Related papers: The Medusa of Spatial Sorting: Topological Constru…
In this paper we present a semantic study of motion complexes (ie. of a motion verb followed by a spatial preposition). We focus on the spatial and the temporal intrinsic semantic properties of the motion verbs, on the one hand, and of the…
An extended interference pattern close to surface may result in both a transmissive or evanescent surface fields for large area manipulation of trapped particles. The affinity of differing particle sizes to a moving standing wave light…
Recent improvements in positioning technology has led to a much wider availability of massive moving object data. A crucial task is to find the moving objects that travel together. Usually, these object sets are called spatio-temporal…
Sentence ordering is the task of arranging the sentences of a given text in the correct order. Recent work using deep neural networks for this task has framed it as a sequence prediction problem. In this paper, we propose a new framing of…
Our objective is to discover and localize monotonic temporal changes in a sequence of images. To achieve this, we exploit a simple proxy task of ordering a shuffled image sequence, with `time' serving as a supervisory signal, since only…
Given an autohomeomorphism on an ordered topological space or its subspace, we show that it is sometimes possible to introduce a new topology-compatible order on that space so that the same map is monotonic with respect to the new ordering.…
What is chaos? Despite several decades of research on this ubiquitous and fundamental phenomenon there is yet no agreed-upon answer to this question. Recently, it was realized that all stochastic and deterministic differential equations,…
A topological measure on a locally compact space is a set function on open and closed subsets which is finitely additive on the collection of open and compact sets, inner regular on open sets, and outer regular on closed sets. Almost all…
We have analyzed the interplay between noise and periodic spatial modulations in bistable systems outside equilibrium and found that noise is able to increase the spatial order of the system, giving rise to periodic patterns which otherwise…
In this letter we present a method of constructing dynamical systems with any preassigned number of equilibria by adding symmetry to another system with at least one equilibrium point. If the resulting system is chaotic, we call this…
A convenient measure of a map or flow's chaotic action is the topological entropy. In many cases, the entropy has a homological origin: it is forced by the topology of the space. For example, in simple toral maps, the topological entropy is…
Mathematical morphology, a field within image processing, includes various filters that either highlight, modify, or eliminate certain information in images based on an application's needs. Key operations in these filters are dilation and…
A novel paradigm for sorting is introduced, based upon resetting. Using simple examples, we demonstrate that sorting is achieved by resetting the velocity component(s) or orientation of the particles, rather than position. The objects to be…
Circuit topology refers to the arrangement of interactions between objects belonging to a linearly ordered object set. Linearly ordered set of objects are common in nature and occur in a wide range of applications in economics, computer…
In sorting situations where the final destination of each item is known, it is natural to repeatedly choose items and place them where they belong, allowing the intervening items to shift by one to make room. (In fact, a special case of…
The field of mathematical morphology offers well-studied techniques for image processing. In this work, we view morphological operations through the lens of persistent homology, a tool at the heart of the field of topological data analysis.…
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…
For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a…
The curvature field is measured from tracer particle trajectories in a two-dimensional fluid flow that exhibits spatiotemporal chaos, and is used to extract the hyperbolic and elliptic points of the flow. These special points are pinned to…
We use topological data analysis and machine learning to study a seminal model of collective motion in biology [D'Orsogna et al., Phys. Rev. Lett. 96 (2006)]. This model describes agents interacting nonlinearly via attractive-repulsive…