objective: to evaluate the feasibility and safety of a novel device designed for transluminal access and closure in a survival porcine model. Subjects: Four adult female Yorkshire pigs were used in the study. Interventions: While under general anesthesia, the animals were prepared with multiple tap water enemas followed by instillation of an antibiotic suspension and povidone-iodine lavage. At a distance of 15 to 20 cm from the anus, the prototype device (LSI Solutions, Victor, NY, USA) deployed a circumscribing purse-string suture around the planned incision site and subsequently used a blade mechanism to create a 2.5-cm linear incision. The transcolonic incision was then closed by cinching and securing the purse-string suture with a titanium knot by use of a separate hand-activated suture-locking device. Main Outcome Measurements: The animals were monitored daily for signs of peritonitis and sepsis and were survived for 14 days. The peritoneal cavity was examined for peritonitis, and the colonic incision site was examined for wound dehiscence, pericolic abscess formation, and gross adhesions. Tissue samples from both incisional and random peritoneal sites were obtained for histologic examination. Results: Transcolonic incision and closure were successful in all 4 animals. The device performed in a rapid and reproducible fashion. All animals recovered without septic complications. At necropsy, there was no evidence of peritonitis, abscesses, or wound dehiscence. Salpingocolonic and colovesicular adhesions were noted in 3 of 4 animals. Histologic examination revealed microabscesses at the incision site in all animals. Conclusions: The prototype incision and closure device represents a promising solution to the problems of transluminal access for NOTES. The presence of incision-related adhesions and microabscesses signal the need for further refinement in aseptic technique. 

Dynamical systems of type (m,n) and their C*-algebras

Given positive integers n and m, we consider dynamical systems in which n copies of a topological space is homeomorphic to m copies of that same space. The universal such system is shown to arise naturally from the study of a C*-algebra we denote by Om;n, which in turn is obtained as a quotient of the well known Leavitt C*-algebra Lm;n, a process meant to transform the generating set of partial isometries of Lm;n into a tame set. Describing Om;n as the crossed-product of the universal (m; n) -dynamical system by a partial action of the free group Fm+n, we show that Om;n is not exact when n and m are both greater than or equal to 2, but the corresponding reduced crossed-product, denoted Or m;n, is shown to be exact and non-nuclear. Still under the assumption that m; n &= 2, we prove that the partial action of Fm+n is topologically free and that Or m;n satisfies property (SP) (small projections). We also show that Or m;n admits no finite dimensional representations. The techniques developed to treat this system include several new results pertaining to the theory of Fell bundles over discrete groups.

Narrative Diagrammatik. Mit einer Modellanalyse: Die Diagrammatik des "Decameron"

Taking as a starting point the seeming inconsistency of late-medieval romances notoriously 'run wild' (verwildert), this article is concerned with the description of an abstract form of narrative coherence that is based on the notion of the diagrammatic. In a first section, this concept is illustrated in a simplified manner by an analysis of Boccaccio's Decameron based on two levels of spatial structure: that of the autograph Berlin manuscript (Codex Hamilton 90) and that of the recipient's mental visualisation of the relations between the frame and the tales of the work. It is argued that the connectivity of the work as a whole depends on the perception of those two spatial representations of the plot. A second section develops this concept in a more theoretical fashion, drawing on Charles Sanders Peirce's notion of diagrammatic reasoning as a way of perceiving relations through mental and material topological representations. Correspondingly, a view of narrative is proposed that does not depend on the traditional perspective of temporal sequence but emphasizes the spatial structure of literary narrative. It is argued that these conditions form the primary ontological mode of narrative, whereas the temporal development of a story is an aesthetic illusion that has been specifically stimulated by the narrative conventions of approximately the past three centuries and must thus be considered a secondary effect. To conclude, an interpretation in miniature of an aspect of Heinrich von Neustadt's Apollonius von Tyrland that seems to have 'run wild' is undertaken from a diagrammatic perspective.

Scaling behavior and equilibrium lengths of knotted polymers

We use numerical simulations to investigate how the chain length and topology of freely fluctuating knotted polymer rings affect their various spatial characteristics such as the radius of the smallest sphere enclosing momentary configurations of simulated polymer chains. We describe how the average value of a characteristic changes with the chain size and how this change depends on the topology of the modeled polymers. Although the scaling profiles of a spatial characteristic for distinct knot types do not intersect (at least, in the range of our data), the profiles for nontrivial knots intersect the corresponding profile obtained for phantom polymers, i.e., those that are free to explore all available topological states. For each knot type, this point of intersection defines its equilibrium length with respect to the spatial characteristic. At this chain length, a polymer forming a given knot type will not tend to increase or decrease. on average, the value of the spatial characteristic when the polymer is released from its topological constraint. We show interrelations between equilibrium lengths defined with respect to spatial characteristics of different character and observe that they are related to the lengths of ideal geometric configurations of the corresponding knot types.

Homologia de Lawson i descens

La meva recerca en els tres anys de gaudiment de beca s'ha centrat en l'estudi de teories semitopològiques definides a través d'espais de cicles algebraics, introduïts per Friedlander i Lawson. Hem estudiat propietats de descens d'aquestes teories i hem construït una successió espectral que calcula explícitament la cohomologia mòrfica d'una varietat tòrica. D'altra banda, estem treballant en l'estudi de propietats d'invariància homotòpica per la cohomologia mòrfica, així com en l'estructura algebraica dels grups d'homologia de Lawson.

Fifteen years SIB Swiss Institute of Bioinformatics: life science databases, tools and support.

The SIB Swiss Institute of Bioinformatics (www.isb-sib.ch) was created in 1998 as an institution to foster excellence in bioinformatics. It is renowned worldwide for its databases and software tools, such as UniProtKB/Swiss-Prot, PROSITE, SWISS-MODEL, STRING, etc, that are all accessible on ExPASy.org, SIB's Bioinformatics Resource Portal. This article provides an overview of the scientific and training resources SIB has consistently been offering to the life science community for more than 15 years.

Localization of breakage points in knotted strings

It is a common macroscopic observation that knotted ropes or fishing lines under tension easily break at the knot. However, a more precise localization of the breakage point in knotted macroscopic strings is a difficult task. In the present work, the tightening of knots was numerically simulated, a comparison of strength of different knots was experimentally performed and a high velocity camera was used to precisely localize the site where knotted macroscopic strings break. In the case of knotted spaghetti, the breakage occurs at the position with high curvature at the entry to the knot. This localization results from joint contributions of loading, bending and friction forces into the complex process of knot breakage. The present simulations and experiments are in agreement with recent molecular dynamics simulations of a knotted polymer chain and with experiments performed on actin and DNA filaments. The strength of the knotted string is greatly reduced (down to 50%) by the presence of a knot, therefore reducing the resistance to tension of all materials containing chains of any sort. The present work with macroscopic strings revels some important aspects, which are not accessible by experiments with microscopic chains.

The transventricular-transseptal access to the aortic root: a new route for extrapleural trans-catheter aortic stent-valve implantation.

Objective: The aim of this study was to investigate the feasibility of transventricular-transseptal approach (TVSA) for extrapleural transcatheter aortic valved stent implantation via a subxyphoidian access. Methods: In five porcine experiments (52.3 +/- 10.9 kg) the right ventricle was exposed via subxyphoidian access. Under the guidance of intracardiac echocardiography (ICE) and fluoroscopy, the transseptal access from right ventricle to left ventricle was created progressively by puncture and dilation with dilators (8F-26F). Valved stents built in-house from commercial tanned pericardium and self-expandable Nitinol stents were loaded into a cartridge. A delivery sheath was then introduced from the right ventricle into the left ventricle and then into the ascending aorta. The cartridge was connected and the valved stent was deployed in the aortic position. Then, the ventricular septal access was sealed with an Amplatzer septal occluder device and the right ventricular access was closed by tying prepared purse-string suture directly. Thirty minutes after the whole procedure, the animals were sacrificed for macroscopic evaluation of the position of valved stent and septal closure device. Result: Procedural success of TVSA was 100% at the first attempt. Mean procedure time was 49 +/- 4 min. Progressive dilatation of the transseptal access resulted in a measurable ventricular septal defect (VSD) after dilator sizes 18F and more. All valved stents were delivered at the target site over the native aortic valve with good acute valve function and no paravalvular leaks. During the procedure, premature beats (5/5) and supraventriclar tachycardias (5/5) were observed, but no atrial-ventricular block (0/5) occurred. Heart rate before (after) was 90 +/- 3 beats min(-1) (100 +/- 2 beats min(-1): p < 0.05), whereas blood pressure was 60 + 1 mm Hg (55 + 2 mm Hg (p < 0.05)). Total blood loss was 280 + 10 ml. The Amplatzer septal occluder devices were fully deployed and the ventricular septal accesses were sealed successfully, without detectable residual shunt. Conclusion: Trans-catheter implantation of aortic valved stent via extrapleural transventricular-transseptal access is technically feasible and has the potential for a simplified procedure under local anaesthesia. (C) 2010 European Association for Cardio-Thoracic Surgery. Published by Elsevier B. V. All rights reserved.