We extend the Calderbank-Shor-Steane (CSS) quantum code construction to Gaussian integer rings & Zopf;q[i], where q is a positive integer whose prime divisors all satisfy p = 1 (mod 4). Using nested principal ideal codes with Hermitian dual containment C perpendicular to H 2 C_ C1 C_ C2, we construct quantum stabilizer codes with dimension K = |C2|/|C1|. To address the challenges of decoding over rings with zero divisors, we introduce an algebraic error model where correctable errors are characterized by the coset structure of C2 relative to C1. This framework operates independently of specific physical noise assumptions, focusing on deterministic coset distinguishability. The associated coset-based decoder is shown to require exactly|epsilon | = [C2 : C1] membership tests, where the coset index is analytically determined by the norm quotient N(alpha 1)/N(alpha 2). Examples over & Zopf;25[i], & Zopf;85[i], and & Zopf;325[i] demonstrate codes encoding K E {5, 17, 5} logical states. Numerical simulations confirm the coding gain of the proposed scheme and provide benchmarks for its performance under additive noise. These results establish that ring-theoretic coset structures provide an algebraically rigorous and computationally efficient foundation for structured error correction over Gaussian integer rings. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
The 6 February 2023 earthquakes in T & uuml;rkiye inflicted widespread damage on transportation infrastructure, resulting in complex, spatially heterogeneous deformation patterns, most notably along the Hatay Airport access road. Situated atop the alluvial deposits of the former Amik Lake basin, this roadway is inherently susceptible to liquefaction-induced settlement and ground instability. This study examines the underlying damage mechanisms affecting this strategically important corridor using advanced signal-processing methodologies that go beyond conventional analytical techniques. High-precision post-event GNSS measurements were employed to characterize the post-earthquake roadway surface profile and its spatial irregularity structure. The statistical characteristics and persistence of the resulting deformation signals were evaluated using Detrended Fluctuation Analysis (DFA), thereby assessing randomness and long-range dependence. Complementarily, the Continuous Wavelet Transform (CWT) was applied to spatially resolve deformation energy and to delineate critical damage hotspot areas along the road alignment. Google Earth Engine-based remote sensing validation was also incorporated. These results provide a quantitative and mathematically grounded interpretation of post-event geometric irregularities and the inferred deformation processes driven by soil-structure interaction and liquefaction phenomena. Collectively, the study underscores the efficacy of fractal and wavelet-based analytical frameworks as robust decision-support tools for post-earthquake damage evaluation and for informing prioritization of targeted rehabilitation and mitigation strategies.
Airline baggage policies generally rely on uniform weight allowances combined with excess-baggage fees. From a payload-allocation perspective, this design may obscure the scarcity value of the aircraft payload and generate implicit incidence patterns across passengers. We study a Total Weight Allocation (TWA) benchmark in which passengers receive tradable baggage rights derived from a fixed per-passenger payload allowance net of body weight and trade these rights in a competitive market. When the payload capacity binds, the TWA implements a payload-efficient allocation by equalizing the marginal valuations of discretionary baggage capacity, exactly under quasi-linear preferences. Efficiency is independent of the initial assignment of rights, whereas incidence depends on endowments: conditional on baggage demand and travel needs, lower-body-weight passengers tend to be net sellers and higher-body-weight passengers tend to be net buyers. A non-tradable seating baseline preserves feasibility without changing the tradable baggage margin. The theoretical results extend to convex weight-cost formulations and multidimensional payload constraints. An illustrative numerical exercise based on assumed parameter distributions reports model-implied efficiency gains relative to non-tradable uniform baggage allowances and the transfer patterns implied by tradable rights; it is not an empirical calibration or a route-specific prediction. A per-kg fee equal to the payload shadow price can replicate the benchmark trading allocation while transferring scarcity rents from passengers to the airline, highlighting the efficiency-incidence trade-off in baggage-policy design.
Rapid urbanisation, the growth of quick commerce and on-demand grocery services, and urban traffic congestion have intensified the complexity of last-mile delivery operations, necessitating integrated delivery solutions. This study proposes a last-mile delivery framework tailored to urban quick-commerce environments, where high-frequency customer orders must be fulfilled from multiple micro-depots. The framework integrates autonomous drones, electric micro-vehicles, and delivery vans within a heterogeneous fleet to improve operational efficiency and environmental performance in dense urban areas.The framework is formulated as a multi-stage optimisation model in which customers are assigned to depots and delivery modes under distance- and weight-based constraints, followed by vehicle route optimisation. Two operational strategies are examined: a fixed-point policy, in which drones are dispatched when the delivery van reaches a selected route-embedded waiting point, and an en-route coordination policy, in which drones may be dispatched earlier and recovered at a feasible downstream waiting point subject to explicit range, endurance, and synchronization conditions. To capture the time-critical nature of quick-commerce operations, the model incorporates priority-based soft service-level agreements and a time-threshold dispatch mechanism, whereby vehicle departures are triggered by predicted service-time exceedance rather than vehicle fill rates. Environmental considerations are incorporated through a carbon-cost term based on vehicle- and load-dependent energy and emission estimates, allowing the environmental sensitivity of delivery-mode selection to be adjusted through alternative carbon-price scenarios.The framework is demonstrated through a real-network case study constructed from historical order records and representative operational assumptions for a dense metropolitan district. Results indicate that en-route drone–van coordination reduces operational time and service delays, whereas fixed-point dispatch reduces vehicle idle time. Sensitivity analyses demonstrate that increasing environmental emphasis yields moderate operational trade-offs, suggesting that environmentally conscious last-mile delivery planning can be achieved without compromising system feasibility.
This study combines machine learning, fragment-based molecular generation, and synthetic-accessibility analysis to identify promising small molecule acceptors (SMAs) for organic solar cells. Twelve regression algorithms were assessed using 60% training, 20% validation, and 20% test partitions. Gradient Boosting showed the strongest generalization, with a test R² of approximately 0.84–0.85. BRICS decomposition of 1027 parent molecules produced 3779 unique fragments, which were recombined to generate 50,000 unique, chemically valid candidates. The trained model predicted electron reorganization energies for the generated library, while the synthetic accessibility (SA) score was used to estimate synthetic feasibility. Chemical-space analysis using principal component analysis and t-distributed stochastic neighbor embedding confirmed broad structural diversity. The 1000 candidates with the lowest predicted reorganization energies were retained, after which 40 structures with the most favorable SA scores were prioritized. Similarity-matrix, hierarchical-clustering, t-SNE, and network analyses showed that the selected candidates span several structural families.
