Persistent path Laplacian

Persistent Path Homology of Directed Networks

Informative Path Planning and Sensor Scheduling for Persistent Monitoring Tasks

In this thesis we consider two combinatorial optimization problems that relate to the field of persistent monitoring. In the first part, we extend the classic problem of finding the maximum weight Hamiltonian cycle in a graph to the case where the objective is a submodular function of the edges. We consider a greedy algorithm and a 2-matching based algorithm, and we show that they have approxim...

Persistent Path Homology of Directed Networks Samir Chowdhury and Facundo

While standard persistent homology has been successful in extracting information from metric datasets, its applicability to more general data, e.g. directed networks, is hindered by its natural insensitivity to asymmetry. We study a construction of homology of digraphs due to Grigor’yan, Lin, Muranov and Yau, and extend this construction to the persistent framework. The result, which we call pe...

Unification of Artificial Intelligence in Robot Motion and Path Planning Via Laplacian Technique

ABSTRACTThe paper deals with Robot motion and path planning in artificial intelligence. The aim of the paper is to develop a path planning programme for mobile robots that is based on laplacian technique. Robot path planning problem is an important combinational content of artificial intelligence and robotics. Its mission is to be independently movement from the starting point to the target poi...

Path Laplacian matrices: Introduction and application to the analysis of consensus in networks

Article history: Received 26 September 2011 Accepted 29 November 2011 Available online 22 December 2011 Submitted by R.A. Brualdi AMS classification: 05C50 15A18 15B99 05C82 05C21