The Smallest Bipartite Intrinsically Knotted Graph

We use the restoring method of Kim, Mattman, and Oh  to prove that the Heawood graph is the only bipartite graph with 21 edges that is intrinsically knotted

Development of a Causal Model for Improving Rural Seniors' Accessibility: Data Evidences

Seniors residing in rural areas often encounter limited accessibility to opportunities, resources, and services. This paper introduces a model proposing that both aging and rural residency are factors contributing to the restricted accessibility faced by rural seniors. Leveraging data from the 2017 National Household Travel Survey, the study examines three hypotheses pertaining to this causal model. Multiple causal pathways emerge in the data analysis, with mobility identified as a mediator in one of them. The study further identifies specific challenges faced by rural seniors, such as the reduced accessibility in reaching medical services and assisting others. These challenges stem primarily from aging and geographic obstacles that not only diminish their willingness to travel but also restrict more in the group from choosing transportation modes with higher mobility. The insights gained from this study serve as a foundation for devising effective methods to enhance transportation accessibility for seniors in rural areas.Comment: 12 pages 5 table

OpenCAEPoro: A Parallel Simulation Framework for Multiphase and Multicomponent Porous Media Flows

OpenCAEPoro is a parallel numerical simulation software developed in C++ for simulating multiphase and multicomponent flows in porous media. The software utilizes a set of general-purpose compositional model equations, enabling it to handle a diverse range of fluid dynamics, including the black oil model, compositional model, and thermal recovery models. OpenCAEPoro establishes a unified solving framework that integrates many widely used methods, such as IMPEC, FIM, and AIM. This framework allows dynamic collaboration between different methods. Specifically, based on this framework, we have developed an adaptively coupled domain decomposition method, which can provide initial solutions for global methods to accelerate the simulation. The reliability of OpenCAEPoro has been validated through benchmark testing with the SPE comparative solution project. Furthermore, its robust parallel efficiency has been tested in distributed parallel environments, demonstrating its suitability for large-scale simulation problems.Comment: 29 pages, 19 figure

Test for high-dimensional mean vectors via the weighted L2L_2-norm

In this paper, we propose a novel approach to test the equality of high-dimensional mean vectors of several populations via the weighted $L_2$-norm. We establish the asymptotic normality of the test statistics under the null hypothesis. We also explain theoretically why our test statistics can be highly useful in weakly dense cases when the nonzero signal in mean vectors is present. Furthermore, we compare the proposed test with existing tests using simulation results, demonstrating that the weighted $L_2$-norm-based test statistic exhibits favorable properties in terms of both size and power

Test for high-dimensional linear hypothesis of mean vectors via random integration

In this paper, we investigate hypothesis testing for the linear combination of mean vectors across multiple populations through the method of random integration. We have established the asymptotic distributions of the test statistics under both null and alternative hypotheses. Additionally, we provide a theoretical explanation for the special use of our test statistics in situations when the nonzero signal in the linear combination of the true mean vectors is weakly dense. Moreover, Monte-Carlo simulations are presented to evaluate the suggested test against existing high-dimensional tests. The findings from these simulations reveal that our test not only aligns with the performance of other tests in terms of size but also exhibits superior power

Complex-valued K-means clustering of interpolative separable density fitting algorithm for large-scale hybrid functional enabled \textit{ab initio} molecular dynamics simulations within plane waves

K-means clustering, as a classic unsupervised machine learning algorithm, is the key step to select the interpolation sampling points in interpolative separable density fitting (ISDF) decomposition. Real-valued K-means clustering for accelerating the ISDF decomposition has been demonstrated for large-scale hybrid functional enabled \textit{ab initio} molecular dynamics (hybrid AIMD) simulations within plane-wave basis sets where the Kohn-Sham orbitals are real-valued. However, it is unclear whether such K-means clustering works for complex-valued Kohn-Sham orbitals. Here, we apply the K-means clustering into hybrid AIMD simulations for complex-valued Kohn-Sham orbitals and use an improved weight function defined as the sum of the square modulus of complex-valued Kohn-Sham orbitals in K-means clustering. Numerical results demonstrate that this improved weight function in K-means clustering algorithm yields smoother and more delocalized interpolation sampling points, resulting in smoother energy potential, smaller energy drift and longer time steps for hybrid AIMD simulations compared to the previous weight function used in the real-valued K-means algorithm. In particular, we find that this improved algorithm can obtain more accurate oxygen-oxygen radial distribution functions in liquid water molecules and more accurate power spectrum in crystal silicon dioxide compared to the previous K-means algorithm. Finally, we describe a massively parallel implementation of this ISDF decomposition to accelerate large-scale complex-valued hybrid AIMD simulations containing thousands of atoms (2,744 atoms), which can scale up to 5,504 CPU cores on modern supercomputers.Comment: 43 pages, 12 figure

Quantification of Genome Editing and Transcriptional Control Capabilities Reveals Hierarchies among Diverse CRISPR/Cas Systems in Human Cells

CRISPR/Cas technologies have revolutionized the ability to redesign genomic information and tailor endogenous gene expression. Nevertheless, the discovery and development of new CRISPR/Cas systems has resulted in a lack of clarity surrounding the relative efficacies among these technologies in human cells. This deficit makes the optimal selection of CRISPR/Cas technologies in human cells unnecessarily challenging, which in turn hampers their adoption, and thus ultimately limits their utility. Here, we designed a series of endogenous testbed systems to methodically quantify and compare the genome editing, CRISPRi, and CRISPRa capabilities among 10 different natural and engineered Cas protein variants spanning Type II and Type V CRISPR/Cas families. We show that although all Cas protein variants are capable of genome editing and transcriptional control in human cells, hierarchies exist, particularly for genome editing and CRISPRa applications, wherein Cas9 ≥ Cas12a > Cas12e/Cas12j. Our findings also highlight the utility of our modular testbed platforms to rapidly and systematically quantify the functionality of practically any natural or engineered genomic-targeting Cas protein in human cells

UniTime: A Language-Empowered Unified Model for Cross-Domain Time Series Forecasting

Multivariate time series forecasting plays a pivotal role in contemporary web technologies. In contrast to conventional methods that involve creating dedicated models for specific time series application domains, this research advocates for a unified model paradigm that transcends domain boundaries. However, learning an effective cross-domain model presents the following challenges. First, various domains exhibit disparities in data characteristics, e.g., the number of variables, posing hurdles for existing models that impose inflexible constraints on these factors. Second, the model may encounter difficulties in distinguishing data from various domains, leading to suboptimal performance in our assessments. Third, the diverse convergence rates of time series domains can also result in compromised empirical performance. To address these issues, we propose UniTime for effective cross-domain time series learning. Concretely, UniTime can flexibly adapt to data with varying characteristics. It also uses domain instructions and a Language-TS Transformer to offer identification information and align two modalities. In addition, UniTime employs masking to alleviate domain convergence speed imbalance issues. Our extensive experiments demonstrate the effectiveness of UniTime in advancing state-of-the-art forecasting performance and zero-shot transferability

TeViS:Translating Text Synopses to Video Storyboards

A video storyboard is a roadmap for video creation which consists of shot-by-shot images to visualize key plots in a text synopsis. Creating video storyboards, however, remains challenging which not only requires cross-modal association between high-level texts and images but also demands long-term reasoning to make transitions smooth across shots. In this paper, we propose a new task called Text synopsis to Video Storyboard (TeViS) which aims to retrieve an ordered sequence of images as the video storyboard to visualize the text synopsis. We construct a MovieNet-TeViS dataset based on the public MovieNet dataset. It contains 10K text synopses each paired with keyframes manually selected from corresponding movies by considering both relevance and cinematic coherence. To benchmark the task, we present strong CLIP-based baselines and a novel VQ-Trans. VQ-Trans first encodes text synopsis and images into a joint embedding space and uses vector quantization (VQ) to improve the visual representation. Then, it auto-regressively generates a sequence of visual features for retrieval and ordering. Experimental results demonstrate that VQ-Trans significantly outperforms prior methods and the CLIP-based baselines. Nevertheless, there is still a large gap compared to human performance suggesting room for promising future work. The code and data are available at: \url{https://ruc-aimind.github.io/projects/TeViS/}Comment: Accepted to ACM Multimedia 202

Acupuncture Treatment for Post-Stroke Depression: Intestinal Microbiota and Its Role

Stroke-induced depression is a common complication and an important risk factor for disability. Besides psychiatric symptoms, depressed patients may also exhibit a variety of gastrointestinal symptoms, and even take gastrointestinal symptoms as the primary reason for medical treatment. It is well documented that stress may disrupt the balance of the gut microbiome in patients suffering from post-stroke depression (PSD), and that disruption of the gut microbiome is closely related to the severity of the condition in depressed patients. Therefore, maintaining the balance of intestinal microbiota can be the focus of research on the mechanism of acupuncture in the treatment of PSD. Furthermore, stroke can be effectively treated with acupuncture at all stages and it may act as a special microecological regulator by regulating intestinal microbiota as well. In this article, we reviewed the studies on changing intestinal microbiota after acupuncture treatment and examined the existing problems and development prospects of acupuncture, microbiome, and poststroke depression, in order to provide new ideas for future acupuncture research