Power equipment defect recognition is challenged by long-tailed labels, subtle state differences, scarce fault images, and variable acquisition conditions. Fixed-crop evaluation can obscure whether errors arise from localization, routing, crop quality, or state recognition. We developed an object-routed framework that links equipment localization to object-specific classifiers while retaining a classical decision path. A simulated low-qubit parameterized quantum circuit (PQC) was evaluated as an auxiliary representation for gated residual fusion. Matched analyses separated encoding, representation capacity, and fusion effects. Under parameter-matched branch substitution, the amplitude-encoded PQC achieved the highest descriptive means for accuracy (0.8870±0.0596), balanced accuracy (0.8648±0.0821), and macro-F1 (0.8539±0.1026). In a separate provenance-supported analysis, risk-aware residual fusion increased macro-F1 by 0.1584 relative to ordinary residual fusion (95% confidence interval, 0.0584–0.2641; p=0.0322). This inference supports the gating strategy rather than any specific residual representation. End-to-end experiments traced failures across the pipeline and identified errors that residual correction could not address. They were not designed to demonstrate industrial deployment benefit. The resulting contribution is an auditable fusion architecture with explicit capability boundaries. Its conclusions do not depend on PQC superiority.
Self-dual MDS codes over finite fields constitute an important family of linear codes with broad applications in combinatorics and cryptography. Twisted generalized Reed–Solomon (TGRS) codes are capable of simultaneously possessing the MDS property and self-duality. In this paper, we derive necessary and sufficient conditions for general TGRS codes to be Hermitian self-dual. Using a new Hermitian-type partition, we develop three families of Hermitian self-dual TGRS codes whose evaluation points are taken from additive cosets, corresponding to code lengths n|q−1,n=q and n=2q. We further give another novel Hermitian self-dual construction relying on multiplicative cosets for length n=q+1. Additionally, we establish necessary and sufficient conditions for TGRS codes to be Hermitian self-dual MDS codes and present an explicit construction for this class of codes.
Population change is closely associated with urban land use structure, yet their nonlinear relationship and distributional heterogeneity remain poorly understood. Drawing on panel data for 2000–2020 from urban districts across 284 Chinese prefecture-level cities, this study applies generalized additive models, segmented regression and quantile regression to investigate the nonlinear association, phase features, and heterogeneity between population change and land use structure. The results indicate that: (1) Urban district land use structures across China became more balanced during 2000–2020; population shrinkage cities underwent larger structural shifts alongside more marked fluctuations. (2) The population change rate shows a significant U-shaped association with land use structure entropy (LUSE), turning at approximately −1% annually; growth cities follow an inverted U-shaped pattern, and shrinkage cities exhibit distinct phase-dependent effects. (3) Cities with higher LUSE demonstrate more substantial land use proportion adjustments, a tendency most salient among population shrinkage cities. These findings offer empirical support for differentiated land use governance and optimized territorial spatial planning for both growth and shrinkage cities.
In this framework, a completed recognition is required to remain distinguishable from its reversal; we formulate this requirement with a ledger of binary state changes.For a closed run, the primitive debit and credit increments balance; reversal therefore leaves the same state-account record. A phase account can retain the missing sign. When its domain is the complement of a recognized loop with process dimension of one, nonzero winding is equivalent to the homological requirement of the companion paper, and that requirement holds exactly when D=3. The account-domain restriction is an explicit premise; an ordered posting history can retain reversal information outside this restriction. The phase domain and recognized ownership of the registration are explicit physical premises. We also compare cubical processes whose recognized and registering trajectories are spheres of the same dimension k. Arity here defines the number of states that one act runs over, and not the number of arguments of an operation. Under the stated ambient homology hypotheses, their recognition substrate has a dimension of 2k+1. With additive tally costs and a sequential ledger, a loop costs exactly eight units to traverse or nine when including a unit phase account. An explicit closed schedule attains a surface minimum of ninety primitive units; every higher process costs more than the loop. If recognition takes the cheapest complete pass among these admissible process dimensions, that pass is the loop, and the substrate dimension is then three. Identifying the recognition substrate with the space carrying these acts gives the corresponding physical dimensional selection. The higher-dimensional alternatives are constructed.
Aggregate economic and infrastructural indicators often display nonlinear dynamics and structural shifts which cannot be adequately defined by conventional trend and volatility measurements. This study presents a segmented multiresolution entropy framework that blends wavelet reconstruction with Approximate Entropy (ApEn) and normalized Permutation Entropy (PE) for the evaluation of time-varying complexity. The main technique is based on applying a discrete wavelet transform with db4 to the whole series at J=3, reconstructing the low frequency component A3 and computing entropy in eight non-overlapping segments. This gives a common reconstruction basis across the sample, and it reduces sensitivity to repeated segment-boundary initialization. The framework is applied to the monthly U.S. Transportation Services Index from January 2000 to April 2026. The ApEn and PE trajectories capture changes in amplitude-based irregularity and temporal ordering consistent with periods of major economic and transportation disruption, including the global financial crisis, the COVID-19 pandemic, and subsequent supply-chain and geopolitical uncertainty. Moving-block-bootstrap intervals assess the conditional uncertainty around the main estimates. Controlled simulations demonstrate an enhanced transition-detection rate following wavelet reconstruction but not all performance criteria are improved. The results indicate that the approach can add to traditional transportation monitoring by identifying changes in system organization, independent of index level fluctuations, without suggesting causal attribution or formally validated regime shifts.
