Radicals, Metals and Magnetism

The interaction between unpaired electrons governs many physical properties of materials. Although in a fundamental sense the interaction is simple, a full understanding of the interaction in molecular systems is complicated by the presence of other bonding and non-bonding electrons. The resulting many body problem is very challenging. Nevertheless, much qualitative understanding can be obtained from applying simple molecular orbital theory and considering only the partly filled orbitals. The resulting model can be used to describe existing diradical and metal-radical systems and also has predicative value in the search for molecular magnets and design of nanoscale devices

Gauge/Gravity Duality and Some Applications

We discuss the AdS/CFT correspondence in which space-time emerges from an interacting theory of D-branes and open strings. These ideas have a historical continuity with QCD which is an interacting theory of quarks and gluons. In particular we review the classic case of D3 branes and the non-conformal D1 brane system. We outline by some illustrative examples the calculations that are enabled in a strongly coupled gauge theory by correspondence with dynamical horizons in semi-classical gravity in one higher dimension. We also discuss implications of the gauge-fluid/gravity correspondence for the information paradox of black hole physics.Comment: 19 pages, 2 figures, Contribution to "Conference in Honor of Murray Gell-Mann's 80th Birthday

Active Internet Traffic Filtering: Real-time Response to Denial of Service Attacks

Denial of Service (DoS) attacks are one of the most challenging threats to Internet security. An attacker typically compromises a large number of vulnerable hosts and uses them to flood the victim's site with malicious traffic, clogging its tail circuit and interfering with normal traffic. At present, the network operator of a site under attack has no other resolution but to respond manually by inserting filters in the appropriate edge routers to drop attack traffic. However, as DoS attacks become increasingly sophisticated, manual filter propagation becomes unacceptably slow or even infeasible. In this paper, we present Active Internet Traffic Filtering, a new automatic filter propagation protocol. We argue that this system provides a guaranteed, significant level of protection against DoS attacks in exchange for a reasonable, bounded amount of router resources. We also argue that the proposed system cannot be abused by a malicious node to interfere with normal Internet operation. Finally, we argue that it retains its efficiency in the face of continued Internet growth.Comment: Briefly describes the core ideas of AITF, a protocol for facing Denial of Service Attacks. 6 pages lon

Average degree conditions forcing a minor

Mader first proved that high average degree forces a given graph as a minor. Often motivated by Hadwiger's Conjecture, much research has focused on the average degree required to force a complete graph as a minor. Subsequently, various authors have consider the average degree required to force an arbitrary graph $H$ as a minor. Here, we strengthen (under certain conditions) a recent result by Reed and Wood, giving better bounds on the average degree required to force an $H$-minor when $H$ is a sparse graph with many high degree vertices. This solves an open problem of Reed and Wood, and also generalises (to within a constant factor) known results when $H$ is an unbalanced complete bipartite graph