On fractional GJMS operators

We describe a new interpretation of the fractional GJMS operators as generalized Dirichlet-to-Neumann operators associated to weighted GJMS operators on naturally associated smooth metric measure spaces. This gives a geometric interpretation of the Caffarelli--Silvestre extension for $(-\Delta)^\gamma$ when $\gamma\in(0,1)$, and both a geometric interpretation and a curved analogue of the higher order extension found by R. Yang for $(-\Delta)^\gamma$ when $\gamma>1$. We give three applications of this correspondence. First, we exhibit some energy identities for the fractional GJMS operators in terms of energies in the compactified Poincar\'e--Einstein manifold, including an interpretation as a renormalized energy. Second, for $\gamma\in(1,2)$, we show that if the scalar curvature and the fractional $Q$-curvature $Q_{2\gamma}$ of the boundary are nonnegative, then the fractional GJMS operator $P_{2\gamma}$ is nonnegative. Third, by assuming additionally that $Q_{2\gamma}$ is not identically zero, we show that $P_{2\gamma}$ satisfies a strong maximum principle.Comment: 38 pages. Final version, to appear in Communications on Pure and Applied Mathematic

Adaptive Complex Contagions and Threshold Dynamical Systems

A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are static. In this paper we extend current theory of finite dynamical systems to cover dynamic thresholds. Three classes of parallel and sequential dynamic threshold systems are introduced and analyzed. Our main result, which is a complete characterization of their attractor structures, show that sequential systems may only have fixed points as limit sets whereas parallel systems may only have period orbits of size at most two as limit sets. The attractor states are characterized for general graphs and enumerated in the special case of paths and cycle graphs; a computational algorithm is outlined for determining the number of fixed points over a tree. We expect our results to be relevant for modeling a broad class of biological, behavioral and socio-technical systems where adaptive behavior is central.Comment: Submitted for publicatio

The epidemiology of gastrointestinal stromal tumors in Taiwan, 1998–2008: a nation-wide cancer registry-based study

BACKGROUND: To investigate the incidence of gastrointestinal stromal tumors (GISTs) in Taiwan and the impact of imatinib on the overall survival (OS) of GIST patients. METHODS: GISTs were identified from the Taiwan Cancer Registry (TCR) from 1998 to 2008. The age-adjusted incidence rates and the observed OS rates were calculated. Cox proportional hazards models were applied to examine the mortality risk in three time periods (1998–2001, 2002–2004, 2005–2008) according to the application and availability of imatinib. RESULTS: From 1998 to 2008, 2,986 GISTs were diagnosed in Taiwan. The incidence increased from 1.13 per 100,000 in 1998 to 1.97 per 100,000 in 2008. The most common sites were stomach (47-59%), small intestine (31-38%), and colon/rectum (6-9%). The 5-year observed OS was 66.5% (60.3% for men, 74.2% for women, P < .0001). GISTs in the stomach had a better 5-year observed OS (69.4%) than those in the small intestine (65.1%) (P < .0001). The outcome of GIST improved significantly after the more widespread use of imatinib; the 5-year observed OS increased from 58.9% during 1998–2001 to 70.2% during 2005–2008 (P < .0001). Younger age, female sex, stomach location, and later diagnostic years were independent predictors of a better survival. CONCLUSIONS: The incidence of GIST has been increasing in Taiwan, partially due to the advancement of diagnostic technology/method and the increased awareness by physicians. The outcome of GIST has improved significantly with the availability and the wider use of imatinib

Comparison of Safety and Efficacy of Insulin Glargine and Neutral Protamine Hagedorn Insulin in Older Adults with Type 2 Diabetes Mellitus: Results from a Pooled Analysis

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90150/1/jgs3773.pd

Association of RENAL nephrometry score with outcomes of minimally invasive partial nephrectomy

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98294/1/iju3222.pd

Belowground competition among invading detritivores

Author Posting. © Ecological Society of America, 2016. This article is posted here by permission of Ecological Society of America for personal use, not for redistribution. The definitive version was published in Ecology 97 (2016): 160–170, doi:10.1890/15-0551.1.The factors regulating soil animal communities are poorly understood. Current theory favors niche complementarity and facilitation over competition as the primary forms of non-trophic interspecific interaction in soil fauna; however, competition has frequently been suggested as an important community-structuring factor in earthworms, ecosystem engineers that influence belowground processes. To date, direct evidence of competition in earthworms is lacking due to the difficulty inherent in identifying a limiting resource for saprophagous animals. In the present study, we offer the first direct evidence of interspecific competition for food in this dominant soil detritivore group by combining field observations with laboratory mesocosm experiments using 13C and 15N double-enriched leaf litter to track consumption patterns. In our experiments, the Asian invasive species Amynthas hilgendorfi was a dominant competitor for leaf litter against two European species currently invading the temperate deciduous forests in North America. This competitive advantage may account for recent invasion success of A. hilgendorfi in forests with established populations of European species, and we hypothesize that specific phenological differences play an important role in determining the outcome of the belowground competition. In contrast, Eisenoides lonnbergi, a common native species in the Eastern United States, occupied a unique trophic position with limited interactions with other species, which may contribute to its persistence in habitats dominated by invasive species. Furthermore, our results supported neither the hypothesis that facilitation occurs between species of different functional groups nor the hypothesis that species in the same group exhibit functional equivalency in C and N translocation in the soil. We propose that species identity is a more powerful approach to understand earthworm invasion and its impacts on belowground processes.EPS Field Funds; National Science Foundation Grant Numbers: EEC-0540832, ACI 1244820, EAR-0748574; Microsoft Researc

The effect of adsorbed volatile organic compounds on an ultrathin water film measurement

Using surface plasmon resonance imaging (SPRi), we have recently shown for the first time the existence of a monolayer water film between droplets during dropwise condensation. This study examines the effect of adsorbed volatile organic compounds (VOCs) on the ultrathin film measurement using SPRi. Further, the work presents the proper surface-treatment process that enables measurements of the ultrathin water layer during high-speed imaging of dropwise condensation at 3000 frame per second. In this study, two methods were applied for cleaning the surface (gold-coated glass)-(1) standard cleaning procedure (SCP) using acetone, isopropyl alcohol, and deionized water and (2) SCP followed by air plasma cleaning. This work discusses the effect of the cleaning procedures on surface roughness, contact angle, and surface chemistry using atomic force microscopy, optical microscopy, and an X-ray photoelectron spectroscope meter. The results showed that SCP before the SPRi is a proper surface-treatment method. The effect of adsorbed VOCs during dropwise condensation on a surface treated with SCP was measured to be 0.0025 (reflectivity unit), which was 70% smaller than the reflectance associated with a monolayer water film. The results of this work confirm a monolayer water film observation during the dropwise condensation, which has been reported before

Effects of Dietary Echinacea purpurea on PRRSV-infected Nursery Pigs

The effect of dietary additions of Echinacea purpurea on the rate of rate of growth, viremia, and ontogeny of the humoral antibody response against porcine reproductive and respiratory syndrome virus (PRRSV) infection was evaluated in weaned pigs. In three replicates, weaned pigs (18 ± 1 day of age) from a PRRSV-naïve herd were randomly allotted to one of four pens (diets) in two rooms, each pen containing five pigs. Each pen of pigs (pens) began one of four dietary treatments 1 week before inoculation with PRRSV: 1) basal ration plus carbadox (0.055 g/kg); 2) basal ration plus Echinacea I (2% of the total ration); 3) basal ration plus Echinacea II (4% of the total ration); and 4) basal ration composed of corn, soybean meal, whey, and supplemented essential vitamins and minerals. E. purpurea was purchased in powder form and determined by chemical analysis to contain 1.35% cichoric acid. Seven days after starting the diets (day 7), all pigs in one room were intranasally inoculated with PRRSV isolate ATCC VR-2332 at a concentration of 10 4 TCID50 /ml. To monitor the effects of diet and PRRSV infection, body weight and blood samples were collected from all pigs at 7-day intervals (day 0 to 42). Serum samples were analyzed for the presence of PRRSV and PRRSV-specific antibodies. All inoculated pigs become infected with PRRSV and all uninoculated pigs remained free of infection. PRRSV-infected pigs had a lower percentage increase in body weight between day 7 and 42 compared with uninfected animals (P\u3c0.06). There were no differences in body weight, average daily gain (ADG), average daily feed intake (ADFI), or gain:feed ratio (G:F) in PRRSV-infected compared with uninfected animals. Animals receiving diets supplemented with Echinacea (treatments 2 and 3), no differences were observed in percentage increase in body weight, ADG, ADFI, and G:F ratio in either the PRRSV-infected and the uninfected pigs. Among PRRSV-infected animals, dietary Echinacea did not affect the rate or level of the ELISAdetectable antibody response day 7 to 42 or the level and duration of PRRSV in serum. Under the conditions of this study, dietary Echinacea did not reverse the growthinhibiting effects of PRRSV, did not exhibit antiviral effects and did not show any evidence of immunostimulatory properties

The effects of remodeling with heart failure on mode of initiation of ventricular fibrillation and its spatiotemporal organization

Purpose The effect of the heart failure substrate on the initiation of ventricular fibrillation (VF) and its resulting mechanism is not known. The objective of this study was to determine the effects of substrate on VF initiation and its spatiotemporal organization in the heart failure model. Methods Optical action potentials were recorded from LV wedge preparations either from structurally normal hearts (control, n = 11) or from congestive heart failure (CHF; n = 7), at the epicardial surface, endocardial surface which included a papillary muscle, and a transmural cross section. Action potential duration (APD80) was determined, and VF was initiated. A fast Fourier transform was calculated, and the dominant frequency (DF) was determined. Results The CHF group showed increased VF vulnerability (69 vs 26 %, p < 0.03), and every mapped surface showed an APD80 gradient which included islands of higher APDs on the transmural surface (M cells) which was not observed in controls. VF in the CHF group was characterized by stable, discrete, high-DF areas that correlated to either foci or spiral waves located on the transmural surface at the site of the papillary muscle. Overall, the top 10 % of DFs correlated to an APD of 101 ms while the bottom 10 % of DFs correlated to an APD of 126 ms (p < 0.01). Conclusions In the CHF model, APD gradients correlated with an increased vulnerability to VF, and the highest stable DFs were located on the transmural surface which was not seen in controls. This indicates that the CHF substrate creates unique APD and DF characteristics