Random graphs on surfaces

Counting labelled planar graphs, and typical properties of random labelled planar graphs, have received much attention recently. We start the process here of extending these investigations to graphs embeddable on any fixed surface S. In particular we show that the labelled graphs embeddable on S have the same growth constant as for planar graphs, and the same holds for unlabelled graphs. Also, if we pick a graph uniformly at random from the graphs embeddable on S which have vertex set {1, . . . , n}, then with probability tending to 1 as n → ∞, this random graph either is connected or consists of one giant component together with a few nodes in small planar components.

On spectral approximation, Folner sequences and crossed products

In this article we review first some of the possibilities in which the notions of Fo lner sequences and quasidiagonality have been applied to spectral approximation problems. We construct then a canonical Fo lner sequence for the crossed product of a concrete C* -algebra and a discrete amenable group. We apply our results to the rotation algebra (which contains interesting operators like almost Mathieu operators or periodic magnetic Schrödinger operators on graphs) and the C* -algebra generated by bounded Jacobi operators.

Comparing Random-based and k-Anonymity-Based Algorithms for Graph Anonymization

Recently, several anonymization algorithms have appeared for privacy preservation on graphs. Some of them are based on random-ization techniques and on k-anonymity concepts. We can use both of them to obtain an anonymized graph with a given k-anonymity value. In this paper we compare algorithms based on both techniques in orderto obtain an anonymized graph with a desired k-anonymity value. We want to analyze the complexity of these methods to generate anonymized graphs and the quality of the resulting graphs.

Comparing Random-based and k-Anonymity-Based Algorithms for Graph Anonymization

Recently, several anonymization algorithms have appeared for privacy preservation on graphs. Some of them are based on random-ization techniques and on k-anonymity concepts. We can use both of them to obtain an anonymized graph with a given k-anonymity value. In this paper we compare algorithms based on both techniques in orderto obtain an anonymized graph with a desired k-anonymity value. We want to analyze the complexity of these methods to generate anonymized graphs and the quality of the resulting graphs.

A note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits.

A Note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits

Orthogonal systems in finite grahps

To a finite graph there corresponds a free partially commutative group: with the given graph as commutation graph. In this paper we construct an orthogonality theory for graphs and their corresponding free partially commutative groups. The theory developed here provides tools for the study of the structure of partially commutative groups, their universal theory and automorphism groups. In particular the theory is applied in this paper to the centraliser lattice of such groups.

Monads in double categories

We extend the basic concepts of Street's formal theory of monads from the setting of 2-categories to that of double categories. In particular, we introduce the double category Mnd(C) of monads in a double category C and dene what it means for a double category to admit the construction of free monads. Our main theorem shows that, under some mild conditions, a double category that is a framed bicategory admits the construction of free monads if its horizontal 2-category does. We apply this result to obtain double adjunctions which extend the adjunction between graphs and categories and the adjunction between polynomial endofunctors and polynomial monads.

Biofeedback : retroalimentación electroencefalográfica : estudio de la efectividad de la adopción de patrones neuronales por entrenamiento para paliar el dolor

S’ha demostrat que la pràctica d'estats de relaxació profunda redueix el dolor i incrementa el benestar i la qualitat de vida. Els estats de relaxació profunda i meditació estan al seu torn associats a patrons electroencefalogràfics (EEG) característics. En el present projecte proposem un procediment pal·liatiu del dolor basat en l 'entrenament autodidàctic per aconseguir aquests estats de relaxació. Per a això es proposa retro-alimentar al subjecte un senyal auditiu reflex de la seva activitat EEG que l'ajudi a modificar voluntàriament la seva activitat cerebral, la qual cosa li permet aproximar-la progressivament al patró EEG corresponent al de relaxació profunda desitjat. S’ha dissenyat un protocol d'entrenament d'estats mentals de relaxació i meditació (entre altres) i implementat un programa que processa el senyal EEG i genera un senyal auditiu reflex de l'activitat cerebral de l'individu. També registra les lectures EEG del progrés de l'individu, genera les gràfiques corresponents i genera dades estadístiques per a futur anàlisi.

Coneixements i usos lingüístics de l'estudiantat de la Universitat de Lleida (2012 / 2013). Estudi comparatiu dels resultats obtinguts el 1993/1994 amb els de l’actualitat

El treball que teniu a les mans és una recerca sociolingüística que té com a objectiu l’anàlisi dels coneixements i els usos lingüístics de la Universitat de Lleida, a partir de la comparació dels resultats obtinguts a “Coneixements i usos lingüístics de l’estudiantat de la Universitat de Lleida” (Curs 1993/1994), un estudi impulsat des dels Servei de Llengua i Terminologia l’any 1993. L’elaboració del treball es divideix en tres etapes: l’etapa d’investigació, l’etapa d’organització i l’etapa d’interpretació. La primera etapa ha estat destinada a la recollida de dades. He demanat a un total de 1046 alumnes provinents de vint-i-un graus o especialitat diferents que contestessin un qüestionari. La segona etapa consisteix en l’organització de les dades. El primer que he fet ha estat entrar els resultats de cadascuna de les enquestes al programa ACCES, el qual m’ha permès fer les posteriors agrupacions partint sempre del model de 1993. Una vegada he tingut totes les agrupacions fetes, he fet tots els percentatges, gràfiques i taules al programa Excel. Finalment, quan ja he tingut tots els gràfics i taules confeccionats he passat ja a l’última etapa del treball: la interpretació de les dades. Primer he fet una lectura de cadascun dels gràfics i taules, comparant-los posteriorment amb els resultats obtinguts el 1993. Una vegada he tingut tots els comentaris fets he passat ja al més important: la redacció de les conclusions, on intento explicar els canvis més importants que he copsat.

On the number of K3,3-minor-free and maximal K3,3-minor-free graphs

"Vegeu el resum a l'inici del document del fitxer adjunt."

Free triples, large indifference classes and the majority rule

We present a new domain of preferences under which the majority relation is always quasi-transitive and thus Condorcet winners always exist. We model situations where a set of individuals must choose one individual in the group. Agents are connected through some relationship that can be interpreted as expressing neighborhood, and which is formalized by a graph. Our restriction on preferences is as follows: each agent can freely rank his immediate neighbors, but then he is indifferent between each neighbor and all other agents that this neighbor "leads to". Hence, agents can be highly perceptive regarding their neighbors, while being insensitive to the differences between these and other agents which are further removed from them. We show quasi-transitivity of the majority relation when the graph expressing the neighborhood relation is a tree. We also discuss a further restriction allowing to extend the result for more general graphs. Finally, we compare the proposed restriction with others in the literature, to conclude that it is independent of any previously discussed domain restriction.

A class of stochastic games with infinitely many interacting agents related to Glauber dynamics on random graphs

We introduce and study a class of infinite-horizon nonzero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove that, as time goes to infinity, the game converges to a Nash equilibrium. Moreover, assuming that all agents adopt the same strategy, using arguments related to those leading to perfect simulation algorithms, spatial mixing and ergodicity are proved. In turn, ergodicity allows us to prove “fixation”, i.e. that players will adopt a constant strategy after a finite time. The resulting dynamics is related to zerotemperature Glauber dynamics on random graphs of possibly infinite volume.

On locally finite transitive two-ended digraphs

Projecte de recerca elaborat a partir d’una estada al Department de Matemàtica Aplicada de la Montanuniversität Leoben, Àustria, entre agost i desembre del 2006. L’ objectiu ha estat fer recerca sobre digrafs infinits amb dos finals, connexos i localment finits, i, en particular, en digrafs amb dos finals i altament arc-transitius. Malnic, Marusic et al. van introduir un nou tipus de relació d’equivalència en els vèrtexs d’un dígraf, anomenades relacions d’assolibilitat, que generalitzen i tenen el seu origen en un problema posat per Cameron et al., on les classes de la relació d’equivalència eren vèrtexs que pertanyien a un camí alternat del dígraf . Malnic et al. en el mencionat article van establir connexions ben estretes entre aquestes relacions d’assolibilitat i l'estructura de finals i creixement dels digrafs localment finits i transitius. En aquest treball, s’ha caracteritzat per complet aquestes relacions d’assolibitat en el cas de dígrafs localment finits i transitius amb exactament dos finals, en termes de la descomposició en números primers del número de línies que genera el digraf amb dos finals. A més, es nega la Conjectura 1 sostinguda per Seifter que afirmava que un digraf connex localment finit amb més d’un final era necessàriament o be 0-, 1- o altament arc-transitiu. Seifer havia donat una solució parcial a la conjectura pel cas de digrafs regulars amb grau primer que tinguin un conjunt de tall connex. En aquest treball, es descriu una família infinita de dígrafs regulars de grau dos, amb dos finals, exactament 2-arc transitius i no 3-arc transitius. Així, es nega la Conjectura de Seifter en el cas general, fins i tot per grau primer. Tot i així, la solució parcial donada per Seifter en el seu article és en cert sentit la millor possible i l'existència un conjunt de tall connex essencial.

Econometrics and decision making: Effects of presentation mode

Much of empirical economics involves regression analysis. However, does thepresentation of results affect economists ability to make inferences for decision makingpurposes? In a survey, 257 academic economists were asked to make probabilisticinferences on the basis of the outputs of a regression analysis presented in a standardformat. Questions concerned the distribution of the dependent variable conditional onknown values of the independent variable. However, many respondents underestimateduncertainty by failing to take into account the standard deviation of the estimatedresiduals. The addition of graphs did not substantially improve inferences. On the otherhand, when only graphs were provided (i.e., with no statistics), respondents weresubstantially more accurate. We discuss implications for improving practice in reportingresults of regression analyses.