arXiv subjects
Publications and source records attributed to Rong Chen.
Recently, Chen and Deng have proved that every graph $G$ with independence number two contains $K_{\ell,χ(G)- \ell}$ as a minor for each integer $\ell$ with $1\leq\ell < χ(G)$. In this paper, we extend this result to odd minor version. That is, we prove that each graph $G$ with independence number two contains $K_{\ell,χ(G)- \ell}$ as an odd minor for each integer $\ell$ with $1\leq\ell < χ(G)$.
The Just-In-Time defect prediction model helps development teams improve software quality and efficiency by assessing whether code changes submitted by developers are likely to introduce defects in real-time, allowing timely identification of potential issues during the commit stage. However, two main challenges exist in current work due to the reality that all deleted and added lines in bug-fixing commits may be related to the root cause of the introduced bug: 1) lack of effective integration of heterogeneous graph information, and 2) lack of semantic relationships between changed code lines. To address these challenges, we propose a method called RC-Detection, which utilizes relational graph convolutional network to capture the semantic relationships between changed code lines. RC-Detection is used to detect root-cause deletion lines in changed code lines, thereby identifying the root cause of introduced bugs in bug-fixing commits. To evaluate the effectiveness of RC-Detection, we used three datasets that contain high-quality bug-fixing and bug-introducing commits. Extensive experiments were conducted to evaluate the performance of our model by collecting data from 87 open-source projects, including 675 bug-fix commits. The experimental results show that, compared to the most advanced root cause detection methods, RC-Detection improved Recall@1, Recall@2, Recall@3, and MFR by at 4.107%, 5.113%, 4.289%, and 24.536%, respectively.
For any pair of edges $e,f$ of a graph $G$, we say that {\em $e,f$ are $P_3$-connected in $G$} if there exists a sequence of edges $e=e_0,e_1,\ldots, e_k=f$ such that $e_i$ and $e_{i+1}$ are two edges of an induced $3$-vertex path in $G$ for every $0\leq i\leq k-1$. If every pair of edges of $G$ are $P_3$-connected in $G$, then $G$ is {\em $P_3$-connected}. $P_3$-connectivity was first defined by Chudnovsky et al. in 2024 to prove that every connected graph not containing $P_5$ as an induced subgraph has cop number at most two. In this paper, we give a characterization of $P_3$-connected graphs and prove that a simple graph is $P_3$-connected if and only if it is connected and has no homogeneous set whose induced subgraph contains an edge.
The two primary tasks in the search recommendation system are search relevance matching and click-through rate (CTR) prediction -- the former focuses on seeking relevant items for user queries whereas the latter forecasts which item may better match user interest. Prior research typically develops two models to predict the CTR and search relevance separately, then ranking candidate items based on the fusion of the two outputs. However, such a divide-and-conquer paradigm creates the inconsistency between different models. Meanwhile, the search relevance model mainly concentrates on the degree of objective text matching while neglecting personalized differences among different users, leading to restricted model performance. To tackle these issues, we propose a unified Personalized Search RElevance Matching and CTR Prediction Fusion Model(PRECTR). Specifically, based on the conditional probability fusion mechanism, PRECTR integrates the CTR prediction and search relevance matching into one framework to enhance the interaction and consistency of the two modules. However, directly optimizing CTR binary classification loss may bring challenges to the fusion model's convergence and indefinitely promote the exposure of items with high CTR, regardless of their search relevance. Hence, we further introduce two-stage training and semantic consistency regularization to accelerate the model's convergence and restrain the recommendation of irrelevant items. Finally, acknowledging that different users may have varied relevance preferences, we assessed current users' relevance preferences by analyzing past users' preferences for similar queries and tailored incentives for different candidate items accordingly. Extensive experimental results on our production dataset and online A/B testing demonstrate the effectiveness and superiority of our proposed PRECTR method.
Woodall (and Seymour independently) in 2001 proposed a conjecture that every graph $G$ contains every complete bipartite graph on $χ(G)$ vertices as a minor, where $χ(G)$ is the chromatic number of $G$. In this paper, we prove that for each positive integer $\ell$ with $2\ell \leq χ(G)$, each graph $G$ with independence number two contains a $K^{\ell}_{\ell,χ(G)-\ell}$-minor, implying that Seymour and Woodall's conjecture holds for graphs with independence number two, where $K^{\ell}_{\ell,χ(G)-\ell}$ is the graph obtained from $K_{\ell,χ(G)-\ell}$ by making every pair of vertices on the side of the bipartition of size $\ell$ adjacent.
State-space models have been used in many applications, including econometrics, engineering, medical research, etc. The maximum likelihood estimation (MLE) of the static parameter of general state-space models is not straightforward because the likelihood function is intractable. It is popular to use the sequential Monte Carlo(SMC) method to perform gradient ascent optimisation in either offline or online fashion. One problem with existing online SMC methods for MLE is that the score estimators are inconsistent, i.e. the bias does not vanish with increasing particle size. In this paper, two SMC algorithms are proposed based on an importance sampling weight function to use each set of generated particles more efficiently. The first one is an offline algorithm that locally approximates the likelihood function using importance sampling, where the locality is adapted by the effective sample size (ESS). The second one is a semi-online algorithm that has a computational cost linear in the particle size and uses score estimators that are consistent. We study its consistency and asymptotic normality. Their computational superiority is illustrated in numerical studies for long time series.
We develop an estimation methodology for a factor model for high-dimensional matrix-valued time series, where common stochastic trends and common stationary factors can be present. We study, in particular, the estimation of (row and column) loading spaces, of the common stochastic trends and of the common stationary factors, and the row and column ranks thereof. In a set of (negative) preliminary results, we show that a projection-based technique fails to improve the rates of convergence compared to a "flattened" estimation technique which does not take into account the matrix nature of the data. Hence, we develop a three-step algorithm where: (i) we first project the data onto the orthogonal complement to the (row and column) loadings of the common stochastic trends; (ii) we subsequently use such "trend free" data to estimate the stationary common component; (iii) we remove the estimated common stationary component from the data, and re-estimate, using a projection-based estimator, the row and column common stochastic trends and their loadings. We show that this estimator succeeds in refining the rates of convergence of the initial, "flattened" estimator. As a by-product, we develop consistent eigenvalue-ratio based estimators for the number of stationary and nonstationary common factors.
Hadwiger's conjecture for the immersion relation posits that every graph $G$ contains an immersion of the complete graph $K_{χ(G)}$. Vergara showed that this is equivalent to saying that every $n$-vertex graph $G$ with $α(G)=2$ contains an immersion of the complete graph on $\lceil\frac{n}{2}\rceil$ vertices. Recently, Botler et al. showed that every $n$-vertex graph $G$ with $α(G)=2$ contains every complete bipartite graph on $\lceil\frac{n}{2}\rceil$ vertices as an immersion. In this paper, we give a much simpler proof of this result.
In 2021, Andrews mentioned that George Beck introduced partition statistics $M_w(r,m,n)$, which denote the total number of ones in the partition of $n$ with crank congruent to $r$ modulo $m$. Recently, a number of congruences and identities involving $M_w(r,m,n)$ for some small $m$ have been developed. We establish the 11-dissection of the generating functions for $M_ω(r,11,n)-M_ω(11-r,11,n)$, where $r=1,2,3,4,5$. In particular, we discover a beautiful identity involving $M_ω(r,11,11n+6)$.
We discovered that a GPU kernel can have both idempotent and non-idempotent instances depending on the input. These kernels, called conditionally-idempotent, are prevalent in real-world GPU applications (490 out of 547 from six applications). Consequently, prior work that classifies GPU kernels as either idempotent or non-idempotent can severely compromise the correctness or efficiency of idempotence-based systems. This paper presents PICKER, the first system for instance-level idempotency validation. PICKER dynamically validates the idempotency of GPU kernel instances before their execution, by utilizing their launch arguments. Several optimizations are proposed to significantly reduce validation latency to microsecond-scale. Evaluations using representative GPU applications (547 kernels and 18,217 instances in total) show that PICKER can identify idempotent instances with no false positives and a false-negative rate of 18.54%, and can complete the validation within 5 us for all instances. Furthermore, by integrating PICKER, a fault-tolerant system can reduce the checkpoint cost to less than 4% and a scheduling system can reduce the preemption latency by 84.2%.
Altermagnet (AM) is a new proposed magnetic state with collinear antiferromagnetic ground state but presents some transport properties that were only believed to exist in ferromagnets or non-collinear antiferromagnets. To have a comprehensive understanding of the transport properties of AMs, especially from the experimental point of view, a promising altermagnetic metal is crucial. In all the proposed altermagnetic metals, RuO$_2$ has a special position, since it is the first proposed AM with the largest spin splitting and several important altermagnetism featured experiments were first performed based on it. However, a very recent report based on sensitive muon-spin measurements suggest a super small local magnetization from Ru, i.e. a nonmagnetic ground state in RuO$_2$. Therefore, a determination of the existence of the altermagnetic ground state is the basic starting point for all the previously altermagnetic transport properties in RuO$_2$. In this work, we propose to identify its magnetic ground state from the Fermi surface (FS) via the electronic transport property of quantum oscillation (QO). We systematically analyzed the FSs of RuO$_2$ in both nonmagnetic and altermagnetic states via first principles calculations. Our work should be helpful for future experiments on QO measurements to confirm its ground state by the interplay between transport measurements and computations.
Searching for new effective risk factors on stock returns is an important research topic in asset pricing. Factor modeling is an active research topic in statistics and econometrics, with many new advances. However, these new methods have not been fully utilized in asset pricing application. In this paper, we adopt the factor models, especially matrix factor models in various forms, to construct new statistical factors that explain the variation of stock returns. Furthermore, we evaluate the contribution of these statistical factors beyond the existing factors available in the asset pricing literature. To demonstrate the power of the new factors, U.S. monthly stock data are analyzed and the partial F test and double selection LASSO method are conducted. The results show that the new statistical factors bring additional information and add explanatory power in asset pricing. Our method opens a new direction for portfolio managers to seek additional risk factors to improve the estimation of portfolio returns.
Metallic bismuth is both non-toxic and cost-effective. Bi-based catalysts have demonstrated the ability to efficiently produce HCOOH through CO2RR while effectively inhibiting the HER. Although many experiments have been reported concerning its performance towards CO2 reduction, the impact its valence states and crystal faces on CO2RR selectivity (e.g. HCOOH versus CO) it still under debate. Here, we performed a comprehensive study via density functional theory, by including three typical valence states of Bi, such as 0 (Bi), +3 (Bi2O3) and +5 (Bi2O5), as well as their often-studied crystal facets. The results show that metallic Bi demonstrates a poor selectivity for HCOOH, but boasts a higher conversion rate for CO2. While Bi2O3 exhibits a good selectivity for HCOOH production, yet it displays a lower conversion rate for CO2. For Bi2O5, all studied surfaces show high energy barriers in both cases of HCOOH and CO production, and lower energy barriers for HER reactions, indicating that Bi at +5 valence state is not the good choice for 2e transfer reactions. Subsequently, we further examined the effects of oxygen contents on the selectivity of HCOOH and the conversion rate for CO2. Interestingly, we found that partial oxidization of Bi benefits both the selectivity and the conversion rate. With these observations, we suggest that a mixture of Bi (0) and Bi2O3 (+3) phases would be a better choice than single crystals for future experiments.
MATLAB(R) releases over the last 3 years have witnessed a continuing growth in the dynamic modeling capabilities offered by the System Identification Toolbox(TM). The emphasis has been on integrating deep learning architectures and training techniques that facilitate the use of deep neural networks as building blocks of nonlinear models. The toolbox offers neural state-space models which can be extended with auto-encoding features that are particularly suited for reduced-order modeling of large systems. The toolbox contains several other enhancements that deepen its integration with the state-of-art machine learning techniques, leverage auto-differentiation features for state estimation, and enable a direct use of raw numeric matrices and timetables for training models.
A matching $M$ in a graph $G$ is {\em connected} if $G$ has an edge linking each pair of edges in $M$. The problem to find large connected matchings in graphs $G$ with $α(G)=2$ is closely related to Hadwiger's conjecture for graphs with independence number 2. The problem of finding a large connected matching in a general graph is NP-hard. F{ü}redi et al. in 2005 conjectured that each $(4t-1)$-vertex graph $G$ with $α(G)=2$ contains a connected matching of size at least $t$. Cambie recently showed that if this conjecture is false, then so is Hadwiger's conjecture. In this paper, we present a number of properties possessed by a counterexample to F{ü}redi et al.'s conjecture, and then using these properties, we prove that F{ü}redi et al.'s conjecture holds for $t\leq22$.
In 2021, Andrews mentioned that George Beck introduced a partition statistic $NT(r,m,n)$ which is related to Dyson's rank statistic. Motivated by Andrews's work, scholars have established a number of congruences and identities involving $NT(r,m,n)$. In this paper, we strengthen and extend a recent work of Mao on the transformation properties of the $NT$ function and provide an analogy of Hickerson and Mortenson's work on the rank function. As an application, we demonstrate how one can deduce from our results many identities involving $NT(r,m,n)$ and another crank-analog statistic $M_ω(r,m,n)$. As a related result, some new properties of generalized Appell-Lerch series are given.
Tensor time series, which is a time series consisting of tensorial observations, has become ubiquitous. It typically exhibits high dimensionality. One approach for dimension reduction is to use a factor model structure, in a form similar to Tucker tensor decomposition, except that the time dimension is treated as a dynamic process with a time dependent structure. In this paper we introduce two approaches to estimate such a tensor factor model by using iterative orthogonal projections of the original tensor time series. These approaches extend the existing estimation procedures and improve the estimation accuracy and convergence rate significantly as proven in our theoretical investigation. Our algorithms are similar to the higher order orthogonal projection method for tensor decomposition, but with significant differences due to the need to unfold tensors in the iterations and the use of autocorrelation. Consequently, our analysis is significantly different from the existing ones. Computational and statistical lower bounds are derived to prove the optimality of the sample size requirement and convergence rate for the proposed methods. Simulation study is conducted to further illustrate the statistical properties of these estimators.
Matrix time series, which consist of matrix-valued data observed over time, are prevalent in various fields such as economics, finance, and engineering. Such matrix time series data are often observed in high dimensions. Matrix factor models are employed to reduce the dimensionality of such data, but they lack the capability to make predictions without specified dynamics in the latent factor process. To address this issue, we propose a two-component dynamic matrix factor model that extends the standard matrix factor model by incorporating a matrix autoregressive structure for the low-dimensional latent factor process. This two-component model injects prediction capability to the matrix factor model and provides deeper insights into the dynamics of high-dimensional matrix time series. We present the estimation procedures of the model and their theoretical properties, as well as empirical analysis of the estimation procedures via simulations, and a case study of New York city taxi data, demonstrating the performance and usefulness of the model.