Stochastic resetting in the Kramers problem: A Monte Carlo approach

Cantisán, Julia; Seoane, Jesús M.; Sanjuán, Miguel A. F.

doi:10.1016/j.chaos.2021.111342

Cited by 10 publications

(7 citation statements)

References 35 publications

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“…We are currently developing a stochastic model that incorporates time-varying factors to simulate and predict the temporal evolution of graft function more accurately. The introduction of stochasticity/noise will necessitate the use of Monte-Carlo simulations 12 and Kramer’s theory to determine the graft’s fate. In addition, improved predictions could be made by applying regression analysis to real-time measurements more frequently and by updating the model parameters 13 .…”

Section: Discussionmentioning

confidence: 99%

A model-driven machine learning approach for personalized kidney graft risk prediction

Savvopoulos,

Scheffner,

Reppas

et al. 2023

Preprint

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Graft failure after renal transplantation is a multifactorial process. Predicting the risk of graft failure accurately is imperative since such knowledge allows for identifying patients at risk and treatment personalization. In this study, we were interested in predicting the temporal evolution of graft function (expressed as estimated glomerular filtration rate; eGFR) based on pretransplant data and early post-operative graft function. Toward this aim, we developed a tailored approach that combines a dynamic GFR mathematical model and machine learning while taking into account the corresponding parameter uncertainty. A cohort of 892 patients was used to train the algorithm and a cohort of 847 patients for validation. Our analysis indicates that an eGFR threshold exists that allows for classifying high-risk patients. Using minimal inputs, our approach predicted the graft outcome with an accuracy greater than 80% for the first and second years after kidney transplantation and risk predictions were robust over time.

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Section: Discussionmentioning

confidence: 99%

A model-driven machine learning approach for personalized kidney graft risk prediction

Savvopoulos,

Scheffner,

Reppas

et al. 2023

Preprint

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“…Future research could be related to the investigation of ergodic properties of finite-velocity HDPs in absence and presence of resetting [35][36][37][94][95][96], including also corresponding higher-dimensional formulations [38,39]. Infiniteand finite-velocity HDPs in presence of time-dependent resetting [97], non-instantaneous [81,98] and space-time coupled returns [99], HDPs in presence of resetting in an interval [100,101] and bounded in complex potential [102], as well as discrete space-time resetting models [103] for HDPs, are other topics worth investigating.…”

Section: Discussionmentioning

confidence: 99%

Stochastic dynamics with multiplicative dichotomic noise: Heterogeneous telegrapher’s equation, anomalous crossovers and resetting

Sandev

Kocarev

Metzler

et al. 2022

Chaos, Solitons & Fractals

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“…The relation in equation ( 12) was first derived in [13], and has since been verified in different systems of interest, e.g. see [147,[153][154][155]172].…”

Section: Optimal Resetting Renders Fluctuations Universalmentioning

confidence: 94%

The inspection paradox in stochastic resetting

Pal

Kostinski

Reuveni

2022

J. Phys. A: Math. Theor.

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The remaining travel time of a plane shortens with every minute that passes from its departure, and a ﬂame diminishes a candle with every second it burns. Such everyday occurrences bias us to think that processes which have already begun will end before those which have just started. Yet, the inspection paradox teaches us that the converse can also happen when randomness is at play. The paradox comes from probability theory, where it is often illustrated by measuring how long passengers wait upon arriving at a bus stop at a random time. Interestingly, such passengers may on average wait longer than the mean time between bus arrivals – a counter-intuitive result, since one expects to wait less when coming some time after the previous bus departed. In this viewpoint, we review the inspection paradox and its origins. The insight gained is then used to explain why, in some situations, stochastic resetting expedites the completion of random processes. Importantly, this is done with elementary mathematical tools which help develop a probabilistic intuition for stochastic resetting and how it works. This viewpoint can thus be used as an accessible introduction to the subject.

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Stochastic resetting in the Kramers problem: A Monte Carlo approach

Cited by 10 publications

References 35 publications

A model-driven machine learning approach for personalized kidney graft risk prediction

A model-driven machine learning approach for personalized kidney graft risk prediction

Stochastic dynamics with multiplicative dichotomic noise: Heterogeneous telegrapher’s equation, anomalous crossovers and resetting

The inspection paradox in stochastic resetting

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