Selfish Jobs with Favorite Machines: Price of Anarchy vs Strong Price of Anarchy

We consider the well-studied game-theoretic version of machine scheduling in which jobs correspond to self-interested users and machines correspond to resources. Here each user chooses a machine trying to minimize her own cost, and such selfish behavior typically results in some equilibrium which is not globally optimal: An equilibrium is an allocation where no user can reduce her own cost by moving to another machine, which in general need not minimize the makespan, i.e., the maximum load over the machines. We provide tight bounds on two well-studied notions in algorithmic game theory, namely, the price of anarchy and the strong price of anarchy on machine scheduling setting which lies in between the related and the unrelated machine case. Both notions study the social cost (makespan) of the worst equilibrium compared to the optimum, with the strong price of anarchy restricting to a stronger form of equilibria. Our results extend a prior study comparing the price of anarchy to the strong price of anarchy for two related machines (Epstein, Acta Informatica 2010), thus providing further insights on the relation between these concepts. Our exact bounds give a qualitative and quantitative comparison between the two models. The bounds also show that the setting is indeed easier than the two unrelated machines: In the latter, the strong price of anarchy is $2$, while in ours it is strictly smaller.Comment: Extended abstract to appear in COCOA'1

Quantifying the FIR interaction enhancement in paired galaxies

The Catalog of Isolated Pairs of Galaxies in the Northern Hemisphere, by Karachentsev (1972), was studied and a well-matched comparison sample taken from the Catalog of Isolated Galaxies, by Karachentseva (1973), in order to quantify the enhanced FIR emission properties of interacting galaxies

Analytical controllability of deterministic scale-free networks and Cayley trees

According to the exact controllability theory, the controllability is investigated analytically for two typical types of self-similar bipartite networks, i.e., the classic deterministic scale-free networks and Cayley trees. Due to their self-similarity, the analytical results of the exact controllability are obtained, and the minimum sets of driver nodes (drivers) are also identified by elementary transformations on adjacency matrices. For these two types of undirected networks, no matter their links are unweighted or (nonzero) weighted, the controllability of networks and the configuration of drivers remain the same, showing a robustness to the link weights. These results have implications for the control of real networked systems with self-similarity.Comment: 7 pages, 4 figures, 1 table; revised manuscript; added discussion about the general case of DSFN; added 3 reference

Proposal for a new scheme for producing a two-photon, high dimensional hyperentangled state

We propose an experimentally feasible scheme for generating a two $2\times4\times4$ dimensional photons hyperentangled state, entangled in polarization, frequency and spatial mode. This scheme is mainly based on a parametric down-conversion source and cross-Kerr nonlinearities, which avoids the complicated uncertain post-selection. Our method can be easily expanded to the production of hyperentangled states with more photons in multidimensions. Hence the expectation for vast quantities of information in quantum information processing will possibly come true. Finally, we put forward a realizable quantum key distribution (QKD) protocol based on the high dimensional hyperentangled state.Comment: 15 pages, 5 figures, to appear in J.Mod Optic

Demonstration of the double Q^2-rescaling model

In this paper we have demonstrated the double Q^2-rescaling model (DQ^2RM) of parton distribution functions of nucleon bounded in nucleus. With different x-region of l-A deep inelastic scattering process we take different approach: in high x-region (0.1\le x\le 0.7) we use the distorted QCD vacuum model which resulted from topologically multi -connected domain vacuum structure of nucleus; in low x-region (10^{-4}\le x\le10^{-3}) we adopt the Glauber (Mueller) multi- scattering formula for gluon coherently rescattering in nucleus. From these two approach we justified the rescaling parton distribution functions in bound nucleon are in agreement well with those we got from DQ^2RM, thus the validity for this phenomenologically model are demonstrated.Comment: 19 page, RevTex, 5 figures in postscrip