An ensemble perspective on multi-layer networks

We study properties of multi-layered, interconnected networks from an ensemble perspective, i.e. we analyze ensembles of multi-layer networks that share similar aggregate characteristics. Using a diffusive process that evolves on a multi-layer network, we analyze how the speed of diffusion depends on the aggregate characteristics of both intra- and inter-layer connectivity. Through a block-matrix model representing the distinct layers, we construct transition matrices of random walkers on multi-layer networks, and estimate expected properties of multi-layer networks using a mean-field approach. In addition, we quantify and explore conditions on the link topology that allow to estimate the ensemble average by only considering aggregate statistics of the layers. Our approach can be used when only partial information is available, like it is usually the case for real-world multi-layer complex systems

Iwasawa Effects in Multi-layer Optics

There are many two-by-two matrices in layer optics. It is shown that they can be formulated in terms of a three-parameter group whose algebraic property is the same as the group of Lorentz transformations in a space with two space-like and one time-like dimensions, or the $Sp(2)$ group which is a standard theoretical tool in optics. Among the interesting mathematical properties of this group, the Iwasawa decomposition drastically simplifies the matrix algebra under certain conditions, and leads to a concise expression for the S-matrix for transmitted and reflected rays. It is shown that the Iwasawa effect can be observed in multi-layer optics, and a sample calculation of the S-matrix is given.Comment: RevTex 10 pages including 1 psfi

Multi-layer virtual transport network design

Service overlay networks and network virtualization enable multiple overlay/virtual networks to run over a common physical network infrastructure. They are widely used to overcome deficiencies of the Internet (e.g., resiliency, security and QoS guarantees). However, most overlay/virtual networks are used for routing/tunneling purposes, and not for providing scoped transport flows (involving all mechanisms such as error and flow control, resource allocation, etc.), which can allow better network resource allocation and utilization. Most importantly, the design of overlay/virtual networks is mostly single-layered, and lacks dynamic scope management, which is important for application and network management. In response to these limitations, we propose a multi-layer approach to Virtual Transport Network (VTN) design. This design is a key part of VTN-based network management, where network management is done via managing various VTNs over different scopes (i.e., ranges of operation). Our simulation and experimental results show that our multi-layer approach to VTN design can achieve better performance compared to the traditional single-layer design used for overlay/virtual networks.This work has been partly supported by National Science Foundation awards: CNS-0963974 and CNS-1346688