848 research outputs found
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
Minimum Decision Cost for Quantum Ensembles
For a given ensemble of independent and identically prepared particles,
we calculate the binary decision costs of different strategies for measurement
of polarised spin 1/2 particles. The result proves that, for any given values
of the prior probabilities and any number of constituent particles, the cost
for a combined measurement is always less than or equal to that for any
combination of separate measurements upon sub-ensembles. The Bayes cost, which
is that associated with the optimal strategy (i.e., a combined measurement) is
obtained in a simple closed form.Comment: 11 pages, uses RevTe
Drag in paired electron-hole layers
We investigate transresistance effects in electron-hole double layer systems
with an excitonic condensate. Our theory is based on the use of a minimum
dissipation premise to fix the current carried by the condensate. We find that
the drag resistance jumps discontinuously at the condensation temperature and
diverges as the temperature approaches zero.Comment: 12 pages, 1 Figure, .eps file attache
ALMA Observations of Gas-Rich Galaxies in z~1.6 Galaxy Clusters: Evidence for Higher Gas Fractions in High-Density Environments
We present ALMA CO (2-1) detections in 11 gas-rich cluster galaxies at z~1.6,
constituting the largest sample of molecular gas measurements in z>1.5 clusters
to date. The observations span three galaxy clusters, derived from the Spitzer
Adaptation of the Red-sequence Cluster Survey. We augment the >5sigma
detections of the CO (2-1) fluxes with multi-band photometry, yielding stellar
masses and infrared-derived star formation rates, to place some of the first
constraints on molecular gas properties in z~1.6 cluster environments. We
measure sizable gas reservoirs of 0.5-2x10^11 solar masses in these objects,
with high gas fractions and long depletion timescales, averaging 62% and 1.4
Gyr, respectively. We compare our cluster galaxies to the scaling relations of
the coeval field, in the context of how gas fractions and depletion timescales
vary with respect to the star-forming main sequence. We find that our cluster
galaxies lie systematically off the field scaling relations at z=1.6 toward
enhanced gas fractions, at a level of ~4sigma, but have consistent depletion
timescales. Exploiting CO detections in lower-redshift clusters from the
literature, we investigate the evolution of the gas fraction in cluster
galaxies, finding it to mimic the strong rise with redshift in the field. We
emphasize the utility of detecting abundant gas-rich galaxies in high-redshift
clusters, deeming them as crucial laboratories for future statistical studies.Comment: 8 pages, 3 figures, published in ApJ Letters; updated to match
published versio
Mean Field Calculations of Bose-Einstein Condensation of 7Li Atoms In a Harmonic Trap
A self-consistent mean-field theory for bosons for T>0 is used to reconcile
predictions of collapse with recent observations of Bose-Einstein condensation
of 7Li. Eigenfunctions of a (non-separable) Hamiltonian that includes the
anisotropic external trap field and atom-atom interactions are obtained by an
iteration process. A sum over the Bose distribution, and the ``alternating
direction implicit'' algorithm are used. Near Tc, the ensemble exhibits a
localized condensate composed of atoms in the few lowest states. For lower T,
numerical instability indicates collapse to a more dense phase.Comment: 11 pages + 4 figure
Classical Equations for Quantum Systems
The origin of the phenomenological deterministic laws that approximately
govern the quasiclassical domain of familiar experience is considered in the
context of the quantum mechanics of closed systems such as the universe as a
whole. We investigate the requirements for coarse grainings to yield decoherent
sets of histories that are quasiclassical, i.e. such that the individual
histories obey, with high probability, effective classical equations of motion
interrupted continually by small fluctuations and occasionally by large ones.
We discuss these requirements generally but study them specifically for coarse
grainings of the type that follows a distinguished subset of a complete set of
variables while ignoring the rest. More coarse graining is needed to achieve
decoherence than would be suggested by naive arguments based on the uncertainty
principle. Even coarser graining is required in the distinguished variables for
them to have the necessary inertia to approach classical predictability in the
presence of the noise consisting of the fluctuations that typical mechanisms of
decoherence produce. We describe the derivation of phenomenological equations
of motion explicitly for a particular class of models. Probabilities of the
correlations in time that define equations of motion are explicitly considered.
Fully non-linear cases are studied. Methods are exhibited for finding the form
of the phenomenological equations of motion even when these are only distantly
related to those of the fundamental action. The demonstration of the connection
between quantum-mechanical causality and causalty in classical phenomenological
equations of motion is generalized. The connections among decoherence, noise,
dissipation, and the amount of coarse graining necessary to achieve classical
predictability are investigated quantitatively.Comment: 100pages, 1 figur
Bose-Einstein Condensation in a Harmonic Potential
We examine several features of Bose-Einstein condensation (BEC) in an
external harmonic potential well. In the thermodynamic limit, there is a phase
transition to a spatial Bose-Einstein condensed state for dimension D greater
than or equal to 2. The thermodynamic limit requires maintaining constant
average density by weakening the potential while increasing the particle number
N to infinity, while of course in real experiments the potential is fixed and N
stays finite. For such finite ideal harmonic systems we show that a BEC still
occurs, although without a true phase transition, below a certain
``pseudo-critical'' temperature, even for D=1. We study the momentum-space
condensate fraction and find that it vanishes as 1/N^(1/2) in any number of
dimensions in the thermodynamic limit. In D less than or equal to 2 the lack of
a momentum condensation is in accord with the Hohenberg theorem, but must be
reconciled with the existence of a spatial BEC in D=2. For finite systems we
derive the N-dependence of the spatial and momentum condensate fractions and
the transition temperatures, features that may be experimentally testable. We
show that the N-dependence of the 2D ideal-gas transition temperature for a
finite system cannot persist in the interacting case because it violates a
theorem due to Chester, Penrose, and Onsager.Comment: 34 pages, LaTeX, 6 Postscript figures, Submitted to Jour. Low Temp.
Phy
Surveying the Dynamic Radio Sky with the Long Wavelength Demonstrator Array
This paper presents a search for radio transients at a frequency of 73.8 MHz
(4 m wavelength) using the all-sky imaging capabilities of the Long Wavelength
Demonstrator Array (LWDA). The LWDA was a 16-dipole phased array telescope,
located on the site of the Very Large Array in New Mexico. The field of view of
the individual dipoles was essentially the entire sky, and the number of
dipoles was sufficiently small that a simple software correlator could be used
to make all-sky images. From 2006 October to 2007 February, we conducted an
all-sky transient search program, acquiring a total of 106 hr of data; the time
sampling varied, being 5 minutes at the start of the program and improving to 2
minutes by the end of the program. We were able to detect solar flares, and in
a special-purpose mode, radio reflections from ionized meteor trails during the
2006 Leonid meteor shower. We detected no transients originating outside of the
solar system above a flux density limit of 500 Jy, equivalent to a limit of no
more than about 10^{-2} events/yr/deg^2, having a pulse energy density >~ 1.5 x
10^{-20} J/m^2/Hz at 73.8 MHz for pulse widths of about 300 s. This event rate
is comparable to that determined from previous all-sky transient searches, but
at a lower frequency than most previous all-sky searches. We believe that the
LWDA illustrates how an all-sky imaging mode could be a useful operational
model for low-frequency instruments such as the Low Frequency Array, the Long
Wavelength Array station, the low-frequency component of the Square Kilometre
Array, and potentially the Lunar Radio Array.Comment: 20 pages; accepted for publication in A
Comparative analysis of homology models of the Ah receptor ligand binding domain: Verification of structure-function predictions by site-directed mutagenesis of a nonfunctional receptor
The aryl hydrocarbon receptor (AHR) is a ligand-dependent transcription factor that mediates the biological and toxic effects of a wide variety of structurally diverse chemicals, including the toxic environmental contaminant 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD). While significant interspecies differences in AHR ligand binding specificity, selectivity, and response have been observed, the structural determinants responsible for those differences have not been determined, and homology models of the AHR ligand-binding domain (LBD) are available for only a few species. Here we describe the development and comparative analysis of homology models of the LBD of 16 AHRs from 12 mammalian and nonmammalian species and identify the specific residues contained within their ligand binding cavities. The ligand-binding cavity of the fish AHR exhibits differences from those of mammalian and avian AHRs, suggesting a slightly different TCDD binding mode. Comparison of the internal cavity in the LBD model of zebrafish (zf) AHR2, which binds TCDD with high affinity, to that of zfAHR1a, which does not bind TCDD, revealed that the latter has a dramatically shortened binding cavity due to the side chains of three residues (Tyr296, Thr386, and His388) that reduce the amount of internal space available to TCDD. Mutagenesis of two of these residues in zfAHR1a to those present in zfAHR2 (Y296H and T386A) restored the ability of zfAHR1a to bind TCDD and to exhibit TCDD-dependent binding to DNA. These results demonstrate the importance of these two amino acids and highlight the predictive potential of comparative analysis of homology models from diverse species. The availability of these AHR LBD homology models will facilitate in-depth comparative studies of AHR ligand binding and ligand-dependent AHR activation and provide a novel avenue for examining species-specific differences in AHR responsiveness. © 2013 American Chemical Society
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