Covering Kids & Families Evaluation: Public Coverage Versus No Coverage for Children: Perceptions and Experiences of Parents in Four Cities

Based on interviews, examines the perceptions and experiences that shape parents' decisions on enrolling their children in Medicaid and State Children's Health Insurance Programs. Considers remaining challenges, including language barriers

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

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

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

On admissibility criteria for weak solutions of the Euler equations

We consider solutions to the Cauchy problem for the incompressible Euler equations satisfying several additional requirements, like the global and local energy inequalities. Using some techniques introduced in an earlier paper we show that, for some bounded compactly supported initial data, none of these admissibility criteria singles out a unique weak solution. As a byproduct we show bounded initial data for which admissible solutions to the p-system of isentropic gas dynamics in Eulerian coordinates are not unique in more than one space dimension.Comment: 33 pages, 1 figure; v2: 35 pages, corrected typos, clarified proof

Precision Pointing of IBEX-Lo Observations

Post-launch boresight of the IBEX-Lo instrument onboard the Interstellar Boundary Explorer (IBEX) is determined based on IBEX-Lo Star Sensor observations. Accurate information on the boresight of the neutral gas camera is essential for precise determination of interstellar gas flow parameters. Utilizing spin-phase information from the spacecraft attitude control system (ACS), positions of stars observed by the Star Sensor during two years of IBEX measurements were analyzed and compared with positions obtained from a star catalog. No statistically significant differences were observed beyond those expected from the pre-launch uncertainty in the Star Sensor mounting. Based on the star observations and their positions in the spacecraft reference system, pointing of the IBEX satellite spin axis was determined and compared with the pointing obtained from the ACS. Again, no statistically significant deviations were observed. We conclude that no systematic correction for boresight geometry is needed in the analysis of IBEX-Lo observations to determine neutral interstellar gas flow properties. A stack-up of uncertainties in attitude knowledge shows that the instantaneous IBEX-Lo pointing is determined to within \sim 0.1\degr in both spin angle and elevation using either the Star Sensor or the ACS. Further, the Star Sensor can be used to independently determine the spacecraft spin axis. Thus, Star Sensor data can be used reliably to correct the spin phase when the Star Tracker (used by the ACS) is disabled by bright objects in its field-of-view. The Star Sensor can also determine the spin axis during most orbits and thus provides redundancy for the Star Tracker.Comment: 22 pages, 18 figure

Navigability is a Robust Property

The Small World phenomenon has inspired researchers across a number of fields. A breakthrough in its understanding was made by Kleinberg who introduced Rank Based Augmentation (RBA): add to each vertex independently an arc to a random destination selected from a carefully crafted probability distribution. Kleinberg proved that RBA makes many networks navigable, i.e., it allows greedy routing to successfully deliver messages between any two vertices in a polylogarithmic number of steps. We prove that navigability is an inherent property of many random networks, arising without coordination, or even independence assumptions

Reproducing Kernels of Generalized Sobolev Spaces via a Green Function Approach with Distributional Operators

In this paper we introduce a generalized Sobolev space by defining a semi-inner product formulated in terms of a vector distributional operator $\mathbf{P}$ consisting of finitely or countably many distributional operators $P_n$, which are defined on the dual space of the Schwartz space. The types of operators we consider include not only differential operators, but also more general distributional operators such as pseudo-differential operators. We deduce that a certain appropriate full-space Green function $G$ with respect to $L:=\mathbf{P}^{\ast T}\mathbf{P}$ now becomes a conditionally positive definite function. In order to support this claim we ensure that the distributional adjoint operator $\mathbf{P}^{\ast}$ of $\mathbf{P}$ is well-defined in the distributional sense. Under sufficient conditions, the native space (reproducing-kernel Hilbert space) associated with the Green function $G$ can be isometrically embedded into or even be isometrically equivalent to a generalized Sobolev space. As an application, we take linear combinations of translates of the Green function with possibly added polynomial terms and construct a multivariate minimum-norm interpolant $s_{f,X}$ to data values sampled from an unknown generalized Sobolev function $f$ at data sites located in some set $X \subset \mathbb{R}^d$. We provide several examples, such as Mat\'ern kernels or Gaussian kernels, that illustrate how many reproducing-kernel Hilbert spaces of well-known reproducing kernels are isometrically equivalent to a generalized Sobolev space. These examples further illustrate how we can rescale the Sobolev spaces by the vector distributional operator $\mathbf{P}$. Introducing the notion of scale as part of the definition of a generalized Sobolev space may help us to choose the "best" kernel function for kernel-based approximation methods.Comment: Update version of the publish at Num. Math. closed to Qi Ye's Ph.D. thesis (\url{http://mypages.iit.edu/~qye3/PhdThesis-2012-AMS-QiYe-IIT.pdf}