The connectivity of wireless network is critical for effective and efficient communications. Yet, it is challenged by mobility, transmission range and density. In terms of increasing node density, there is a transition phase of connectivity when a network starts transforming from partition to connected state. In this paper, we study the upperand lowerbounds of critical density for the transitio...

A main feature of a novel tool is described, the algorthmic translation of formal queueing network descriptions into transition class models. Transition classes are a highlevel modelling paradigm for the structured and compact definition of Markov chains. Transition class models can be solved with many known solution techniques for Markov chains, exact and approximate, and simulation, even hybr...

The transition from a pure IPv4 network to a network where IPv4 and IPv6 coexist brings a number of extra security considerations that need to be taken into account when deploying IPv6 and operating the dual-protocol network and the associated transition mechanisms. This document attempts to give an overview of the various issues grouped into three categories: o issues due to the IPv6 protocol ...

Mutual learning of a pair of tree parity machines with continuous and discrete weight vectors is studied analytically. The analysis is based on a mapping procedure that maps the mutual learning in tree parity machines onto mutual learning in noisy perceptrons. The stationary solution of the mutual learning in the case of continuous tree parity machines depends on the learning rate where a phase...

In neural circuits, statistical connectivity rules strongly depend on cell-type identity. We study dynamics of neural networks with cell-type-specific connectivity by extending the dynamic mean-field method and find that these networks exhibit a phase transition between silent and chaotic activity. By analyzing the locus of this transition, we derive a new result in random matrix theory: the sp...

Networks in which the formation of connections is governed by a random process often undergo a percolation transition, wherein around a critical point, the addition of a small number of connections causes a sizable fraction of the network to suddenly become linked together. Typically such transitions are continuous, so that the percentage of the network linked together tends to zero right above...

Microplasmodia of the slime mold Physarum polycephalum form a small link degree transportation network in a percolation transition in order to forage. We model this transition analytically within the configuration model of graph theory utilizing all partaking types of nodes. Quite generally, we find that at the percolation transition the formation of a small link degree network is topologically...