Suppose that f (x) E 1[8[x1, ... , xn] and g(x) E 1[8[x1, ... , xn] are two real polynomials of degree d in n variables. If the polynomials f and g are the same up to orthogonal symmetry, a natural question is then what element of the orthogonal group induces the orthogonal symmetry; i.e. to find the element R E O(n) such that f (R inverted perpendicular x) = g(x). One may directly solve this problem by constructing a nonlinear system of equations induced by the relation f (R inverted perpendicular x) = g(x) along with the identities of the orthogonal group. However, this approach becomes quite computationally expensive for larger values of nand d. To give an alternative and significantly more scalable solution to this problem, we introduce the concept of Polynomial-Weighted Principal Component Analys is (PW-PCA). We in particular show how PW-PCA can be effectively computed and how these techniques can be used to obtain a certificate of orthogonal equivalence, that is we find the R E O(n) such that f (R inverted perpendicular x) = g(x). (c) 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Spin glasses occupy a central position in materials science as prototypical systems in which collective freezing emerges from disorder and frustration without conventional structural order. They exhibit slow, history-dependent dynamics that reflect a rugged free-energy landscape. This review provides a critical and integrative account of spin-glass physics, emphasizing how microscopic ingredients (quenched randomness, competing exchange interactions, frustration, and random fields) give rise to macroscopic glassy behavior across materials platforms. We introduce foundational theoretical frameworks, including the Edwards-Anderson and Sherrington-Kirkpatrick models, to establish key concepts such as extensive degeneracy, metastability, and long relaxation times manifested as aging, memory, and rejuvenation. We then synthesize experimental approaches used to identify and characterize spin-glass freezing, combining thermodynamic signatures with dynamical probes that reveal timescale separation and sensitivity to thermal and magnetic histories. Building on these foundations, the review compares spin-glass phenomenology across major material classes, including metallic alloys, insulating oxides, semiconductors, and geometrically frustrated lattices, highlighting the roles of intrinsic versus induced disorder. Recent advances in reentrant and room-temperature spin-glass materials are discussed in the context of functional systems. The review concludes by outlining emerging opportunities enabled by modern computational approaches and by identifying open challenges at the interface of classical and quantum spin glasses.
Traditional industrial robotics relies on rigid programming that is often insufficient for the variability inherent in End-of-Use (EoU) product disassembly, necessitating more adaptive control frameworks. Vision-Language-Action (VLA) models represent a transformative step in this domain by integrating visual perception, natural language understanding, and motor control within a unified architecture. This review systematically examines the convergence of Disassembly Sequence Planning (DSP), VLA architectures, and Human-Robot Collaboration (HRC) to address the challenges of sustainable manufacturing. Based on an analysis of core studies and high-impact preprints from 2019 to January 2026 in these domains, this review evaluates architectural paradigms ranging from end-to-end policies to hierarchical systems. The findings indicate that hierarchical architectures, which decouple high-level symbolic DSP planners from low-level execution policies, offer superior adaptability in unstructured environments. Furthermore, VLA models are identified as key enablers of negotiated autonomy, enabling robots to resolve ambiguities and recover from errors through natural language dialogue with human operators. The review concludes that bridging symbolic planning with embodied action is essential for disassembly systems and proposes a research roadmap focused on data-efficient, transparent, and verifiable human-centric robotic systems.
Anaerobic digestion (AD) is a mature technology for converting organic waste into renewable methane, with growing interest in capturing the co-produced biogenic carbon dioxide (CO2) for atmospheric carbon removal. This study addresses key knowledge gaps by designing and evaluating greenfield, industrial-scale AD facilities integrated with CO2 capture across four representative feedstock categories: wastewater, food waste, industrial ethanol waste, and agricultural/animal waste. Each waste stream was extensively characterized for total solids (TS), volatile solids (VS), and biochemical methane potential (BMP), with results informing life cycle assessments (LCAs) and techno-economic analyses (TEAs). Among the feedstocks, food waste achieved the lowest carbon capture cost at $755/tonne CO2 captured, followed by agricultural/animal waste ($785), industrial ethanol waste ($808), and wastewater ($3,791). Agricultural/animal waste exhibited the highest BMP (544 mL-CH4/g-VS), while wastewater yielded the lowest (341 mL-CH4/g-VS), but had the highest methane content in biogas (79%). When accounting for life-cycle emissions, carbon removal costs were lowest for agricultural/animal waste at $789/tonne CO2, compared to $1,325 for food waste and $2,182 for industrial ethanol waste. Sensitivity analyses identified feedstock capacity, discount rate, methane selling price, CO2 concentration, and biomass transport distance as major cost drivers. Through the design and analysis of feedstock-specific AD systems with integrated CO2 capture, this work provides one of the first comprehensive evaluations of carbon removal via AD. While removal costs remain higher than some alternatives, scaling and technology optimization could enhance the role of AD in integrated waste valorization and carbon management systems.
This Systematization of Knowledge (SoK) examines the evolving landscape of intelligent, interactive honeypots, which are deception-based cybersecurity tools that utilize AI/ML to engage attackers proactively. We introduce a novel taxonomy linking interaction levels to Cyber Kill Chain stages and systematically analyze peer-reviewed studies. Our findings expose key design trends, empirical evaluation strategies, and highlight critical research gaps, including scalability, standardization, and dataset diversity. We discuss the roles of LLMs and reinforcement learning, together with the emerging use of federated learning, in advancing honeypot realism and interactivity. This work aims to guide future research in developing adaptive, resilient deception systems for next-generation cyber defense.
