Strong Shift Equivalence of C∗C^*-correspondences

We define a notion of strong shift equivalence for $C^*$-correspondences and show that strong shift equivalent $C^*$-correspondences have strongly Morita equivalent Cuntz-Pimsner algebras. Our analysis extends the fact that strong shift equivalent square matrices with non-negative integer entries give stably isomorphic Cuntz-Krieger algebras.Comment: 26 pages. Final version to appear in Israel Journal of Mathematic

Isometric Representations of Totally Ordered Semigroups

Let S be a subsemigroup of an abelian torsion-free group G. If S is a positive cone of G, then all C*-algebras generated by faithful isometrical non-unitary representations of S are canonically isomorphic. Proved by Murphy, this statement generalized the well-known theorems of Coburn and Douglas. In this note we prove the reverse. If all C*-algebras generated by faithful isometrical non-unitary representations of S are canonically isomorphic, then S is a positive cone of G. Also we consider G = Z\times Z and prove that if S induces total order on G, then there exist at least two unitarily not equivalent irreducible isometrical representation of S. And if the order is lexicographical-product order, then all such representations are unitarily equivalent.Comment: February 21, 2012. Kazan, Russi

T-duality for principal torus bundles

In this paper we study T-duality for principal torus bundles with H-flux. We identify a subset of fluxes which are T-dualizable, and compute both the dual torus bundle as well as the dual H-flux. We briefly discuss the generalized Gysin sequence behind this construction and provide examples both of non T-dualizable and of T-dualizable H-fluxes.Comment: 9 pages, typos removed and minor corrections mad

Classification of graph C*-algebras with no more than four primitive ideals

We describe the status quo of the classification problem of graph C*-algebras with four primitive ideals or less

Magnetotransport properties of iron microwires fabricated by focused electron beam induced autocatalytic growth

We have prepared iron microwires in a combination of focused electron beam induced deposition (FEBID) and autocatalytic growth from the iron pentacarbonyl, Fe(CO)5, precursor gas under UHV conditions. The electrical transport properties of the microwires were investigated and it was found that the temperature dependence of the longitudinal resistivity (rhoxx) shows a typical metallic behaviour with a room temperature value of about 88 micro{\Omega} cm. In order to investigate the magnetotransport properties we have measured the isothermal Hall-resistivities in the range between 4.2 K and 260 K. From these measurements positive values for the ordinary and the anomalous Hall coefficients were derived. The relation between anomalous Hall resistivity (rhoAN) and longitudinal resistivity is quadratic, rhoAN rho^2 xx, revealing an intrinsic origin of the anomalous Hall effect. Finally, at low temperature in the transversal geometry a negative magnetoresistance of about 0.2 % was measured

The Clinical Relevance of Manometric Esophagogastric Junction Outflow Obstruction Can Be Determined Using Rapid Drink Challenge and Solid Swallows

INTRODUCTION: Esophagogastric junction outflow obstruction (EGJOO) defined on high-resolution esophageal manometry (HRM) poses a management dilemma given marked variability in clinical manifestations. We hypothesized that findings from provocative testing (rapid drink challenge and solid swallows) could determine the clinical relevance of EGJOO. METHODS: In a retrospective cohort study, we included consecutive subjects between May 2016 and January 2020 with EGJOO. Standard HRM with 5-mL water swallows was followed by provocative testing. Barium esophagography findings were obtained. Cases with structural obstruction were separated from functional EGJOO, with the latter categorized as symptom-positive or symptom-negative. Only symptom-positive subjects were considered for achalasia-type therapies. Sensitivity and specificity for clinically relevant EGJOO during 5-mL water swallows, provocative testing, and barium were calculated. RESULTS: Of the 121 EGJOO cases, 76% had dysphagia and 25% had holdup on barium. Ninety-seven cases (84%) were defined as functional EGJOO. Symptom-positive EGJOO subjects were more likely to demonstrate abnormal motility and pressurization patterns and to reproduce symptoms during provocative testing, but not with 5-mL water swallows. Twenty-nine (30%) functional EGJOO subjects underwent achalasia-type therapy, with symptomatic response in 26 (90%). Forty-eight (49%) functional EGJOO cases were managed conservatively, with symptom remission in 78%. Although specificity was similar, provocative testing demonstrated superior sensitivity in identifying treatment responders from spontaneously remitting EGJOO (85%) compared with both 5-mL water swallows (54%; P < 0.01) and barium esophagography (54%; P = 0.02). DISCUSSION: Provocative testing during HRM is highly accurate in identifying clinically relevant EGJOO that benefits from therapy and should be routinely performed as part of the manometric protocol

Impaired motility in Barrett's esophagus: A study using high-resolution manometry with physiologic challenge

BACKGROUND: Esophageal dysmotility may predispose to Barrett's esophagus (BE). We hypothesized that high-resolution manometry (HRM) performed with additional physiologic challenge would better delineate dysmotility in BE. METHODS: Included patients had typical reflux symptoms and underwent endoscopy, HRM with single water swallows and adjunctive testing with solids and rapid drink challenge (RDC) before ambulatory pH-impedance monitoring. BE and endoscopy-negative reflux disease (ENRD) subjects were compared against functional heartburn patient-controls (FHC). Primary outcome was incidence of HRM contractile abnormalities with standard and adjunctive swallows. Secondary outcomes included clearance measures and symptom association on pH-impedance. KEY RESULTS: Seventy-eight patients (BE 25, ENRD 27, FHC 26) were included. Water swallow contractility was reduced in both BE (median DCI 87 mm Hg/cm/s) and ENRD (442 mm Hg/cm/s) compared to FHC (602 mm Hg/cm/s; P < .001 and .04, respectively). With the challenge of solid swallows and RDC, these parameters improved in ENRD (solids = 1732 mm Hg/cm/s), becoming similar to FHC (1242 mm Hg/cm/s; P = .93), whereas abnormalities persisted in BE (818 mm Hg/cm/s; P < .01 c.f. FHC). In BE and ENRD, reflux events (67 vs 57 events/24 hour) and symptom frequency were similar; yet symptom correlation was significantly better in ENRD compared to BE, which was comparable to FHC (symptom index 30% vs 4% vs 0%, respectively). Furthermore, bolus clearance and exposure times were more pronounced in BE (P < .01). CONCLUSIONS & INFERENCES: Reduced contractile effectiveness persisted in BE with the more representative esophageal challenge of swallowing solids and free drinking; while in ENRD and FHC peristalsis usually improved, demonstrating peristaltic reserve. Furthermore, symptom association and refluxate clearance were reduced in BE. These factors may underlie BE pathogenesis

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

Wavelets and graph C∗C^*-algebras

Here we give an overview on the connection between wavelet theory and representation theory for graph $C^{\ast}$-algebras, including the higher-rank graph $C^*$-algebras of A. Kumjian and D. Pask. Many authors have studied different aspects of this connection over the last 20 years, and we begin this paper with a survey of the known results. We then discuss several new ways to generalize these results and obtain wavelets associated to representations of higher-rank graphs. In \cite{FGKP}, we introduced the "cubical wavelets" associated to a higher-rank graph. Here, we generalize this construction to build wavelets of arbitrary shapes. We also present a different but related construction of wavelets associated to a higher-rank graph, which we anticipate will have applications to traffic analysis on networks. Finally, we generalize the spectral graph wavelets of \cite{hammond} to higher-rank graphs, giving a third family of wavelets associated to higher-rank graphs

Perturbations of nuclear C*-algebras

Kadison and Kastler introduced a natural metric on the collection of all C*-subalgebras of the bounded operators on a separable Hilbert space. They conjectured that sufficiently close algebras are unitarily conjugate. We establish this conjecture when one algebra is separable and nuclear. We also consider one-sided versions of these notions, and we obtain embeddings from certain near inclusions involving separable nuclear C*-algebras. At the end of the paper we demonstrate how our methods lead to improved characterisations of some of the types of algebras that are of current interest in the classification programme.Comment: 45 page