We will make a link between the steepest descent method for an unconstrained minimisation problem and fixed-point iterations for its Euler-Lagrange equation. In this context, we shall rediscover the preconditioned algebraic conjugate gradient method for the discretised problem. The benefit of the connection of those concepts will be illustrated by a numerical experiment.
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http://dx.doi.org/10.1007/s11590-022-01867-9 | DOI Listing |
Sci Rep
November 2024
Department of Rheumatology and immunology, The Second Hospital of Shanxi Medical University, Taiyuan, 030001, Shanxi, China.
To develop a clinical imaging method for monitoring macrophage migration to the defect site after implantation of various stem cells and evaluating immune responses in the context of knee arthritis, T2 mapping was correlated with CD68-positive cell densities in defects and the bone marrow. This study, which was approved by the Institutional Animal Care and Use Committee, used 32 New Zealand white rabbits preloaded with ultrasmall superparamagnetic iron oxide particles (USPIOs). They were divided into groups that received different stem cell implants after osteochondral defect induction.
View Article and Find Full Text PDFJ Glob Health
October 2024
Department of Social and Behavioral Sciences, Harvard T. H. Chan School of Public Health, Boston, Massachusetts, USA.
BMC Public Health
December 2023
Department of Pediatrics, David Geffen School of Medicine, University of California, Los Angeles (UCLA), Center for Healthier Children, Families, and Communities, Los Angeles, USA.
Background: Early childhood health development is positively associated with income, but the strength of this relationship with ethnoracial background remains unclear. This study examined the extent of health development inequities among California kindergarteners based on ethnoracial backgrounds and neighborhood-level income.
Methods: This cross-sectional study assessed health development inequities by analyzing neighborhood-level income, ethnoracial background, and health development data for California kindergarteners.
Optim Lett
March 2022
Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG UK.
We will make a link between the steepest descent method for an unconstrained minimisation problem and fixed-point iterations for its Euler-Lagrange equation. In this context, we shall rediscover the preconditioned algebraic conjugate gradient method for the discretised problem. The benefit of the connection of those concepts will be illustrated by a numerical experiment.
View Article and Find Full Text PDFJ Phys Condens Matter
December 2022
Materials Science Engineering Department, Virginia Tech, Blacksburg, VA 24061, United States of America.
The steepest-entropy-ascent quantum thermodynamic (SEAQT) framework was used to calculate the stability of a collection of point defects in 2D PtSeand predict the kinetics with which defects rearrange during thermal annealing. The framework provides a non-equilibrium, ensemble-based framework with a self-consistent link between mechanics (both quantum and classical) and thermodynamics. It employs an equation of motion derived from the principle of steepest entropy ascent (maximum entropy production) to predict the time evolution of a set of occupation probabilities that define the states of a system undergoing a non-equilibrium process.
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