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

Green synthesis of carbon dots using expired agar for a label-free fluorescence signal-amplified detection of ferric ion utilizing oxalate functionalization

Surface passivation strategies for functional carbon-based nanoparticles can provide unrivalled performance whilst fine-tuning their optical properties in addition to giving routes for large-scale syntheses. Herein, the synthesis of highly fluorescent agar-derived and oxalate-functionalized carbon dots (ag-oxCDs) is presented. We deployed a facile hydrothermal protocol, using expired potato dextrose agar and oxalate as “green” precursors to prepare fluorescent ag-oxCDs with a relative fluorescence (FL) quantum yield of ∼32% (emission/excitation wavelengths: 445/340 nm). The switchable fluorescence properties of the prepared ag-oxCDs was used for developing a sensitive nanosensor for ferric ion [Fe(III)] detection. Through Fe(III) coordination to the oxalate passivated surface of ag-oxCDs, the FL of ag-oxCDs was enhanced by an aggregation-induced emission enhancement mechanism. The tested and optimized concentration of Fe(III) was within a broad linear range of 0.5–1500 μM, with a detection limit of 75 nM (s/N = 3). The practical application of the ag-oxCDs-based FL nanosensor for real-time quantitative monitoring of Fe(III) was demonstrated by detecting up to 0.15 μM of Fe(III) in spiked human serum and water samples

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.

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

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

High Energy Neutrinos from Quasars

We review and clarify the assumptions of our basic model for neutrino production in the cores of quasars, as well as those modifications to the model subsequently made by other workers. We also present a revised estimate of the neutrino background flux and spectrum obtained using more recent empirical studies of quasars and their evolution. We compare our results with other thoeretical calculations and experimental upper limits on the AGN neutrino background flux. We also estimate possible neutrino fluxes from the jets of blazars detected recently by the EGRET experiment on the Compton Gamma Ray Observatory. We discuss the theoretical implications of these estimates.Comment: 14 pg., ps file (includes figures), To be published in Space Science Review

SO(2N) (0,2) SCFT and M Theory on AdS7×RP4AdS_7 \times {RP}^4

We study M theory on AdS_7 \times \RP^4 corresponding to 6 dimensional SO(2N) $(0, 2)$ superconformal field theory on a circle which becomes 5 dimensional super Yang-Mills theory at low energies. For SU(N) (0,2) theory, a wrapped D4 brane on $\S^4$ which is connected to a D4 brane on the boundary of $AdS_7$ by N fundamental strings can be interpreted as baryon vertex. For SO(2N) (0,2) theory, by using the property of homology of \RP^4, we classify various wrapping branes. Then we consider particles, strings, twobranes, domain walls and the baryon vertex in Type IIA string theory.Comment: 20 papges, The discussion on N=8 3D SCFT is corrected. Minor corrections, Added acknowledgment

Functional immunomics: Microarray analysis of IgG autoantibody repertoires predicts the future response of NOD mice to an inducer of accelerated diabetes

One's present repertoire of antibodies encodes the history of one's past immunological experience. Can the present autoantibody repertoire be consulted to predict resistance or susceptibility to the future development of an autoimmune disease? Here we developed an antigen microarray chip and used bioinformatic analysis to study a model of type 1 diabetes developing in non-obese diabetic (NOD) male mice in which the disease was accelerated and synchronized by exposing the mice to cyclophosphamide at 4 weeks of age. We obtained sera from 19 individual mice, treated the mice to induce cyclophosphamide-accelerated diabetes (CAD), and found, as expected, that 9 mice became severely diabetic while 10 mice permanently resisted diabetes. We again obtained serum from each mouse afterCAD induction. We then analyzed the patterns of antibodies in the individualmice to 266 different antigens spotted on the antigen chip. We identified a select panel of 27 different antigens (10% of the array) that revealed a pattern of IgG antibody reactivity in the pre-CAD serathat discriminated between the mice resistant or susceptible to CAD with 100% sensitivity and 82% specificity (p=0.017). Surprisingly, the set of IgG antibodies that was informative before CAD induction did not separate the resistant and susceptible groups after the onset of CAD; new antigens became criticalfor post-CAD repertoire discrimination. Thus, at least for a model disease, present antibody repertoires can predict future disease; predictive and diagnostic repertoires can differ; and decisive information about immune system behavior can be mined by bioinformatic technology. Repertoires matter.Comment: See Advanced Publication on the PNAS website for final versio