Weak systems of Gandy, Jensen and Devlin

In Part I, we formulate and examine some systems that have arisen in the study of the constructible hierarchy; we find numerous transitive models for them, among which are supertransitive models containing all ordinals that show that Devlin's system BS lies strictly between Gandy's systems PZ and BST'; and we use our models to show that BS fails to handle even the simplest rudimentary functions, and is thus inadequate for the use intended for it in Devlin's treatise. In Part II we propose and study an enhancement of the underlying logic of these systems, build further models to show where the previous hierarchy of systems is preserved by our enhancement; and consider three systems that might serve for Devlin's purposes: one the enhancement of a version of BS, one a formulation of Gandy-Jensen set theory, and the third a subsystem common to those two. In Part III we give new proofs of results of Boffa by constructing three models in which, respectively, TCo, AxPair and AxSing fail; we give some sufficient conditions for a set not to belong to the rudimentary closure of another set, and thus answer a question of McAloon; and we comment on Gandy's numerals and correct and sharpen other of his observations.

Restricted walks in regular trees

Let T be the Cayley graph of a finitely generated free group F. Given two vertices in T consider all the walks of a given length between these vertices that at a certain time must follow a number of predetermined steps. We give formulas for the number of such walks by expressing the problem in terms of equations in F and solving the corresponding equations.

Stable rank of leavitt path algebra

We characterize the values of the stable rank for Leavitt path algebras, by giving concrete criteria in terms of properties of the underlying graph.

Chain conditions for Leavitt path algebras

In this paper, results known about the artinian and noetherian conditions for the Leavitt path algebras of graphs with finitely many vertices are extended to all row-finite graphs. In our first main result, necessary and sufficient conditions on a row-finite graph E are given so that the corresponding (not necessarily unital) Leavitt path K-algebra L(E) is semisimple. These are precisely the algebras L(E)for which every corner is left (equivalently, right)artinian. They are also precisely the algebras L(E) for which every finitely generated left (equivalently, right) L(E)-module is artinian. In our second main result, we give necessary and sufficient conditions for every corner of L(E) to be left (equivalently, right) noetherian. They also turn out to be precisely those algebras L(E) for which every finitely generated left(equivalently, right) L(E)-module is noetherian. In both situations, isomorphisms between these algebras and appropriate direct sums of matrix rings over K or K[x, x−1] are provided. Likewise, in both situations, equivalent graph theoretic conditions on E are presented.

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.

Parabolic and quasiparabolic subgroups of free partially commutative groups

Let Γ be a finite graph and G be the corresponding free partially commutative group. In this paper we study subgroups generated by vertices of the graph Γ, which we call canonical parabolic subgroups. A natural extension of the definition leads to canonical quasiparabolic subgroups. It is shown that the centralisers of subsets of G are the conjugates of canonical quasiparabolic centralisers satisfying certain graph theoretic conditions.

Dance movement patterns recognition

"Es tracta d'un projecte dividit en dues parts independents però complementàries, realitzades per autors diferents. Aquest document conté originàriament altre material i/o programari només consultable a la Biblioteca de Ciència i Tecnologia"

Properties of functional brain networks correlate with frequency of psychogenic non-epileptic seizures.

Abnormalities in the topology of brain networks may be an important feature and etiological factor for psychogenic non-epileptic seizures (PNES). To explore this possibility, we applied a graph theoretical approach to functional networks based on resting state EEGs from 13 PNES patients and 13 age- and gender-matched controls. The networks were extracted from Laplacian-transformed time-series by a cross-correlation method. PNES patients showed close to normal local and global connectivity and small-world structure, estimated with clustering coefficient, modularity, global efficiency, and small-worldness (SW) metrics, respectively. Yet the number of PNES attacks per month correlated with a weakness of local connectedness and a skewed balance between local and global connectedness quantified with SW, all in EEG alpha band. In beta band, patients demonstrated above-normal resiliency, measured with assortativity coefficient, which also correlated with the frequency of PNES attacks. This interictal EEG phenotype may help improve differentiation between PNES and epilepsy. The results also suggest that local connectivity could be a target for therapeutic interventions in PNES. Selective modulation (strengthening) of local connectivity might improve the skewed balance between local and global connectivity and so prevent PNES events.

Procesamiento de imágenes biológicas

Este proyecto se ha desarrollado a petición del CSIC. El proyecto consiste en crear una aplicación que automatice la localización y obtención de la intensidad de unos puntos luminosos en las células que aparecen en el vídeo. También se desea identificar en qué estadio celular se encuentran las células y si los puntos hallados están en la zona del septim ring. Para ello, se ha hecho un estudio y probado dos métodos para la localización de los puntos y se ha realizado un filtro mediante Adaboost para la localización de las células. También se ha realizado una interfaz gráfica para el usuario final.

EEG-based functional brain networks: does the network size matter?

Functional connectivity in human brain can be represented as a network using electroencephalography (EEG) signals. These networks--whose nodes can vary from tens to hundreds--are characterized by neurobiologically meaningful graph theory metrics. This study investigates the degree to which various graph metrics depend upon the network size. To this end, EEGs from 32 normal subjects were recorded and functional networks of three different sizes were extracted. A state-space based method was used to calculate cross-correlation matrices between different brain regions. These correlation matrices were used to construct binary adjacency connectomes, which were assessed with regards to a number of graph metrics such as clustering coefficient, modularity, efficiency, economic efficiency, and assortativity. We showed that the estimates of these metrics significantly differ depending on the network size. Larger networks had higher efficiency, higher assortativity and lower modularity compared to those with smaller size and the same density. These findings indicate that the network size should be considered in any comparison of networks across studies.

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.

Bioinformática: interfaz gráfica para comparación de genomas vía web

El proyecto consiste en un entorno gráfico cuyo fin es el de visualizar, estudiar e interpretar la conservación de código genético existente entre los diferentes genomas. Una interface que permite cargar hasta ocho genomas para ser comparados en detalle, por pares o entre todos ellos a la vez. El gráfico que se muestra en la interfaz, representa los Maximal Unique Matchings entre cada par de genomas, lo que significa coincidencias de la mayor longitud posible no repetidas, en las secuencias de ADN de las especies comparadas. La finalidad es el estudio de las evoluciones que han ido apareciendo entre diferentes organismos o los genes que comparten unas especies con otras.

Reproducibility and feasibility of a 22 joints ultrasound score in rheumatoid arthritis: a study among rheumatologists with diverse expertise in musculoskeletal ultrasound

Objective: To assess reproducibility and feasibility of amusculoskeletal ultrasound (US) score for rheumatoid arthritis amongrheumatologist with diverse expertise in US, working in private orhospital practice.Methods: The Swiss Sonography in Arthritis and Rheumatism(SONAR) group has developed a semi-quantitative score for RA usingOMERACT criteria for synovitis and erosion. The score was taught torheumatologists trained in US through two workshops. Subsequently,they were encouraged to practice in their office. For the study, we used6 US machines of different quality, each with a different patient.19 readers randomly selected among rheumatologists who haveattended both workshops, were asked to score anonymously at leastone patient. To assess whether some factors influence the score, weasked each reader to answer questionnaire describing his experiencewith US.Results: 19 rheumatologists have performed 29 scans, each patienthaving been evaluated by 4 to 6 readers. Median time for examcompletion was 20 minutes (range 15 to 60 mn). 53% ofrheumatologists work in private practice. Graph 1 show the global greyscale score for each patient. Weighted kappa was calculated for eachpair of reader using stata11. Almost all kappa of poor agreement wereobtained with a low quality device or by an assessor who havepreviously performed less than 5 scores himself.Conclusions: This is the first study to show an US score for RAfeasible by rheumatologists with diverse expertise in US both in privateand hospital practice. Reproducibility seemed to be influenced by thequality of device and previous experience with the score.

Statistical properties of subgroups of free groups

The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so-called word-based distribution: subgroups are generated (finite presentations are determined) by randomly chosen k-tuples of reduced words, whose maximal length is allowed to tend to infinity. In this paper we adopt a different, though equally natural point of view: we investigate the statistical properties of the same objects, but with respect to the so-called graph-based distribution, recently introduced by Bassino, Nicaud and Weil. Here, subgroups (and finite presentations) are determined by randomly chosen Stallings graphs whose number of vertices tends to infinity. Our results show that these two distributions behave quite differently from each other, shedding a new light on which properties of finitely generated subgroups can be considered frequent or rare. For example, we show that malnormal subgroups of a free group are negligible in the raph-based distribution, while they are exponentially generic in the word-based distribution. Quite surprisingly, a random finite presentation generically presents the trivial group in this new distribution, while in the classical one it is known to generically present an infinite hyperbolic group.

Dynamical modeling and analysis of large cellular regulatory networks.

The dynamical analysis of large biological regulatory networks requires the development of scalable methods for mathematical modeling. Following the approach initially introduced by Thomas, we formalize the interactions between the components of a network in terms of discrete variables, functions, and parameters. Model simulations result in directed graphs, called state transition graphs. We are particularly interested in reachability properties and asymptotic behaviors, which correspond to terminal strongly connected components (or "attractors") in the state transition graph. A well-known problem is the exponential increase of the size of state transition graphs with the number of network components, in particular when using the biologically realistic asynchronous updating assumption. To address this problem, we have developed several complementary methods enabling the analysis of the behavior of large and complex logical models: (i) the definition of transition priority classes to simplify the dynamics; (ii) a model reduction method preserving essential dynamical properties, (iii) a novel algorithm to compact state transition graphs and directly generate compressed representations, emphasizing relevant transient and asymptotic dynamical properties. The power of an approach combining these different methods is demonstrated by applying them to a recent multilevel logical model for the network controlling CD4+ T helper cell response to antigen presentation and to a dozen cytokines. This model accounts for the differentiation of canonical Th1 and Th2 lymphocytes, as well as of inflammatory Th17 and regulatory T cells, along with many hybrid subtypes. All these methods have been implemented into the software GINsim, which enables the definition, the analysis, and the simulation of logical regulatory graphs.