Homology and K--Theory Methods for Classes of Branes Wrapping Nontrivial Cycles

We apply some methods of homology and K-theory to special classes of branes wrapping homologically nontrivial cycles. We treat the classification of four-geometries in terms of compact stabilizers (by analogy with Thurston's classification of three-geometries) and derive the K-amenability of Lie groups associated with locally symmetric spaces listed in this case. More complicated examples of T-duality and topology change from fluxes are also considered. We analyse D-branes and fluxes in type II string theory on ${\mathbb C}P^3\times \Sigma_g \times {\mathbb T}^2$ with torsion $H-$flux and demonstrate in details the conjectured T-duality to ${\mathbb R}P^7\times X^3$ with no flux. In the simple case of $X^3 = {\mathbb T}^3$, T-dualizing the circles reduces to duality between ${\mathbb C}P^3\times {\mathbb T}^2 \times {\mathbb T}^2$ with $H-$flux and ${\mathbb R}P^7\times {\mathbb T}^3$ with no flux.Comment: 27 pages, tex file, no 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

Reverse Foam Sclerotherapy of the Great Saphenous Vein with Sapheno-Femoral Ligation Compared to Standard and Invagination Stripping: a Prospective Clinical Series

AbstractObjectivesComparison of Reverse Foam Sclerotherapy of the great saphenous vein (GSV) combed with sapheno-femoral junction (SFJ) ligation to standard (Babcock) stripping and invagination (Pin) stripping in a prospective clinical series.DesignProspective clinical series.Materials and methods90 consecutive limbs of 82 patients with incompetence of the GSV resulting in varicose veins were prospectively randomised into 3 groups of 30, treated by SFJ ligation and either reverse foam sclerotherapy, standard stripping or invagination stripping of the GSV. Outcomes were assessed post-operatively and at 2-weeks follow-up. Peri-operative blood loss (24 hrs), analgesic requirement, bruising and residual varicosities were assessed. Bruising was assessed by both patients and independent assessors using questionnaires.ResultsSFJ ligation plus reverse foam sclerotherapy of the GSV was associated with significantly less blood loss, bruising and post-op discomfort than either of the stripping techniques. (p<0.001, Mann-Whitney)ConclusionStandard stripping of the GSV and invagination stripping are not associated with major discomfort and problems in the early post-operative period. SFJ ligation and GSV reverse foam sclerotherapy yielded greater patient satisfaction with less post-op bruising and discomfort and reduced analgesic requirements

Ground state properties and dynamics of the bilayer t-J model

We present an exact diagonalization study of bilayer clusters of t-J model. Our results indicate a crossover between two markedly different regimes which occurs when the ratio J_perp/J between inter-layer and intra-layer exchange constants increases: for small J_perp/J the data suggest the development of 3D antiferromagnetic correlations without appreciable degradation of the intra-layer spin order and the d_(x2-y2) hole pairs within the planes persist. For larger values of J_perp/J local singlets along the inter-layer bonds dominate, leading to an almost complete suppression of the intra-layer spin correlation and the breaking of the intra-layer pairs. The ground state with two holes in this regime has s-like symmetry. The data suggest that the crossover may occur for values of J_perp/J as small as 0.2. We present data for static spin correlations, spin gap, and electron momentum distribution and spectral function of the `inter-layer RVB state' realized for large J_perp/J. The latter deviates from the single layer ground state, making it an implausible candidate for modelling high-temperature superconductors.Comment: Revtex-file, 6 PRB pages, figures appended as uu-encoded postscript. Hardcopies of figures (or the entire manuscript) can be obtained by e-mailing to: [email protected]

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

The weakly coupled fractional one-dimensional Schr\"{o}dinger operator with index 1<α≤2\bf 1<\alpha \leq 2

We study fundamental properties of the fractional, one-dimensional Weyl operator $\hat{\mathcal{P}}^{\alpha}$ densely defined on the Hilbert space $\mathcal{H}=L^2({\mathbb R},dx)$ and determine the asymptotic behaviour of both the free Green's function and its variation with respect to energy for bound states. In the sequel we specify the Birman-Schwinger representation for the Schr\"{o}dinger operator $K_{\alpha}\hat{\mathcal{P}}^{\alpha}-g|\hat{V}|$ and extract the finite-rank portion which is essential for the asymptotic expansion of the ground state. Finally, we determine necessary and sufficient conditions for there to be a bound state for small coupling constant $g$.Comment: 16 pages, 1 figur

KO-Homology and Type I String Theory

We study the classification of D-branes and Ramond-Ramond fields in Type I string theory by developing a geometric description of KO-homology. We define an analytic version of KO-homology using KK-theory of real C*-algebras, and construct explicitly the isomorphism between geometric and analytic KO-homology. The construction involves recasting the Cl(n)-index theorem and a certain geometric invariant into a homological framework which is used, along with a definition of the real Chern character in KO-homology, to derive cohomological index formulas. We show that this invariant also naturally assigns torsion charges to non-BPS states in Type I string theory, in the construction of classes of D-branes in terms of topological KO-cycles. The formalism naturally captures the coupling of Ramond-Ramond fields to background D-branes which cancel global anomalies in the string theory path integral. We show that this is related to a physical interpretation of bivariant KK-theory in terms of decay processes on spacetime-filling branes. We also provide a construction of the holonomies of Ramond-Ramond fields in Type II string theory in terms of topological K-chains.Comment: 40 pages; v4: Clarifying comments added, more detailed proof of main isomorphism theorem given; Final version to be published in Reviews in Mathematical Physic

Subdiffusion-limited reactions

We consider the coagulation dynamics A+A -> A and A+A A and the annihilation dynamics A+A -> 0 for particles moving subdiffusively in one dimension. This scenario combines the "anomalous kinetics" and "anomalous diffusion" problems, each of which leads to interesting dynamics separately and to even more interesting dynamics in combination. Our analysis is based on the fractional diffusion equation