Asymmetrical structure of ionization and kinematics in the Seyfert galaxy NGC 5033

We present integral field spectroscopy of NGC 5033, a low luminosity Seyfert galaxy. The observations were made with INTEGRAL, a fiber based system operating at the WHT. The intensity map of the H$\beta$ emission line represents a spiral or ring-like pattern of HII regions. On the contrary, the [OIII] intensity map morphology is markedly anisotropic. The strong morphological differences imply that the [OIII] emitters represent highly ionized gas illuminated by the central source. The [OIII] map morphology is compatible with a biconical structure of ionization induced by strong extinction in the galaxy disc that also obscures half of the spheroidal stellar bulge. We identify the spectrum corresponding to the Seyfert 1 nucleus from the presence of H$\beta$ broad emission lines. This spectrum is located in a region where strong extinction is expected but exhibits the bluest spectral energy distribution. The Seyfert 1 nucleus seems to be offcenter with respect to the stellar rotation center. This result has been also found in other Seyfert galaxies and interpreted in terms of a past merger. The offcentering could indicate the presence of nonsymmetric departures in the gravitational potential which could be fueling the active nucleus. The kinematics of the [OIII] emitters show important deviations at a kpc scale with respect to the stellar velocity field and show features related to the asymmetrical morphology of the high ionization region.Comment: 9 pages, accepted for publication in Astronomy and Astrophysics. Figures 1 and 7 are attached as .gif file

Shape Outlier Detection and Visualization for Functional Data: the Outliergram

We propose a new method to visualize and detect shape outliers in samples of curves. In functional data analysis we observe curves defined over a given real interval and shape outliers are those curves that exhibit a different shape from the rest of the sample. Whereas magnitude outliers, that is, curves that exhibit atypically high or low values at some points or across the whole interval, are in general easy to identify, shape outliers are often masked among the rest of the curves and thus difficult to detect. In this article we exploit the relation between two depths for functional data to help visualizing curves in terms of shape and to develop an algorithm for shape outlier detection. We illustrate the use of the visualization tool, the outliergram, through several examples and asses the performance of the algorithm on a simulation study. We apply them to the detection of outliers in a children growth dataset in which the girls sample is contaminated with boys curves and viceversa.Comment: 27 pages, 5 figure

Kangaroos, Cities and Space: A First Approach to the Australian Urban System

Australia conforms a unique urban system. This paper examines the Australian urban system using data for urban centres and localities in 1996 and 2001. A summary and a basic descriptive analysis of the database is provided, followed by an examination of whether the system follows Zipf’s and Gibrat’s laws. The latter is found to hold for all but one of the especifiactions used while the former does not seem to apply. A Exploratory Spatial Data Analysis (ESDA) as well as a confirmatory analysis are carried out to analyize the spatial dimension of city size and growth, finding no relation for the former but a significant one for the latter.

Integral field optical spectroscopy of a representative sample of ULIRGs: II. Two-dimensional kpc-scale extinction structure

We investigate the two-dimensional kpc-scale structure of the extinction in a representative sample of local ULIRGs using the Halpha/Hbeta line ratio.We use optical integral field spectroscopy obtained with the INTEGRAL instrument at the William Herschel Telescope. Complementary optical and near-IR high angular resolution HST images have also been used. The extinction exhibits a very complex and patchy structure in ULIRGs on kpc scales, from basically transparent regions to others deeply embedded in dust (Av~0.0 to Av~8.0 mag). Nuclear extinction covers a broad range in Av from 0.6 to 6 mag, 69% of the nuclei having Av>2.0 mag. Extinction in the external regions is substantially lower than in the nuclei with 64% of the ULIRGs in the sample having median Av of less than 2 mag for the entire galaxy. While post-coalescence nuclei tend to cluster around Av values of 2 to 3 mag, pre-coalescence nuclei appear more homogeneously distributed over the entire 0.4 mag <Av< 7.7 mag range. For the average extinction (Av~2.0 derived for the ULIRGs of the sample, the ratio of the de-reddened to observed SFR values is 6. The extinction-corrected, Halpha-based SFR ranges from 10 to 300 Msun/yr. For only 28% of the cases the de-reddened SFR is <20 Msun/yr, whereas for the observed SFR this percentage increases to 72%. The IR-based SFR is always higher than the optical-based one, with differences ranging from about 2 to up to 30. The nuclear observed SFR has an average contribution to the total one of 16% for the entire sample. Once corrected for extinction, the average value becomes 31%. Because of mostly extinction effects, the optical (I-band) half-light radius in the sample galaxies is on average a factor 2.3 larger than the corresponding near-IR (H-band) value.Comment: To appear in A&

REPEATED GAMES WITH PROBABILISTIC HORIZON

Repeated games with probabilistic horizon are defined as those games where players have a common probability structure over the length of the game's repetition, T. In particular, for each t, they assign a probability pt to the event that "the game ends in period t". In this framework we analyze Generalized Prisoners' Dilemma games in both finite stage and differentiable stage games. Our construction shows that it is possible to reach cooperative equilibria under some conditions on the distribution of the discrete random variable T even if the expected length of the game is finite. More precisely, we completely characterize the existence of sub-game perfect cooperative equilibria in finite stage games by the (first order) convergence speed: the behavior in the limit of the ratio between the ending probabilities of two consecutive periods. Cooperation in differentiable stage games is determined by the second order convergence speed, which gives a finer analysis of the probability convergence process when the first convergence speed is zero.Leptokurtic distributions are defined as those distributions for which the (first order) convergence speed is zero and they preclude cooperation in finite stage games with probabilistic horizon. However, this negative result is obtained in differential stage games only for a subset of these distributions.repeated games, probabilistic horizon, cooperation

NASH EQUILIBRIA IN A MODEL OF MULTIPRODUCT PRICE COMPETITION: AN ASSIGNMENT PROBLEM

We study the market interaction of a finite number of single-product firms and a representative buyer, where the buyer consumes bundles of these goods. The buyers' value function determines their willingness to pay for subsets of goods. We show that subgame perfect Nash-equilibrium outcomes are solutions of the linear relaxation of an integer programming assignment problem and that they always exits. The (subgame perfect) Nash-equilibrium price set is characterized by the Pareto frontier of the associated dual problem's projection on the firms' price vectors. We identify the Nash-equilibrium prices for monotonic buyers' value functions and, more importantly, we show that some central solution concepts in cooperative game theory are (subgame perfect) equilibrium prices of our strategic game.Multiproduct price competition, interger programming, subgame perfect nash equilibria

MIXED BUNDLING STRATEGIES AND MULTIPRODUCT PRICE COMPETITION

This paper deals with price competition among multiproduct firms. We consider a model with n firms and one representative buyer. Each firm produces a set of products that can be different or identical to the other firms' products. The buyer is characterized by her willingness to pay -in monetary terms- for every subset of products. To handle the combinatorial complexity of this general setting we use the linear relaxation of an integer programming package assignment problem. This approach allows to characterize all the equilibrium outcomes. We look for subgame perfect Nash equilibrium prices in mixed bundling strategies, i.e., when firms offer consumers the option of buying goods separately or else packages of them at a discount over the single good prices. We find that a mixed bundling subgame perfect Nash equilibrium price vector always exists. Also, the associated equilibrium outcome is always efficient, in the sense that it maximizes the social surplus. We extend the analysis to a model with m buyers and offer the conditions under which the equilibrium outcome set is non-empty.Multiproduct price competition, Integer Programming, Mixed Bundling Strategies, Subgame Perfect Nash Equilibria.