Bilipschitz invariant theory concerns low-distortion embeddings of orbit spaces into Euclidean space. To date, embeddings with the smallest-possible distortion are known for only a few cases, to include: (a) planar rotations, (b) real phase retrieval, and (c) finite reflection groups. Here, we prove that for all three of these cases, the smallest possible distortion is nearly achieved by a composition of a "max filter bank" with a linear transformation. Our proof amounts to a two-step process: first, we show it suffices to demonstrate a certain inclusion of Lipschitz function spaces, and second, we prove that inclusion, using fundamentally different approaches for the three cases. We also show that these cases interact differently with a few related function spaces, which suggests that a unified treatment would be nontrivial.
Abstract Transmission line towers experience frequent fluctuations in wind loads, which can cause fatigue damage in bolted connections, thereby risking their long-term reliability. Direct probabilistic fatigue assessment of transmission towers using nonlinear time-domain simulations under stochastic wind loading is computationally infeasible for long-term reliability and inspection planning, motivating the use of surrogate models to enable efficient uncertainty propagation and decision analysis. This study introduces a surrogate-based probabilistic framework to evaluate fatigue damage and inform inspection scheduling. High-fidelity finite-element models simulate joint responses under both preloaded and loosened bolt conditions, with fatigue assessed through rainflow cycle counting and Miner’s rule. The resulting simulation database is used to train neural network surrogates, enabling rapid prediction of fatigue accumulation across wind speeds and directions. These surrogates are integrated with joint wind probability distributions and a Poisson-based extreme-event model to estimate annual damage and account for uncertainty through sampling. Results identify critical fatigue-prone connections and examine how stress factors and bolt preloading influence vulnerability. Using these findings, inspection strategies are optimized by considering detection probabilities and cost-risk trade-offs. Overall, this approach offers a fast and reliability-based tool for evaluating fatigue risk and planning inspections of transmission systems.
The paper considers the construction of two new orthogonal multiwavelets with supercompact support by using the Fast Bauer's method for matrix spectral factorization on the matrix product filter of the orthogonal CL multiwavelet filter. The new multiwavelets possess orthogonality, symmetry/antisymmetry, and one of them provides better coding and smoothness than other supercompact multiwavelets. The performance of the new multiwavelet filters in subband-based edge detection, grayscale and color image compression and 1D and 2D signal denoising is compared with the GHM, SA4, CL, Integer Haar and Alpert multifilters. The comparative analysis shows that new multiwavelets can provides better human visual measures, SSIM and MS-SSIM in image compression and denoising applications.
Cytosolic detoxification through vacuolar sequestration is essential for plant growth and stress tolerance. A key driver of this process is the vacuolar ABC transporter, ABCC1, which sequesters diverse amphiphilic anions including glutathione (GS)-conjugates, glucuronic acid-conjugates, and thiol-coordinated metal complexes. However, mechanistic studies of plant ABCC1 have largely relied on Arabidopsis genetics and crude membrane transport assays. Here, phylogenetic and sequence-guided analysis of ABCC1 orthologs from multiple plant species was combined with in vitro functional assays with purified protein to investigate plant ABCC1 transporter activity. Compared to mammalian ABCC1, all plant ABCC1 orthologs contain a conserved bipartite binding pocket with a cationic pocket for anion recognition and a hydrophobic pocket. Key differences between mammalian and plant ABCC1 include a substitution in the cation coordinating histidine residue that is compensated by a peripheral arginine mutation to preserve the cationic electrostatic environment. Furthermore, the plant ABCC1 hydrophobic pocket is enlarged relative to its mammalian counterpart due to several substitutions with smaller side-chain residues. To investigate the in vitro activity of plant ABCC1, several orthologs were screened for expression, and those from maize, date palm, and rice exhibited high biochemical stability and comparable substrate-stimulated ATPase activity. ZmABCC1 was further characterized through a series of assay optimization experiments, which found that its ATPase activity is strongly stimulated by E217βG and GS-conjugates, and inhibited by orthovanadate. This study verifies that ABCC1 is widely conserved across plant species with a consistent substrate binding pocket and activity, supporting its role in cytosolic detoxification in plants.
Optimal transmission switching (OTS) determines which transmission lines to remove from service to minimize dispatch costs. Unlike topology design, it alters the operational status of operating lines. Sensitivity-based methods, as advanced optimization techniques, select lines whose outage yields a significant cost reduction. However, these methods overlook bus splitting, an effective congestion management strategy that our work incorporates to achieve improved economic gains. In this work, we formulate an optimal transmission reconfiguration (OTR) problem that incorporates both line switching and bus splitting. We develop a novel approach to quantify the sensitivity of the OTR objective to line switching and bus splitting, establish connections between the proposed sensitivity framework and existing heuristic metrics, prove the equivalence between bus splitting and a generalized line switching to enable unified treatment, and provide a simpler derivation of Bus Split Distribution Factor (BSDF). Simulations on nine IEEE test systems spanning 118 to 13,659 buses demonstrate the high effectiveness of our proposed sensitivity method. They also demonstrate that incorporating bus splitting into transmission reconfiguration achieves greater cost savings than line switching alone. The results confirm the economic advantage of this comprehensive approach to transmission system operation.
