Unraveling intermittent features in single-particle trajectories by a local convex hull method

Lanoiselée, Yann; Grebenkov, Denis S.

doi:10.1103/physreve.96.022144

Cited by 36 publications

(34 citation statements)

References 93 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Given that the tracks of animal displacements are typically recorded at discrete time steps (e.g., daily observations) and relatively short, the subleading terms play an important role. The asymptotic formulas can also be used for calibrating new estimators, based on the local convex hull, that were proposed for the analysis of intermittent processes in microbiology [21]. Finally, the knowledge of the mean perimeter of the convex hull can be used to estimate the scaling exponent and the scale of symmetric Lévy flights, for which the conventional mean and variance estimators are useless.…”

Section: Discussionmentioning

confidence: 99%

Mean perimeter and mean area of the convex hull over planar random walks

Lanoiselée¹,

Majumdar²

2017

J. Stat. Mech.

Self Cite

View full text Add to dashboard Cite

We investigate the geometric properties of the convex hull over n successive positions of a planar random walk, with a symmetric continuous jump distribution. We derive the large n asymptotic behavior of the mean perimeter. In addition, we compute the mean area for the particular case of isotropic Gaussian jumps. While the leading terms of these asymptotics are universal, the subleading (correction) terms depend on finer details of the jump distribution and describe a "finite size effect" of discrete-time jump processes, allowing one to accurately compute the mean perimeter and the mean area even for small n, as verified by Monte Carlo simulations. This is particularly valuable for applications dealing with discrete-time jumps processes and ranging from the statistical analysis of single-particle tracking experiments in microbiology to home range estimations in ecology.

show abstract

Section: Discussionmentioning

confidence: 99%

Mean perimeter and mean area of the convex hull over planar random walks

Lanoiselée¹,

Majumdar²

2017

J. Stat. Mech.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Alternatively, universal model-free methods enable the identification of change points in an individual trajectory by considering a local functional that transforms the trajectory into a new time series. This new time series can then be used to characterize intermittent behavior [29,30]. Examples of local functionals that have been employed include the diffusivity [31], convex hull [29], anomalous exponent of the local MSD [32], and directional changes [22,33].…”

Section: Introductionmentioning

confidence: 99%

Elucidating distinct ion channel populations on the surface of hippocampal neurons via single-particle tracking recurrence analysis

et al. 2017

View full text Add to dashboard Cite

Protein and lipid nanodomains are prevalent on the surface of mammalian cells. In particular, it has been recently recognized that ion channels assemble into surface nanoclusters in the soma of cultured neurons. However, the interactions of these molecules with surface nanodomains display a considerable degree of heterogeneity. Here, we investigate this heterogeneity and develop statistical tools based on the recurrence of individual trajectories to identify subpopulations within ion channels in the neuronal surface. We specifically study the dynamics of the K + channel Kv1.4 and the Na + channel Nav1.6 on the surface of cultured hippocampal neurons at the single-molecule level. We find that both these molecules are expressed in two different forms with distinct kinetics with regards to surface interactions, emphasizing the complex proteomic landscape of the neuronal surface. Further, the tools presented in this work provide new methods for the analysis of membrane nanodomains, transient confinement, and identification of populations within single-particle trajectories.

show abstract

“…These quantities are used, usually in two dimensions, to describe home ranges of animals [30,31]. But also, very recently, to detect different phases in intermittent stochastic trajectories, like the run and tumble phases in the movement of bacteria [32]. The convex hull of a RW is the smallest convex polytope * hendrik.schawe@uni-oldenburg.de † a.hartmann@uni-oldenburg.de ‡ satya.majumdar@u-psud.fr containing the whole trace of the RW, i.e., it is a nonlocal characteristic that depends on the full history of the walker, namely all visited points.…”

Section: Introductionmentioning

confidence: 99%

Convex hulls of random walks in higher dimensions: A large-deviation study

2017

View full text Add to dashboard Cite

The distribution of the hypervolume V and surface ∂V of convex hulls of (multiple) random walks in higher dimensions are determined numerically, especially containing probabilities far smaller than P=10^{-1000} to estimate large deviation properties. For arbitrary dimensions and large walk lengths T, we suggest a scaling behavior of the distribution with the length of the walk T similar to the two-dimensional case and behavior of the distributions in the tails. We underpin both with numerical data in d=3 and d=4 dimensions. Further, we confirm the analytically known means of those distributions and calculate their variances for large T.

show abstract

Unraveling intermittent features in single-particle trajectories by a local convex hull method

Cited by 36 publications

References 93 publications

Mean perimeter and mean area of the convex hull over planar random walks

Mean perimeter and mean area of the convex hull over planar random walks

Elucidating distinct ion channel populations on the surface of hippocampal neurons via single-particle tracking recurrence analysis

Convex hulls of random walks in higher dimensions: A large-deviation study

Contact Info

Product

Resources

About