Lagrangian descriptors for open maps

A Theoretical Framework for Lagrangian Descriptors

This paper provides a theoretical background for Lagrangian Descriptors (LDs). The goal of achieving rigourous proofs that justify the ability of LDs to detect invariant manifolds is simplified by introducing an alternative definition for LDs. The definition is stated for n-dimensional systems with general time dependence, however we rigorously prove that this method reveals the stable and unst...

Collaborative Descriptors: Convolutional Maps for Preprocessing

The paper presents a novel concept for collaborative descriptors between deeply learned and hand-crafted features. To achieve this concept, we apply convolutional maps for pre-processing, namely the convovlutional maps are used as input of hand-crafted features. We recorded an increase in the performance rate of +17.06% (multiclass object recognition) and +24.71% (car detection) from grayscale ...

Augmented-lagrangian Regularization of Matrix-valued Maps

We propose a novel framework for fast regularization of matrix-valued images. The resulting algorithms allow a unified treatment for a broad set of matrix groups and manifolds. Using an augmented-Lagrangian technique, we formulate a fast and highly parallel algorithm for matrixvalued image regularization. We demonstrate the applicability of the framework for various problems, such as motion ana...

Semi-θ-Open Sets and New Classes of Maps

Bisimulation from Open Maps

An abstract definition of bisimulation is presented. It enables a uniform definition of bisimulation across a range of different models for parallel computation presented as categories. As examples, transition systems, synchronisation trees, transition systems with independence (an abstraction from Petri nets) and labelled event structures are considered. On transition systems the abstract defi...