390 research outputs found
Simple, optimal and efficient auctions
Proceedings of the 7th International Workshop, WINE 2011, Singapore, December 11-14, 2011.We study the extent to which simple auctions can simultaneously achieve good revenue and efficiency guarantees in single-item settings. Motivated by the optimality of the second price auction with monopoly reserves when the biddersâ values are drawn i.i.d. from regular distributions [12], and its approximate optimality when they are drawn from independent regular distributions [11], we focus our attention to the second price auction with general (not necessarily monopoly) reserve prices, arguably one of the simplest and most intuitive auction formats. As our main result, we show that for a carefully chosen set of reserve prices this auction guarantees at least 20% of both the optimal welfare and the optimal revenue, when the biddersâ values are distributed according to independent, not necessarily identical, regular distributions. We also prove a similar guarantee, when the values are drawn i.i.d. from aâpossibly irregularâdistribution.National Science Foundation (U.S.) (award CCF-0953960)National Science Foundation (U.S.) (CCF-1101491
Majority Dynamics and Aggregation of Information in Social Networks
Consider n individuals who, by popular vote, choose among q >= 2
alternatives, one of which is "better" than the others. Assume that each
individual votes independently at random, and that the probability of voting
for the better alternative is larger than the probability of voting for any
other. It follows from the law of large numbers that a plurality vote among the
n individuals would result in the correct outcome, with probability approaching
one exponentially quickly as n tends to infinity. Our interest in this paper is
in a variant of the process above where, after forming their initial opinions,
the voters update their decisions based on some interaction with their
neighbors in a social network. Our main example is "majority dynamics", in
which each voter adopts the most popular opinion among its friends. The
interaction repeats for some number of rounds and is then followed by a
population-wide plurality vote.
The question we tackle is that of "efficient aggregation of information": in
which cases is the better alternative chosen with probability approaching one
as n tends to infinity? Conversely, for which sequences of growing graphs does
aggregation fail, so that the wrong alternative gets chosen with probability
bounded away from zero? We construct a family of examples in which interaction
prevents efficient aggregation of information, and give a condition on the
social network which ensures that aggregation occurs. For the case of majority
dynamics we also investigate the question of unanimity in the limit. In
particular, if the voters' social network is an expander graph, we show that if
the initial population is sufficiently biased towards a particular alternative
then that alternative will eventually become the unanimous preference of the
entire population.Comment: 22 page
Gorenstein homological algebra and universal coefficient theorems
We study criteria for a ringâor more generally, for a small categoryâto be Gorenstein and for a module over it to be of finite projective dimension. The goal is to unify the universal coefficient theorems found in the literature and to develop machinery for proving new ones. Among the universal coefficient theorems covered by our methods we find, besides all the classic examples, several exotic examples arising from the KK-theory of C*-algebras and also Neemanâs BrownâAdams representability theorem for compactly generated categories
Worldline Superfield Actions for N=2 Superparticles
We propose doubly supersymmetric actions in terms of n=2(D-2) worldline
superfields for N=2 superparticles in D=3,4 and Type IIA D=6 superspaces. These
actions are obtained by dimensional reduction of superfield actions for N=1
superparticles in D=4,6 and 10, respectively. We show that in all these models
geometrodynamical constraints on target superspace coordinates do not put the
theory on the mass shell, so the actions constructed consistently describe the
dynamics of the corresponding N=2 superparticles. We also find that in contrast
to the IIA D=6 superparticle a chiral IIB D=6 superparticle, which is not
obtainable by dimensional reduction from N=1, D=10, is described by superfield
constraints which produce dynamical equations. This implies that for the IIB
D=6 superparticle the doubly supersymmetric action does not exist in the
conventional form.Comment: Latex, 20 pp. Minor corrections, acknowledgements adde
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Nano-sized SQUID-on-tip for scanning probe microscopy
We present a SQUID of novel design, which is fabricated on the tip of a pulled quartz tube in a simple 3-step evaporation process without need for any additional processing, patterning, or lithography. The resulting devices have SQUID loops with typical diameters in the range 75â300 nm. They operate in magnetic fields up to 0.6 T and have flux sensitivity of 1.8 ΌΊ0/Hz1/2 and magnetic field sensitivity of 10â7 T/Hz1/2, which corresponds to a spin sensitivity of 65 ÎŒB/Hz1/2 for aluminum SQUIDs. The shape of the tip and the small area of the SQUID loop, together with its high sensitivity, make our device an excellent tool for scanning SQUID microscopy: With the SQUID-on-tip glued to a tine of a quartz tuning fork, we have succeeded in obtaining magnetic images of a patterned niobium film and of vortices in a superconducting film in a magnetic field.Physic
On Albanese torsors and the elementary obstruction
We show that the elementary obstruction to the existence of 0-cycles of
degree 1 on an arbitrary variety X (over an arbitrary field) can be expressed
in terms of the Albanese 1-motives associated with dense open subsets of X.
Arithmetic applications are given
The Universality of Einstein Equations
It is shown that for a wide class of analytic Lagrangians which depend only
on the scalar curvature of a metric and a connection, the application of the
so--called ``Palatini formalism'', i.e., treating the metric and the connection
as independent variables, leads to ``universal'' equations. If the dimension
of space--time is greater than two these universal equations are Einstein
equations for a generic Lagrangian and are suitably replaced by other universal
equations at bifurcation points. We show that bifurcations take place in
particular for conformally invariant Lagrangians and prove
that their solutions are conformally equivalent to solutions of Einstein
equations. For 2--dimensional space--time we find instead that the universal
equation is always the equation of constant scalar curvature; the connection in
this case is a Weyl connection, containing the Levi--Civita connection of the
metric and an additional vectorfield ensuing from conformal invariance. As an
example, we investigate in detail some polynomial Lagrangians and discuss their
bifurcations.Comment: 15 pages, LaTeX, (Extended Version), TO-JLL-P1/9
Comparative Study for Inference of Hidden Classes in Stochastic Block Models
Inference of hidden classes in stochastic block model is a classical problem
with important applications. Most commonly used methods for this problem
involve na\"{\i}ve mean field approaches or heuristic spectral methods.
Recently, belief propagation was proposed for this problem. In this
contribution we perform a comparative study between the three methods on
synthetically created networks. We show that belief propagation shows much
better performance when compared to na\"{\i}ve mean field and spectral
approaches. This applies to accuracy, computational efficiency and the tendency
to overfit the data.Comment: 8 pages, 5 figures AIGM1
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