Optimal Competitive Auctions

We study the design of truthful auctions for selling identical items in unlimited supply (e.g., digital goods) to n unit demand buyers. This classic problem stands out from profit-maximizing auction design literature as it requires no probabilistic assumptions on buyers' valuations and employs the framework of competitive analysis. Our objective is to optimize the worst-case performance of an auction, measured by the ratio between a given benchmark and revenue generated by the auction. We establish a sufficient and necessary condition that characterizes competitive ratios for all monotone benchmarks. The characterization identifies the worst-case distribution of instances and reveals intrinsic relations between competitive ratios and benchmarks in the competitive analysis. With the characterization at hand, we show optimal competitive auctions for two natural benchmarks. The most well-studied benchmark $\mathcal{F}^{(2)}(\cdot)$ measures the envy-free optimal revenue where at least two buyers win. Goldberg et al. [13] showed a sequence of lower bounds on the competitive ratio for each number of buyers n. They conjectured that all these bounds are tight. We show that optimal competitive auctions match these bounds. Thus, we confirm the conjecture and settle a central open problem in the design of digital goods auctions. As one more application we examine another economically meaningful benchmark, which measures the optimal revenue across all limited-supply Vickrey auctions. We identify the optimal competitive ratios to be $(\frac{n}{n-1})^{n-1}-1$ for each number of buyers n, that is $e-1$ as $n$ approaches infinity

Monomial Testing and Applications

In this paper, we devise two algorithms for the problem of testing $q$-monomials of degree $k$ in any multivariate polynomial represented by a circuit, regardless of the primality of $q$. One is an $O^*(2^k)$ time randomized algorithm. The other is an $O^*(12.8^k)$ time deterministic algorithm for the same $q$-monomial testing problem but requiring the polynomials to be represented by tree-like circuits. Several applications of $q$-monomial testing are also given, including a deterministic $O^*(12.8^{mk})$ upper bound for the $m$-set $k$-packing problem.Comment: 17 pages, 4 figures, submitted FAW-AAIM 2013. arXiv admin note: substantial text overlap with arXiv:1302.5898; and text overlap with arXiv:1007.2675, arXiv:1007.2678, arXiv:1007.2673 by other author

U.N. General Assembly Meetings Held Outside New York

The decision taken by the United Nations General Assembly on December 2, 1988 to consider the question of Palestine… in plenary, at the United Nations Office at Geneva during the period from December 13-15, 1988 has raised some questions regarding the procedural requirements that have to be fulfilled for General Assembly meetings to be held away from U.N. Headquarters in New York. For a better understanding of the issues involved, it would seem appropriate to summarize briefly the background and developments that led to the General Assembly\u27s decision

U.N. General Assembly Meetings Held Outside New York

The decision taken by the United Nations General Assembly on December 2, 1988 to consider the question of Palestine… in plenary, at the United Nations Office at Geneva during the period from December 13-15, 1988 has raised some questions regarding the procedural requirements that have to be fulfilled for General Assembly meetings to be held away from U.N. Headquarters in New York. For a better understanding of the issues involved, it would seem appropriate to summarize briefly the background and developments that led to the General Assembly\u27s decision

Quantum dynamics of the avian compass

The ability of migratory birds to orient relative to the Earth's magnetic field is believed to involve a coherent superposition of two spin states of a radical electron pair. However, the mechanism by which this coherence can be maintained in the face of strong interactions with the cellular environment has remained unclear. This Letter addresses the problem of decoherence between two electron spins due to hyperfine interaction with a bath of spin 1/2 nuclei. Dynamics of the radical pair density matrix are derived and shown to yield a simple mechanism for sensing magnetic field orientation. Rates of dephasing and decoherence are calculated ab initio and found to yield millisecond coherence times, consistent with behavioral experiments

Lattice calculation of the lowest order hadronic contribution to the muon anomalous magnetic moment

We present a quenched lattice calculation of the lowest order (alpha^2) hadronic contribution to the anomalous magnetic moment of the muon which arises from the hadronic vacuum polarization. A general method is presented for computing entirely in Euclidean space, obviating the need for the usual dispersive treatment which relies on experimental data for e^+e^- annihilation to hadrons. While the result is not yet of comparable accuracy to those state-of-the-art calculations, systematic improvement of the quenched lattice computation to this level of accuracy is straightforward and well within the reach of present computers. Including the effects of dynamical quarks is conceptually trivial, the computer resources required are not.Comment: 12 pages, including two figures. Added reference and footnote Replaced with published version; minor changes asked for by referees and minor deletions to stay within page limi

Anomaly Free Non-Supersymmetric Large NN Gauge Theories from Orientifolds

We construct anomaly free non-supersymmetric large N gauge theories from orientifolds of Type IIB on C^3/G orbifolds. In particular, massless as well as tachyonic one-loop tadpoles are cancelled in these models. This is achieved by starting with ${\cal N}=1,2$ supersymmetric orientifolds with well defined world-sheet description and including discrete torsion (which breaks supersymmetry) in the orbifold action. In this way we obtain non-trivial non-chiral as well as anomaly free chiral large N gauge theories. We point out certain subtleties arising in the chiral cases. Subject to certain assumptions, these theories are shown to have the property that computation of any M-point correlation function in these theories reduces to the corresponding computation in the parent ${\cal N}=4$ oriented theory. This generalizes the analogous results recently obtained in supersymmetric large N gauge theories from orientifolds, as well as in (non)supersymmetric large N gauge theories without orientifold planes.Comment: 18 pages, revtex, minor misprints corrected, a clarifying footnote added (to appear in Phys. Rev. D

D=4, N=1, Type IIA Orientifolds

We study D=4, N=1, type IIA orientifold with orbifold group $Z_N$ and $Z_N \times Z_M$. We calculate one-loop vacuum amplitudes for Klein bottle, cylinder and Mobius strip and extract the tadpole divergences. We find that the tadpole cancellation conditions thus obtained are satisfied by the $Z_4$, $Z_8$, $Z'_8$, $Z'_{12}$ orientifolds while there is no solution for $Z_3$, $Z_7$, $Z_6$, $Z'_6$, $Z_{12}$. The $Z_4 \times Z_4$ type IIA orientifold is also constructed by introducing four different configurations of 6-branes. We argue about perturbative versus non-perturbative orientifold vacua under T- duality between the type IIA and the type IIB $Z_N$ orientifolds in four dimensions.Comment: 32 pages, LaTe

Type IIB Orientifolds with NS-NS Antisymmetric Tensor Backgrounds

We consider six dimensional N=1 space-time supersymmetric Type IIB orientifolds with non-zero untwisted NS-NS sector B-field. The B-field is quantized due to the requirement that the Type IIB spectrum be left-right symmetric. The presence of the B-field results in rank reduction of both 99 and 55 open string sector gauge groups. We point out that in some of the models with non-zero B-field there are extra tensor multiplets in the Z_2 twisted closed string sector, and we explain their origin in a simple example. Also, the 59 open string sector states come with a multiplicity that depends on the B-field. These two facts are in accord with anomaly cancellation requirements. We point out relations between various orientifolds with and without the B-field, and also discuss the F-theory duals of these models.Comment: 13 pages, revtex, minor misprints correcte

Ariel - Volume 2 Number 5

Editors Delvyn C. Case, Jr. Paul M. Fernhoff News Editors Richard Bonanno Robin A. Edwards Features Editors Stephen P. Flynn Steven A. Ager Lay-Out Editor Carol Dolinskas Contributing Editors Michael J. Blecker W. Cherry Light Eugenia Miller Lin Sey Edwards Jack Guralnik Tom Williams James Noco