In the singularly perturbed limit of an asymptotically small diffusivity ratio ε 2 , the existence and stability of localized quasi-equilibrium multispot patterns is analyzed for the Brusselator reactiondiffusion model on the unit sphere. Formal asymptotic methods are used to derive a nonlinear algebraic system that characterizes quasi-equilibrium spot patterns and to formulate eigenvalue problems governing the stability of spot patterns to three types of "fast" O(1) time-scale instabilities: self-replication, competition, and oscillatory instabilities of the spot amplitudes. The nonlinear algebraic system and the spectral problems are then studied using simple numerical methods, with emphasis on the special case where the spots have a common amplitude. Overall, the theoretical framework provides a hybrid asymptotic-numerical characterization of the existence and stability of spot patterns that is asymptotically correct to within all logarithmic correction terms in powers of ν = −1/ log ε. From a leading-order-in-ν analysis, and with an asymptotically large inhibitor diffusivity, some rigorous results for competition and oscillatory instabilities are obtained from an analysis of a new class of nonlocal eigenvalue problem (NLEP). Theoretical results for the stability of spot patterns are confirmed with full numerical computations of the Brusselator PDE system on the sphere using the closest point method. [39] proposed that localized peaks in the concentration of a chemical substance, known as a morphogen, could be responsible for the process of morphogenesis, which describes the development of a complex organism from a single cell. By means of a linearized analysis, he showed how stable spatially inhomogeneous patterns can develop from small perturbations of spatially homogeneous initial data for a coupled system of reaction-diffusion (RD) equations. Introduction. Turing inMotivated by this initial work, a systematic and rigorous approach has been developed over the last few decades for the analysis of small amplitude patterns in RD systems. After linearizing the RD system around a spatially uniform state to identify bifurcation points for the emergence of spatially nonuniform patterns, a weakly nonlinear analysis based on a
Magnetic resonance fingerprinting (MRF) is a method to extract quantitative tissue properties such as T1 and T2 relaxation rates from arbitrary pulse sequences using conventional MRI hardware. MRF pulse sequences have thousands of tunable parameters, which can be chosen to maximize precision and minimize scan time. Here, we perform de novo automated design of MRF pulse sequences by applying physics-inspired optimization heuristics. Our experimental data suggest that systematic errors dominate over random errors in MRF scans under clinically relevant conditions of high undersampling. Thus, in contrast to prior optimization efforts, which focused on statistical error models, we use a cost function based on explicit first-principles simulation of systematic errors arising from Fourier undersampling and phase variation. The resulting pulse sequences display features qualitatively different from previously used MRF pulse sequences and achieve fourfold shorter scan time than prior human-designed sequences of equivalent precision in T1 and T2. Furthermore, the optimization algorithm has discovered the existence of MRF pulse sequences with intrinsic robustness against shading artifacts due to phase variation.
Cotyledon morphogenesis is more complex geometrically in conifers than in angiosperms, involving 2-D patterning which deforms a surface in three dimensions. This work develops a quantitative framework for understanding the growth and patterning dynamics involved in conifer cotyledon development, and applies more generally to the morphogenesis of whorls with many primordia.
Parallel tempering Monte Carlo has proven to be an efficient method in optimization and sampling applications. Having an optimized temperature set enhances the efficiency of the algorithm through more-frequent replica visits to the temperature limits. The approaches for finding an optimal temperature set can be divided into two main categories. The methods of the first category distribute the replicas such that the swapping ratio between neighbouring replicas is constant and independent of the temperature values. The second-category techniques including the feedback-optimized method, on the other hand, aim for a temperature distribution that has higher density at simulation bottlenecks, resulting in temperature-dependent replica-exchange probabilities. In this paper, we compare the performance of various temperature setting methods on both sparse and fully-connected spin-glass problems as well as fully-connected Wishart problems that have planted solutions. These include two classes of problems that have either continuous or discontinuous phase transitions in the order parameter. Our results demonstrate that there is no performance advantage for the methods that promote nonuniform swapping probabilities on spin-glass problems where the order parameter has a smooth transition between phases at the critical temperature. However, on Wishart problems that have a first-order phase transition at low temperatures, the feedback-optimized method exhibits a time-to-solution speedup of at least a factor of two over the other approaches.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.