K-Theory of non-linear projective toric varieties

We define a category of quasi-coherent sheaves of topological spaces on projective toric varieties and prove a splitting result for its algebraic K-theory, generalising earlier results for projective spaces. The splitting is expressed in terms of the number of interior lattice points of dilations of a polytope associated to the variety. The proof uses combinatorial and geometrical results on polytopal complexes. The same methods also give an elementary explicit calculation of the cohomology groups of a projective toric variety over any commutative ring.

ALK translocation is associated with ALK immunoreactivity and extensive signet-ring morphology in primary lung adenocarcinoma.

BACKGROUND: ALK rearrangement is particularly observed in signet-ring sub-type adenocarcinoma. Since fluorescence in situ hybridization (FISH) is not suitable for mass screening, we aimed to characterize the predictive utility of tumour morphology and ALK immunoreactivity to identify ALK rearrangement, in a primary lung adenocarcinoma dataset enriched for signet-ring morphology, compared with that of other morphology. METHODS: 7 adenocarcinomas from diagnostic archives reported with signet-ring morphology were assessed and compared with 11 adenocarcinomas without signet-ring features over the same time period. Growth patterns were reviewed, ALK expression was assessed by standard immunohistochemistry using ALK1 clone and Envision detection (Dako), and ALK rearrangement was assessed by FISH (Abbott Molecular). Associations between groups and predictive utility of tumour morphology and ALK expression using FISH as gold standard were calculated. RESULTS: 2 excision lung biopsy cases with pure (100%) signet-ring morphology and solid patterns demonstrated diffuse moderate cytoplasmic ALK immunoreactivity (2+) and harboured ALK rearrangements (p=0.007), unlike 5 mixed-signet-ring and 11 non-signet-ring adenocarcinomas, which showed negative or 1+ immunoreactivity; and did not harbour ALK rearrangements (p>0.1). ALK expression was not associated with ALK copy number. 6 of 7 cases with signet ring morphology stained for TTF-1. Pure signet-ring morphology and moderate ALK expression were both associated with ALK rearranged tumours. CONCLUSION: ALK rearrangement is strongly associated with ALK immunoreactivity, and was seen only in tumours with pure signet-ring morphology and solid growth pattern. Tumour morphology, growth pattern and ALK immunoreactivity appear to be good indicators of ALK rearrangement, with TTF-1 positivity aiding in proving primary pulmonary origin.

K1 of Chevalley groups are nilpotent

Abstract Let F be a reduced irreducible root system and R be a commutative ring. Further, let G(F,R) be a Chevalley group of type F over R and E(F,R) be its elementary subgroup. We prove that if the rank of F is at least 2 and the Bass-Serre dimension of R is finite, then the quotient G(F,R)/E(F,R) is nilpotent by abelian. In particular, when G(F,R) is simply connected the quotient K1(F,R)=G(F,R)/E(F,R) is nilpotent. This result was previously established by Bak for the series A1 and by Hazrat for C1 and D1. As in the above papers we use the localisation-completion method of Bak, with some technical simplifications.

Multidimensional operator multipliers

We introduce multidimensional Schur multipliers and characterise them, generalising well-known results by Grothendieck and Peller. We define a multidimensional version of the two-dimensional operator multipliers studied recently by Kissin and Shulman. The multidimensional operator multipliers are defined as elements of the minimal tensor product of several C *-algebras satisfying certain boundedness conditions. In the case of commutative C*-algebras, the multidimensional operator multipliersreduce to continuousmul-tidimensional Schur multipliers. We show that the multiplierswith respect to some given representations of the corresponding C*-algebrasdo not change if the representations are replaced by approximately equivalent ones. We establish a non-commutative and multidimensional version of the characterisations by Grothendieck and Peller which shows that universal operator multipliers can be obtained ascertain weak limits of elements of the algebraic tensor product of the corresponding C *-algebras.

On the derived category of a regular toric scheme

Let X be a quasi-compact scheme, equipped with an open covering by affine schemes U s = Spec A s . A quasi-coherent sheaf on X gives rise, by taking sections over the U s , to a diagram of modules over the coordinate rings A s , indexed by the intersection poset S of the covering. If X is a regular toric scheme over an arbitrary commutative ring, we prove that the unbounded derived category of quasi-coherent sheaves on X can be obtained from a category of Sop-diagrams of chain complexes of modules by inverting maps which induce homology isomorphisms on hyper-derived inverse limits. Moreover, we show that there is a finite set of weak generators, one for each cone in the fan S. The approach taken uses the machinery of Bousfield–Hirschhorn colocalisation of model categories. The first step is to characterise colocal objects; these turn out to be homotopy sheaves in the sense that chain complexes over different open sets U s agree on intersections up to quasi-isomorphism. In a second step it is shown that the homotopy category of homotopy sheaves is equivalent to the derived category of X.

Local operator multipliers and positivity

We establish an unbounded version of Stinespring's Theorem and a lifting result for Stinespring representations of completely positive modular maps defined on the space of all compact operators. We apply these results to study positivity for Schur multipliers. We characterise positive local Schur multipliers, and provide a description of positive local Schur multipliers of Toeplitz type. We introduce local operator multipliers as a non-commutative analogue of local Schur multipliers, and characterise them extending both the characterisation of operator multipliers from [16] and that of local Schur multipliers from [27]. We provide a description of the positive local operator multipliers in terms of approximation by elements of canonical positive cones.

Splitting monoidal stable model categories

If C is a stable model category with a monoidal product then the set of homotopy classes of self-maps of the unit forms a commutative ring, [S,S]C. An idempotent e of this ring will split the homotopy category: [X,Y]C≅e[X,Y]C⊕(1−e)[X,Y]C. We prove that provided the localised model structures exist, this splitting of the homotopy category comes from a splitting of the model category, that is, C is Quillen equivalent to LeSC×L(1−e)SC and [X,Y]LeSC≅e[X,Y]C. This Quillen equivalence is strong monoidal and is symmetric when the monoidal product of C is.

A monoidal algebraic model for rational SO(2)-spectra

The category of rational SO(2)--equivariant spectra admits an algebraic model. That is, there is an abelian category A(SO(2)) whose derived category is equivalent to the homotopy category of rational$SO(2)--equivariant spectra. An important question is: does this algebraic model capture the smash product of spectra? The category A(SO(2)) is known as Greenlees' standard model, it is an abelian category that has no projective objects and is constructed from modules over a non--Noetherian ring. As a consequence, the standard techniques for constructing a monoidal model structure cannot be applied. In this paper a monoidal model structure on A(SO(2)) is constructed and the derived tensor product on the homotopy category is shown to be compatible with the smash product of spectra. The method used is related to techniques developed by the author in earlier joint work with Roitzheim. That work constructed a monoidal model structure on Franke's exotic model for the K_(p)--local stable homotopy category. A monoidal Quillen equivalence to a simpler monoidal model category that has explicit generating sets is also given. Having monoidal model structures on the two categories removes a serious obstruction to constructing a series of monoidal Quillen equivalences between the algebraic model and rational SO(2)--equivariant spectra.

Development and evaluation of a vaginal ring device for sustained delivery of HIV microbicides to non-human primate

Background There is considerable interest in developing coitally indepen- dent, sustained release formulations for long-term administration of HIV microbicides. Vaginal ring devices are at the forefront of this formulation strategy. Methods Non-medicated silicone elastomer vaginal rings were prepared having a range of appropriate dimensions for testing vaginal ?t in pig- tailed and Chinese rhesus macaques. Cervicovaginal proin?ammatory markers were evaluated. Compression testing was performed to compare the relative ?exibility of various macaque and commercial human rings. Results All rings remained in place during the study period and no tissue irritation or signi?cant induction of cervicovaginal proin?ammatory mark- ers or signs of physical discomfort were observed during the 8-week study period. Conclusions Qualitative evaluation suggests that the 25 · 5-mm ring pro- vided optimal ?t in both macaque species. Based on the results presented here, low-consistency silicone elastomers do not cause irritation in maca-

Experimental linear-optics simulation of multipartite non-locality in the ground state of a quantum Ising ring

Critical phenomena involve structural changes in the correlations of its constituents. Such changes can be reproduced and characterized in quantum simulators able to tackle medium-to-large-size systems. We demonstrate these concepts by engineering the ground state of a three-spin Ising ring by using a pair of entangled photons. The effect of a simulated magnetic field, leading to a critical modification of the correlations within the ring, is analysed by studying two- and three-spin entanglement. In particular, we connect the violation of a multipartite Bell inequality with the amount of tripartite entanglement in our ring.

Design of a silicone reservoir intravaginal ring for the delivery of oxybutynin.

Oxybutynin, a drug of choice in the treatment of urinary incontinence, has low oral bioavailability due to extensive first-pass metabolism. A toxic metabolite, N-desethyloxybutynin, has been linked to adverse reactions to oral oxybutynin. This study, therefore, reports on the design of an oxybutynin intravaginal ring (IVR) of reservoir design, comprising an oxybutynin silicone elastomer core encased in a non-medicated silicone sheath, manufactured by reaction injection moulding at 50oC. An unusually high initial burst release of oxybutynin (42.7 mg in 24 h) was observed in vitro with a full length core (100 mg drug loading), with subsequent non-zero order drug release. Use of fractional segment cores substantially reduced the burst effect, yielding linear cumulative drug release versus time plots from days 2 to 14. Thus, a 1/8 fractional segment core gave a 24 h burst of 11.28 mg oxybutynin and, thereafter, zero order release at the target dose of 5 mg/day over 14 days. Two oxybutynin cores, each 1/16 of full length, gave a greater release than a single 1/8 core, due to core segment end effects resulting in an increased surface area for release. The burst release was investigated by determining drug solubilities in the propan-1-ol product of elastomer condensation cure (390 mg/ml) and in the elastomer itself (13.9-20.21 mg/ml, by direct extraction and indirect thermal methods). These high oxybutynin solubilities were considered the major contributors to the burst effect. It was concluded that use of a fractional segment core would allow development of a suitable oxybutynin reservoir IVR.

Intravaginal ring delivery of the reverse transcriptase inhibitor TMC 120 as an HIV microbicide

TMC 120 (Dapivirine) is a potent non-nucleoside reverse transcriptase inhibitor that is presently being developed as a vaginal HIV microbicide. To date, most vaginal microbicides under clinical investigation have been formulated as single-dose semi-solid gels, designed for application to the vagina before each act of intercourse. However, a clear rationale exists for providing long-term, controlled release of vaginal microbicides in order to afford continuous protection against heterosexually transmitted HIV infection and to improve user compliance. In this study we report on the incorporation of various pharmaceutical excipients into TMC 120 silicone, reservoir-type intravaginal rings (IVRs) in order to modify the controlled release characteristics of the microbicide. The results demonstrate that TMC 120 is released in zero-order fashion from the rings over a 28-day period and that release parameters could be modified by the inclusion of release-modifying excipients in the IVR. The hydrophobic liquid excipient isopropyl myristate had little effect on steady-state daily release rates, but did increase the magnitude and duration of burst release in proportion to excipient loading in the IVR. By comparison, the hydrophobic liquid poly(dimethylsiloxane) had little effect on TMC 120 release parameters. A hydrophilic excipient, lactose, had the surprising effect of decreasing TMC 120 burst release while increasing the apparent steady-state daily release in a concentration-dependent manner. Based on previous cell culture data and vaginal physiology, TMC120 is released from the various ring formulations in amounts potentially capable of maintaining a protective vaginal concentration. It is further predicted that the observed release rates may be maintained for at least a period of 1 year from a single ring device. TMC 120 release profiles and the mechanical properties of rings could be modified by the physicochemical nature of hydrophobic and hydrophilic excipients incorporated into the IVRs.

Dramatic solvent effects on ring-opening metathesis polymerization of cycloalkenes

A series of metathesis polymers and copolymers have been formed and their structures were analysed by C-13 NMR spectroscopy. Noble metal and non-noble metal salt catalysts are distinguished by their behaviour in various solvents. Thus, in phenolic solvents, the former class produce alternating copolymers from cyclopentene and norbornene, while the latter are unaffected and produce random copolymers. In contrast, ether solvents have the effect of markedly increasing the cis content of polymers from the latter catalysts while the former are unaffected.

Pre-treatment with Depo-Provera modifies the pharmacokinetics of CMPD167 in rhesus macaques following vaginal ring administration

BACKGROUND: Vaginal ring devices are being developed to provide sustained release of HIV microbicides. To date, only limited pharmacokinetic data is available from animal or human studies. Here we report the effect of Depo-Provera (DP) pre- treatment, commonly used to thin the vaginal epithelium in challenge experiments, on the pharmacokinetic profile of CMPD167 (a small molecule CCR5 co-receptor antagonist) in rhesus macaques following vaginal ring administration.

METHODS: A single 400mg CMPD167 silicone elastomer vaginal ring was inserted into each of twelve female rhesus macaques. Six macaques were treated with (DP) 30 days before ring placement; the other six macaques were untreated. Blood, vaginal fluid and vaginal biopsies were collected prior to and at various times during 28 days of ring placement and assayed for CMPD167 levels by HPLC. Rings were assayed for residual CMPD167 at the end of the study and the calculated amount of CMPD167 released in vivo compared with in vitro release data.

RESULTS: Vaginal fluid, plasma and tissue levels of CMPD167 were detectable throughout ring placement. Significant differences were observed in mean daily vaginal fluid levels between the DP-treated (16–56 mcg/mL) and untreated groups (48–181 mcg/mL). Plasma CMPD167 levels were significantly higher peaking at 4 ng/mL and maintaining levels of 1–2 nM throughout the 14 days of testing in animals pre-treated with DP compared to non DP-treated macaques (<1 ng/mL maintained). Tissue levels were varied between 2–10 g/mL CMPD167 with no significant difference between the DP-treated and untreated macaques.

CONCLUSIONS: The study demonstrates that clinically relevant, and possibly protective doses of CMPD167 are released in the vaginal vault of rhesus macaques from vaginal rings through 28 days duration. DP is known to induce vaginal epithelial thinning and lower vaginal fluid levels, which accounts for the increased plasma levels of CMPD167. In contrast, macaques not treated with DP had minimal absorption into plasma compartments and significantly higher levels of CMPD167 in the vagina, similar to those previously shown to be protective against vaginal challenge.

Non-thiazolidinedione antihyperglycemic agents. 2: alpha-Carbon substituted-beta-phenylpropanoic acids.

Buckle, D. R.; Cantello, B. C. C.; Cawthorne, M. A.; Coyle, P. J.; Dean, D. K.; Faller, A.; Haigh, D.; Hindley, R. M.; Lefcott, L. J.; et al. Dep. Medicinal Chem., Smithkline Beecham Pharmaceuticals, Surrey, UK. Bioorganic & Medicinal Chemistry Letters (1996), 6(17), 2127-2130. Publisher: Elsevier, CODEN: BMCLE8 ISSN: 0960-894X. Journal written in English. CAN 125:238227 AN 1996:573179 CAPLUS (Copyright (C) 2009 ACS on SciFinder (R)) Abstract The thiazolidine-2,4-dione ring of insulin-sensitizing antidiabetic agents can be replaced by ?-acyl-, ?-alkyl- and ?-(aralkyl)-carboxylic acids. The inclusion of an addnl. lipophilic moiety affords compds., equipotent to BRL 48482.