Steklov eigenvalues of submanifolds with prescribed boundary in Euclidean space

We obtain upper and lower bounds for Steklov eigenvalues of submanifolds with prescribed boundary in Euclidean space. A very general upper bound is proved, which depends only on the geometry of the fixed boundary and on the measure of the interior. Sharp lower bounds are given for hypersurfaces of revolution with connected boundary: We prove that each eigenvalue is uniquely minimized by the ball. We also observe that each surface of revolution with connected boundary is Steklov isospectral to the disk

Phone a Friend or Ask Alexa? Children’s Trust in Voice-Activated Devices

Voice-activated devices such as Google Home, Siri, and Alexa are in many homes and children are interacting with these devices. It is unclear if they treat these devices the way they treat human informants. Children prefer human informants that are reliable and familiar. This study examined whether children believe voice-activated devices provide accurate information. Participants included 40 4- and 5-year-olds and 40 7- and 8-year-olds. Children were introduced to two informants: the experimenter’s good friend and the experimenter’s new device. Children heard questions about personal information (e.g., the experimenter’s favorite color), facts that do not change (e.g., the color of a kiwano fruit), and timely information (e.g., which state had the most rain yesterday). After the informant provided an answer, the child indicated whether the answer was correct. Older children were significantly more likely to trust the device’s stable fact responses and the human informant’s personal fact responses. Surprisingly, younger children did not show greater trust for either informant for stable facts, but were significantly more likely to trust personal facts given by the device. These findings suggest that younger children have greater difficulty than older children trusting the appropriate informant, and thus need more guidance from adults to understand and use voice-activated devices.https://ir.library.louisville.edu/uars/1036/thumbnail.jp

Pointwise Bounds for Steklov Eigenfunctions

Let (Ω,g) be a compact, real-analytic Riemannian manifold with real-analytic boundary ∂Ω. The harmonic extensions of the boundary Dirichlet-to-Neumann eigenfunctions are called Steklov eigenfunctions. We show that the Steklov eigenfunctions decay exponentially into the interior in terms of the Dirichlet-to-Neumann eigenvalues and give a sharp rate of decay to first order at the boundary. The proof uses the Poisson representation for the Steklov eigenfunctions combined with sharp h-microlocal concentration estimates for the boundary Dirichlet-to-Neumann eigenfunctions near the cosphere bundle S∗∂Ω. These estimates follow from sharp estimates on the concentration of the FBI transforms of solutions to analytic pseudodifferential equations Pu=0 near the characteristic set {σ(P)=0}

Regional differences in APD restitution can initiate wavebreak and re-entry in cardiac tissue: A computational study

Background Regional differences in action potential duration (APD) restitution in the heart favour arrhythmias, but the mechanism is not well understood. Methods We simulated a 150 × 150 mm 2D sheet of cardiac ventricular tissue using a simplified computational model. We investigated wavebreak and re-entry initiated by an S1S2S3 stimulus protocol in tissue sheets with two regions, each with different APD restitution. The two regions had a different APD at short diastolic interval (DI), but similar APD at long DI. Simulations were performed twice; once with both regions having steep (slope > 1), and once with both regions having flat (slope < 1) APD restitution. Results Wavebreak and re-entry were readily initiated using the S1S2S3 protocol in tissue sheets with two regions having different APD restitution properties. Initiation occurred irrespective of whether the APD restitution slopes were steep or flat. With steep APD restitution, the range of S2S3 intervals resulting in wavebreak increased from 1 ms with S1S2 of 250 ms, to 75 ms (S1S2 180 ms). With flat APD restitution, the range of S2S3 intervals resulting in wavebreak increased from 1 ms (S1S2 250 ms), to 21 ms (S1S2 340 ms) and then 11 ms (S1S2 400 ms). Conclusion Regional differences in APD restitution are an arrhythmogenic substrate that can be concealed at normal heart rates. A premature stimulus produces regional differences in repolarisation, and a further premature stimulus can then result in wavebreak and initiate re-entry. This mechanism for initiating re-entry is independent of the steepness of the APD restitution curve

Detection of Potential Transit Signals in the First Three Quarters of Kepler Mission Data

We present the results of a search for potential transit signals in the first three quarters of photometry data acquired by the Kepler Mission. The targets of the search include 151,722 stars which were observed over the full interval and an additional 19,132 stars which were observed for only 1 or 2 quarters. From this set of targets we find a total of 5,392 detections which meet the Kepler detection criteria: those criteria are periodicity of the signal, an acceptable signal-to-noise ratio, and a composition test which rejects spurious detections which contain non-physical combinations of events. The detected signals are dominated by events with relatively low signal-to-noise ratio and by events with relatively short periods. The distribution of estimated transit depths appears to peak in the range between 40 and 100 parts per million, with a few detections down to fewer than 10 parts per million. The detected signals are compared to a set of known transit events in the Kepler field of view which were derived by a different method using a longer data interval; the comparison shows that the current search correctly identified 88.1% of the known events. A tabulation of the detected transit signals, examples which illustrate the analysis and detection process, a discussion of future plans and open, potentially fruitful, areas of further research are included

Detection of Potential Transit Signals in Sixteen Quarters of Kepler Mission Data

We present the results of a search for potential transit signals in four years of photometry data acquired by the Kepler Mission. The targets of the search include 111,800 stars which were observed for the entire interval and 85,522 stars which were observed for a subset of the interval. We found that 9,743 targets contained at least one signal consistent with the signature of a transiting or eclipsing object, where the criteria for detection are periodicity of the detected transits, adequate signal-to-noise ratio, and acceptance by a number of tests which reject false positive detections. When targets that had produced a signal were searched repeatedly, an additional 6,542 signals were detected on 3,223 target stars, for a total of 16,285 potential detections. Comparison of the set of detected signals with a set of known and vetted transit events in the Kepler field of view shows that the recovery rate for these signals is 96.9%. The ensemble properties of the detected signals are reviewed.Comment: Accepted by ApJ Supplemen

Overview of the Kepler Science Processing Pipeline

The Kepler Mission Science Operations Center (SOC) performs several critical functions including managing the ~156,000 target stars, associated target tables, science data compression tables and parameters, as well as processing the raw photometric data downlinked from the spacecraft each month. The raw data are first calibrated at the pixel level to correct for bias, smear induced by a shutterless readout, and other detector and electronic effects. A background sky flux is estimated from ~4500 pixels on each of the 84 CCD readout channels, and simple aperture photometry is performed on an optimal aperture for each star. Ancillary engineering data and diagnostic information extracted from the science data are used to remove systematic errors in the flux time series that are correlated with these data prior to searching for signatures of transiting planets with a wavelet-based, adaptive matched filter. Stars with signatures exceeding 7.1 sigma are subjected to a suite of statistical tests including an examination of each star's centroid motion to reject false positives caused by background eclipsing binaries. Physical parameters for each planetary candidate are fitted to the transit signature, and signatures of additional transiting planets are sought in the residual light curve. The pipeline is operational, finding planetary signatures and providing robust eliminations of false positives.Comment: 8 pages, 3 figure

The prevalence of injection-site reactions with disease-modifying therapies and their effect on adherence in patients with multiple sclerosis: an observational study

<p>Abstract</p> <p>Background</p> <p>Interferon beta (IFNβ) and glatiramer acetate (GA) are administered by subcutaneous (SC) or intramuscular (IM) injection. Patients with multiple sclerosis (MS) often report injection-site reactions (ISRs) as a reason for noncompliance or switching therapies. The aim of this study was to compare the proportion of patients on different formulations of IFNβ or GA who experienced ISRs and who switched or discontinued therapy because of ISRs.</p> <p>Methods</p> <p>The Swiss MS Skin Project was an observational multicenter study. Patients with MS or clinically isolated syndrome who were on the same therapy for at least 2 years were enrolled. A skin examination was conducted at the first study visit and 1 year later.</p> <p>Results</p> <p>The 412 patients enrolled were on 1 of 4 disease-modifying therapies for at least 2 years: IM IFNβ-1a (n = 82), SC IFNβ-1b (n = 123), SC IFNβ-1a (n = 184), or SC GA (n = 23). At first evaluation, ISRs were reported by fewer patients on IM IFNβ-1a (13.4%) than on SC IFNβ-1b (57.7%; <it>P </it>< 0.0001), SC IFNβ-1a (67.9%; <it>P </it>< 0.0001), or SC GA (30.4%; <it>P </it>= not significant [NS]). No patient on IM IFNβ-1a missed a dose in the previous 4 weeks because of ISRs, compared with 5.7% of patients on SC IFNβ-1b (<it>P </it>= 0.044), 7.1% of patients on SC IFNβ-1a (<it>P </it>= 0.011), and 4.3% of patients on SC GA (<it>P </it>= NS). Primary reasons for discontinuing or switching therapy were ISRs or lack of efficacy. Similar patterns were observed at 1 year.</p> <p>Conclusions</p> <p>Patients on IM IFNβ-1a had fewer ISRs and were less likely to switch therapies than patients on other therapies. This study may have implications in selecting initial therapy or, for patients considering switching or discontinuing therapy because of ISRs, selecting an alternative option.</p

A statistical investigation of normal regional intra-subject heterogeneity of brain metabolism and perfusion by F-18 FDG and O-15 H(2)O PET imaging

BACKGROUND: The definite evaluation of the regional cerebral heterogeneity using perfusion and metabolism by a single modality of PET imaging has not been well addressed. Thus a statistical analysis of voxel variables from identical brain regions on metabolic and perfusion PET images was carried out to determine characteristics of the regional heterogeneity of F-18 FDG and O-15 H(2)O cerebral uptake in normal subjects. METHODS: Fourteen normal subjects with normal CT and/or MRI and physical examination including MMSE were scanned by both F-18 FDG and O-15 H(2)O PET within same day with head-holder and facemask. The images were co-registered and each individual voxel counts (Q) were normalized by the gloabl maximal voxel counts (M) as R = Q/M. The voxel counts were also converted to z-score map by z = (Q - mean)/SD. Twelve pairs of ROIs (24 total) were systematically placed on the z-score map at cortical locations 15-degree apart and identically for metabolism and perfusion. Inter- and intra-subject correlation coefficients (r) were computed, both globally and hemispherically, from metabolism and perfusion: between regions for the same tracer and between tracers for the same region. Moments of means and histograms were computed globally along with asymmetric indices as their hemispherical differences. RESULTS: Statistical investigations verified with data showed that, for a given scan, correlation analyses are expectedly alike regardless of variables (Q, R, z) used. The varieties of correlation (r's) of normal subjects, showing symmetry, were mostly around 0.8 and with coefficient of variations near 10%. Analyses of histograms showed non-Gaussian behavior (skew = -0.3 and kurtosis = 0.4) of metabolism on average, in contrast to near Gaussian perfusion. CONCLUSION: The co-registered cerebral metabolism and perfusion z maps demonstrated regional heterogeneity but with attractively low coefficient of variations in the correlation markers