On the Saddle-point Solution and the Large-Coalition Asymptotics of Fingerprinting Games

We study a fingerprinting game in which the number of colluders and the collusion channel are unknown. The encoder embeds fingerprints into a host sequence and provides the decoder with the capability to trace back pirated copies to the colluders. Fingerprinting capacity has recently been derived as the limit value of a sequence of maximin games with mutual information as their payoff functions. However, these games generally do not admit saddle-point solutions and are very hard to solve numerically. Here under the so-called Boneh-Shaw marking assumption, we reformulate the capacity as the value of a single two-person zero-sum game, and show that it is achieved by a saddle-point solution. If the maximal coalition size is k and the fingerprinting alphabet is binary, we show that capacity decays quadratically with k. Furthermore, we prove rigorously that the asymptotic capacity is 1/(k^2 2ln2) and we confirm our earlier conjecture that Tardos' choice of the arcsine distribution asymptotically maximizes the mutual information payoff function while the interleaving attack minimizes it. Along with the asymptotic behavior, numerical solutions to the game for small k are also presented.Comment: submitted to IEEE Trans. on Information Forensics and Securit

Tradeoff between Smoother and Sooner "Little Rip"

There exists dark energy models that predict the occurrence of "little rip". At the point of little rip the Hubble rate and its cosmic time derivative approach infinity, which is quite similar to the big rip singularity except that the former happens at infinite future while the latter at a finite cosmic time; both events happen in the future and at high energies. In the case of the big rip, a combination of ultra-violet and infra-red effects can smooth its doomsday. We therefore wonder if the little rip can also be smoothed in a similar way. We address the ultra-violet and infra-red effects in general relativity through a brane-world model with a Gauss-Bonnet term in the bulk and an induced gravity term on the brane. We find that the little rip is transformed in this case into a sudden singularity, or a "big brake". Even though the big brake is smoother than the little rip in that the Hubble rate is finite at the event, the trade-off is that it takes place sooner, at a finite cosmic time. In our estimate, the big brake would happen at roughly 1300Gyr.Comment: 9 pages, 4 figures. RevTex4-1. Title modified and discussion expanded. Version accepted in European Physical Journal

Adaptive T-S fuzzy-neural modeling and control for general MIMO unknown nonaffine nonlinear systems using projection update laws

[[abstract]]This paper describes a novel design of an on-line Takagi–Sugeno (T–S) fuzzy-neural controller for a class of general multiple input multiple output (MIMO) systems with unknown nonlinear functions and external disturbances. Instead of modeling the unknown systems directly, the T–S fuzzy-neural model approximates a virtual linearized system (VLS) of a real system with modeling errors and external disturbances. Compared with previous approaches, the main contribution of this paper is an investigation of more general MIMO unknown systems using on-line adaptive T–S fuzzy-neural controllers. In this paper, we also use projection update laws, which generalize the projection algorithm, to tune the adjustable parameters. This prevents parameter drift and ensures that the parameter matrix is bounded away from singularity. We prove that the closed-loop system controlled by the proposed controller is robust stable and the effect of all the modeling errors and external disturbances on the tracking error can be attenuated. Finally, two examples covering four cases are simulated in order to confirm the effectiveness and applicability of the proposed approach in this paper.[[booktype]]紙

Constraints on single entity driven inflationary and radition eras

We present a model that attempts to fuse the inflationary era and the subsequent radiation dominated era under a unified framework so as to provide a smooth transition between the two. The model is based on a modification of the generalized Chaplygin gas. We constrain the model observationally by mapping the primordial power spectrum of the scalar perturbations to the latest data of WMAP7. We compute as well the spectrum of the primordial gravitational waves as would be measured today.Comment: 4 pages, 6 figures. Contribution to the Spanish Relativity Meeting (ERE2011), Madrid, Spai

Cosmological Imprints of a Generalized Chaplygin Gas Model for the Early Universe

We propose a phenomenological model for the early universe where there is a smooth transition between an early "quintessence" phase and a radiation dominated era. The matter content is modelled by an appropriately modified Chaplygin gas for the early universe. We constrain the model observationally by mapping the primordial power spectrum of the scalar perturbations to the latest data of WMAP7. We compute as well the spectrum of the primordial gravitational waves as would be measured today. We show that the high frequencies region of the spectrum depends on the free parameter of the model and most importantly this region of the spectrum can be within the reach of future gravitational waves detectors.Comment: 10 pages, 8 figures. RevTex