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1. Direct detection of molecular intermediates from first-passage times

   https://doi.org/10.1126/sciadv.aaz4642  

   Thorneywork, Alice L.; Gladrow, Jannes; Qing, Yujia; Rico-Pasto, Marc; Ritort, Felix; Bayley, Hagan; Kolomeisky, Anatoly B.; Keyser, Ulrich F. (May 2020, Science Advances)

   All natural phenomena are governed by energy landscapes. However, the direct measurement of this fundamental quantity remains challenging, particularly in complex systems involving intermediate states. Here, we uncover key details of the energy landscapes that underpin a range of experimental systems through quantitative analysis of first-passage time distributions. By combined study of colloidal dynamics in confinement, transport through a biological pore, and the folding kinetics of DNA hairpins, we demonstrate conclusively how a short-time, power-law regime of the first-passage time distribution reflects the number of intermediate states associated with each of these processes, despite their differing length scales, time scales, and interactions. We thereby establish a powerful method for investigating the underlying mechanisms of complex molecular processes. 

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2. Time-asymptotic convergence rates towards discrete steady states of a nonlocal selection-mutation model

   https://doi.org/10.1142/S0218202519500404  

   Cai, Wenli; Jabin, Pierre-Emmanuel; Liu, Hailiang (October 2019, Mathematical Models and Methods in Applied Sciences)

   This paper is concerned with large time behavior of solutions to a semi-discrete model involving nonlinear competition that describes the evolution of a trait-structured population. Under some threshold assumptions, the steady solution is shown unique and strictly positive, and also globally stable. The exponential convergence rate to the steady state is also established. These results are consistent with the results in [P.-E. Jabin, H. L. Liu. Nonlinearity 30 (2017) 4220–4238] for the continuous model. 

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3. The effect of time resolution on the observed first passage times in diffusive dynamics

   https://doi.org/10.1063/5.0142166  

   Song, Kevin; Makarov, Dmitrii E.; Vouga, Etienne (March 2023, The Journal of Chemical Physics)

   Single-molecule and single-particle tracking experiments are typically unable to resolve fine details of thermal motion at short timescales where trajectories are continuous. We show that, when a diffusive trajectory [Formula: see text] is sampled at finite time intervals δt, the resulting error in measuring the first passage time to a given domain can exceed the time resolution of the measurement by more than an order of magnitude. Such surprisingly large errors originate from the fact that the trajectory may enter and exit the domain while being unobserved, thereby lengthening the apparent first passage time by an amount that is larger than δt. Such systematic errors are particularly important in single-molecule studies of barrier crossing dynamics. We show that the correct first passage times, as well as other properties of the trajectories such as splitting probabilities, can be recovered via a stochastic algorithm that reintroduces unobserved first passage events probabilistically. 

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4. Chronostratigraphy of Miocene strata in the Berkeley Hills (California Coast Ranges, USA) and the arrival of the San Andreas transform boundary

   https://doi.org/10.1130/GES02650.1  

   Gerasimov, Stacey H; Hodgin, Eben B; Crowley, James L; Swanson-Hysell, Nicholas L (January 2024, Geosphere)

   Miocene strata of the Claremont, Orinda, and Moraga formations of the Berkeley Hills (California Coast Ranges, USA) record sedimentation and volcanism during the passage of the Mendocino triple junction and early evolution of the San Andreas fault system. Detrital zircon laser ablation–inductively coupled plasma–mass spectrometry (LA-ICP-MS) age spectra indicate a change in sedimentary provenance between the marine Claremont formation (Monterey Group) and the terrestrial Orinda and Moraga Formations associated with uplift of Franciscan Complex lithologies. A sandstone from the Claremont formation produced a detrital zircon chemical abrasion–isotope dilution–thermal ionization mass spectrometry (CA-ID-TIMS) maximum depositional age of 13.298 ± 0.046 Ma, indicating younger Claremont deposition than previously interpreted. A trachydacite tuff clast within the uppermost Orinda Formation yielded a CA-ID-TIMS U-Pb zircon date of 10.094 ± 0.018 Ma, and a dacitic tuff within the Moraga Formation produced a CA-ID-TIMS U-Pb zircon date of 9.974 ± 0.014 Ma. These results indicate rapid progression from subsidence in which deep-water siliceous sediments of the Claremont formation were deposited to uplift that was followed by subsidence during deposition of terrestrial sediments of the Orinda Formation and subsequent eruption of the Moraga Formation volcanics. We associate the Orinda tuff clast and Moraga volcanics with slab-gap volcanism that followed the passage of the Mendocino triple junction. Given the necessary time lag between triple junction passage and the removal of the slab that led to this volcanism, subsidence associated with ca. 13 Ma Claremont sedimentation and subsequent Orinda to Moraga deposition can be attributed to basin formation along the newly arrived transform boundary. 

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5. Optimal Periodic Replenishment Policies for Spectrally Positive Lévy Demand Processes

   Pérez, José-Luis; Yamazaki, Kazutoshi; Bensoussan, Alain (January 2020, SIAM journal on control and optimization)

   null (Ed.)

   We consider a version of the stochastic inventory control problem for a spectrally positive Lévy demand process, in which the inventory can only be replenished at independent exponential times. We show the optimality of a periodic barrier replenishment policy that restocks any shortage below a certain threshold at each replenishment opportunity. The optimal policies and value functions are concisely written in terms of the scale functions. Numerical results are also provided. 

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