Spectral properties of Sturm-Liouville operators on infinite metric graphs

This paper mainly deals with the Sturm-Liouville operator \begin{equation*} \mathbf{H}=\frac{1}{w(x)}\left( -\frac{\mathrm{d}}{\mathrm{d}x}p(x)\frac{ \mathrm{d}}{\mathrm{d}x}+q(x)\right) ,\text{ }x\in \Gamma \end{equation*} acting in $L_{w}^{2}\left( \Gamma \right) ,$ where $\Gamma$ is a metric graph. We establish a relationship between the bottom of the spectrum and the positive solutions of quantum graphs, which is a generalization of the classical Allegretto-Piepenbrink theorem. Moreover, we prove the Persson-type theorem, which characterizes the infimum of the essential spectrum

Long-term air pollution exposure impact on COVID-19 morbidity in China

Although previous studies have proved the association between air pollution and respiratory viral infection, given the relatively short history of human infection with the severe acute respiratory syndrome coronavirus (SARS-CoV-2), the linkage between long-term air pollution exposure and the morbidity of 2019 novel coronavirus (COVID-19) pneumonia remains poorly understood. To fill this gap, this study investigates the influences of particulate matters (PM2.5 and PM10), nitrogen dioxide (NO2), ozone (O3), sulfur dioxide (SO2) and carbon monoxide (CO) on COVID-19 incidence rate based on the prefecture-level morbidity count and air quality data in China. Annual means for ambient PM2.5, PM10, SO2, NO2, CO and O3 concentrations in each prefecture are used to estimate the population’s exposure. We leverage identical statistical methods, i.e., Spearman’s rank correlation and negative binomial regression model, to demonstrate that people who are chronically exposed to ambient air pollution are more likely to be infected by COVID-19. Our statistical analysis indicates that a 1 μg m-3 increase of PM2.5, PM10, NO2 and O3 can result in 1.95% (95% CI: 0.83 to 3.08% ), 0.55% (95% CI: -0.05 to 1.17% ), 4.63% (95% CI: 3.07 to 6.22% ) rise and 2.05% (95% CI: 0.51 to 3.59 % ) decrease of COVID-19 morbidity. However, we observe nonsignificant association with long-term SO2 and CO exposure to COVID-19 morbidity in this study. Our results’ robustness is examined based on sensitivity analyses that adjust for a wide range of confounders, including socio-economic, demographic, weather, healthcare, and mobility-related variables. We acknowledge that more laboratory results are required to prove the etiology of these associations

Studies of Rater and Item Effects in Rater Models

The goal underlying educational testing is to measure psychological constructs in a particular domain and to produce valid inferences about examinees’ ability. To achieve this goal of getting a precise ability evaluation, test developers construct questions with different formats, such as multiple-choice (MC) items, and open-ended questions or constructed response (CR) test items, for example, essay items. In recent years, large-scale assessments have implemented CR items in addition to MC items as an essential component of the educational assessment landscape. However, utilizing CR items in testing involves two main challenges, including rater effects and rater correlations. One challenge is the error added by human raters’ subjective judgments, such as rater severity and rater central tendency. Rater severity effect refers to the effect that raters may tend to give consistently low or high ratings that cause biased ability evaluation (Leckie & Baird, 2011). Central tendency describes when raters tend to use middle categories in the scoring rubric and avoid using extreme criteria (Saal et al., 1980). The second challenge is that multiple raters usually grade an examinee’s essay for quality control purposes; however, ratings based on the same item are correlated and need to be handled carefully by appropriate statistical procedures (Eckes, 2011; Kim, 2009). To solve these problems, DeCarlo (2010) proposed an HRM-SDT model that extended the traditional signal detection theory (SDT) model used in the first level of HRM. The HRM-SDT model not only considers the hierarchical structure of rating data but also deals with various rater effects beyond rater severity. This research examined to what extent the HRM-SDT separates rater effects (i.e., rater severity and rater central tendency) from item effects (i.e., item difficulty). Accordingly, one goal of this study was to simulate various rater effects and item effects to investigate the performance of the HRM-SDT model with respect to separating these effects. The other goal was to compare the fit of the HRM-SDT model with one commonly used model in language assessments, the Rasch model, in different simulation conditions and to examine the difference between these two models in terms of segregating rater and item effects. To answer these questions, Simulation A and Simulation B were conducted. In Simulation A, seven sets of parameters were varied in the first set of simulations. Simulation B addressed some questions of particular interest using another four sets of parameters, where both the rater and item parameters were simultaneously varied. This study found the HRM-SDT accurately recovered parameters, and clearly detected and separated changes in rater severity, rater central tendency, and item difficulty in most conditions

PromptTTS: Controllable Text-to-Speech with Text Descriptions

Using a text description as prompt to guide the generation of text or images (e.g., GPT-3 or DALLE-2) has drawn wide attention recently. Beyond text and image generation, in this work, we explore the possibility of utilizing text descriptions to guide speech synthesis. Thus, we develop a text-to-speech (TTS) system (dubbed as PromptTTS) that takes a prompt with both style and content descriptions as input to synthesize the corresponding speech. Specifically, PromptTTS consists of a style encoder and a content encoder to extract the corresponding representations from the prompt, and a speech decoder to synthesize speech according to the extracted style and content representations. Compared with previous works in controllable TTS that require users to have acoustic knowledge to understand style factors such as prosody and pitch, PromptTTS is more user-friendly since text descriptions are a more natural way to express speech style (e.g., ''A lady whispers to her friend slowly''). Given that there is no TTS dataset with prompts, to benchmark the task of PromptTTS, we construct and release a dataset containing prompts with style and content information and the corresponding speech. Experiments show that PromptTTS can generate speech with precise style control and high speech quality. Audio samples and our dataset are publicly available.Comment: Submitted to ICASSP 202

Generative Watermarking Against Unauthorized Subject-Driven Image Synthesis

Large text-to-image models have shown remarkable performance in synthesizing high-quality images. In particular, the subject-driven model makes it possible to personalize the image synthesis for a specific subject, e.g., a human face or an artistic style, by fine-tuning the generic text-to-image model with a few images from that subject. Nevertheless, misuse of subject-driven image synthesis may violate the authority of subject owners. For example, malicious users may use subject-driven synthesis to mimic specific artistic styles or to create fake facial images without authorization. To protect subject owners against such misuse, recent attempts have commonly relied on adversarial examples to indiscriminately disrupt subject-driven image synthesis. However, this essentially prevents any benign use of subject-driven synthesis based on protected images. In this paper, we take a different angle and aim at protection without sacrificing the utility of protected images for general synthesis purposes. Specifically, we propose GenWatermark, a novel watermark system based on jointly learning a watermark generator and a detector. In particular, to help the watermark survive the subject-driven synthesis, we incorporate the synthesis process in learning GenWatermark by fine-tuning the detector with synthesized images for a specific subject. This operation is shown to largely improve the watermark detection accuracy and also ensure the uniqueness of the watermark for each individual subject. Extensive experiments validate the effectiveness of GenWatermark, especially in practical scenarios with unknown models and text prompts (74% Acc.), as well as partial data watermarking (80% Acc. for 1/4 watermarking). We also demonstrate the robustness of GenWatermark to two potential countermeasures that substantially degrade the synthesis quality

Towards Hierarchical Cluster Analysis Heatmaps as Visual Data Analysis of Entire Student Cohort Longitudinal Trajectories and Outcomes from Grade 9 through College

Research on data use and school Early Warning Systems (EWS) notes a central practice of researchers and practitioners is to search for patterns in student data to predict outcomes so schools can support success when students experience challenges. Yet, the domain lacks a means to visualize the rich longitudinal data that schools collect. Here, we use visual data analytic hierarchical cluster analysis (HCA) heatmaps to pattern and visualize entire longitudinal grading histories of a national sample of n=14,290 students from grade 9 to college in every enrolled subject and year, visualizing 6,728,920 individual datapoints. We provide both the open access code in R and an open-access online tool allowing anyone to upload their data and create a HCA heatmap, providing support for visual data analytic and data science practice for both education researchers and schooling organizations. Keywords: cluster analysis, heatmap, early warning indicator, early warning system, data use, education data mining, education data science, visual data analytics, longitudinal data, grades, dropout, high school, post-secondary, degree, STE

Geochemical evidence for in situ accumulation of tight gas in the Xujiahe Formation coal measures in the central Sichuan Basin, China

The study of accumulation mechanisms of tight gas has attracted much attention in recent years. One of the focuses is whether natural gas can migrate on a large scale in tight reservoirs. In this work, geochemical parameters (such as C1/C1+, C1/(C2+ C3), C1+, δ13C1, δ13C2, iC4/nC4, iC5/nC5) of the tight gas reservoirs in the central Sichuan Basin, China have been studied to characterize the accumulation mechanisms in these fields. Results show that the tight gas accumulation in the Xujiahe Formation in the central Sichuan is in situ, and natural gas has not experienced large-scale migration. In gases from the central Sichuan Basin, δ13C1 ranges from −44.1‰ to −37.1‰ with an average of −40.1‰, and C1/C1+ ranges from 0.80 to 0.97 with an average of 0.91. While in the gases from the western Sichuan Basin, δ13C1 is between −35.5‰ and − 30‰ with an average of −32.2‰, and C1/C1+ ranges from 0.95to 0.99with an average of 0.98. Based on geochemical indicators of natural gas, the gases of Xujiahe Formation in the Central Sichuan Basin originated from the local coal measures of the Xujiahe Formation in horizontal direction with little contribution from the western Sichuan. In central Sichuan Basin, there is also no horizontal migration of natural gas in the same formation between adjacent gas fields. Vertically, the Xujiahe Formation is an independent gas generating system and has no relationship with the underlying Mid-Lower Triassic formations and the Jurassic natural gas formation above it. The δ13C2of Xujiahe Formation in central Sichuan ranges from −28.3‰ to −25.9‰, with an average of −27.5‰. However, the δ13C2 of Lower Jurassic above Xujiahe Formation ranges from −36.8‰ to −30.5‰, with an average of −33.0‰. Under the Xujiahe Formation, the δ13C2 in Leikoupo Formation ranges from −35.5‰ to −32.1‰, with an average of −33.1‰, and in Jialingjiang Formation ranges from −34.6‰ to −33.2‰, with an average of −33.8‰. There is also a clear distinction in the geochemical characteristics of natural gas between the upper and lower gas reservoirs in the Xujiahe Formation, indicating that there is no obvious vertical migration of natural gas. Geochemical evidence shows that there is no large-scale gas migration in the Xujiahe Formation. The tight gas is generated in situ and accumulated in the formation in the central Sichuan Basin