On LpL^p--LqL^q trace inequalities

We give necessary and sufficient conditions in order that inequalities of the type $$\| T_K f\|_{L^q(d\mu)}\leq C \|f\|_{L^p(d\sigma)}, \qquad f \in L^p(d\sigma),$$ hold for a class of integral operators $T_K f(x) = \int_{R^n} K(x, y) f(y) d \sigma(y)$ with nonnegative kernels, and measures $d \mu$ and $d\sigma$ on $\R^n$, in the case where $p>q>0$ and $p>1$. An important model is provided by the dyadic integral operator with kernel $K_{\mathcal D}(x, y) \sum_{Q\in{\mathcal D}} K(Q) \chi_Q(x) \chi_Q(y)$, where $\mathcal D=\{Q\}$ is the family of all dyadic cubes in $\R^n$, and $K(Q)$ are arbitrary nonnegative constants associated with $Q \in{\mathcal D}$. The corresponding continuous versions are deduced from their dyadic counterparts. In particular, we show that, for the convolution operator $T_k f = k\star f$ with positive radially decreasing kernel $k(|x-y|)$, the trace inequality $$\| T_k f\|_{L^q(d\mu)}\leq C \|f\|_{L^p(d x)}, \qquad f \in L^p(dx),$$ holds if and only if ${\mathcal W}_{k}[\mu] \in L^s (d\mu)$, where $s = {\frac{q(p-1)}{p-q}}$. Here ${\mathcal W}_{k}[\mu]$ is a nonlinear Wolff potential defined by ${\mathcal W}_{k}[\mu](x)=\int_0^{+\infty} k(r) \bar{k}(r)^{\frac 1 {p-1}} \mu (B(x,r))^{\frac 1{p-1}} r^{n-1} dr,$ and $\bar{k}(r)=\frac1{r^n}\int_0^r k(t) t^{n-1} dt$. Analogous inequalities for $1\le q < p$ were characterized earlier by the authors using a different method which is not applicable when $q<1$

Geometrical Optics applied to 1D Site Response of Inhomogeneous Soil Deposits

The technique referred as Geometrical Optics entails considering the wave propagation in a heterogeneous medium as if it happened with infinitely small wavelength. This classic simplification allows to obtain useful approximate analytical results in cases where complete description of the waveform behavior is virtually unattainable, hence its wide use in Physics. This approximation is also commonly termed Ray Theory, and it has already been thoroughly applied in Seismology. This text presents an application of Geometrical Optics to 1D Site Response (1DSR): it is used herein to, first, explain and elucidate the generality of some previous observations and results; second, to partially settle an open question in 1DSR, namely “what are the equivalent homogeneous properties that yield the same response, in terms of natural frequencies and resonance amplitude, for a certain inhomogeneous site?”, provided few assumptions

Precision Assessment of the HPLC Phytoplankton Pigment Dataset Analyzed by NASA to Quantify Global Variability in Support of Ocean Color Remote Sensing

The ability to generate chlorophyll a (Chl a) assessments from ocean color orbital sensors, such as VIIRS and MODIS, that satisfy the requirements to be climate-quality data record (CDR) quality is contingent in part on the quality of the in situ ground or sea truth observations that serve as datasets for vicarious calibration and algorithm validation activities. NASA has a mandate to collect, analyze, and distribute in situ data of the highest possible quality with documented uncertainties and in keeping with established performance metrics. Using a dataset of over 18,000 HPLC phytoplankton pigment samples representing water collected in all major ocean basins analyzed a central laboratory (Field Support Group (FSG) of the Ocean Ecology Laboratory (OEL) at NASA Goddard Space Flight Center (GSFC)), we performed an assessment of the global precision among sample replicates of Chl a as well as major accessory pigments. We investigated the impacts of filtration volume, water basin, collection technique, pigment concentration, and different filtration volumes for replicate filters on replicate filter precision, as well as investigating any pigment-specific differences. Our results quantify sample variability with the goal of understanding any systemic biases or biogeographic influences

Spin 1/2 Fermions in the Unitary Regime at Finite Temperature

We have performed a fully non-perturbative calculation of the thermal properties of a system of spin 1/2 fermions in 3D in the unitary regime. We have determined the critical temperature for the superfluid-normal phase transition. The thermodynamic behavior of this system presents a number of unexpected features, and we conclude that spin 1/2 fermions in the BCS-BEC crossover should be classified as a new type of superfluid.Comment: 6 pages, 2 figures, version for the Proceedings of QMBT1

Windows .NET Network Distributed Basic Local Alignment Search Toolkit (W.ND-BLAST)

BACKGROUND: BLAST is one of the most common and useful tools for Genetic Research. This paper describes a software application we have termed Windows .NET Distributed Basic Local Alignment Search Toolkit (W.ND-BLAST), which enhances the BLAST utility by improving usability, fault recovery, and scalability in a Windows desktop environment. Our goal was to develop an easy to use, fault tolerant, high-throughput BLAST solution that incorporates a comprehensive BLAST result viewer with curation and annotation functionality. RESULTS: W.ND-BLAST is a comprehensive Windows-based software toolkit that targets researchers, including those with minimal computer skills, and provides the ability increase the performance of BLAST by distributing BLAST queries to any number of Windows based machines across local area networks (LAN). W.ND-BLAST provides intuitive Graphic User Interfaces (GUI) for BLAST database creation, BLAST execution, BLAST output evaluation and BLAST result exportation. This software also provides several layers of fault tolerance and fault recovery to prevent loss of data if nodes or master machines fail. This paper lays out the functionality of W.ND-BLAST. W.ND-BLAST displays close to 100% performance efficiency when distributing tasks to 12 remote computers of the same performance class. A high throughput BLAST job which took 662.68 minutes (11 hours) on one average machine was completed in 44.97 minutes when distributed to 17 nodes, which included lower performance class machines. Finally, there is a comprehensive high-throughput BLAST Output Viewer (BOV) and Annotation Engine components, which provides comprehensive exportation of BLAST hits to text files, annotated fasta files, tables, or association files. CONCLUSION: W.ND-BLAST provides an interactive tool that allows scientists to easily utilizing their available computing resources for high throughput and comprehensive sequence analyses. The install package for W.ND-BLAST is freely downloadable from . With registration the software is free, installation, networking, and usage instructions are provided as well as a support forum

Fractionized Exercise Lowers Morning Central Blood Pressure Under Conditions of Recommended and Long Sleep Durations

Long sleep duration (9+ hours) is gaining attention as a parameter that may increase the risk for cardiovascular disease with reports of habitually long duration sleepers having higher nighttime blood pressure (BP), higher day-to-day BP variability, and pulse pressure (PP). PURPOSE: The aims of the study were to determine the effect of one week of long duration sleep on central BP, and examine the impact of fractionized exercise on central BP under controlled sleep duration conditions. METHODS: Eleven participants (46± 5 years; 9 women) spent six nights with 8 or 10+ hours in bed to achieve recommended (7-8 hours) and long sleep durations as measured using a wrist-worn accelerometer (GT9x, Actigraph). On the sixth day, fractionized exercise consisted of three 10-minute bouts of brisk walking at a set cadence to reach an intensity of 60-75% age-predicted maximum heart rate. Central BP was measured the morning before and after fractionized exercise using applanation tonometry of the right radial artery (SphygmoCor PVx, AtCor Medical). Pulse wave analysis yielded other important indices including forward and reflected pressure waves along with pulse wave velocity (PWV). Two-way repeated-measures analyses of variance with factors of sleep duration (recommended vs. long) and time (pre- vs. post-exercise) were used to assess for differences in central BP. RESULTS: Sleep duration was significantly different between the 8 and 10+ hours in bed protocols (426 ± 19 vs. 550 ± 18 minutes, p\u3c0.001). Long duration sleep did not alter central BP or pulse wave pressures as compared to the recommended sleep duration (p\u3e0.05). A main effect for time was observed for central PP such that PP was significantly reduced following fractionized exercise as compared to baseline (29 ± 2 vs. 27 ± 2 mmHg, p = 0.04). The lower central PP was accompanied by reduced reflected wave pressure (14 ± 1 vs. 13 ± 1 mmHg, p \u3c 0.01), reflection magnitude (72 ± 4% vs. 65 ± 4%, p = 0.01), and PWV (7.5 ± 0.2 vs. 7.2 ± 0.2 m/s, p = 0.01). CONCLUSION: One week of long duration sleep does not alter central BP in middle-aged adults, but fractionized exercise is effective at reducing central PP under conditions of recommended and long sleep durations

Investing in Creativity: A Study of the Support Structure for U.S. Artists

Documents and analyzes the environment of support for individual artists. Provides a framework for analysis of various dimensions of the support structure, nationally and in specific sites across the U.S. Includes support programs and policy initiatives