Search Results (905)

Green and Schroll introduced Brauer configurations to construct Brauer graph algebras and their generalizations, named Brauer configuration algebras, to investigate algebras of tame and wild representation types. It is worth pointing out that giving closed formulas for algebraic and combinatorial invariants (such as their dimensions, the dimensions of their centers, or degree sequences of their induced covering graphs) associated with significant families of Brauer configurations is, in general, a hard problem. The analysis of such algebraic and combinatorial invariants is said to be an extended Brauer analysis of the data defining the configurations. Since finite graphs are examples of Brauer configurations, this paper gives formulas for the dimensions of their induced Brauer configuration algebras and corresponding centers. Brauer configurations also induce some simple graphs called covering graphs. To date, it is not clear which properties a given graph must satisfy to be isomorphic to its induced covering graph. This paper fills this gap by establishing that the so-called hair graphs satisfy this condition. This approach allows us to use properties of morphisms in the graph category to provide set-theoretical solutions of the Yang–Baxter equation. Along these lines, we also note that giving a complete classification of the solutions to the Yang–Baxter equation remains an open problem. Full article

Document-level Event Extraction (DEE) requires identifying complex event records and arguments dispersed across unstructured texts. However, applying general Large Language Models (LLMs) to DEE is intrinsically hindered by their lack of inductive bias for rigid structural constraints, often leading to schema violations and suboptimal performance in complex structural prediction tasks. To address this, we propose the S tructure-Aware Lightweight DEE, termed SALE, which leverages the structural reasoning potential of Code-Based LLMs (Code-LLMs) as a favorable inductive preference. We leverage the natural isomorphism between event schemas and programming object definitions, formulating event extraction as a Python 3.9 class instantiation task to bridge the gap between semantic understanding and structural adherence. Specifically, SALE employs a novel two-stage training paradigm: First, a Structure-Aware Fine-tuning stage injects general structural knowledge via diverse code-style instruction tasks derived from broad Information Extraction (IE) datasets; second, an Event Extraction Alignment stage utilizes a reward-based alignment loss—optimized via policy gradient—to adapt this capability to document-level intricacies. The effectiveness of SALE stems from the synergy between its structure-aware prompting and the specialized alignment stage built on a code-oriented backbone. Extensive experiments on established news-domain benchmarks (RAMS and WikiEvents) demonstrate that our approach significantly outperforms representative supervised and general LLM baselines in cross-task zero-shot and few-shot transfer settings (e.g., surpassing supervised baselines by over 7% in F1 score). Furthermore, SALE maintains a highly efficient inference profile and parameter-efficient footprint, offering a practical and scalable solution for vertical domain applications. Full article

The Flexible Job-shop Scheduling Problem (FJSP), a pivotal NP-hard challenge in intelligent manufacturing, has been increasingly addressed by Deep Reinforcement Learning (DRL) methods. However, existing approaches face a dilemma: Proximal Policy Optimization (PPO) ensures stability but suffers from conservative exploration, while Soft Actor–Critic (SAC) enhances exploration but lacks stability in discrete scheduling spaces. To resolve this trade-off, this study proposes PPO-Graph Explorer, a novel framework that integrates a Graph Isomorphism Attention Network (GIAN) with an Entropy-Adjusted PPO (EAE-PPO). Unlike generic Graph Transformers, our GIAN employs a structure-aware hybrid design specifically tailored for FJSP’s disjunctive graph topology. EAE-PPO introduces a structured exploration curriculum that enables the agent to mimic aggressive search behaviors early in training without sacrificing on-policy stability. Extensive experiments on standard benchmarks (Brandimarte, Hurink, Dauzère–Pérès) demonstrate our method’s superiority. Compared to state-of-the-art DRL baselines, it achieves an average makespan gap reduction of 5.1 percentage points with zero statistical outliers. Qualitative analysis further reveals an 8.95% reduction in makespan on representative instances, accompanied by a significant increase in average machine utilization from 89.0% to 98.1%. Full article

Chiral and racemic forms of a pyridyl ligand (R-L and rac-L, respectively), containing urea groups at their core and synthesised by the condensation of 3-aminopyridine and α-methylbenzylisocyante, were incorporated into silver complexes. The resulting species depend on the enantiopurity of the ligand alongside an influence from the counter-anion. The enantiopure ligand generated isomorphous, one-dimensional polymeric compounds [Ag(R-L)X] (where X = NO₃, CF₃SO₃) or [Ag(R-L)]X (where X = BF₄, PF₆). The polymeric chains, connected by N and O coordination of the ligands, have outwards facing urea groups that form hydrogen bonds to the counter-anions, which play little role in determining the overall structure. Despite all syntheses containing an excess of Ag(I) salt, the racemic ligand formed only discrete complexes of [Ag(rac-L)₂]⁺ in the presence of each of the above anions. Three of these complexes contain ligands of the same chirality (i.e., complexes with R,R and S,S ligand pairs within the centrosymmetric structures) with only the PF₆-containing compound being different. The anions play a role in dictating the structure of hydrogen-bonded chains, although PF₆⁻ is unique with urea···urea interactions present between complexes. Overall, this system highlights the nuances associated with predicting the structure, and even speciation, of related chiral/achiral systems in addition to influences of counter-anions on structural motifs. Full article

This article develops a comprehensive theory of multiary graded polyadic algebras, extending the classical concept of group-graded algebras to higher-arity structures. We introduce the notion of grading by multiary groups and investigate various compatibility conditions between the arity of algebra operations and grading group operations. Key results include quantization rules connecting arities, classification of graded homomorphisms, the First Isomorphism Theorem for graded polyadic algebras and concrete examples including ternary superalgebras and polynomial algebras over n-ary matrices. The theory reveals fundamentally new phenomena not present in the binary case, such as the existence of higher power gradings and nontrivial constraints on arity compatibility. Full article

A theorem of Sheshadri (Proc. Nat. Acad. Sci. USA 44 (1958) 456–458) shows that, when $\Lambda$ is a commutative principal ideal domain, finitely generated projective modules over the polynomial ring $\Lambda \left[t\right]$ are all free. The ring $\Gamma$ of Hurwitz quaternions, that is, the unique maximal order in the ring of rational quaternions, is the simplest example of a non-commutative principal ideal domain which is not a division ring. In contrast to the commutative case, we show that $\Gamma \left[t\right]$ has infinitely many isomorphically distinct projective modules; these are stably free of rank 1. Full article

This review develops a unified geometric framework for synthesizing global asymptotic laws, termed classical entanglement. The central tool is the entanglement operator, a Minkowski–$L_a$ metric blend that couples asymptotic regimes through an index $a>1$, producing a nonlinear global state whose intermediate region is metrically non-separable and cannot be written as a linear combination of its limits. The framework reveals a universal transition knee whose curvature scales linearly with a, independent of amplitudes or local scales. We show that this geometric mechanism encompasses Orlicz norms, weighted Hölder metrics, and iterated Hölder constructions, the latter being structurally isomorphic to self-similar root approximants. A conceptual “Rosetta Stone” links practitioner terminology, geometric meta-language, and functional-analytic structures, clarifying how classical entanglement unifies empirical blending, metric curvature, and Calderón-type interpolation. Applications to turbulence (Darcy friction factor), fractional dynamics, and scale-dependent diffusion illustrate how classical entanglement provides stable, asymptotically consistent global states across multi-scale systems. Full article

A graph is said to be symmetric if the action of its automorphism group on the set of arcs is transitive (arc-transitive). Building upon prior work regarding the classification of symmetric graphs of valency five, this article investigates connected symmetric graphs of order $40pq$, where p and q are distinct primes. We establish that the full automorphism group of any such graph is isomorphic to ${\mathbb{Z}}_5\times \mathrm{PSL}(2,479)$, $\mathrm{PSL}(2,479):D_{10}$, or ${\mathbb{Z}}_5\times (\mathrm{PSL}(2,479):{\mathbb{Z}}_2)$. Moreover, the vertex stabilizers are shown to be isomorphic to $A_5$ in the first instance and to $S_5$ in the latter two cases. Full article

In this study, we construct a prestack over the site of open subsets of the complex plane. Its total category has the set of objects canonically isomorphic to the set of all spaces of pseudoanalytic functions, and this is over all open subsets of the complex plane with respect to all the possible generating pairs. This is carried out by defining suitable morphisms between the spaces of pseudoanalytic functions over the same open subset using pseudodifferentiation, and, accordingly, obtaining for each open subset of the complex plain a category whose objects are the spaces of pseudoanalytic functions defined on the subset. It is shown that assigning to open sets the appropriate categories of spaces of pseudoanalytic functions along with suitable restriction functors for inclusions of open subsets results in a 2-presheaf satisfying the gluing of morphisms. A sufficient condition for a descent datum to be effective is presented, relating the effectiveness of a descent datum to the admissibility of coefficients of a Carleman–Bers–Vekua equation. Full article

This study extends the literature on peer effects by revealing that technological linkages drive cross-firm emulation of corporate governance practices, a core determinant of firms’ sustainable development capacity. Using a comprehensive sample of China’s A-share listed firms over the period 2004–2022, we document that R&D-intensive firms strategically extract governance insights from their technological peers. Our empirical analyses identify three distinct mechanisms underlying this governance emulation: information bridging, competitive isomorphism, and market feedback. Furthermore, this peer effect exhibits significant heterogeneity across firms with different corporate performance, R&D investment levels, and resource intensity. Notably, firms adopting peer-based governance practices experience a substantial improvement in financial performance, which reflects rational adaptation rather than blind herd behavior. Overall, this paper introduces technological peer relationship as a novel determinant of governance decisions and provides a micro-foundation for how firms optimize their governance arrangements to enhance long-term sustainable operation within technologically interdependent markets. Full article

Graph Neural Networks (GNNs) have become a central methodology for modelling biological systems where entities and their interactions form inherently non-Euclidean structures. From protein interaction networks and gene regulatory circuits to molecular graphs and multi-omics integration, the relational nature of biological data makes GNNs particularly well-suited for capturing complex dependencies that traditional deep learning methods fail to represent. Despite their rapid adoption, the effectiveness of GNNs in bioinformatics depends not only on model design but also on how biological graphs are constructed, parameterised and trained. In this review, we provide a structured framework for understanding and applying GNNs in bioinformatics, organised around three key dimensions: (1) graph construction and representation, including strategies for deriving biological networks from heterogeneous sources and selecting biologically meaningful node and edge features; (2) GNN architectures, covering spectral and spatial formulations, representative models such as Graph Convolutional Networks (GCNs), Graph Attention Networks (GATs), Graph Sample and AggregatE (GraphSAGE) and Graph Isomorphism Network (GIN), and recent advances including transformer-based and self-supervised paradigms; and (3) applications in biomedical domains, spanning disease–gene association prediction, drug discovery, protein structure and function analysis, multi-omics integration and biomedical knowledge graphs. We further examine training considerations, including optimisation techniques, regularisation strategies and challenges posed by data sparsity and noise in biological settings. By synthesising methodological foundations with domain-specific applications, this review clarifies how graph quality, architectural choice and training dynamics jointly influence model performance. We also highlight emerging challenges such as modelling temporal biological processes, improving interpretability, and enabling robust multimodal fusion that will shape the next generation of GNNs in computational biology. Full article

We used synchrotron X-ray diffraction (XRD) and ac-impedance spectroscopy (AIS) to uncover the structural and chemical modifications undergone by RbH₂PO₄ (RDP) at intermediate temperatures (150 °C < T < 300 °C) and investigate their relationship with RDP’s proton conductivity, σ. Nyquist plots collected on RDP samples sealed in a small volume (~50 mL) of dry air show a gradual increase in σ upon heating from 180 to 260 °C, but not the three-order-of-magnitude superprotonic jump observed in the Cs-based compound CsH₂PO₄ (CDP) within the same temperature range. Correspondingly, XRD measurements using synchrotron radiation (λ = 0.922 Å) on RDP crystalline powders sealed in a quartz capillary exhibit no evidence of a monoclinic-to-cubic superprotonic phase transition like the one observed in CDP. Instead, these temperature-resolved powder XRD patterns demonstrate that the intermediate-temperature RDP monoclinic phase (P2₁/m, a = 7.733 Å, b = 6.189 Å, c = 4.793 Å, and β = 109.21 deg) persists up to the melting point of the title compound. Our most significant finding comes from heating RDP under high pressure (P = 1 GPa), which leads to markedly different structural behavior. Indeed, our full profile refinements against XRD data collected on RDP crystals compressed at ~1 GPa show evidence of a polymorphic phase transition (at T_c = 300 °C) to a high-temperature cubic phase (Pm-3m, a = 4.784 Å) that is isomorphic with its CDP counterpart. This is significant, as it indicates that the superprotonic conduction in phosphate solid acids is not cation-specific, and a general highly efficient proton conduction mechanism is present in the high-temperature phases of these materials. Full article

Equimolar crystals of a high-entropy Ca_0.25Sr_0.25Ba_0.25Nd_0.25F_2.25 (CaSrBaNdF₉) fluoride solid solution were grown from a melt by the Bridgman technique, and their optical, electrical, and thermal properties were studied for the first time. This solid solution crystallizes in a fluorite-type structure (space group Fm-3m with lattice parameter a = 5.807 Å), is transparent over a wide spectral range, and has a refractive index of n_D = 1.5035(5). In terms of ionic conductivity (σ_dc increases monotonically from 3.7 × 10⁻⁵ to 3.9 × 10⁻⁴ S/cm in the studied temperature range of 643–810 K), it significantly exceeds the parameters of binary and ternary NdF₃-based single crystals, such as M_1−xNd_xF_2+x (M = Ca, Sr, Ba; x = 0.24–0.25) and Ca_0.58Sr_0.21Nd_0.21F_2.21. The grown multicomponent material is a hard (H_V~3.6 GPa) isomorphic-capacious crystalline matrix for various applications in solid-state ionics, optics and photonics, and opens up prospects for the development of new functional isotropic optical crystalline materials in quaternary CaF₂–SrF₂–BaF₂–RF₃ and higher-order complex fluoride systems nMF₂–mRF₃, where n + m ≥ 4, M and R are ions of alkaline earth and rare earth elements, respectively. Full article

International accreditation has become a pivotal mechanism through which universities outside Europe seek legitimacy and alignment with global quality regimes, particularly regarding sustainable development goals (SDGs). This study investigates how non-EU universities adapt to ASIIN accreditation, focusing on its role in developing a sustainable quality culture that supports long-term educational excellence and social responsibility. Drawing on new institutionalism, the analysis views accreditation as a process of institutional change under isomorphic pressures necessary for the sustainability of quality assurance (QA). Data were derived from a triangulated dataset, including 78 publicly available final accreditation reports via the DEQAR database and expert on-site observations across multiple non-EU universities. The analysis identifies systemic challenges, such as ‘facade conformity’ in learning outcomes and fragmented QA loops, which reveal an ‘adaptive lag’ impeding the sustainable implementation of quality standards. The study concludes by proposing an “Expert-Facilitated, Institutionally-Embedded Evidence Loop” framework to bridge external compliance and internal quality enhancement, thereby ensuring the long-term viability and global relevance of engineering education in alignment with SDGs. Full article

Recent advances in artificial intelligence have made power efficiency a primary objective in system design. In this context, stochastic computing (SC), which processes probabilistic bitstreams using simple logic, and spiking neural networks (SNNs), a neuromorphic paradigm, have gained prominence as alternative approaches. This study proposes a Stochastic Computing Neural Network (SC-NN) framework that minimizes the intrinsic errors of stochastic computing and leverages the isomorphism between one-count operations on bitstreams and spike-rate computations in spiking neural networks, yielding improvements in accuracy and hardware efficiency. In contrast to earlier studies that utilized independent random number sequences of 10 bits or higher, our study employed a practically implementable 8-bit linear feedback shift Register (LFSR)-based pseudo-random bitstream. Using 4 taps and 255 seeds improves the realism of the hardware. Despite the inherent accuracy ceiling of pseudo-random sequences, the proposed method achieves higher accuracy. Applied to an 8-bit SC-based neural network accelerator, the proposed design improves accuracy by 35% over a conventional FSM baseline, while reducing power and area by 43.8% and 17.2%, respectively, and decreasing delay by 5.5%. These improvements translate to a 2.3× enhancement in the Figure of Merit (FoM), which was further verified through physical layout and FPGA results. Overall, this work introduces a new paradigm that enables simultaneous gains in accuracy and efficiency for low-power AI by suppressing the error sources and embedding the structural similarity between SNNs and SC into the design. Full article