A VLSI pipeline design of a fast prime factor DFT on a finite field

A conventional prime factor discrete Fourier transform (DFT) algorithm is used to realize a discrete Fourier-like transform on the finite field, GF(q sub n). A pipeline structure is used to implement this prime factor DFT over GF(q sub n). This algorithm is developed to compute cyclic convolutions of complex numbers and to decode Reed-Solomon codes. Such a pipeline fast prime factor DFT algorithm over GF(q sub n) is regular, simple, expandable, and naturally suitable for VLSI implementation. An example illustrating the pipeline aspect of a 30-point transform over GF(q sub n) is presented

Tendency of spherically imploding plasma liners formed by merging plasma jets to evolve toward spherical symmetry

Three dimensional hydrodynamic simulations have been performed using smoothed particle hydrodynamics (SPH) in order to study the effects of discrete jets on the processes of plasma liner formation, implosion on vacuum, and expansion. The pressure history of the inner portion of the liner was qualitatively and quantitatively similar from peak compression through the complete stagnation of the liner among simulation results from two one dimensional radiationhydrodynamic codes, 3D SPH with a uniform liner, and 3D SPH with 30 discrete plasma jets. Two dimensional slices of the pressure show that the discrete jet SPH case evolves towards a profile that is almost indistinguishable from the SPH case with a uniform liner, showing that non-uniformities due to discrete jets are smeared out by late stages of the implosion. Liner formation and implosion on vacuum was also shown to be robust to Rayleigh-Taylor instability growth. Interparticle mixing for a liner imploding on vacuum was investigated. The mixing rate was very small until after peak compression for the 30 jet simulation.Comment: 28 pages, 16 figures, submitted to Physics of Plasmas (2012

Privacy and Truthful Equilibrium Selection for Aggregative Games

We study a very general class of games --- multi-dimensional aggregative games --- which in particular generalize both anonymous games and weighted congestion games. For any such game that is also large, we solve the equilibrium selection problem in a strong sense. In particular, we give an efficient weak mediator: a mechanism which has only the power to listen to reported types and provide non-binding suggested actions, such that (a) it is an asymptotic Nash equilibrium for every player to truthfully report their type to the mediator, and then follow its suggested action; and (b) that when players do so, they end up coordinating on a particular asymptotic pure strategy Nash equilibrium of the induced complete information game. In fact, truthful reporting is an ex-post Nash equilibrium of the mediated game, so our solution applies even in settings of incomplete information, and even when player types are arbitrary or worst-case (i.e. not drawn from a common prior). We achieve this by giving an efficient differentially private algorithm for computing a Nash equilibrium in such games. The rates of convergence to equilibrium in all of our results are inverse polynomial in the number of players $n$. We also apply our main results to a multi-dimensional market game. Our results can be viewed as giving, for a rich class of games, a more robust version of the Revelation Principle, in that we work with weaker informational assumptions (no common prior), yet provide a stronger solution concept (ex-post Nash versus Bayes Nash equilibrium). In comparison to previous work, our main conceptual contribution is showing that weak mediators are a game theoretic object that exist in a wide variety of games -- previously, they were only known to exist in traffic routing games

Properties of holographic dark energy at the Hubble length

We consider holographic cosmological models of dark energy in which the infrared cutoff is set by the Hubble's radius. We show that any interacting dark energy model, regardless of its detailed form, can be recast as a non interacting model in which the holographic parameter $c^{2}$ evolves slowly with time. Two specific cases are analyzed. We constrain the parameters of both models with observational data, and show that they can be told apart at the perturbative level.Comment: 4 pages, 6 figures. Contribution to the Proceedings ERE201