An Index Theorem for Toeplitz Operators on Odd Dimensional Manifolds with Boundary

We establish an index theorem for Toeplitz operators on odd dimensional spin manifolds with boundary. It may be thought of as an odd dimensional analogue of the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with boundary. In particular, there occurs naturally an invariant of $\eta$ type associated to $K^1$ representatives on even dimensional manifolds, which should be of independent interests. For example, it gives an intrinsic interpretation of the so called Wess-Zumino term in the WZW theory in physics.Comment: Completely revised. A gap in the proof fixed. To appear in JF

Higher Spectral Flow

AbstractFor a continuous curve of families of Dirac type operators we define a higher spectral flow as aK-group element. We show that this higher spectral flow can be computed analytically byη-forms and is related to the family index in the same way as the spectral flow is related to the index. We introduce a notion of Toeplitz family and relate its index to the higher spectral flow. Applications to family indices for manifolds with boundary are also given

Large-Scale VCE Consequence Modeling for Industrial Facility Siting, Risk Assessment, Hazard Mitigation Design, and Response Planning

PresentationNew, fully three dimensional, technologies are now making it possible to more quickly and accurately simulate and predict the consequences of accidental releases leading to vapor cloud explosions (VCE) at a wide variety of industrial facilities. The primary objective of these explosion consequence analysis (ECA) technologies is to assess building damage and occupant injury levels for both ‘individual’ and ‘all possible’ release and explosion scenarios. A typical industrial facility can have hundreds of potential release scenarios and hundreds of potential VCE locations leading to an exponential number of possible explosion scenarios. High speed 3D modeling techniques can provide updateable, on-going and real-time capabilities for analyzing individual and all possible release and explosion scenarios. These ECA technologies, combined with release probabilities, make possible quantitative risk assessments (QRA) which lead to better risk evaluations, mitigation strategies, risk management, and emergency response planning. In this paper, the Vapor Cloud Explosion Damage Assessment module in BREEZE ExDAM is used to demonstrate a high speed 3D modeling technique that can quickly 1) generate 3D models of large-scale chemical/petroleum facilities with hundreds of building structures, hundreds of release locations, and hundreds of congestion zones, 2) simulate, display, and document the consequences of individual release scenarios involving a subset of congestion zones within a single plume geometry, and 3) compute, display, and document the maximum consequence levels resulting from explosions at all identified congestion zones

Causes of death and conditional survival estimates of long-term lung cancer survivors.

INTRODUCTION: Lung cancer ranks the leading cause of cancer-related death worldwide. This retrospective cohort study was designed to determine time-dependent death hazards of diverse causes and conditional survival of lung cancer. METHODS: We collected 816,436 lung cancer cases during 2000-2015 in the SEER database, after exclusion, 612,100 cases were enrolled for data analyses. Cancer-specific survival, overall survival and dynamic death hazard were assessed in this study. Additionally, based on the FDA approval time of Nivolumab in 2015, we evaluated the effect of immunotherapy on metastatic patients\u27 survival by comparing cases in 2016-2018 (immunotherapy era, n=7135) and those in 2013-2016 (non-immunotherapy era, n=42061). RESULTS: Of the 612,100 patients, 285,705 were women, the mean (SD) age was 68.3 (11.0) years old. 252,558 patients were characterized as lung adenocarcinoma, 133,302 cases were lung squamous cell carcinoma, and only 78,700 cases were small cell lung carcinomas. TNM stage was I in 140,518 cases, II in 38,225 cases, III in 159,095 cases, and IV in 274,262 patients. 164,394 cases underwent surgical intervention. The 5-y overall survival and cancer-specific survival were 54.2% and 73.8%, respectively. The 5-y conditional survival rate of cancer-specific survival is improved in a time-dependent pattern, while conditional overall survival tends to be steady after 5-y follow-up. Except from age, hazard disparities of other risk factors (such as stage and surgery) diminished over time according to the conditional survival curves. After 8 years since diagnosis, mortality hazard from other causes became higher than that from lung cancer. This critical time point was earlier in elder patients while was postponed in patients with advanced stages. Moreover, both cancer-specific survival and overall survival of metastatic patients in immunotherapy era were significantly better than those in non-immunotherapy era (P CONCLUSIONS: Our findings expand on previous studies by demonstrating that non-lung-cancer related death risk becomes more and more predominant over the course of follow-up, and we establish a personalized web-based calculator to determine this critical time point for long-term survivors. We also confirmed the survival benefit of advanced lung cancer patients in immunotherapy era

Quantitative and functional post-translational modification proteomics reveals that TREPH1 plays a role in plant thigmomorphogenesis

Plants can sense both intracellular and extracellular mechanical forces and can respond through morphological changes. The signaling components responsible for mechanotransduction of the touch response are largely unknown. Here, we performed a high-throughput SILIA (stable isotope labeling in Arabidopsis)-based quantitative phosphoproteomics analysis to profile changes in protein phosphorylation resulting from 40 seconds of force stimulation in Arabidopsis thaliana. Of the 24 touch-responsive phosphopeptides identified, many were derived from kinases, phosphatases, cytoskeleton proteins, membrane proteins and ion transporters. TOUCH-REGULATED PHOSPHOPROTEIN1 (TREPH1) and MAP KINASE KINASE 2 (MKK2) and/or MKK1 became rapidly phosphorylated in touch-stimulated plants. Both TREPH1 and MKK2 are required for touch-induced delayed flowering, a major component of thigmomorphogenesis. The treph1-1 and mkk2 mutants also exhibited defects in touch-inducible gene expression. A non-phosphorylatable site-specific isoform of TREPH1 (S625A) failed to restore touch-induced flowering delay of treph1-1, indicating the necessity of S625 for TREPH1 function and providing evidence consistent with the possible functional relevance of the touch-regulated TREPH1 phosphorylation. Bioinformatic analysis and biochemical subcellular fractionation of TREPH1 protein indicate that it is a soluble protein. Altogether, these findings identify new protein players in Arabidopsis thigmomorphogenesis regulation, suggesting that protein phosphorylation may play a critical role in plant force responses

Graphite Equivalent Evaluation of Anthracite-Associated Graphite by Raman Spectroscopy

Anthracite-associated graphite is an important graphite resource with a wide range of applications besides being used as a fuel. This paper introduces a method for evaluating the graphite equivalent evaluation of anthracite-associated graphite. A series of graphite-anthracite standard samples with known graphite content were prepared, and their Raman spectra were obtained using a Raman spectrometer. By employing peak-fitting analysis to decipher the peak spectrum information of the D peak and G peak, trends in the peak position, peak intensity ratio, half-width, and peak area of the D peak and G peak in standard samples with different graphite contents were obtained. Subsequently, a standard curve and fitting equation were established using the peak area data. The goodness of fit for the equation (R2 ) was 0.9984. Then the equation was used to evaluate 100 natural anthracite-associated graphite samples with unknown graphite content, obtaining a corresponding graphite equivalent evaluation

Adaptive Initialization Method Based on Spatial Local Information for k

k-means algorithm is a widely used clustering algorithm in data mining and machine learning community. However, the initial guess of cluster centers affects the clustering result seriously, which means that improper initialization cannot lead to a desirous clustering result. How to choose suitable initial centers is an important research issue for k-means algorithm. In this paper, we propose an adaptive initialization framework based on spatial local information (AIF-SLI), which takes advantage of local density of data distribution. As it is difficult to estimate density correctly, we develop two approximate estimations: density by t-nearest neighborhoods (t-NN) and density by ϵ-neighborhoods (ϵ-Ball), leading to two implements of the proposed framework. Our empirical study on more than 20 datasets shows promising performance of the proposed framework and denotes that it has several advantages: (1) can find the reasonable candidates of initial centers effectively; (2) it can reduce the iterations of k-means’ methods significantly; (3) it is robust to outliers; and (4) it is easy to implement

Micro/Nano Gas Sensors: A New Strategy Towards In-Situ Wafer-Level Fabrication of High-Performance Gas Sensing Chips

Nano-structured gas sensing materials, in particular nanoparticles, nanotubes, and nanowires, enable high sensitivity at a ppb level for gas sensors. For practical applications, it is highly desirable to be able to manufacture such gas sensors in batch and at low cost. We present here a strategy of in-situ wafer-level fabrication of the high-performance micro/nano gas sensing chips by naturally integrating microhotplatform (MHP) with nanopore array (NPA). By introducing colloidal crystal template, a wafer-level ordered homogenous SnO_2 NPA is synthesized in-situ on a 4-inch MHP wafer, able to produce thousands of gas sensing units in one batch. The integration of micromachining process and nanofabrication process endues micro/nano gas sensing chips at low cost, high throughput, and with high sensitivity (down to ~20 ppb), fast response time (down to ~1 s), and low power consumption (down to ~30 mW). The proposed strategy of integrating MHP with NPA represents a versatile approach for in-situ wafer-level fabrication of high-performance micro/nano gas sensors for real industrial applications