Direct and Inverse Results on Bounded Domains for Meshless Methods via Localized Bases on Manifolds

This article develops direct and inverse estimates for certain finite dimensional spaces arising in kernel approximation. Both the direct and inverse estimates are based on approximation spaces spanned by local Lagrange functions which are spatially highly localized. The construction of such functions is computationally efficient and generalizes the construction given by the authors for restricted surface splines on $\mathbb{R}^d$. The kernels for which the theory applies includes the Sobolev-Mat\'ern kernels for closed, compact, connected, $C^\infty$ Riemannian manifolds.Comment: 29 pages. To appear in Festschrift for the 80th Birthday of Ian Sloa

The generalized Robinson-Foulds metric

The Robinson-Foulds (RF) metric is arguably the most widely used measure of phylogenetic tree similarity, despite its well-known shortcomings: For example, moving a single taxon in a tree can result in a tree that has maximum distance to the original one; but the two trees are identical if we remove the single taxon. To this end, we propose a natural extension of the RF metric that does not simply count identical clades but instead, also takes similar clades into consideration. In contrast to previous approaches, our model requires the matching between clades to respect the structure of the two trees, a property that the classical RF metric exhibits, too. We show that computing this generalized RF metric is, unfortunately, NP-hard. We then present a simple Integer Linear Program for its computation, and evaluate it by an all-against-all comparison of 100 trees from a benchmark data set. We find that matchings that respect the tree structure differ significantly from those that do not, underlining the importance of this natural condition.Comment: Peer-reviewed and presented as part of the 13th Workshop on Algorithms in Bioinformatics (WABI2013

Jump at the onset of saltation

We reveal a discontinuous transition in the saturated flux for aeolian saltation by simulating explicitly particle motion in turbulent flow. The discontinuity is followed by a coexistence interval with two metastable solutions. The modification of the wind profile due to momentum exchange exhibits a second maximum at high shear strength. The saturated flux depends on the strength of the wind as $q_s=q_0+A(u_*-u_t)(u_*^2+u_t^2)$

Regularity for eigenfunctions of Schr\"odinger operators

We prove a regularity result in weighted Sobolev spaces (or Babuska--Kondratiev spaces) for the eigenfunctions of a Schr\"odinger operator. More precisely, let K_{a}^{m}(\mathbb{R}^{3N}) be the weighted Sobolev space obtained by blowing up the set of singular points of the Coulomb type potential V(x) = \sum_{1 \le j \le N} \frac{b_j}{|x_j|} + \sum_{1 \le i < j \le N} \frac{c_{ij}}{|x_i-x_j|}, x in \mathbb{R}^{3N}, b_j, c_{ij} in \mathbb{R}. If u in L^2(\mathbb{R}^{3N}) satisfies (-\Delta + V) u = \lambda u in distribution sense, then u belongs to K_{a}^{m} for all m \in \mathbb{Z}_+ and all a \le 0. Our result extends to the case when b_j and c_{ij} are suitable bounded functions on the blown-up space. In the single-electron, multi-nuclei case, we obtain the same result for all a<3/2.Comment: to appear in Lett. Math. Phy

Upside-down fluxes Down Under: CO2 net sink in winter and net source in summer in a temperate evergreen broadleaf forest

Predicting the seasonal dynamics of ecosystem carbon fluxes is challenging in broadleaved evergreen forests because of their moderate climates and subtle changes in canopy phenology. We assessed the climatic and biotic drivers of the seasonality of net ecosystem–atmosphere CO2 exchange (NEE) of a eucalyptus-dominated forest near Sydney, Australia, using the eddy covariance method. The climate is characterised by a mean annual precipitation of 800mm and a mean annual temperature of 18°C, hot summers and mild winters, with highly variable precipitation. In the 4-year study, the ecosystem was a sink each year (−225gCm−2yr−1 on average, with a standard deviation of 108gCm−2yr−1); inter-annual variations were not related to meteorological conditions. Daily net C uptake was always detected during the cooler, drier winter months (June through August), while net C loss occurred during the warmer, wetter summer months (December through February). Gross primary productivity (GPP) seasonality was low, despite longer days with higher light intensity in summer, because vapour pressure deficit (D) and air temperature (Ta) restricted surface conductance during summer while winter temperatures were still high enough to support photosynthesis. Maximum GPP during ideal environmental conditions was significantly correlated with remotely sensed enhanced vegetation index (EVI; r2 = 0.46) and with canopy leaf area index (LAI; r2= 0.29), which increased rapidly after mid-summer rainfall events. Ecosystem respiration (ER) was highest during summer in wet soils and lowest during winter months. ER had larger seasonal amplitude compared to GPP, and therefore drove the seasonal variation of NEE. Because summer carbon uptake may become increasingly limited by atmospheric demand and high temperature, and because ecosystem respiration could be enhanced by rising temperatures, our results suggest the potential for large-scale seasonal shifts in NEE in sclerophyll vegetation under climate change.The Australian Education Investment Fund, Australian Terrestrial Ecosystem Research Network, Australian Research Council and Hawkesbury Institute for the Environment at Western Sydney University supported this work. We thank Jason Beringer, Helen Cleugh, Ray Leuning and Eva van Gorsel for advice and support. Senani Karunaratne provided soil classification details

A Dimension-Adaptive Multi-Index Monte Carlo Method Applied to a Model of a Heat Exchanger

We present an adaptive version of the Multi-Index Monte Carlo method, introduced by Haji-Ali, Nobile and Tempone (2016), for simulating PDEs with coefficients that are random fields. A classical technique for sampling from these random fields is the Karhunen-Lo\`eve expansion. Our adaptive algorithm is based on the adaptive algorithm used in sparse grid cubature as introduced by Gerstner and Griebel (2003), and automatically chooses the number of terms needed in this expansion, as well as the required spatial discretizations of the PDE model. We apply the method to a simplified model of a heat exchanger with random insulator material, where the stochastic characteristics are modeled as a lognormal random field, and we show consistent computational savings

Discrete exterior calculus (DEC) for the surface Navier-Stokes equation

We consider a numerical approach for the incompressible surface Navier-Stokes equation. The approach is based on the covariant form and uses discrete exterior calculus (DEC) in space and a semi-implicit discretization in time. The discretization is described in detail and related to finite difference schemes on staggered grids in flat space for which we demonstrate second order convergence. We compare computational results with a vorticity-stream function approach for surfaces with genus 0 and demonstrate the interplay between topology, geometry and flow properties. Our discretization also allows to handle harmonic vector fields, which we demonstrate on a torus.Comment: 21 pages, 9 figure

Numerical Computations with H(div)-Finite Elements for the Brinkman Problem

The H(div)-conforming approach for the Brinkman equation is studied numerically, verifying the theoretical a priori and a posteriori analysis in previous work of the authors. Furthermore, the results are extended to cover a non-constant permeability. A hybridization technique for the problem is presented, complete with a convergence analysis and numerical verification. Finally, the numerical convergence studies are complemented with numerical examples of applications to domain decomposition and adaptive mesh refinement.Comment: Minor clarifications, added references. Reordering of some figures. To appear in Computational Geosciences, final article available at http://www.springerlink.co

Anxiolytic activity of pyridoindole derivatives SMe1EC2 and SMe1M2: behavioral analysis using rat model

Anxiety and mood disorders have become very significant affections in the last decades. According to WHO at least one mental disease occurred per year in 27% of EU inhabitants (more than 82 mil. people). It is estimated that by 2020, depression will be the main cause of morbidity in the developed countries. These circumstances call for research for new prospective drugs with anxiolytic and antidepressive properties exhibiting no toxicity and withdrawal effect and possessing beneficial properties, like antioxidant and/or neuroprotective effects. The aim of this study was to obtain information about psychopharmacological properties of pyridoindole derivatives SMe1EC2 and SMe1M2, using non-invasive behavioral methods in rats