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 $N$ 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 $g$ is increased to a special value $g_t$, the string susceptibility exponent suddenly jumps from its conventional value $\gamma$ to ${\gamma\over\gamma-1}$. We study this effect in \L\ gravity and attribute it to a change of the interaction term from $O e^{\alpha_+ \phi}$ for $g<g_t$ to $O e^{\alpha_- \phi}$ for $g=g_t$ ($\alpha_+$ and $\alpha_-$ are the two roots of the conformal invariance condition for the \L\ dressing of a matter operator $O$). 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 c=1c=1 Strings.

The quantum and classical aspects of a deformed $c=1$ 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 $c<1$ 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}]$\lambda$4363 emission. The study of this object provides a rare opportunity to investigate the physical conditions and kinematics of the region(s) emitting the FHILs. By comparison with photoionisation model results, we find that the FHIL region has high densities (10$^{5.5}$ $<$ $n_H$ $<10^{8.0}$ 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 $\sim$ 360$\pm$30 km/s), with no evidence for a significant shift between the velocity centroid of the FHILs and the rest frame of the host galaxy. The deduced physical conditions lie between those of the Broad-Line (n$_H$$>10^9$ cm\textsuperscript{-3}) and Narrow-Line Regions ($n_H$$<10^6$ 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 $<$ $r_{FHIL}$ $<$ 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