2,339 research outputs found
Inapproximability of Truthful Mechanisms via Generalizations of the VC Dimension
Algorithmic mechanism design (AMD) studies the delicate interplay between
computational efficiency, truthfulness, and optimality. We focus on AMD's
paradigmatic problem: combinatorial auctions. We present a new generalization
of the VC dimension to multivalued collections of functions, which encompasses
the classical VC dimension, Natarajan dimension, and Steele dimension. We
present a corresponding generalization of the Sauer-Shelah Lemma and harness
this VC machinery to establish inapproximability results for deterministic
truthful mechanisms. Our results essentially unify all inapproximability
results for deterministic truthful mechanisms for combinatorial auctions to
date and establish new separation gaps between truthful and non-truthful
algorithms
Nanowire Acting as a Superconducting Quantum Interference Device
We present the results from an experimental study of the magneto-transport of
superconducting wires of amorphous Indium-Oxide, having widths in the range 40
- 120 nm. We find that, below the superconducting transition temperature, the
wires exhibit clear, reproducible, oscillations in their resistance as a
function of magnetic field. The oscillations are reminiscent of those which
underlie the operation of a superconducting quantum interference device.Comment: 4 pages, 4 figures, 1 tabl
Excessive noise as a test for many-body localization
Recent experimental reports suggested the existence of a finite-temperature insulator in the vicinity of the superconductor-insulator transition. The rapid decay of conductivity over a narrow temperature range was theoretically linked to both a finite-temperature transition to a many-body-localized state, and to a charge-Berezinskii-Kosterlitz-Thouless transition. Here we report of low-frequency noise measurements of such insulators to test for many-body localization. We observed a huge enhancement of the low-temperatures noise when exceeding a threshold voltage for nonlinear conductivity and discuss our results in light of the theoretical models
The Quantized Hall Insulator: A New Insulator in Two-Dimensions
Quite generally, an insulator is theoretically defined by a vanishing
conductivity tensor at the absolute zero of temperature. In classical
insulators, such as band insulators, vanishing conductivities lead to diverging
resistivities. In other insulators, in particular when a high magnetic field
(B) is added, it is possible that while the magneto-resistance diverges, the
Hall resistance remains finite, which is known as a Hall insulator. In this
letter we demonstrate experimentally the existence of another, more exotic,
insulator. This insulator, which terminates the quantum Hall effect series in a
two-dimensional electron system, is characterized by a Hall resistance which is
approximately quantized in the quantum unit of resistance h/e^2. This insulator
is termed a quantized Hall insulator. In addition we show that for the same
sample, the insulating state preceding the QHE series, at low-B, is of the HI
kind.Comment: 4 page
Evidence for a Quantum Hall Insulator in an InGaAs/InP Heterostructure
We study the quantum critical behavior of the plateau-insulator (PI)
transition in a low mobility InGaAs/InP heterostructure. By reversing the
direction of the magnetic field (B) we find an averaged Hall resistance \rho_xy
which remains quantized at the plateau value h/e^2 throughout the PI
transition. We extract a critical exponent \kappa'= 0.57 +/- 0.02 for the PI
transition which is slightly different from (and possibly more accurate than)
the established value 0.42 +/- 0.04 as previously obtained from the
plateau-plateau (PP) transitions.Comment: 3pages, 2 figures; submitted to EP2DS-14 conference proceeding
The fastest way to circle a black hole
Black-hole spacetimes with a "photonsphere", a hypersurface on which massless
particles can orbit the black hole on circular null geodesics, are studied. We
prove that among all possible trajectories (both geodesic and non-geodesic)
which circle the central black hole, the null circular geodesic is
characterized by the {\it shortest} possible orbital period as measured by
asymptotic observers. Thus, null circular geodesics provide the fastest way to
circle black holes. In addition, we conjecture the existence of a universal
lower bound for orbital periods around compact objects (as measured by
flat-space asymptotic observers): , where is the
mass of the central object. This bound is saturated by the null circular
geodesic of the maximally rotating Kerr black hole.Comment: 5 page
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