Geometry and Topology of Complex Networks
Abstract
The current vision of many military leaders and policy makers about network-centric technology portrays a future in which networked systems provide unprecedented levels of performance, robustness, and efficiency. Unfortunately, there are fundamental, basic obstacles to realizing this vision. Some of these obstacles stems from a lack of a fundamental theory and our lack of comprehensive understanding of he mathematics of interconnected technological, information, and social networks. To address these challenges, we embarked on a multi-investigator, multidisciplinary project on mathematics of networks and networked systems, that addresses fundamental issues from topology to geometry of networks. This multi-year, multidisciplinary effort, lead to training of a large group of students and postdocs, involved in academic research activity upon completion of their studies. Aside from many theses and research papers, the research has lead to fundamental understanding along multiple domains. The highlights include the following developments:1) Spectral methods in networks: a) A theory of random walks on directed networks b) A theory of random walks on simplicial complexes 2) Discrete Dirichlet problems, Heat kernel PageRank, and PageRank on simplicial Complexes 3) Developed concept of quantum state transfer on graphs 4) Developed new notions of curvature on graphs 5) New algorithms for distributed optimization using spectral graph theory 6) new algorithms for sensor and actuator placement using spectral methods and sparsification theory.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 06, 2018
- Accession Number
- AD1057354
Entities
People
- Ali Jadbabaie