And\^o dilations for a pair of commuting contractions: two explicit constructions and functional models

One of the most important results in operator theory is And\^o's \cite{ando} generalization of dilation theory for a single contraction to a pair of commuting contractions acting on a Hilbert space. While there are two explicit constructions (Sch\"affer \cite{sfr} and Douglas \cite{Doug-Dilation}) of the minimal isometric dilation of a single contraction, there was no such explicit construction of an And\^o dilation for a commuting pair $(T_1,T_2)$ of contractions, except in some special cases \cite{A-M-Dist-Var, D-S, D-S-S}. In this paper, we give two new proofs of And\^o's dilation theorem by giving both Sch\"affer-type and Douglas-type explicit constructions of an And\^o dilation with function-theoretic interpretation, for the general case. The results, in particular, give a complete description of all possible factorizations of a given contraction $T$ into the product of two commuting contractions. Unlike the one-variable case, two minimal And\^o dilations need not be unitarily equivalent. However, we show that the compressions of the two And\^o dilations constructed in this paper to the minimal dilation spaces of the contraction $T_1T_2$, are unitarily equivalent. In the special case when the product $T=T_1T_2$ is pure, i.e., if $T^{* n}\to 0$ strongly, an And\^o dilation was constructed recently in \cite{D-S-S}, which, as this paper will show, is a corollary to the Douglas-type construction. We define a notion of characteristic triple for a pair of commuting contractions and a notion of coincidence for such triples. We prove that two pairs of commuting contractions with their products being pure contractions are unitarily equivalent if and only if their characteristic triples coincide. We also characterize triples which qualify as the characteristic triple for some pair $(T_1,T_2)$ of commuting contractions such that $T_1T_2$ is a pure contraction.Comment: 24 page

Proteomic analysis of differentially expressed proteins in hepatitis B virus-related hepatocellular carcinoma tissues

<p>Abstract</p> <p>Background</p> <p>Hepatocellular carcinoma (HCC), a major cause of cancer death in China, is preceded by chronic hepatitis and liver cirrhosis (LC). Although hepatitis B virus (HBV) has been regarded as a clear etiology of human hepatocarcinogenesis, the mechanism is still needs to be further clarified. In this study, we used a proteomic approach to identify the differential expression protein profiles between HCC and the adjacent non-tumorous liver tissues.</p> <p>Methods</p> <p>Eighteen cases of HBV-related HCC including 12 cases of LC-developed HCC and 6 cases of chronic hepatitis B (CHB)-developed HCC were analyzed by two-dimensional electrophoresis (2-DE) combined with matrix-assisted laser desorption/ionization time of flight mass spectrometry (MALDI-TOF-MS), and the results were compared to those of paired adjacent non-tumorous liver tissues.</p> <p>Results</p> <p>A total of 17 differentially expressed proteins with diverse biological functions were identified. Among these, 10 proteins were up-regulated, whereas the other 7 proteins were down-regulated in cancerous tissues. Two proteins, c-Jun N-terminal kinase 2 and ADP/ATP carrier protein were found to be up-regulated only in CHB-developed HCC tissues. Insulin-like growth factor binding protein 2 and Rho-GTPase-activating protein 4 were down-regulated in LC-developed and CHB-developed HCC tissues, respectively. Although 11 out of these 17 proteins have been already described by previous studies, or are already known to be involved in hepatocarcinogenesis, this study revealed 6 new proteins differentially expressed in HBV-related HCC.</p> <p>Conclusion</p> <p>These findings elucidate that there are common features between CHB-developed HCC and LC-developed HCC. The identified proteins are valuable for studying the hepatocarcinogenesis, and may be potential diagnostic markers or therapeutic targets for HBV-related HCC.</p

Multi-Dimensional Refinement Graph Convolutional Network with Robust Decouple Loss for Fine-Grained Skeleton-Based Action Recognition

Graph convolutional networks have been widely used in skeleton-based action recognition. However, existing approaches are limited in fine-grained action recognition due to the similarity of inter-class data. Moreover, the noisy data from pose extraction increases the challenge of fine-grained recognition. In this work, we propose a flexible attention block called Channel-Variable Spatial-Temporal Attention (CVSTA) to enhance the discriminative power of spatial-temporal joints and obtain a more compact intra-class feature distribution. Based on CVSTA, we construct a Multi-Dimensional Refinement Graph Convolutional Network (MDR-GCN), which can improve the discrimination among channel-, joint- and frame-level features for fine-grained actions. Furthermore, we propose a Robust Decouple Loss (RDL), which significantly boosts the effect of the CVSTA and reduces the impact of noise. The proposed method combining MDR-GCN with RDL outperforms the known state-of-the-art skeleton-based approaches on fine-grained datasets, FineGym99 and FSD-10, and also on the coarse dataset NTU-RGB+D X-view version

Lighting-Up Tumor for Assisting Resection via Spraying NIR Fluorescent Probe of γ-Glutamyltranspeptidas

For the precision resection, development of near-infrared (NIR) fluorescent probe based on specificity identification tumor-associated enzyme for lighting-up the tumor area, is urgent in the field of diagnosis and treatment. Overexpression of γ-glutamyltranspeptidase, one of the cell-membrane enzymes, known as a biomarker is concerned with the growth and progression of ovarian, liver, colon and breast cancer compared to normal tissue. In this work, a remarkable enzyme-activated NIR fluorescent probe NIR-SN-GGT was proposed and synthesized including two moieties: a NIR dicyanoisophorone core as signal reporter unit; γ-glutamyl group as the specificity identification site. In the presence of γ-GGT, probe NIR-SN-GGT was transformed into NIR-SN-NH2, the recovery of Intramolecular Charge Transfer (ICT), liberating the NIR fluorescence signal, which was firstly employed to distinguish tumor tissue and normal tissues via simple “spraying” manner, greatly promoting the possibility of precise excision. Furthermore, combined with magnetic resonance imaging by T2 weight mode, tumor transplanted BABL/c mice could be also lit up for first time by NIR fluorescence probe having a large stokes, which demonstrated that probe NIR-SN-GGT would be a useful tool for assisting surgeon to diagnose and remove tumor in clinical practice

Structure characteristics and valence state study for La 1−x K x TiO 3 synthesized under high-pressure and high-temperature

Abstract By using a high-pressure and high-temperature method, perovskite oxides of the type La 1−x K x TiO 3 (x = 0.30, 0.35, 0.40, 0.45, 0.50) with mixed valence state were synthesized. This new synthesis route has several advantages. XRD analysis shows a cubic cell for the samples. XPS of the surface and EPR measurements indicate that the Ti ions have a mixed valence of 3+ and 4+ and that A-cation vacancies exist in the samples. As x increases, the amount of Ti 3+ ions and A-cation vacancies decreases. The valence state of the Ti ions can be altered by changing both pressure and temperature