We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Resilience and survivability in communication networks: Strategies, principles, and survey of disciplines

GENI: A federated testbed for innovative network experiments

The work is giving estimations of the discrepancy between solutions of the initial and the homogenized problems for a one{dimensional second order elliptic operators with random coeecients satisfying strong or uniform mixing conditions. We obtain several sharp estimates in terms of the corresponding mixing coeecient. Abstract. In the theory of homogenisation it is of particular interest to determine the classes of problems which are stable on taking the homogenisation limits. A notable situation where the limit enlarges the class of original problems is known as memory (nonlocal) eeects. A number of results in that direction has been obtained for linear problems. Tartar (1990) innitiated the study of the eeective equation corresponding to nonlinear equation: @ t u n + a n u 2 n = f: Signiicant progress has been hampered by the complexity of required computations needed in order to obtain the terms in power{series expansion. We propose a method which overcomes that diiculty by introducing graphs representing the domain of integration of the integrals in each term. The graphs are relatively simple, it is easy to calculate with them and they give us a clear image of the form of each term. The method allows us to discuss the form of the eeective equation and the convergence of power{series expansions. The feasibility of our method for other types of nonlinearities will be discussed as well.

Applied Mathematics and Computation

As the Internet becomes increasingly important to all aspects of society, the consequences of disruption become increasingly severe. Thus it is critical to increase the resilience and survivability of future networks. We define resilience as the ability of the network to provide desired service even when challenged by attacks, large-scale disasters, and other failures. This paper describes a comprehensive methodology to evaluate network resilience using a combination of topology generation, analytical, simulation, and experimental emulation techniques with the goal of improving the resilience and survivability of the Future Internet.

https://cdn.jprohrer.org/documents/publications/Sterbenz-Cetinkaya-Hameed-Jabbar-Qian-Rohrer-2011.pdf

Evaluation of network resilience, survivability, and disruption tolerance: analysis, topology generation, simulation, and experimentation

Optimizing algebraic connectivity by edge rewiring

The Great Plains Environment for Network Innovation – GpENI is an international programmable network testbed centered on a regional optical network in the Midwest US, providing flexible infrastructure across the entire protocol stack. The goal of GpENI is to build a collaborative research infrastructure enabling the community to conduct experiments in future Internet architecture. GpENI is funded in part by the US National Science Foundation GENI (Global Environments for Network Innovation) program and by the EU FIRE (Future Internet Research and Experimentation) Programme, and is affiliated with a project funded by the NSF FIND (Future Internet Design) Program.

/pdf/the-great-plains-environment-for-network-innovation-gpeni-a-y59d8e0wrq.pdf

The Great Plains Environment for Network Innovation (GpENI): A Programmable Testbed for Future Internet Architecture Research

In this paper, a maximum power tracking technique is presented for doubly fed induction generator-based wind turbines. The presented technique is a novel version of the conventional method, i.e., the electrical torque is proportional to the square of the rotor speed, in which the proportional coefficient is adaptively adjusted in real-time through three control laws. The first control law calculates the desired electrical torque using feedback linearization, assuming that the power capture coefficient and the desired rotor speed are instantaneously identified. The second control law estimates the real-time values of the power capture coefficient from a Lyapunov-based analysis, and the third control law provides the desired rotor speed. These control laws cause the turbine to adaptively adjust the rotor speed toward a desired speed in which the operating point moves in the direction of increasing the power capture coefficient. The proposed maximum power tracking method differs distinctly from the perturb-and-observe scheme by eliminating a need for adding a dither or perturbation signal, and robustly tracks the trajectory of maximum power points even in the event of a sudden wind speed change that can cause the perturb-and-observe technique to fail. In this paper, the National Renewal Energy Laboratory 5-MW reference wind turbine model is used to demonstrate the validity and robustness of the proposed method.

A Maximum Power Tracking Technique for Grid-Connected DFIG-Based Wind Turbines

The study of epidemics is a crucial issue to several areas. An epidemic can have devastating economic and social consequences. A single crop disease in Kansas could destroy the yearly income of many farmers. Previous work using graph theory has determined a universal epidemic threshold found in the graph topology for a binary contact network in the compartmental susceptible-infected (SI) analysis. We expand this threshold to a more realistic measure. A binary uniform level of contact within a society is too idealistic and an improved threshold is found in allowing a spectrum of contact within a contact network. The expanded contact network also allows for asymmetric contact such as a mother caring for her child. Further study in this area should lead to improved simulators, disease modeling, policies and control of infectious diseases and viruses.

Don Gruenbacher

Papers

Optimizing algebraic connectivity by edge rewiring

The Great Plains Environment for Network Innovation (GpENI): A Programmable Testbed for Future Internet Architecture Research

A Maximum Power Tracking Technique for Grid-Connected DFIG-Based Wind Turbines

Epidemic spreading on weighted contact networks

Using GENI for experimental evaluation of Software Defined Networking in smart grids