Banach空间上的算子幂级数理论

本文提出了Banach空间中的一种幂级数模式一算子幂级数。以此为起点,希冀能建立Banach空间中的算子幂级数理论,并使之成为Banach空间级数理论中的一个组成部分[8],[9],[10]。文中例子表明,经典幂级数理论大体上在本文算子幂级数有关定理中得到了相当的反映。本文定理12给出了一个新的不动点定理。     

Increased methylation variation in epigenetic domains across cancer types

Tumor heterogeneity is a major barrier to effective cancer diagnosis and treatment. We recently identified cancer-specific differentially DNA-methylated regions (cDMRs) in colon cancer, which also distinguish normal tissue types from each other, suggesting that these cDMRs might be generalized across cancer types. Here we show stochastic methylation variation of the same cDMRs, distinguishing cancer from normal tissue, in colon, lung, breast, thyroid and Wilms' tumors, with intermediate variation in adenomas. Whole-genome bisulfite sequencing shows these variable cDMRs are related to loss of sharply delimited methylation boundaries at CpG islands. Furthermore, we find hypomethylation of discrete blocks encompassing half the genome, with extreme gene expression variability. Genes associated with the cDMRs and large blocks are involved in mitosis and matrix remodeling, respectively. We suggest a model for cancer involving loss of epigenetic stability of well-defined genomic domains that underlies increased methylation variability in cancer that may contribute to tumor heterogeneity.     

Algorithms for ℓ<Subscript>1</Subscript>-Embeddability and Related Problems

Assouad has shown that a real-valued distance d = (d_ij)_{1 ≤ i < j ≤ n} is isometrically embeddable in ℓ₁space if and only if it belongs to the cut cone on n points. Determining if this condition holds is NP-complete. We use Assouad's result in a constructive column generation algorithm for ℓ₁-embeddability. The subproblem is an unconstrained 0-1 quadratic program, solved by Tabu Search and Variable Neighborhood Search heuristics as well as by an exact enumerative algorithm. Computational results are reported. Several ways to approximate a distance which is not ℓ₁-embeddable by another one which is are also studied.     

Compositional maps of Saturn's moon Phoebe from imaging spectroscopy

The origin of Phoebe, which is the outermost large satellite of Saturn, is of particular interest because its inclined, retrograde orbit suggests that it was gravitationally captured by Saturn, having accreted outside the region of the solar nebula in which Saturn formed. By contrast, Saturn's regular satellites (with prograde, low-inclination, circular orbits) probably accreted within the sub-nebula in which Saturn itself formed. Here we report imaging spectroscopy of Phoebe resulting from the Cassini-Huygens spacecraft encounter on 11 June 2004. We mapped ferrous-iron-bearing minerals, bound water, trapped CO2, probable phyllosilicates, organics, nitriles and cyanide compounds. Detection of these compounds on Phoebe makes it one of the most compositionally diverse objects yet observed in our Solar System. It is likely that Phoebe's surface contains primitive materials from the outer Solar System, indicating a surface of cometary origin.     

Identification of the familial cylindromatosis tumour-suppressor gene

Familial cylindromatosis is an autosomal dominant genetic predisposition to multiple tumours of the skin appendages. The susceptibility gene (CYLD) has previously been localized to chromosome 16q and has the genetic attributes of a tumour-suppressor gene (recessive oncogene). Here we have identified CYLD by detecting germline mutations in 21 cylindromatosis families and somatic mutations in 1 sporadic and 5 familial cylindromas. All mutations predict truncation or absence of the encoded protein. CYLD encodes three cytoskeletal-associated-protein-glycine-conserved (CAP-GLY) domains, which are found in proteins that coordinate the attachment of organelles to microtubules. CYLD also has sequence homology to the catalytic domain of ubiquitin carboxy-terminal hydrolases (UCH).     

The U1 snRNP protein U1C recognizes the 5' splice site in the absence of base pairing

Splicing of precursor messenger RNA takes place in the spliceosome, a large RNA/protein macromolecular machine. Spliceosome assembly occurs in an ordered pathway in vitro and is conserved between yeast and mammalian systems. The earliest step is commitment complex formation in yeast or E complex formation in mammals, which engages the pre-mRNA in the splicing pathway and involves interactions between U1 small nuclear ribonucleoprotein (snRNP) and the pre-mRNA 5' splice site. Complex formation depends on highly conserved base pairing between the 5' splice site and the 5' end of U1 snRNA, both in vivo and in vitro. U1 snRNP proteins also contribute to U1 snRNP activity. Here we show that U1 snRNP lacking the 5' end of its snRNA retains 5'-splice-site sequence specificity. We also show that recombinant yeast U1C protein, a U1 snRNP protein, selects a 5'-splice-site-like sequence in which the first four nucleotides, GUAU, are identical to the first four nucleotides of the yeast 5'-splice-site consensus sequence. We propose that a U1C 5'-splice-site interaction precedes pre-mRNA/U1 snRNA base pairing and is the earliest step in the splicing pathway.     

Decreasing overflow from the Nordic seas into the Atlantic Ocean through the Faroe Bank channel since 1950.

The overflow of cold, dense water from the Nordic seas, across the Greenland-Scotland ridge and into the Atlantic Ocean is the main source for the deep water of the North Atlantic Ocean. This flow also helps drive the inflow of warm, saline surface water into the Nordic seas. The Faroe Bank channel is the deepest path across the ridge, and the deep flow through this channel accounts for about one-third of the total overflow. Previous work has demonstrated that the overflow has become warmer and less saline over time. Here we show, using direct measurements and historical hydrographic data, that the volume flux of the Faroe Bank channel overflow has also decreased. Estimating the volume flux conservatively, we find a decrease by at least 20 per cent relative to 1950. If this reduction in deep flow from the Nordic seas is not compensated by increased flow from other sources, it implies a weakened global thermohaline circulation and reduced inflow of Atlantic water to the Nordic seas.