Extending the range of error estimates for radial approximation in Euclidean space and on spheres

We adapt Schaback's error doubling trick [R. Schaback. Improved error bounds for scattered data interpolation by radial basis functions. Math. Comp., 68(225):201--216, 1999.] to give error estimates for radial interpolation of functions with smoothness lying (in some sense) between that of the usual native space and the subspace with double the smoothness. We do this for both bounded subsets of R^d and spheres. As a step on the way to our ultimate goal we also show convergence of pseudoderivatives of the interpolation error.Comment: 10 page

Transfinite thin plate spline interpolation

Duchon's method of thin plate splines defines a polyharmonic interpolant to scattered data values as the minimizer of a certain integral functional. For transfinite interpolation, i.e. interpolation of continuous data prescribed on curves or hypersurfaces, Kounchev has developed the method of polysplines, which are piecewise polyharmonic functions of fixed smoothness across the given hypersurfaces and satisfy some boundary conditions. Recently, Bejancu has introduced boundary conditions of Beppo Levi type to construct a semi-cardinal model for polyspline interpolation to data on an infinite set of parallel hyperplanes. The present paper proves that, for periodic data on a finite set of parallel hyperplanes, the polyspline interpolant satisfying Beppo Levi boundary conditions is in fact a thin plate spline, i.e. it minimizes a Duchon type functional

An Empirical Test of Staw and Ross Prescriptions for the Management of Escalation of Commitment Behavior in organizations

Tests two major prescriptions of Staw and Ross about the management of escalation behavior in organizations. Since these prescriptions are primarily based on research using students in controlled settings, the efficacy of the prescriptions was tested in the context of a real, functioning organization. The results provide conditional support for separating initial decision responsibility from subsequent responsibility as a means of reducing escalation behavior. However, the findings did not support a reduction of project failure risk as a means of minimizing escalation of commitment to a failing course of action

Local 4/5-Law and Energy Dissipation Anomaly in Turbulence

A strong local form of the ``4/3-law'' in turbulent flow has been proved recently by Duchon and Robert for a triple moment of velocity increments averaged over both a bounded spacetime region and separation vector directions, and for energy dissipation averaged over the same spacetime region. Under precisely stated hypotheses, the two are proved to be proportional, by a constant 4/3, and to appear as a nonnegative defect measure in the local energy balance of singular (distributional) solutions of the incompressible Euler equations. Here we prove that the energy defect measure can be represented also by a triple moment of purely longitudinal velocity increments and by a mixed moment with one longitudinal and two tranverse velocity increments. Thus, we prove that the traditional 4/5- and 4/15-laws of Kolmogorov hold in the same local sense as demonstrated for the 4/3-law by Duchon-Robert.Comment: 14 page

Single Image Super-Resolution Using Multi-Scale Convolutional Neural Network

Methods based on convolutional neural network (CNN) have demonstrated tremendous improvements on single image super-resolution. However, the previous methods mainly restore images from one single area in the low resolution (LR) input, which limits the flexibility of models to infer various scales of details for high resolution (HR) output. Moreover, most of them train a specific model for each up-scale factor. In this paper, we propose a multi-scale super resolution (MSSR) network. Our network consists of multi-scale paths to make the HR inference, which can learn to synthesize features from different scales. This property helps reconstruct various kinds of regions in HR images. In addition, only one single model is needed for multiple up-scale factors, which is more efficient without loss of restoration quality. Experiments on four public datasets demonstrate that the proposed method achieved state-of-the-art performance with fast speed

PATIENT PROTECTION AND AFFORDABLE CARE ACT OF 2010: Advancing Health Equity for Racially and Ethnically Diverse Populations

Racial/ethnic disparities in health and health care in the United States are persistent and well documented. Communities of color fare far worse than their white counterparts across a range of health indicators: life expectancy, infant mortality, prevalence of chronic diseases, self-rated health status, insurance coverage, and many others.1 As the nation’s population continues to become increasingly diverse—people of color are projected to comprise 54% of the U.S. population by 2050 and more than half of U.S. children by 20232— these disparities are likely to grow if left unaddressed. Recent health care reform legislation, while not a panacea for eliminating health disparities, off ers an important fi rst step and an unprecedented opportunity to improve health equity in the United States. Reforming the nation’s health care system was President Obama’s top domestic priority when he was sworn into offi ce in January 2009. Th e road to reform was complex and unoffi cially started in summer of 2009 when House and Senate committees began to draft legislation. On November 7, 2009, the House of Representatives passed its health care reform proposal, Th e Aff ordable Health Choices Act of 2009 (H.R. 3962). On December 24, 2009, the Senate passed its own proposal for health care reform, Th e Patient Protection and Aff ordable Care Act (H.R. 3590)*, which was a merged version of the Senate Finance Committee’s America’s Health Future Act (S.1796) and the Senate Committee on Health, Education, Labor, and Pensions’ Aff ordable Health Choices Act (S. 1697).† Eff orts to reconcile diff erences between the Senate and House bills were stymied by the death of Senator Edward Kennedy (D-MA), a lifelong proponent of health care reform and critical force in securing a proposal’s passage in the Senate. Faced with limited options and expecting that a compromise bill could not get Senate support, the House passed the Senate’s proposal and Th e Patient Protection and Aff ordable Care Act (ACA) was signed into law by President Obama on March 23, 2010 (Pub. L. No. 111-148).‡ On March 30, 2010, the ACA was amended by Th e Health Care and Education Reconciliation Act of 2010 (H.R. 4872). According to Congressional Budget Offi ce (CBO) estimates, the ACA, as reconciled by H.R. 4872, will reduce the defi cit by $143 billion over the next decade and decrease the number of non-elderly uninsured by 32 million, leaving 23 million uninsured— approximately one-third of whom would be undocumented immigrants.3 Th is report provides a comprehensive review of general and specifi c ACA provisions with the potential to signifi cantly improve health and health care for millions of diverse populations and their communities. Th e narrative that follows identifi es these provisions, discusses why they are important, and considers challenges that may lie ahead in implementing them. We have organized this presentation in three major sections. Th e next section discusses provisions that explicitly address health disparities, such as those concerning data collection by race/ethnicity, workforce diversity, cultural competence, health disparities research, health disparities initiatives in prevention, and health equity in health insurance reform, and discusses their implications for racially and ethnically diverse communities. Section III describes general provisions, including health insurance reforms, access to care, quality improvement, cost containment, public health and social determinants of health, all of which are likely to have major implications for diverse communities. An accompanying appendix identifi es these provisions, provides a timetable and, where identifi ed in the legislation, the federal agencies responsible for implementation, as well as allocations as of June 30, 2010. Section IV discusses issues that will be critical in realizing the full potential of health care reform and highlights questions and directions for the future, particularly in context of important priorities for reducing racial/ethnic health disparities that were left unaddressed

Coordinated field study for CaPE: Analysis of energy and water budgets

The objectives of this hydrologic cycle study are to understand and model (1) surface energy and land-atmosphere water transfer processes, and (2) interactions between convective storms and surface energy fluxes. A surface energy budget measurement campaign was carried out by an interdisciplinary science team during the period July 8 - August 19, 1991 as part of the Convection and Precipitation/Electrification Experiment (CaPE) in the vicinity of Cape Canaveral, FL. Among the research themes associated with CaPE is the remote estimation of rainfall. Thus, in addition to surface radiation and energy budget measurements, surface mesonet, special radiosonde, precipitation, high-resolution satellite (SPOT) data, geosynchronous (GOES) and polar orbiting (DMSP SSM/I, OLS; NOAA AVHRR) satellite data, and high altitude airplane data (AMPR, MAMS, HIS) were collected. Initial quality control of the seven surface flux station data sets has begun. Ancillary data sets are being collected and assembled for analysis. Browsing of GOES and radar data has begun to classify days as disturbed/undisturbed to identify the larger scale forcing of the pre-convective environment, convection storms and precipitation. The science analysis plan has been finalized and tasks assigned to various investigators

Non-innocent role of fluorine as an electron donor in oxides

Engineering of reducible oxides is generally focused on the cation sites. As such, anion doping remains an underutilized tool despite its unique potential in altering the defect chemistry and steering redox processes. In this contribution, we explore the possibilities offered by substitution on the anion site on the case of a prototypical reducible oxide, namely cerium oxide, doped with fluorine. The choice of fluorine is motivated by the general stability of fluorine in oxide lattices and the fact that it can be readily incorporated in these up to very high concentration with minimal structural distortion [1]. Utilizing photoemission spectroscopy in combination with density functional theory [2], we show that the general notion of fluorine acting as a straightforward ionic donor fails to capture the intricacies of electronic interactions at play. Specifically, we provide evidence for covalent hybridization in the nominally ionic fluorine-cerium interaction that allows for altering the anion derived electron density in cerium oxide beyond the oxygen 2p band (see Figure 1), contrary to the simplified picture of solely introducing a deeper-laying fluorine 2p band [3]. The emergent electronic configuration can be further coupled to standard valence band engineering methods, such as strain manipulation, to provide an unprecedented playground for designing the oxide properties. Our results also demonstrate the practicality of interatomic resonant photoemission spectroscopy as a gauge of non-trivial electronic effects of ligand origin, allowing to efficiently probe the above-mentioned effects. We note that fluorine doping represents a complement to oxygen vacancy engineering and highlight the fact that, unlike oxygen vacancies, the electronic effects generated by fluorine can persist in an oxidizing environment. The latter represents an important contribution the electronic modification of mixed-anion oxides can provide to a breadth of fields, ranging from superoxide stabilization to resistive switching. Please click Additional Files below to see the full abstract

A geometric condition implying energy equality for solutions of 3D Navier-Stokes equation

We prove that every weak solution $u$ to the 3D Navier-Stokes equation that belongs to the class $L^3L^{9/2}$ and \n u belongs to $L^3L^{9/5}$ localy away from a 1/2-H\"{o}lder continuous curve in time satisfies the generalized energy equality. In particular every such solution is suitable.Comment: 10 page

Simple Systems with Anomalous Dissipation and Energy Cascade

We analyze a class of linear shell models subject to stochastic forcing in finitely many degrees of freedom. The unforced systems considered formally conserve energy. Despite being formally conservative, we show that these dynamical systems support dissipative solutions (suitably defined) and, as a result, may admit unique (statistical) steady states when the forcing term is nonzero. This claim is demonstrated via the complete characterization of the solutions of the system above for specific choices of the coupling coefficients. The mechanism of anomalous dissipations is shown to arise via a cascade of the energy towards the modes ($a_n$) with higher $n$; this is responsible for solutions with interesting energy spectra, namely \EE |a_n|^2 scales as $n^{-\alpha}$ as $n\to\infty$. Here the exponents $\alpha$ depend on the coupling coefficients $c_n$ and \EE denotes expectation with respect to the equilibrium measure. This is reminiscent of the conjectured properties of the solutions of the Navier-Stokes equations in the inviscid limit and their accepted relationship with fully developed turbulence. Hence, these simple models illustrate some of the heuristic ideas that have been advanced to characterize turbulence, similar in that respect to the random passive scalar or random Burgers equation, but even simpler and fully solvable.Comment: 32 Page