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

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

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

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

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

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

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

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

Quantized reduction as a tensor product

Symplectic reduction is reinterpreted as the composition of arrows in the category of integrable Poisson manifolds, whose arrows are isomorphism classes of dual pairs, with symplectic groupoids as units. Morita equivalence of Poisson manifolds amounts to isomorphism of objects in this category. This description paves the way for the quantization of the classical reduction procedure, which is based on the formal analogy between dual pairs of Poisson manifolds and Hilbert bimodules over C*-algebras, as well as with correspondences between von Neumann algebras. Further analogies are drawn with categories of groupoids (of algebraic, measured, Lie, and symplectic type). In all cases, the arrows are isomorphism classes of appropriate bimodules, and their composition may be seen as a tensor product. Hence in suitable categories reduction is simply composition of arrows, and Morita equivalence is isomorphism of objects.Comment: 44 pages, categorical interpretation adde

Efficacy of Percutaneous Posterior Tibial Nerve Stimulation for the Management of Fecal Incontinence in Multiple Sclerosis: A Pilot Study

BACKGROUND: Fecal incontinence is a debilitating and highly prevalent problem among multiple sclerosis patients. Conservative therapies often fail to provide benefit. Posterior tibial nerve stimulation is a minimally invasive neuromodulatory therapy with proven efficacy for fecal incontinence in non-neurological settings. OBJECTIVE: To evaluate the efficacy of posterior tibial nerve stimulation in treating multiple sclerosis-related fecal incontinence. METHODS: Consecutive multiple sclerosis patients with fecal incontinence that had failed conservative therapy received posterior tibial nerve stimulation between 2012 and 2015. All patients had previously undergone anorectal physiology tests and endoanal ultrasound. Patients whose Wexner incontinence score reduced below 10 post-therapy or halved from baseline were deemed responders. RESULTS: Thirty-three patients (25 female, median age 43 years) were included. Twenty-three (70%) had urge, 4 (12%) passive, and 9 (27%) mixed fecal incontinence. Twenty-six (79%) were classified as responders. The majority of subjects had relapsing-remitting multiple sclerosis (67%); those had a significantly higher response rate (95% vs. 67% and 50% in primary and secondary progressive respectively, P < 0.05). Responders tended to be more symptomatic at baseline and had greater improvements in bowel symptom scores and quality of life scores with therapy. CONCLUSION: Posterior tibial nerve stimulation demonstrates potential as an effective therapy for fecal incontinence in multiple sclerosis. These findings provide the basis for future more definitive controlled studies