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A key contribution to X-ray dark-field (XDF) contrast is the diffusion of X-rays by sample structures smaller than the imaging system's spatial resolution; this is related to position-dependent small-angle X-ray scattering. However, some experimental XDF techniques have reported that XDF contrast is also generated by resolvable sample edges. Speckle-based X-ray imaging (SBXI) extracts the XDF by analyzing sample-imposed changes to a reference speckle pattern's visibility.
View Article and Find Full Text PDFOn latent dynamics learning in nonlinear reduced order modeling.
Neural Netw
January 2025
MOX, Department of Mathematics, Politecnico di Milano, Piazza Leonardo da Vinci 32, Milan, 20133, Italy. Electronic address:
In this work, we present the novel mathematical framework of latent dynamics models (LDMs) for reduced order modeling of parameterized nonlinear time-dependent PDEs. Our framework casts this latter task as a nonlinear dimensionality reduction problem, while constraining the latent state to evolve accordingly to an unknown dynamical system. A time-continuous setting is employed to derive error and stability estimates for the LDM approximation of the full order model (FOM) solution.
View Article and Find Full Text PDFOn spectral bias reduction of multi-scale neural networks for regression problems.
Neural Netw
January 2025
Department of Mathematics, Southern Methodist University, Dallas, 75275, TX, USA. Electronic address:
In this paper, we derive diffusion equation models in the spectral domain to study the evolution of the training error of two-layer multiscale deep neural networks (MscaleDNN) (Cai and Xu, 2019; Liu et al., 2020), which is designed to reduce the spectral bias of fully connected deep neural networks in approximating oscillatory functions. The diffusion models are obtained from the spectral form of the error equation of the MscaleDNN, derived with a neural tangent kernel approach and gradient descent training and a sine activation function, assuming a vanishing learning rate and infinite network width and domain size.
View Article and Find Full Text PDFRegulating the Thermodynamic Uniformity and Kinetic Diffusion of Zinc Anodes for Deep Cycling of Ah-Level Aqueous Zinc-Metal Batteries.
ACS Nano
January 2025
Power Battery & Systems Research Center, State Key Laboratory of Catalysis, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China.
Zn metal anodes in mildly acidic electrolytes usually suffer from a series of problems, including parasitic dendrite growth and severe side reactions, significantly limiting the Zn utilization efficiency and cycling life. A deep understanding of the Zn stripping/plating process is essential to obtain high-efficiency and long-life Zn metal anodes. Here, the factors affecting the Zn stripping/plating process are revealed, suggesting that thermodynamic uniformity in bulk structures promotes an orderly Zn stripping process, and a fast kinetic diffusion rate on the Zn surface facilitates uniform Zn deposition.
View Article and Find Full Text PDFTrigeminal Neuralgia: Disease Characterization and Prediction of Response to Surgical Intervention.
Curr Pain Headache Rep
January 2025
Department of Neurosurgery, University of Michigan, Ann Arbor, MI, USA.
Purpose Of Review: Trigeminal neuralgia (TN) is a highly heterogeneous condition with a wide choice of successful treatment options. However, differences between subtypes are poorly understood and it remains unknown which patients will respond to different treatments. This review aims to summarize the current state of the TN field and explore the problem of predicting surgical outcomes.
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