Ricci curvature and monotonicity for harmonic functions

Original manuscript September 20, 2012In this paper we generalize the monotonicity formulas of “Colding (Acta Math 209:229–263, 2012)” for manifolds with nonnegative Ricci curvature. Monotone quantities play a key role in analysis and geometry; see, e.g., “Almgren (Preprint)”, “Colding and Minicozzi II (PNAS, 2012)”, “Garofalo and Lin (Indiana Univ Math 35:245–267, 1986)” for applications of monotonicity to uniqueness. Among the applications here is that level sets of Green’s function on open manifolds with nonnegative Ricci curvature are asymptotically umbilic.National Science Foundation (U.S.) (Grant DMS 11040934)National Science Foundation (U.S.) (Grant DMS 1206827)National Science Foundation (U.S.). Focused Research Group (Grant DMS 0854774)National Science Foundation (U.S.). Focused Research Group (Grant DMS 0853501

Effect of dietary omega-3 fatty acids on castrate-resistant prostate cancer and tumor-associated macrophages.

BackgroundM2-like macrophages are associated with the pathogenesis of castrate-resistant prostate cancer (CRPC). We sought to determine if dietary omega-3 fatty acids (ω-3 FAs) delay the development and progression of CRPC and inhibit tumor-associated M2-like macrophages.MethodsMycCap cells were grown subcutaneously in immunocompetent FVB mice. Mice were castrated when tumors reached 300 mm2. To study effects of dietary ω-3 FAs on development of CRPC, ω-3 or ω-6 diets were started 2 days after castration and mice sacrificed after early regrowth of tumors. To study ω-3 FA effects on progression of CRPC, tumors were allowed to regrow after castration before starting the diets. M2 (CD206+) macrophages were isolated from allografts to examine ω-3 FA effects on macrophage function. Omega-3 fatty acid effects on androgen-deprived RAW264.7 M2 macrophages were studied by RT-qPCR and a migration/ invasion assay.ResultsThe ω-3 diet combined with castration lead to greater MycCap tumor regression (tumor volume reduction: 182.2 ± 33.6 mm3) than the ω-6 diet (tumor volume reduction: 148.3 ± 35.2; p = 0.003) and significantly delayed the time to CRPC (p = 0.006). Likewise, the ω-3 diet significantly delayed progression of established castrate-resistant MycCaP tumors (p = 0.003). The ω-3 diet (as compared to the ω-6 diet) significantly reduced tumor-associated M2-like macrophage expression of CSF-1R in the CRPC development model, and matrix metallopeptidase-9 (MMP-9) and vascular endothelial growth factor (VEGF) in the CRPC progression model. Migration of androgen-depleted RAW264.7 M2 macrophages towards MycCaP cells was reversed by addition of docosahexaenoic acid (ω-3).ConclusionsDietary omega-3 FAs (as compared to omega-6 FAs) decreased the development and progression of CRPC in an immunocompetent mouse model, and had inhibitory effects on M2-like macrophage function. Clinical trials are warranted evaluating if a fish oil-based diet can delay the time to castration resistance in men on androgen deprivation therapy, whereas further preclinical studies are warranted evaluating fish oil for more advanced CRPC

Molecular hydrogen emission in the interstellar medium of the Large Magellanic Cloud

We present the detection and analysis of molecular hydrogen emission toward ten interstellar regions in the Large Magellanic Cloud. We examined low-resolution infrared spectral maps of twelve regions obtained with the Spitzer infrared spectrograph (IRS). The pure rotational 0--0 transitions of H$_2$ at 28.2 and 17.1${\,\rm \mu m}$ are detected in the IRS spectra for ten regions. The higher level transitions are mostly upper limit measurements except for three regions, where a 3$\sigma$ detection threshold is achieved for lines at 12.2 and 8.6${\,\rm \mu m}$. The excitation diagrams of the detected H$_2$ transitions are used to determine the warm H$_2$ gas column density and temperature. The single-temperature fits through the lower transition lines give temperatures in the range $86-137\,{\rm K}$. The bulk of the excited H$_2$ gas is found at these temperatures and contributes $\sim$5-17% to the total gas mass. We find a tight correlation of the H$_2$ surface brightness with polycyclic aromatic hydrocarbon and total infrared emission, which is a clear indication of photo-electric heating in photodissociation regions. We find the excitation of H$_2$ by this process is equally efficient in both atomic and molecular dominated regions. We also present the correlation of the warm H$_2$ physical conditions with dust properties. The warm H$_2$ mass fraction and excitation temperature show positive correlations with the average starlight intensity, again supporting H$_2$ excitation in photodissociation regions.Comment: Accepted for publication in MNRA

Reflected Light from Sand Grains in the Terrestrial Zone of a Protoplanetary Disk

We show that grains have grown to ~mm size (sand sized) or larger in the terrestrial zone (within ~3 AU) of the protoplanetary disk surrounding the 3 Myr old binary star KH 15D. We also argue that the reflected light in the system reaches us by back scattering off the far side of the same ring whose near side causes the obscuration.Comment: 22 pages, 5 figures. To be published in Nature, March 13, 2008. Contains a Supplemen

Reinterpretation of the RRISP-77 Iceland shear-wave profiles

Two shear-wave profiles, E and G, collected during the 1977 Reykjanes Ridge Iceland Seismic Experiment have played an important role in models of the Icelandic crust. They were originally interpreted as indicating very low shear-wave velocities and abnormally low shear-wave quality factors in the 10–15 km depth range. These attributes, which are indicative of near-solidus temperatures, were used to support the hypothesis that the crust of Iceland is relatively thin (10–15 km) and underlain by partially molten material. More recent seismic data, however, contradict this hypothesis and suggest that the crust is thicker (20–30 km) and cooler. A re-examination of the RRISP-77 data indicates that the low shear-wave velocities are artefacts arising from source static anomalies (in the case of profile G) and misidentification of a secondary shear phase, SmS, as S (in the case of profile E). Furthermore, the attenuation occurs at ranges when rays from the shots pass near the Askja (profile E) and Katla and Oraefajokull (profile G) volcanoes. It may therefore have a localized source, and not be diagnostic of Icelandic crust as a whole. This new interpretation of the RRISP-77 shear-wave data is consistent with models having a thick, cold crust.We thank 0. Flovenz, one of the principal investigators of the SIST experiment, G. Foulger and B. Julian, principal investigators of the Hengill experiment, and the Incorporated Research Institutions for Seismology for providing us with copies of the data. Lamont Doherty Contribution Number 5513Peer Reviewe

Habits and Attitudes of Video Gaming and Information Technology Use in People with Schizophrenia: Cross-Sectional Survey

Background: Information technology and video gaming have potential advantages in the treatment of schizophrenia. However, information regarding the habits and attitudes related to internet use and video gaming in people with schizophrenia is limited.Objective: The aim of this study was to explore the habits and attitudes regarding video gaming and information technology usage and their associated factors in people with schizophrenia in Hong Kong.Methods: In this cross-sectional survey, service users with schizophrenia were recruited from 6 halfway hostels and 7 integrated centers for mental wellness in Hong Kong. A 79-item self-report questionnaire was utilized to explore the habits of internet use and video gaming in these people with schizophrenia. The attitude toward video gaming was assessed using the Gaming Attitudes, Motivations, and Experiences Scales. Of the 148 individuals in a convenience sample who were invited to participate in this study, 110 willingly participated (a response rate of 74.3%). The data were analyzed using descriptive statistics, a two-tailed independent t test, Pearson correlation, and principal analysis with 3 methods of rotation (varimax, equimax, and promax).Results: Most participants (100/110, 90.9%) had access to the internet and half of them (54/110, 49.1%) used the internet daily mostly to watch videos (66/110, 60.0%) or read news or books, etc (42/110, 38.2%). One-third of the participants (36/110, 32.7%) used the internet to play web-based games, and most of them (88/110, 80.0%) had played a video game in the past year. The most favorable gaming platforms were cellular phones (43/88, 49%) followed by computers (19/88, 22%) and arcade cabinets (6/88, 7%). The most favorable game genre was action games (34/145, 23.4%). Those who had a bachelor's degree or higher scored lower in social interaction than those with a lower education level (P=.03). Those who played video games daily scored higher in the category of story than those who did not play daily (t(86) =2.03, P=.05). The most popular gaming category was autonomy and the least popular categories were violent catharsis and violent reward. Two motives, "social playing" and "evasive playing," were formed to describe the characteristics of playing video games.Conclusions: Our data showed a high internet utilization rate among people with schizophrenia in Hong Kong. Only a few of them used the internet to search for health-related information. Our study also exemplified the unique habits of gaming among the participants. Health care professionals could utilize video games to engage people with schizophrenia and promote coping with stress and provide social skills training to such people with schizophrenia. Identification of the gaming attitudes can contribute to the development of serious games for the schizophrenic population. Further investigation is vital for the promotion of mental health through web-based platforms.</div

The Dawn of Open Access to Phylogenetic Data

The scientific enterprise depends critically on the preservation of and open access to published data. This basic tenet applies acutely to phylogenies (estimates of evolutionary relationships among species). Increasingly, phylogenies are estimated from increasingly large, genome-scale datasets using increasingly complex statistical methods that require increasing levels of expertise and computational investment. Moreover, the resulting phylogenetic data provide an explicit historical perspective that critically informs research in a vast and growing number of scientific disciplines. One such use is the study of changes in rates of lineage diversification (speciation - extinction) through time. As part of a meta-analysis in this area, we sought to collect phylogenetic data (comprising nucleotide sequence alignment and tree files) from 217 studies published in 46 journals over a 13-year period. We document our attempts to procure those data (from online archives and by direct request to corresponding authors), and report results of analyses (using Bayesian logistic regression) to assess the impact of various factors on the success of our efforts. Overall, complete phylogenetic data for ~60% of these studies are effectively lost to science. Our study indicates that phylogenetic data are more likely to be deposited in online archives and/or shared upon request when: (1) the publishing journal has a strong data-sharing policy; (2) the publishing journal has a higher impact factor, and; (3) the data are requested from faculty rather than students. Although the situation appears dire, our analyses suggest that it is far from hopeless: recent initiatives by the scientific community -- including policy changes by journals and funding agencies -- are improving the state of affairs