Long-lived oscillons from asymmetric bubbles

The possibility that extremely long-lived, time-dependent, and localized field configurations (``oscillons'') arise during the collapse of asymmetrical bubbles in 2+1 dimensional phi^4 models is investigated. It is found that oscillons can develop from a large spectrum of elliptically deformed bubbles. Moreover, we provide numerical evidence that such oscillons are: a) circularly symmetric; and b) linearly stable against small arbitrary radial and angular perturbations. The latter is based on a dynamical approach designed to investigate the stability of nonintegrable time-dependent configurations that is capable of probing slowly-growing instabilities not seen through the usual ``spectral'' method.Comment: RevTeX 4, 9 pages, 11 figures. Revised version with a new approach to stability. Accepted to Phys. Rev.

Ad auctions and cascade model: GSP inefficiency and algorithms

The design of the best economic mechanism for Sponsored Search Auctions (SSAs) is a central task in computational mechanism design/game theory. Two open questions concern the adoption of user models more accurate than that one currently used and the choice between Generalized Second Price auction (GSP) and Vickrey-Clark-Groves mechanism (VCG). In this paper, we provide some contributions to answer these questions. We study Price of Anarchy (PoA) and Price of Stability (PoS) over social welfare and auctioneer's revenue of GSP w.r.t. the VCG when the users follow the famous cascade model. Furthermore, we provide exact, randomized, and approximate algorithms, showing that in real-world settings (Yahoo! Webscope A3 dataset, 10 available slots) optimal allocations can be found in less than 1s with up to 1000 ads, and can be approximated in less than 20ms even with more than 1000 ads with an average accuracy greater than 99%.Comment: AAAI16, to appea

Quantum Knitting

We analyze the connections between the mathematical theory of knots and quantum physics by addressing a number of algorithmic questions related to both knots and braid groups. Knots can be distinguished by means of `knot invariants', among which the Jones polynomial plays a prominent role, since it can be associated with observables in topological quantum field theory. Although the problem of computing the Jones polynomial is intractable in the framework of classical complexity theory, it has been recently recognized that a quantum computer is capable of approximating it in an efficient way. The quantum algorithms discussed here represent a breakthrough for quantum computation, since approximating the Jones polynomial is actually a `universal problem', namely the hardest problem that a quantum computer can efficiently handle.Comment: 29 pages, 5 figures; to appear in Laser Journa