Linear degree growth in lattice equations

We conjecture recurrence relations satisfied by the degrees of some linearizable lattice equations. This helps to prove linear growth of these equations. We then use these recurrences to search for lattice equations that have linear growth and hence are linearizable

Dynamics of horizontal-like maps in higher dimension

We study the regularity of the Green currents and of the equilibrium measure associated to a horizontal-like map in C^k, under a natural assumption on the dynamical degrees. We estimate the speed of convergence towards the Green currents, the decay of correlations for the equilibrium measure and the Lyapounov exponents. We show in particular that the equilibrium measure is hyperbolic. We also show that the Green currents are the unique invariant vertical and horizontal positive closed currents. The results apply, in particular, to Henon-like maps, to regular polynomial automorphisms of C^k and to their small pertubations.Comment: Dedicated to Professor Gennadi Henkin on the occasion of his 65th birthday, 37 pages, to appear in Advances in Mat

The binding constraint on firms'growth in developing countries

Firms in developing countries face numerous and serious constraints on their growth, ranging from corruption to lack of infrastructure to inability to access finance. Countries lack the resources to remove all the constraints at once and so would be better off removing the most binding one first. This paper uses data from World Bank Enterprise Surveys in 2006-10 to identify the most binding constraints on firm operations in developing countries. While each country faces a different set of constraints, these constraints also vary by firm characteristics, especially firm size. Across all countries, access to finance is among the most binding constraints; other obstacles appear to matter much less. This result is robust for all regions. Smaller firms must rely more on their own funds to invest and would grow significantly faster if they had greater access to external funds. As a result, a low level of financial development skews the firm size distribution by increasing the relative share of small firms. The results suggest that financing constraints play a significant part in explaining the"missing middle"-- the failure of small firms in developing countries to grow into medium-size or large firms.Access to Finance,Environmental Economics&Policies,Microfinance,Debt Markets,Banks&Banking Reform

On "the authentic damping mechanism" of the phonon damping model

Some general features of the phonon damping model are presented. It is concluded that the fits performed within this model have no physical content

A theorem of Tits type for compact Kahler manifolds

We prove a theorem of Tits type about automorphism groups for compact Kahler manifolds, which has been conjectured in the paper [KOZ].Comment: Inventiones Mathematicae (to appear), 11 page

Molecular Gas in the Powerful Radio Galaxies 3C~31 and 3C~264: Major or Minor Mergers?

We report the detection of $^{12}$CO~($1 \to 0$) and $^{12}$CO~($2 \to 1$) emission from the central regions ($\lesssim 5$--$10 {\rm kpc}$) of the two powerful radio galaxies 3C~31 and 3C~264. Their individual CO emission exhibits a double-horned line profile that is characteristic of an inclined rotating disk with a central depression at the rising part of its rotation curve. The inferred disk or ring distributions of the molecular gas is consistent with the observed presence of dust disks or rings detected optically in the cores of both galaxies. For a CO to H$_2$ conversion factor similar to that of our Galaxy, the corresponding total mass in molecular hydrogen gas is $(1.3 \pm 0.2) \times 10^9 {\rm M_{\odot}}$ in 3C~31 and $(0.31 \pm 0.06) \times 10^9 {\rm M_{\odot}}$ in 3C~264. Despite their relatively large molecular-gas masses and other peculiarities, both 3C~31 and 3C~264, as well as many other powerful radio galaxies in the (revised) 3C catalog, are known to lie within the fundamental plane of normal elliptical galaxies. We reason that if their gas originates from the mergers of two gas-rich disk galaxies, as has been invoked to explain the molecular gas in other radio galaxies, then both 3C~31 and 3C~264 must have merged a long time (a few billion years or more) ago but their remnant elliptical galaxies only recently (last tens of millions of years or less) become active in radio. Instead, we argue that the cannibalism of gas-rich galaxies provides a simpler explanation for the origin of molecular gas in the elliptical hosts of radio galaxies. Given the transient nature of their observed disturbances, these galaxies probably become active in radio soon after the accretion event when sufficient molecular gas agglomerates in their nuclei.Comment: 16 pages, 1 JPEG figure attached, accepted for publication in ApJ

Agent-Based Modeling of Intracellular Transport

We develop an agent-based model of the motion and pattern formation of vesicles. These intracellular particles can be found in four different modes of (undirected and directed) motion and can fuse with other vesicles. While the size of vesicles follows a log-normal distribution that changes over time due to fusion processes, their spatial distribution gives rise to distinct patterns. Their occurrence depends on the concentration of proteins which are synthesized based on the transcriptional activities of some genes. Hence, differences in these spatio-temporal vesicle patterns allow indirect conclusions about the (unknown) impact of these genes. By means of agent-based computer simulations we are able to reproduce such patterns on real temporal and spatial scales. Our modeling approach is based on Brownian agents with an internal degree of freedom, $\theta$, that represents the different modes of motion. Conditions inside the cell are modeled by an effective potential that differs for agents dependent on their value $\theta$. Agent's motion in this effective potential is modeled by an overdampted Langevin equation, changes of $\theta$ are modeled as stochastic transitions with values obtained from experiments, and fusion events are modeled as space-dependent stochastic transitions. Our results for the spatio-temporal vesicle patterns can be used for a statistical comparison with experiments. We also derive hypotheses of how the silencing of some genes may affect the intracellular transport, and point to generalizations of the model