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26 pages, 3304 KB  
Article
Geo-CRDT: Geometry-Aware Collaborative Spatial Editing with Robust Topology Preservation
by Pengcheng Zhang, Zhongbo Shao, Lin Xu, Jingju Gao, Tian Yu, Jifa Chen and Ling Hu
ISPRS Int. J. Geo-Inf. 2026, 15(7), 302; https://doi.org/10.3390/ijgi15070302 - 2 Jul 2026
Viewed by 106
Abstract
In distributed Geographic Information Systems (GIS), preserving topological validity without sacrificing real-time interactivity under high-frequency concurrent editing of spatial polygons remains a persistent challenge. Recent distance-based heuristic methods suffer from scale-dependent bottlenecks and unreliable topology preservation, while more robust application-layer caching mechanisms still [...] Read more.
In distributed Geographic Information Systems (GIS), preserving topological validity without sacrificing real-time interactivity under high-frequency concurrent editing of spatial polygons remains a persistent challenge. Recent distance-based heuristic methods suffer from scale-dependent bottlenecks and unreliable topology preservation, while more robust application-layer caching mechanisms still incur severe queuing latency under intense concurrency. To overcome these limitations, we propose Geo-CRDT, a geometry-aware distributed data structure that integrates spatial constraints directly into its underlying architecture. By dynamically isolating concurrent spatial entanglements into a strictly bounded local scope S, the system deterministically resolves complex 2D conflicts via scalar projection, repairing the local topology in O(|S|) time. Rigorous simulations and a 15-participant real-world case study validate that Geo-CRDT sustains low-latency responsiveness and structural reliability under extreme concurrency, offering a robust foundation for large-scale crowdsourced spatial collaboration. Full article
19 pages, 12795 KB  
Article
Deep Spatiotemporal Surrogate Modeling of Natural Gas Pipeline Networks for Heterogeneous Equipment and Long-Horizon Forecasting
by Hongtao Diao, Weichao Yu, Chenxiao Zhao, Xiong Yin, Jie Chen, Dongyan Zheng, Yuming Lin, Chen Liu and Yuxuan He
Processes 2026, 14(13), 2069; https://doi.org/10.3390/pr14132069 - 25 Jun 2026
Viewed by 176
Abstract
Accurate multistep-ahead prediction of natural gas pipeline-network states is essential for intelligent dispatching, yet such networks contain physically heterogeneous components (gas sources, pipelines, compressors, valves), and historical states and future dispatching commands are decoupled in both temporal scale and physical semantics. This causes [...] Read more.
Accurate multistep-ahead prediction of natural gas pipeline-network states is essential for intelligent dispatching, yet such networks contain physically heterogeneous components (gas sources, pipelines, compressors, valves), and historical states and future dispatching commands are decoupled in both temporal scale and physical semantics. This causes conventional data-driven models to suffer from semantic entanglement and cumulative error during long-horizon forecasting. This study proposes a deep spatiotemporal surrogate model with three coordinated designs: (i) type-specific feature encoding combined with global latent-graph mapping and a shared graph convolutional network (GCN) to disentangle heterogeneous-equipment attributes and represent network-wide topological coupling; (ii) a residual-gated temporal coupling mechanism that adaptively fuses historical operating inertia with future external disturbances; and (iii) a temporal-gradient multi-objective loss with a 12-step autoregressive rolling strategy over a 6 h horizon to suppress cumulative divergence. On 85,248 samples built from field monitoring data and commercial mechanistic simulations, the model attains median relative errors of 1.15% for nodal pressure and 2.10% for pipeline flow, capturing macroscopic pressure decay and high-frequency transient flow induced by valve and compressor switching without noticeable delay, providing an efficient tool for online simulation, real-time warning, and decision support in complex natural gas pipeline networks. Full article
(This article belongs to the Section Energy Systems)
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31 pages, 548 KB  
Article
Measure-Theoretic Diagnostics of Architectural Entanglement in Asymmetric Multiprocessing Systems: A Boltzmann Uniqueness Approach
by Steven D. Harris, Christopher D. Gill and Roger D. Chamberlain
Modelling 2026, 7(4), 124; https://doi.org/10.3390/modelling7040124 - 23 Jun 2026
Viewed by 220
Abstract
Orchestration of Asymmetric Multiprocessing Platforms (AMPs), such as ARM big.LITTLE, frequently relies on the heuristic assumption of cluster independence, wherein high-performance (“Big”) and high-efficiency (“Little”) cores operate as computationally orthogonal resources. These cores are partitioned into “islands” of separate power/performance clusters, operating on [...] Read more.
Orchestration of Asymmetric Multiprocessing Platforms (AMPs), such as ARM big.LITTLE, frequently relies on the heuristic assumption of cluster independence, wherein high-performance (“Big”) and high-efficiency (“Little”) cores operate as computationally orthogonal resources. These cores are partitioned into “islands” of separate power/performance clusters, operating on independent/voltage frequency rails. However, these platforms share resources, including Last-Level Cache (LLC), main memory, and interconnects across all cores. Therefore, we assume that islands interact, operating in a functionally “coupled state.” To conduct a measure-theoretic evaluation of this assumption, we apply the Boltzmann uniqueness theorem, recently demonstrated to be the singular method to determine the veracity of this assumption. Mathematically, we define an “uncoupled” system as one whose joint resource measurement is strictly the convolution of its subsystem measures. We evaluate two distinct AMP topologies—Orange Pi 5 and Cubie A7A under controlled saturation—and demonstrate a systemic failure of convolution commutativity. We subsequently expand this investigation to high-performance x86 hybrid architectures via the Intel i7-12800H platform. Our findings, characterized by significant negative power correlations and the failure of predictive convolution models, constitute a counterexample for cluster independence. We identify shared architectural resources, specifically the LLC and shared power rails, as the likely physical mechanisms of “architectural entanglement,” rendering traditional additive performance models underspecified. Full article
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24 pages, 4627 KB  
Article
A State Space Model-Driven Feature Disentanglement Network for Real-Time Detection of Morphologically Complex Insect Pests in Agricultural Fields
by Jiaren Sun, Yating Jiang, Shuai Teng, Zongchao Liu and Nuo Chen
Modelling 2026, 7(3), 122; https://doi.org/10.3390/modelling7030122 - 21 Jun 2026
Viewed by 225
Abstract
Accurate detection of field insect pests remains a significant challenge for precision agriculture due to the elongated and variable morphology of the target organisms, their frequent resemblance to complex background textures, and the long-tail distribution of species in natural datasets. While deep convolutional [...] Read more.
Accurate detection of field insect pests remains a significant challenge for precision agriculture due to the elongated and variable morphology of the target organisms, their frequent resemblance to complex background textures, and the long-tail distribution of species in natural datasets. While deep convolutional neural networks (CNNs) have advanced the field, they are often constrained by a limited effective receptive field and the entanglement of semantic and spatial features, which can lead to elevated false-positive rates and missed detections for low-contrast or rare targets. This paper introduces a novel detection framework that integrates state space modeling with multi-stream feature disentanglement to address these limitations. First, a visual state space module is employed as the backbone feature extractor, enabling the establishment of a global receptive field with linear computational complexity and thereby improving the perception of long-range morphological structures. Second, a Topological Feature Disentanglement Pyramid Network is proposed. This architecture explicitly separates feature representations into semantic and spatial streams and recombines them through graph convolutional interactions, which serves to suppress background interference and enhance localization precision. A meta-auxiliary detection head, active only during training, is introduced to amplify supervision signals for hard, low-contrast samples via adversarial gradient modulation. Furthermore, an implicit neural radiance field augmentation pipeline is used to generate physically consistent synthetic views of underrepresented pest classes, mitigating the negative effects of long-tail data distributions. Experimental evaluations on the public BAU-Insectv2 benchmark demonstrate that the proposed method achieves a mean average precision (mAP@0.5) of 81.8%, representing a 4.4-percentage-point improvement over a comparable baseline, while maintaining a compact parameter count of 2.33 M and an inference speed of 178.6 FPS. The framework exhibits particular efficacy in detecting elongated, minute, and rare pests, suggesting a promising technical approach for real-time, field-based pest surveillance in precision agriculture. Full article
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24 pages, 2473 KB  
Article
Quantum Deep Q-Network for Intelligent Packet Routing in 6G Heterogeneous Wireless Networks
by Tong Xie, Taoyong Li, Xinxin Yuan and Jiacheng Ni
Appl. Sci. 2026, 16(12), 6096; https://doi.org/10.3390/app16126096 - 16 Jun 2026
Viewed by 146
Abstract
Intelligent packet routing in sixth-generation (6G) heterogeneous wireless networks must contend with stochastic link failures, heterogeneous delay profiles, and the severe memory constraints of edge nodes. We propose a quantum deep Q-network (Q-DQN) that replaces the multi-layer perceptron in a standard DQN agent [...] Read more.
Intelligent packet routing in sixth-generation (6G) heterogeneous wireless networks must contend with stochastic link failures, heterogeneous delay profiles, and the severe memory constraints of edge nodes. We propose a quantum deep Q-network (Q-DQN) that replaces the multi-layer perceptron in a standard DQN agent with a six-qubit variational quantum circuit (VQC) employing ring-topology entanglement and angle embedding. The total trainable parameter count follows the closed-form expression |ϕ|=12L+7n, growing at only seven parameters per additional network node. On a 10-node heterogeneous topology with stochastic link failures, Q-DQN achieves an average end-to-end delay of 54.29±1.72 ms with only 106 parameters, a 49.6× reduction relative to the MLP-based DQN baseline (5258 parameters, 52.89±2.67 ms). A three-seed scalability evaluation across n{6,8,10,12} nodes shows that under a limited 200-episode training budget DQN converges more consistently, while Q-DQN matches DQN performance under full 500-episode training at a fraction of the parameter cost. Ablation experiments confirm that local-topology entanglement substantially outperforms full-connection alternatives. These results indicate that VQC-based routing agents can match classical counterparts at a fraction of the parameter cost, providing a path toward ultra-lightweight intelligent routing in 6G edge deployments. Full article
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33 pages, 489 KB  
Review
Geometry of Quantum Information Beyond Complex Numbers: A Review from Clifford Algebras, Division Algebras and Hopf Fibrations
by Johan H. Rúa Muñoz and Santiago Pineda Montoya
Symmetry 2026, 18(6), 1024; https://doi.org/10.3390/sym18061024 - 14 Jun 2026
Viewed by 259
Abstract
We develop a comparative synthesis of quantum-information geometry beyond complex numbers, with emphasis on what different algebraic frameworks contribute to information-processing structure rather than on their formal novelty alone. The organizing idea is a layer-by-layer test of the standard complex Hilbert-space formalism: each [...] Read more.
We develop a comparative synthesis of quantum-information geometry beyond complex numbers, with emphasis on what different algebraic frameworks contribute to information-processing structure rather than on their formal novelty alone. The organizing idea is a layer-by-layer test of the standard complex Hilbert-space formalism: each non-complex or deformed framework modifies the scalar field, phase group, projective state space, Born-probability semantics, composition rule, measurement geometry, symmetry algebra or representation category. The central thesis is that such frameworks are physically meaningful when they identify which assumptions make complex quantum mechanics operationally stable: positive probabilities, associative multipartite composition, reversible dynamics, experimentally testable phases, locality constraints, informationally complete measurements, error bases and clear operational semantics. Real quantum theory probes the necessity of complex phases and local tomography; quaternionic quantum mechanics probes non-Abelian phase while retaining associativity and admitting complex embeddings; octonionic proposals probe the boundary where exceptional geometry survives but generic circuit composition is obstructed by non-associativity; Jordan algebras test ordered probabilistic state spaces; Clifford algebras and Bott periodicity provide the spinorial and topological grammar connecting gates, Hopf maps and periodic dimensions; and quantum-group or q-deformed constructions probe coproducts, braiding and representation categories rather than scalar amplitudes. We distinguish three roles that are often conflated: genuine hypercomplex kinematics, Hopf-fibration coordinates for ordinary complex multipartite entanglement, and deformed algebraic or categorical structures. The resulting map separates established equivalence and experimental-constraint results from useful representation tools and speculative programs, while identifying concrete open problems for non-complex quantum information. Full article
23 pages, 6479 KB  
Review
Stereoselective Synthesis of Topologically Chiral Knots and Links: Synthesis and Applications
by Benteng Ma, Yan Sun, Haifeng Tian, Xiao Zhang, Yuheng Ju, Saiwen Gao and Lin Wu
Molecules 2026, 31(11), 1953; https://doi.org/10.3390/molecules31111953 - 4 Jun 2026
Viewed by 246
Abstract
Topologically chiral molecular knots and links represent a unique class of stereochemical architectures in which handedness is encoded by the global crossing pattern of an entangled framework rather than by a local stereogenic element. Their configurational robustness and shape-persistent chiral environments make them [...] Read more.
Topologically chiral molecular knots and links represent a unique class of stereochemical architectures in which handedness is encoded by the global crossing pattern of an entangled framework rather than by a local stereogenic element. Their configurational robustness and shape-persistent chiral environments make them promising platforms for molecular recognition, catalysis, chiroptical response, and spin-selective transport. This review summarizes recent progress in the stereoselective synthesis of topologically chiral knots and links, with emphasis on chirality transfer from point, axial and helical elements into persistent topological handedness. Major synthetic strategies are organized into helicity-driven approaches, template-free dynamic systems, coordination-driven self-assembly, and chiral self-sorting. The applications of knots in host–guest confinement, asymmetric catalysis, chiral recognition, and spin-selective transport are also discussed. Full article
(This article belongs to the Special Issue New Sights in Stereoselective Synthesis)
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13 pages, 1540 KB  
Article
Concurrence Percolation Behavior in Diluted Quantum Networks
by Gaogao Dong, Yili Shen, Xinqi Hu and Ruijin Du
Entropy 2026, 28(6), 590; https://doi.org/10.3390/e28060590 - 26 May 2026
Viewed by 282
Abstract
The evolution of connectivity in quantum networks under decoherence and link degradation is a central problem in quantum information, calling for further understanding of the nature of its transition during structural network degradation. By diluting each link with probability 1f, [...] Read more.
The evolution of connectivity in quantum networks under decoherence and link degradation is a central problem in quantum information, calling for further understanding of the nature of its transition during structural network degradation. By diluting each link with probability 1f, we focus on connectivity strength transitions in diluted hierarchical scale-free quantum networks, the (u,v) flowers, which are analytically tractable through two adjustable path-length parameters, uv. Incorporating quantum concurrence percolation and comparing it with classical percolation, we analyze the transitions of critical thresholds for various values of f and v from analytical, numerical, and simulation perspectives. The results demonstrate that quantum percolation exhibits consistently lower critical thresholds than classical percolation, even under various topologies and dilution levels. Our work implies that quantum multipath entanglement provides an intrinsic compensatory mechanism against structural degradation and that the hierarchical scale-free topology contributes to the failure resistance and robustness of quantum networks with multipath coupling. Full article
(This article belongs to the Special Issue Analysis of Critical Behavior in Complex Systems)
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36 pages, 3212 KB  
Review
Bipolar Entropy vs. Entropy/Negentropy: From Quantum Emergence to Agentic AI&QI with Collectively Entangled Bipolar Strings ER ≥≥ EPR
by Wen-Ran Zhang and Hengyu Zhang
Quantum Rep. 2026, 8(2), 36; https://doi.org/10.3390/quantum8020036 - 20 Apr 2026
Viewed by 2745
Abstract
While the quantum emergence of spacetime is becoming a major research topic in physics, the quantum emergence of intelligence has not been widely researched in quantum information science (QIS). Following causal-logical quantum gravity theory, bipolar entropy vs. entropy and negative entropy (or negentropy) [...] Read more.
While the quantum emergence of spacetime is becoming a major research topic in physics, the quantum emergence of intelligence has not been widely researched in quantum information science (QIS). Following causal-logical quantum gravity theory, bipolar entropy vs. entropy and negative entropy (or negentropy) are reviewed and distinguished for quantum emergence/submergence of quantum agent (QA) and quantum intelligence (QI) in algebraic terms. This work refers to QA as an entangled bipolar string/superstring in bipolar dynamic equilibrium (BDE) and QI being centered on logically definable causality in regularity, mind-light-matter unity, and brain-universe similarity. ER = EPR is extended to ER ≥≥ EPR for the mathematical scalability of bipolar strings and their collective entanglement. The extension leads to a number of conjectures, testable predictions, and theorems. The term equilibraton is proposed as a type of EPR or bipolar generic string to serve as an entropic stitch to collectively hold the universe together as a quantum entanglement in BDE with ubiquitous, regulated local emergence and submergence of QA&QI. Equilibraton leads to the concept of bipolar entropy square—a complete entropic solution to the background issue in quantum gravity. With complete background independence, energy/information conservational bipolar entropy, energy/information invariance, bipolar entropy non-additivity, and equilibrium-based plateau concavity are introduced. The nature of the one-dimensional arrow of time is conjectured. As a unification of order and disorder for equilibrium-based regulation, bipolar entropy bridges QA&QI to agentic AI, where quantum-bio-economics can be viewed as a topological intervention of a natural dynamic equilibrium in a social or natural world. Use cases are reviewed to illustrate the practical and theoretical aspects of bipolar entropy in business management, quantum-bio-economics, quantum cryptography, physics, and biology. Eddington–Einstein’s comments on entropy are revisited. It is expected that bipolar entropy will bring quantum emergence/submergence to agentic AI&QI for entangled machine thinking and imagination as a naturally scalable and testable foundation of real-world quantum gravity, quantum information science (QIS), quantum cognition and quantum biology (QCQB) to enhance Large Language AI Models (LLMs) and machine intelligence. Full article
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30 pages, 6016 KB  
Review
Macromolecular Design Principles Governing Electrospinning of Polymer Nanofibers
by Lan Yi and Christian Dreyer
Polymers 2026, 18(8), 929; https://doi.org/10.3390/polym18080929 - 10 Apr 2026
Viewed by 946
Abstract
Electrospinning is a versatile technique for producing polymer nanofibers with high ratios of surface area to volume and tunable porosity. Conventional approach to the optimization of processing parameters such as voltage and flow rate frequently encounters limitations in reproducibility and scalability. This review [...] Read more.
Electrospinning is a versatile technique for producing polymer nanofibers with high ratios of surface area to volume and tunable porosity. Conventional approach to the optimization of processing parameters such as voltage and flow rate frequently encounters limitations in reproducibility and scalability. This review proposes a comprehensive framework that integrates macromolecular design principles with established electrohydrodynamic theories. We analyze how intrinsic molecular traits, specifically chain entanglement density, molecular weight distribution (MWD), topological architecture, and polymer–solvent thermodynamic interactions, define the boundaries of jet stability and solidification. Key findings highlight that while molecular weight establishes a baseline for spinnability, the MWD dictates the dynamic response under extreme deformation. Notably, high-molecular-weight fractions act as elastic load-bearers that suppress capillary breakup. Furthermore, we discuss here how molecular architecture and solvent-mediated segmental mobility determine whether molecular orientation is kinetically trapped or relaxed during the nanosecond timescales of jet flight. By establishing a hierarchical design logic prioritizing molecular and formulation variables over processing parameters, this framework provides a robust strategy to overcome challenges in scalability and reproducibility, positioning electrospinning as a sensitive probe for macromolecular dynamics under extreme elongation. Full article
(This article belongs to the Section Polymer Processing and Engineering)
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16 pages, 526 KB  
Article
Symmetric and Antisymmetric Quantum States from Graph Structure and Orientation
by Matheus R. de Jesus, Eduardo O. C. Hoefel and Renato M. Angelo
Entropy 2026, 28(4), 386; https://doi.org/10.3390/e28040386 - 1 Apr 2026
Viewed by 499
Abstract
Graph states provide a powerful framework for describing multipartite entanglement in quantum information science. In their standard formulation, graph states are generated by controlled-Z interactions and naturally encode symmetric exchange properties. Here we establish a precise correspondence between graph topology and exchange [...] Read more.
Graph states provide a powerful framework for describing multipartite entanglement in quantum information science. In their standard formulation, graph states are generated by controlled-Z interactions and naturally encode symmetric exchange properties. Here we establish a precise correspondence between graph topology and exchange symmetry by proving that a graph state is fully symmetric under particle permutations if and only if the underlying graph is complete. We then introduce a generalized graph-based construction using a non-commutative two-qudit gate, denoted GR, which requires directed edges and an explicit vertex ordering. We show that complete directed graphs generate fully antisymmetric multipartite states when endowed with appropriate orientations. Together, these results provide a unified graph-theoretic description of bosonic and fermionic exchange symmetry based on graph completeness and edge orientation. Full article
(This article belongs to the Special Issue Graph Theory and Its Applications in Quantum Mechanics)
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54 pages, 570 KB  
Article
Quantum Blockchains: Post-Quantum and Intrinsically Quantum Schemes
by Andrea Addazi
Electronics 2026, 15(7), 1447; https://doi.org/10.3390/electronics15071447 - 30 Mar 2026
Viewed by 1262
Abstract
The advent of fault-tolerant quantum computers poses an existential threat to the current blockchain technology, which relies on cryptographic primitives like elliptic-curve cryptography and SHA-256 hashing. This manuscript surveys the emerging field of quantum-secure blockchains, categorizing the main research directions into two paradigms. [...] Read more.
The advent of fault-tolerant quantum computers poses an existential threat to the current blockchain technology, which relies on cryptographic primitives like elliptic-curve cryptography and SHA-256 hashing. This manuscript surveys the emerging field of quantum-secure blockchains, categorizing the main research directions into two paradigms. The first, post-quantum blockchain, seeks to replace classical cryptographic elements with quantum-resistant algorithms. The second, more radical approach aims to construct an intrinsically quantum blockchain, where the ledger’s security and state are encoded directly in quantum mechanical principles. We delve into three promising intrinsic schemes: those based on Greenberger–Horne–Zeilinger (GHZ) states and entanglement in time, those leveraging multi-time states and pseudo-density matrices, and hypergraph-based approaches. As the principal original contribution of this work, we present a comprehensive theoretical framework for a topological quantum blockchain based on non-Abelian anyons, providing the first detailed encoding scheme mapping classical blockchain data to braiding sequences. We further develop the connection to Chern–Simons theory, establishing a field-theoretic foundation where the blockchain’s history is encoded in Wilson loops, and its immutability follows from topological and gauge invariance. Extending this framework, we introduce a holographic AdS/CFT interpretation, revealing that the topological blockchain can be understood as a dual description of a black hole analog in anti-de Sitter space, where the blockchain’s history is encoded in the microstates of a black hole and linking braids between blocks correspond to wormholes. We provide a detailed physical and mathematical analysis of each scheme, comparing their security assumptions, resource requirements, and feasibility in the near and long terms. The topological approach, in particular, offers a compelling new path toward a blockchain with inherent fault tolerance, where the chain’s history is encoded in the topology of anyon worldlines, making it naturally resistant to decoherence and local tampering. Full article
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19 pages, 393 KB  
Article
Topology-Dependent Performance of Free-Space Photonic Quantum Networks Under Noise
by Stefalo Acha and Sun Yi
Photonics 2026, 13(4), 310; https://doi.org/10.3390/photonics13040310 - 24 Mar 2026
Viewed by 597
Abstract
Photonic quantum communication enables secure and high-fidelity information transfer beyond classical limits, with direct relevance to emerging quantum networks operating in free-space environments. While physical-layer models of depolarizing noise, Gamma–Gamma turbulence statistics, entanglement swapping, and decoy-state QKD security bounds are individually well established, [...] Read more.
Photonic quantum communication enables secure and high-fidelity information transfer beyond classical limits, with direct relevance to emerging quantum networks operating in free-space environments. While physical-layer models of depolarizing noise, Gamma–Gamma turbulence statistics, entanglement swapping, and decoy-state QKD security bounds are individually well established, prior work typically treats these components in isolation or under fixed network assumptions. In this work, we develop a unified topology-aware analytical framework that simultaneously integrates free-space optical link budgets, turbulence-induced visibility degradation, depolarizing qubit noise, multi-hop entanglement cascade dynamics, teleportation fidelity thresholds, CHSH nonlocality certification, and asymptotic decoy-state secret key rate bounds across star, mesh, and ring graph structures. Rather than introducing new physical channel models, we demonstrate that identical physical links exhibit fundamentally different end-to-end performance once embedded within different network topologies. Mesh architectures minimize visibility cascade through hop-count reduction but incur quadratic hardware scaling. Star topologies minimize link count but concentrate noise and synchronization overhead at the hub. Ring configurations offer linear hardware scaling with multiplicative fidelity degradation. The results establish topology as a first-order design parameter in near-term free-space quantum networks operating without full quantum repeater infrastructures. While motivated by distributed multi-agent architectures, the framework applies broadly to terrestrial, airborne, and satellite-assisted photonic quantum communication systems. Full article
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34 pages, 852 KB  
Article
Equivalence of Doubly Periodic Tangles
by Ioannis Diamantis, Sofia Lambropoulou and Sonia Mahmoudi
Mathematics 2026, 14(6), 1071; https://doi.org/10.3390/math14061071 - 22 Mar 2026
Cited by 1 | Viewed by 567
Abstract
Doubly periodic tangles, or DP tangles, are embeddings of curves in the thickened plane that are periodically repeated in two directions. They are defined as universal covers of their generating cells, the flat motifs, which represent knots and links in the [...] Read more.
Doubly periodic tangles, or DP tangles, are embeddings of curves in the thickened plane that are periodically repeated in two directions. They are defined as universal covers of their generating cells, the flat motifs, which represent knots and links in the thickened torus, and which can be chosen in infinitely many ways. DP tangles are used in modeling materials and physical systems of entangled filaments. In this paper, we establish the complete mathematical framework of the topological theory of DP tangles. We present an exhaustive analysis of DP tangle isotopies. These are distinguished in local isotopies and global isotopies. Our analysis yields the characterization of DP isotopy as an equivalence relation on the level of their (flat) motifs, called DP tangle equivalence. Along the way, we also discuss motif minimality. We further generalize our results to other diagrammatic categories, namely framed, virtual, welded, singular, pseudo, tied and bonded DP tangles, which could be used in novel applications. Full article
(This article belongs to the Special Issue Mathematical Modeling of Complex Entangled Structures)
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22 pages, 7487 KB  
Article
MPM-Based Computational Mechanics Method for Tendon-Driven Hyperelastic Robots Under Target Deformations
by Manjia Su, Ying Yin, Ruiwei Liu, Shichao Gu and Yisheng Guan
Mathematics 2026, 14(5), 818; https://doi.org/10.3390/math14050818 - 28 Feb 2026
Viewed by 491
Abstract
This work introduces an integrated Material Point Method (MPM) framework for optimizing tendon-driven hyperelastic robots under extreme 3D deformations. To overcome the mesh distortion limitations of the traditional FEM at large strains, we develop a coupled MPM–tendon hyperelastic model that integrates Yeoh constitutive [...] Read more.
This work introduces an integrated Material Point Method (MPM) framework for optimizing tendon-driven hyperelastic robots under extreme 3D deformations. To overcome the mesh distortion limitations of the traditional FEM at large strains, we develop a coupled MPM–tendon hyperelastic model that integrates Yeoh constitutive laws with discrete tendon actuation forces. The model enables robust simulation of anisotropic stress propagation through Lagrangian particle tracking and Eulerian grid discretization, eliminating mesh entanglement artifacts. A strain-gradient-driven tendon path algorithm ensures mechanical efficiency using Fréchet distance-based similarity metrics and curvature smoothness screenin, enforcing spatial continuity in complex topologies. Validation demonstrates: (1) Sub 3 mm geometric errors and about 89% volumetric overlap in worm-inspired deformations; (2) optimal computational efficiency at 0.4–0.6 mm grid densities, balancing accuracy and resource overhead; and (3) projected alignment errors of 0.8 mm (XY), 1.3 mm (XZ), and 2.9 mm (YZ) in multi-view spatial analyses. The framework achieves about 89% ± 2% volumetric overlap in quadrupedal morphing via agonist–antagonist tendon optimization, demonstrating efficacy for extreme 3D deformation control. Full article
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