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Detection of anomalous situations for complex mission-critical systems hold paramount importance when their service continuity needs to be ensured. A major challenge in detecting anomalies from the operational data arises due to the…
Anomaly detection is crucial for understanding unusual behaviors in data, as anomalies offer valuable insights. This paper introduces Dependency-based Anomaly Detection (DepAD), a general framework that utilizes variable dependencies to…
Unlike code completion, debugging requires localizing faults and applying targeted edits. We observe that frontier LLMs often regenerate correct but over-edited solutions during debugging. To evaluate how far LLMs are from precise…
We consider the infinite-horizon average-reward restless bandit problem. We propose a novel \emph{two-set policy} that maintains two dynamic subsets of arms: one subset of arms has a nearly optimal state distribution and takes actions…
We investigate a modified version of the $AB$ random sequential adsorption model. Specifically, this model involves the deposition of two distinct types of particles onto a lattice, with the constraint that different types cannot occupy…
The alternating direction method of multipliers (ADMM) is widely used for solving large-scale semidefinite programs (SDPs), yet on instances with multiple primal-dual optimal solution pairs, it often enters prolonged slow-convergence…
Control systems are inevitably affected by external disturbances, and a major objective of the control design is to attenuate or eliminate their adverse effects on the system performance. This paper presents a disturbance rejection approach…
Stable basis algebras were introduced by Fountain and Gould and developed in a series of articles. They form a class of universal algebras, extending that of independence algebras. If a stable basis algebra $\mathbb{B}$ of finite rank…
We consider a first-order aggregation model in both discrete and continuum formulations and show rigorously how it can be obtained as zero inertia limits of second-order models. In the continuum case the procedure consists in a macroscopic…
Error bound analysis, which estimates the distance of a point to the solution set of an optimization problem using the optimality residual, is a powerful tool for the analysis of first-order optimization algorithms. In this paper, we use…
In this paper, we will develop a systematic approach to deriving guaranteed bounds for approximate dynamic programming (ADP) schemes in optimal control problems. Our approach is inspired by our recent results on bounding the performance of…
We establish sharp global regularity results for solutions to nonhomogeneous, nonunifomrly elliptic systems with zero boundary conditions. In particular, we obtain everywhere Lipschitz continuity under borderline Lorentz assumptions on the…
The Bethe Ansatz equations for the one-dimensional Hubbard model are reexamined. A new procedure is introduced to properly include bound states. The corrected equations lead to new elementary excitations away from half-filling.
The chase procedure is a fundamental algorithmic tool in database theory with a variety of applications. A key problem concerning the chase procedure is all-instances termination: for a given set of tuple-generating dependencies (TGDs), is…
In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…
Anomaly detection (AD) has been extensively studied and applied in a wide range of scenarios in the recent past. However, there are still gaps between achieved and desirable levels of recognition accuracy for making AD for practical…
Acyclic schemes posses known benefits for database design, speeding up queries, and reducing space requirements. An acyclic join dependency (AJD) is lossless with respect to a universal relation if joining the projections associated with…
Transformers have recently been shown to be capable of reliably performing logical reasoning over facts and rules expressed in natural language, but abductive reasoning - inference to the best explanation of an unexpected observation - has…
We derive a priori residual-type bounds for the Arnoldi approximation of a matrix function and a strategy for setting the iteration accuracies in the inexact Arnoldi approximation of matrix functions. Such results are based on the decay…
The classical concept of bounded completeness and its relation to sufficiency and ancillarity play a fundamental role in unbiased estimation, unbiased testing, and the validity of inference in the presence of nuisance parameters. In this…