A Comparative Assessment of the Methods-of-Moments for Estimating the Correlation Length of One-Dimensional Random Fields

Christodoulou, Panagiotis; Pantelidis, Lysandros; Gravanis, Elias

doi:10.1007/s11831-020-09408-2

Cited by 7 publications

(5 citation statements)

References 45 publications

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“…To exclude possible intrinsic HS-AFM noise, the average ACF plot was fitted starting at lag 1 because the autocorrelation coefficient at lag 1 could be computed mostly from intrinsic noise. Furthermore, given the fact that autocorrelation coefficients become less reliable as the time-lag increases, only the coefficients above a threshold of 95% confidence interval were fitted (Christodoulou et al, 2021).…”

Section: Estimation Of Decay Times From Acfs In Hs-afm Datamentioning

confidence: 99%

Dynamic molecular mechanism of the nuclear pore complex permeability barrier

Kozai

Fernández-Martı́nez

Eeuwen

et al. 2023

Preprint

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Nuclear pore complexes (NPCs) mediate nucleocytoplasmic transport of specific macromolecules while impeding the exchange of unsolicited material. However, key aspects of this gating mechanism remain controversial. To address this issue, we determined the nanoscopic behavior of the permeability barrier directly within yeast S. cerevisiae NPCs at transport-relevant timescales. We show that the large intrinsically disordered domains of phenylalanine-glycine repeat nucleoporins (FG Nups) exhibit highly dynamic fluctuations to create transient voids in the permeability barrier that continuously shape-shift and reseal, resembling a radial polymer brush. Together with cargo-carrying transport factors the FG domains form a feature called the central plug, which is also highly dynamic. Remarkably, NPC mutants with longer FG domains show interweaving meshwork-like behavior that attenuates nucleocytoplasmic transport in vivo. Importantly, the bona fide nanoscale NPC behaviors and morphologies are not recapitulated by in vitro FG domain hydrogels. NPCs also exclude self-assembling FG domain condensates in vivo, thereby indicating that the permeability barrier is not generated by a self-assembling phase condensate, but rather is largely a polymer brush, organized by the NPC scaffold, whose dynamic gating selectivity is strongly enhanced by the presence of transport factors.

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Section: Estimation Of Decay Times From Acfs In Hs-afm Datamentioning

confidence: 99%

Dynamic molecular mechanism of the nuclear pore complex permeability barrier

Kozai

Fernández-Martı́nez

Eeuwen

et al. 2023

Preprint

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“…The correlation length θ for clay may be taken 0.20m (see e.g., Pantelidis and Christodoulou [30]; in the paper in question, the θ value of two clay fields in Cyprus was calculated using the more convenient Fluctuation Function Method. A comparative assessment of the methods-of-moments for estimating the correlation length of one-dimensional random fields can be found in [31]). For a probability of failure PF = 0.0001, the minimum safety factor F PF is estimated 2.3.…”

Section: The Optimal Safety Factor Valuementioning

confidence: 99%

“…In this respect, small correlation lengths, i.e., more spatially variable soils, require higher safety factor for any given desired probability of failure and vice versa. of one-dimensional random fields can be found in [31]). For a probability of failure PF = 0.0001, the minimum safety factor FPF is estimated 2.3.…”

Section: The Optimal Safety Factor Valuementioning

confidence: 99%

An Analytical Random Field Solution for the Reliability of Axially Loaded Piles in the Ultimate Limit State Considering the Effect of Soil Sampling

2020

Self Cite

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The present work is concerned with the effect of soil spatial variability on estimating the ultimate soil resistance of floating axially loaded piles from point measurements of soil properties along the pile. The ultimate limit state is considered. In particular, closed form formulae for (i) determining the optimal sampling depth for minimizing statistical uncertainty and (ii) the optimal—minimum required—safety factor for a desired failure probability level are derived. A dimensionless parameter, the cohesion-to-friction parameter Λ, is introduced which quantifies the weight of soil’s cohesion contribution relative to that of soil’s friction in the linear trend of the ultimate soil strength. The analysis shows that the probability of failure profile with the sampling depth attains a minimum, designating the optimal sampling point. This depends on the scaled spatial correlation length of the soil Θ (i.e., the spatial correlation length of soil over the length of the pile) and the parameter Λ, but not on the coefficient of variance of the ultimate soil strength (covu) or the safety factor. Furthermore, it was found that the optimal depth is always at the lower half of the pile, approaching the mid-point or the bottom end of the pile for Λ>>1 or Λ<<1, respectively. In addition, it was found that for large Θ, the optimal depth tends to be closer to the mid-point of the pile, while for small Θ, the optimal sampling depth arises closer to the bottom end. The practical usefulness of the results is related to a suitable choice of the safety factor. Inverting the probability of failure formula at its minimum value, an optimal safety factor is obtained as a function of the desired (acceptable) probability of failure, and the parameters Θ, Λ and covu. The optimal safety factor is the minimum value required for a desired level of the probability of failure.

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“…Such analyses have previously been executed in the field of geosciences. In (Christodoulou et al, 2021), the influence of the sampling domain length and the sampling interval on the correlation length has been investigated. Here it was found that the domain length strongly affects the results from the estimation of the correlation length, where larger domains improve the estimate.…”

Section: Introductionmentioning

confidence: 99%

Numerical and Experimental Investigation of a Correlation Model to Describe Spatial Variability of Concrete Properties

Botte

Vereecken

Caspeele

2023

ASCE-ASME J. Risk Uncertainty Eng. Syst., Part A: Civ. Eng.

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The heterogeneous character of concrete results in spatial variation of its material properties. Random field models are often used to account for this effect. Due to the large scatter on the correlation lengths suggested in literature, tests could be performed to determine the most appropriate correlation model and corresponding correlation length. Subsequently, different techniques can be employed to fit an analytical model to the experimental semivariogram resulting in the most appropriate correlation model and corresponding correlation length. However, the resulting correlation lengths can largely depend on the experimental design. In this work, the effect of several parameters and choices to be made by an engineer in deriving the correlation model based on experimental data from destructive tests has been investigated. It was found that the curve fitting method generally leads to better estimates of the scale of fluctuation compared to the maximum likelihood method. Moreover, there is a clear benefit of applying a bootstrapping procedure to the experimental data to estimate the covariance matrix adopted in the fitting procedures as well as to estimate the uncertainty related to the estimated parameters. When a measurement error is suspected to be present and cannot be neglected, the nugget should be estimated together with the variance and the scale of fluctuation. Furthermore, the Gaussian correlation model was found to be the most robust choice, even if the actual correlation model is not Gaussian. the latter was confirmed for actual experimental data on the material properties of concrete, where a linear model was found to fit the data best but the Gaussian model provided comparable results.

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A Comparative Assessment of the Methods-of-Moments for Estimating the Correlation Length of One-Dimensional Random Fields

Cited by 7 publications

References 45 publications

Dynamic molecular mechanism of the nuclear pore complex permeability barrier

Dynamic molecular mechanism of the nuclear pore complex permeability barrier

An Analytical Random Field Solution for the Reliability of Axially Loaded Piles in the Ultimate Limit State Considering the Effect of Soil Sampling

Numerical and Experimental Investigation of a Correlation Model to Describe Spatial Variability of Concrete Properties

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