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

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

Generation of transgenic rodent malaria parasites by transfection of cell culture-derived merozoites

Malaria research is greatly dependent on and has drastically advanced with the possibility of genetically modifying Plasmodium parasites. The commonly used transfection protocol by Janse and colleagues utilizes blood stage-derived Plasmodium berghei schizonts that have been purified from a blood culture by density gradient centrifugation. Naturally, this transfection protocol depends on the availability of suitably infected mice, constituting a time-based variable. In this study, the potential of transfecting liver stage-derived merozoites was explored. In cell culture, upon merozoite development, infected cells detach from the neighbouring cells and can be easily harvested from the cell culture supernatant. This protocol offers robust experimental timing and temporal flexibility. HeLa cells are infected with P. berghei sporozoites to obtain liver stage-derived merozoites, which are harvested from the cell culture supernatant and are transfected using the Amaxa Nucleofector(®) electroporation technology. Using this protocol, wild type P. berghei ANKA strain and marker-free PbmCherryHsp70-expressing P. berghei parasites were successfully transfected with DNA constructs designed for integration via single- or double-crossover homologous recombination. An alternative protocol for Plasmodium transfection is hereby provided, which uses liver stage-derived P. berghei merozoites for transfection. This protocol has the potential to substantially reduce the number of mice used per transfection, as well as to increase the temporal flexibility and robustness of performing transfections, if mosquitoes are routinely present in the laboratory. Transfection of liver stage-derived P. berghei parasites should enable generation of transgenic parasites within 8-18 days

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

Differential Proteome Analysis of Bone Marrow Mesenchymal Stem Cells from Adolescent Idiopathic Scoliosis Patients

Adolescent idiopathic scoliosis (AIS) is a complex three-dimensional deformity of the spine. The cause and pathogenesis of scoliosis and the accompanying generalized osteopenia remain unclear despite decades of extensive research. In this study, we utilized two-dimensional fluorescence difference gel electrophoresis (2D-DIGE) coupled with mass spectrometry (MS) to analyze the differential proteome of bone marrow mesenchymal stem cells (BM-MSCs) from AIS patients. In total, 41 significantly altered protein spots were detected, of which 34 spots were identified by MALDI-TOF/TOF analysis and found to represent 25 distinct gene products. Among these proteins, five related to bone growth and development, including pyruvate kinase M2, annexin A2, heat shock 27 kDa protein, γ-actin, and β-actin, were found to be dysregulated and therefore selected for further validation by Western blot analysis. At the protein level, our results supported the previous hypothesis that decreased osteogenic differentiation ability of MSCs is one of the mechanisms leading to osteopenia in AIS. In summary, we analyzed the differential BM-MSCs proteome of AIS patients for the first time, which may help to elucidate the underlying molecular mechanisms of bone loss in AIS and also increase understanding of the etiology and pathogenesis of AIS

Prolonged Application of High Fluid Shear to Chondrocytes Recapitulates Gene Expression Profiles Associated with Osteoarthritis

BACKGROUND: Excessive mechanical loading of articular cartilage producing hydrostatic stress, tensile strain and fluid flow leads to irreversible cartilage erosion and osteoarthritic (OA) disease. Since application of high fluid shear to chondrocytes recapitulates some of the earmarks of OA, we aimed to screen the gene expression profiles of shear-activated chondrocytes and assess potential similarities with OA chondrocytes. METHODOLOGY/PRINCIPAL FINDINGS: Using a cDNA microarray technology, we screened the differentially-regulated genes in human T/C-28a2 chondrocytes subjected to high fluid shear (20 dyn/cm(2)) for 48 h and 72 h relative to static controls. Confirmation of the expression patterns of select genes was obtained by qRT-PCR. Using significance analysis of microarrays with a 5% false discovery rate, 71 and 60 non-redundant transcripts were identified to be ≥2-fold up-regulated and ≤0.6-fold down-regulated, respectively, in sheared chondrocytes. Published data sets indicate that 42 of these genes, which are related to extracellular matrix/degradation, cell proliferation/differentiation, inflammation and cell survival/death, are differentially-regulated in OA chondrocytes. In view of the pivotal role of cyclooxygenase-2 (COX-2) in the pathogenesis and/or progression of OA in vivo and regulation of shear-induced inflammation and apoptosis in vitro, we identified a collection of genes that are either up- or down-regulated by shear-induced COX-2. COX-2 and L-prostaglandin D synthase (L-PGDS) induce reactive oxygen species production, and negatively regulate genes of the histone and cell cycle families, which may play a critical role in chondrocyte death. CONCLUSIONS/SIGNIFICANCE: Prolonged application of high fluid shear stress to chondrocytes recapitulates gene expression profiles associated with osteoarthritis. Our data suggest a potential link between exposure of chondrocytes/cartilage to abnormal mechanical loading and the pathogenesis/progression of OA

Cdk1 Targets Srs2 to Complete Synthesis-Dependent Strand Annealing and to Promote Recombinational Repair

Cdk1 kinase phosphorylates budding yeast Srs2, a member of UvrD protein family, displays both DNA translocation and DNA unwinding activities in vitro. Srs2 prevents homologous recombination by dismantling Rad51 filaments and is also required for double-strand break (DSB) repair. Here we examine the biological significance of Cdk1-dependent phosphorylation of Srs2, using mutants that constitutively express the phosphorylated or unphosphorylated protein isoforms. We found that Cdk1 targets Srs2 to repair DSB and, in particular, to complete synthesis-dependent strand annealing, likely controlling the disassembly of a D-loop intermediate. Cdk1-dependent phosphorylation controls turnover of Srs2 at the invading strand; and, in absence of this modification, the turnover of Rad51 is not affected. Further analysis of the recombination phenotypes of the srs2 phospho-mutants showed that Srs2 phosphorylation is not required for the removal of toxic Rad51 nucleofilaments, although it is essential for cell survival, when DNA breaks are channeled into homologous recombinational repair. Cdk1-targeted Srs2 displays a PCNA–independent role and appears to have an attenuated ability to inhibit recombination. Finally, the recombination defects of unphosphorylatable Srs2 are primarily due to unscheduled accumulation of the Srs2 protein in a sumoylated form. Thus, the Srs2 anti-recombination function in removing toxic Rad51 filaments is genetically separable from its role in promoting recombinational repair, which depends exclusively on Cdk1-dependent phosphorylation. We suggest that Cdk1 kinase counteracts unscheduled sumoylation of Srs2 and targets Srs2 to dismantle specific DNA structures, such as the D-loops, in a helicase-dependent manner during homologous recombinational repair

Cytokine preconditioning of engineered cartilage provides protection against interleukin-1 insult

Research reported in this publication was supported in part by the National Institute of Arthritis and Musculoskeletal and Skin Diseases and National Institute of Biomedical Imaging and Bioengineering of the National Institutes of Health under Award Number R01AR60361, R01AR061988, P41EB002520). The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. ART was supported by a National Science Foundation Graduate Fellowship