" r? Let X~= X and Y~= Y for t = 1, 2 . . . . . X, ,= ~ X ~ and !1, = Y~. Let S be any set, cg = {w(. 1" I s ) lseS} t = l t = l n be a set of (a x 2) stochastic matrices w( ' l ' ls) , and St=S , t= 1 . . . . . n. For every sn=(s 1 . . . . . s " ) e H S t n t = l define P (. ]" Is.) by P (y.[x.ls.) = I~ w (yt]x~lst) for every x. = (x a . . . . . x")~ X . and every y. = (yl, ... , y.)e 11.. t =...

• Delay sensitive multimedia applications are booming over a variety of time-varying networks (e.g. sensor networks, WiMax, Wireless LAN, etc.) • Existing dynamic distributed network environments cannot provide adequate support for delay-sensitive multimedia applications • This problem has been investigated for a decade, but we still do not have efficient solutions for it.

Many exist studies always use Markov decision processes (MDPs) in modeling optimal route choice in stochastic, time-varying networks. However, taking many variable traffic data and transforming them into optimal route decision is a computational challenge by employing MDPs in real transportation networks. In this paper we model finite horizon MDPs using directed hypergraphs. It is shown that th...

In this thesis we contribute to the understanding of the pivotal role of the temporal dimension in networked social systems, previously neglected and now uncovered by the data revolution recently blossomed in this field. To this aim, we first introduce the time-varying networks formalism and analyze some empirical data of social dynamics, extensively used in the rest of the thesis. We discuss t...

| The random-code capacity region of the multiple-access arbitrarily varying channel subject to both state and input constraints is determined. Consideration of a simple erasure channel shows that the capacity region is not convex in general.

The spread of an infection on a real-world social network is determined by the interplay of two processes – the dynamics of the network, whose structure changes over time according to the encounters between individuals, and the dynamics on the network, whose nodes can infect each other after an encounter. Physical encounter is the most common vehicle for the spread of infectious diseases, but d...

Consensus problems in time-varying networks are studied in this paper. We consider two cases. In the first case, the networks are basically connected and the conditions for reaching consensus are described by means of the algebraic properties of connectivity for network graph. In the second case, the networks are possibly disconnected all time. A concept called integral connectivity of networks...

We consider the problem of communicating over an unknown and arbitrarily varying channel, using feedback. This paper focuses on the problem of determining the input behavior, or more specifically, a prior which is used to randomly generate a codebook. We pose the problem of setting the prior as a universal sequential prediction problem using information theoretic abstractions of the communicati...

Tensors are effective representations for complex and time-varying networks. The factorization of a tensor provides a high-quality low-rank compact basis for each dimension of the tensor, which facilitates the interpretation of important structures of the represented data. Many existing tensor factorization (TF) methods assume there is one tensor that needs to be decomposed to low-rank factors....