Enumeration of symmetry classes of convex polyominoes on the honeycomb lattice

Hexagonal polyominoes are polyominoes on the honeycomb lattice. We enumerate the symmetry classes of convex hexagonal polyominoes. Here convexity is to be understood as convexity along the three main column directions. We deduce the generating series of free (i.e. up to reflection and rotation) and of asymmetric convex hexagonal polyominoes, according to area and half-perimeter. We give explicit formulas or implicit functional equations for the generating series, which are convenient for computer algebra.Comment: 21 pages, 16 figures, 2 tables. This is the full version of a paper presented at the FPSAC Conference in Vancouver, Canada, June 28 -- July 2, 200

Local reionizations histories with merger tree of HII regions

We constrain the initial stage of the reionization process around progenitors of galaxies, such as the extent of the initial HII region before its fusion with the UV background and the duration of its propagation. We use a set of reionisation simulations with different resolutions and ionizing source recipes. A catalog of the HII regions properties is built thanks to a merger tree of HII regions. We draw local reionization histories as a function of time and investigate variations according to the halo mass progenitors of the regions. We then extrapolate the halo mass inside the region from high z to z=0 to make predictions about the reionization histories of z=0 galaxies. We found that the later an HII region appears, the smaller will be its related lifetime and volume before it sees the global UV background. Quantitatively the duration and the extent of the initial growth of an HII region is strongly dependent on the mass of the inner halo and can be as long as 50 % of the reionization epoch. We found that the most massive is a halo today, the earlier it appears and the larger are the extension and the duration of propagation of its HII region. Quantitative predictions differ depending on the box size or the source model: small simulated volumes are affected by proximity effects between HII regions and halo-based source models predict smaller regions and slower I-front expansion than in models using star particles as ionizing sources. Our results suggests that Milky Way-type halos have a maximal extent of 1.1 Mpc/h for the initial HII region that established itself in 150-200$\pm 20$ Myrs. This is consistent with prediction made using constrained Local Group simulation. Considering halos with masses comparable to those of the Local Group (MW+M31), our result suggests that statistically it has not been influenced by an external front coming from a Virgo-like cluster.Comment: 16 pages, 9 figures, Accepted for publication in A&

An Upper Bound on the Complexity of Recognizable Tree Languages

The third author noticed in his 1992 PhD Thesis [Sim92] that every regular tree language of infinite trees is in a class $\Game (D\_n({\bf\Sigma}^0\_2))$ for some natural number $n\geq 1$, where $\Game$ is the game quantifier. We first give a detailed exposition of this result. Next, using an embedding of the Wadge hierarchy of non self-dual Borel subsets of the Cantor space $2^\omega$ into the class ${\bf\Delta}^1\_2$, and the notions of Wadge degree and Veblen function, we argue that this upper bound on the topological complexity of regular tree languages is much better than the usual ${\bf\Delta}^1\_2$

Dynamic Management of Portfolios with Transaction Costs under Tychastic Uncertainty.

We use in this chapter the viability/capturability approach for studying the problem of dynamic valuation and management of a portfolio with transaction costs in the framework of tychastic control systems (or dynamical games against nature) instead of stochastic control systems. Indeed, the very definition of the guaranteed valuation set can be formulated directly in terms of guaranteed viable-capture basin of a dynamical game. Hence, we shall “compute” the guaranteed viable-capture basin and find a formula for the valuation function involving an underlying criterion, use the tangential properties of such basins for proving that the valuation function is a solution to Hamilton-Jacobi-Isaacs partial differential equations. We then derive a dynamical feedback providing an adjustment law regulating the evolution of the portfolios obeying viability constraints until it achieves the given objective in finite time. We shall show that the Pujal—Saint-Pierre viability/capturability algorithm applied to this specific case provides both the valuation function and the associated portfolios.dynamic games; dynamic valuation; tychastic control systems; management of portfolio;

A study of simulated histories of reionization with merger trees of HII regions

We describe a new methodology to analyze the reionization process in numerical simulations: the chronology and the geometry of reionization is investigated by means of merger histories of individual HII regions. From the merger tree of ionized patches, one can track the individual evolution of the regions properties such as e.g. their size, or the intensity of the percolation process by looking at the formation rate, the frequency of mergers and the number of individual HII regions involved in the mergers. We apply the merger tree technique to simulations of reionization with three different kinds of ionizing source models and two resolutions. Two of them use star particles as ionizing sources. In this case we confront two emissivity evolutions for the sources in order to reach the reionization at z ~ 6. As an alternative we built a semi-analytical model where the dark matter halos extracted from the density fields are assumed as ionizing sources. We then show how this methodology is a good candidate to quantify the impact of the adopted star formation on the history of the observed reionization. The semi-analytical model shows a homogeneous reionization history with 'local' hierarchical growth steps for individual HII regions. On the other hand auto-consistent models for star formation tend to present fewer regions with a dominant region in size which governs the fusion process early in the reionization at the expense of the 'local' reionizations. The differences are attenuated when the resolution of the simulation is increased.Comment: Accepted for publication in A&

An Econometric Study of Vine Copulas

We present a new recursive algorithm to construct vine copulas based on an underlying tree structure. This new structure is interesting to compute multivariate distributions for dependent random variables. We proove the asymptotic normality of the vine copula parameter estimator and show that all vine copula parameter estimators have comparable variance. Both results are crucial to motivate any econometrical work based on vine copulas. We provide an application of vine copulas to estimate the VaR of a portfolio, and show they offer significant improvement as compared to a benchmark estimator based on a GARCH model.Vines, multivariate copulas, risk management.

New Prospects on Vines

In this paper, we present a new methodology based on vine copulas to estimate multivariate distributions in high dimensions, taking advantage of the diversity of vine copulas. Considering the huge number of vine copulas in dimension n, we introduce an efficient selection algorithm to build and select vine copulas with respect to any test T. Our methodology offers a great flexibility to practitioners to compute VaR associated to a portfolio in high dimension.Vine copulas, multivariate copulas, model selection, VaR.