Recovering a stochastic process from super-resolution noisy ensembles of single-particle trajectories

a b s t r a c tRecords of relative paleointensity are subject to several sources of error. Temporal averaging due to gradual acquisition of magnetization removes high-frequency fluctuations, whereas random errors introduce fluctuations at high frequency. Both sources of error limit our ability to construct stochastic models from paleomagnetic observations. We partially circumvent these difficulties by recognizing that the largest affects occur at high frequency. To illustrate we construct a stochastic model from two recent inversions of paleomagnetic observations for the axial dipole moment. An estimate of the noise term in the stochastic model is recovered from a high-resolution inversion (CALS10k.2), while the drift term is estimated from the low-frequency part of the power spectrum for a long, but lower-resolution inversion (PADM2M). Realizations of the resulting stochastic model yield a composite, broadband power spectrum that agrees well with the spectra from both PADM2M and CALS10k.2. A simple generalization of the stochastic model permits predictions for the mean rate of magnetic reversals. We show that the reversal rate depends on the time-averaged dipole moment, the variance of the dipole moment and a slow timescale that characterizes the adjustment of the dipole toward the time-averaged value. Predictions of the stochastic model give a mean rate of 4.2 Myr À1, which is in good agreement with observations from marine magnetic anomalies.

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“…Even when Dx and Dg are uncorrelated, and gðtÞ represents the effects of white noise, we are left with (Hoze and Holeman, 2015) DðyÞ…”

Section: Influence Of Random Errormentioning

confidence: 99%

Constructing stochastic models for dipole fluctuations from paleomagnetic observations

Buffett

Puranam

2017

Physics of the Earth and Planetary Interiors

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“…2C), where a Gaussian error of amplitude σ is added to the physical position Z phys , so that the measured position is Z measured = Z phys + σξ. Such localization error affects the value of the effective diffusion coefficient compared to the physical diffusion coefficient D phys , leading to shift D measured = D phys + σ 2 2∆t + Aσ 2 divf , where A is a constant and f is the force applied to the tagged loci [37]. The noise localization error influences differently the values of the four biophysical parameters, in particular, the anomalous exponent α should not vary when ∆t changes because…”

Section: Influence Of the Sampling Time Step ∆T On The Four Measured mentioning

confidence: 99%

Single particle trajectory statistic to reconstruct chromatin organization and dynamics

Shukron

Seeber

Amitai

et al. 2019

Preprint

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Chromatin organization remains complex and far from understood. We discuss here recent statistical methods to extract biophysical parameters from in vivo single particle trajectories of loci to reconstruct chromatin reorganization in response to cellular stress such as DNA damages. We look at the methods to analyze both single loci as well as multiple loci tracked simultaneously and explain how to quantify and describe chromatin motion using a combination of extractable parameters. These parameters can be converted into information about chromatin dynamics and function. Furthermore, we discuss how the time scale of recurrent motion of a locus can be extracted and converted into local chromatin dynamics. We also discuss the effect of various sampling rates on the estimated parameters. Finally, we discuss polymer methods based on cross-linkers that account for minimal loop constraints hidden in tracked loci, that reveal chromatin organization at the 250nm spatial scale. We list and refer to some algorithm packages that are now publicly available. To conclude, chromatin organization and dynamics at hundreds of nanometers can be reconstructed from locus trajectories and predicted based on polymer models.

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“…In this section, we present the construction of empirical estimators that serve to recover physical properties from parametric [37,41,87] and non-parametric statistics [4]. Retrieving statistical parameters of a diffusion process from one-dimensional time series statistics have been studied using Bayesian inference in [30,65].…”

Section: Empirical Estimation Of the Drift And Diffusion Tensor Of A mentioning

confidence: 99%

“…where η n are i.i.d m-dimensional standard gaussian variable and σ is a small parameter. Then, the estimator for the drift is [41]…”

Section: Generalization In Dimension Mmentioning

confidence: 99%

Statistical methods for large ensemble of super-resolution stochastic single particle trajectories

Hozé¹,

Holcman

2017

Preprint

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Following recent progresses in super-resolution microscopy obtained in the last decade, massive amount of redundant single stochastic trajectories are now available for statistical analysis. Flows of trajectories of molecules or proteins are sampling the cell membrane or its interior at a very high time and space resolution. Several statistical analysis were developed to extract information contained in these data, such as the biophysical parameters of the underlying stochastic motion to reveal the cellular organization. These trajectories can further reveal hidden subcellular organization. We present here the statistical analysis of these trajectories based on the classical Langevin equation, which serves as a model of trajectories. Parametric and non-parametric estimators are constructed by discretizing the stochastic equations and they allow recovering tethering forces, diffusion tensor or membrane organization from measured trajectories, that differ from physical ones by a localization noise. Modeling, data analysis and automatic detection algorithms serve extracting novel biophysical features such as potential wells and other sub-structures, such as rings at an unprecedented spatiotemporal resolution. It is also possible to reconstruct the surface membrane of a biological cell from the statistics of projected random trajectories.

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Recovering a stochastic process from super-resolution noisy ensembles of single-particle trajectories

Cited by 18 publications

References 18 publications

Constructing stochastic models for dipole fluctuations from paleomagnetic observations

Constructing stochastic models for dipole fluctuations from paleomagnetic observations

Single particle trajectory statistic to reconstruct chromatin organization and dynamics

Statistical methods for large ensemble of super-resolution stochastic single particle trajectories

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