Related papers: Cinematica Topologica
For control systems that either have a fast explicit periodic dependence on time and bounded controls or have periodic solutions and small controls, we define an average control system that takes into account all possible variations of the…
Mathematical models of street traffic allowing assessment of the importance of their individual segments for the functionality of the street system is considering. Based on methods of cooperative games and the reliability theory the…
A short survey on applications of algebraic geometry in topological data analysis.
This work mainly presents a relativistic analytical calculating method for the finite speed-of-light effect in atom gravimeters, which can simplify the deriva- tion and give a more complete expression for the associated correction.
We propose an algorithm to estimate the topology of an embedded metric graph from a well-sampled finite subset of the underlying graph.
This paper presents a unified approach for localizing some relevant graph topological indices via majorization techniques. Through this method, old and new bounds are derived and numerical examples are provided, showing how former results…
Video interpolation is an important problem in computer vision, which helps overcome the temporal limitation of camera sensors. Existing video interpolation methods usually assume uniform motion between consecutive frames and use linear…
An analytical method to compute thermodynamic properties of a given Hamiltonian system is proposed. This method combines ideas of both dynamical systems and ensemble approaches to thermodynamics, providing de facto a possible alternative to…
A technique is presented for producing synthetic images from numerical simulations whereby the image resolution is adapted around prominent features. In so doing, adaptive image ray-tracing (AIR) improves the efficiency of a calculation by…
The simple realistic model of the tippe top is considered. An averaged system of equations of motion is obtained in special evolutionary variables. Through the qualitative analysis of this system the general features of the motion of the…
In this paper, we present an algorithm that computes the topological signature for a given periodic motion sequence. Such signature consists of a vector obtained by persistent homology which captures the topological and geometric changes of…
The Birkhoff Ergodic Theorem asserts under mild conditions that Birkhoff averages (i.e. time averages computed along a trajectory) converge to the space average. For sufficiently smooth systems, our small modification of numerical Birkhoff…
This research addresses a new tool for data analysis known as Topological Data Analysis TDA It underlies an area of Mathematics known as Combinatorial Algebra or more recently Algebraic Topology which through making strong use of…
We are addressing the optical speedup of movements of layers in moire patterns. We introduce a set of equations for computing curved patterns, where the formulas of optical speedup and moire periods are kept in their simplest form. We…
Over the past few decades, a significant rise of camera-based applications for traffic monitoring has occurred. Governments and local administrations are increasingly relying on the data collected from these cameras to enhance road safety…
In this article we prove two formulas for the topological entropy of an F-optical Hamiltonian flow induced by a C^{\infty} Hamiltonian, where F is a Lagrangian distribution. In these formulas, we calculate the topological entropy as the…
In this paper, we propose a global method for estimating the motion of a camera which films a static scene. Our approach is direct, fast and robust, and deals with adjacent frames of a sequence. It is based on a quadratic approximation of…
Topological statistics, in the form of persistence diagrams, are a class of shape descriptors that capture global structural information in data. The mapping from data structures to persistence diagrams is almost everywhere differentiable,…
A stochastic algorithm is proposed, finding the set of generalized means associated to a probability measure on a compact Riemannian manifold M and a continuous cost function on the product of M by itself. Generalized means include p-means…
Recurrence is a fundamental characteristic of dynamical systems with complicated behavior. Understanding the inner structure of recurrence is challenging, especially if the system has many degrees of freedom and is subject to noise. We…