Twisted K-theory and K-theory of bundle gerbes

In this note we introduce the notion of bundle gerbe K-theory and investigate the relation to twisted K-theory. We provide some examples. Possible applications of bundle gerbe K-theory to the classification of D-brane charges in non-trivial backgrounds are discussed.Comment: 29 pages, corrected typos, added references, included new section on twisted Chern character in non-torsion cas

Cyclic cocycles on twisted convolution algebras

We give a construction of cyclic cocycles on convolution algebras twisted by gerbes over discrete translation groupoids. For proper \'etale groupoids, Tu and Xu provide a map between the periodic cyclic cohomology of a gerbe-twisted convolution algebra and twisted cohomology groups which is similar to a construction of Mathai and Stevenson. When the groupoid is not proper, we cannot construct an invariant connection on the gerbe; therefore to study this algebra, we instead develop simplicial techniques to construct a simplicial curvature 3-form representing the class of the gerbe. Then by using a JLO formula we define a morphism from a simplicial complex twisted by this simplicial curvature 3-form to the mixed bicomplex computing the periodic cyclic cohomology of the twisted convolution algebras. The results in this article were originally published in the author's Ph.D. thesis.Comment: 39 page

Factors influencing quality of life of patients living with mental illness: a case study of Mathari National Teaching and Referral Hospital

Objective: To determine the quality of life and associated factors of people living with mental illness attending the outpatient clinics at Mathari National Teaching and Referral Hospital.Design: A cross-sectional studySetting: The outpatient clinics at Mathari National Teaching and Referral HospitaL.Subject: 384 patients living with mental illness on follow-up were recruited into the study. Those consenting filled in the quality of life instrument (WHOQOL-BREF), as well as a socio-demographic questionnaire.Results: The study found that quality of life was lower than general statistical comparisons, and was found to be related to the marital status of the patient and their income level.Conclusion: Quality of life tends to be somewhat lower than average in people living with mental illness. It may be affected by marital status and income

Random matrix theory within superstatistics

We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted averages of the corresponding quantities in the standard theory assuming that the mean level spacing itself is a stochastic variable. We illustrate the method by calculating the level density, the nearest-neighbor-spacing distributions and the two-level correlation functions for system in transition from order to chaos. The calculated spacing distribution fits the resonance statistics of random binary networks obtained in a recent numerical experiment.Comment: 20 pages, 6 figure

Yang-Mills theory for bundle gerbes

Given a bundle gerbe with connection on an oriented Riemannian manifold of dimension at least equal to 3, we formulate and study the associated Yang-Mills equations. When the Riemannian manifold is compact and oriented, we prove the existence of instanton solutions to the equations and also determine the moduli space of instantons, thus giving a complete analysis in this case. We also discuss duality in this context.Comment: Latex2e, 7 pages, some typos corrected, to appear in J. Phys. A: Math. and Ge

Congenital coronary artery anomalies in adult population detected using dual source ECG-gated CTA in a single institution

Background: Congenital anomalies of the coronary arteries (CAs) are rare and are often diagnosed incidentally during a conventional coronary angiography. Recently, the incidence of these congenital defects is on the rise particularly after the introduction of the electrocardiography (ECG) gated coronary computed tomographic angiography (CCTA). This innovative radiological screening modality has led to the most precise mapping of the course of the CAs on computed tomographic scan. The aim of the study is to determine the prevalence and describe the CAs congenital anomalies and their variations in Kuwaiti population at a single institution experience. Materials and methods: We analysed the CCTA data obtained consecutively from 842 patients (2013–2014), retrospectively. The inclusion criteria for patients’ selection were: atypical chest pain, equivocal ECG, assessment of patency of coronary stents or grafts and pre-operative screening. Information was acquiesced using a dual-source CT scanner with ECG gating. Results: Data analysis revealed that 22 (2.61%) patients were found to have CA anomalies out of the 842 patients who underwent CCTA. Out of these CA anomalies, 13 cases showed more than two ostia, 7 cases showed the ectopic origin of a CA from opposite sinus or non-aortic sinus, 2 cases showed single coronary ostium and 1 case showed coronary artery with pulmonary fistula. Also, myocardial bridging was identified in 78 (9.26%) patients whereas ramus intermedius branch was identified in 160 (19%) patients. Conclusions: The prevalence of CA anomalies in Kuwait was 2.6%, which is relatively higher than previously reported studies from different countries

Statistical properties of Klauder-Perelomov coherent states for the Morse potential

We present in this paper a realistic construction of the coherent states for the Morse potential using the Klauder-Perelomov approach . We discuss the statistical properties of these states, by deducing the Q- and P-distribution functions. The thermal expectations for the quantum canonical ideal gas of the Morse oscillators are also calculated

Gauge-invariant perturbation theory for trans-Planckian inflation

The possibility that the scale-invariant inflationary spectrum may be modified due to the hidden assumptions about the Planck scale physics -- dubbed as trans-Planckian inflation -- has received considerable attention. To mimic the possible trans-Planckian effects, among various models, modified dispersion relations have been popular in the literature. In almost all the earlier analyzes, unlike the canonical scalar field driven inflation, the trans-Planckian effects are introduced to the scalar/tensor perturbation equations in an ad hoc manner -- without calculating the stress-tensor of the cosmological perturbations from the covariant Lagrangian. In this work, we perform the gauge-invariant cosmological perturbations for the single-scalar field inflation with the Jacobson-Corley dispersion relation by computing the fluctuations of all the fields including the unit time-like vector field which defines a preferred rest frame. We show that: (i) The non-linear effects introduce corrections only to the perturbed energy density. The corrections to the energy density vanish in the super-Hubble scales. (ii) The scalar perturbations, in general, are not purely adiabatic. (iii) The equation of motion of the Mukhanov-Sasaki variable corresponding to the inflaton field is different than those presumed in the earlier analyzes. (iv) The tensor perturbation equation remains unchanged. We perform the classical analysis for the resultant system of equations and also compute the power-spectrum of the scalar perturbations in a particular limit. We discuss the implications of our results and compare with the earlier results.Comment: 19 Pages, Revtex4; V2 Final version, To appear in Phys. Rev. D., 1 figure and references adde

A Rigorous Path Integral for Supersymmetric Quantum Mechanics and the Heat Kernel

In a rigorous construction of the path integral for supersymmetric quantum mechanics on a Riemann manifold, based on B\"ar and Pf\"affle's use of piecewise geodesic paths, the kernel of the time evolution operator is the heat kernel for the Laplacian on forms. The path integral is approximated by the integral of a form on the space of piecewise geodesic paths which is the pullback by a natural section of Mathai and Quillen's Thom form of a bundle over this space. In the case of closed paths, the bundle is the tangent space to the space of geodesic paths, and the integral of this form passes in the limit to the supertrace of the heat kernel.Comment: 14 pages, LaTeX, no fig

Asymptotic solutions of decoupled continuous-time random walks with superheavy-tailed waiting time and heavy-tailed jump length distributions

We study the long-time behavior of decoupled continuous-time random walks characterized by superheavy-tailed distributions of waiting times and symmetric heavy-tailed distributions of jump lengths. Our main quantity of interest is the limiting probability density of the position of the walker multiplied by a scaling function of time. We show that the probability density of the scaled walker position converges in the long-time limit to a non-degenerate one only if the scaling function behaves in a certain way. This function as well as the limiting probability density are determined in explicit form. Also, we express the limiting probability density which has heavy tails in terms of the Fox $H$-function and find its behavior for small and large distances.Comment: 16 pages, 1 figur