Complex symmetric partial isometries

An operator T \in B(\h) is complex symmetric if there exists a conjugate-linear, isometric involution C:\h\to\h so that $T = CT^*C$. We provide a concrete description of all complex symmetric partial isometries. In particular, we prove that any partial isometry on a Hilbert space of dimension $\leq 4$ is complex symmetric.Comment: 9 page

C∗C^*-algebras generated by truncated Toeplitz operators

We obtain an analogue of Coburn's description of the Toeplitz algebra in the setting of truncated Toeplitz operators. As a byproduct, we provide several examples of complex symmetric operators which are not unitarily equivalent to truncated Toeplitz operators having continuous symbols.Comment: 12 page

Spatial isomorphisms of algebras of truncated Toeplitz operators

We examine when two maximal abelian algebras in the truncated Toeplitz operators are spatially isomorphic. This builds upon recent work of N. Sedlock, who obtained a complete description of the maximal algebras of truncated Toeplitz operators.Comment: 24 page

Norm estimates of complex symmetric operators applied to quantum systems

This paper communicates recent results in theory of complex symmetric operators and shows, through two non-trivial examples, their potential usefulness in the study of Schr\"odinger operators. In particular, we propose a formula for computing the norm of a compact complex symmetric operator. This observation is applied to two concrete problems related to quantum mechanical systems. First, we give sharp estimates on the exponential decay of the resolvent and the single-particle density matrix for Schr\"odinger operators with spectral gaps. Second, we provide new ways of evaluating the resolvent norm for Schr\"odinger operators appearing in the complex scaling theory of resonances

Have mysterious topological valley currents been observed in graphene superlattices?

Altres ajuts: ICN2 is funded by the CERCA Programme/Generalitat de CatalunyaWe provide a critical discussion concerning the claim of topological valley currents, driven by a global Berry curvature and valley Hall effect proposed in recent literature. After pointing out a major inconsistency of the theoretical scenario proposed to interpret giant nonlocal resistance, we discuss various possible alternative explanations and open directions of research to solve the mystery of nonlocal transport in graphene superlattices

Charge and Spin Transport Anisotropy in Nanopatterned Graphene

Anisotropic electronic transport is a possible route towards nanoscale circuitry design, particularly in two-dimensional materials. Proposals to introduce such a feature in patterned graphene have to date relied on large-scale structural inhomogeneities. Here we theoretically explore how a random, yet homogeneous, distribution of zigzag-edged triangular perforations can generate spatial anisotropies in both charge and spin transport. Anisotropic electronic transport is found to persist under considerable disordering of the perforation edges, suggesting its viability under realistic experimental conditions. Furthermore, controlling the relative orientation of perforations enables spin filtering of the transmitted electrons, resulting in a half-metallic anisotropic transport regime. Our findings point towards a co-integration of charge and spin control in a two-dimensional platform of relevance for nanocircuit design. We further highlight how geometrical effects allow finite samples to display finite transverse resistances, reminiscent of Spin Hall effects, in the absence of any bulk fingerprints of such mechanisms, and explore the underlying symmetries behind this behaviour.Comment: 11 pages, 6 figure

Added Value of Tomoelastography for Characterization of Pancreatic Neuroendocrine Tumor Aggressiveness Based on Stiffness

Simple Summary: The prediction of pancreatic neuroendocrine tumor (PNET) aggressiveness is important for treatment planning. The aim of this study was to evaluate the diagnostic performance of magnetic resonance elastography (MRE) with tomoelastography postprocessing (tomoelastography) in differentiating PNET from healthy pancreatic tissue and to correlate PNET stiffness with aggressiveness using asphericity derived from positron emission tomography (PET) as reference. In this prospective study we showed in a group of 13 patients with PNET that tomoelastography detected PNET by increased stiffness (p < 0.01) with a high diagnostic performance (AUC = 0.96). PNET was positively correlated with PET derived asphericity (r = 0.81). Tomoelastography provides quantitative imaging markers for the detection of PNET and the prediction of greater tumor aggressiveness by increased stiffness. Abstract: Purpose: To evaluate the diagnostic performance of tomoelastography in differentiating pancreatic neuroendocrine tumors (PNETs) from healthy pancreatic tissue and to assess the prediction of tumor aggressiveness by correlating PNET stiffness with PET derived asphericity. Methods: 13 patients with PNET were prospectively compared to 13 age-/sex-matched heathy volunteers (CTR). Multifrequency MR elastography was combined with tomoelastography-postprocessing to provide high-resolution maps of shear wave speed (SWS in m/s). SWS of pancreatic neuroendocrine tumor (PNET-T) were compared with nontumorous pancreatic tissue in patients with PNET (PNET-NT) and heathy pancreatic tissue (CTR). The diagnostic performance of tomoelastography was evaluated by ROC-AUC analysis. PNET-SWS correlations were calculated with Pearson’s r. Results: SWS was higher in PNET-T (2.02 ± 0.61 m/s) compared to PNET-NT (1.31 ± 0.18 m/s, p < 0.01) and CTR (1.26 ± 0.09 m/s, p < 0.01). An SWS-cutoff of 1.46 m/s distinguished PNET-T from PNET-NT (AUC = 0.89; sensitivity = 0.85; specificity = 0.92) and a cutoff of 1.49 m/s differentiated pancreatic tissue of CTR from PNET-T (AUC = 0.96; sensitivity = 0.92; specificity = 1.00). The SWS of PNET-T was positively correlated with PET derived asphericity (r = 0.81; p = 0.01). Conclusions: Tomoelastography provides quantitative imaging markers for the detection of PNET and the prediction of greater tumor aggressiveness by increased stiffness

On the relationship between metabolic capacities and in vivo viscoelastic properties of the liver

The liver is the central metabolic organ. It constantly adapts its metabolic capacity to current physiological requirements. However, the relationship between tissue structure and hepatic function is incompletely understood; this results in a lack of diagnostic markers in medical imaging that can provide information about the liver's metabolic capacity. Therefore, using normal rabbit livers, we combined magnetic resonance elastography (MRE) with proteomics-based kinetic modeling of central liver metabolism to investigate the potential role of MRE for predicting the liver's metabolic function in vivo. Nineteen New Zealand white rabbits were investigated by multifrequency MRE and positron emission tomography (PET). This yielded maps of shear wave speed (SWS), penetration rate (PR) and standardized uptake value (SUV). Proteomic analysis was performed after the scans. Hepatic metabolic functions were assessed on the basis of the HEPATOKIN1 model in combination with a model of hepatic lipid-droplet metabolism using liquid chromatography-mass spectrometry. Our results showed marked differences between individual livers in both metabolic functions and stiffness properties, though not in SUV. When livers were divided into 'stiff' and 'soft' subgroups (cutoff SWS = 1.6 m/s), stiff livers showed a lower capacity for triacylglycerol storage, while at the same time showing an increased capacity for gluconeogenesis and cholesterol synthesis. Furthermore, SWS was correlated with gluconeogenesis and PR with urea production and glutamine exchange. In conclusion, our study indicates a close relationship between the viscoelastic properties of the liver and metabolic function. This could be used in future studies to predict non-invasively the functional reserve capacity of the liver in patients

Neuregulins mediate calcium-induced glucose transport during muscle contraction

Neuregulin, a growth factor involved in myogenesis, has rapid effects on muscle metabolism. In a manner analogous to insulin and exercise, neuregulins stimulate glucose transport through recruitment of glucose transporters to surface membranes in skeletal muscle. Like muscle contraction, neuregulins have additive effects with insulin on glucose uptake. Therefore, we examined whether neuregulins are involved in the mechanism by which muscle contraction regulates glucose transport. We show that caffeine-induced increases in cytosolic Ca2+ mediate a metalloproteinase-dependent release of neuregulins, which stimulates tyrosine phosphorylation of ErbB4 receptors. Activation of ErbB4 is necessary for Ca2+-derived effects on glucose transport. Furthermore, blockage of ErbB4 abruptly impairs contraction-induced glucose uptake in slow twitch muscle fibers, and to a lesser extent, in fast twitch muscle fibers. In conclusion, we provide evidence that contraction-induced activation of neuregulin receptors is necessary for the stimulation of glucose transport and a key element of energetic metabolism during muscle contraction

Shear Wave Elastography for Assessing Liver Stiffness in HCV-Infected Kidney Transplant Recipients after Direct-Acting Antiviral Treatment: A Comparative Study with Magnetic Resonance Elastography

Hepatitis C virus (HCV) infection can lead to hepatic fibrosis. The advent of direct-acting antivirals (DAAs) has substantially improved sustained virological response (SVR) rates. In this context, kidney transplant recipients (KTRs) are of particular interest due to their higher HCV infection rates and uncertain renal excretion and bioavailability of DAAs. We investigated liver stiffness after DAA treatment in 15 HCV-infected KTRs using ultrasound shear wave elastography (SWE) in comparison with magnetic resonance elastography (MRE). KTRs were treated with DAAs (daclatasvir and sofosbuvir) for three months and underwent SWE at baseline, end of therapy (EOT), and 3 (EOT+3) and 12 months (EOT+12) after EOT. Fourteen patients achieved SVR12. Shear wave speed (SWS)-as a surrogate parameter for tissue stiffness-was substantially lower at all three post-therapeutic timepoints compared with baseline (EOT: -0.42 m/s, p < 0.01; CI = -0.75--0.09, EOT+3: -0.43 m/s, p < 0.01; CI = -0.75--0.11, and EOT+12: -0.52 m/s, p < 0.001; CI = -0.84--0.19), suggesting liver regeneration after viral eradication and end of inflammation. Baseline SWS correlated positively with histopathological fibrosis scores (r = 0.48; CI = -0.11-0.85). Longitudinal results correlated moderately with APRI (r = 0.41; CI = 0.12-0.64) but not with FIB-4 scores (r = 0.12; CI = -0.19-0.41). Although higher on average, SWE-derived measurements correlated strongly with MRE (r = 0.64). In conclusion, SWE is suitable for non-invasive therapy monitoring in KTRs with HCV infection