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In this paper, a trust-region algorithm is proposed for large-scale nonlinear equations, where the limited-memory BFGS (L-M-BFGS) update matrix is used in the trust-region subproblem to improve the effectiveness of the algorithm for large-scale problems. The global convergence of the presented method is established under suitable conditions. The numerical results of the test problems show that the method is competitive with the norm method.
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http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4423997 | PMC |
http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0120993 | PLOS |
Math Biosci Eng
July 2025
Department of Mathematics, College of Health and Natural Sciences, Zayed University, Abu Dhabi United Arab Emirates.
This study introduces a novel multivariable optimal control framework for hemodialysis, which uniquely integrates five physiological states (blood urea concentration, fluid volume, blood pressure, electrolytes, and hemoglobin) with three clinically adjustable inputs (ultrafiltration rate, blood flow, and dialysate composition). By employing the limited-memory Broyden-Fletcher-Goldfarb-Shanno-B (L-BFGS-B) algorithm with patient-specific box constraints, the model enforces patient-specific physiological safety limits while dynamically balancing clinical targets. Numerical simulations demonstrate the stabilization of key parameters within ±5% of clinical benchmarks (e.
View Article and Find Full Text PDFJ Imaging
May 2025
Department of Computer and Data Sciences, Case Western Reserve University, Olin 516, 2101 Martin Luther King Jr Dr, Cleveland, OH 44106, USA.
Magnetic resonance fingerprinting (MRF), a quantitative MRI technique, enables the acquisition of multiple tissue properties in a single scan. In this paper, we study a proposed extension of MRF, MRF with exchange (MRF-X), which can enable acquisition of the six tissue properties T1a,T2a, T1b, T2b, ρ and τ simultaneously. In MRF-X, 'a' and 'b' refer to distinct compartments modeled in each voxel, while ρ is the fractional volume of component 'a', and τ is the exchange rate of protons between the two components.
View Article and Find Full Text PDFMath Biosci
February 2025
Maxwell Institute for Mathematical Sciences, The University of Edinburgh and Heriot-Watt University, Bayes Centre, Edinburgh, Scotland, UK; School of Mathematics, The University of Edinburgh, James Clerk Maxwell Building, Edinburgh, Scotland, UK. Electronic address:
We consider a numerical framework tailored to identifying optimal parameters in the context of modelling disease propagation. Our focus is on understanding the behaviour of optimisation algorithms for such problems, where the dynamics are described by a system of ordinary differential equations associated with the epidemiological SIRD model. Applying an optimise-then-discretise approach, we examine properties of the solution operator and determine existence of optimal parameters for the problem considered.
View Article and Find Full Text PDFComput Biol Med
February 2025
Shandong Technology and Business University, 191 Binhai Middle Road, Yantai, Shandong, China.
The classification of Doppler ultrasound images plays an important role in the diagnosis of pregnancy. However, it is a challenging problem that suffers from a variable length of these images with a dimension gap between them. In this study, we propose a latent representation weights learning method (LRWL) for pregnancy prediction using Doppler ultrasound images.
View Article and Find Full Text PDFMaterials (Basel)
September 2024
Guangxi Liuzhou LEGN Technology Co., Ltd., Liuzhou 545000, China.
The initial gap (IG) is frequently occurring in the process of resistance spot welding (RSW) for automotive body-in-white structures. It is an inevitable challenge that the RSW with IG can negatively impact the welding quality, subsequently reducing the structural integrity and safety of the vehicle. This research aims to study the influence of the IG on RSW mechanical behaviors based on the refined finite element model (FEM) of RSW with different IGs under tensile shear load.
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