Architectural aspects of QoS-aware personal networks

Personal Networks (PN) are future communication systems that combine wireless and infracuture based networks to provide users a variety of services anywhere and anytime. PNs introduce new design challenges due to the heterogeneity of the involved technologies, the need for self-organization, the dynamics of the system composition, the application-driven nature, the co-operation with infrastructure-based networks, and the security hazards. This paper discusses the challenges of security and QoS provisioning in designing self-organized personal networks and combines them all into an integrated architectural framework

Explosive phase transition in susceptible-infected-susceptible epidemics with arbitrary small but nonzero self-infection rate

The -susceptible-infected-susceptible (SIS) epidemic model on a graph adds an independent, Poisson self-infection process with rate to the "classical" Markovian SIS process. The steady state in the classical SIS process (with =0) on any finite graph is the absorbing or overall-healthy state, in which the virus is eradicated from the network. We report that there always exists a phase transition around τc=O-1N-1 in the -SIS process on the complete graph KN with N nodes, above which the effective infection rate τ>τc causes the average steady-state fraction of infected nodes to approach that of the mean-field approximation, no matter how small, but not zero, the self-infection rate is. For τ<τc and small, the network is almost overall healthy. The observation was found by mathematical analysis on the complete graph KN, but we claim that the phase transition of explosive type may also occur in any other finite graph. We thus conclude that the overall-healthy state of the classical Markovian SIS model is unstable in the -SIS process and, hence, unlikely to exist in reality, where "background" infection >0 is imminent.Network Architectures and Service

Origin of the fractional derivative and fractional non-Markovian continuous-time processes

A complex fractional derivative can be derived by formally extending the integer k in the kth derivative of a function, computed via Cauchy's integral, to complex α. This straightforward approach reveals fundamental problems due to inherent nonanalyticity. A consequence is that the complex fractional derivative is not uniquely defined. We explain in detail the anomalies (not closed paths, branch cut jumps) and try to interpret their meaning physically in terms of entropy, friction and deviations from ideal vector fields. Next, we present a class of non-Markovian continuous-time processes by replacing the standard derivative by a Caputo fractional derivative in the classical Chapman-Kolmogorov governing equation of a continuous-time Markov process. The fractional derivative leads to a replacement of the set of exponential base functions by a set of Mittag-Leffler functions, but also creates a complicated dependence structure between states. This fractional non-Markovian process may be applied to generalize the Markovian SIS epidemic process on a contact graph to a more realistic setting. Network Architectures and Service

Time Evolution of SIS epidemics in the Complete Graph

Network Architectures and Service

Network localization is unalterable by infections in bursts

To shed light on the disease localization phenomenon, we study a bursty susceptible-infected-susceptible (SIS) model and analyze the model under the mean-field approximation. In the bursty SIS model, the infected nodes infect all their neighbors periodically, and the near-threshold steady-state prevalence is non-constant and maximized by a factor equal to the largest eigenvalue λ1 of the adjacency matrix of the network. We show that the maximum near-threshold prevalence of the bursty SIS process on a localized network tends to zero even if λ1 diverges in the thermodynamic limit, which indicates that the burst of infection cannot turn a localized spreading into a delocalized spreading. Our result is evaluated both on synthetic and real networks

Time dependence of susceptible-infected-susceptible epidemics on networks with nodal self-infections

The average fraction of infected nodes, in short the prevalence, of the Markovian ɛ-SIS (susceptible-infected-susceptible) process with small self-infection rate ɛ&gt;0 exhibits, as a function of time, a typical "two-plateau" behavior, which was first discovered in the complete graph KN. Although the complete graph is often dismissed as an unacceptably simplistic approximation, its analytic tractability allows to unravel deeper details, that are surprisingly also observed in other graphs as demonstrated by simulations. The time-dependent mean-field approximation for KN performs only reasonably well for relatively large self-infection rates, but completely fails to mimic the typical Markovian ɛ-SIS process with small self-infection rates. While self-infections, particularly when their rate is small, are usually ignored, the interplay of nodal self-infection and spread over links may explain why absorbing processes are hardly observed in reality, even over long time intervals.</p

Über neue Darstellungsverfahren, Isomerisierungen und Alkylierungsreaktionen von beta-, gamma-ungesättigten Oxoverbindungen sowie ihrer Derivate

Multicast routing algorithms that are capable of providing quality of service (QoS) to its members will play an important role in future communications networks. This paper discusses some fundamental properties of multicast routing subject to multiple QoS requirements. We will show that guaranteeing QoS and optimizing resource utilization are conflicting objectives and require a trade-off. We also present MAMCRA, a Multicast Adaptive Multiple Constraints Routing Algorithm, that guarantees QoS to the multicast members in an efficient, but not always optimal manner

On lower bounds for the largest eigenvalue of a symmetric matrix

We consider lower bounds for the largest eigenvalue of a symmetric matrix. In particular we extend a recent approach by Piet Van Mieghe