Closure to “Hurst on Reservoir Capacity”

Hurst, H. E.

doi:10.1061/taceat.0006517

Cited by 25 publications

(10 citation statements)

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“…FBM and the related GLE are used to describe processes such as long term storage capacity of water reservoirs [53], climate fluctuations [54], economical market dynamics [55], single file diffusion [56], and elastic models [57]. Motion of this type has also been associated with the relative motion of aminoacids in proteins [58], and the free diffusion of biopolymers under molecular crowding conditions [10,19,59].…”

Section: B Fractional Brownian Motionmentioning

confidence: 99%

Single particle tracking in systems showing anomalous diffusion: the role of weak ergodicity breaking

Burov

Jeon

Metzler

et al. 2011

Phys. Chem. Chem. Phys.

372

510

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Anomalous diffusion has been widely observed by single particle tracking microscopy in complex systems such as biological cells. The resulting time series are usually evaluated in terms of time averages. Often anomalous diffusion is connected with non-ergodic behaviour. In such cases the time averages remain random variables and hence irreproducible. Here we present a detailed analysis of the time averaged mean squared displacement for systems governed by anomalous diffusion, considering both unconfined and restricted (corralled) motion. We discuss the behaviour of the time averaged mean squared displacement for two prominent stochastic processes, namely, continuous time random walks and fractional Brownian motion. We also study the distribution of the time averaged mean squared displacement around its ensemble mean, and show that this distribution preserves typical process characteristics even for short time series. Recently, velocity correlation functions were suggested to distinguish between these processes. We here present analytical expressions for the velocity correlation functions. The knowledge of the results presented here is expected to be relevant for the correct interpretation of single particle trajectory data in complex systems.

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Section: B Fractional Brownian Motionmentioning

confidence: 99%

Single particle tracking in systems showing anomalous diffusion: the role of weak ergodicity breaking

Burov

Jeon

Metzler

et al. 2011

Phys. Chem. Chem. Phys.

372

510

View full text Add to dashboard Cite

show abstract

“…For example, almost no two snowflakes are the same. One measure of stochasticity in fractals is to calculate the Hurst exponent H introduced by Hurst [38], see the Methods section. For noisy time series the Hurst exponent will be in the interval between 0 and 1 whereas for a random walk type time series, it will be above 1.…”

Section: Introductionmentioning

confidence: 99%

Multifractality nature of microtubule dynamic instability process

Rezania

Sudirga

Tuszyński

2021

Physica A: Statistical Mechanics and its Applications

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The irregularity of growing and shortening patterns observed experimentally in microtubules reflects a dynamical system that fluctuates stochastically between assembly and disassembly phases. The observed time series of microtubule lengths have been extensively analyzed to shed light on structural and dynamical properties of microtubules. Here, for the first time, Multifractal Detrended Fluctuation analysis (MFDFA) has been employed to investigate the multifractal and topological properties of both experimental and simulated microtubule time series. We find that the time dependence of microtubule length possesses true multifractal characteristics and cannot be described by monofractal distributions. Based on the multifractal spectrum profile, a set of multifractal indices have been calculated that can be related to the level of dynamical activities of microtubules. We also show that the resulting multifractal spectra for the simulated data might not be comparable with experimental data. Statement of SignificanceMicrotubules are some of the most important subcellular structures involved in a multitude of functions in all eukaryotic cells. In addition to their cylindrical geometry, their polymerization/depolymerization dynamics, termed dynamic instability, is unique among all protein polymers. In this paper we demonstrate that there is a very specific mathematical representation of microtubule growth and shrinkage time series in terms of multifractality. We further show that using this characteristic, one can distinguish real experimental data from synthetic time series generated from computer simulations..

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“…This would allow for the recognition of suboptimal outcomes earlier than their identification with standard post hoc statistical analytical tools. The CUSUM method was first described in 1950, 13 and its value as an analytical tool for medical data was almost immediately realized. 14 Essentially, CUSUM analysis repeatedly applies a sequential probability test to any data whose results can be simplified to either a "success" or "failure."…”

Section: Discussionmentioning

confidence: 99%

Cumulative sum failure analysis of the learning curve with endovascular abdominal aortic aneurysm repair

Forbes

DeRose

Kribs

et al. 2004

Journal of Vascular Surgery

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Success rates with endovascular aneurysm repair will improve with an individual's experience. The CUSUM method is a valuable tool in the evaluation of this learning curve, which has credentialing and training implications. Although acceptable results were obtained throughout the study period, this analysis indicates that 60 endovascular aneurysm repairs, or 20 with an individual device, are necessary before optimal rates of initial clinical success can be achieved. These results can be achieved more readily with aortouniiliac grafts than with bifurcated grafts.

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Closure to “Hurst on Reservoir Capacity”

Cited by 25 publications

References 0 publications

Single particle tracking in systems showing anomalous diffusion: the role of weak ergodicity breaking

Single particle tracking in systems showing anomalous diffusion: the role of weak ergodicity breaking

Multifractality nature of microtubule dynamic instability process

Cumulative sum failure analysis of the learning curve with endovascular abdominal aortic aneurysm repair

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