Factorisation of Lie resolvents

AbstractLet G be a group, F a field of prime characteristic p, and V a finite-dimensional FG-module. For each positive integer r, the rth homogeneous component of the free Lie algebra on V is an FG-module called the rth Lie power of V. Lie powers are determined, up to isomorphism, by certain functions Φr on the Green ring of FG, called ‘Lie resolvents’. Our main result is the factorisation Φpmk=Φpm∘Φk whenever k is not divisible by p. This may be interpreted as a reduction to the key case of p-power degree

Reduced Expression of miRNA-27a Modulates Cisplatin Resistance in Bladder Cancer by Targeting the Cystine/Glutamate Exchanger SLC7A11

Purpose: Resistance to cisplatin-based chemotherapy is a major obstacle to bladder cancer treatment. We aimed to identify microRNAs (miRNA) that are dysregulated in cisplatin-resistant disease, ascertain how these contribute to a drug-resistant phenotype, and how this resistance might be overcome. Experimental Design: miRNA expression in paired cisplatin-resistant and -sensitive cell lines was measured. Dysregulated miRNAs were further studied for their ability to mediate resistance. The nature of the cisplatin-resistant phenotype was established by measurement of cisplatin/DNA adducts and intracellular glutathione (GSH). Candidate miRNAs were examined for their ability to (i) mediate resistance and (ii) alter the expression of a candidate target protein (SLC7A11); direct regulation of SLC7A11 was confirmed using a luciferase assay. SLC7A11 protein and mRNA, and miRNA-27a were quantified in patient tumor material. Results: A panel of miRNAs were found to be dysregulated in cisplatin-resistant cells. miRNA-27a was found to target the cystine/glutamate exchanger SLC7A11 and to contribute to cisplatin resistance through modulation of GSH biosynthesis. In patients, SLC7A11 expression was inversely related to miRNA-27a expression, and those tumors with high mRNA expression or high membrane staining for SLC7A11 experienced poorer clinical outcomes. Resistant cell lines were resensitized by restoring miRNA-27a expression or reducing SLC7A11 activity with siRNA or with sulfasalazine. Conclusion: Our findings indicate that miRNA-27a negatively regulates SLC7A11 in cisplatin-resistant bladder cancer, and shows promise as a marker for patients likely to benefit from cisplatin-based chemotherapy. SLC7A11 inhibition with sulfasalazine may be a promising therapeutic approach to the treatment of cisplatin-resistant disease

Intersecting 6-branes from new 7-manifolds with G_2 holonomy

We discuss a new family of metrics of 7-manifolds with G_2 holonomy, which are R^3 bundles over a quaternionic space. The metrics depend on five parameters and have two Abelian isometries. Certain singularities of the G_2 manifolds are related to fixed points of these isometries; there are two combinations of Killing vectors that possess co-dimension four fixed points which yield upon compactification only intersecting D6-branes if one also identifies two parameters. Two of the remaining parameters are quantized and we argue that they are related to the number of D6-branes, which appear in three stacks. We perform explicitly the reduction to the type IIA model.Comment: 25 pages, 1 figure, Latex, small changes and add refs, version appeared in JHE

Spin and energy transfer in nanocrystals without transport of charge

We describe a mechanism of spin transfer between individual quantum dots that does not require tunneling. Incident circularly-polarized photons create inter-band excitons with non-zero electron spin in the first quantum dot. When the quantum-dot pair is properly designed, this excitation can be transferred to the neighboring dot via the Coulomb interaction with either {\it conservation} or {\it flipping} of the electron spin. The second dot can radiate circularly-polarized photons at lower energy. Selection rules for spin transfer are determined by the resonant conditions and by the strong spin-orbit interaction in the valence band of nanocrystals. Coulomb-induced energy and spin transfer in pairs and chains of dots can become very efficient under resonant conditions. The electron can preserve its spin orientation even in randomly-oriented nanocrystals.Comment: 13 pages, 3 figure

The UKIDSS Galactic Plane Survey

'The definitive version is available at www.blackwell-synergy.com .' Copyright Blackwell Publishing DOI: 10.1111/j.1365-2966.2008.13924.xThe UKIDSS Galactic Plane Survey (GPS) is one of the five near-infrared Public Legacy Surveys that are being undertaken by the UKIDSS consortium, using the Wide Field Camera on the United Kingdom Infrared TelescopePeer reviewe

Automorphism groups of polycyclic-by-finite groups and arithmetic groups

We show that the outer automorphism group of a polycyclic-by-finite group is an arithmetic group. This result follows from a detailed structural analysis of the automorphism groups of such groups. We use an extended version of the theory of the algebraic hull functor initiated by Mostow. We thus make applicable refined methods from the theory of algebraic and arithmetic groups. We also construct examples of polycyclic-by-finite groups which have an automorphism group which does not contain an arithmetic group of finite index. Finally we discuss applications of our results to the groups of homotopy self-equivalences of K(\Gamma, 1)-spaces and obtain an extension of arithmeticity results of Sullivan in rational homotopy theory

Critical point network for drainage between rough surfaces

In this paper, we present a network method for computing two-phase flows between two rough surfaces with significant contact areas. Low-capillary number drainage is investigated here since one-phase flows have been previously investigated in other contributions. An invasion percolation algorithm is presented for modeling slow displacement of a wetting fluid by a non wetting one between two rough surfaces. Short-correlated Gaussian process is used to model random rough surfaces.The algorithm is based on a network description of the fracture aperture field. The network is constructed from the identification of critical points (saddles and maxima) of the aperture field. The invasion potential is determined from examining drainage process in a flat mini-channel. A direct comparison between numerical prediction and experimental visualizations on an identical geometry has been performed for one realization of an artificial fracture with a moderate fractional contact area of about 0.3. A good agreement is found between predictions and observations

Perinatal morbidity and health utilization among mothers of medically fragile infants

Objective: To determine the burden of perinatal morbidity among mothers of medically fragile infants. Study design: We conducted a retrospective cohort study of 6849 mothers who delivered liveborn infants at a quaternary care hospital during a two-year period. We compared mothers of well babies with mothers of infants admitted to the Neonatal Intensive Care Unit (NICU), and we used logistic regression to model predictors of postpartum acute care utilization among NICU mothers. Results: Rates of obstetric morbidity were highest for mothers of infants staying ≥72 h in the NICU; 54.2% underwent cesarean birth, 7.5% experienced severe maternal morbidity, and 6.6% required a blood transfusion. Factors independently associated with postpartum acute care use included gestational age 38 °C and receiving psychiatric medication during the birth hospitalization. Conclusion: Focused support for mothers of NICU infants has the potential to reduce maternal morbidity and improve health

The Complexity of the Empire Colouring Problem

We investigate the computational complexity of the empire colouring problem (as defined by Percy Heawood in 1890) for maps containing empires formed by exactly $r > 1$ countries each. We prove that the problem can be solved in polynomial time using $s$ colours on maps whose underlying adjacency graph has no induced subgraph of average degree larger than $s/r$. However, if $s \geq 3$, the problem is NP-hard even if the graph is a forest of paths of arbitrary lengths (for any $r \geq 2$, provided $s < 2r - \sqrt(2r + 1/4+ 3/2)$. Furthermore we obtain a complete characterization of the problem's complexity for the case when the input graph is a tree, whereas our result for arbitrary planar graphs fall just short of a similar dichotomy. Specifically, we prove that the empire colouring problem is NP-hard for trees, for any $r \geq 2$, if $3 \leq s \leq 2r-1$ (and polynomial time solvable otherwise). For arbitrary planar graphs we prove NP-hardness if $s<7$ for $r=2$, and $s < 6r-3$, for $r \geq 3$. The result for planar graphs also proves the NP-hardness of colouring with less than 7 colours graphs of thickness two and less than $6r-3$ colours graphs of thickness $r \geq 3$.Comment: 23 pages, 12 figure