Would any of you clever with-actual-knowledge nice people like to be brutally take-no-prisoners-ly nitpicker-ly honest in tearing apart my abstract so that I can improve it? Any sort of remark is more than welcome - obviously, the language and grammar, as well as sentence and paragraph structure, but of course I'd love any comment on pretty much anything and everything you find is lacking.

It's still somewhat at a draft stage, considering I've written and re-written and deleted and tweaked and went back again and lather-rinse-repeat so much, I can't see anymore what works and what doesn't. I know I have some crazy long and convoluted sentences in there, and that I have to cut it a bit, but I am too close - technically - to all this mess right now to be able to properly edit. So I turn to you guys.

Instead of bogging Natter down with too much meMeME, I posted it here. Comments there, here, e-mails to my profile address, smoke signals or little paper airplanes are all not only welcome, but deeply appreciated.

(I will only see them after shabbat, though, so my actual corrections and questions for clarification and returning small paper airplanes will be delayed. It's not that I'm not filled with gratitude, it's just that I'm sleeping.)

Here goes:

__Dynamics of Data Traffic in Communication Networks__

Networks play an important role in many research areas, including physics, biology, sociology, computer science, and electrical engineering. Communication networks, most notably the Internet, have become a critical resource of modern life. Not only does the amount of data traffic in them keep growing, but its various types and uses keep expanding, as well.

Classical models for networks are based on regular lattices and random graph theory derived by Erdos and Renyi in the 1960's. In recent years it became clear that these models were insufficient as a description to many real world networks, which exhibit different characteristics. The most notable difference is in the degree (number of links per node) distribution, which, in real world networks is usually a power-law, in contrast to the Poisson distribution predicted by random graph theory. Such structures have fractal properties, i.e., have no characteristic scale, and are therefore called scale-free networks.

The structure of these networks was thoroughly studied, both in theoretical models as well as in real world networks. On top of the comprehensive understanding of the topology of such networks, many properties deriving from this topology were explored, as well. For example, their very small mean hop distance, resilience to random attacks and vulnerability to targeted ones.

A question related to this abovementioned network's stability is the dynamics of virus and worm spreading through it. A network which is not resilient to random breakdown of nodes is also vulnerable to such infections. Efficient immunization of large computer networks becomes extremely important in light of epidemic spreading in human populations as well as large productivity losses due to virus infections.

We explored several efficient immunization strategies, i.e. strategies for selecting key nodes for immunization and blocking of viruses and worms. Immunizing random nodes had the benefit of not requiring any previous knowledge of the system, but a large percentage of immunized nodes was needed in order to stop the epidemic. Immunizing the most highly connected nodes enabled a very small fraction of immunized nodes to stop the spread of the epidemic, however it also required full knowledge of the entire system.

An immunization strategy which combined both advantages of the two abovementioned strategies was explored as well - the acquaintance immunization strategy. Immunizing random neighbors of randomly chosen nodes required no prior knowledge of any of the system's nodes. However, due to the scale-free nature of the network, there was a high probability that the randomly chosen immunized neighbor was one of the highly-connected nodes (hubs) of the system, therefore ensuring that a relatively small fraction of immunized nodes managed to block the spread of the epidemic. A double-acquaintance immunization strategy, repeating the random choice process, was studied as well.

But the static characteristics of epidemics and immunizations are not enough for a complete picture, since they cannot capture the time-dependent progress of the disease, the time required for extinguishing it, the fraction of infected nodes at each time step and so forth.

Therefore, we also studied these dynamic properties, both regarding the spreading of epidemics as well as in assessing the efficiency of the various immunization strategies against them. We used the well-known SIR model, describing diseases dynamics, as well as its mapping to known results from percolation theory.

Naturally, this is not the single area in which the dynamics of the flow of the data through the network is affected by the network's topology. The deep and comprehensive description of that topology as well as its effect on the netwrok's properties makes it possible to take the next step and use it not just for the static characteristics of the network, but for attempting to describe and even optimize the dynamic properties, as well.

Many communication networks are highly dynamic by nature. Nodes and links may constantly be added or removed and links become congested. Thus, to ensure reliable and efficient operations on the network, algorithms for dynamical routing of the data flowing through it are required, either optimal or sub-optimal. The current existing algorithms, employing large tables of data, whose pace of update isn't quick enough, do not give a good enough answer to the problem.

The size and complexity of such communication networks may be dealt with through an efficient routing or search algorithm employing heuristics and taking the scale-free network structure into account. We investigated extensively the first steps for formulating such an efficient dynamic routing algorithm, based on the A* algorithm, which is a well-known heuristic search that is used to find an optimal path in a graph.

Search algorithms are a well-studied field in computer science, with algorithms ranging from Brute-Force simplistic ones to sophisticated heuristics. Despite that, no attempt to use the underlining topological structure of the network was conducted so far, in order to improve the running time of a search algorithm.

We suggest a heuristic search, based on the well-known A* search algorithm, which takes into account the actual topology of the network. The logic behind it follows similar lines to those behind the acquaintance immunization strategy mentioned above, namely that there is a high probability that a random neighbor of a random node is one of the highly-connected nodes.

Our A* search assumes that each node contains a small information table, regarding a fixed number of nodes. Once each node is expanded, not just his nearest neighbors are generated, but also the nodes in its information table. Thus, the search for the shortest path between two random nodes, can enjoy the high probability of such a path going through a hub, and of that hub to be included in the abovementioned information table, and its running time shortens accordingly.

Extensive statistical analysis was conducted regarding the various characteristics of the A* search and its improved efficiency over simple searches (mainly the Breadth-First-Search, also known as BFS). Several variations of it were taken into account, with different information table sizes, either of a fixed number of nodes or of a certain percentage of the whole network, and more. We showed that a dramatic improvement in the search's efficiency was achieved even for very small information-table sizes, regardless of the size of the network, and even the possibilities of its future growth.

Finally, in order to study network performance, topology is not the only factor, but one needs also to consider traffic. Thus, we need to better understand the traffic's spatial and temporal behavior. In the study of vehicular traffic, similar analyses were a crucial step in developing optimization strategies for better traffic flow.

Various measurements have shown that data packet interarrival times are correlated over a long term and much more heterogeneous than the classical Poisson model. We applied statistical physics methods such as detrended fluctuation analysis (DFA) in order to deepen our understanding of the data traffic, and help in combining the our findings into developing better data routing algorithms for traffic flow on scale-free networks.