OPERATOR RANGES OF SHIFTS AND C*-ALGEBRAS (STRANGE RANGE, QUASI-SIMILARITY, LATTICE)

It is shown that Lat(, 1/2)(H(\u27(INFIN))(S)), the invariant operator ranges of the commutant of the unilateral shift, is a proper sub-lattice of the lattice of invariant operator ranges of the unilateral shift, S. The notion of a strange operator range for S of order n where n (ELEM) is introduced and it is demonstrated that there exist strange ranges for S of every order. This is done by deriving an operator range condition which is sufficient to insure that a pair of quasi-similar compressions of shifts really be similar. A set of operator ranges which forms a sub-lattice of Lat(, 1/2)(H(\u27(INFIN))(S)) is introduced, which is conjectured to be Lat(, 1/2)(H(\u27(INFIN))(S)). The conjecture is shown to be equivalent to the assertion that the image of S under certain homomorphisms of H(\u27(INFIN))(S) into B(H) is similar to a contraction. It is proven that the ranges of operators from a commutative C*-algebra form a lattice under intersection and vector sum. If P and Q are projections in B(H) with non zero intersection and so that the angle between their ranges is 0, then it is shown that the ranges of the operators in the C*-algebra generated by P and Q does not contain the intersection of the ranges of P and Q. Thus, non-commutative C*-algebras need not have ranges which form a lattice. The question of whether the ranges of operators from different kinds of algebras form lattices is taken up and examples are provided. It is proven that any pair of subspaces of a Hilbert space can be the ranges of a pair of commuting operators. A family of one dimen- sional subspaces of a Hilbert space, H, is shown to representable as the set of ranges of a family of commuting operators if and only if for each subspace the linear span of the union of the remaining sub-spaces is not dense in H. The sets of three subspaces of C(\u273) which can be the ranges of commuting operators are characterized

02/21/1947 Letter from Lucien Roy, M.D.

Handwritten letter from Lucien Roy, M.D., to Louis-Philippe Gagné.https://digitalcommons.usm.maine.edu/fac-lpg-1947-01-03/1026/thumbnail.jp

Intégration d'approches par problèmes en sciences de la nature : phase 1 intégration d'une activité de synthèse en fin de programme /

Titre de l'écran-titre (visionné le 7 mai 2009).Également disponible en format papier.Bibliogr

On the Interval of Boolean Strong Partial Clones Containing Only Projections as Total Operations

International audienceA strong partial clone is a set of partial operations closed under composition and containing all partial projections. Let X be the set of all Boolean strong partial clones whose total operations are the projections. This set is of practical interest since it induces a partial order on the complexity of NP-complete constraint satisfaction problems. In this paper we study X from the algebraic point of view, and prove that there exists two intervals in X , corresponding to natural constraint satisfaction problems, such that one is at least countably infinite and the other has the cardinality of the continuum

« Il Cinema ritrovato »

Inutile d’insister une nouvelle fois sur la richesse de la programmation bolognaise. Il Cinema ritrovato, année après année, prouve la dimension patrimoniale du cinéma comme référence culturelle majeure de l’histoire du xxe siècle. Pour sa 28e édition, la manifestation s’est encore enrichie, dédoublant ses projections nocturnes et alimentant en continu quatre salles. Et pour ajouter encore à une offre pléthorique, Il Cinema ritrovato était précédé cette année par un colloque « 100 anni di Cha..

Identification of Two Critically Deleted Regions within Chromosome Segment 7q35-q36 in EVI1 Deregulated Myeloid Leukemia Cell Lines

Chromosomal rearrangements involving the EVI1 proto-oncogene are a recurrent finding in myeloid leukemias and are indicative of a poor prognosis. Rearrangements of the EVI1 locus are often associated with monosomy 7 or cytogenetic detectable deletions of part of 7q. As EVI1 overexpression alone is not sufficient to induce leukemia, loss of a 7q tumour suppressor gene might be a required cooperating event. To test this hypothesis, we performed high-resolution array comparative genomic hybridization analysis of twelve EVI1 overexpressing patients and three EVI1 deregulated cell lines to search for 7q submicroscopic deletions. This analysis lead to the delineation of two critical regions, one of 0.39 Mb on 7q35 containing the CNTNAP2 gene and one of 1.33 Mb on chromosome bands 7q35–q36 comprising nine genes in EVI1 deregulated cell lines. These findings open the way to further studies aimed at identifying the culprit EVI1 implicated tumour suppressor genes on 7q

Abundant copy-number loss of CYCLOPS and STOP genes in gastric adenocarcinoma

Background Gastric cancer, a leading cause of cancer death worldwide, has been little studied compared with other cancers that impose similar health burdens. Our goal is to assess genomic copy-number loss and the possible functional consequences and therapeutic implications thereof across a large series of gastric adenocarcinomas. Methods We used high-density single-nucleotide polymorphism microarrays to determine patterns of copy-number loss and allelic imbalance in 74 gastric adenocarcinomas. We investigated whether suppressor of tumorigenesis and/or proliferation (STOP) genes are associated with genomic copy-number loss. We also analyzed the extent to which copy-number loss affects Copy-number alterations Yielding Cancer Liabilities Owing to Partial losS (CYCLOPS) genes–genes that may be attractive targets for therapeutic inhibition when partially deleted. Results The proportion of the genome subject to copy-number loss varies considerably from tumor to tumor, with a median of 5.5 %, and a mean of 12 % (range 0–58.5 %). On average, 91 STOP genes were subject to copy-number loss per tumor (median 35, range 0–452), and STOP genes tended to have lower copy-number compared with the rest of the genes. Furthermore, on average, 1.6 CYCLOPS genes per tumor were both subject to copy-number loss and downregulated, and 51.4 % of the tumors had at least one such gene. Conclusions The enrichment of STOP genes in regions of copy-number loss indicates that their deletion may contribute to gastric carcinogenesis. Furthermore, the presence of several deleted and downregulated CYCLOPS genes in some tumors suggests potential therapeutic targets in these tumors.Singapore. Ministry of Health (Duke-NUS Signature Research Programs)Singapore. Agency for Science, Technology and ResearchSingapore-MIT Allianc

EVI1 overexpression in t(3;17) positive myeloid malignancies results from juxtaposition of EVI1 to the MSI2 locus at 17q22

Chromosomal translocations involving the EVI1 locus are a recurrent finding in myeloid leukemia and are associated with poor prognosis. In this study, we performed a detailed molecular characterization of the recurrent translocation t(3;17)(q26;q22) in 13 hematologic malignancies. The EVI1 gene locus was rearranged in all 13 patients and was associated with EVI1 overexpression. In 9 out of 13 patients, the 17q breakpoints clustered in a 250 kb region on band 17q22 encompassing the MSI2 (musashi homologue 2) gene. Expression analyses failed to demonstrate ectopic MSI2 expression or the presence of an MSI2/EVI1 fusion gene. In conclusion, we show for the first time that the t(3;17) is indeed a recurrent chromosomal aberration in myeloid malignancies. In keeping with findings in other recurrent 3q26 rearrangements, overexpression of the EVI1 gene appears to be the major contributor to leukemogenesis in patients with a t(3; 17)