Cornerstones of Sampling of Operator Theory

This paper reviews some results on the identifiability of classes of operators whose Kohn-Nirenberg symbols are band-limited (called band-limited operators), which we refer to as sampling of operators. We trace the motivation and history of the subject back to the original work of the third-named author in the late 1950s and early 1960s, and to the innovations in spread-spectrum communications that preceded that work. We give a brief overview of the NOMAC (Noise Modulation and Correlation) and Rake receivers, which were early implementations of spread-spectrum multi-path wireless communication systems. We examine in detail the original proof of the third-named author characterizing identifiability of channels in terms of the maximum time and Doppler spread of the channel, and do the same for the subsequent generalization of that work by Bello. The mathematical limitations inherent in the proofs of Bello and the third author are removed by using mathematical tools unavailable at the time. We survey more recent advances in sampling of operators and discuss the implications of the use of periodically-weighted delta-trains as identifiers for operator classes that satisfy Bello's criterion for identifiability, leading to new insights into the theory of finite-dimensional Gabor systems. We present novel results on operator sampling in higher dimensions, and review implications and generalizations of the results to stochastic operators, MIMO systems, and operators with unknown spreading domains

Hepatocyte growth factor in human osteoarthritic cartilage

AbstractObjective Hepatocyte growth factor/scatter factor is a potent mitogen, morphogen and motogen for a variety of mainly epithelial cells. Hepatocyte growth factor is synthesized by mesenchymal cells and can be found in various tissues. The objective of this study was to investigate the expression and distribution patterns of this pleiotropic growth factor and its receptor, the product of the proto-oncogene c-met in normal and osteoarthritic human knee cartilage.Methods Five normal and 14 osteoarthritic human cartilage samples graded histomorphologically by Mankin Score, were studied by radioactive in-situ hybridization and immunohistochemistry for the expression of Hepatocyte growth factor and the c-met receptor.Results Hepatocyte growth factor could be found by immunohistochemistry in the territorial matrix surrounding the chondrocytes of calcified cartilage and within the deep zone of normal cartilage. Chondrocytes of these cartilage zones showed also positive c-met receptor-staining. Moreover, a small number of chondrocytes in the superficial and intermediate zone showed c-met staining. In accordance with the increased hepatocyte growth factor staining of osteoarthritic cartilage, an enhanced expression of hepatocyte growth factor-RNA by chondrocytes of the deep zone as well as the deeper mid zone was observed. Contrary to normal cartilage,c-met was identified immunohistochemically in osteoarthritic chondrocytes of all cartilage zones.Conclusion These results indicate that hepatocyte growth factor seems to be acting in an autocrine/paracrine manner in normal and osteoarthritic cartilage. The ubiquitous presence of the HGF/HGF-receptor complex in osteoarthritic chondrocytes suggests that hepatocyte growth factor may contribute to the altered metabolism in osteoarthritic cartilage.{copy

Restricted Isometries for Partial Random Circulant Matrices

In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and compressible signals. Many recovery algorithms are known to succeed when the restricted isometry constants of the sampling matrix are small. Many potential applications of compressed sensing involve a data-acquisition process that proceeds by convolution with a random pulse followed by (nonrandom) subsampling. At present, the theoretical analysis of this measurement technique is lacking. This paper demonstrates that the $s$th order restricted isometry constant is small when the number $m$ of samples satisfies $m \gtrsim (s \log n)^{3/2}$, where $n$ is the length of the pulse. This bound improves on previous estimates, which exhibit quadratic scaling

Alkanes-assisted low temperature formation of highly ordered SBA-15 with large cylindrical mesopores

Highly ordered SBA-15 silicas with large cylindrical mesopores (similar to 15 nm) are successfully obtained with the help of NH4F by controlling the initial reaction temperatures in the presence of excess amounts of alkanes

Slx8 removes Pli1-dependent protein-SUMO conjugates including SUMOylated Topoisomerase I to promote genome stability

Peer reviewedPublisher PD

Genome-Wide Gene Expression Analysis Suggests an Important Role of Hypoxia in the Pathogenesis of Endemic Osteochondropathy Kashin-Beck Disease

Kashin-Beck Disease (KBD) is an endemic osteochondropathy, the pathogenesis of which remains unclear now. In this study, we compared gene expression profiles of articular cartilage derived respectively from KBD patients and normal controls. Total RNA were isolated, amplified, labeled and hybridized to Agilent human 1A 22 k whole genome microarray chip. qRT-PCR was conducted to validate our microarray data. We detected 57 up-regulated genes (ratios ≥2.0) and 24 down-regulated genes (ratios ≤0.5) in KBD cartilage. To further identify the key genes involved in the pathogenesis of KBD, Bayesian analysis of variance for microarrays(BAM) software was applied and identified 12 potential key genes with an average ratio 6.64, involved in apoptosis, metabolism, cytokine & growth factor and cytoskeleton & cell movement. Gene Set Enrichment Analysis (GSEA) software was used to identify differently expressed gene ontology categories and pathways. GSEA found that a set of apoptosis, hypoxia and mitochondrial function related gene ontology categories and pathways were significantly up-regulated in KBD compared to normal controls. Based on the results of this study, we suggest that chronic hypoxia-induced mitochondrial damage and apoptosis might play an important role in the pathogenesis of KBD. Our efforts may help to understand the pathogenesis of KBD as well as other osteoarthrosis with similar articular cartilage lesions

HIF-1α determines the metastatic potential of gastric cancer cells

Gastric adenocarcinoma is characterised by rapid emergence of systemic metastases, resulting in poor prognosis due to vanished curative treatment options. Better understanding of the molecular basis of gastric cancer spread is needed to design innovative treatments. The transcription factor HIF-1α (hypoxia-inducible factor 1α) is frequently overexpressed in human gastric cancer, and inhibition of HIF-1α has proven antitumour efficacy in rodent models, whereas the relevance of HIF-1α for the metastatic phenotype of gastric adenocarcinoma remains elusive. Therefore, we have conducted a comprehensive analysis of the role of HIF-1α for pivotal metastasis-associated processes of human gastric cancer. Immunhistochemistry for HIF-1α showed specific staining at the invading tumour edge in 90% of human gastric cancer samples, whereas normal gastric tissue was negative and only a minority of early gastric cancers (T1 tumours) showed specific staining. Hypoxia-inducible factor 1α-deficient cells showed a significant reduction of migratory, invasive and adhesive properties in vitro. Furthermore, the HIF-1α-inhibitor 2-methoxy-estradiol significantly reduced metastatic properties of gastric cancer cells. The accentuated expression at the invading edge together with the in vitro requirement of HIF-1α for migration, invasion and adherence argues for a pivotal role of HIF-1α in local invasion and, ultimately, systemic tumour spread. These results warrant the exploration of HIF-1α-inhibiting substances in clinical treatment studies of advanced gastric cancer