Robust Transitivity for Endomorphisms

We address the problem about under what conditions an endomorphism having a dense orbit, verifies that a sufficiently close perturbed map also exhibits a dense orbit. In this direction, we give sufficient conditions, that cover a large class of examples, for endomorphisms on the n-dimensional torus to be robustly transitive: the endomorphism must be volume expanding and any large connected arc must contain a point such that its future orbit belong to an expanding region.Comment: 32 pages, 13 figure

Exact expressions for the mobility and electrophoretic mobility of a weakly charged sphere in a simple electrolyte

We present (asymptotically) exact expressions for the mobility and electrophoretic mobility of a weakly charged spherical particle in an $1:1$ electrolyte solution. This is done by analytically solving the electro and hydrodynamic equations governing the electric potential and fluid flow with respect to an electric field and a nonelectric force. The resulting formulae are cumbersome, but fully explicit and trivial for computation. In the case of a very small particle compared to the Debye screening length ($R \ll r_D$) our results reproduce proper limits of the classical Debye and Onsager theories, while in the case of a very large particle ($R \gg r_D$) we recover, both, the non-monotonous charge dependence discovered by Levich (1958) as well as the scaling estimate given by Long, Viovy, and Ajdari (1996), while adding the previously unknown coefficients and corrections. The main applicability condition of our solution is charge smallness in the sense that screening remains linear.Comment: 6 pages, 1 figur

Double-digest RADseq loci using standard Illumina indexes improve deep and shallow phylogenetic resolution of Lophodermium, a widespread fungal endophyte of pine needles.

The phylogenetic and population genetic structure of symbiotic microorganisms may correlate with important ecological traits that can be difficult to directly measure, such as host preferences or dispersal rates. This study develops and tests a low-cost double-digest restriction site-associated DNA sequencing (ddRADseq) protocol to reveal among- and within-species genetic structure for Lophodermium, a genus of fungal endophytes whose evolutionary analyses have been limited by the scarcity of informative markers. The protocol avoids expensive barcoded adapters and incorporates universal indexes for multiplexing. We tested for reproducibility and functionality by comparing shared loci from sample replicates and assessed the effects of numbers of ambiguous sites and clustering thresholds on coverage depths, number of shared loci among samples, and phylogenetic reconstruction. Errors between technical replicates were minimal. Relaxing the quality-filtering criteria increased the mean coverage depth per locus and the number of loci recovered within a sample, but had little effect on the number of shared loci across samples. Increasing clustering threshold decreased the mean coverage depth per cluster and increased the number of loci recovered within a sample but also decreased the number of shared loci across samples, especially among distantly related species. The combination of low similarity clustering (70%) and relaxed quality-filtering (allowing up to 30 ambiguous sites per read) performed the best in phylogenetic analyses at both recent and deep genetic divergences. Hence, this method generated sufficient number of shared homologous loci to investigate the evolutionary relationships among divergent fungal lineages with small haploid genomes. The greater genetic resolution also revealed new structure within species that correlated with ecological traits, providing valuable insights into their cryptic life histories

Effects of city-size heterogeneity on epidemic spreading in a metapopulation: A reaction-diffusion approach

We review and introduce a generalized reaction-diffusion approach to epidemic spreading in a metapopulation modeled as a complex network. The metapopulation consists of susceptible and infected individuals that are grouped in subpopulations symbolising cities and villages that are coupled by human travel in a transportation network. By analytic methods and numerical simulations we calculate the fraction of infected people in the metaopoluation in the long time limit, as well as the relevant parameters characterising the epidemic threshold that separates an epidemic from a non-epidemic phase. Within this model, we investigate the effect of a heterogeneous network topology and a heterogeneous subpopulation size distribution. Such a system is suited for epidemic modeling where small villages and big cities exist simultaneously in the metapopulation. We find that the heterogeneous conditions cause the epidemic threshold to be a non-trivial function of the reaction rates (local parameters), the network's topology (global parameters) and the cross-over population size that separates "village dynamics" from "city dynamics".Comment: 17 pages, 3 figure

Zero-Crossing Statistics for Non-Markovian Time Series

In applications spaning from image analysis and speech recognition, to energy dissipation in turbulence and time-to failure of fatigued materials, researchers and engineers want to calculate how often a stochastic observable crosses a specific level, such as zero. At first glance this problem looks simple, but it is in fact theoretically very challenging. And therefore, few exact results exist. One exception is the celebrated Rice formula that gives the mean number of zero-crossings in a fixed time interval of a zero-mean Gaussian stationary processes. In this study we use the so-called Independent Interval Approximation to go beyond Rice's result and derive analytic expressions for all higher-order zero-crossing cumulants and moments. Our results agrees well with simulations for the non-Markovian autoregressive model

Transport Policies in Latin America

The issues of air pollution and traffic congestion in Latin America have been growing increasingly important since the end of the 20th century. The latter may help explain why several cities around the continent have tried different combination of public policies with vary-ing degrees of success. We describe the policies that outline the Latin American experience in this matter and hope to be a useful reference to subsequent research in the area.Transport policies, driving restrictions, public transport, air pollution, car use

Holographic renormalisation group flows and renormalisation from a Wilsonian perspective

From the Wilsonian point of view, renormalisable theories are understood as submanifolds in theory space emanating from a particular fixed point under renormalisation group evolution. We show how this picture precisely applies to their gravity duals. We investigate the Hamilton-Jacobi equation satisfied by the Wilson action and find the corresponding fixed points and their eigendeformations, which have a diagonal evolution close to the fixed points. The relevant eigendeformations are used to construct renormalised theories. We explore the relation of this formalism with holographic renormalisation. We also discuss different renormalisation schemes and show that the solutions to the gravity equations of motion can be used as renormalised couplings that parametrise the renormalised theories. This provides a transparent connection between holographic renormalisation group flows in the Wilsonian and non-Wilsonian approaches. The general results are illustrated by explicit calculations in an interacting scalar theory in AdS space.Comment: 63 pages. Minor changes and references added. Matches JHEP versio