394 research outputs found
A one-phase interior point method for nonconvex optimization
The work of Wachter and Biegler suggests that infeasible-start interior point
methods (IPMs) developed for linear programming cannot be adapted to nonlinear
optimization without significant modification, i.e., using a two-phase or
penalty method. We propose an IPM that, by careful initialization and updates
of the slack variables, is guaranteed to find a first-order certificate of
local infeasibility, local optimality or unboundedness of the (shifted)
feasible region. Our proposed algorithm differs from other IPM methods for
nonconvex programming because we reduce primal feasibility at the same rate as
the barrier parameter. This gives an algorithm with more robust convergence
properties and closely resembles successful algorithms from linear programming.
We implement the algorithm and compare with IPOPT on a subset of CUTEst
problems. Our algorithm requires a similar median number of iterations, but
fails on only 9% of the problems compared with 16% for IPOPT. Experiments on
infeasible variants of the CUTEst problems indicate superior performance for
detecting infeasibility.
The code for our implementation can be found at
https://github.com/ohinder/OnePhase .Comment: fixed typo in sign of dual multiplier in KKT syste
Global Charges in Chern-Simons theory and the 2+1 black hole
We use the Regge-Teitelboim method to treat surface integrals in gauge
theories to find global charges in Chern-Simons theory. We derive the affine
and Virasoro generators as global charges associated with symmetries of the
boundary. The role of boundary conditions is clarified. We prove that for
diffeomorphisms that do not preserve the boundary there is a classical
contribution to the central charge in the Virasoro algebra. The example of
anti-de Sitter 2+1 gravity is considered in detail.Comment: Revtex, no figures, 26 pages. Important changes introduced. One
section added
Semi-infinite Throat as the End-state Geometry of two-dimensional Black Hole Evaporation
We study a modified two-dimensional dilaton gravity theory which is exactly
solvable in the semiclassical approximation including back-reaction. The vacuum
solutions of this modified theory are asymptotically flat static space-times.
Infalling matter forms a black hole if its energy is above a certain threshold.
The black hole singularity is initially hidden behind a timelike apparent
horizon. As the black hole evaporates by emitting Hawking radiation, the
singularity meets the shrinking horizon in finite retarded time to become
naked. A natural boundary condition exists at the naked singularity such that
for general infalling matter-configuration the evaporating black hole
geometries can be matched continuously to a unique static end-state geometry.
This end-state geometry is asymptotically flat at its right spatial infinity,
while its left spatial infinity is a semi-infinite throat extending into the
strong coupling region.Comment: Tex + compressed uuencoded ps version with one figure included, 11
Touching Random Surfaces and Liouville Gravity
Large matrix models modified by terms of the form g(\Tr\Phi^n)^2
generate random surfaces which touch at isolated points. Matrix model results
indicate that, as is increased to a special value , the string
susceptibility exponent suddenly jumps from its conventional value to
. We study this effect in \L\ gravity and attribute it
to a change of the interaction term from for to
for ( and are the two roots
of the conformal invariance condition for the \L\ dressing of a matter operator
). Thus, the new critical behavior is explained by the unconventional branch
of \L\ dressing in the action.Comment: 15 pages, PUPT-1486 (last paragraph of sec. 2 revised
Quantum and Classical Aspects of Deformed Strings.
The quantum and classical aspects of a deformed matrix model proposed
by Jevicki and Yoneya are studied. String equations are formulated in the
framework of Toda lattice hierarchy. The Whittaker functions now play the role
of generalized Airy functions in strings. This matrix model has two
distinct parameters. Identification of the string coupling constant is thereby
not unique, and leads to several different perturbative interpretations of this
model as a string theory. Two such possible interpretations are examined. In
both cases, the classical limit of the string equations, which turns out to
give a formal solution of Polchinski's scattering equations, shows that the
classical scattering amplitudes of massless tachyons are insensitive to
deformations of the parameters in the matrix model.Comment: 52 pages, Latex
The forbidden high ionisation line region of the type 2 quasar Q1131+16: a clear view of the inner face of the torus?
We present spectroscopic observations of the type 2 quasar SDSS
J11311.05+162739.5 (Q1131+16 hereafter; z=0.1732), which has the richest
spectrum of forbidden high ionisation lines (FHIL, e.g. [Fe \textsc{vii}], [Fe
\textsc{x}], [Fe \textsc{xi}] and [Ne \textsc{v}]) yet reported for an AGN, as
well as unusually strong [O \textsc{iii}]4363 emission. The study of
this object provides a rare opportunity to investigate the physical conditions
and kinematics of the region(s) emitting the FHILs. By comparison with
photoionisation model results, we find that the FHIL region has high densities
(10 cm\textsuperscript{-3}) and ionisation
parameters (-1.5 log[U] 0), yet its kinematics are similar to those of
the low ionisation emission line region detected in the same object (FWHM
36030 km/s), with no evidence for a significant shift between the
velocity centroid of the FHILs and the rest frame of the host galaxy. The
deduced physical conditions lie between those of the Broad-Line (n
cm\textsuperscript{-3}) and Narrow-Line Regions (
cm\textsuperscript{-3}) of active galactic nuclei (AGN), and we demonstrate
that the FHIL regions must be situated relatively close to the illuminating AGN
(0.32 50pc). We suggest that the inner torus wall is the
most likely location for the FHIL region, and that the unusual strength of the
FHILs in this object is due to a specific viewing angle of the far wall of the
torus, coupled with a lack of dust on larger scales that might otherwise
obscure our view of the torus.Comment: Accepted for publication in the Monthly Notices of the Royal
Astronomical Society (3rd of March 2011). 23 Pages (including tables 5 and 6
in the source file), 21 figure
M-Theory as a Holographic Field Theory
We suggest that M-theory could be non-perturbatively equivalent to a local
quantum field theory. More precisely, we present a ``renormalizable'' gauge
theory in eleven dimensions, and show that it exhibits various properties
expected of quantum M-theory, most notably the holographic principle of
't~Hooft and Susskind. The theory also satisfies Mach's principle: A
macroscopically large space-time (and the inertia of low-energy excitations) is
generated by a large number of ``partons'' in the microscopic theory. We argue
that at low energies in large eleven dimensions, the theory should be
effectively described by eleven-dimensional supergravity. This effective
description breaks down at much lower energies than naively expected, precisely
when the system saturates the Bekenstein bound on energy density. We show that
the number of partons scales like the area of the surface surrounding the
system, and discuss how this holographic reduction of degrees of freedom
affects the cosmological constant problem. We propose the holographic field
theory as a candidate for a covariant, non-perturbative formulation of quantum
M-theory.Comment: 27 pp. v2: typos corrected; a small paragraph on naturalness of small
cosmological constant in four dimensions added at end of sect 5.1; final
version to appear in Phys. Rev.
DNA Repair Biomarker for Lung Cancer Risk and its Correlation With Airway Cells Gene Expression.
Background: Improving lung cancer risk assessment is required because current early-detection screening criteria miss most cases. We therefore examined the utility for lung cancer risk assessment of a DNA Repair score obtained from OGG1, MPG, and APE1 blood tests. In addition, we examined the relationship between the level of DNA repair and global gene expression. Methods: We conducted a blinded case-control study with 150 non-small cell lung cancer case patients and 143 control individuals. DNA Repair activity was measured in peripheral blood mononuclear cells, and the transcriptome of nasal and bronchial cells was determined by RNA sequencing. A combined DNA Repair score was formed using logistic regression, and its correlation with disease was assessed using cross-validation; correlation of expression to DNA Repair was analyzed using Gene Ontology enrichment. Results: DNA Repair score was lower in case patients than in control individuals, regardless of the case's disease stage. Individuals at the lowest tertile of DNA Repair score had an increased risk of lung cancer compared to individuals at the highest tertile, with an odds ratio (OR) of 7.2 (95% confidence interval [CI] = 3.0 to 17.5; P < .001), and independent of smoking. Receiver operating characteristic analysis yielded an area under the curve of 0.89 (95% CI = 0.82 to 0.93). Remarkably, low DNA Repair score correlated with a broad upregulation of gene expression of immune pathways in patients but not in control individuals. Conclusions: The DNA Repair score, previously shown to be a lung cancer risk factor in the Israeli population, was validated in this independent study as a mechanism-based cancer risk biomarker and can substantially improve current lung cancer risk prediction, assisting prevention and early detection by computed tomography scanning.This work was funded by grants from NIH/NCI/EDRN (#1 U01 CA111219), the Flight Attendant Medical Research Institute, Florida, the Mike Rosenbloom Foundation and Weizmann Institute of Science to ZL and TPE; and by grants from Cancer Research UK to BP and to the Cancer Research UK Cambridge Centre; and by a UK National Institute for Health Research Senior Fellowship to BP; and by the Cambridge Biomedical Research Centre and the Cancer Research UK Cambridge Centre to RCR. Volunteer participant recruitment through the Cambridge Bioresource was funded by the Cambridge Biomedical Research Centre
- …