Distributions of functionals of Brownian bridge arise as limiting distributions in non-parametric statistics. In this paper we will give a derivation of distributions of extrema of the Brownian bridge based on excursion theory for Brownian motion. The idea of rescaling and conditioning on the local time has been used widely in the literature. In this paper it is used to give a unified derivation of a number of known distributions, and a few new ones. Particular cases of calculations include the distribution of the Kolmogorov-Smirnov statistic and the Kuiper statistic.
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http://dx.doi.org/10.1016/j.spa.2014.04.008 | DOI Listing |
Nat Commun
January 2025
Institute for Molecular Science, National Institutes of Natural Sciences, Okazaki, Aichi, Japan.
DNA-nanoparticle motor is a burnt-bridge Brownian ratchet moving on RNA-modified surface driven by Ribonuclease H (RNase H), and one of the fastest nanoscale artificial motors. However, its speed is still much lower than those of motor proteins. Here we resolve elementary processes of motion and reveal long pauses caused by slow RNase H binding are the bottleneck.
View Article and Find Full Text PDFJ Environ Manage
February 2025
Graduate School of Media and Governance, Keio University, 5322 Endo, Fujisawa City, Kanagawa Prefecture, 252-0882, Japan. Electronic address:
The adoption of residential renewable energy is pivotal for achieving the 'Net Zero' goal, yet financial assessments of household investments in this area remain complex due to dynamic market conditions. This study introduces a novel closed-form financial valuation framework for residential solar photovoltaic (PV) systems, explicitly addressing the uncertainties of electricity market price fluctuations (market risk) and energy policy changes (policy risk) using Geometric Brownian Motion (GBM). A case study in France demonstrates the framework's application, revealing that the discount rate is the most influential factor in solar PV valuation, followed by system lifespan and policy-driven Feed-in Tariff (FiT) rates.
View Article and Find Full Text PDFJ Chem Phys
January 2025
School of Chemistry, Beihang University, Beijing 100191, China.
Dynamic density functional theory (DDFT) is a fruitful approach for modeling polymer dynamics, benefiting from its multiscale and hybrid nature. However, the Onsager coefficient, the only free parameter in DDFT, is primarily derived empirically, limiting the accuracy and broad application of DDFT. Herein, we propose a machine learning-based, bottom-up workflow to directly extract the Onsager coefficient from molecular simulations, circumventing partly heuristic assumptions in traditional approaches.
View Article and Find Full Text PDFPhys Rev Lett
December 2024
Chan Zuckerberg Biohub-San Francisco, 499 Illinois Street, San Francisco, California 94158, USA.
Influenza A viruses (IAVs) must navigate through a dense extracellular mucus to infect airway epithelial cells. The mucous layer, composed of glycosylated biopolymers (mucins), presents sialic acid that binds to ligands on the viral envelope and can be irreversibly cleaved by viral enzymes. It was recently discovered that filamentous IAVs exhibit directed persistent motion along their long axis on sialic acid-coated surfaces.
View Article and Find Full Text PDFNat Commun
November 2024
Department of Molecular Biosciences, Kyoto Sangyo University, Kamigamo-Motoyama, Kita-ku, Kyoto, 603-8555, Japan.
ATP synthases play a crucial role in energy production by utilizing the proton motive force (pmf) across the membrane to rotate their membrane-embedded rotor c-ring, and thus driving ATP synthesis in the hydrophilic catalytic hexamer. However, the mechanism of how pmf converts into c-ring rotation remains unclear. This study presents a 2.
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