Combinatorial Hopf algebras in quantum field theory I

This manuscript stands at the interface between combinatorial Hopf algebra theory and renormalization theory. Its plan is as follows: Section 1 is the introduction, and contains as well an elementary invitation to the subject. The rest of part I, comprising Sections 2-6, is devoted to the basics of Hopf algebra theory and examples, in ascending level of complexity. Part II turns around the all-important Faa di Bruno Hopf algebra. Section 7 contains a first, direct approach to it. Section 8 gives applications of the Faa di Bruno algebra to quantum field theory and Lagrange reversion. Section 9 rederives the related Connes-Moscovici algebras. In Part III we turn to the Connes-Kreimer Hopf algebras of Feynman graphs and, more generally, to incidence bialgebras. In Section10 we describe the first. Then in Section11 we give a simple derivation of (the properly combinatorial part of) Zimmermann's cancellation-free method, in its original diagrammatic form. In Section 12 general incidence algebras are introduced, and the Faa di Bruno bialgebras are described as incidence bialgebras. In Section 13, deeper lore on Rota's incidence algebras allows us to reinterpret Connes-Kreimer algebras in terms of distributive lattices. Next, the general algebraic-combinatorial proof of the cancellation-free formula for antipodes is ascertained; this is the heart of the paper. The structure results for commutative Hopf algebras are found in Sections 14 and 15. An outlook section very briefly reviews the coalgebraic aspects of quantization and the Rota-Baxter map in renormalization.Comment: 94 pages, LaTeX figures, precisions made, typos corrected, more references adde

Comparison of dynamical decoupling protocols for a nitrogen-vacancy center in diamond

We perform a detailed theoretical-experimental study of the dynamical decoupling (DD) of the nitrogen-vacancy (NV) center in diamond. We investigate the DD sequences applied to suppress the dephasing of the electron spin of the NV center induced by the coupling to a spin bath composed of the substitutional nitrogen atoms. The decoupling efficiency of various DD schemes is studied, including both periodic and periodic pulse sequences. For ideal control pulses, we find that the DD protocols with the Carr-Purcell-Meiboom-Gill (CPMG) timing of the pulses provides best performance. We show that, as the number of control pulses increases, the decoupling fidelity scaling differs qualitatively from the predictions of the Magnus expansion, and explain the origin of this difference. In particular, more advanced symmetrized or concatenated protocols do not improve the DD performance. Next, we investigate the impact of the systematic instrumental pulse errors in different periodic and aperiodic pulse sequences. The DD protocols with the single-axis control do not preserve all spin components in the presence of the pulse errors, and the two-axis control is needed. We demonstrate that the two-axis control sequence with the CPMG timing is very robust with respect to the pulse errors. The impact of the pulse errors can be diminished further by symmetrizing this protocol. For all protocols studied here, we present a detailed account of the pulse error parameters which make strongest impact on the DD performance. In conclusion, we give specific recommendations about choosing the decoupling protocol for the system under investigation.Comment: 16 pages, 11 figure

BubR1 as a prognostic marker for recurrence-free survival rates in epithelial ovarian cancers

BACKGROUND: Epithelial ovarian cancer is one of the most lethal malignancies, and has a high recurrence rate. Thus, prognostic markers for recurrence are crucial for the care of ovarian cancer. As ovarian cancers frequently exhibit chromosome instability, we aimed at assessing the prognostic significance of two key mitotic kinases, BubR1 and Aurora A. METHODS: We analysed paraffin-embedded tissue sections from 160 ovarian cancer patients whose clinical outcomes had been tracked after first-line treatment. RESULTS: The median recurrence-free survival in patients with a positive and negative expression of BubR1 was 27 and 83 months, respectively (Po0.001). A positive BubR1 expression was also associated with advanced stage, serous histology and high grade. In contrast, Aurora A immunostaining did not correlate with any of the clinical parameters analysed. CONCLUSION: BubR1, but not Aurora A, is a prognostic marker for recurrence-free survival rates in epithelial ovarian cancers.Research in the H Lee laboratory is funded by the National Research Laboratory Program from the Korean ministry of Education and Science (ROA-2008-000-20023-0). This work was also supported by the Seoul National University Hospital Grant (0420080450), the 21C Frontier Functional Genome Project (FG06- 2-14) of the Korean ministry of Education and Science, Korea Research Foundation (KRF-2005-C00097), and the National R&D Program for Cancer Control (0620070) from the Korean ministry of Health welfare and Family Affairs. Imaging facilities in the H Lee laboratory are funded by RCFC (R11-2005-009-04003-0) of the SRC program from KOSEF