Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching

In this paper, we prove that a stochastic logistic population under regime switching controlled by a Markov chain is either stochastically permanent or extinctive, and we obtain the sufficient and necessary conditions for stochastic permanence and extinction under some assumptions. In the case of stochastic permanence we estimate the limit of the average in time of the sample path of the solution by two constants related to the stationary probability distribution of the Markov chain and the parameters of the subsystems of the population model. Finally, we illustrate our conclusions through two examples

Multibody Multipole Methods

A three-body potential function can account for interactions among triples of particles which are uncaptured by pairwise interaction functions such as Coulombic or Lennard-Jones potentials. Likewise, a multibody potential of order $n$ can account for interactions among $n$-tuples of particles uncaptured by interaction functions of lower orders. To date, the computation of multibody potential functions for a large number of particles has not been possible due to its $O(N^n)$ scaling cost. In this paper we describe a fast tree-code for efficiently approximating multibody potentials that can be factorized as products of functions of pairwise distances. For the first time, we show how to derive a Barnes-Hut type algorithm for handling interactions among more than two particles. Our algorithm uses two approximation schemes: 1) a deterministic series expansion-based method; 2) a Monte Carlo-based approximation based on the central limit theorem. Our approach guarantees a user-specified bound on the absolute or relative error in the computed potential with an asymptotic probability guarantee. We provide speedup results on a three-body dispersion potential, the Axilrod-Teller potential.Comment: To appear in Journal of Computational Physic

Mapping Crop Cycles in China Using MODIS-EVI Time Series

As the Earth’s population continues to grow and demand for food increases, the need for improved and timely information related to the properties and dynamics of global agricultural systems is becoming increasingly important. Global land cover maps derived from satellite data provide indispensable information regarding the geographic distribution and areal extent of global croplands. However, land use information, such as cropping intensity (defined here as the number of cropping cycles per year), is not routinely available over large areas because mapping this information from remote sensing is challenging. In this study, we present a simple but efficient algorithm for automated mapping of cropping intensity based on data from NASA’s (NASA: The National Aeronautics and Space Administration) MODerate Resolution Imaging Spectroradiometer (MODIS). The proposed algorithm first applies an adaptive Savitzky-Golay filter to smooth Enhanced Vegetation Index (EVI) time series derived from MODIS surface reflectance data. It then uses an iterative moving-window methodology to identify cropping cycles from the smoothed EVI time series. Comparison of results from our algorithm with national survey data at both the provincial and prefectural level in China show that the algorithm provides estimates of gross sown area that agree well with inventory data. Accuracy assessment comparing visually interpreted time series with algorithm results for a random sample of agricultural areas in China indicates an overall accuracy of 91.0% for three classes defined based on the number of cycles observed in EVI time series. The algorithm therefore appears to provide a straightforward and efficient method for mapping cropping intensity from MODIS time series data

Solar variability and climate

Recent precise observations of solar global parameters are used to calibrate an upgraded solar model which takes into account magnetic fields in the solar interior. Historical data about sunspot numbers (from 1500 to the present) and solar radius changes (between 1715 and 1979) are used to compute solar variability on years to centuries timescales. The results show that although the 11 year variability of the total irradiance is of the order of 0.1%, additional, longer lived changes of the order of 0.1% may have occurred in the past centuries. These could, for example, account for the occurrence of climate excursions such as little ice ages.Comment: LaTeX, JGR preprint with AGU++ v16.b and AGUTeX 5.0, use packages graphicx; 6 pages, 4 figures, submitted to JGR-Space physic

A key to selected rockfishes (Sebastes spp.) based on mitochondrial DNA restriction fragment analysis

Larval and juvenile rockfishes (Sebastes spp.) are difficult to identify using morphological characters. We developed a key based on sizes of restriction endonuclease fragments of the NADH dehydrogenase-3 and -4 (ND3/ND4) and 12S and 16S ribosomal RNA (12S/16S) mitochondrial regions. The key makes use of variation in the ND3/ND4 region. Restriction endonuclease Dde I variation can corroborate identifications, as can 12S/16S variation. The key, based on 71 species, includes most North American taxa, several Asian species, and Sebastolobus alascanus and Helicolenus hilgendorfi that are closely related to rockfishes. Fifty-eight of 71 rockfish species in our database can be distinguished unequivocally, using one to five restriction enzymes; identities of the remaining species are narrowed to small groups: 1) S. polyspinis, S. crameri, and S. ciliatus or variabilis (the two species could not be distinguished and were considered as a single species) ; 2) S. chlorostictus, S. eos, and S. rosenblatti; 3) S. entomelas and S. mystinus; 4)S. emphaeus, S. variegatus, and S. wilsoni; and 5) S. carnatus and S. chrysomelas

Countable locally 2-arc-transitive bipartite graphs

We present an order-theoretic approach to the study of countably infinite locally 2-arc-transitive bipartite graphs. Our approach is motivated by techniques developed by Warren and others during the study of cycle-free partial orders. We give several new families of previously unknown countably infinite locally-2-arc-transitive graphs, each family containing continuum many members. These examples are obtained by gluing together copies of incidence graphs of semilinear spaces, satisfying a certain symmetry property, in a tree-like way. In one case we show how the classification problem for that family relates to the problem of determining a certain family of highly arc-transitive digraphs. Numerous illustrative examples are given.Comment: 29 page

The Formal Laplace-Borel Transform of Fliess Operators and the Composition Product

The formal Laplace-Borel transform of an analytic integral operator, known as a Fliess operator, is defined and developed. Then, in conjunction with the composition product over formal power series, the formal Laplace-Borel transform is shown to provide an isomorphism between the semigroup of all Fliess operators under operator composition and the semigroup of all locally convergent formal power series under the composition product. Finally, the formal Laplace-Borel transform is applied in a systems theory setting to explicitly derive the relationship between the formal Laplace transform of the input and output functions of a Fliess operator. This gives a compact interpretation of the operational calculus of Fliess for computing the output response of an analytic nonlinear system. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved

Nearly Optimal Private Convolution

We study computing the convolution of a private input $x$ with a public input $h$, while satisfying the guarantees of $(\epsilon, \delta)$-differential privacy. Convolution is a fundamental operation, intimately related to Fourier Transforms. In our setting, the private input may represent a time series of sensitive events or a histogram of a database of confidential personal information. Convolution then captures important primitives including linear filtering, which is an essential tool in time series analysis, and aggregation queries on projections of the data. We give a nearly optimal algorithm for computing convolutions while satisfying $(\epsilon, \delta)$-differential privacy. Surprisingly, we follow the simple strategy of adding independent Laplacian noise to each Fourier coefficient and bounding the privacy loss using the composition theorem of Dwork, Rothblum, and Vadhan. We derive a closed form expression for the optimal noise to add to each Fourier coefficient using convex programming duality. Our algorithm is very efficient -- it is essentially no more computationally expensive than a Fast Fourier Transform. To prove near optimality, we use the recent discrepancy lowerbounds of Muthukrishnan and Nikolov and derive a spectral lower bound using a characterization of discrepancy in terms of determinants