310 research outputs found
Templates for Convex Cone Problems with Applications to Sparse Signal Recovery
This paper develops a general framework for solving a variety of convex cone
problems that frequently arise in signal processing, machine learning,
statistics, and other fields. The approach works as follows: first, determine a
conic formulation of the problem; second, determine its dual; third, apply
smoothing; and fourth, solve using an optimal first-order method. A merit of
this approach is its flexibility: for example, all compressed sensing problems
can be solved via this approach. These include models with objective
functionals such as the total-variation norm, ||Wx||_1 where W is arbitrary, or
a combination thereof. In addition, the paper also introduces a number of
technical contributions such as a novel continuation scheme, a novel approach
for controlling the step size, and some new results showing that the smooth and
unsmoothed problems are sometimes formally equivalent. Combined with our
framework, these lead to novel, stable and computationally efficient
algorithms. For instance, our general implementation is competitive with
state-of-the-art methods for solving intensively studied problems such as the
LASSO. Further, numerical experiments show that one can solve the Dantzig
selector problem, for which no efficient large-scale solvers exist, in a few
hundred iterations. Finally, the paper is accompanied with a software release.
This software is not a single, monolithic solver; rather, it is a suite of
programs and routines designed to serve as building blocks for constructing
complete algorithms.Comment: The TFOCS software is available at http://tfocs.stanford.edu This
version has updated reference
Survival probability and order statistics of diffusion on disordered media
We investigate the first passage time t_{j,N} to a given chemical or
Euclidean distance of the first j of a set of N>>1 independent random walkers
all initially placed on a site of a disordered medium. To solve this
order-statistics problem we assume that, for short times, the survival
probability (the probability that a single random walker is not absorbed by a
hyperspherical surface during some time interval) decays for disordered media
in the same way as for Euclidean and some class of deterministic fractal
lattices. This conjecture is checked by simulation on the incipient percolation
aggregate embedded in two dimensions. Arbitrary moments of t_{j,N} are
expressed in terms of an asymptotic series in powers of 1/ln N which is
formally identical to those found for Euclidean and (some class of)
deterministic fractal lattices. The agreement of the asymptotic expressions
with simulation results for the two-dimensional percolation aggregate is good
when the boundary is defined in terms of the chemical distance. The agreement
worsens slightly when the Euclidean distance is used.Comment: 8 pages including 9 figure
Quantum central limit theorem for continuous-time quantum walks on odd graphs in quantum probability theory
The method of the quantum probability theory only requires simple structural
data of graph and allows us to avoid a heavy combinational argument often
necessary to obtain full description of spectrum of the adjacency matrix. In
the present paper, by using the idea of calculation of the probability
amplitudes for continuous-time quantum walk in terms of the quantum probability
theory, we investigate quantum central limit theorem for continuous-time
quantum walks on odd graphs.Comment: 19 page, 1 figure
Implementation of an Optimal First-Order Method for Strongly Convex Total Variation Regularization
We present a practical implementation of an optimal first-order method, due
to Nesterov, for large-scale total variation regularization in tomographic
reconstruction, image deblurring, etc. The algorithm applies to -strongly
convex objective functions with -Lipschitz continuous gradient. In the
framework of Nesterov both and are assumed known -- an assumption
that is seldom satisfied in practice. We propose to incorporate mechanisms to
estimate locally sufficient and during the iterations. The mechanisms
also allow for the application to non-strongly convex functions. We discuss the
iteration complexity of several first-order methods, including the proposed
algorithm, and we use a 3D tomography problem to compare the performance of
these methods. The results show that for ill-conditioned problems solved to
high accuracy, the proposed method significantly outperforms state-of-the-art
first-order methods, as also suggested by theoretical results.Comment: 23 pages, 4 figure
Electron transport across a quantum wire in the presence of electron leakage to a substrate
We investigate electron transport through a mono-atomic wire which is tunnel
coupled to two electrodes and also to the underlying substrate. The setup is
modeled by a tight-binding Hamiltonian and can be realized with a scanning
tunnel microscope (STM). The transmission of the wire is obtained from the
corresponding Green's function. If the wire is scanned by the contacting STM
tip, the conductance as a function of the tip position exhibits oscillations
which may change significantly upon increasing the number of wire atoms. Our
numerical studies reveal that the conductance depends strongly on whether or
not the substrate electrons are localized. As a further ubiquitous feature, we
observe the formation of charge oscillations.Comment: 7 pages, 7 figure
Resonant tunneling through ultrasmall quantum dots: zero-bias anomalies, magnetic field dependence, and boson-assisted transport
We study resonant tunneling through a single-level quantum dot in the
presence of strong Coulomb repulsion beyond the perturbative regime. The level
is either spin-degenerate or can be split by a magnetic field. We, furthermore,
discuss the influence of a bosonic environment. Using a real-time diagrammatic
formulation we calculate transition rates, the spectral density and the
nonlinear characteristic. The spectral density shows a multiplet of Kondo
peaks split by the transport voltage and the boson frequencies, and shifted by
the magnetic field. This leads to zero-bias anomalies in the differential
conductance, which agree well with recent experimental results for the electron
transport through single-charge traps. Furthermore, we predict that the sign of
the zero-bias anomaly depends on the level position relative to the Fermi level
of the leads.Comment: 27 pages, latex, 21 figures, submitted to Phys. Rev.
The management of iron deficiency in inflammatory bowel disease
__Background__ Iron deficiency is a common and undertreated problem in inflammatory bowel disease (IBD).
__Aim__ To develop an online tool to support treatment choice at the patient-specific level.
__Methods__ Using the RAND/UCLA Appropriateness Method (RUAM), a European expert panel assessed the appropriateness of treatment regimens for a variety of clinical scenarios in patients with non-anaemic iron deficiency (NAID) and iron deficiency anaemia (IDA). Treatment options included adjustment of IBD medication only, oral iron supplementation, high-/low-dose intravenous (IV) regimens, IV iron plus erythropoietin-stimulating agent (ESA), and blood transfusion. The panel process consisted of two individual rating rounds and three plenary discussion meetings.
__Results__ The panel reached agreement on 71% of treatment indications. 'No treatment' was never considered appropriate, and repeat treatment after previous failure was generally discouraged. For 98% of scenarios, at least one treatment was appropriate. Adjustment of IBD medication was deemed appropriate in all patients with active disease. Use of oral iron was mainly considered an option in NAID and mildly anaemic patients without disease activity. IV regimens were often judged appropriate, with high-dose IV iron being the preferred option in 77% of IDA scenarios. Blood transfusion and IV+ESA were indicated in exceptional cases only.
__Conclusions__ The RUAM revealed high agreement amongst experts on the management of iron deficiency in patients with IBD. High-dose IV iron was more often considered appropriate than other options. To facilitate dissemination of the recommendations, panel outcomes were embedded in an online tool, accessible via http://ferroscope.com/
Fitting the integrated Spectral Energy Distributions of Galaxies
Fitting the spectral energy distributions (SEDs) of galaxies is an almost
universally used technique that has matured significantly in the last decade.
Model predictions and fitting procedures have improved significantly over this
time, attempting to keep up with the vastly increased volume and quality of
available data. We review here the field of SED fitting, describing the
modelling of ultraviolet to infrared galaxy SEDs, the creation of
multiwavelength data sets, and the methods used to fit model SEDs to observed
galaxy data sets. We touch upon the achievements and challenges in the major
ingredients of SED fitting, with a special emphasis on describing the interplay
between the quality of the available data, the quality of the available models,
and the best fitting technique to use in order to obtain a realistic
measurement as well as realistic uncertainties. We conclude that SED fitting
can be used effectively to derive a range of physical properties of galaxies,
such as redshift, stellar masses, star formation rates, dust masses, and
metallicities, with care taken not to over-interpret the available data. Yet
there still exist many issues such as estimating the age of the oldest stars in
a galaxy, finer details ofdust properties and dust-star geometry, and the
influences of poorly understood, luminous stellar types and phases. The
challenge for the coming years will be to improve both the models and the
observational data sets to resolve these uncertainties. The present review will
be made available on an interactive, moderated web page (sedfitting.org), where
the community can access and change the text. The intention is to expand the
text and keep it up to date over the coming years.Comment: 54 pages, 26 figures, Accepted for publication in Astrophysics &
Space Scienc
Heavy quarkonium: progress, puzzles, and opportunities
A golden age for heavy quarkonium physics dawned a decade ago, initiated by
the confluence of exciting advances in quantum chromodynamics (QCD) and an
explosion of related experimental activity. The early years of this period were
chronicled in the Quarkonium Working Group (QWG) CERN Yellow Report (YR) in
2004, which presented a comprehensive review of the status of the field at that
time and provided specific recommendations for further progress. However, the
broad spectrum of subsequent breakthroughs, surprises, and continuing puzzles
could only be partially anticipated. Since the release of the YR, the BESII
program concluded only to give birth to BESIII; the -factories and CLEO-c
flourished; quarkonium production and polarization measurements at HERA and the
Tevatron matured; and heavy-ion collisions at RHIC have opened a window on the
deconfinement regime. All these experiments leave legacies of quality,
precision, and unsolved mysteries for quarkonium physics, and therefore beg for
continuing investigations. The plethora of newly-found quarkonium-like states
unleashed a flood of theoretical investigations into new forms of matter such
as quark-gluon hybrids, mesonic molecules, and tetraquarks. Measurements of the
spectroscopy, decays, production, and in-medium behavior of c\bar{c}, b\bar{b},
and b\bar{c} bound states have been shown to validate some theoretical
approaches to QCD and highlight lack of quantitative success for others. The
intriguing details of quarkonium suppression in heavy-ion collisions that have
emerged from RHIC have elevated the importance of separating hot- and
cold-nuclear-matter effects in quark-gluon plasma studies. This review
systematically addresses all these matters and concludes by prioritizing
directions for ongoing and future efforts.Comment: 182 pages, 112 figures. Editors: N. Brambilla, S. Eidelman, B. K.
Heltsley, R. Vogt. Section Coordinators: G. T. Bodwin, E. Eichten, A. D.
Frawley, A. B. Meyer, R. E. Mitchell, V. Papadimitriou, P. Petreczky, A. A.
Petrov, P. Robbe, A. Vair
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