Polynomial functors and trees

We explore the relationship between polynomial functors and trees. In the first part we characterise trees as certain polynomial functors and obtain a completely formal but at the same time conceptual and explicit construction of two categories of rooted trees, whose main properties we describe in terms of some factorisation systems. The second category is the category Ω of Moerdijk and Weiss. Although the constructions are motivated and explained in terms of polynomial functors, they all amount to elementary manipulations with finite sets. Included in Part 1 is also an explicit construction of the free monad on a polynomial endofunctor, given in terms of trees. In the second part we describe polynomial endofunctors and monads as structures built from trees, characterising the images of several nerve functors from polynomial endofunctors and monads into presheaves on categories of trees. Polynomial endofunctors and monads over a base are characterised by a sheaf condition on categories of decorated trees. In the absolute case, one further condition is needed, a projectivity condition, which serves also to characterise polynomial endofunctors and monads among (coloured) collections and operads.

Dynamics in Thompson's group F

We describe an explicit relationship between strand diagrams and piecewise-linear functions for elements of Thompson’s group F. Using this correspondence, we investigate the dynamics of elements of F, and we show that conjugacy of one-bump functions can be described by a Mather-type invariant.

Still in the Era of Area Studies? Political-Scientific Perspectives on European Competition Policy in the 2000s

This note reviews the political-scientific literature on European competition policy (ECP) in the 2000s. Based on a data set extracted from four well-known journals, and using an upfront methodology and explicit criteria, it analyzes the literature both quantitatively and qualitatively. On the quantitative side, it shows that, although a few sub-policy areas are still neglected, ECP is not the under-researched policy it used to be. On the qualitative side, the literature has greatly improved since the 1990s: Almost all articles now present a clear research question, and most advance specific theoretical claims/hypotheses. Yet, improvements can be made on research design, statistical testing, and, above all, state-of-the-art theorizing (e.g. in the game-theoretical treatment of delegation problems). Indeed, it is paradoxical that ECP specialists do not pay more attention to theoretical questions which are so central to the actual policy area they study.

The role of fixed delays in neuronal rate models

Fixed delays in neuronal interactions arise through synaptic and dendritic processing. Previous work has shown that such delays, which play an important role in shaping the dynamics of networks of large numbers of spiking neurons with continuous synaptic kinetics, can be taken into account with a rate model through the addition of an explicit, fixed delay. Here we extend this work to account for arbitrary symmetric patterns of synaptic connectivity and generic nonlinear transfer functions. Specifically, we conduct a weakly nonlinear analysis of the dynamical states arising via primary instabilities of the stationary uniform state. In this way we determine analytically how the nature and stability of these states depend on the choice of transfer function and connectivity. While this dependence is, in general, nontrivial, we make use of the smallness of the ratio in the delay in neuronal interactions to the effective time constant of integration to arrive at two general observations of physiological relevance. These are: 1 - fast oscillations are always supercritical for realistic transfer functions. 2 - Traveling waves are preferred over standing waves given plausible patterns of local connectivity.

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.

On rigid analytic uniformizations of Jacobians of Shimura curves

The main goal of this article is to give an explicit rigid analytic uniformization of the maximal toric quotient of the Jacobian of a Shimura curve over Q at a prime dividing exactly the level. This result can be viewed as complementary to the classical theorem of Cerednik and Drinfeld which provides rigid analytic uniformizations at primes dividing the discriminant. As a corollary, we offer a proof of a conjecture formulated by M. Greenberg in hispaper on Stark-Heegner points and quaternionic Shimura curves, thus making Greenberg's construction of local points on elliptic curves over Q unconditional.

Equations of hyperelliptic Shimura curves

We describe an algorithm that computes explicit models of hyperelliptic Shimura curves attached to an indefinite quaternion algebra over Q and Atkin-Lehner quotients of them. It exploits Cerednik-Drinfeld’s nonarchimedean uniformisation of Shimura curves, a formula of Gross and Zagier for the endomorphism ring of Heegner points over Artinian rings and the connection between Ribet’s bimodules and the specialization of Heegner points, as introduced in [21]. As an application, we provide a list of equations of Shimura curves and quotients of them obtained by our algorithm that had been conjectured by Kurihara.

Civil war and foreign influence

We study a symmetric information bargaining model of civil war where a third (foreign) party can affect the probabilities of winning the conflict and the size of the post conflict spoils. We show that the possible alliance with a third party makes peaceful agreements difficult to reach and might lead to new commitment problems that trigger war. Also, we argue that the foreign party is likely to induce persistent informational asymmetries which might explain long lasting civil wars. We explore both political and economic incentives for a third party to intervene. The explicit consideration of political incentives leads to two predictions that allow for identifying the influence of foreign intervention on civil war incidence. Both predictions are confirmed for the case of the U.S. as a potential intervening nation: (i) civil wars around the world are more likely under Republican governments and (ii) the probability of civil wars decreases with U.S. presidential approval rates.

Mecanismes neuronals de la facilitació de l'aprenentatge i la memoria per autoestimulació eléctrica intracranial en rates: espines dendrítiques

La potenciación de procesos de aprendizaje y memoria por autoestimación eléctrica intracraneal (AEIC) se ha observado principalmente en tareas de aprendizaje de tipo implícito, caracterizado por necesitar de múltiples ensayos y por dar lugar a una respuesta conductual rígida. Los efectos de la AEIC sobre formas de aprendizaje consideradas más complejas, como la memoria de navegación espacial, son menos conocidos. En nuestro laboratorio hemos observado recientemente que el tratamiento de AEIC es también capaz de facilitar tanto la adquisición como la retención de una tarea relacional, en el laberinto acuático de Morris (MWM) (Ruiz-Medina et al., 2008). El proyecto de investigación objeto de esta memoria continúa el estudio de este efecto potenciador yendo un paso más allá al profundizar en los mecanismos neurales de este efecto. Lo relativo a las espinas dendríticas, su tamaño, forma y aparición es uno de los campos más actuales en el estudio de las bases neurales de la memoria. Trabajos previos apuntan a un incremento en la densidad de espinas inmaduras -las consideradas de aprendizaje- como efecto tanto del entrenamiento en el MWM como de la AEIC. Relacionar la potenciación de memoria en el MWM resultado de la AEIC con cambios significativos en la población de espinas dendríticas hipocampales sería uno de los principales objetivos del presente trabajo, que se realizará en colaboración con el Instituto Ramón y Cajal de Madrid.

Regulación de la movilidad celular por Profilina 1

Mi proyecto de tesis se basaba en el estudio del papel de profilina 1 en la formación de lamelas, para ello generamos una proteína recombinante y transducible, con el objetivo de poder modificar los niveles endógenos de profilina. Objetivos: i-caracterización bioquímica los tres sitios de union conocidos de la proteína de transducción, el sitio de unión a fosfo-inocitoles (PIP), el de unión a actina (Ac) y el de unión a poli-prolinas (PLP). ii-estudio de la polimerización in-vitro de actina - PTD4-Profilina1 iii-estudio de las proteínas componentes de lamelas inducidas por PTD4-Profilina1. Plan de trabajo: i-Para comprobar la funcionalidad los 3 sitios de unión fueron necesarias las primeras 6 semanas, ya que en primer lugar había que expresar y purificar el peptido Srv2, necesario para el ensayo de PLP. En segundo lugar, se obtuvieron los datos de las concentraciones adecuadas de lípidos para el ensayo de fosfo-inocitoles y por ultimo, se purifico la actina necesaria para el ensayo de unión a actina. Una vez establecida la funcionalidad de la proteína, se procedió a: ii-el estudio de polimerización in-vitro, que llevo 2 semanas. Demostrando que in-vitro era capaz de inhibir la polimerización de una manera similar a la endógena. Una vez terminados estos ensayos, se procedio a: iii-la caracterización inmunohistoquímica de las proteínas componentes de la lamela que fue llevado a cabo en 4 semanas. Para ello se usaron anticuerpos contra: alfa-actinina, talina, vinculina, ENA/Vasp y paxillina. Conclusiones: i-las propiedades bioquímicas de la PTD4-Profilina1 son similares a las de la profilina endógena. ii-los estudios de polimerización indican que la polimerización se produce de manera similar a la endogena. iii-los ensayos de inmunohistoquímica sugieren que, talina esta ausente y que las demás están presentes aunque en menor concentración y con otra distribución comparadas con los controles.

A geometric mechanism of diffusion: Rigorous verification in a priori unstable Hamiltonian systems

In this paper we consider a representative a priori unstable Hamiltonian system with 2+1/2 degrees of freedom, to which we apply the geometric mechanism for diffusion introduced in the paper Delshams et al., Mem.Amer.Math. Soc. 2006, and generalized in Delshams and Huguet, Nonlinearity 2009, and provide explicit, concrete and easily verifiable conditions for the existence of diffusing orbits. The simplification of the hypotheses allows us to perform explicitly the computations along the proof, which contribute to present in an easily understandable way the geometric mechanism of diffusion. In particular, we fully describe the construction of the scattering map and the combination of two types of dynamics on a normally hyperbolic invariant manifold.

Cronyism in Business, Public Sector and Politics

This paper contrasts the incentives for cronyism in business, the public sector and politics within an agency problem model with moral hazard. The analysis is focused on the institutional differences between private, public and political organizations. In business, when facing a residual claimant contract, a chief manager ends up with a relatively moderate …rst-best level of cronyism within a …firm. The institutional framework of the public sector does not allow explicit contracting, which leads to a more severe cronyism problem within public organizations. Finally, it is shown that the nature of political appointments (such that the subordinate's reappointment is conditioned on the chief's re-election) together with implicit contracting makes political cronyism the most extreme case. JEL classifi…cation: D72, D73, D86. Keywords: Cronyism; Meritocracy; Manager; Bureaucrat; Politician.

The β-Meixner model

We propose to approximate the Meixner model by a member of the B-family introduced in [Kuz10a]. The advantage of such approximations are the semi-explicit formulas for the running extrema under the B-family processes which enables us to produce more efficient algorithms for certain path dependent options.

Analisi espacial del canvi climàtic al continent europeu. Incerteses i exposicions principals

El canvi climàtic del segle XXI és una realitat, hi ha moltes evidències científiques que indiquen que l’escalfament del sistema climàtic és inequívoc. Malgrat això, també hi ha moltes incerteses respecte els impactes que pot comportar aquest canvi climàtic global. L’objectiu d’aquest projecte és estudiar la possible evolució futura de tres variables climàtiques, que són el rang de la temperatura diürna a prop de la superfície (DTR), la temperatura mitjana a prop de la superfície (MT) i la precipitació mensual (PL_mes) i valorar l’exposició que poden experimentar diferents cobertes del sòl i diferents regions biogeogràfiques del continent europeu davant d’aquests possibles patrons de canvi. Per això s’han utilitzat Models Climàtics Globals que fan projeccions de variables climàtiques que permeten preveure el possible clima futur. Mitjançant l’aplicatiu informàtic Tetyn s’han extret els paràmetres climàtics dels conjunts de dades del Tyndall Centre for Climate Change Research, del futur (TYN SC) i del passat (CRU TS). Les variables obtingudes s’han processat amb eines de sistemes d’informació geogràfica (SIG) per obtenir els patrons de canvi de les variables a cada coberta del sòl. Els resultats obtinguts mostren que hi ha una gran variabilitat, que augmenta amb el temps, entre els diferents models climàtics i escenaris considerats, que posa de manifest la incertesa associada a la modelització climàtica, a la generació d’escenaris d’emissions i a la naturalesa dinàmica i no determinista del sistema climàtic. Però en general, mostren que les glaceres seran una de les cobertes més exposades al canvi climàtic, i la mediterrània, una de les regions més vulnerables

Evaluating antitrust leniency programs

This paper identifies and then quantifies econometrically the impact of leniency programs on the perception of the effectiveness of antitrust policies using country level panel data for a 10-year span. Leniency programs have been introduced gradually in antitrust legislation across the globe to fight more effectively against cartels. We use the dynamics of the diffusion of such policy innovation across countries and over time to evaluate the impact of the program. We find that leniency programs have had a significant impact on the perception among the business community of the effectiveness of each country‟s antitrust policy. Leniency programs have become weapons of mass dissuasion in the hands of antitrust enforcers against the more damaging forms of explicit collusion among rival firms in the market place.