Geodesic Distance Function Learning via Heat Flow on Vector Fields

Learning a distance function or metric on a given data manifold is of great importance in machine learning and pattern recognition. Many of the previous works first embed the manifold to Euclidean space and then learn the distance function. However, such a scheme might not faithfully preserve the distance function if the original manifold is not Euclidean. Note that the distance function on a manifold can always be well-defined. In this paper, we propose to learn the distance function directly on the manifold without embedding. We first provide a theoretical characterization of the distance function by its gradient field. Based on our theoretical analysis, we propose to first learn the gradient field of the distance function and then learn the distance function itself. Specifically, we set the gradient field of a local distance function as an initial vector field. Then we transport it to the whole manifold via heat flow on vector fields. Finally, the geodesic distance function can be obtained by requiring its gradient field to be close to the normalized vector field. Experimental results on both synthetic and real data demonstrate the effectiveness of our proposed algorithm

A Dynamic Equivalent Energy Storage Model of Natural Gas Networks for Joint Optimal Dispatch of Electricity-Gas Systems

The development of energy conversion techniques enhances the coupling between the gas network and power system. However, challenges remain in the joint optimal dispatch of electricity-gas systems. The dynamic model of the gas network, described by partial differential equations, is complex and computationally demanding for power system operators. Furthermore, information privacy concerns and limited accessibility to detailed gas network models by power system operators necessitate quantifying the equivalent energy storage capacity of gas networks. This paper proposes a multi-port energy storage model with time-varying capacity to represent the dynamic gas state transformation and operational constraints in a compact and intuitive form. The model can be easily integrated into the optimal dispatch problem of the power system. Test cases demonstrate that the proposed model ensures feasible control strategies and significantly reduces the computational burden while maintaining high accuracy in the joint optimal dispatch of electricity-gas systems. In contrast, the existing static equivalent model fails to capture the full flexibility of the gas network and may yield infeasible results.Comment: 12 pages, 8 figure

Novel glucose sensor based on enzymeimmobilized 81° tilted fiber grating

We demonstrate a novel glucose sensor based on an optical fiber grating with an excessively tilted index fringe structure and its surface modified by glucose oxidase (GOD). The aminopropyltriethoxysilane (APTES) was utilized as binding site for the subsequent GOD immobilization. Confocal microscopy and fluorescence microscope were used to provide the assessment of the effectiveness in modifying the fiber surface. The resonance wavelength of the sensor exhibited red-shift after the binding of the APTES and GOD to the fiber surface and also in the glucose detection process. The red-shift of the resonance wavelength showed a good linear response to the glucose concentration with a sensitivity of 0.298nm(mg/ml)-1 in the very low concentration range of 0.0∼3.0mg/ml. Compared to the previously reported glucose sensor based on the GOD-immobilized long period grating (LPG), the 81° tilted fiber grating (81°-TFG) based sensor has shown a lower thermal cross-talk effect, better linearity and higher Q-factor in sensing response. In addition, its sensitivity for glucose concentration can be further improved by increasing the grating length and/or choosing a higher-order cladding mode for detection. Potentially, the proposed techniques based on 81°-TFG can be developed as sensitive, label free and micro-structural sensors for applications in food safety, disease diagnosis, clinical analysis and environmental monitoring

Sensing the Pulse of the Pandemic: Geovisualizing the Demographic Disparities of Public Sentiment toward COVID-19 through Social Media

Social media offers a unique lens to observe users emotions and subjective feelings toward critical events or topics and has been widely used to investigate public sentiment during crises, e.g., the COVID-19 pandemic. However, social media use varies across demographic groups, with younger people being more inclined to use social media than the older population. This digital divide could lead to biases in data representativeness and analysis results, causing a persistent challenge in research based on social media data. This study aims to tackle this challenge through a case study of estimating the public sentiment about the COVID-19 using social media data. We analyzed the pandemic-related Twitter data in the United States from January 2020 to December 2021. The objectives are: (1) to elucidate the uneven social media usage among various demographic groups and the disparities of their emotions toward COVID-19, (2) to construct an unbiased measurement for public sentiment based on social media data, the Sentiment Adjusted by Demographics (SAD) index, through the post-stratification method, and (3) to evaluate the spatially and temporally evolved public sentiment toward COVID-19 using the SAD index. The results show significant discrepancies among demographic groups in their COVID-19-related emotions. Female and under or equal to 18 years old Twitter users expressed long-term negative sentiment toward COVID-19. The proposed SAD index in this study corrected the underestimation of negative sentiment in 31 states, especially in Vermont. According to the SAD index, Twitter users in Wyoming (Vermont) posted the largest (smallest) percentage of negative tweets toward the pandemic