Related papers: Development of the Poincare cross-section method: …
In this article, we prove the finite dimensionality of the global attractor and estimate the numbers of the determining modes for the 2D Boussinesq system in a periodic channel with fractional Laplacian in subcritical case.
We propose an optical flow-guided approach for semi-supervised video object segmentation. Optical flow is usually exploited as additional guidance information in unsupervised video object segmentation. However, its relevance in…
In this paper we use the parameterization method to provide a complete description of the dynamics of an $n$-dimensional oscillator beyond the classical phase reduction. The parameterization method allows, via efficient algorithms, to…
The paper presents an alternative way to classical stereocorrelation. First, 2D image processing of random patterns is described. Sub-pixel displacements are determined using phase analysis. Then distortion evaluation is presented. The…
Scientists aim to extract simplicity from observations of the complex world. An important component of this process is the exploration of data in search of trends. In practice, however, this tends to be more of an art than a science. Among…
Geometric phase has historically been defined using closed cycles of polarization states, often derived using differential geometry on the Poincare sphere. Using the recently-developed wave model of geometric phase, we show that it is…
Recent developments in machine learning and signal processing have resulted in many new techniques that are able to effectively capture the intrinsic yet complex properties of hyperspectral imagery. Tasks ranging from anomaly detection to…
We classify the global dynamics of a family of Kolmogorov systems depending on three parameters which has ecological meaning as it modelizes a predator-prey system. We obtain all their topologically distinct global phase portraits in the…
For a class of flows on polytopes, including many examples from Evolutionary Game Theory, we describe a piecewise linear model which encapsulates the asymptotic dynamics along the heteroclinic network formed out of the polytope's vertexes…
We clarify the connection between attractor solutions known from studies of Bjorken flow in conformal models of relativistic fluid dynamics and the more general description of attractors as submanifolds in phase space. We show how to…
In this paper, we introduce a new concept of incorporating factorized flow maps as mid-level representations, for bridging the perception and the control modules in modular learning based robotic frameworks. To investigate the advantages of…
A comprehensive framework for detection and characterization of overlapping intrinsic symmetry over 3D shapes is proposed. To identify prominent symmetric regions which overlap in space and vary in form, the proposed framework is decoupled…
Dimensionality reduction is a common method for analyzing and visualizing high-dimensional data. However, reasoning dynamically about the results of a dimensionality reduction is difficult. Dimensionality-reduction algorithms use complex…
Even though the analysis of unsteady 2D flow fields is challenging, fluid mechanics experts generally have an intuition on where in the simulation domain specific features are expected. Using this intuition, showing similar regions enables…
We recently described a specific type of attractors of two-dimensional discontinuous piecewise linear maps, characterized by two discontinuity lines dividing the phase plane into three partitions, related to economic applications. To our…
We present a fully automated method that identifies attractors and their basins of attraction without approximations of the dynamics. The method works by defining a finite state machine on top of the system flow. The input to the method is…
Perception research provides strong evidence in favor of part based representation of shapes in human visual system. Despite considerable differences among different theories in terms of how part boundaries are found, there is substantial…
We report on recent progress we made towards the four-dimensional formulation of the sector improved residue subtraction. We explain how the subtraction scheme STRIPPER is generalized to higher multiplicities and therefore furnishes a…
Poincar\'e maps are an integral aspect to our understanding and analysis of nonlinear dynamical systems. Despite this fact, the construction of these maps remains elusive and is primarily left to simple motivating examples. In this…
This paper presents a method that improve state-of-the-art of the concave point detection methods as a first step to segment overlapping objects on images. It is based on the analysis of the curvature of the objects contour. The method has…