On the use of blow up to study regularizations of singularities of piecewise smooth dynamical systems in R3\mathbb{R}^3

In this paper we use the blow up method of Dumortier and Roussarie \cite{dumortier_1991,dumortier_1993,dumortier_1996}, in the formulation due to Krupa and Szmolyan \cite{krupa_extending_2001}, to study the regularization of singularities of piecewise smooth dynamical systems \cite{filippov1988differential} in $\mathbb R^3$. Using the regularization method of Sotomayor and Teixeira \cite{Sotomayor96}, first we demonstrate the power of our approach by considering the case of a fold line. We quickly recover a main result of Bonet and Seara \cite{reves_regularization_2014} in a simple manner. Then, for the two-fold singularity, we show that the regularized system only fully retains the features of the singular canards in the piecewise smooth system in the cases when the sliding region does not include a full sector of singular canards. In particular, we show that every locally unique primary singular canard persists the regularizing perturbation. For the case of a sector of primary singular canards, we show that the regularized system contains a canard, provided a certain non-resonance condition holds. Finally, we provide numerical evidence for the existence of secondary canards near resonance.Comment: To appear in SIAM Journal of Applied Dynamical System

Maintaining exercise and healthful eating in older adults: The SENIOR project II: Study design and methodology

The Study of Exercise and Nutrition in Older Rhode Islanders (SENIOR) Project II is an intervention study to promote the maintenance of both exercise and healthful eating in older adults. It is the second phase of an earlier study, SENIOR Project I, that originally recruited 1277 community-dwelling older adults to participate in behavior-specific interventions designed to increase exercise and/or fruit and vegetable consumption. The general theoretical framework for this research is the Transtheoretical Model (TTM) of Health Behavior Change. The current intervention occurs over a 48-month period, using a manual, newsletters, and phone coaching calls. Annual assessments collect standardized data on behavioral outcomes (exercise and diet), TTM variables (stage of change and self-efficacy), psychosocial variables (social support, depression, resilience, and life satisfaction), physical activity and functioning (SF-36, Up and Go, Senior Fitness Test, and disability assessment), cognitive functioning (Trail Making Test and Forward and Backward Digit Span), physical measures (height, weight, and waist circumference), and demographics. The SENIOR Project II is designed to answer the following question as its primary objective: (1) Does an individualized active-maintenance intervention with older adults maintain greater levels of healthful exercise and dietary behaviors for 4 years, compared to a control condition? In addition, there are two secondary objectives: (2) What are the psychosocial factors associated with the maintenance of health-promoting behaviors in the very old? (3) What are the effects of the maintenance of health-promoting behaviors on reported health outcomes, psychosocial measures, anthropometrics, and cognitive status

Endometrial Histopathology in Patients with Laparoscopic Proven Salpingitis and HIV-1 Infection

Study Objective. To identify sensitive and specific histological criteria for endometritis in women with laparoscopically-confirmed acute salpingitis. Methods. Women, age 18–40 years of age presenting with complaints of lower abdominal pain ≤2 weeks and no antibiotics use in past two weeks, were enrolled. They underwent clinical examination, screening for HIV; other sexually transmitted infections plus endometrial biopsy sampling for histopathology. Diagnostic laparoscopy confirmed the diagnosis of acute salpingitis. Controls were women undergoing tubal ligation and HIV-1 infected women asymptomatic for genital tract infection. Results. Of 125 women with laparoscopically-confirmed salpingitis, 38% were HIV-1 seropositive. Nineteen HIV-1 negative controls were recruited. For the diagnosis of endometritis, ≥1 plasma cells (PC) and ≥3 polymorphonuclear lymphocytes (PMN) per HPF in the endometrium had a sensitivity of 74% for HIV-1-seropositive, 63% for HIV-1-seronegative women with a specificity of 75% and positive predictive value of 85% regardless of HIV-1-infection for predicting moderate to severe salpingitis. For HIV-1-seronegative women with mild salpingitis, ≥1 PC and ≥3 PMN had a sensitivity of 16% and a PPV of 57%. Conclusion. Endometrial histology, did not perform well as a surrogate marker for moderate to severe salpingitis, and failed as a surrogate marker for mild salpingitis

Review and Recommendations for Zero-Inflated Count Regression Modeling of Dental Caries Indices in Epidemiological Studies

Over the past five to ten years, zero-inflated count regression models have been increasingly applied to the analysis of dental caries indices (e.g., DMFT, dfms, etc). The main reason for that is linked to the broad decline in children’s caries experience, such that dmf and DMF indices more frequently generate low or even zero counts. This article specifically reviews the application of zero-inflated Poisson and zero-inflated negative binomial regression models to dental caries, with emphasis on the description of the models and the interpretation of fitted model results given the study goals. The review finds that interpretations provided in the published caries research are often imprecise or inadvertently misleading, particularly with respect to failing to discriminate between inference for the class of susceptible persons defined by such models and inference for the sampled population in terms of overall exposure effects. Recommendations are provided to enhance the use as well as the interpretation and reporting of results of count regression models when applied to epidemiological studies of dental caries

Surface Grafting of Poly(L-glutamates). 3. Block Copolymerization

This paper describes for the first time the synthesis of surface-grafted AB-block copolypeptides, consisting of poly(γ-benzyl L-glutamate) (PBLG) as the A-block and poly(γ-methyl L-glutamate) (PMLG) as the B-block. Immobilized primary amine groups of (γ-aminopropyl)triethoxysilane (APS) on silicon wafers initiated the ring-opening polymerization of N-carboxyanhydrides of glutamic acid esters (NCAs). After removal of the BLG-NCA monomer solution after a certain reaction time, the amine end groups of the formed PBLG blocks acted as initiators for the second monomers. This method provides the possibility of making layered structures of surface-grafted block copolymers with tuned properties. Ellipsometry and small-angle X-ray reflection (SAXR) measurements revealed the thickness of the polypeptide layers ranging from 45-100 Å of the first block to 140-270 Å for the total block copolypeptides. The chemical composition of the blocks was determined by X-ray photoelectron spectroscopy (XPS). In addition, Fourier transform infrared transmission spectroscopy (FT-IR) revealed that the polypeptide main chains of both blocks consisted of pure R-helices. The average orientation of the helices ranging from 22-42° with respect to the substrate within the first block to 31-35° in the second block could be derived with FT-IR as well.

Imperfect Homoclinic Bifurcations

Experimental observations of an almost symmetric electronic circuit show complicated sequences of bifurcations. These results are discussed in the light of a theory of imperfect global bifurcations. It is shown that much of the dynamics observed in the circuit can be understood by reference to imperfect homoclinic bifurcations without constructing an explicit mathematical model of the system.Comment: 8 pages, 11 figures, submitted to PR

The unidentified TeV source (TeVJ2032+4130) and surrounding field: Final HEGRA IACT-System results

The unidentified TeV source in Cygnus is now confirmed by follow-up observations from 2002 with the HEGRA stereoscopic system of Cherenkov Telescopes. Using all data (1999 to 2002) we confirm this new source as steady in flux over the four years of data taking, extended with radius 6.2 arcmin (+-1.2 arcmin (stat) +-0.9 arcmin (sys)) and exhibiting a hard spectrum with photon index -1.9. It is located in the direction of the dense OB stellar association, Cygnus OB2. Its integral flux above energies E>1 TeV amounts to \~5% of the Crab assuming a Gaussian profile for the intrinsic source morphology. There is no obvious counterpart at radio, optical nor X-ray energies, leaving TeVJ2032+4130 presently unidentified. Observational parameters of this source are updated here and some astrophysical discussion is provided. Also included are upper limits for a number of other interesting sources in the FoV, including the famous microquasar Cygnus X-3.Comment: 7 pages, 3 figures. Accepted for publication in Astronomy & Astrophysic

Simultaneous X-Ray and TeV Gamma-Ray Observations of the TeV Blazar Markarian 421 during February and May 2000

In this paper we present the results of simultaneous observations of the TeV blazar Markarian 421 (Mrk 421) at X-ray and TeV Gamma-ray energies with the Rossi X-Ray Timing Explorer (RXTE) and the stereoscopic Cherenkov Telescope system of the HEGRA (High Energy Gamma Ray Astronomy) experiment, respectively. The source was monitored from February 2nd to February 16th and from May 3rd to May 8th, 2000. We discuss in detail the temporal and spectral properties of the source. Remarkably, the TeV observations of February 7th/8th showed statistically significant evidence for substantial TeV flux variability on 30 min time scale. We show the results of modeling the data with a time dependent homogeneous Synchrotron Self-Compton (SSC) model. The X-ray and TeV gamma-ray emission strengths and energy spectra together with the rapid flux variability strongly suggest that the emission volume is approaching the observer with a Doppler factor of 50 or higher. The different flux variability time scales observed at X-rays and TeV Gamma-rays indicate that a more detailed analysis will require inhomogeneous models with several emission zones.Comment: Accepted for Publication in ApJ, 21 Pages, 5 Figure

Conceptualizing Communication Capital for a Changing Environment

With rapidly evolving technologies, boundaries between traditional modes of communication have blurred, creating an environment that scholars still describe from viewpoints as researchers in interpersonal, organizational or mass communication. This manuscript looks at the social capital literature and argues for conceptualizing “communication capital” to help understand the impact of communication phenomena in a changing environment. The literature has treated interpersonal communication variables as components of social capital and mass communication variables as factors affecting social capital, but scholars long ago recognized their reinforcing nature, leading us to develop a concept of communication capital merging symbolic activity across domains in its potential for impacting civic engagement, defined as persistent communication patterns that facilitate social problem solving in the community. Analysis of survey data shows that 4 dimensions of communication capital explain variance in civic engagement beyond that accounted for by traditional measures of social capital, media use, neighborhood communication, and efficacy