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)

Some comments about Schwarzschield black holes in Matrix theory

In the present paper we calculate the statistical partition function for any number of extended objects in Matrix theory in the one loop approximation. As an application, we calculate the statistical properties of K clusters of D0 branes and then the statistical properties of K membranes which are wound on a torus.Comment: 15 page

Classical instability in Lovelock gravity

We introduce a simple method for the investigation of the classical stability of static solutions with a horizon in Lovelock gravity. The method is applicable to the investigation of high angular momentum instabilities, similar to those found by Dotti and Gleiser for Gauss-Bonnet black holes. The method does not require the knowledge of the explicit analytic form of the black hole solution. In this paper we apply our method to a case where the explicit solution is known and show that it identifies correctly the resulting unstable modes.Comment: 13 pages, 2 figure

N=1 Supergravity Chaotic Inflation in the Braneworld Scenario

We study a N=1 Supergravity chaotic inflationary model, in the context of the braneworld scenario. It is shown that successful inflation and reheating consistent with phenomenological constraints can be achieved via the new terms in the Friedmann equation arising from brane physics. Interestingly, the model satisfies observational bounds with sub-Planckian field values, implying that chaotic inflation on the brane is free from the well known difficulties associated with the presence of higher order non-renormalizable terms in the superpotential. A bound on the mass scale of the fifth dimension, M_5 \gsim 1.3 \times 10^{-6} M_P, is obtained from the requirement that the reheating temperature be higher than the temperature of the electroweak phase transition.Comment: 5 pages, 1 Table, Revtex

Semiclassical Approach to Black Hole Evaporation

Black hole evaporation may lead to massive or massless remnants, or naked singularities. This paper investigates this process in the context of two quite different two dimensional black hole models. The first is the original CGHS model, the second is another two dimensional dilaton-gravity model, but with properties much closer to physics in the real, four dimensional, world. Numerical simulations are performed of the formation and subsequent evaporation of black holes and the results are found to agree qualitatively with the exactly solved modified CGHS models, namely that the semiclassical approximation breaks down just before a naked singularity appears.Comment: 15 pages, PUPT-1340, harvmac, 11 figures available on reques

The Moduli Space and M(atrix) Theory of 9d N=1 Backgrounds of M/String Theory

We discuss the moduli space of nine dimensional N=1 supersymmetric compactifications of M theory / string theory with reduced rank (rank 10 or rank 2), exhibiting how all the different theories (including M theory compactified on a Klein bottle and on a Mobius strip, the Dabholkar-Park background, CHL strings and asymmetric orbifolds of type II strings on a circle) fit together, and what are the weakly coupled descriptions in different regions of the moduli space. We argue that there are two disconnected components in the moduli space of theories with rank 2. We analyze in detail the limits of the M theory compactifications on a Klein bottle and on a Mobius strip which naively give type IIA string theory with an uncharged orientifold 8-plane carrying discrete RR flux. In order to consistently describe these limits we conjecture that this orientifold non-perturbatively splits into a D8-brane and an orientifold plane of charge (-1) which sits at infinite coupling. We construct the M(atrix) theory for M theory on a Klein bottle (and the theories related to it), which is given by a 2+1 dimensional gauge theory with a varying gauge coupling compactified on a cylinder with specific boundary conditions. We also clarify the construction of the M(atrix) theory for backgrounds of rank 18, including the heterotic string on a circle.Comment: 43 pages, 7 figures, JHEP format. v3: typos correcte

Phase structure of matrix quantum mechanics at finite temperature

We study matrix quantum mechanics at finite temperature by Monte Carlo simulation. The model is obtained by dimensionally reducing 10d U(N) pure Yang-Mills theory to 1d. Following Aharony et al., one can view the same model as describing the high temperature regime of (1+1)d U(N) super Yang-Mills theory on a circle. In this interpretation an analog of the deconfinement transition was conjectured to be a continuation of the black-hole/black-string transition in the dual gravity theory. Our detailed analysis in the critical regime up to N=32 suggests the existence of the non-uniform phase, in which the eigenvalue distribution of the holonomy matrix is non-uniform but gapless. The transition to the gapped phase is of second order. The internal energy is constant (giving the ground state energy) in the uniform phase, and rises quadratically in the non-uniform phase, which implies that the transition between these two phases is of third order.Comment: 17 pages, 9 figures, (v2) refined arguments in section 3 ; reference adde

Black Hole Entropy and Superconformal Field Theories on Brane-Antibrane Systems

We obtain the enropy of Schwarzschild and charged black holes in D>4 from superconformal gases that live on p=10-D dimensional brane-antibrane systems wrapped on T^p. The preperties of the strongly coupled superconformal theories such as the appearance of hidden dimensions (for p=1,4) and fractional strings (for p=5) are crucial for our results. In all cases, the Schwarzschild radius is given by the transverse fluctuations of the branes and antibranes due to the finite temperature. We show that our results can be generalized to multicharged black holes.Comment: 24 pages in phyzzx.te

Schwarzschild Black Holes from Matrix Theory

We consider Matrix theory compactified on T^3 and show that it correctly describes the properties of Schwarzschild black holes in 7+1 dimensions, including the energy-entropy relation, the Hawking temperature and the physical size, up to numerical factors of order unity. The most economical description involves setting the cut-off N in the discretized light-cone quantization to be of order the black hole entropy. A crucial ingredient necessary for our work is the recently proposed equation of state for 3+1 dimensional SYM theory with 16 supercharges. We give detailed arguments for the range of validity of this equation following the methods of Horowitz and Polchinski.Comment: 9 pages, latex; minor typos correcte

The O(N) model on a squashed S^3 and the Klebanov-Polyakov correspondence

We solve the O(N) vector model at large N on a squashed three-sphere with a conformal mass term. Using the Klebanov-Polyakov version of the AdS_4/CFT_3 correspondence we match various aspects of the strongly coupled theory with the physics of the bulk AdS Taub-NUT and AdS Taub-Bolt geometries. Remarkably, we find that the field theory reproduces the behaviour of the bulk free energy as a function of the squashing parameter. The O(N) model is realised in a symmetric phase for all finite values of the coupling and squashing parameter, including when the boundary scalar curvature is negative.Comment: 1+27 pages. 6 figures. LaTeX. References adde