Related papers: Persistence in Practice
Assume that a finite set of points is randomly sampled from a subspace of a metric space. Recent advances in computational topology have provided several approaches to recovering the geometric and topological properties of the underlying…
A great deal of recent data on event-by-event fluctuation and correlation measurements has been released by several experiments at the SPS and RHIC. Recent results on charge fluctuations, balance functions in pseudorapidity, and average…
We present a general scheme to calculate within the independent interval approximation generalized (level-dependent) persistence properties for processes having a finite density of zero-crossings. Our results are especially relevant for the…
To quantitatively characterize height distributions (HDs), one uses adimensional ratios of their first central moments ($m_n$) or cumulants ($\kappa_n$), especially the skewness $S$ and kurtosis $K$, whose accurate estimate demands an…
Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field.…
We study the persistence probability of a centered stationary Gaussian process on $\mathbb{Z}$ or $\mathbb{R}$, that is, its probability to remain positive for a long time. We describe the delicate interplay between this probability and the…
Consider a realization of a Poisson process in R^2 with intensity 1 and take a maximal up/right path from the origin to (N,N) consisting of line segments between the points, where maximal means that it contains as many points as possible.…
One of the ultimate goals of nuclear collision experiments at high energy is to map the phase diagram of strongly interacting matter. A very challenging task is the determination of the QCD phase structure including the search for critical…
For the moving average process $X_n=\rho \xi_{n-1}+\xi_n$, $n\in\mathbb{N}$, where $\rho\in\mathbb{R}$ and $(\xi_i)_{i\ge -1}$ is an i.i.d. sequence of normally distributed random variables, we study the persistence probabilities…
We study the complete probability distribution $\mathcal{P}\left(\bar{H},t\right)$ of the time-averaged height $\bar{H}=(1/t)\int_0^t h(x=0,t')\,dt'$ at point $x=0$ of an evolving 1+1 dimensional Kardar-Parisi-Zhang (KPZ) interface…
A statistical method for the estimation of spatial correlation lengths of Gaussian-shaped fluctuating signals with two measurement points is examined to quantitatively evaluate its reliability (variance) and accuracy (bias error). The…
Persistence modules are a central algebraic object arising in topological data analysis. The notion of interleaving provides a natural way to measure distances between persistence modules. We consider various classes of persistence modules,…
The concept of topological persistence, introduced recently in computational topology, finds applications in studying a map in relation to the topology of its domain. Since its introduction, it has been extended and generalized in various…
The theory of multidimensional persistent homology was initially developed in the discrete setting, and involved the study of simplicial complexes filtered through an ordering of the simplices. Later, stability properties of…
Persistent homology provides a robust methodology to infer topological structures from point cloud data. Here we explore the persistent homology of point clouds embedded into a probabilistic setting, exploiting the theory of point…
A fluid in a non-equilibrium state exhibits long-ranged correlations of its hydrodynamic fluctuations. In this article, we examine the effect of a transpiration interface on these correlations -- specifically, we consider a dilute gas in a…
This paper provides a method to calculate the bar codes of a PCD (point cloud data) with real coefficients in Section 3. With Dan Burghelea and Tamal Dey we developed a persistence theory which involves level sets discussed in Section 4.…
We study the persistence probability for processes with stationary increments. Our results apply to a number of examples: sums of stationary correlated random variables whose scaling limit is fractional Brownian motion, random walks in…
We propose that the recently defined persistent homology dimensions are a practical tool for fractal dimension estimation of point samples. We implement an algorithm to estimate the persistent homology dimension, and compare its performance…
The quantum fluctuations of fields can exhibit subtle correlations in space and time. As the interval between a pair of measurements varies, the correlation function can change sign, signaling a shift between correlation and…