Self-Similar Random Processes and Infinite-Dimensional Configuration Spaces

We discuss various infinite-dimensional configuration spaces that carry measures quasiinvariant under compactly-supported diffeomorphisms of a manifold M corresponding to a physical space. Such measures allow the construction of unitary representations of the diffeomorphism group, which are important to nonrelativistic quantum statistical physics and to the quantum theory of extended objects in d-dimensional Euclidean space. Special attention is given to measurable structure and topology underlying measures on generalized configuration spaces obtained from self-similar random processes (both for d = 1 and d > 1), which describe infinite point configurations having accumulation points

On the Fock space for nonrelativistic anyon fields and braided tensor products

We realize the physical N-anyon Hilbert spaces, introduced previously via unitary representations of the group of diffeomorphisms of the plane, as N-fold braided-symmetric tensor products of the 1-particle Hilbert space. This perspective provides a convenient Fock space construction for nonrelativistic anyon quantum fields along the more usual lines of boson and fermion fields, but in a braided category. We see how essential physical information is thus encoded. In particular we show how the algebraic structure of our anyonic Fock space leads to a natural anyonic exclusion principle related to intermediate occupation number statistics, and obtain the partition function for an idealised gas of fixed anyonic vortices.Comment: Added some references, more explicit formulae for the discrete case and remark on partition function. 25 pages latex, no figure

Interpretation of HRCT Scans in the Diagnosis of IPF: Improving Communication Between Pulmonologists and Radiologists.

Idiopathic pulmonary fibrosis (IPF) is a progressive fibrosing interstitial lung disease (ILD). In this review, we describe the central role of high-resolution computed tomography (HRCT) in the diagnosis of IPF and discuss how communication between pulmonologists and radiologists might be improved to make the interpretation of HRCT scans more effective. Clinical information is important in the interpretation of HRCT scans, as the likelihood that specific radiologic features reflect IPF is not absolute, but dependent on the clinical context. In cases where the clinical context or HRCT pattern are inconclusive, multidisciplinary discussion (MDD) between a pulmonologist and radiologist (and, where relevant, a pathologist and rheumatologist) experienced in the differential diagnosis of ILD is necessary to establish a diagnosis. While it can be challenging to convene a face-to-face meeting, MDD can be conducted virtually or by telephone to enable each specialty group to contribute. To make the MDD most effective, it is important that relevant clinical information (for example, on the patient's clinical history, exposures and the results of serological tests) is shared with all parties in advance. A common lexicon to describe HRCT features observed in ILD can also help improve the effectiveness of MDD. A working diagnosis may be made in patients who do not fulfill all the diagnostic criteria for any specific type of ILD, but this diagnosis should be reviewed at regular intervals, with repeat of clinical, radiological, and laboratory assessments as appropriate, as new information pertinent to the patient's diagnosis may become available

Decoupling Transition I. Flux Lattices in Pure Layered Superconductors

We study the decoupling transition of flux lattices in a layered superconductors at which the Josephson coupling J is renormalized to zero. We identify the order parameter and related correlations; the latter are shown to decay as a power law in the decoupled phase. Within 2nd order renormalization group we find that the transition is always continuous, in contrast with results of the self consistent harmonic approximation. The critical temperature for weak J is ~1/B, where B is the magnetic field, while for strong J it is~1/sqrt{B} and is strongly enhanced. We show that renormaliztion group can be used to evaluate the Josephson plasma frequency and find that for weak J it is~1/BT^2 in the decoupled phase.Comment: 14 pages, 5 figures. New sections III, V. Companion to following article on "Decoupling and Depinning II: Flux lattices in disordered layered superconductors

Some Variations on Maxwell's Equations

In the first sections of this article, we discuss two variations on Maxwell's equations that have been introduced in earlier work--a class of nonlinear Maxwell theories with well-defined Galilean limits (and correspondingly generalized Yang-Mills equations), and a linear modification motivated by the coupling of the electromagnetic potential with a certain nonlinear Schroedinger equation. In the final section, revisiting an old idea of Lorentz, we write Maxwell's equations for a theory in which the electrostatic force of repulsion between like charges differs fundamentally in magnitude from the electrostatic force of attraction between unlike charges. We elaborate on Lorentz' description by means of electric and magnetic field strengths, whose governing equations separate into two fully relativistic Maxwell systems--one describing ordinary electromagnetism, and the other describing a universally attractive or repulsive long-range force. If such a force cannot be ruled out {\it a priori} by known physical principles, its magnitude should be determined or bounded experimentally. Were it to exist, interesting possibilities go beyond Lorentz' early conjecture of a relation to (Newtonian) gravity.Comment: 26 pages, submitted to a volume in preparation to honor Gerard Emch v. 2: discussion revised, factors of 4\pi corrected in some equation

Energy Spectrum of Anyons in a Magnetic Field

For the many-anyon system in external magnetic field, we derive the energy spectrum as an exact solution of the quantum eigenvalue problem with particular topological constraints. Our results agree with the numerical spectra recently obtained for the 3- and the 4-anyon systems.Comment: 11 pages in Plain LaTeX (plus 4 figures available on request), DFPD 92/TH/4

Gauge Transformations in Quantum Mechanics and the Unification of Nonlinear Schr\"odinger Equations

Beginning with ordinary quantum mechanics for spinless particles, together with the hypothesis that all experimental measurements consist of positional measurements at different times, we characterize directly a class of nonlinear quantum theories physically equivalent to linear quantum mechanics through nonlinear gauge transformations. We show that under two physically-motivated assumptions, these transformations are uniquely determined: they are exactly the group of time-dependent, nonlinear gauge transformations introduced previously for a family of nonlinear Schr\"odinger equations. The general equation in this family, including terms considered by Kostin, by Bialynicki-Birula and Mycielski, and by Doebner and Goldin, with time-dependent coefficients, can be obtained from the linear Schr\"odinger equation through gauge transformation and a subsequent process we call gauge generalization. We thus unify, on fundamental grounds, a rather diverse set of nonlinear time-evolutions in quantum mechanics.Comment: RevTeX, 20 pages, no figures. also available on http://www.pt.tu-clausthal.de/preprints/asi-tpa/021-96.htm

Prediction of progression in idiopathic pulmonary fibrosis using CT scans atbaseline: A quantum particle swarm optimization - Random forest approach

Idiopathic pulmonary fibrosis (IPF) is a fatal lung disease characterized by an unpredictable progressive declinein lung function. Natural history of IPF is unknown and the prediction of disease progression at the time ofdiagnosis is notoriously difficult. High resolution computed tomography (HRCT) has been used for the diagnosisof IPF, but not generally for monitoring purpose. The objective of this work is to develop a novel predictivemodel for the radiological progression pattern at voxel-wise level using only baseline HRCT scans. Mainly, thereare two challenges: (a) obtaining a data set of features for region of interest (ROI) on baseline HRCT scans andtheir follow-up status; and (b) simultaneously selecting important features from high-dimensional space, andoptimizing the prediction performance. We resolved the first challenge by implementing a study design andhaving an expert radiologist contour ROIs at baseline scans, depending on its progression status in follow-upvisits. For the second challenge, we integrated the feature selection with prediction by developing an algorithmusing a wrapper method that combines quantum particle swarm optimization to select a small number of featureswith random forest to classify early patterns of progression. We applied our proposed algorithm to analyzeanonymized HRCT images from 50 IPF subjects from a multi-center clinical trial. We showed that it yields aparsimonious model with 81.8% sensitivity, 82.2% specificity and an overall accuracy rate of 82.1% at the ROIlevel. These results are superior to other popular feature selections and classification methods, in that ourmethod produces higher accuracy in prediction of progression and more balanced sensitivity and specificity witha smaller number of selected features. Our work is the first approach to show that it is possible to use onlybaseline HRCT scans to predict progressive ROIs at 6 months to 1year follow-ups using artificial intelligence

Spirometry of healthy adult South African men

Aim. To detennine normative spirometric values for black and white South African men.Methods. A population of 796 bank personnel were subjected to spirometry and anthropometric measurements. An exhaustive questionnaire and radiographic screening process was used to identify a healthy population. Spirometry was performed using two calibrated instruments, a sleeve sealed piston spirometer (Autolink) and a bellows spirometer (Vitalograph). The methodological guidelines of the American Thoracic Society were observed. In the regression analysis Mallow's CP statistic was used to identify the best prediction models.Results. Compelling evidence was found in support of incorporating sitting height in prediction equations. For the Autolink studies the prediction equations (based on age, slanding height and weight) for forced vital capacity (FVC) (litres) were as follows: blacks: 0.053 height- 0.030 age 3.54; and whites: 0.056 height - 0.038 age - 3.07; for forced expiratory volume in the 1st second (FEV,) (litres) blacks: 0.038 height- 0.032 age - 1.18; and whites: 0.042 height- 0.038 age - 1.45. For the VitaJograph the equations were: FVC: blacks 0.048 height - 0.024 age 3.08 L; whites 0.056 height- 0.031 age - 3.42; FEV,: blacks 0.029 height - 0.027 age - 0.535; whites 0.042 height- 0.036 age - 1.84.Conclusion. The VitaJograph yielded significantly lower values than the Autolink for FVC measurements despite absolute consistency in methods. In view of the fact that the present study was conducted on healthy men, free from noxious industrial exposure, using state-of-the-art methods, these prediction equations may be regarded as the definitive norms for adult South African males