For diffusive dynamics, Kramers' expressions for the transition rates between two basins separated by a high barrier has been rederived in many ways. Here, we will do it using the Bennett-Chandler method which focuses on the time derivative of the occupation number correlation function that describes fluctuations of the basin populations at equilibrium. This derivative is infinite at = 0 for diffusive dynamics. We show that on a slightly longer time scale, comparable to the time it takes the system to fall off the barrier, this time derivative is proportional to the spatial derivative of the committor evaluated at the barrier top. The committor or splitting probability is the probability that the system starting on the barrier ends up in one basin before the other. This probability can be found analytically. By asymptotic evaluation of the relevant integrals, we recover Kramers' result without having had to rely on his formidable physical intuition.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1021/acs.jpcb.3c01233 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Assessing blood flow in uterine fibroids using intravoxel incoherent motion imaging compared with dynamic contrast-enhanced MRI.
Sci Rep
January 2025
Department of Radiology, Turku University Hospital and University of Turku, Kiinamyllynkatu 4-8, Turku, 20521, Finland.
To assess the utility of IVIM parameters in evaluating uterine fibroid blood flow compared to dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) derived blood flow. Sixteen premenopausal women with uterine fibroids were enrolled in this prospective study. Pelvic MRI scans were obtained for each subject, both with and without continuous intravenous infusion of oxytocin, known to decrease significantly uterine fibroid blood flow, to assess the changes in blood flow of uterine fibroids.
View Article and Find Full Text PDFComparisons of integrated slice-specific dynamic shimming EPI and single-shot EPI diffusion-weighted imaging of the liver.
Eur J Radiol
January 2025
Department of Radiology, The Second Xiangya Hospital, Central South University, No.139 Middle Renmin Road, Changsha, Hunan, 410011, China; Department of Radiology Quality Control Center, Changsha, Hunan Province, 410011, China; The Key Laboratory of Biomedical Information Engineering of Ministry of Education, School of Life Science and Technology, Institute of Health and Rehabilitation Science, Xi'an Jiaotong University, Xi'an 710049,China. Electronic address:
Purpose: To compare the quality of DWI images, signal loss of left hepatic lobe and diagnostic performance of apparent diffusion coefficient (ADC) values between SS-EPI and iShim-EPI in liver lesions.
Methods: Totally 142 patients were involved, images using SS-EPI and the prototype iShim-EPI were acquired before injection of gadoxetic acid-enhanced liver MRI.Image quality of demarcation of liver capsule, resolution, lesion distortion, artifacts, lesion confidence score, and signal loss in left hepatic lobe was assessed by two radiologists.
Interpretable COVID-19 chest X-ray detection based on handcrafted feature analysis and sequential neural network.
Comput Biol Med
January 2025
University of Rwanda, Rwanda. Electronic address:
Deep learning methods have significantly improved medical image analysis, particularly in detecting COVID-19 chest X-rays. Nonetheless, these methodologies frequently inhibit some drawbacks, such as limited interpretability, extensive computational resources, and the need for extensive datasets. To tackle these issues, we introduced two novel algorithms: the Dynamic Co-Occurrence Grey Level Matrix (DC-GLM) and the Contextual Adaptation Multiscale Gabor Network (CAMSGNeT).
View Article and Find Full Text PDFBasal ganglia components have distinct computational roles in decision-making dynamics under conflict and uncertainty.
PLoS Biol
January 2025
Carney Institute for Brain Science, Department of Cognitive & Psychological Sciences, Brown University, Providence, Rhode Island, United States of America.
The basal ganglia (BG) play a key role in decision-making, preventing impulsive actions in some contexts while facilitating fast adaptations in others. The specific contributions of different BG structures to this nuanced behavior remain unclear, particularly under varying situations of noisy and conflicting information that necessitate ongoing adjustments in the balance between speed and accuracy. Theoretical accounts suggest that dynamic regulation of the amount of evidence required to commit to a decision (a dynamic "decision boundary") may be necessary to meet these competing demands.
View Article and Find Full Text PDFNon-spatial Dynamics and Spatiotemporal Patterns Formation in a Predator-Prey Model with Double Allee and Dome-shaped Response Function.
Bull Math Biol
January 2025
Department of Mathematics, Vivekananda College, Kolkata, West Bengal, 700063, India.
The extinction of species is a major threat to the biodiversity. Allee effects are strongly linked to population extinction vulnerability. Emerging ecological evidence from numerous ecosystems reveals that the Allee effect, which is brought on by two or more processes, can work on a single species concurrently.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!