176 research outputs found

    p-Laplace equations in conformal geometry

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    In this paper we introduce the p-Laplace equations for the intermediate Schouten curvature in conformal geometry. These p-Laplace equations provide more tools for the study of geometry and topology of manifolds. First, the positivity of the intermediate Schouten curvature yields the vanishing of Betti numbers on locally conformally flat manifolds as consequences of the B\"{o}chner formula as in the works of Nayatani and Guan-Lin-Wang. Secondly and more interestingly, when the intermediate Schouten curvature is nonnegative, these p-Laplace equations facilitate the geometric applications of p-superharmonic functions and the nonlinear potential theory. This leads to the estimates on Hausdorff dimension of singular sets and vanishing of homotopy groups that is inspired by and extends the work of Schoen-Yau. In the forthcoming paper we will present our results on the asymptotic behavior of p-superharmonic functions at singularities.Comment: 19 pag

    On the asymptotic behavior of p-superharmonic functions at singularities

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    In this paper we develop the p-thinness and the p-fine topology for the asymptotic behavior of p-superharmonic functions at singular points. We consider these as extensions of earlier works on superharmonic functions in dimension 2, on the Riesz and Log potentials in higher dimensions,, and on p-harmonic functions. It is remarkable that, contrary to the above cases, the p-thinness for the singular behavior differs from the p-thinness for continuity by the Wiener criterion for p-superharmonic functions. As applications of asymptotic estimates of p-superharmonic functions, we also obtain asymptotic estimates of solutions to a class of fully nonlinear elliptic equations. This paper grows out of our recent papers on the potential theory in conformal geometry.Comment: 26 page

    Orthogonal Temporal Interpolation for Zero-Shot Video Recognition

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    Zero-shot video recognition (ZSVR) is a task that aims to recognize video categories that have not been seen during the model training process. Recently, vision-language models (VLMs) pre-trained on large-scale image-text pairs have demonstrated impressive transferability for ZSVR. To make VLMs applicable to the video domain, existing methods often use an additional temporal learning module after the image-level encoder to learn the temporal relationships among video frames. Unfortunately, for video from unseen categories, we observe an abnormal phenomenon where the model that uses spatial-temporal feature performs much worse than the model that removes temporal learning module and uses only spatial feature. We conjecture that improper temporal modeling on video disrupts the spatial feature of the video. To verify our hypothesis, we propose Feature Factorization to retain the orthogonal temporal feature of the video and use interpolation to construct refined spatial-temporal feature. The model using appropriately refined spatial-temporal feature performs better than the one using only spatial feature, which verifies the effectiveness of the orthogonal temporal feature for the ZSVR task. Therefore, an Orthogonal Temporal Interpolation module is designed to learn a better refined spatial-temporal video feature during training. Additionally, a Matching Loss is introduced to improve the quality of the orthogonal temporal feature. We propose a model called OTI for ZSVR by employing orthogonal temporal interpolation and the matching loss based on VLMs. The ZSVR accuracies on popular video datasets (i.e., Kinetics-600, UCF101 and HMDB51) show that OTI outperforms the previous state-of-the-art method by a clear margin

    BMAL1 but not CLOCK is associated with monochromatic green light-induced circadian rhythm of melatonin in chick pinealocytes

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    The avian pineal gland, an independent circadian oscillator, receives external photic cues and translates them for the rhythmical synthesis of melatonin. Our previous study found that monochromatic green light could increase the secretion of melatonin and expression of CLOCK and BMAL1 in chick pinealocytes. This study further investigated the role of BMAL1 and CLOCK in monochromatic green light-induced melatonin secretion in chick pinealocytes using siRNAs interference and overexpression techniques. The results showed that si-BMAL1 destroyed the circadian rhythms of AANAT and melatonin, along with the disruption of the expression of all the seven clock genes, except CRY1. Furthermore, overexpression of BMAL1 also disturbed the circadian rhythms of AANAT and melatonin, in addition to causing arrhythmic expression of BMAL1 and CRY1/2, but had no effect on the circadian rhythms of CLOCK, BMAL2 and PER2/3. The knockdown or overexpression of CLOCK had no impact on the circadian rhythms of AANAT, melatonin, BMAL1 and PER2, but it significantly deregulated the circadian rhythms of CLOCK, BMAL2, CRY1/2 and PER3. These results suggested that BMAL1 rather than CLOCK plays a critical role in the regulation of monochromatic green light-induced melatonin rhythm synthesis in chicken pinealocytes. Moreover, both knockdown and overexpression of BMAL1 could change the expression levels of CRY2, it indicated CRY2 may be involved in the BMAL1 pathway by modulating the circadian rhythms of AANAT and melatonin

    Measurement and Analysis of Mobile Web Cache Performance

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    The Web browser is a killer app on mobile devices such as smartphones. However, the user experience of mobile Web browsing is undesirable because of the slow resource loading. To improve the performance of Web resource loading, caching has been adopted as a key mechanism. However, the existing passive measurement studies cannot comprehensively characterize the performance of mobile Web caching. For example, most of these studies mainly focus on client-side implementations but not server-side configurations, suffer from biased user behaviors, and fail to study 'miscached' resources. To address these issues, in this paper, we present a proactive approach for a comprehensive measurement study on mobile Web cache performance. The key idea of our approach is to proactively crawl resources from hundreds of websites periodically with a fine-grained time interval. Thus, we are able to uncover the resource update history and cache configurations at the server side, and analyze the cache performance in various time granularities. Based on our collected data, we build a new cache analysis model and study the upper bound of how high percentage of resources could potentially be cached and how effective the caching works in practice. We report detailed analysis results of different websites and various types of Web resources, and identify the problems caused by unsatisfactory cache performance. In particular, we identify two major problems - Redundant Transfer and Miscached Resource, which lead to unsatisfactory cache performance. We investigate three main root causes: Same Content, Heuristic Expiration, and Conservative Expiration Time, and discuss what mobile Web developers can do to mitigate those problems.EI691-70

    Long-term trends and drivers of aerosol pH in eastern China

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    Aerosol acidity plays a key role in regulating the chemistry and toxicity of atmospheric aerosol particles. The trend of aerosol pH and its drivers is crucial in understanding the multiphase formation pathways of aerosols. Here, we reported the first trend analysis of aerosol pH from 2011 to 2019 in eastern China, calculated with the ISORROPIA model based on observed gas and aerosol compositions. The implementation of the Air Pollution Prevention and Control Action Plan led to −35.8 %, −37.6 %, −9.6 %, −81.0 % and 1.2 % changes of PM2.5, SO42-, NHx, non-volatile cations (NVCs) and NO3- in the Yangtze River Delta (YRD) region during this period. Different from the drastic changes of aerosol compositions due to the implementation of the Air Pollution Prevention and Control Action Plan, aerosol pH showed a minor change of −0.24 over the 9 years. Besides the multiphase buffer effect, the opposite effects from the changes of SO42- and non-volatile cations played key roles in determining this minor pH trend, contributing to a change of +0.38 and −0.35, respectively. Seasonal variations in aerosol pH were mainly driven by the temperature, while the diurnal variations were driven by both temperature and relative humidity. In the future, SO2, NOx and NH3 emissions are expected to be further reduced by 86.9 %, 74.9 % and 41.7 % in 2050 according to the best health effect pollution control scenario (SSP1-26-BHE). The corresponding aerosol pH in eastern China is estimated to increase by ∼0.19, resulting in 0.04 less NO3- and 0.12 less NH4+ partitioning ratios, which suggests that NH3 and NOx emission controls are effective in mitigating haze pollution in eastern China.</p
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