There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

The structure and dynamics of multilayer networks

Praise for the Third Edition: "This is one of the best books available. Its excellent organizational structure allows quick reference to specific models and its clear presentation . . . solidifies the understanding of the concepts being presented."IIE Transactions on Operations EngineeringThoroughly revised and expanded to reflect the latest developments in the field, Fundamentals of Queueing Theory, Fourth Edition continues to present the basic statistical principles that are necessary to analyze the probabilistic nature of queues. Rather than presenting a narrow focus on the subject, this update illustrates the wide-reaching, fundamental concepts in queueing theory and its applications to diverse areas such as computer science, engineering, business, and operations research.This update takes a numerical approach to understanding and making probable estimations relating to queues, with a comprehensive outline of simple and more advanced queueing models. Newly featured topics of the Fourth Edition include:Retrial queuesApproximations for queueing networksNumerical inversion of transformsDetermining the appropriate number of servers to balance quality and cost of serviceEach chapter provides a self-contained presentation of key concepts and formulae, allowing readers to work with each section independently, while a summary table at the end of the book outlines the types of queues that have been discussed and their results. In addition, two new appendices have been added, discussing transforms and generating functions as well as the fundamentals of differential and difference equations. New examples are now included along with problems that incorporate QtsPlus software, which is freely available via the book's related Web site.With its accessible style and wealth of real-world examples, Fundamentals of Queueing Theory, Fourth Edition is an ideal book for courses on queueing theory at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners who analyze congestion in the fields of telecommunications, transportation, aviation, and management science.

Fundamentals of Queueing Theory

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems Consequently, it is necessary to generalize "traditional" network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others We also survey and discuss existing data sets that can be represented as multilayer networks We review attempts to generalize single-layer-network diagnostics to multilayer networks We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks We conclude with a summary and an outlook

Multilayer Networks

An important security challenge is to protect the execution of security-sensitive code on legacy systems from malware that may infect the OS, applications, or system devices. Prior work experienced a tradeoff between the level of security achieved and efficiency. In this work, we leverage the features of modern processors from AMD and Intel to overcome the tradeoff to simultaneously achieve a high level of security and high performance. We present TrustVisor, a special-purpose hypervisor that provides code integrity as well as data integrity and secrecy for selected portions of an application. TrustVisor achieves a high level of security, first because it can protect sensitive code at a very fine granularity, and second because it has a very small code base (only around 6K lines of code) that makes verification feasible. TrustVisor can also attest the existence of isolated execution to an external entity. We have implemented TrustVisor to protect security-sensitive code blocks while imposing less than 7% overhead on the legacy OS and its applications in the common case.

http://www.cse.psu.edu/~trj1/cse597-s11/docs/trustvisor_oakland10.pdf

TrustVisor: Efficient TCB Reduction and Attestation

We argue that the traditional notion of trust as a relation among entities, while useful, becomes insufficient for emerging data-centric mobile ad hoc networks. In these systems, setting the data trust level equal to the trust level of the data- providing entity would ignore system salient features, rendering applications ineffective and systems inflexible. This would be even more so if their operation is ephemeral, i.e., characterized by short-lived associations in volatile environments. In this paper, we address this challenge by extending the traditional notion of trust to data-centric trust: trustworthiness attributed to node-reported data per se. We propose a framework for data-centric trust establishment: First, trust in each individual piece of data is computed; then multiple, related but possibly contradictory, data are combined; finally, their validity is inferred by a decision component based on one of several evidence evaluation techniques. We consider and evaluate an instantiation of our framework in vehicular networks as a case study. Our simulation results show that our scheme is highly resilient to attackers and converges stably to the correct decision.

/pdf/on-data-centric-trust-establishment-in-ephemeral-ad-hoc-3l3evdtsa6.pdf

On Data-Centric Trust Establishment in Ephemeral Ad Hoc Networks

We present the Crossfire attack -- a powerful attack that degrades and often cuts off network connections to a variety of selected server targets (e.g., servers of an enterprise, a city, a state, or a small country) by flooding only a few network links. In Crossfire, a small set of bots directs low intensity flows to a large number of publicly accessible servers. The concentration of these flows on the small set of carefully chosen links floods these links and effectively disconnects selected target servers from the Internet. The sources of the Crossfire attack are undetectable by any targeted servers, since they no longer receive any messages, and by network routers, since they receive only low-intensity, individual flows that are indistinguishable from legitimate flows. The attack persistence can be extended virtually indefinitely by changing the set of bots, publicly accessible servers, and target links while maintaining the same disconnection targets. We demonstrate the attack feasibility using Internet experiments, show its effects on a variety of chosen targets (e.g., servers of universities, US states, East and West Coasts of the US), and explore several countermeasures.

The Crossfire Attack

We study the diffusion of influence in random multiplex networks where links can be of $r$ different types, and, for a given content (e.g., rumor, product, or political view), each link type is associated with a content-dependent parameter ${c}_{i}$ in $[0,\ensuremath{\infty}]$ that measures the relative bias type $i$ links have in spreading this content. In this setting, we propose a linear threshold model of contagion where nodes switch state if their ``perceived'' proportion of active neighbors exceeds a threshold $\ensuremath{\tau}$. Namely a node connected to ${m}_{i}$ active neighbors and ${k}_{i}\ensuremath{-}{m}_{i}$ inactive neighbors via type $i$ links will turn active if $\ensuremath{\sum}{c}_{i}{m}_{i}/\ensuremath{\sum}{c}_{i}{k}_{i}$ exceeds its threshold $\ensuremath{\tau}$. Under this model, we obtain the condition, probability and expected size of global spreading events. Our results extend the existing work on complex contagions in several directions by (i) providing solutions for coupled random networks whose vertices are neither identical nor disjoint, (ii) highlighting the effect of content on the dynamics of complex contagions, and (iii) showing that content-dependent propagation over a multiplex network leads to a subtle relation between the giant vulnerable component of the graph and the global cascade condition that is not seen in the existing models in the literature.

/pdf/analysis-of-complex-contagions-in-random-multiplex-networks-2hdpyqgrpi.pdf

Analysis of complex contagions in random multiplex networks.

Recent trends in public-key infrastructure research explore the tradeoff between decreased trust in Certificate Authorities (CAs), resilience against attacks, communication overhead (bandwidth and latency) for setting up an SSL/TLS connection, and availability with respect to verifiability of public key information. In this paper, we propose AKI as a new public-key validation infrastructure, to reduce the level of trust in CAs. AKI integrates an architecture for key revocation of all entities (e.g., CAs, domains) with an architecture for accountability of all infrastructure parties through checks-and-balances. AKI efficiently handles common certification operations, and gracefully handles catastrophic events such as domain key loss or compromise. We propose AKI to make progress towards a public-key validation infrastructure with key revocation that reduces trust in any single entity.

/pdf/accountable-key-infrastructure-aki-a-proposal-for-a-public-254wlbhlvp.pdf

Virgil D. Gligor

Papers

TrustVisor: Efficient TCB Reduction and Attestation

On Data-Centric Trust Establishment in Ephemeral Ad Hoc Networks

The Crossfire Attack

Analysis of complex contagions in random multiplex networks.

Accountable key infrastructure (AKI): a proposal for a public-key validation infrastructure