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

Evaluation of the current knowledge limitations in breast cancer research: a gap analysis

BACKGROUND A gap analysis was conducted to determine which areas of breast cancer research, if targeted by researchers and funding bodies, could produce the greatest impact on patients. METHODS Fifty-six Breast Cancer Campaign grant holders and prominent UK breast cancer researchers participated in a gap analysis of current breast cancer research. Before, during and following the meeting, groups in seven key research areas participated in cycles of presentation, literature review and discussion. Summary papers were prepared by each group and collated into this position paper highlighting the research gaps, with recommendations for action. RESULTS Gaps were identified in all seven themes. General barriers to progress were lack of financial and practical resources, and poor collaboration between disciplines. Critical gaps in each theme included: (1) genetics (knowledge of genetic changes, their effects and interactions); (2) initiation of breast cancer (how developmental signalling pathways cause ductal elongation and branching at the cellular level and influence stem cell dynamics, and how their disruption initiates tumour formation); (3) progression of breast cancer (deciphering the intracellular and extracellular regulators of early progression, tumour growth, angiogenesis and metastasis); (4) therapies and targets (understanding who develops advanced disease); (5) disease markers (incorporating intelligent trial design into all studies to ensure new treatments are tested in patient groups stratified using biomarkers); (6) prevention (strategies to prevent oestrogen-receptor negative tumours and the long-term effects of chemoprevention for oestrogen-receptor positive tumours); (7) psychosocial aspects of cancer (the use of appropriate psychosocial interventions, and the personal impact of all stages of the disease among patients from a range of ethnic and demographic backgrounds). CONCLUSION Through recommendations to address these gaps with future research, the long-term benefits to patients will include: better estimation of risk in families with breast cancer and strategies to reduce risk; better prediction of drug response and patient prognosis; improved tailoring of treatments to patient subgroups and development of new therapeutic approaches; earlier initiation of treatment; more effective use of resources for screening populations; and an enhanced experience for people with or at risk of breast cancer and their families. The challenge to funding bodies and researchers in all disciplines is to focus on these gaps and to drive advances in knowledge into improvements in patient care

Perturbed myoepithelial cell differentiation in BRCA mutation carriers and in ductal carcinoma in situ.

Myoepithelial cells play key roles in normal mammary gland development and in limiting pre-invasive to invasive breast tumor progression, yet their differentiation and perturbation in ductal carcinoma in situ (DCIS) are poorly understood. Here, we investigated myoepithelial cells in normal breast tissues of BRCA1 and BRCA2 germline mutation carriers and in non-carrier controls, and in sporadic DCIS. We found that in the normal breast of non-carriers, myoepithelial cells frequently co-express the p63 and TCF7 transcription factors and that p63 and TCF7 show overlapping chromatin peaks associated with differentiated myoepithelium-specific genes. In contrast, in normal breast tissues of BRCA1 mutation carriers the frequency of p63+TCF7+ myoepithelial cells is significantly decreased and p63 and TCF7 chromatin peaks do not overlap. These myoepithelial perturbations in normal breast tissues of BRCA1 germline mutation carriers may play a role in their higher risk of breast cancer. The fraction of p63+TCF7+ myoepithelial cells is also significantly decreased in DCIS, which may be associated with invasive progression

A novel spontaneous model of epithelial-mesenchymal transition (EMT) using a primary prostate cancer derived cell line demonstrating distinct stem-like characteristics

Cells acquire the invasive and migratory properties necessary for the invasion-metastasis cascade and the establishment of aggressive, metastatic disease by reactivating a latent embryonic programme: epithelial-to-mesenchymal transition (EMT). Herein, we report the development of a new, spontaneous model of EMT which involves four phenotypically distinct clones derived from a primary tumour-derived human prostate cancer cell line (OPCT-1), and its use to explore relationships between EMT and the generation of cancer stem cells (CSCs) in prostate cancer. Expression of epithelial (E-cadherin) and mesenchymal markers (vimentin, fibronectin) revealed that two of the four clones were incapable of spontaneously activating EMT, whereas the others contained large populations of EMT-derived, vimentin-positive cells having spindle-like morphology. One of the two EMT-positive clones exhibited aggressive and stem cell-like characteristics, whereas the other was non-aggressive and showed no stem cell phenotype. One of the two EMT-negative clones exhibited aggressive stem cell-like properties, whereas the other was the least aggressive of all clones. These findings demonstrate the existence of distinct, aggressive CSC-like populations in prostate cancer, but, importantly, that not all cells having a potential for EMT exhibit stem cell-like properties. This unique model can be used to further interrogate the biology of EMT in prostate cancer

The role of autophagy in the cross-talk between epithelial-mesenchymal transitioned tumor cells and cancer stem-like cells

Epithelial-mesenchymal transition (EMT) and cancer stem-like cells (CSC) are becoming highly relevant targets in anticancer drug discovery. A large body of evidence suggests that epithelial-mesenchymal transitioned tumor cells (EMT tumor cells) and CSCs have similar functions. There is also an overlap regarding the stimuli that can induce the generation of EMT tumor cells and CSCs. Moreover, direct evidence has been brought that EMT can give rise to CSCs. It is unclear however, whether EMT tumor cells should be considered CSCs or if they have to undergo further changes. In this article we summarize available evidence suggesting that, indeed, additional programs must be engaged and we propose that macroautophagy (hereafter, autophagy) represents a key trait distinguishing CSCs from EMT tumor cells. Thus, CSCs have often been reported to be in an autophagic state and blockade of autophagy inhibits CSCs. On the other hand, there is ample evidence showing that EMT and autophagy are distinct events. CSCs, however, represent, by themselves, a heterogeneous population. Thus, CSCs have been distinguished in predominantly noncycling and cycling CSCs, the latter representing CSCs that self-renew and replenish the pool of differentiated tumor cells. We now suggest that the non-cycling CSC subpopulation is in an autophagic state. We propose also two models to explain the relationship between EMT tumor cells and these two major CSC subpopulations: a branching model in which EMT tumor cells can give rise to cycling or non-cycling CSCs, respectively, and a hierarchical model in which EMT tumor cells are first induced to become autophagic CSCs and, subsequently, cycling CSCs. Finally, we address the therapeutic consequences of these insights

Metformin as an Adjunctive Therapy for Pancreatic Cancer: A Review of the Literature on Its Potential Therapeutic Use

Pancreatic ductal adenocarcinoma has the worst prognosis of any cancer. New adjuvant chemotherapies are urgently required, which are well tolerated by patients with unresectable cancers. This paper reviews the existing proof of concept data, namely laboratory, pharmacoepidemiological, experimental medicine and clinical trial evidence for investigating metformin in patients with pancreatic ductal adenocarcinoma. Laboratory evidence shows metformin inhibits mitochondrial ATP synthesis which directly and indirectly inhibits carcinogenesis. Drug–drug interactions of metformin with proton pump inhibitors and histamine H2-receptor antagonists may be of clinical relevance and pertinent to future research of metformin in pancreatic ductal adenocarcinoma. To date, most cohort studies have demonstrated a positive association with metformin on survival in pancreatic ductal adenocarcinoma, although there are many methodological limitations with such study designs. From experimental medicine studies, there are sparse data in humans. The current trials of metformin have methodological limitations. Two small randomized controlled trials (RCTs) reported null findings, but there were potential inequalities in cancer staging between groups and poor compliance with the intervention. Proof of concept data, predominantly from laboratory work, supports assessing metformin as an adjunct for pancreatic ductal adenocarcinoma in RCTs. Ideally, more experimental medicine studies are needed for proof of concept. However, many feasibility criteria need to be answered before such trials can progress