Extension of a theorem of Shi and Tam

In this note, we prove the following generalization of a theorem of Shi and Tam \cite{ShiTam02}: Let $(\Omega, g)$ be an $n$-dimensional ($n \geq 3$) compact Riemannian manifold, spin when $n>7$, with non-negative scalar curvature and mean convex boundary. If every boundary component $\Sigma_i$ has positive scalar curvature and embeds isometrically as a mean convex star-shaped hypersurface ${\hat \Sigma}_i \subset \R^n$, then \int_{\Sigma_i} H d \sigma \le \int_{{\hat \Sigma}_i} \hat{H} d {\hat \sigma} where $H$ is the mean curvature of $\Sigma_i$ in $(\Omega, g)$, $\hat{H}$ is the Euclidean mean curvature of ${\hat \Sigma}_i$ in $\R^n$, and where $d \sigma$ and $d {\hat \sigma}$ denote the respective volume forms. Moreover, equality in (\ref{eqn: main theorem}) holds for some boundary component $\Sigma_i$ if, and only if, $(\Omega, g)$ is isometric to a domain in $\R^n$. In the proof, we make use of a foliation of the exterior of the $\hat \Sigma_i$'s in $\R^n$ by the $\frac{H}{R}$-flow studied by Gerhardt \cite{Gerhardt90} and Urbas \cite{Urbas90}. We also carefully establish the rigidity statement in low dimensions without the spin assumption that was used in \cite{ShiTam02}Comment: Shortened title and revised. To appear in Calculus of Variations and PDE'

Distribution of Surficial Eolian and Outwash Sand Deposits, Lee County, Illinois

Map of a general view of sand distribution.published or submitted for publicatio

Deconfinement Phase Transition Heating and Thermal Evolution of Neutron Stars

The deconfinement phase transition will lead to the release of latent heat during spins down of neutron stars if the transition is the first-order one.We have investigated the thermal evolution of neutron stars undergoing such deconfinement phase transition. The results show that neutron stars may be heated to higher temperature.This feature could be particularly interesting for high temperature of low-magnetic field millisecond pulsar at late stage.Comment: 4 pages, to be published by American Institute of Physics, ed. D.Lai, X.D.Li and Y.F.Yuan, as the Proceedings of the conference Astrophysics of Compact Object

Benign Oscillation of Stochastic Gradient Descent with Large Learning Rates

In this work, we theoretically investigate the generalization properties of neural networks (NN) trained by stochastic gradient descent (SGD) algorithm with large learning rates. Under such a training regime, our finding is that, the oscillation of the NN weights caused by the large learning rate SGD training turns out to be beneficial to the generalization of the NN, which potentially improves over the same NN trained by SGD with small learning rates that converges more smoothly. In view of this finding, we call such a phenomenon "benign oscillation". Our theory towards demystifying such a phenomenon builds upon the feature learning perspective of deep learning. Specifically, we consider a feature-noise data generation model that consists of (i) weak features which have a small $\ell_2$-norm and appear in each data point; (ii) strong features which have a larger $\ell_2$-norm but only appear in a certain fraction of all data points; and (iii) noise. We prove that NNs trained by oscillating SGD with a large learning rate can effectively learn the weak features in the presence of those strong features. In contrast, NNs trained by SGD with a small learning rate can only learn the strong features but makes little progress in learning the weak features. Consequently, when it comes to the new testing data which consist of only weak features, the NN trained by oscillating SGD with a large learning rate could still make correct predictions consistently, while the NN trained by small learning rate SGD fails. Our theory sheds light on how large learning rate training benefits the generalization of NNs. Experimental results demonstrate our finding on "benign oscillation".Comment: 63 pages, 10 figure

Assessing Cost-Effectiveness of the Conservation Reserve Program and its Interaction with Crop Insurance Subsidies

Strong demand for agricultural commodities, high crop prices and pressure to reduce government budget deficits heighten the need for land retirement programs to be designed to maximize environmental benefits for any given budget outlay. The Conservation Reserve Program (CRP) is the largest land retirement program while the federal crop insurance program (FCIP) is the largest federal program supporting U.S. agriculture. We examine the environmental and budgetary implications of alternative CRP enrollment mechanisms in the context of the program’s interactions with FCIP. We demonstrate that the current CRP enrollment mechanism is inconsistent with cost-effective targeting. We also identify a cost-effective targeting enrollment mechanism that maximizes total environmental benefits under a budget constraint. Since federal crop insurance subsidies will not be incurred when a tract of land is retired from agricultural production, we consider the impacts when avoided subsidies are accounted for in designing a land-retirement program. Based on contract-level CRP offer data in 2003 and 2011 across the contiguous United States, we find that adopting the cost-effective targeting enrollment mechanism can increase CRP acreage by up to 45% and total environmental benefits by up to 21% while leaving government outlay unchanged. Incorporating crop insurance subsidies into the land retirement design can increase avoided subsidies caused by CRP enrollment and environmental benefits obtained from CRP. The government can enroll significant acres at zero real cost. Under cost-effective targeting, CRP acreage and payments would increase in the Great Plains and the Southeastern states but would decrease in the Midwest

A hybrid decision support system with golden cut and bipolar q-ROFSs for evaluating the risk-based strategic priorities of fintech lending for clean energy projects

In the last decade, the risk evaluation and the investment decision are among the most prominent issues of efficient project management. Especially, the innovative financial sources could have some specific risk appetite due to the increasing return of investment. Hence, it is important to uncover the risk factors of fintech investments and investigate the possible impacts with an integrated approach to the strategic priorities of fintech lending. Accordingly, this study aims to analyze a unique risk set and the strategic priorities of fintech lending for clean energy projects. The most important contributions to the literature can be listed as to construct an impact-direction map of risk-based strategic priorities for fintech lending in clean energy projects and to measure the possible influences by using a hybrid decision making system with golden cut and bipolar q-rung orthopair fuzzy sets. The extension of multi stepwise weight assessment ratio analysis (M-SWARA) is applied for weighting the risk factors of fintech lending. The extension of elimination and choice translating reality (ELECTRE) is employed for constructing and ranking the risk-based strategic priorities for clean energy projects. In this process, data is obtained with the evaluation of three different decision makers. The main superiority of the proposed model by comparing with the previous models in the literature is that significant improvements are made to the classical SWARA method so that a new technique is created with the name of M-SWARA. Hence, the causality analysis between the criteria can also be performed in this proposed model. The findings demonstrate that security is the most critical risk factor for fintech lending system. Moreover, volume is found as the most critical risk-based strategy for fintech lending. In this context, fintech companies need to take some precautions to effectively manage the security risk. For this purpose, the main risks to information technologies need to be clearly identified. Next, control steps should be put for these risks to be managed properly. Furthermore, it has been determined that the most appropriate strategy to increase the success of the fintech lending system is to increase the number of financiers integrated into the system. Within this framework, the platform should be secure and profitable to persuade financiers.Optimization and upgrading of Industrial structure in Henan Province ; Key Scientific Research Project of Colleges and Universities in Henan Provinc

Remote sensing and three-dimensional photogrammetric analysis of glaciofluvial sand and gravel deposits for aggregate resource assessment in McHenry County, Illinois, USA

Sand and gravel deposits, one of the most common natural resources, are used as aggregates mostly by the construction industry, and their extraction contributes significantly to a region\u27s economy. Thus, it is critical to locate sand and gravel deposits, and evaluate their quantity and quality safely and quickly. However, information on aggregate resources is generally only available from conventional two-dimensional (2-D) geologic maps, and direct field measurements for quality analysis at outcrops are time consuming and are often not possible due to safety concerns, or simply because exposures are too difficult to access. In this study, we presented a methodology to locate and evaluate aggregate resources, including the traditional methods of field surveying and borehole investigation for the entire McHenry County, Illinois, USA and new three-dimensional (3-D) photogrammetric models and remote sensing technologies at an active gravel pit. Thus acquired data sets allowed us to obtain key information for successful aggregate resource management: spatial occurrence, thickness, texture, paleocurrents, lithology and land use compatibility. In addition, remote sensing and photogrammetric techniques allowed for very quick and safe assessment of fundamental properties like particle size, paleocurrent direction and sorting, especially in inaccessible and/or unsafe outcrops. In summary, this paper demonstrated how remote sensing and photogrammetric technology can improve the efficiency and safety in resource assessment strategies, and the methodology used in our study can be applied to the development of autonomous mining and resource asset management elsewhere

Late Quaternary aggradation and incision in the headwaters of the Yangtze River, eastern Tibetan Plateau, China

River aggradation or incision at different spatial-temporal scales are governed by tectonics, climate change, and surface processes which all adjust the ratio of sediment load to transport capacity of a channel. But how the river responds to differential tectonic and extreme climate events in a catchment is still poorly understood. Here, we address this issue by reconstructing the distribution, ages, and sedimentary process of fluvial terraces in a tectonically active area and monsoonal environment in the headwaters of the Yangtze River in the eastern Tibetan Plateau, China. Field observations, topographic analyses, and optically stimulated luminescence dating reveal a remarkable fluvial aggradation, followed by terrace formations at elevations of 55-62 m (T7), 42-46 m (T6), 38 m (T5), 22-36 m (T4), 18 m (T3), 12-16 m (T2), and 2-6 m (T1) above the present floodplain. Gravelly fluvial accumulation more than 62 m thick has been dated prior to 24-19 ka. It is regarded as a response to cold climate during the last glacial maximum. Subsequently, the strong monsoon precipitation contributed to cycles of rapid incision and lateral erosion, expressed as cut-in-fill terraces. The correlation of terraces suggests that specific tectonic activity controls the spatial scale and geomorphic characteristics of the terraces, while climate fluctuations determine the valley filling, river incision and terrace formation. Debris and colluvial sediments are frequently interbedded in fluvial sediment sequences, illustrating the episodic, short-timescale blocking of the channel ca. 20 ka. This indicates the potential impact of extreme events on geomorphic evolution in rugged terrain