Shuang Liu

This survey reviews some recent progress on principal eigenvalues for second-order non-self-adjoint elliptic operators and time-periodic parabolic operators. We study their dependence on diffusion rate, advection strength, and temporal frequency, focusing on monotonicity and asymptotic behavior. These analyses lead to a classification of the topological structures of level sets for principal eigenvalues in the parameter space, which in turn provides new insights into the dependence of the principal eigenvalue on multiple parameters. We then apply the theory of the principal eigenvalue to species competition, mixing enhancement in incompressible fluids, and the outbreak of infectious diseases. Some open mathematical questions are also included.

Slow queries frequently cause severe performance bottlenecks in Database Management Systems (DBMSs). Due to the severe risk of exacerbating online resource contention, diagnosing their root causes online is usually infeasible; offline diagnosis has thus become the de facto approach. However, strict data privacy regulations prohibit accessing original user data. Therefore, synthesizing a proxy database, one that induces the query optimizer to generate identical physical execution plans as in production, from non-intrusive metadata, is critical for reproducing and diagnosing slow queries offline. Achieving high-fidelity reproduction demands satisfying both global statistical distributions and exact local cardinality constraints. Existing works fundamentally fail to achieve both simultaneously: data-driven approaches cannot enforce strict local cardinalities, whereas workload-aware approaches severely distort the overall data distribution, misleading the optimizer into divergent execution plans. To bridge this gap, we introduce DBRepro, an automated end-to-end database synthesis framework that synergistically integrates data-driven and workload-aware methodologies. DBRepro formulates database generation as a constrained distribution synthesis problem. It initializes a global data distribution from lightweight column statistics, extracts execution constraints from the target queries, and progressively adjusts the distribution to satisfy these constraints, ensuring the global distribution is maximally preserved while exact local cardinalities are strictly enforced. Extensive evaluations on the TPC-H and SSB benchmarks demonstrate that DBRepro outperforms state-of-the-art baselines across comprehensive fidelity metrics. Compared to the data-driven baseline, it reduces cardinality error by up to 20.3% while maintaining identical plan consistency. Against a workload-aware baseline, it reproduces 15% more consistent execution plans and lowers the latency proportion error by 21.5%. Furthermore, we validate its industrial practicality on a nearly 1 TB real-world dataset from a specific industrial sector, managed by KingbaseES, successfully reproducing the execution performance of complex slow queries with high fidelity.

Cholera originated in the Ganges Delta of India in 1817 and then spread globally through several overlapping waves of epidemics. Its prevalence has since been reported to vary widely across different regions. Spatial heterogeneity plays a crucial role in shaping cholera transmission through the interplay of environment, population, and infrastructure. In this paper, we propose a new reaction‐advection‐diffusion equation model in a closed advective environment, which extends the ODE model introduced in Wang et al. (Wang W., Y. Lou, X. Wang, “Modeling Cholera Transmission Dynamics with Antibiotic Resistance and Mutation: A Case Study in Zimbabwe,” Mathematical Biosciences 390 (2025): 109545). We establish three critical thresholds and analyze the dependence of the basic reproduction number on model parameters by studying the principal eigenvalue of a series of cooperative elliptic systems with weight and potential. We further derive threshold‐type results for the global dynamics, and investigate the asymptotic profiles of the coexistence endemic steady state when the diffusion rate of the susceptible individuals is small. Interestingly, for a spatially homogeneous case, we numerically find the spatially inhomogeneous steady state. We also observe that bacterial advection exhibits antibiotic‐resistance‐dependent effects on cholera outbreaks, and this dependence can be modified by environmental mutation of Vibrio cholerae . These results underscore the critical roles of antibiotic resistance and bacterial mutation in shaping spatial cholera transmission dynamics with geographical heterogeneity and population mobility.

How does the movement of individuals influence the persistence of a single population? A surprising phenomenon known as dispersal-induced growth (DIG) occurs when the population would become extinct if isolated or well mixed, but migration, at an appropriate rate, can induce the persistence of the population. In this paper, we investigate this phenomenon based on a time-periodic two-patch model incorporating asymmetric migration matrices. Through comprehensive analysis of the qualitative properties of the associated principal eigenvalue, including monotonicity, asymptotic behaviors, and the topological structure of the level sets as a function of the migration rate and frequency, we characterize the important factors driving the occurrence of DIG under fixed environmental oscillation frequencies. Our results provide new insights into how the interplay between spatial connectivity and temporal environmental variation enables the population persistence.

Competitive exclusion principle, which states that two or more species limited by the same resource cannot coexist indefinitely, is a very common phenomenon in population dynamics. It is well-known that competitive exclusion principle occurs in deterministic competition models, diffusive competition models, and evolutionary competition models. In this paper, we consider an age-structured competition model among N species and obtain an interesting result: under suitable scaled birth and death rates, the species with the smallest maximum age always wins the competition to exclude the other species; that is, the competitive exclusion principle occurs in age-structured competition models.

Relational Database Management Systems (RDBMSs) are crucial infrastructures supporting a wide range of applications, making bug mitigation within these systems essential. This study presents the first comprehensive analysis of bugs in three popular open-source RDBMSs—MySQL, SQLite, and openGauss. We manually examined 777 bugs across four dimensions, i.e., bug root causes, bug symptoms, bug distribution across modules, and the correlations between the studied aspects. We also analyzed the bug-triggering SQL statements to uncover test cases that cannot be generated by existing tools. We have made 12 findings, which throw lights on the development, maintenance and testing of RDBMS systems. Particularly, our findings reveal that bugs related to SQL data types and complex features, such as database triggers, procedures and database parameter settings, present significant opportunities for enhancing RDBMS bug detection and mitigation. Leveraging these insights, we developed a tool, SQLT, which effectively identified eight RDBMS bugs (five type-related), all verified by developers, with four subsequently fixed.

Deep learning (DL) systems have been widely utilized across various domains. However, the evolution of DL systems can result in regression faults. In addition to the evolution of DL systems through the incorporation of new data, feature evolution, such as the addition of new features, is also common and can introduce regression faults. In this work, we first investigate the underlying factors that are correlated with regression faults in feature evolution scenarios, i.e., redundancy and contribution shift. Based on our investigation, we propose a novel mitigation approach called FeaProtect, which aims to minimize the impact of these two factors. To evaluate the performance of FeaProtect, we conducted an extensive study comparing it with state-of-the-art approaches. The results show that FeaProtect outperforms the in-processing baseline approaches, with an average improvement of 50.6%–56.4% in terms of regression fault mitigation. We also show that FeaProtect can further enhance the effectiveness of mitigating regression faults by integrating with state-of-the-art post-processing approaches.

The compiler bug duplication problem (where many test failures are caused by the same compiler bug) can lead to huge waste of time and resource in diagnosing test failures produced by compiler testing. It is particularly challenging with regard to the silent compiler bugs that do not produce any error messages. To address this problem, multiple white-box techniques were proposed, but they are inapplicable in many practical scenarios. Black-box techniques are more practical, but the existing ones are less effective as they often rely on irrelevant syntactic information. To bridge this gap, we propose a novel black-box technique (BLADE), which aims to improve the effectiveness of black-box de-duplication by extracting failure-relevant semantic information from failure-triggering test programs in a black-box manner. It first learns failure-relevant semantic information based on intermediate representation learning by employing the classification of failure-triggering and failure-free test programs as the auxiliary objective, and then extracts such information based on model interpretation. Our experiments on four widely-used datasets (collected from GCC and LLVM) show that BLADE significantly outperforms the two existing black-box techniques with an average improvement of 36% and 12% in identifying unique silent compiler bugs when analyzing the same number of test failures respectively, and achieves competitive effectiveness with the state-of-the-art white-box techniques.