Related papers: Stability for layer points
We show that specific higher dimensional shape information of point cloud data can be recovered by observing lower dimensional hierarchical clustering dynamics. We generate multiple point samples from point clouds and perform hierarchical…
We prove two related concentration inequalities concerning the number of rational points of hyperelliptic curves over subsets of a finite field. In particular, we investigate the probability of a large discrepancy between the numbers of…
Here we report experiments on particle cluster settling at high Reynolds number in quiescent fluid contained in a vessel. The particles were observed to settle in a near-circular shape irrespective of the shape of the vessel cross-section…
Algorithms increasingly operate within complex physical, social, and engineering systems where they are exposed to disturbances, noise, and interconnections with other dynamical systems. This article extends known convergence guarantees of…
The dynamical system for inertial particles in fluid flow has both attracting and repelling regions, the interplay of which can localize particles. In laminar flow experiments we find that particles, initially moving throughout the fluid…
In this paper, we examine linear conditions on finite sets of points in projective space implied by the Cayley-Bacharach condition. In particular, by bounding the number of points satisfying the Cayley-Bacharach condition, we force them to…
A pair of complex-conjugate fixed points that lie close to the real axis generates a large mass hierarchy in the real renormalization group flow that passes in between them. We show that pairs of complex fixed points that are close to the…
The study of the interplay between the structure and dynamics of complex multilevel systems is a pressing challenge nowadays. In this paper, we use a semi-annealed approximation to study the stability properties of Random Boolean Networks…
The network topology can be described by the number of nodes and the interconnections among them. The degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability…
What is the "right" topological invariant of a large point cloud X? Prior research has focused on estimating the full persistence diagram of X, a quantity that is very expensive to compute, unstable to outliers, and far from a sufficient…
We investigate a simple network, which has a branching-merging structure, using the totally asymmetric simple exclusion process, considering conflicts at the merging point. For both periodic and open boundary conditions, the system exhibits…
Multiplex networks are a type of multilayer network in which entities are connected to each other via multiple types of connections. We propose a method, based on computing pairwise similarities between layers and then doing community…
We prove a general finite convergence theorem for "upward-guarded" fixpoint expressions over a well-quasi-ordered set. This has immediate applications in regular model checking of well-structured systems, where a main issue is the eventual…
We consider a system hierarchically modular, if besides its hierarchical structure it shows a sequence of scale separations from the point of view of some functionality or property. Starting from regular, deterministic objects like the…
This work concerns the theoretical foundations of persistence-based topological data analysis. We develop theory of topological inference in the multidimensional persistence setting, and directly at the (topological) level of filtrations…
The instability of mixing in the Kuramoto model of coupled phase oscillators is the key to understanding a range of spatiotemporal patterns, which feature prominently in collective dynamics of systems ranging from neuronal networks, to…
A novel method to obtain hierarchical and overlapping clusters from network data -i.e., a set of nodes endowed with pairwise dissimilarities- is presented. The introduced method is hierarchical in the sense that it outputs a nested…
Distributed consensus protocols provide a mechanism for spreading information within clustered networks, allowing agents and clusters to make decisions without requiring direct access to the state of the ensemble. In this work, we propose a…
In a standard cluster analysis, such as k-means, in addition to clusters locations and distances between them, it's important to know if they are connected or well separated from each other. The main focus of this paper is discovering the…
An unsupervised classification method for point events occurring on a network of lines is proposed. The idea relies on the distributional flexibility and practicality of random partition models to discover the clustering structure featuring…