On breaking the age-metallicity degeneracy in early-type galaxies: Outflows versus Star Formation Efficiency

A simple model of chemical enrichment in cluster early-type galaxies is presented where the main parameters driving the formation of the stellar component are reduced to four: infall timescale (tf), formation epoch (zF), star formation efficiency (Ceff) and fraction of gas ejected in outflows (Bout). We find that only variations in Bout or Ceff can account for the colour-magnitude relation, so that the most luminous galaxies had low values of ejected gas and high efficiencies. The combination of chemical enrichment tracks with population synthesis models is used to explore the correlation between mass-to-light ratios and masses. A significant slope mismatch is found between stellar and total M/L ratios, which cannot be explained by an age spread and implies a non-linear correlation between total and stellar mass. The sequences driven by star formation efficiency and outflows are shown to predict different trends at high redshift. Measurement of the dependence of the tilt of the fundamental plane on redshift will break the degeneracy between outflows and star formation efficiency, which will enable us to determine whether the colour-magnitude relation is controlled by age or metallicity.Comment: 8 pages, 5 figures. To be published in MNRA

The expected area of the filled planar Brownian loop is Pi/5

Let B_t be a planar Brownian loop of time duration 1 (a Brownian motion conditioned so that B_0 = B_1). We consider the compact hull obtained by filling in all the holes, i.e. the complement of the unique unbounded component of R^2\B[0,1]. We show that the expected area of this hull is Pi/5. The proof uses, perhaps not surprisingly, the Schramm Loewner Evolution (SLE). Also, using the result of Yor about the law of the index of a Brownian loop, we show that the expected areas of the regions of non-zero index n equal 1/(2 Pi n^2). As a consequence, we find that the expected area of the region of index zero inside the loop is Pi/30; this value could not be obtained directly using Yor's index description.Comment: 15 pages, 3 figure

The necessity of dark matter in MOND within galactic scales

To further test MOdified Newtonian Dynamics (MOND) on galactic scales -- originally proposed to explain the rotation curves of disk galaxies without dark matter -- we study a sample of six strong gravitational lensing early-type galaxies from the CASTLES database. To determine whether dark matter is present in these galaxies, we compare the total mass (from lensing) with the stellar mass content (from a comparison of photometry and stellar population synthesis). We find that strong gravitational lensing on galactic scales requires a significant amount of dark matter, even within MOND. On such scales a 2 eV neutrino cannot explain this excess matter -- in contrast with recent claims to explain the lensing data of the bullet cluster. The presence of dark matter is detected in regions with a higher acceleration than the characteristic MONDian scale of $\sim 10^{-10}$m/s$^2$. This is a serious challenge to MOND unless the proper treatment of lensing is qualitatively different (possibly to be developed within a consistent theory such as TeVeS)

Characterization of reward functions in networks with costs

In this paper we study network structures in which the possibilities for cooperation are restricted and can not be described by a cooperative game. The benefits of a group of players depend on how these players are internally connected. One way to represent this type of situations is the so-called reward function, which represents the profits obtainable by the total coalition if links can be used to coordinate agents' actions. The starting point of this paper is the work of Vilaseca et al. where they characterized the reward function. We concentrate on those situations where there exist costs for establishing communication links. Given a reward function and a costs function, our aim is to analyze under what conditions it is possible to associate a cooperative game to it. We characterize the reward function in networks structures with costs for establishing links by means of two conditions, component permanence and component additivity. Finally, an economic application is developed to illustrate the main theoretical result.En aquest article s'estudien les estructures de xarxa en què les possibilitats de cooperació són restringides i no poden ser descrites mitjançant un joc cooperatiu. Els beneficis d'un grup de jugadors dependran de com aquests jugadors estan internament connectats. Una forma de representar aquest tipus de situacions és l'anomenada funció reward, que representa els beneficis obtinguts per la coalició total quan les connexions poden ser utilitzades per coordinar les accions dels agents. El punt de partida d'aquest article és el treball de Vilaseca et al. on es caracteritza la funció reward. Nosaltres ens centrem en aquelles situacions on hi ha costos per a l'establiment d'enllaços de comunicació. Donada una funció reward i una funció de costos, el nostre objectiu és analitzar sota quines condicions és possible associar un joc cooperatiu a la funció reward. Nosaltres caracteritzem la funció reward en estructures de xarxa amb costos per a l'establiment d'enllaços mitjançant dues condicions, la component permanència i la component additivitat. Finalment, es desenvolupa una aplicació econòmica per il·lustrar el resultat teòric principal.En este artículo se estudian las estructuras de red en la que las posibilidades de cooperación están restringidas y no pueden ser descritas por medio de un juego cooperativo. Los beneficios de un grupo de jugadores dependerán de cómo estos jugadores están internamente conectados. Una forma de representar este tipo de situaciones es la llamada función reward, que representa los beneficios obtenibles por la coalición total cuando los enlaces pueden ser utilizados para coordinar las acciones de los agentes. El punto de partida de este artículo es el trabajo de Vilaseca et al. donde se caracteriza la función reward. Nosotros nos centramos en aquellas situaciones donde existen costes para el establecimiento de enlaces de comunicación. Dada una función reward y una función de costes, nuestro objetivo es analizar bajo qué condiciones es posible asociar un juego cooperativo a la función reward. Nosotros caracterizamos la función reward en estructuras de red con costes para el establecimiento de enlaces por medio de dos condiciones, la componente permanencia y la componente aditividad. Por último, se desarrolla una aplicación económica para ilustrar el resultado teórico principal