December 2025

Let 1 < a1 < a2 < · · · be integers with ( sum_{k=1}^infty a_k^{-1}<infty ), and set ( F(s)=1+sum_{k=1}^infty a_k^{-s}, qquad Re s>1. ) A question of Erdős and Ingham, recorded as Erdős Problem #967 in a compilation by T. F. Bloom (accessed 2025–12–01), asks whether one always has ( F(1+it)neq 0 ) for all real t. This paper does not resolve the problem; instead, it develops a modern dynamical-systems framework for its study. Using the […]

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To address the practical challenges of diverse anomaly patterns, strongly coupled dependencies, and high labeling costs in large-scale complex infrastructures, this paper presents an unsupervised anomaly detection method that integrates graph neural networks with Transformer models. The approach learns normal system behavior and identifies deviations without relying on anomaly labels. Infrastructure components are abstracted as nodes in a dependency graph, where nodes are characterized by multiple source observability signals. A graph encoder aggregates neighborhood information to produce structure-enhanced […]

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In the modern microservice environment, library dependencies for inter-system communication have become bloated, and conflicts and complications during build and operation have become problems. In particular, in the conventional communication architecture that depends on the MySQL database, the multi-layer dependencies included in texttt{libmysqlclient} restrict the flexibility of system design. In this study, a replication-protocol-compatible patch was applied to the lightweight MySQL client library Trilogy, and a loosely coupled, low-footprint IPC library connecting the control plane and the data […]

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Background: Automated visual field testing is fundamental in ophthalmology, but differences in stimulus scaling and luminance between devices hinder direct comparison of sensitivity values. Virtual reality (VR)–based perimetry has emerged as a portable alternative, yet its relationship with conventional perimetry requires clarification. Methods: This prospective cross-sectional study included 60 healthy participants stratified into younger (&lt; 50 years) and older (≥ 50 years) groups. Differential light sensitivity was assessed in the right eye using Humphrey Automated Perimetry (HFA 30-2) […]

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We integrate static taint analysis with dynamic fuzzing to target high-impact kernel code paths. A pruning mechanism removes irrelevant taint propagation, while symbolic constraints are applied only to tainted regions to control overhead. Evaluated on 18 kernel subsystems, the hybrid fuzzer achieves 44% more taint-relevant path hits, identifying 13 bugs, including buffer overflows and pointer dereferences. Symbolic overhead remains limited (≤18%) through selective propagation. This hybrid design efficiently directs fuzzing toward semantically meaningful kernel logic, demonstrating a productive […]

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Lexicographic Preference Trees (LP-Trees) offer a compact and expressive framework for modeling complex decision-making scenarios. However, efficiently measuring similarity between complete or partial structures remains a challenge. This study introduces PLPSim, a novel metric for quantifying alignment between Partial Lexicographic Preference Trees (PLP-Trees), and develops three coalition formation algorithms—HRECS1, HRECS2, and HRECS3—that leverage PLPSim to group agents with similar preferences. We further propose ContractLex and PriceLex protocols (comprising five lexicographic protocols CLF, CFB, CFW, CFA, CFP), along with […]

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In the theory of mixed-type equations, there are many works in bounded domains with smooth boundaries bounded by a normal curve for first and second-kind mixed-type equations. In this paper, for a second-kind mixed-type equation in an unbounded domain whose elliptic part is a horizontal half-strip, a Bitsadze-Samarskii type problem is investigated. The uniqueness of the solution is proved using the extremum principle, and the existence of the solution is proved by the Green’s function method and the […]

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This study addresses the challenge of long-term dependency modeling in agent behavior planning for long-horizon tasks and proposes a memory-driven agent planning framework. The method introduces hierarchical memory encoding and dynamic memory retrieval structures, enabling the agent to selectively retain and effectively utilize historical information across multiple time scales, thereby maintaining policy stability and goal consistency in complex dynamic environments. The core idea is to construct an interaction mechanism between short-term and long-term memory, where attention-guided retrieval integrates […]

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Large Language Model (LLM)-based multi-agent systems have emerged as a promising paradigm for tackling complex tasks that exceed individual agent capabilities. However, existing approaches often suffer from coordination inefficiencies, a lack of trust mechanisms, and suboptimal role assignment strategies. This paper presents a novel trust-aware coordination framework that enhances multi-agent collaboration through dynamic role assignment and context sharing. Our framework introduces a multi-dimensional trust evaluation mechanism that continuously assesses agent reliability based on performance history, interaction quality, and […]

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This paper addresses the challenges in traditional enterprise performance analysis, including complex multi-source data structures, ambiguous indicator correlations, and poor decision interpretability. It proposes an enterprise performance optimization decision model that integrates knowledge graphs with causal inference. The model constructs a multi-entity and multi-relation knowledge graph to semantically integrate heterogeneous information from financial, market, and operational dimensions, enabling high-level representation of structured relationships among enterprise features. It further incorporates causal structure learning and inference mechanisms to identify key […]

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