Optimal Scale-Free Small-World Graphs with Minimum Scaling of Cover Time

The cover time of random walks on a graph has found wide practical applications in different fields of computer science, such as crawling and searching on the World Wide Web and query processing in sensor networks, with the application effects dependent on the behavior of cover time: the smaller the cover time, the better the application performance. It was proved that over all graphs with $N$ nodes, complete graphs have the minimum cover time $N\log N$. However, complete graphs cannot mimic real-world networks with small average degree and scale-free small-world properties, for which the cover time has not been examined carefully, and its behavior is still not well understood. In this paper, we first experimentally evaluate the cover time for various real-world networks with scale-free small-world properties, which scales as $N\log N$. To better understand the behavior of the cover time for real-world networks, we then study the cover time of three scale-free small-world model networks by using the connection between cover time and resistance diameter. For all the three networks, their cover time also behaves as $N\log N$. This work indicates that sparse networks with scale-free and small-world topology are favorable architectures with optimal scaling of cover time. Our results deepen understanding the behavior of cover time in real-world networks with scale-free small-world structure, and have potential implications in the design of efficient algorithms related to cover time

Against the Tide. A Critical Review by Scientists of How Physics and Astronomy Get Done

Nobody should have a monopoly of the truth in this universe. The censorship and suppression of challenging ideas against the tide of mainstream research, the blacklisting of scientists, for instance, is neither the best way to do and filter science, nor to promote progress in the human knowledge. The removal of good and novel ideas from the scientific stage is very detrimental to the pursuit of the truth. There are instances in which a mere unqualified belief can occasionally be converted into a generally accepted scientific theory through the screening action of refereed literature and meetings planned by the scientific organizing committees and through the distribution of funds controlled by "club opinions". It leads to unitary paradigms and unitary thinking not necessarily associated to the unique truth. This is the topic of this book: to critically analyze the problems of the official (and sometimes illicit) mechanisms under which current science (physics and astronomy in particular) is being administered and filtered today, along with the onerous consequences these mechanisms have on all of us.\ud \ud The authors, all of them professional researchers, reveal a pessimistic view of the miseries of the actual system, while a glimmer of hope remains in the "leitmotiv" claim towards the freedom in doing research and attaining an acceptable level of ethics in science

A new Wiener-Hopf identity for a general class of reflected processes

We derive a new "Wiener-Hopf identity" for a class of preemptive-resume queueing systems, with batch arrivals and catastrophes that, whenever they occur, eliminate multiple customers present in the system. These processes are quite general, as they can be used to approximate Lévy processes, diffusion processes, and certain types of growth-collapse processes: thus, all of the processes mentioned above also satisfy this type of Wiener-Hopf identity. In the Lévy case, this identity simplifies to the well-known Wiener-Hopf factorization. We also show how the ideas can be used to derive transforms for some well-known state-dependent/inhomogeneous birth-death processes and diffusion processes

Improving Collaborative Drawing using HTML5

This research looks into improving online web-based collaborative drawing using HTML5. Although many systems have been developed over a number of years, none of the applications released have been satisfactory for many artists; the core drawing experience was too different from a stand-alone drawing applications. Stand-alone drawing applications have better freedom of control with functions like undo and allow artists to work efficiently with hotkeys. The advent of the HTML5 Canvas Element and Websockets in recent browsers has provided new opportunities for collaborative online interaction. This research used an incremental development approach to build a prototype HTML5 drawing application providing new functionality for online collaborative drawing. The project was supported by two experienced artists throughout investigation, design, implementation and testing. The project artists helped validate design decisions and evaluate the implementation. As a result, a robust HTML5 collaborative drawing application was built. The prototype contains core drawing functionality that existing applications did not. Features include: undo and redo, free canvas transformation, complex hotkey interaction, custom canvas size support, colour wheel, and layers. All these features work smoothly in a fully synchronized network environment under a client-server model. The collaboration system uses an authoritative server structure with local prediction and re-synchronization to hide latency. Although the result is only a prototype, the evaluations from the project artists were very positive. Once more functionality targeted towards social interaction is built, the prototype will be ready for mass public testing. Although there are some issues caused by the immaturity of HTML5 technology, this project affirms its capability for collaborative web applications

Dependent Risk Modelling and Ruin Probability: Numerical Computation and Applications

In this thesis, we are concerned with the finite-time ruin probabilities in two alternative dependent risk models, the insurance risk model and the dual risk model, including the numerical evaluation of the explicit expressions for these quantities and the application of the probabilistic results obtained. We first investigate the numerical properties of the formulas for the finite-time ruin probability derived by Ignatov and Kaishev (2000, 2004) and Ignatov et al. (2001) for a generalized insurance risk model allowing dependence. Efficient numerical algorithms are proposed for computing the ruin probability with a prescribed accuracy in order to facilitate the following studies. We then propose a new definition of alarm time in the insurance risk model, which generalizes that of Das and Kratz (2012), expressed in terms of the joint distribution of the time to ruin and the deficit at ruin. The alarm time is devised to warn that the future ruin probability within a finite-time window has reached a pre-specified critical level and capital injection is required. Due to our definition, the implementation of the alarm time highly relies on the computation of the finite-time ruin probability, which utilizes the previous results on computing the ruin probability with a prescribed accuracy. The results of the ruin probability and the alarm time are then transferred nicely to a generalized dual risk model, whose name stems from its duality to the insurance risk model, through an enlightening link established between the two risk models. Finally, based on the two alternative risk models, we introduce a framework for analyzing the risk of systems failure based on estimating the failure probability, and illustrate how the probabilistic models and results obtained can be applied as risk analytic tools in various practical risk assessment situations, such as systems reliability, inventory management, flood control via dam management, infection disease spread and financial insolvency

Dagstuhl News January - December 2006

"Dagstuhl News" is a publication edited especially for the members of the Foundation "Informatikzentrum Schloss Dagstuhl" to thank them for their support. The News give a summary of the scientific work being done in Dagstuhl. Each Dagstuhl Seminar is presented by a small abstract describing the contents and scientific highlights of the seminar as well as the perspectives or challenges of the research topic