Related papers: A Graphical-Based Method for Plotting Local Bifurc…
The goal of this paper is to show how to produce a piece of rigorous bifurcation diagram of periodic orbits for an ODE. We study the Rossler system, one of the textbook examples of ODEs generating nontrivial dynamics, for the parameter…
Graph vertex ordering is widely employed in spatial data analysis, especially in urban analytics, where street graphs serve as spatial discretization for modeling and simulation. It is also crucial for visualization, as many methods require…
Dynamically changing graphs are used in many applications of graph algorithms. The scope of these graphs are in graphics, communication networks and in VLSI designs where graphs are subjected to change, such as addition and deletion of…
Dynamical System has been widely used for encoding trajectories from human demonstration, which has the inherent adaptability to dynamically changing environments and robustness to perturbations. In this paper we propose a framework to…
Drawings of non-planar graphs always result in edge crossings. When there are many edges crossing at small angles, it is often difficult to follow these edges, because of the multiple visual paths resulted from the crossings that slow down…
Urban intersections are prone to delays and inefficiencies due to static precedence rules and occlusions limiting the view on prioritized traffic. Existing approaches to improve traffic flow, widely known as automatic intersection…
Network systems have become a ubiquitous modeling tool in many areas of science where nodes in a graph represent distributed processes and edges between nodes represent a form of dynamic coupling. When a network topology is already known…
Complex systems which can be represented in the form of static and dynamic graphs arise in different fields, e.g. communication, engineering and industry. One of the interesting problems in analysing dynamic network structures is to monitor…
Dynamical systems are used to model a variety of phenomena in which the bifurcation structure is a fundamental characteristic. Here we propose a statistical machine-learning approach to derive lowdimensional models that automatically…
Motivated by deep learning regimes with multiple interacting yet distinct model components, we introduce learning diagrams, graphical depictions of training setups that capture parameterized learning as data rather than code. A learning…
Charts are an excellent way to convey patterns and trends in data, but they do not facilitate further modeling of the data or close inspection of individual data points. We present a fully automated system for extracting the numerical…
We consider discrete-time one-dimensional random dynamical systems with bounded noise, which generate an associated set-valued dynamical system. We provide necessary and sufficient conditions for a discontinuous bifurcation of a minimal…
It is well known that conventional simulation algorithms are inefficient for the statistical description of macroscopic systems exactly at the critical point due to the divergence of the corresponding relaxation time (critical slowing…
Forecasting system behaviour near and across bifurcations is crucial for identifying potential shifts in dynamical systems. While machine learning has recently been used to learn critical transitions and bifurcation structures from data,…
We obtain novel criteria for the existence of local bifurcation for periodic solutions of Hamiltonian systems by a comparison principle of the spectral flow. Our method allows to find the appearance of new solutions by a simple inspection…
Factor graph, as a bipartite graphical model, offers a structured representation by revealing local connections among graph nodes. This study explores the utilization of factor graphs in modeling the autonomous racecar planning problem,…
The ability of a soft robot to perform specific tasks is determined by its contact configuration, and transitioning between configurations is often necessary to reach a desired position or manipulate an object. Based on this observation, we…
Diagrams matter. Unfortunately, the deep learning community has no standard method for diagramming architectures. The current combination of linear algebra notation and ad-hoc diagrams fails to offer the necessary precision to understand…
We have developed (1) a graph visualization system that allows users to explore graphs by viewing them as a succession of spanning trees selected interactively, (2) a radial graph layout algorithm, and (3) an animation algorithm that…
Diagrammatic Teaching is a paradigm for robots to acquire novel skills, whereby the user provides 2D sketches over images of the scene to shape the robot's motion. In this work, we tackle the problem of teaching a robot to approach a…