Model validation for a noninvasive arterial stenosis detection problem

Copyright @ 2013 American Institute of Mathematical SciencesA current thrust in medical research is the development of a non-invasive method for detection, localization, and characterization of an arterial stenosis (a blockage or partial blockage in an artery). A method has been proposed to detect shear waves in the chest cavity which have been generated by disturbances in the blood flow resulting from a stenosis. In order to develop this methodology further, we use both one-dimensional pressure and shear wave experimental data from novel acoustic phantoms to validate corresponding viscoelastic mathematical models, which were developed in a concept paper [8] and refined herein. We estimate model parameters which give a good fit (in a sense to be precisely defined) to the experimental data, and use asymptotic error theory to provide confidence intervals for parameter estimates. Finally, since a robust error model is necessary for accurate parameter estimates and confidence analysis, we include a comparison of absolute and relative models for measurement error.The National Institute of Allergy and Infectious Diseases, the Air Force Office of Scientific Research, the Deopartment of Education and the Engineering and Physical Sciences Research Council (EPSRC)

Massive IIA flux compactifications and U-dualities

We attempt to find a rigorous formulation for the massive type IIA orientifold compactifications of string theory introduced in hep-th/0505160. An approximate double T-duality converts this background into IIA string theory on a twisted torus, but various arguments indicate that the back reaction of the orientifold on this geometry is large. In particular, an AdS calculation of the entropy suggests a scaling appropriate for N M2-branes, in a certain limit of the compactification, though not the one studied in hep-th/0505160. The M-theory lift of this specific regime is not 4 dimensional. We suggest that the generic limit of the background corresponds to a situation analogous to F-theory, where the string coupling is small in some regions of a compact geometry, and large in others, so that neither a long wavelength 11D SUGRA expansion, nor a world sheet expansion exists for these compactifications. We end with a speculation on the nature of the generic compactification.Comment: JHEP3 LaTeX - 34 pages - 3 figures; v2: Added references; v3: mistake in entropy scaling corrected, major changes in conclusions; v4: changed claims about original DeWolfe et al. setup, JHEP versio

Holographic Description of AdS Cosmologies

To gain insight in the quantum nature of the big bang, we study the dual field theory description of asymptotically anti-de Sitter solutions of supergravity that have cosmological singularities. The dual theories do not appear to have a stable ground state. One regularization of the theory causes the cosmological singularities in the bulk to turn into giant black holes with scalar hair. We interpret these hairy black holes in the dual field theory and use them to compute a finite temperature effective potential. In our study of the field theory evolution, we find no evidence for a "bounce" from a big crunch to a big bang. Instead, it appears that the big bang is a rare fluctuation from a generic equilibrium quantum gravity state.Comment: 34 pages, 8 figures, v2: minor changes, references adde

Supersymmetry Breaking in the Early Universe

Supersymmetry breaking in the early universe induces scalar soft potentials with curvature of order the Hubble constant. This has a dramatic effect on the coherent production of scalar fields along flat directions. For the moduli problem it generically gives a concrete realization of the problem by determining the field value subsequent to inflation. However it might suggest a solution if the minimum of the induced potential coincides with the true minimum. The induced Hubble scale mass also has important implications for the Affleck-Dine mechanism of baryogenesis. This mechanism requires large squark or slepton expectation values to develop along flat directions in the early universe. This is generally not the case if the induced mass squared is positive, but does occur if it is negative. The resulting baryon to entropy ratio depends mainly on the dimension of the nonrenormalizable operator in the superpotential which stabilizes the flat direction, and the reheat temperature after inflation. Unlike the original scenario, it is possible to obtain an acceptable baryon asymmetry without subsequent entropy releases.Comment: 11 pages, requires phyzz

Relations among Zero Momentum Correlators for Heavy-Light Systems in QCD

Relations connecting various zero momentum correlators of interpolating fields for pseudoscalar and scalar channel, containing one heavy and one light quark field, are derived from the Euclidean space formulation of the QCD functional integral. These relations may serve as constraints on the phenomenological models or approaches motivated from QCD, and suggest a method to extract the chiral quark condensates. It is also found that the correlator for pseudoscalar channel differs from that for scalar channel even in the large heavy quark mass limit.Comment: 9 pages in ReVTeX, UMD preprint #94-14

Holography at an Extremal De Sitter Horizon

Rotating maximal black holes in four-dimensional de Sitter space, for which the outer event horizon coincides with the cosmological horizon, have an infinite near-horizon region described by the rotating Nariai metric. We show that the asymptotic symmetry group at the spacelike future boundary of the near-horizon region contains a Virasoro algebra with a real, positive central charge. This is evidence that quantum gravity in a rotating Nariai background is dual to a two-dimensional Euclidean conformal field theory. These results are related to the Kerr/CFT correspondence for extremal black holes, but have two key differences: one of the black hole event horizons has been traded for the cosmological horizon, and the near-horizon geometry is a fiber over dS_2 rather than AdS_2.Comment: 15 page

Numerical study of duality and universality in a frozen superconductor

The three-dimensional integer-valued lattice gauge theory, which is also known as a "frozen superconductor," can be obtained as a certain limit of the Ginzburg-Landau theory of superconductivity, and is believed to be in the same universality class. It is also exactly dual to the three-dimensional XY model. We use this duality to demonstrate the practicality of recently developed methods for studying topological defects, and investigate the critical behavior of the phase transition using numerical Monte Carlo simulations of both theories. On the gauge theory side, we concentrate on the vortex tension and the penetration depth, which map onto the correlation lengths of the order parameter and the Noether current in the XY model, respectively. We show how these quantities behave near the critical point, and that the penetration depth exhibits critical scaling only very close to the transition point. This may explain the failure of superconductor experiments to see the inverted XY model scaling.Comment: 17 pages, 18 figures. Updated to match the version published in PRB (http://link.aps.org/abstract/PRB/v67/e014525) on 27 Jan 200

A Hexagonal Theory of Flavor

We construct a supersymmetric theory of flavor based on the discrete gauge group (D_6)^2, where D_6 describes the symmetry of a regular hexagon under proper rotations in three dimensions. The representation structure of the group allows one to distinguish the third from the lighter two generations of matter fields, so that in the symmetry limit only the top quark Yukawa coupling is allowed and scalar superpartners of the first two generations are degenerate. Light fermion Yukawa couplings arise from a sequential breaking of the flavor symmetry, and supersymmetric flavor-changing processes remain adequately suppressed. We contrast our model with others based on non-Abelian discrete gauge symmetries described in the literature, and discuss the challenges in constructing more minimal flavor models based on this approach.Comment: 19 pages, ReVTeX, 1 eps figur

The Zero Temperature Chiral Phase Transition in SU(N) Gauge Theories

We investigate the zero temperature chiral phase transition in an SU(N) gauge theory as the number of fermions $N_f$ is varied. We argue that there exists a critical number of fermions $N_f^c$, above which there is no chiral symmetry breaking or confinement, and below which both chiral symmetry breaking and confinement set in. We estimate $N_f^c$ and discuss the nature of the phase transition.Comment: 13 pages, LaTeX, version published in PR

Maximal Neutrino Mixing from a Minimal Flavor Symmetry

We study a number of models, based on a non-Abelian discrete group, that successfully reproduce the simple and predictive Yukawa textures usually associated with U(2) theories of flavor. These models allow for solutions to the solar and atmospheric neutrino problems that do not require altering successful predictions for the charged fermions or introducing sterile neutrinos. Although Yukawa matrices are hierarchical in the models we consider, the mixing between second- and third-generation neutrinos is naturally large. We first present a quantitative analysis of a minimal model proposed in earlier work, consisting of a global fit to fermion masses and mixing angles, including the most important renormalization group effects. We then propose two new variant models: The first reproduces all important features of the SU(5)xU(2) unified theory with neither SU(5) nor U(2). The second demonstrates that discrete subgroups of SU(2) can be used in constructing viable supersymmetric theories of flavor without scalar universality even though SU(2) by itself cannot.Comment: 34 pages LaTeX, 1 eps figure, minor revisions and references adde