4,080 research outputs found
The SDSS Damped Lya Survey: Data Release 1
We present the results from an automated search for damped Lya (DLA) systems
in the quasar spectra of Data Release 1 from the Sloan Digital Sky Survey
(SDSS-DR1). At z~2.5, this homogeneous dataset has greater statistical
significance than the previous two decades of research. We derive a statistical
sample of 71 damped Lya systems (>50 previously unpublished) at z>2.1 and
measure HI column densities directly from the SDSS spectra. The number of DLA
systems per unit redshift is consistent with previous measurements and we
expect our survey has >95% completeness. We examine the cosmological baryonic
mass density of neutral gas Omega_g inferred from the damped Lya systems from
the SDSS-DR1 survey and a combined sample drawn from the literature. Contrary
to previous results, the Omega_g values do not require a significant correction
from Lyman limit systems at any redshift. We also find that the Omega_g values
for the SDSS-DR1 sample do not decline at high redshift and the combined sample
shows a (statistically insignificant) decrease only at z>4. Future data
releases from SDSS will provide the definitive survey of DLA systems at z~2.5
and will significantly reduce the uncertainty in Omega_g at higher redshift.Comment: 12 pages, includes color figures. Accepted to PASP, April 20 200
Small violations of full correlation Bell inequalities for multipartite pure random states
We estimate the probability of random -qudit pure states violating
full-correlation Bell inequalities with two dichotomic observables per site.
These inequalities can show violations that grow exponentially with , but we
prove this is not the typical case. For many-qubit states the probability to
violate any of these inequalities by an amount that grows linearly with is
vanishingly small. If each system's Hilbert space dimension is larger than two,
on the other hand, the probability of seeing \emph{any} violation is already
small. For the qubits case we discuss furthermore the consequences of this
result for the probability of seeing arbitrary violations (\emph i.e., of any
order of magnitude) when experimental imperfections are considered.Comment: 16 pages, one colum
Eigenvalue variance bounds for Wigner and covariance random matrices
This work is concerned with finite range bounds on the variance of individual
eigenvalues of Wigner random matrices, in the bulk and at the edge of the
spectrum, as well as for some intermediate eigenvalues. Relying on the GUE
example, which needs to be investigated first, the main bounds are extended to
families of Hermitian Wigner matrices by means of the Tao and Vu Four Moment
Theorem and recent localization results by Erd\"os, Yau and Yin. The case of
real Wigner matrices is obtained from interlacing formulas. As an application,
bounds on the expected 2-Wasserstein distance between the empirical spectral
measure and the semicircle law are derived. Similar results are available for
random covariance matrices
Beta-Adrenergic Receptors in the Lateral Nucleus of the Amygdala Contribute to the Acquisition but Not the Consolidation of Auditory Fear Conditioning
Beta-adrenergic receptors (ÎČARs) have long been associated with fear disorders and with learning and memory. However, the contribution of these receptors to Pavlovian fear conditioning, a leading behavioral model for studying fear learning and memory, is still poorly understood. The aim of this study was to investigate the involvement of ÎČAR activation in the acquisition, consolidation and expression of fear conditioning. We focused on manipulations of ÎČARs in the lateral nucleus of the amygdala (LA) because of the well-established contribution of this area to fear conditioning. Specifically, we tested the effects of intra-LA microinfusions of the ÎČAR antagonist, propranolol, on learning and memory for auditory Pavlovian fear conditioning in rats. Pre-training propranolol infusions disrupted the initial acquisition, short-term memory (STM), and long-term memory (LTM) for fear conditioning, but infusions immediately after training had no effect. Further, infusion of propranolol prior to testing fear responses did not affect fear memory expression. These findings indicate that amygdala ÎČARs are important for the acquisition but not the consolidation of fear conditioning
Sparsity and Incoherence in Compressive Sampling
We consider the problem of reconstructing a sparse signal from a
limited number of linear measurements. Given randomly selected samples of
, where is an orthonormal matrix, we show that minimization
recovers exactly when the number of measurements exceeds where is the number of
nonzero components in , and is the largest entry in properly
normalized: . The smaller ,
the fewer samples needed.
The result holds for ``most'' sparse signals supported on a fixed (but
arbitrary) set . Given , if the sign of for each nonzero entry on
and the observed values of are drawn at random, the signal is
recovered with overwhelming probability. Moreover, there is a sense in which
this is nearly optimal since any method succeeding with the same probability
would require just about this many samples
Perimeter of sublevel sets in infinite dimensional spaces
We compare the perimeter measure with the Airault-Malliavin surface measure
and we prove that all open convex subsets of abstract Wiener spaces have finite
perimeter. By an explicit counter-example, we show that in general this is not
true for compact convex domains
The central limit problem for random vectors with symmetries
Motivated by the central limit problem for convex bodies, we study normal
approximation of linear functionals of high-dimensional random vectors with
various types of symmetries. In particular, we obtain results for distributions
which are coordinatewise symmetric, uniform in a regular simplex, or
spherically symmetric. Our proofs are based on Stein's method of exchangeable
pairs; as far as we know, this approach has not previously been used in convex
geometry and we give a brief introduction to the classical method. The
spherically symmetric case is treated by a variation of Stein's method which is
adapted for continuous symmetries.Comment: AMS-LaTeX, uses xy-pic, 23 pages; v3: added new corollary to Theorem
Fluctuations of the partition function in the GREM with external field
We study Derrida's generalized random energy model in the presence of uniform
external field. We compute the fluctuations of the ground state and of the
partition function in the thermodynamic limit for all admissible values of
parameters. We find that the fluctuations are described by a hierarchical
structure which is obtained by a certain coarse-graining of the initial
hierarchical structure of the GREM with external field. We provide an explicit
formula for the free energy of the model. We also derive some large deviation
results providing an expression for the free energy in a class of models with
Gaussian Hamiltonians and external field. Finally, we prove that the
coarse-grained parts of the system emerging in the thermodynamic limit tend to
have a certain optimal magnetization, as prescribed by strength of external
field and by parameters of the GREM.Comment: 24 page
On Hastings' counterexamples to the minimum output entropy additivity conjecture
Hastings recently reported a randomized construction of channels violating
the minimum output entropy additivity conjecture. Here we revisit his argument,
presenting a simplified proof. In particular, we do not resort to the exact
probability distribution of the Schmidt coefficients of a random bipartite pure
state, as in the original proof, but rather derive the necessary large
deviation bounds by a concentration of measure argument. Furthermore, we prove
non-additivity for the overwhelming majority of channels consisting of a Haar
random isometry followed by partial trace over the environment, for an
environment dimension much bigger than the output dimension. This makes
Hastings' original reasoning clearer and extends the class of channels for
which additivity can be shown to be violated.Comment: 17 pages + 1 lin
Large Deviation Bounds for k-designs
We present a technique for derandomising large deviation bounds of functions
on the unitary group. We replace the Haar distribution with a pseudo-random
distribution, a k-design. k-designs have the first k moments equal to those of
the Haar distribution. The advantage of this is that (approximate) k-designs
can be implemented efficiently, whereas Haar random unitaries cannot. We find
large deviation bounds for unitaries chosen from a k-design and then illustrate
this general technique with three applications. We first show that the von
Neumann entropy of a pseudo-random state is almost maximal. Then we show that,
if the dynamics of the universe produces a k-design, then suitably sized
subsystems will be in the canonical state, as predicted by statistical
mechanics. Finally we show that pseudo-random states are useless for
measurement based quantum computation.Comment: 20 page
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