Facilitating Graph Neural Networks with Random Walk on Simplicial Complexes

Node-level random walk has been widely used to improve Graph Neural Networks. However, there is limited attention to random walk on edge and, more generally, on $k$-simplices. This paper systematically analyzes how random walk on different orders of simplicial complexes (SC) facilitates GNNs in their theoretical expressivity. First, on $0$-simplices or node level, we establish a connection between existing positional encoding (PE) and structure encoding (SE) methods through the bridge of random walk. Second, on $1$-simplices or edge level, we bridge edge-level random walk and Hodge $1$-Laplacians and design corresponding edge PE respectively. In the spatial domain, we directly make use of edge level random walk to construct EdgeRWSE. Based on the spectral analysis of Hodge $1$-Laplcians, we propose Hodge1Lap, a permutation equivariant and expressive edge-level positional encoding. Third, we generalize our theory to random walk on higher-order simplices and propose the general principle to design PE on simplices based on random walk and Hodge Laplacians. Inter-level random walk is also introduced to unify a wide range of simplicial networks. Extensive experiments verify the effectiveness of our random walk-based methods.Comment: Accepted by NeurIPS 202

Distance-Restricted Folklore Weisfeiler-Leman GNNs with Provable Cycle Counting Power

The ability of graph neural networks (GNNs) to count certain graph substructures, especially cycles, is important for the success of GNNs on a wide range of tasks. It has been recently used as a popular metric for evaluating the expressive power of GNNs. Many of the proposed GNN models with provable cycle counting power are based on subgraph GNNs, i.e., extracting a bag of subgraphs from the input graph, generating representations for each subgraph, and using them to augment the representation of the input graph. However, those methods require heavy preprocessing, and suffer from high time and memory costs. In this paper, we overcome the aforementioned limitations of subgraph GNNs by proposing a novel class of GNNs -- $d$-Distance-Restricted FWL(2) GNNs, or $d$-DRFWL(2) GNNs. $d$-DRFWL(2) GNNs use node pairs whose mutual distances are at most $d$ as the units for message passing to balance the expressive power and complexity. By performing message passing among distance-restricted node pairs in the original graph, $d$-DRFWL(2) GNNs avoid the expensive subgraph extraction operations in subgraph GNNs, making both the time and space complexity lower. We theoretically show that the discriminative power of $d$-DRFWL(2) GNNs strictly increases as $d$ increases. More importantly, $d$-DRFWL(2) GNNs have provably strong cycle counting power even with $d=2$: they can count all 3, 4, 5, 6-cycles. Since 6-cycles (e.g., benzene rings) are ubiquitous in organic molecules, being able to detect and count them is crucial for achieving robust and generalizable performance on molecular tasks. Experiments on both synthetic datasets and molecular datasets verify our theory. To the best of our knowledge, our model is the most efficient GNN model to date (both theoretically and empirically) that can count up to 6-cycles

Chaos Synchronization of delayed systems in the presence of delay time modulation

We investigate synchronization in the presence of delay time modulation for application to communication. We have observed that the robust synchronization is established by a common delay signal and its threshold is presented using Lyapunov exponents analysis. The influence of the delay time modulation in chaotic oscillators is also discussed.Comment: 9 pages, 6 figure

Barrett’s Esophagus and Intestinal Metaplasia

Intestinal metaplasia refers to the replacement of the differentiated and mature normal mucosal epithelium outside the intestinal tract by the intestinal epithelium. This paper briefly describes the etiology and clinical significance of intestinal metaplasia in Barrett’s esophagus. This article summarizes the impact of intestinal metaplasia on the diagnosis, monitoring, and treatment of Barrett’s esophagus according to different guidelines. We also briefly explore the basis for the endoscopic diagnosis of intestinal metaplasia in Barrett’s esophagus. The identification techniques of goblet cells in Barrett’s esophagus are also elucidated by some scholars. Additionally, we further elaborate on the current treatment methods related to Barrett’s esophagus

A Nearest-Neighbor Nonparametric Multiple Imputation Approach for Incomplete Categorical Data under Missing at Random

Incomplete categorical data is a common problem in medical research. If researchers simply use complete cases for data analysis, the estimation might be biased and/or inefficient due to ignoring the missing values. Under the assumption of missing at random (MAR), i.e. missing values depend only on the observed data but not on the unobserved data, an increasing number of approaches have been proposed to handle missing data. However, most of the existing missing-data methods for incomplete categorical data are either not robust or sensitive to extreme missingness probabilities. In my dissertation, I study a nearest-neighbor nonparametric multiple imputation approach (NNMI) using two working models to impute values for a missing at random categorical variable, and to estimate marginal mean as well as conditional mean under three different study designs. In the first paper, I adopt the NNMI for dealing with a categorical outcome with missing values and estimating the proportion of each category. Specifically, multinomial logistic regression/cumulative logistic regression is performed to construct a working model for predicting the incomplete categorical outcome. Logistic regression is performed to fit a working model for predicting the missingness probabilities. The predicted values from the two working models are used as scores for calculating distances between each missing value with other non-missing values. A weighting scheme is used to accommodate contributions from two working models when generating predictive scores. A missing value is imputed by randomly selecting one of the non-missing values with the smallest distances (donors) from each of the missing observations. I conduct a simulation study to evaluate the performance of the NNMI method and compare it with several alternative methods. A real-data application is presented using a dataset from the 2013 Behavioral Risk Factor Surveillance System (BRFSS) survey. In the second paper, I use the NNMI method to handle missing covariate in logistic regression. Similarly, two working models are used to predict the incomplete covariate and the missingness probabilities. First, I perform a computation to assess the potential factors related to selecting an optimal size of donors. Second, the performance of the proposed method is compared with several alternative methods. Finally, the NNMI is applied on the 2013 BRFSS survey data to impute an incomplete categorical covariate and estimate the regression coefficients from a logistic regression model. In the third paper, the NNMI is extended to handle missing covariate under a matched case-control study. The estimation is conducted using a conditional logistic regression model. The performance of the NNMI is compared with complete cases and six parametric multiple imputation methods. The objective is to assess whether the NNMI demonstrates a doubly robust property compared with parametric methods. Then the NNMI is applied to impute an incomplete categorical covariate under a nested case-control cohort using the 2013 BRFSS survey data. To summarize the three papers, the proposed NNMI is a reasonable approach to dealing with an incomplete categorical outcome with more than two levels for assessing the distribution of the outcome. In terms of the choices for the working models, we suggest a multinomial logistic regression model to predict the missing outcome and a logistic regression model to predict the missingness probability. For imputing an incomplete covariate and estimating logistic regression coefficients, the NNMI demonstrates a doubly robust property and works stably when missingness probabilities are close to 0 or 1. When missing values occur in the covariates under a matched case-control design, the NNMI can be used on multiple incomplete covariates as long as the misspecification is moderate.Dissertation not available (per author’s request

A nonparametric multiple imputation approach for missing categorical data

Abstract Background Incomplete categorical variables with more than two categories are common in public health data. However, most of the existing missing-data methods do not use the information from nonresponse (missingness) probabilities. Methods We propose a nearest-neighbour multiple imputation approach to impute a missing at random categorical outcome and to estimate the proportion of each category. The donor set for imputation is formed by measuring distances between each missing value with other non-missing values. The distance function is calculated based on a predictive score, which is derived from two working models: one fits a multinomial logistic regression for predicting the missing categorical outcome (the outcome model) and the other fits a logistic regression for predicting missingness probabilities (the missingness model). A weighting scheme is used to accommodate contributions from two working models when generating the predictive score. A missing value is imputed by randomly selecting one of the non-missing values with the smallest distances. We conduct a simulation to evaluate the performance of the proposed method and compare it with several alternative methods. A real-data application is also presented. Results The simulation study suggests that the proposed method performs well when missingness probabilities are not extreme under some misspecifications of the working models. However, the calibration estimator, which is also based on two working models, can be highly unstable when missingness probabilities for some observations are extremely high. In this scenario, the proposed method produces more stable and better estimates. In addition, proper weights need to be chosen to balance the contributions from the two working models and achieve optimal results for the proposed method. Conclusions We conclude that the proposed multiple imputation method is a reasonable approach to dealing with missing categorical outcome data with more than two levels for assessing the distribution of the outcome. In terms of the choices for the working models, we suggest a multinomial logistic regression for predicting the missing outcome and a binary logistic regression for predicting the missingness probability

Molecular Dynamics Simulation on the Interfacial Behavior of Over-Molded Hybrid Fiber Reinforced Thermoplastic Composites

Hybrid fiber reinforced thermoplastic composites are receiving important attention in lightweight applications. The fabrication process of hybrid thermoplastic composites is that discontinuous fiber reinforced thermoplastics are injected onto the continuous fiber reinforced thermoplastics by over-molding techniques. The key issue during this process is to get a reliable interfacial bonding strength. To understand the bonding mechanism at the heterogeneous interface of hybrid thermoplastic composites which is difficult to obtain through experimental investigations, a series of molecular dynamic (MD) simulations were conducted in this paper. The influence of processing parameters on the interfacial characteristics, i.e., the distribution of interfacial high-density enrichment areas, radius of gyration, diffusion coefficient and interfacial energy, were investigated during the forming process of a heterogeneous interface. Simulation results reveal that some of molecule chains get across the interface and tangle with the molecules from the other layer, resulting in the penetration phenomenon near the interface zone. In addition, the melting temperature and injection pressure exhibit positive effects on the interfacial properties of hybrid composites. To further investigate the interfacial bonding strength and fracture mechanism of the heterogeneous interface, the uniaxial tensile and sliding simulations were performed. Results show that the non-bonded interaction energy plays a crucial role during the fracture process of heterogeneous interface. Meanwhile, the failure mode of the heterogeneous interface was demonstrated to evolve with the processing parameters

Cytotoxin-Associated Gene A-Positive Helicobacter pylori Promotes Autophagy in Colon Cancer Cells by Inhibiting miR-125b-5p

Objectives. To investigate the effects of cytotoxin-associated gene A- (CagA-) positive Helicobacter pylori on proliferation, invasion, autophagy, and expression of miR-125b-5p in colon cancer cells. Methods. Colon cancer cells were cocultured with H. pylori (CagA+) to analyze the effects of H. pylori on miR-125b-5p and autophagy. Colon cancer cells infected with H. pylori (CagA+) were mimicked by transfection of CagA plasmid. The effects of CagA on the proliferation, invasion, and autophagy of colon cancer cells were analyzed. Cell counting kit-8 (CCK-8), clone formation, and Transwell assays were used to detect cell viability, proliferation, and invasion ability, respectively. Proteins and miRNAs were detected by western blotting and qPCR, respectively. Results. H. pylori (CagA+) inhibited expression of miR-125b-5p and promoted autophagy in colon cancer cells. MiR-125 b-5p was underexpressed in colon cancer cells after CagA overexpression. CagA promoted colon cancer cell proliferation, invasion, and autophagy. Overexpression of miR-125b-5p inhibited the proliferation, invasion, and autophagy of colon cancer cells and reversed the effects of CagA. Conclusion. H. pylori (CagA+) infection may promote the development and invasion of colon cancer by inhibiting miR-125b-5p