Showing papers by "Daniel Potts published in 2015"
TL;DR: Algorithms for the approximation of multivariate periodic functions by trigonometric polynomials and an algorithm for sampling multivariate functions on perturbed rank-1 lattices are presented and numerical stability of the suggested method is shown.
69 citations
TL;DR: The Ewald summation formulas and the fast summation approach based on the nonequispaced fast Fourier transform (NFFT) are combined in order to develop efficient methods for calculating the Coulomb energies as well as the acting forces in charged particle systems subject to mixed periodic boundary conditions.
31 citations
TL;DR: The ESPRIT algorithm based on partial SVD and fast Hankel matrix-vector multiplications has much lower cost and high performance for noisy sampled data with relatively large error terms is demonstrated.
28 citations
TL;DR: In this paper, an approximation of multivariate periodic functions in periodic Hilbert spaces of isotropic and dominating mixed smoothness by trigonometric polynomials is presented. But the approximation is based on sampling of the multivariate functions on rank-1 lattices, and the aliasing error of that approximation is of the same order as the error of the approximation using the partial sum of the Fourier series.
23 citations
25 May 2015
TL;DR: An algorithm for constructing suitable rank-1 Chebyshev lattices based on a component-by-component approach and a method for the fast and exact reconstruction of such polynomials from samples along such lattices are presented.
Abstract: We describe a fast method for the evaluation of an arbitrary high-dimensional multivariate algebraic polynomial in Chebyshev form at the nodes of an arbitrary rank-1 Chebyshev lattice. Our main focus is on conditions on rank-1 Chebyshev lattices allowing for the exact reconstruction of such polynomials from samples along such lattices. We present an algorithm for constructing suitable rank-1 Chebyshev lattices based on a component-by-component approach. Moreover, we give a method for the fast and exact reconstruction.
16 citations
TL;DR: Stream reach data collected during a basin-wide environmental assessment of the extensively urbanized upper Niagara River watershed suggest that riparian forests may provide the additional benefit of reducing the abundance of some, but not all, invasive plants.
Abstract: Urban riparian plant communities exist at the interface between terrestrial and aquatic habitats, and they are rich sources of species biodiversity and ecosystem services. The periodic floods that promote species diversity in riparian plant communities also increase their vulnerability to nonnative plant invasions. Plant invasions are constrained by seed and suitable habitat availability. However, how seed dispersal and establishment limitations interact to shape nonnative plant invasions in riparian communities is poorly understood. We use Stream Visual Assessment Protocol data to evaluate the hydrological and geomorphological parameters that influence the seeding and establishment of six common nonnative species in urban riparian habitats: garlic mustard, purple loosestrife, reed canarygrass, common reed, Japanese knotweed, and multiflora rose. To address this objective, we analyzed stream reach data collected during a basin-wide environmental assessment of the extensively urbanized upper Niagara River watershed. We found limited support for our prediction that propagule limitation constrains the distribution of nonnative riparian species, likely because these species are well established in the study area. Instead, we found that opportune stream reach characteristics better predict the distribution of the common invasive riparian species—most notably open tree canopy. Given that there is widespread investment in urban riparian forest restoration to improve water quality, increase stream-bank stability, enhance wildlife habitat and promote recreation, our data suggest that riparian forests may provide the additional benefit of reducing the abundance of some, but not all, invasive plants. Nomenclature: Garlic mustard, Alliaria petiolata (Bieb.) Cavara & Grande; purple loosestrife, Lythrum salicaria L.; reed canarygrass, Phalaris arundinacea L.; common reed, Phragmites australis (Cav.) Trin. ex Steud.; Japanese
13 citations
TL;DR: Results suggest influences of N- and P-addition on ecosystem processes are seasonally dynamic and by differentially influencing above and below ground components of ecosystems, the availability of N and P in soils may interact to influence ecosystem CO2 exchange.
Abstract: Nitrogen (N) and phosphorus (P) affect the structure and function of grasslands by altering plant competitive interactions, shifting patterns of above and below ground biomass allocation, and increasing net primary production. However, the influence of N and P on net ecosystem CO2 exchange (NEE) is poorly understood. In a field-based factorial N- and P-addition experiment, we measured shallow soil moisture, leaf area index, and component fluxes of midday ecosystem CO2 exchange throughout the growing season in a restored temperate grassland near Buffalo, New York. Throughout the growing season, N-addition increased gross ecosystem CO2 exchange (GEE) and correspondingly altered NEE to increase ecosystem CO2 uptake. In contrast N-addition caused a seasonally dynamic decline in leaf area adjusted GEE, a pattern consistent with increased photosynthetic light limitation. P-addition did not significantly increase Re, and N- and P-addition interacted to significantly weaken the ecosystem as a midday CO2 ...
6 citations
16 Feb 2015
TL;DR: An algorithm for constructing suitable rank-1 Chebyshev lattices based on a component-by-component approach is presented and a method for the fast, exact and stable reconstruction of an arbitrary high-dimensional multivariate algebraic polynomials is given.
Abstract: We describe a fast method for the evaluation of an arbitrary high-dimensional multivariate algebraic polynomial in Chebyshev form at the nodes of an arbitrary rank-1 Chebyshev lattice. Our main focus is on conditions on rank-1 Chebyshev lattices allowing for the exact reconstruction of such polynomials from samples along such lattices and we present an algorithm for constructing suitable rank-1 Chebyshev lattices based on a component-by-component approach. Moreover, we give a method for the fast, exact and stable reconstruction.
1 citations