Related papers: Metric for attractor overlap
Accurate velocity estimation of surrounding moving objects and their trajectories are critical elements of perception systems in Automated/Autonomous Vehicles (AVs) with a direct impact on their safety. These are non-trivial problems due to…
The two main data categories of vehicular traffic flow, stationary detector data and floating-car data, are also available for many Marathons and other mass-sports events: Loop detectors and other stationary data sources find their…
In this paper we introduce an interlacing condition on the elements of a family of operators that allows us to gather together a number of results on fixed points and common fixed points for single and families of mappings defined on metric…
In this study, the global convergence properties of the Oja flow, a continuous-time algorithm for principal component extraction, was established for general square matrices. The Oja flow is a matrix differential equation on the Stiefel…
We study an old geometric optimization problem in the plane. Given a perfect matching $M$ on a set of $n$ points in the plane, we can transform it to a non-crossing perfect matching by a finite sequence of flip operations. The flip…
We study the attractor of Iterated Function Systems composed of infinitely many affine, homogeneous maps. In the special case of second generation IFS, defined herein, we conjecture that the attractor consists of a finite number of…
In most modern object detection pipelines, the detection proposals are processed independently given the feature map. Therefore, they overlook the underlying relationships between objects and the surrounding background, which could have…
Practical data assimilation algorithms often contain hyper-parameters, which may arise due to, for instance, the use of certain auxiliary techniques like covariance inflation and localization in an ensemble Kalman filter, the…
We introduce a LiDAR inertial odometry (LIO) framework, called LiPO, that enables direct comparisons of different iterative closest point (ICP) point cloud registration methods. The two common ICP methods we compare are point-to-point (P2P)…
A simple and transparent example of a non-autonomous flow system, with hyperbolic strange attractor is suggested. The system is constructed on a basis of two coupled van der Pol oscillators, the characteristic frequencies differ twice, and…
Open-set supervised anomaly detection (OSAD) aims to identify unseen anomalies using limited anomalous supervision. However, existing prototype-based methods typically model normal data via a unimodal Gaussian prior, failing to capture…
This paper proposes and evaluates a new metric. This metric will overcome a limitation of the Optimal Subpattern Assignment (OSPA) metric mentioned by Schuhmacher et al.: the OSPA distance between two sets of points is insensitive to the…
In this paper, we provide a comprehensive rigorous modeling for multidimensional spaces with hierarchically structured dimensions in several layers of abstractions and data cubes that live in such spaces. We model cube queries and their…
Most metrics between finite point measures currently used in the literature have the flaw that they do not treat differing total masses in an adequate manner for applications. This paper introduces a new metric $\bar{d}_1$ that combines…
Michor and Mumford showed that the mean curvature flow is a gradient flow on a Riemannian structure with a degenerate geodesic distance. It is also known to destroy the uniform density of gridpoints on the evolving surfaces. We introduce a…
Bayesian statistics has two common measures of central tendency of a posterior distribution: posterior means and Maximum A Posteriori (MAP) estimates. In this paper, we discuss a connection between MAP estimates and posterior means. We…
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…
Metric mean dimension is a geometric invariant of dynamical systems with infinite topological entropy. We relate this concept with the fractal structure of the phase space and the H\"older regularity of the map. Afterwards we improve our…
The motion of a contact line is examined, and comparisons drawn, for a variety of models proposed in the literature. Pressure and stress behaviours at the contact line are examined in the prototype system of quasistatic spreading of a thin…
We use simple equations in order to compare the basins of attraction on the complex plane, corresponding to a large collection of numerical methods, of several order. Two cases are considered, regarding the total number of the roots, which…