Abstract This dissertation addresses learning in complex dynamic systems with applications to perpetual flight, energy management, collaborative decision making, and social networks. By increasing the size and complexity of network systems, decentralized optimization schemes or machine learning algorithms are desired for scaling up the automated learning process, reducing data transmission, and ensuring robustness in the presence of local failures. This work approaches these challenges from two fronts: complex dynamics associated with individual agents in the network; and protocols which are run on individual agents in the network.

## Complex Dynamics in Communication Networks | Ljupco Kocarev | Springer

In this direction, energy management for aerial vehicles and small smart grids have been studied. With the objective to develop smart autonomous distributed systems performing in a highly uncertain environment, online distributed learning algorithms have been proposed.

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These algorithms allow the network topology to adapt and each agent learns the model based on its local data and the information it receives from its neighboring agents. Most of these reported "power laws" fail when challenged with rigorous statistical testing, but the more general idea of heavy-tailed degree distributions—which many of these networks do genuinely exhibit before finite-size effects occur -- are very different from what one would expect if edges existed independently and at random i.

There are many different ways to build a network with a power-law degree distribution.

### Submission history

The Yule process is a canonical generative process for power laws, and has been known since However, it is known by many other names due to its frequent reinvention, e. Recently, Hyperbolic Geometric Graphs have been suggested as yet another way of constructing scale-free networks.

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Some networks with a power-law degree distribution and specific other types of structure can be highly resistant to the random deletion of vertices—i. When the graph is uniformly random except for the degree distribution, these critical vertices are the ones with the highest degree, and have thus been implicated in the spread of disease natural and artificial in social and communication networks, and in the spread of fads both of which are modeled by a percolation or branching process.

While random graphs ER have an average distance of order log N [7] between nodes, where N is the number of nodes, scale free graph can have a distance of log log N. Such graphs are called ultra small world networks. A network is called a small-world network [7] by analogy with the small-world phenomenon popularly known as six degrees of separation.

## Dynamic information routing in complex networks

The small world hypothesis, which was first described by the Hungarian writer Frigyes Karinthy in , and tested experimentally by Stanley Milgram , is the idea that two arbitrary people are connected by only six degrees of separation, i. In , Duncan J. Watts and Steven Strogatz published the first small-world network model, which through a single parameter smoothly interpolates between a random graph and a lattice. It is known that a wide variety of abstract graphs exhibit the small-world property, e.

Further, real world networks such as the World Wide Web and the metabolic network also exhibit this property. In the scientific literature on networks, there is some ambiguity associated with the term "small world". In addition to referring to the size of the diameter of the network, it can also refer to the co-occurrence of a small diameter and a high clustering coefficient.

The clustering coefficient is a metric that represents the density of triangles in the network. For instance, sparse random graphs have a vanishingly small clustering coefficient while real world networks often have a coefficient significantly larger. Scientists point to this difference as suggesting that edges are correlated in real world networks.

From Wikipedia, the free encyclopedia. Network science. Metrics Algorithms. Main article: Scale-free networks. Main article: Small-world network. Community structure Complex adaptive system Complex systems Dual-phase evolution Dynamic network analysis Interdependent networks Network theory Network science Percolation theory Random graph Scale-free networks Small world networks Spatial network Trophic coherence.

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## Complex Dynamics in Communication Networks / Edition 1

Abstract The significance of temporal changes in the topology of organizational communication networks during a crisis is studied using static and dynamic social network analysis SNA. Citing Literature.

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