Generalized multiresolution analyses with given multiplicity functions

Generalized multiresolution analyses are increasing sequences of subspaces of a Hilbert space \H that fail to be multiresolution analyses in the sense of wavelet theory because the core subspace does not have an orthonormal basis generated by a fixed scaling function. Previous authors have studied a multiplicity function $m$ which, loosely speaking, measures the failure of the GMRA to be an MRA. When the Hilbert space \H is $L^2(\mathbb R^n)$, the possible multiplicity functions have been characterized by Baggett and Merrill. Here we start with a function $m$ satisfying a consistency condition which is known to be necessary, and build a GMRA in an abstract Hilbert space with multiplicity function $m$.Comment: 16 pages including bibliograph

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

Generalized multiresolution analyses with given multiplicity functions

Generalized multiresolution analyses are increasing sequences of subspaces of a Hilbert space H that fail to be multiresolution analyses in the sense of wavelet theory because the core subspace does not have an orthonormal basis generated by a fixed scaling function. Previous authors have studied a multiplicity function m which, loosely speaking, measures the failure of the GMRA to be an MRA. When the Hilbert space H is L2(Rn), the possible multiplicity functions have been characterized by Baggett and Merrill. Here we start with a function m satisfying a consistency condition which is known to be necessary, and build a GMRA in an abstract Hilbert space with multiplicity function m

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

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

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

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

Disordered protein-graphene oxide co-assembly and supramolecular biofabrication of functional fluidic devices

Supramolecular chemistry offers an exciting opportunity to assemble materials with molecular precision. However, there remains an unmet need to turn molecular self-assembly into functional materials and devices. Harnessing the inherent properties of both disordered proteins and graphene oxide (GO), we report a disordered protein-GO co-assembling system that through a diffusion-reaction process and disorder-to-order transitions generates hierarchically organized materials that exhibit high stability and access to non-equilibrium on demand. We use experimental approaches and molecular dynamics simulations to describe the underlying molecular mechanism of formation and establish key rules for its design and regulation. Through rapid prototyping techniques, we demonstrate the system's capacity to be controlled with spatio-temporal precision into well-defined capillary-like fluidic microstructures with a high level of biocompatibility and, importantly, the capacity to withstand flow. Our study presents an innovative approach to transform rational supramolecular design into functional engineering with potential widespread use in microfluidic systems and organ-on-a-chip platforms

‘Being Yourself’ in the Electronic Sweatshop: New Forms of Normative Control

This article extends research about high-commitment management practices in tightly controlled work environments typified by the call centre. One promising research avenue suggests that normative management systems in such contexts, involving ‘fun’ exercises and culture programmes, etc., are more about distracting employee attention away from other, more taxing controls. This article develops such an approach by exploring the specific nature and conditions of such distraction. An empirical study of a call centre in which employees were encouraged to ‘just be themselves’ (in relation to lifestyle differences, sexuality, diverse identities, etc.) reveals how the distractions are partly informed by the dysfunctions of existing technical, bureaucratic and conventional cultural controls, all of which homogenize workers. Furthermore, the new regime not only serves to distract employees, but proves instrumental in capturing their sociality, energy and ‘authentic’ or ‘non-work’ personalities as emotional labour. At the same time, it gives rise to some contestation and less individualistic forms of authenticity. These outcomes have wider implications for our understanding of worker autonomy in and around hybrid control systems