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

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

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

Differentially Private ERM Based on Data Perturbation

In this paper, after observing that different training data instances affect the machine learning model to different extents, we attempt to improve the performance of differentially private empirical risk minimization (DP-ERM) from a new perspective. Specifically, we measure the contributions of various training data instances on the final machine learning model, and select some of them to add random noise. Considering that the key of our method is to measure each data instance separately, we propose a new `Data perturbation' based (DB) paradigm for DP-ERM: adding random noise to the original training data and achieving ($\epsilon,\delta$)-differential privacy on the final machine learning model, along with the preservation on the original data. By introducing the Influence Function (IF), we quantitatively measure the impact of the training data on the final model. Theoretical and experimental results show that our proposed DBDP-ERM paradigm enhances the model performance significantly

Transient analysis of arm locking controller

Arm locking is one of the key technologies to suppress the laser phase noise in spaced-based gravitational waves observatories. Since arm locking was proposed, phase margin criterion was always used as the fundamental design strategy for the controller development. In this paper, we find that this empirical method from engineering actually cannot guarantee the arm locking stability. Therefore, most of the advanced arm locking controllers reported so far may have instable problems. After comprehensive analysis of the single arm locking's transient responses, strict analytical stability criterions are summarized for the first time. These criterions are then generalized to dual arm locking, modified-dual arm locking and common arm locking, and special considerations for the design of arm locking controllers in different architectures are also discussed. It is found that PI controllers can easily meet our stability criterions in most of the arm locking systems. Using a simple high gain PI controller, it is possible to suppress the laser phase noise by 5 orders of magnitude within the science band. Our stability criterions can also be used in other feedback systems, where several modules with different delays are connected in parallel.Comment: 24 pages, 24 figure

Semantic-aware Node Synthesis for Imbalanced Heterogeneous Information Networks

Heterogeneous graph neural networks (HGNNs) have exhibited exceptional efficacy in modeling the complex heterogeneity in heterogeneous information networks (HINs). The critical advantage of HGNNs is their ability to handle diverse node and edge types in HINs by extracting and utilizing the abundant semantic information for effective representation learning. However, as a widespread phenomenon in many real-world scenarios, the class-imbalance distribution in HINs creates a performance bottleneck for existing HGNNs. Apart from the quantity imbalance of nodes, another more crucial and distinctive challenge in HINs is semantic imbalance. Minority classes in HINs often lack diverse and sufficient neighbor nodes, resulting in biased and incomplete semantic information. This semantic imbalance further compounds the difficulty of accurately classifying minority nodes, leading to the performance degradation of HGNNs. To tackle the imbalance of minority classes and supplement their inadequate semantics, we present the first method for the semantic imbalance problem in imbalanced HINs named Semantic-aware Node Synthesis (SNS). By assessing the influence on minority classes, SNS adaptively selects the heterogeneous neighbor nodes and augments the network with synthetic nodes while preserving the minority semantics. In addition, we introduce two regularization approaches for HGNNs that constrain the representation of synthetic nodes from both semantic and class perspectives to effectively suppress the potential noises from synthetic nodes, facilitating more expressive embeddings for classification. The comprehensive experimental study demonstrates that SNS consistently outperforms existing methods by a large margin in different benchmark datasets

Association Between Atherosclerosis-Related Cardiovascular Disease and Uveitis: A Systematic Review and Meta-Analysis

Background: Uveitis is not only an intraocular inflammatory disease, but also an indicator of systemic inflammation. It is unclear whether uveitis can increase the risk of cardiovascular disease (CVD) through the atherosclerotic pathway. Methods: PubMed and Embase databases were searched until 5 September, 2022. Original studies investigating uveitis and cardiovascular events were selected. The random-effects model was used to calculate the difference of groups in pooled estimates. Results: A total of six observational studies that included mainly ankylosing spondylitis (AS) patients were included. Of these, three studies reported data on carotid plaques and carotid intima-media thickness (cIMT) and the other three studies provided data on atherosclerosis-related CVD. No significant difference was found in cIMT between uveitis and controls (MD = 0.01, 95% CI = -0.03-0.04, p = 0.66), consistent with the findings of carotid plaque incidence (OR = 1.30, 95% CI = 0.71-2.41, p = 0.39). However, uveitis was associated with a 1.49-fold increase in atherosclerosis-related CVD (HR = 1.49, 95% CI = 1.20-1.84, p = 0.0002). Conclusions: Uveitis is a predictor of atherosclerosis-related CVD in AS patients. For autoimmune disease patients with uveitis, earlier screening of cardiovascular risk factors and the implementation of corresponding prevention strategies may be associated with a better prognosis