Graph complexes in deformation quantization

Kontsevich's formality theorem and the consequent star-product formula rely on the construction of an $L_\infty$-morphism between the DGLA of polyvector fields and the DGLA of polydifferential operators. This construction uses a version of graphical calculus. In this article we present the details of this graphical calculus with emphasis on its algebraic features. It is a morphism of differential graded Lie algebras between the Kontsevich DGLA of admissible graphs and the Chevalley-Eilenberg DGLA of linear homomorphisms between polyvector fields and polydifferential operators. Kontsevich's proof of the formality morphism is reexamined in this light and an algebraic framework for discussing the tree-level reduction of Kontsevich's star-product is described.Comment: 39 pages; 3 eps figures; uses Xy-pic. Final version. Details added, mainly concerning the tree-level approximation. Typos corrected. An abridged version will appear in Lett. Math. Phy

Molecular-orbital-free algorithm for excited states in time-dependent perturbation theory

A non-linear conjugate gradient optimization scheme is used to obtain excitation energies within the Random Phase Approximation (RPA). The solutions to the RPA eigenvalue equation are located through a variational characterization using a modified Thouless functional, which is based upon an asymmetric Rayleigh quotient, in an orthogonalized atomic orbital representation. In this way, the computational bottleneck of calculating molecular orbitals is avoided. The variational space is reduced to the physically-relevant transitions by projections. The feasibility of an RPA implementation scaling linearly with system size, N, is investigated by monitoring convergence behavior with respect to the quality of initial guess and sensitivity to noise under thresholding, both for well- and ill-conditioned problems. The molecular- orbital-free algorithm is found to be robust and computationally efficient providing a first step toward a large-scale, reduced complexity calculation of time-dependent optical properties and linear response. The algorithm is extensible to other forms of time-dependent perturbation theory including, but not limited to, time-dependent Density Functional theory.Comment: 9 pages, 7 figure

The Hopf Algebra of Renormalization, Normal Coordinates and Kontsevich Deformation Quantization

Using normal coordinates in a Poincar\'e-Birkhoff-Witt basis for the Hopf algebra of renormalization in perturbative quantum field theory, we investigate the relation between the twisted antipode axiom in that formalism, the Birkhoff algebraic decomposition and the universal formula of Kontsevich for quantum deformation.Comment: 21 pages, 15 figure

Topological entropy of a stiff ring polymer and its connection to DNA knots

We discuss the entropy of a circular polymer under a topological constraint. We call it the {\it topological entropy} of the polymer, in short. A ring polymer does not change its topology (knot type) under any thermal fluctuations. Through numerical simulations using some knot invariants, we show that the topological entropy of a stiff ring polymer with a fixed knot is described by a scaling formula as a function of the thickness and length of the circular chain. The result is consistent with the viewpoint that for stiff polymers such as DNAs, the length and diameter of the chains should play a central role in their statistical and dynamical properties. Furthermore, we show that the new formula extends a known theoretical formula for DNA knots.Comment: 14pages,11figure

Advances in low-memory subgradient optimization

One of the main goals in the development of non-smooth optimization is to cope with high dimensional problems by decomposition, duality or Lagrangian relaxation which greatly reduces the number of variables at the cost of worsening differentiability of objective or constraints. Small or medium dimensionality of resulting non-smooth problems allows to use bundle-type algorithms to achieve higher rates of convergence and obtain higher accuracy, which of course came at the cost of additional memory requirements, typically of the order of n2, where n is the number of variables of non-smooth problem. However with the rapid development of more and more sophisticated models in industry, economy, finance, et all such memory requirements are becoming too hard to satisfy. It raised the interest in subgradient-based low-memory algorithms and later developments in this area significantly improved over their early variants still preserving O(n) memory requirements. To review these developments this chapter is devoted to the black-box subgradient algorithms with the minimal requirements for the storage of auxiliary results, which are necessary to execute these algorithms. To provide historical perspective this survey starts with the original result of N.Z. Shor which opened this field with the application to the classical transportation problem. The theoretical complexity bounds for smooth and non-smooth convex and quasi-convex optimization problems are briefly exposed in what follows to introduce to the relevant fundamentals of non-smooth optimization. Special attention in this section is given to the adaptive step-size policy which aims to attain lowest complexity bounds. Unfortunately the non-differentiability of objective function in convex optimization essentially slows down the theoretical low bounds for the rate of convergence in subgradient optimization compared to the smooth case but there are different modern techniques that allow to solve non-smooth convex optimization problems faster then dictate lower complexity bounds. In this work the particular attention is given to Nesterov smoothing technique, Nesterov Universal approach, and Legendre (saddle point) representation approach. The new results on Universal Mirror Prox algorithms represent the original parts of the survey. To demonstrate application of non-smooth convex optimization algorithms for solution of huge-scale extremal problems we consider convex optimization problems with non-smooth functional constraints and propose two adaptive Mirror Descent methods. The first method is of primal-dual variety and proved to be optimal in terms of lower oracle bounds for the class of Lipschitz-continuous convex objective and constraints. The advantages of application of this method to sparse Truss Topology Design problem are discussed in certain details. The second method can be applied for solution of convex and quasi-convex optimization problems and is optimal in a sense of complexity bounds. The conclusion part of the survey contains the important references that characterize recent developments of non-smooth convex optimization

Derivation of Myoepithelial Progenitor Cells from Bipotent Mammary Stem/Progenitor Cells

There is increasing evidence that breast and other cancers originate from and are maintained by a small fraction of stem/progenitor cells with self-renewal properties. Recent molecular profiling has identified six major subtypes of breast cancer: basal-like, ErbB2-overexpressing, normal breast epithelial-like, luminal A and B, and claudin-low subtypes. To help understand the relationship among mammary stem/progenitor cells and breast cancer subtypes, we have recently derived distinct hTERT-immortalized human mammary stem/progenitor cell lines: a K5+/K19− type, and a K5+/K19+ type. Under specific culture conditions, bipotent K5+/K19− stem/progenitor cells differentiated into stable clonal populations that were K5−/K19− and exhibit self-renewal and unipotent myoepithelial differentiation potential in contrast to the parental K5+/K19− cells which are bipotent. These K5−/K19− cells function as myoepithelial progenitor cells and constitutively express markers of an epithelial to mesenchymal transition (EMT) and show high invasive and migratory abilities. In addition, these cells express a microarray signature of claudin-low breast cancers. The EMT characteristics of an un-transformed unipotent mammary myoepithelial progenitor cells together with claudin-low signature suggests that the claudin-low breast cancer subtype may arise from myoepithelial lineage committed progenitors. Availability of immortal MPCs should allow a more definitive analysis of their potential to give rise to claudin-low breast cancer subtype and facilitate biological and molecular/biochemical studies of this disease

Differential In Vitro Effects of Intravenous versus Oral Formulations of Silibinin on the HCV Life Cycle and Inflammation

Silymarin prevents liver disease in many experimental rodent models, and is the most popular botanical medicine consumed by patients with hepatitis C. Silibinin is a major component of silymarin, consisting of the flavonolignans silybin A and silybin B, which are insoluble in aqueous solution. A chemically modified and soluble version of silibinin, SIL, has been shown to potently reduce hepatitis C virus (HCV) RNA levels in vivo when administered intravenously. Silymarin and silibinin inhibit HCV infection in cell culture by targeting multiple steps in the virus lifecycle. We tested the hepatoprotective profiles of SIL and silibinin in assays that measure antiviral and anti-inflammatory functions. Both mixtures inhibited fusion of HCV pseudoparticles (HCVpp) with fluorescent liposomes in a dose-dependent fashion. SIL inhibited 5 clinical genotype 1b isolates of NS5B RNA dependent RNA polymerase (RdRp) activity better than silibinin, with IC50 values of 40–85 µM. The enhanced activity of SIL may have been in part due to inhibition of NS5B binding to RNA templates. However, inhibition of the RdRps by both mixtures plateaued at 43–73%, suggesting that the products are poor overall inhibitors of RdRp. Silibinin did not inhibit HCV replication in subgenomic genotype 1b or 2a replicon cell lines, but it did inhibit JFH-1 infection. In contrast, SIL inhibited 1b but not 2a subgenomic replicons and also inhibited JFH-1 infection. Both mixtures inhibited production of progeny virus particles. Silibinin but not SIL inhibited NF-κB- and IFN-B-dependent transcription in Huh7 cells. However, both mixtures inhibited T cell proliferation to similar degrees. These data underscore the differences and similarities between the intravenous and oral formulations of silibinin, which could influence the clinical effects of this mixture on patients with chronic liver diseases

Analysis of the TGFβ functional pathway in epithelial ovarian carcinoma

Epithelial ovarian carcinoma is often diagnosed at an advanced stage of disease and is the leading cause of death from gynaecological neoplasia. The genetic changes that occur during the development of this carcinoma are poorly understood. It has been proposed that IGFIIR, TGFβ1 and TGFβRII act as a functional unit in the TGFβ growth inhibitory pathway, and that somatic loss-of-function mutations in any one of these genes could lead to disruption of the pathway and subsequent loss of cell cycle control. We have examined these 3 genes in 25 epithelial ovarian carcinomas using single-stranded conformational polymorphism analysis and DNA sequence analysis. A total of 3 somatic missense mutations were found in the TGFβRII gene, but none in IGFRII or TGFβ1. An association was found between TGFβRII mutations and histology, with 2 out of 3 clear cell carcinomas having TGFβRII mutations. This data supports other evidence from mutational analysis of the PTEN and β-catenin genes that there are distinct developmental pathways responsible for the progression of different epithelial ovarian cancer histologic subtypes. © 2001 Cancer Research Campaign http://www.bjcancer.co