Continuous Data Assimilation with Stochastically Noisy Data

We analyze the performance of a data-assimilation algorithm based on a linear feedback control when used with observational data that contains measurement errors. Our model problem consists of dynamics governed by the two-dimension incompressible Navier-Stokes equations, observational measurements given by finite volume elements or nodal points of the velocity field and measurement errors which are represented by stochastic noise. Under these assumptions, the data-assimilation algorithm consists of a system of stochastically forced Navier-Stokes equations. The main result of this paper provides explicit conditions on the observation density (resolution) which guarantee explicit asymptotic bounds, as the time tends to infinity, on the error between the approximate solution and the actual solutions which is corresponding to these measurements, in terms of the variance of the noise in the measurements. Specifically, such bounds are given for the the limit supremum, as the time tends to infinity, of the expected value of the $L^2$-norm and of the $H^1$ Sobolev norm of the difference between the approximating solution and the actual solution. Moreover, results on the average time error in mean are stated

A connection between the Camassa-Holm equations and turbulent flows in channels and pipes

In this paper we discuss recent progress in using the Camassa-Holm equations to model turbulent flows. The Camassa-Holm equations, given their special geometric and physical properties, appear particularly well suited for studying turbulent flows. We identify the steady solution of the Camassa-Holm equation with the mean flow of the Reynolds equation and compare the results with empirical data for turbulent flows in channels and pipes. The data suggests that the constant $\alpha$ version of the Camassa-Holm equations, derived under the assumptions that the fluctuation statistics are isotropic and homogeneous, holds to order $\alpha$ distance from the boundaries. Near a boundary, these assumptions are no longer valid and the length scale $\alpha$ is seen to depend on the distance to the nearest wall. Thus, a turbulent flow is divided into two regions: the constant $\alpha$ region away from boundaries, and the near wall region. In the near wall region, Reynolds number scaling conditions imply that $\alpha$ decreases as Reynolds number increases. Away from boundaries, these scaling conditions imply $\alpha$ is independent of Reynolds number. Given the agreement with empirical and numerical data, our current work indicates that the Camassa-Holm equations provide a promising theoretical framework from which to understand some turbulent flows.Comment: tex file, 29 pages, 4 figures, Physics of Fluids (in press

Pulsation of EE Cam

EE Cam is a previously little studied Delta Scuti pulsator with amplitudes between those of the HADS (High-Amplitude Delta Scuti stars) group and the average low-amplitude pulsators. Since the size of stellar rotation determines both which pulsation modes are selected by the star as well as their amplitudes, the star offers a great opportunity to examine the astrophysical connections. Extensive photometric measurements covering several months were carried out. 15 significant pulsation frequencies were extracted. The dominant mode at 4.934 cd$^{-1}$ was identified as a radial mode by examining the phase shifts at different wavelengths. Medium-dispersion spectra yielded a $v\sin i$ value of $40 \pm 3$ km s$^{-1}$. This shows that EE Cam belongs to the important transition region between the HADS and normal Delta Scuti stars.Comment: 13 pages, 3 figures, 3 table

Understanding the measurement of hunger and food insecurity in the elderly

The elderly are one of the population subgroups at greatest risk for hunger and food insecurity. To date, no accurate measures of this problem have been developed. What is needed are a thorough understanding of the phenomenon, and an assessment of how the elderly perceive and answer items commonly used to measure hunger and food insecurity in other subgroups. In-depth, open-ended interviews were conducted with forty-one low-income urban black and rural white residents of upstate New York. Results suggest a conceptual framework of food insecurity in the elderly with two significant differences from frameworks proposed for younger families: the major role of health problems and physical disabilities, and the impact of personal history on perceptions of food insecurity. In a telephone follow-up (approximately six months after the initial interviews) twenty-four respondents were asked commonly used food insecurity questionnaire items from six different sources. Results suggest that hunger and food insecurity among the elderly can be measured directly. The commonly used measures tested here will help categorize the stages of food insecurity. However, these direct measures might underestimate the prevalence of food insecurity because of a perceived reluctance to report problems with food.

Nutritional Consequences of Food Insecurity in a Rural New York State County

This study of women with children in a rural county of upstate New York examined the relationships of food insecurity and income with two nutritional consequences (adiposity and fruit and vegetables consumption), and assessed whether disordered eating patterns is a mediator for the effects of food insecurity and income on these nutritional consequences. Each of 193 respondents was interviewed twice in her home. Data were collected on household food stores, socioeconomic and demographic characteristics, methods of obtaining food, food program participation, household expenditures, food intake, the Radimer/Cornell hunger and food insecurity items, height, weight, frequency of fruit and vegetable consumption, and disordered eating patterns. Regression analysis was used to analyze the relationships of body mass index and an obesity classification with height, income, education, single parenthood, employment, food insecurity, disordered eating, and frequency of fruit and vegetable consumption. Regression analysis was also used to examine the relationships of disordered eating and frequency of fruit and vegetable consumption with the other variables. Lower income and unemployment were related to higher adiposity. The effects of income on adiposity were not mediated through disordered eating patterns or through fruit and vegetable consumption. Food insecurity was related to adiposity, and part of this effect of food insecurity was mediated through disordered eating. This mediating effect of disordered eating partially explained why those experiencing the least severe food insecurity were more likely to be overweight than those who were food secure, but those experiencing the most severe food insecurity were less likely to be overweight than those who were food secure. Food insecurity was related to lower fruit and vegetable consumption, but this did not translate into effects on adiposity.

Solicitors General Panel on the Legacy of the Rehnquist Court

All of us who are speaking probably share the same giddy feeling in front of a microphone with no red light. For years, my daughter told people that the greatest threat to Western civilization was her father at a podium without a red light. Before becoming Solicitor General, I spent my career as a trial lawyer, arguing only a few appeals. I found this red light tradition a little peculiar. More often than not, timers and lights in courts of appeals are viewed as advisory at best. I\u27ve had arguments where ten minutes were allocated per side, and yet argument extended until the afternoon. In another case that allocated ninety minutes per side and began at nine o\u27clock, we didn\u27t actually finish until four o\u27clock in the afternoon. So coming into the SG\u27s office, my view about the red light was, well, perhaps it shows your time has nominally expired, but undoubtedly the Justices will have other questions. And in any event, I might want to take a few extra minutes to address additional points. That was so wrong. The red light ended everything-absolutely everything-and not just for the advocates; it also ended the questioning of the Associate Justices. The Chief Justice was an equal opportunity cutter-offer. On many occasions, he cut off oral argument when a Justice was at the outset of a question he or she had been trying to get out in the open oral combat that was advocacy in the Supreme Court of Chief Justice Rehnquist

Is It Worth It? Examining the Educational Benefits of Synchronous Activities in an Online Theology Course

To explore the effect of adding synchronous activities to an online course, one section of a theology course was conducted in an asynchronous environment while the second section incorporated weekly Adobe Connect sessions. No significant differences were found on measures of academic achievement, student satisfaction, or classroom community

Estimating the prevalence of hunger and food insecurity: The validity of questionnaire-based measures for the identification of households

This study had three objectives: (1) to assess the validity of questionnaire-based measures in identifying households experiencing hunger and food insecurity, (2) to examine the interrelationships of different questionnaire-based measures, and (3) to examine the construction of a continuous food insecurity scale intended to differentiate three levels of food insecurity within households. A 1993 survey of 193 randomly sampled rural households with women and children living at home provided data on demographics, risk factors for food insecurity, Radimer/Cornell, CCHIP, and NHANES III hunger and food insecurity items, coping strategies, fruit and vegetable consumption, disordered eating behaviors, height, weight, dietary recall, and household food-stores inventory. This information was used to develop a definitive criterion measure for hunger and food insecurity, against which the Radimer/Cornell and CCHIP questionnaire-based measures, the NHANES III item, and the continuous food insecurity scale were tested for their specificity and sensitivity in measuring levels of food insecurity.