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We compute the regularity of powers and symbolic powers of edge ideals of all cubic circulant graphs. In particular, we establish Conjecture of Minh for cubic circulant graphs.

Code completion is essential in software development, helping developers by predicting code snippets based on context. Among completion tasks, Method Body Completion (MBC) is particularly challenging as it involves generating complete method bodies based on their signatures and context. This task becomes significantly harder in large repositories, where method bodies must integrate repositoryspecific elements such as custom APIs, inter-module dependencies, and project-specific conventions. In this paper, we introduce RAMBO, a novel RAG-based approach for repository-level MBC. Instead of retrieving similar method bodies, RAMBO identifies essential repository-specific elements, such as classes, methods, and variables/fields, and their relevant usages. By incorporating these elements and their relevant usages into the code generation process, RAMBO ensures more accurate and contextually relevant method bodies. Our experimental results with leading code LLMs across 40 Java projects show that RAMBO significantly outperformed the state-of-the-art repository-level MBC approaches, with the improvements of up to 46% in BLEU, 57% in CodeBLEU, 36% in Compilation Rate, and up to 3X in Exact Match. Notably, RAMBO surpassed RepoCoder Oracle method by up to 12% in Exact Match, setting a new benchmark for repository-level MBC.

In this paper, we first establish general bounds on the Fisher information distance to the class of normal distributions of Malliavin differentiable random variables. We then study the rate of Fisher information convergence in the central limit theorem for the solution of small noise stochastic differential equations and its additive functionals. We also show that the convergence rate is of optimal order., Comment: To appear in Stochastic Processes and their Applications

In this study, based on the quantum kinetic equation approach, we systematically present the radio-electric effect in asymmetric semi-parabolic quantum wells under the influence of a laser radiation field taking into account the electron-longitudinal optical phonon scattering mechanism. The numerical results show that the blue-shift of the maximum peaks in the photon energy range is less than 60 meV. The height of maximum peaks increases according to an exponential rule, depending nonlinearly on the structural parameters of the asymmetric semi-parabolic quantum wells. In the photon energy range greater than 100 meV, the saturated radio-electric field increases with temperature and geometric parameters of the quantum well. Temperature also strongly affects full-width at half-maximum with rules consistent with previous theoretical calculations and experimental observations. The results show the differences between symmetric and asymmetric semi-parabolic quantum wells, highlighting the influence of asymmetric structures on radio-electric effects in two-dimensional quantum well systems., Comment: The manuscript was rejected by the journal

Large Language Models for Code (code LLMs) have demonstrated remarkable performance across various software engineering (SE) tasks, increasing the application of code LLMs in software development. Despite the success of code LLMs, there remain significant concerns about the actual capabilities and reliability of these models, "whether these models really learn the semantics of code from the training data and leverage the learned knowledge to perform the SE tasks". In this paper, we introduce EMPICA, a comprehensive framework designed to systematically and empirically evaluate the capabilities of code LLMs in understanding code semantics. Specifically, EMPICA systematically introduces controlled modifications/transformations into the input code and examines the models' responses. Generally, code LLMs must be robust to semantically equivalent code inputs and be sensitive to non-equivalent ones for all SE tasks. Specifically, for every SE task, given an input code snippet c and its semantic equivalent variants, code LLMs must robustly produce consistent/equivalent outputs while they are expected to generate different outputs for c and its semantic non-equivalent variants. Our experimental results on three representative code understanding tasks, including code summarization, method name prediction, and output prediction, reveal that the robustness and sensitivity of the state-of-the-art code LLMs to code transformations vary significantly across tasks and transformation operators. In addition, the code LLMs exhibit better robustness to the semantic preserving transformations than their sensitivity to the semantic non-preserving transformations. These results highlight a need to enhance the model's capabilities of understanding code semantics, especially the sensitivity property.

As the adoption of Artificial Intelligence (AI) models expands into critical real-world applications, ensuring the explainability of these models becomes paramount, particularly in sensitive fields such as medicine and finance. Linear Discriminant Analysis (LDA) remains a popular choice for classification due to its interpretable nature, derived from its capacity to model class distributions and enhance class separation through linear combinations of features. However, real-world datasets often suffer from incomplete data, posing substantial challenges for both classification accuracy and model interpretability. In this paper, we introduce a novel and robust classification method, termed Weighted missing Linear Discriminant Analysis (WLDA), which extends LDA to handle datasets with missing values without the need for imputation. Our approach innovatively incorporates a weight matrix that penalizes missing entries, thereby refining parameter estimation directly on incomplete data. This methodology not only preserves the interpretability of LDA but also significantly enhances classification performance in scenarios plagued by missing data. We conduct an in-depth theoretical analysis to establish the properties of WLDA and thoroughly evaluate its explainability. Experimental results across various datasets demonstrate that WLDA consistently outperforms traditional methods, especially in challenging environments where missing values are prevalent in both training and test datasets. This advancement provides a critical tool for improving classification accuracy and maintaining model transparency in the face of incomplete data.

Missing data is a prevalent issue that can significantly impair model performance and interpretability. This paper briefly summarizes the development of the field of missing data with respect to Explainable Artificial Intelligence and experimentally investigates the effects of various imputation methods on the calculation of Shapley values, a popular technique for interpreting complex machine learning models. We compare different imputation strategies and assess their impact on feature importance and interaction as determined by Shapley values. Moreover, we also theoretically analyze the effects of missing values on Shapley values. Importantly, our findings reveal that the choice of imputation method can introduce biases that could lead to changes in the Shapley values, thereby affecting the interpretability of the model. Moreover, and that a lower test prediction mean square error (MSE) may not imply a lower MSE in Shapley values and vice versa. Also, while Xgboost is a method that could handle missing data directly, using Xgboost directly on missing data can seriously affect interpretability compared to imputing the data before training Xgboost. This study provides a comprehensive evaluation of imputation methods in the context of model interpretation, offering practical guidance for selecting appropriate techniques based on dataset characteristics and analysis objectives. The results underscore the importance of considering imputation effects to ensure robust and reliable insights from machine learning models.

We investigate matrix-weighted bounds for the sublinear non-kernel operators considered by F. Bernicot, D. Frey, and S. Petermichl. We extend their result to sublinear operators acting upon vector-valued functions. First, we dominate these operators by bilinear convex body sparse forms, adapting a recent general principle due to T. Hyt\"onen. Then we use this domination to derive matrix-weighted bounds, adapting arguments of F. Nazarov, S. Petermichl, S. Treil, and A. Volberg. Our requirements on the weight are formulated in terms of two-exponent matrix Muckenhoupt conditions, which surprisingly exhibit a rich structure that is absent in the scalar case. Consequently, we deduce that our matrix-weighted bounds improve the ones that were recently obtained by A. Laukkarinen. The methods we use are flexible, which allows us to complement our results with a limited range extrapolation theorem for matrix weights, extending the results of P. Auscher and J. M. Martell, as well as M. Bownik and D. Cruz-Uribe., Comment: 59 pages

Despite its technological breakthroughs, eXplainable Artificial Intelligence (XAI) research has limited success in producing the {\em effective explanations} needed by users. In order to improve XAI systems' usability, practical interpretability, and efficacy for real users, the emerging area of {\em Explainable Interfaces} (EIs) focuses on the user interface and user experience design aspects of XAI. This paper presents a systematic survey of 53 publications to identify current trends in human-XAI interaction and promising directions for EI design and development. This is among the first systematic survey of EI research.

We compute the projective dimension and regularity of $3$-path ideals of arbitrary graphs with at most one cycle.

Software patches are pivotal in refining and evolving codebases, addressing bugs, vulnerabilities, and optimizations. Patch descriptions provide detailed accounts of changes, aiding comprehension and collaboration among developers. However, manual description creation poses challenges in terms of time consumption and variations in quality and detail. In this paper, we propose PATCHEXPLAINER, an approach that addresses these challenges by framing patch description generation as a machine translation task. In PATCHEXPLAINER, we leverage explicit representations of critical elements, historical context, and syntactic conventions. Moreover, the translation model in PATCHEXPLAINER is designed with an awareness of description similarity. Particularly, the model is explicitly trained to recognize and incorporate similarities present in patch descriptions clustered into groups, improving its ability to generate accurate and consistent descriptions across similar patches. The dual objectives maximize similarity and accurately predict affiliating groups. Our experimental results on a large dataset of real-world software patches show that PATCHEXPLAINER consistently outperforms existing methods, with improvements up to 189% in BLEU, 5.7X in Exact Match rate, and 154% in Semantic Similarity, affirming its effectiveness in generating software patch descriptions., Comment: Accepted for publication in Information and Software Technology

Missing data is a common problem in practical data science settings. Various imputation methods have been developed to deal with missing data. However, even though the labels are available in the training data in many situations, the common practice of imputation usually only relies on the input and ignores the label. We propose Classification Based on MissForest Imputation (CBMI), a classification strategy that initializes the predicted test label with missing values and stacks the label with the input for imputation, allowing the label and the input to be imputed simultaneously. In addition, we propose the imputation using labels (IUL) algorithm, an imputation strategy that stacks the label into the input and illustrates how it can significantly improve the imputation quality. Experiments show that CBMI has classification accuracy when the test set contains missing data, especially for imbalanced data and categorical data. Moreover, for both the regression and classification, IUL consistently shows significantly better results than imputation based on only the input data.

Let $I$ be the edge ideal of a Cohen-Macaulay tree of dimension $d$ over a polynomial ring $S = \mathrm{k}[x_1,\ldots,x_{d},y_1,\ldots,y_d]$. We prove that for all $t \ge 1$, $$\operatorname{depth} (S/I^t) = \operatorname{max} \{d -t + 1, 1 \}.$$

Multivariate time series classification is an important computational task arising in applications where data is recorded over time and over multiple channels. For example, a smartwatch can record the acceleration and orientation of a person's motion, and these signals are recorded as multivariate time series. We can classify this data to understand and predict human movement and various properties such as fitness levels. In many applications classification alone is not enough, we often need to classify but also understand what the model learns (e.g., why was a prediction given, based on what information in the data). The main focus of this paper is on analysing and evaluating explanation methods tailored to Multivariate Time Series Classification (MTSC). We focus on saliency-based explanation methods that can point out the most relevant channels and time series points for the classification decision. We analyse two popular and accurate multivariate time series classifiers, ROCKET and dResNet, as well as two popular explanation methods, SHAP and dCAM. We study these methods on 3 synthetic datasets and 2 real-world datasets and provide a quantitative and qualitative analysis of the explanations provided. We find that flattening the multivariate datasets by concatenating the channels works as well as using multivariate classifiers directly and adaptations of SHAP for MTSC work quite well. Additionally, we also find that the popular synthetic datasets we used are not suitable for time series analysis., Comment: Accepted at AALTD '23 (8th International Workshop on Advanced Analytics and Learning on Temporal Data, ECMLPKDD 2023)

Persistent homology is a mathematical tool used for studying the shape of data by extracting its topological features. It has gained popularity in network science due to its applicability in various network mining problems, including clustering, graph classification, and graph neural networks. The definition of persistent homology for graphs is relatively straightforward, as graphs possess distinct intrinsic distances and a simplicial complex structure. However, hypergraphs present a challenge in preserving topological information since they may not have a simplicial complex structure. In this paper, we define several topological characterizations of hypergraphs in defining hypergraph persistent homology to prioritize different higher-order structures within hypergraphs. We further use these persistent homology filtrations in classifying four different real-world hypergraphs and compare their performance to the state-of-the-art graph neural network models. Experimental results demonstrate that persistent homology filtrations are effective in classifying hypergraphs and outperform the baseline models. To the best of our knowledge, this study represents the first systematic attempt to tackle the hypergraph classification problem using persistent homology.

Learning and remembering to use APIs are difficult. Several techniques have been proposed to assist developers in using APIs. Most existing techniques focus on recommending the right API methods to call, but very few techniques focus on recommending API arguments. In this paper, we propose ARIST, a novel automated argument recommendation approach which suggests arguments by predicting developers' expectations when they define and use API methods. To implement this idea in the recommendation process, ARIST combines program analysis (PA), language models (LMs), and several features specialized for the recommendation task which consider the functionality of formal parameters and the positional information of code elements (e.g., variables or method calls) in the given context. In ARIST, the LMs and the recommending features are used to suggest the promising candidates identified by PA. Meanwhile, PA navigates the LMs and the features working on the set of the valid candidates which satisfy syntax, accessibility, and type-compatibility constraints defined by the programming language in use. Our evaluation on a large dataset of real-world projects shows that ARIST improves the state-of-the-art approach by 19% and 18% in top-1 precision and recall for recommending arguments of frequently-used libraries. For general argument recommendation task, i.e., recommending arguments for every method call, ARIST outperforms the baseline approaches by up to 125% top-1 accuracy. Moreover, for newly-encountered projects, ARIST achieves more than 60% top-3 accuracy when evaluating on a larger dataset. For working/maintaining projects, with a personalized LM to capture developers' coding practice, ARIST can productively rank the expected arguments at the top-1 position in 7/10 requests.