Equivalence of concentration inequalities for linear and non-linear functions

We consider a random variable $X$ that takes values in a (possibly infinite-dimensional) topological vector space $\mathcal{X}$. We show that, with respect to an appropriate "normal distance" on $\mathcal{X}$, concentration inequalities for linear and non-linear functions of $X$ are equivalent. This normal distance corresponds naturally to the concentration rate in classical concentration results such as Gaussian concentration and concentration on the Euclidean and Hamming cubes. Under suitable assumptions on the roundness of the sets of interest, the concentration inequalities so obtained are asymptotically optimal in the high-dimensional limit.Comment: 19 pages, 5 figure

The effect of nonlinearities on the dynamic response of a large shuttle payload

The STS Centaur was designed to be a high energy upper stage for use with the Space Shuttle. Two versions were designed under development when the program was cancelled. The first version, designated G-prime, was for planetary missions. The second version, designated G, was to place spacecraft in geosynchronous orbit. As a part of the STS Centaur finite-element model verification effort, test articles of both versions were subjected to a series of static tests. In addition the Centaur G-prime test article was subjected to a series of dynamic tests including a modal survey. Both the static and dynamic tests showed that nonlinearities existed in the Centaur and its support system. The support system included flight-like latches. The nonlinearities were particularly apparent in tests that loaded the forward support structure of the Centaur. These test results were used to aid in the development of two improved finite-element models. The first was a linear model, while the second contained nonlinear elements at the boundaries. Results from both models were compared with the transient response obtained from a step-relaxation or twang test. The linear model was able to accurately match the low frequency response found in the test data. However, only the nonlinear model was able to match higher frequency response that was present in some of the test data. In addition the nonlinear model was able to predict other nonlinear behavior such as the dynamic jump that occurs in systems with nonlinear stiffness

The Effects of the Mad Dog Diet on Bowel Function, Body Composition, Neuropathic Pain, and Depression in a Spinal Cord Injury and Multiple Sclerosis Population

Inflammation has been shown to negatively influence bowel function, body composition, neuropathic pain, and depression within the spinal cord injury (SCI) and multiple sclerosis (MS) populations. Four individuals with varying levels of SCI’s (C5-T1/AIS A-D/3 male 1 female) and two individuals with varying diagnoses of MS (SPMS & RRMS, female) were recruited for the study. Bowel function was assessed via The Bowel Management subset of the Spinal Cord Injury Quality of Life (SCI-QOL) and Neurological Bowel Dysfunction (NBD) questionnaires, body composition was assessed via dual-energy X-ray absorptiometry (DXA) scans, neuropathic pain was assessed via the neuropathic pain questionnaire, and depression was measured via the Center for Epidemiologic Studies Depression Scale (CES-D) questionnaire. This study investigated the effects of 6-weeks of the Mad Dog diet, which aimed to reduce inflammation, and improve the aforementioned ailments. The 6-week Mad Dog diet was associated with a significant reduction in total body mass (p=0.006), lean mass (p=0.046) and fat mass (p=0.038). Despite the significant reduction in fat mass, there were no significant changes in subcutaneous fat mass (p=0.091), or visceral mass (p=0.33), which suggests that the study was underpowered and could not distinguish the relative contribution of either fat source to the losses in total fat mass. Likewise, there were no significant changes in bowel function as determined by SCI-QOL scores (p=0.33), or NBD scores (p=0.29), and no significant changes in any domain of neuropathic pain (sensory, p=0.55; affective, p=0.15; sensitivity, p=0.12), or depression (CES-D scores, p=0.34). These findings demonstrate that 6 weeks of the Mad Dog diet may be beneficial for body composition in the SCI and MS populations. Findings from this research provide the basis for a larger study that can more fully assess the outcomes from this study along with changes in biological measures of inflammation

The dynamical state of a young stellar cluster

The dynamical state of the young star-forming cluster Rho Ophiuchi is considered, with emphasis on the L1688 cloud. Radial velocities are derived for 32 YSOs, with some being multi-epoch, using Markov-Chain Monte Carlo routines based upon the package emcee. Sources are chosen based upon their spectral index to focus on the earlier stages of star formation, in this case, Class I and Flat spectrum objects, and compared with a sample of Class II and III objects from the same embedded cluster. It is found that the radial velocity dispersion for these younger objects is Δv = 2.8 ± 0:6 km s-1 which is about 2σ higher than the dispersion for Class II and III objects. The implication is that there are either small number statistics at play, or the cluster\u27s dispersion is being increased as an inverse function of the distance from the center of the cluster due to a collapse-and-rebound phase that has been proposed in recent simulations --Abstract, page iii

Teaching College Economics in a High School Setting: Lessons Learned and Implementation Strategies

Interest in exposing high school seniors to college level economics has risen in recent years. Under one delivery option, a dual-enrollment program, students are concurrently enrolled in college and high school, and receive credit at both institutions for the same course. These programs benefit high schools by increasing the academic rigor in the senior year, and may also aid colleges' external relations and recruitment. Colleges and universities considering such a program must recognize important administrative and student body differences between the university and high school settings. This paper summarizes the experiences of Southern Illinois University, where a dual-enrollment program was implemented in the mid 1990s, and uses this case to illustrate key differences between the two classroom environments. Suggested strategies for coping with these differences are described.