Sparse image reconstruction on the sphere: implications of a new sampling theorem.

We study the impact of sampling theorems on the fidelity of sparse image reconstruction on the sphere. We discuss how a reduction in the number of samples required to represent all information content of a band-limited signal acts to improve the fidelity of sparse image reconstruction, through both the dimensionality and sparsity of signals. To demonstrate this result, we consider a simple inpainting problem on the sphere and consider images sparse in the magnitude of their gradient. We develop a framework for total variation inpainting on the sphere, including fast methods to render the inpainting problem computationally feasible at high resolution. Recently a new sampling theorem on the sphere was developed, reducing the required number of samples by a factor of two for equiangular sampling schemes. Through numerical simulations, we verify the enhanced fidelity of sparse image reconstruction due to the more efficient sampling of the sphere provided by the new sampling theorem.

The Kramer sampling theorem revisited

The classical Kramer sampling theorem provides a method for obtaining orthogonal sampling formulas. Besides, it has been the cornerstone for a significant mathematical literature on the topic of sampling theorems associated with differential and difference problems. In this work we provide, in an unified way, new and old generalizations of this result corresponding to various different settings; all these generalizations are illustrated with examples. All the different situations along the paper share a basic approach: the functions to be sampled are obtaining by duality in a separable Hilbert space H through an H -valued kernel K defined on an appropriate domain.

Sobolev Type Decomposition of Paley-Wiener-Schwartz Space with Application to Sampling Theory

2000 Mathematics Subject Classification: 94A12, 94A20, 30D20, 41A05.

Analytic Kramer kernels, Lagrange-type interpolation series and de Branges spaces

The classical Kramer sampling theorem provides a method for obtaining orthogonal sampling formulas. In particular, when the involved kernel is analytic in the sampling parameter it can be stated in an abstract setting of reproducing kernel Hilbert spaces of entire functions which includes as a particular case the classical Shannon sampling theory. This abstract setting allows us to obtain a sort of converse result and to characterize when the sampling formula associated with an analytic Kramer kernel can be expressed as a Lagrange-type interpolation series. On the other hand, the de Branges spaces of entire functions satisfy orthogonal sampling formulas which can be written as Lagrange-type interpolation series. In this work some links between all these ideas are established.

Adaptive Sampling with Mobile Sensor Networks

Mobile sensor networks have unique advantages compared with wireless sensor networks. The mobility enables mobile sensors to flexibly reconfigure themselves to meet sensing requirements. In this dissertation, an adaptive sampling method for mobile sensor networks is presented. Based on the consideration of sensing resource constraints, computing abilities, and onboard energy limitations, the adaptive sampling method follows a down sampling scheme, which could reduce the total number of measurements, and lower sampling cost. Compressive sensing is a recently developed down sampling method, using a small number of randomly distributed measurements for signal reconstruction. However, original signals cannot be reconstructed using condensed measurements, as addressed by Shannon Sampling Theory. Measurements have to be processed under a sparse domain, and convex optimization methods should be applied to reconstruct original signals. Restricted isometry property would guarantee signals can be recovered with little information loss. While compressive sensing could effectively lower sampling cost, signal reconstruction is still a great research challenge. Compressive sensing always collects random measurements, whose information amount cannot be determined in prior. If each measurement is optimized as the most informative measurement, the reconstruction performance can perform much better. Based on the above consideration, this dissertation is focusing on an adaptive sampling approach, which could find the most informative measurements in unknown environments and reconstruct original signals. With mobile sensors, measurements are collect sequentially, giving the chance to uniquely optimize each of them. When mobile sensors are about to collect a new measurement from the surrounding environments, existing information is shared among networked sensors so that each sensor would have a global view of the entire environment. Shared information is analyzed under Haar Wavelet domain, under which most nature signals appear sparse, to infer a model of the environments. The most informative measurements can be determined by optimizing model parameters. As a result, all the measurements collected by the mobile sensor network are the most informative measurements given existing information, and a perfect reconstruction would be expected. To present the adaptive sampling method, a series of research issues will be addressed, including measurement evaluation and collection, mobile network establishment, data fusion, sensor motion, signal reconstruction, etc. Two dimensional scalar field will be reconstructed using the method proposed. Both single mobile sensors and mobile sensor networks will be deployed in the environment, and reconstruction performance of both will be compared.In addition, a particular mobile sensor, a quadrotor UAV is developed, so that the adaptive sampling method can be used in three dimensional scenarios.

The Zero-Removing Property and Lagrange-Type Interpolation Series

The classical Kramer sampling theorem, which provides a method for obtaining orthogonal sampling formulas, can be formulated in a more general nonorthogonal setting. In this setting, a challenging problem is to characterize the situations when the obtained nonorthogonal sampling formulas can be expressed as Lagrange-type interpolation series. In this article a necessary and sufficient condition is given in terms of the zero removing property. Roughly speaking, this property concerns the stability of the sampled functions on removing a finite number of their zeros.

Large multi-gene phylogenetic trees of the grasses (Poaceae): progress towards complete tribal and generic level sampling.

In this paper we included a very broad representation of grass family diversity (84% of tribes and 42% of genera). Phylogenetic inference was based on three plastid DNA regions rbcL, matK and trnL-F, using maximum parsimony and Bayesian methods. Our results resolved most of the subfamily relationships within the major clades (BEP and PACCMAD), which had previously been unclear, such as, among others the: (i) BEP and PACCMAD sister relationship, (ii) composition of clades and the sister-relationship of Ehrhartoideae and Bambusoideae + Pooideae, (iii) paraphyly of tribe Bambuseae, (iv) position of Gynerium as sister to Panicoideae, (v) phylogenetic position of Micrairoideae. With the presence of a relatively large amount of missing data, we were able to increase taxon sampling substantially in our analyses from 107 to 295 taxa. However, bootstrap support and to a lesser extent Bayesian inference posterior probabilities were generally lower in analyses involving missing data than those not including them. We produced a fully resolved phylogenetic summary tree for the grass family at subfamily level and indicated the most likely relationships of all included tribes in our analysis.

Post-mortem tissue sampling using computed tomography guidance

PURPOSE: Currently, in forensic medicine cross-sectional imaging gains recognition and a wide use as a non-invasive examination approach. Today, computed tomography (CT) or magnetic resonance imaging that are available for patients are unable to provide tissue information on the cellular level in a non-invasive manner and also diatom detection, DNA, bacteriological, chemical toxicological and other specific tissue analyses are impossible using radiology. We hypothesised that post-mortem minimally invasive tissue sampling using needle biopsies under CT guidance might significantly enhance the potential of virtual autopsy. The purpose of this study was to test the use of a clinically approved biopsy needle for minimally invasive post-mortem sampling of tissue specimens under CT guidance. MATERIAL AND METHODS: ACN III biopsy core needles 14 gauge x 160 mm with automatic pistol device were used on three bodies dedicated to research from the local anatomical institute. Tissue probes from the brain, heart, lung, liver, spleen, kidney and muscle tissue were obtained under CT fluoroscopy. RESULTS: CT fluoroscopy enabled accurate placement of the needle within the organs and tissues. The needles allowed for sampling of tissue probes with a mean width of 1.7 mm (range 1.2-2 mm) and the maximal length of 20 mm at all locations. The obtained tissue specimens were of sufficient size and adequate quality for histological analysis. CONCLUSION: Our results indicate that, similar to the clinical experience but in many more organs, the tissue specimens obtained using the clinically approved biopsy needle are of a sufficient size and adequate quality for a histological examination. We suggest that post-mortem biopsy using the ACN III needle under CT guidance may become a reliable method for targeted sampling of tissue probes of the body.

Temporal variation of the phytoplankton community at short sampling intervals in the Mundaú reservoir, Northeastern Brazil

The aim of this study was to determine how abiotic factors drive the phytoplankton community in a water supply reservoir within short sampling intervals. Samples were collected at the subsurface (0.1 m) and bottom of limnetic (8 m) and littoral (2 m) zones in both the dry and rainy seasons. The following abiotic variables were analyzed: water temperature, dissolved oxygen, electrical conductivity, total dissolved solids, turbidity, pH, total nitrogen, nitrite, nitrate, total phosphorus, total dissolved phosphorus and orthophosphate. Phytoplankton biomass was determined from biovolume values. The role abiotic variables play in the dynamics of phytoplankton species was determined by means of Canonical Correspondence Analysis. Algae biomass ranged from 1.17×10(4) to 9.21×10(4) µg.L-1; cyanobacteria had biomass values ranging from 1.07×10(4) to 8.21×10(4) µg.L-1. High availability of phosphorous, nitrogen limitation, alkaline pH and thermal stability all favored cyanobacteria blooms, particularly during the dry season. Temperature, pH, total phosphorous and turbidity were key factors in characterizing the phytoplankton community between sampling times and stations. Of the species studied, Cylindrospermopsis raciborskii populations were dominant in the phytoplankton in both the dry and rainy seasons. We conclude that the phytoplankton was strongly influenced by abiotic variables, particularly in relation to seasonal distribution patterns.

Nyssomyia intermedia (Lutz & Neiva) and Nyssomyia neivai (Pinto) (Diptera, Psychodidae, Phlebotominae) in a sympatric area: seasonal and nocturnal hourly rhythm in black and white modified Shannon traps

Captures with black and white Shannon traps were undertaken to identify aspects of the behavior of the two cryptic and sympatric species implicated as vectors of cutaneous leishmaniasis, Nyssomyia intermedia (Lutz & Neiva, 1912) and Nyssomyia neivai (Pinto, 1926). The traps were installed side by side, monthly, from July 2001 to June 2002, from 18 to 07 hours, in a peridomicile of Iporanga municipality, state of São Paulo, Brazil. A total of 2,142 specimens were captured, Ny. intermedia (47.4%) and Ny. neivai (50.5%). The white trap was more attractive to both sexes of both species. Males of Ny. neivai predominated (70%) over those of Ny. intermedia on the two traps; on the black trap, the females of Ny. intermedia predominated (63.3%) over those of Ny. neivai (36.7%). Seventy percent of the specimens of both species were captured between 18 and 24 h. Females of Ny. intermedia presented the highest peak at 19-20 h, and those of Ny. neivai at 20-21 h. The highest hourly average for females of Ny. intermedia on the black trap occurred in the winter and that for males in the summer. For Ny. neivai, both sexes predominated in the summer. The two species probably transmit the cutaneous leishmaniasis in the area due to their great predominance.

Precision of distances and ordering of microsatellite markers in consensus linkage maps of chromosomes 1, 3 and 4 from two reciprocal chicken populations using bootstrap sampling

Some factors complicate comparisons between linkage maps from different studies. This problem can be resolved if measures of precision, such as confidence intervals and frequency distributions, are associated with markers. We examined the precision of distances and ordering of microsatellite markers in the consensus linkage maps of chromosomes 1, 3 and 4 from two F 2 reciprocal Brazilian chicken populations, using bootstrap sampling. Single and consensus maps were constructed. The consensus map was compared with the International Consensus Linkage Map and with the whole genome sequence. Some loci showed segregation distortion and missing data, but this did not affect the analyses negatively. Several inversions and position shifts were detected, based on 95% confidence intervals and frequency distributions of loci. Some discrepancies in distances between loci and in ordering were due to chance, whereas others could be attributed to other effects, including reciprocal crosses, sampling error of the founder animals from the two populations, F(2) population structure, number of and distance between microsatellite markers, number of informative meioses, loci segregation patterns, and sex. In the Brazilian consensus GGA1, locus LEI1038 was in a position closer to the true genome sequence than in the International Consensus Map, whereas for GGA3 and GGA4, no such differences were found. Extending these analyses to the remaining chromosomes should facilitate comparisons and the integration of several available genetic maps, allowing meta-analyses for map construction and quantitative trait loci (QTL) mapping. The precision of the estimates of QTL positions and their effects would be increased with such information.

Phylogenetic relationships within the speciose family Characidae (Teleostei: Ostariophysi: Characiformes) based on multilocus analysis and extensive ingroup sampling

Background: With nearly 1,100 species, the fish family Characidae represents more than half of the species of Characiformes, and is a key component of Neotropical freshwater ecosystems. The composition, phylogeny, and classification of Characidae is currently uncertain, despite significant efforts based on analysis of morphological and molecular data. No consensus about the monophyly of this group or its position within the order Characiformes has been reached, challenged by the fact that many key studies to date have non-overlapping taxonomic representation and focus only on subsets of this diversity. Results: In the present study we propose a new definition of the family Characidae and a hypothesis of relationships for the Characiformes based on phylogenetic analysis of DNA sequences of two mitochondrial and three nuclear genes (4,680 base pairs). The sequences were obtained from 211 samples representing 166 genera distributed among all 18 recognized families in the order Characiformes, all 14 recognized subfamilies in the Characidae, plus 56 of the genera so far considered incertae sedis in the Characidae. The phylogeny obtained is robust, with most lineages significantly supported by posterior probabilities in Bayesian analysis, and high bootstrap values from maximum likelihood and parsimony analyses. Conclusion: A monophyletic assemblage strongly supported in all our phylogenetic analysis is herein defined as the Characidae and includes the characiform species lacking a supraorbital bone and with a derived position of the emergence of the hyoid artery from the anterior ceratohyal. To recognize this and several other monophyletic groups within characiforms we propose changes in the limits of several families to facilitate future studies in the Characiformes and particularly the Characidae. This work presents a new phylogenetic framework for a speciose and morphologically diverse group of freshwater fishes of significant ecological and evolutionary importance across the Neotropics and portions of Africa.

Comparative analysis of two sampling techniques for pollen gathered by Nannotrigona testaceicornis Lepeletier (Apidae, Meliponini)

Pollen counts from samples taken from storage pots throughout one year (from October to September) were adjusted by Tasei's volumetric correction coefficient for the determination of pollen sources exploited by two colonies of Nannotrigona testaceicornis in Sao Paulo, Brazil. The results obtained by this sampling technique for seven months (December to June) were compared with those from corbicula load samples taken within the same period. This species visited a large variety of plant species, but few of them were frequently used. As a rule, pollen sources that appeared at frequencies greater than 1% were found with both sampling methods and significant positive correlations (Spearman correlation coefficient) were found between their values. The pollen load sample data showed that N. testaceicornis gathered pollen throughout the external activity period.

A Goldstone theorem in thermal relativistic quantum field theory

We prove a Goldstone theorem in thermal relativistic quantum field theory, which relates spontaneous symmetry breaking to the rate of spacelike decay of the two-point function. The critical rate of fall-off coincides with that of the massless free scalar field theory. Related results and open problems are briefly discussed. (C) 2011 American Institute of Physics. [doi:10.1063/1.3526961]

An algorithmic Friedman-Pippenger theorem on tree embeddings and applications

An (n, d)-expander is a graph G = (V, E) such that for every X subset of V with vertical bar X vertical bar <= 2n - 2 we have vertical bar Gamma(G)(X) vertical bar >= (d + 1) vertical bar X vertical bar. A tree T is small if it has at most n vertices and has maximum degree at most d. Friedman and Pippenger (1987) proved that any ( n; d)- expander contains every small tree. However, their elegant proof does not seem to yield an efficient algorithm for obtaining the tree. In this paper, we give an alternative result that does admit a polynomial time algorithm for finding the immersion of any small tree in subgraphs G of (N, D, lambda)-graphs Lambda, as long as G contains a positive fraction of the edges of Lambda and lambda/D is small enough. In several applications of the Friedman-Pippenger theorem, including the ones in the original paper of those authors, the (n, d)-expander G is a subgraph of an (N, D, lambda)-graph as above. Therefore, our result suffices to provide efficient algorithms for such previously non-constructive applications. As an example, we discuss a recent result of Alon, Krivelevich, and Sudakov (2007) concerning embedding nearly spanning bounded degree trees, the proof of which makes use of the Friedman-Pippenger theorem. We shall also show a construction inspired on Wigderson-Zuckerman expander graphs for which any sufficiently dense subgraph contains all trees of sizes and maximum degrees achieving essentially optimal parameters. Our algorithmic approach is based on a reduction of the tree embedding problem to a certain on-line matching problem for bipartite graphs, solved by Aggarwal et al. (1996).