Effective bound of linear series on arithmetic surfaces

We prove an effective upper bound on the number of effective sections of a hermitian line bundle over an arithmetic surface. It is an effective version of the arithmetic Hilbert--Samuel formula in the nef case. As a consequence, we obtain effective lower bounds on the Faltings height and on the self-intersection of the canonical bundle in terms of the number of singular points on fibers of the arithmetic surface

Innovations Autoencoder and its Application in One-class Anomalous Sequence Detection

An innovations sequence of a time series is a sequence of independent and identically distributed random variables with which the original time series has a causal representation. The innovation at a time is statistically independent of the history of the time series. As such, it represents the new information contained at present but not in the past. Because of its simple probability structure, an innovations sequence is the most efficient signature of the original. Unlike the principle or independent component analysis representations, an innovations sequence preserves not only the complete statistical properties but also the temporal order of the original time series. An long-standing open problem is to find a computationally tractable way to extract an innovations sequence of non-Gaussian processes. This paper presents a deep learning approach, referred to as Innovations Autoencoder (IAE), that extracts innovations sequences using a causal convolutional neural network. An application of IAE to the one-class anomalous sequence detection problem with unknown anomaly and anomaly-free models is also presented

Adaptive Subband Compression for Streaming of Continuous Point-on-Wave and PMU Data

A data compression system capable of providing real-time streaming of high-resolution continuous point-on-wave (CPOW) and phasor measurement unit (PMU) measurements is proposed. Referred to as adaptive subband compression (ASBC), the proposed technique partitions the signal space into subbands and adaptively compresses subband signals based on each subband's active bandwidth. The proposed technique conforms to existing industry phasor measurement standards, making it suitable for streaming high-resolution CPOW and PMU data either in continuous or burst on-demand/event-triggered modes. Experiments on synthetic and real data show that ASBC reduces the CPOW sampling rates by several orders of magnitude for real-time streaming while maintaining the precision required by industry standards

Grid Monitoring and Protection with Continuous Point-on-Wave Measurements and Generative AI

Purpose This article presents a case for a next-generation grid monitoring and control system, leveraging recent advances in generative artificial intelligence (AI), machine learning, and statistical inference. Advancing beyond earlier generations of wide-area monitoring systems built upon supervisory control and data acquisition (SCADA) and synchrophasor technologies, we argue for a monitoring and control framework based on the streaming of continuous point-on-wave (CPOW) measurements with AI-powered data compression and fault detection. Methods and Results: The architecture of the proposed design originates from the Wiener-Kallianpur innovation representation of a random process that transforms causally a stationary random process into an innovation sequence with independent and identically distributed random variables. This work presents a generative AI approach that (i) learns an innovation autoencoder that extracts innovation sequence from CPOW time series, (ii) compresses the CPOW streaming data with innovation autoencoder and subband coding, and (iii) detects unknown faults and novel trends via nonparametric sequential hypothesis testing. Conclusion: This work argues that conventional monitoring using SCADA and phasor measurement unit (PMU) technologies is ill-suited for a future grid with deep penetration of inverter-based renewable generations and distributed energy resources. A monitoring system based on CPOW data streaming and AI data analytics should be the basic building blocks for situational awareness of a highly dynamic future grid

On the expected number of facets for the convex hull of samples

This paper studies the convex hull of $d$-dimensional samples i.i.d. generated from spherically symmetric distributions. Specifically, we derive a complete integration formula for the expected facet number of the convex hull. This formula is with respect to the CDF of the radial distribution. As the number of samples approaches infinity, the integration formula enables us to obtain the asymptotic value of the expected facet number for three categories of spherically symmetric distributions. Additionally, the asymptotic result can be applied to estimating the sample complexity in order that the probability measure of the convex hull tends to one

Non-parametric Probabilistic Time Series Forecasting via Innovations Representation

Probabilistic time series forecasting predicts the conditional probability distributions of the time series at a future time given past realizations. Such techniques are critical in risk-based decision-making and planning under uncertainties. Existing approaches are primarily based on parametric or semi-parametric time-series models that are restrictive, difficult to validate, and challenging to adapt to varying conditions. This paper proposes a nonparametric method based on the classic notion of {\em innovations} pioneered by Norbert Wiener and Gopinath Kallianpur that causally transforms a nonparametric random process to an independent and identical uniformly distributed {\em innovations process}. We present a machine-learning architecture and a learning algorithm that circumvent two limitations of the original Wiener-Kallianpur innovations representation: (i) the need for known probability distributions of the time series and (ii) the existence of a causal decoder that reproduces the original time series from the innovations representation. We develop a deep-learning approach and a Monte Carlo sampling technique to obtain a generative model for the predicted conditional probability distribution of the time series based on a weak notion of Wiener-Kallianpur innovations representation. The efficacy of the proposed probabilistic forecasting technique is demonstrated on a variety of electricity price datasets, showing marked improvement over leading benchmarks of probabilistic forecasting techniques

Challenging Low Homophily in Social Recommendation

Social relations are leveraged to tackle the sparsity issue of user-item interaction data in recommendation under the assumption of social homophily. However, social recommendation paradigms predominantly focus on homophily based on user preferences. While social information can enhance recommendations, its alignment with user preferences is not guaranteed, thereby posing the risk of introducing informational redundancy. We empirically discover that social graphs in real recommendation data exhibit low preference-aware homophily, which limits the effect of social recommendation models. To comprehensively extract preference-aware homophily information latent in the social graph, we propose Social Heterophily-alleviating Rewiring (SHaRe), a data-centric framework for enhancing existing graph-based social recommendation models. We adopt Graph Rewiring technique to capture and add highly homophilic social relations, and cut low homophilic (or heterophilic) relations. To better refine the user representations from reliable social relations, we integrate a contrastive learning method into the training of SHaRe, aiming to calibrate the user representations for enhancing the result of Graph Rewiring. Experiments on real-world datasets show that the proposed framework not only exhibits enhanced performances across varying homophily ratios but also improves the performance of existing state-of-the-art (SOTA) social recommendation models.Comment: This paper has been accepted by The Web Conference (WWW) 202

Model development of dust emission and heterogeneous chemistry within the Community Multiscale Air Quality modeling system and its application over East Asia

The Community Multiscale Air Quality (CMAQ) model has been further developed in terms of simulating natural wind-blown dust in this study, with a series of modifications aimed at improving the model\u27s capability to predict the emission, transport, and chemical reactions of dust. The default parameterization of initial threshold friction velocity constants are revised to correct the double counting of the impact of soil moisture in CMAQ by the reanalysis of field experiment data; source-dependent speciation profiles for dust emission are derived based on local measurements for the Gobi and Taklamakan deserts in East Asia; and dust heterogeneous chemistry is also implemented. The improved dust module in the CMAQ is applied over East Asia for March and April from 2006 to 2010. The model evaluation result shows that the simulation bias of PM10 and aerosol optical depth (AOD) is reduced, respectively, from −55.42 and −31.97 % by the original CMAQ to −16.05 and −22.1 % by the revised CMAQ. Comparison with observations at the nearby Gobi stations of Duolun and Yulin indicates that applying a source-dependent profile helps reduce simulation bias for trace metals. Implementing heterogeneous chemistry also results in better agreement with observations for sulfur dioxide (SO2), sulfate (SO42−), nitric acid (HNO3), nitrous oxides (NOx), and nitrate (NO3−). The investigation of a severe dust storm episode from 19 to 21 March 2010 suggests that the revised CMAQ is capable of capturing the spatial distribution and temporal variation of dust. The model evaluation also indicates potential uncertainty within the excessive soil moisture used by meteorological simulation. The mass contribution of fine-mode particles in dust emission may be underestimated by 50 %. The revised CMAQ model provides a useful tool for future studies to investigate the emission, transport, and impact of wind-blown dust over East Asia and elsewhere

RobGC: Towards Robust Graph Condensation

Graph neural networks (GNNs) have attracted widespread attention for their impressive capability of graph representation learning. However, the increasing prevalence of large-scale graphs presents a significant challenge for GNN training due to their computational demands, limiting the applicability of GNNs in various scenarios. In response to this challenge, graph condensation (GC) is proposed as a promising acceleration solution, focusing on generating an informative compact graph that enables efficient training of GNNs while retaining performance. Despite the potential to accelerate GNN training, existing GC methods overlook the quality of large training graphs during both the training and inference stages. They indiscriminately emulate the training graph distributions, making the condensed graphs susceptible to noises within the training graph and significantly impeding the application of GC in intricate real-world scenarios. To address this issue, we propose robust graph condensation (RobGC), a plug-and-play approach for GC to extend the robustness and applicability of condensed graphs in noisy graph structure environments. Specifically, RobGC leverages the condensed graph as a feedback signal to guide the denoising process on the original training graph. A label propagation-based alternating optimization strategy is in place for the condensation and denoising processes, contributing to the mutual purification of the condensed graph and training graph. Additionally, as a GC method designed for inductive graph inference, RobGC facilitates test-time graph denoising by leveraging the noise-free condensed graph to calibrate the structure of the test graph. Extensive experiments show that RobGC is compatible with various GC methods, significantly boosting their robustness under different types and levels of graph structural noises