Formality properties of finitely generated groups and Lie algebras

We explore the graded and filtered formality properties of finitely generated groups by studying the various Lie algebras over a field of characteristic 0 attached to such groups, including the Malcev Lie algebra, the associated graded Lie algebra, the holonomy Lie algebra, and the Chen Lie algebra. We explain how these notions behave with respect to split injections, coproducts, direct products, as well as field extensions, and how they are inherited by solvable and nilpotent quotients. A key tool in this analysis is the 1-minimal model of the group, and the way this model relates to the aforementioned Lie algebras. Another approach to formality is provided by Taylor expansions from the group to the completion of the associated graded algebra of the group ring. We illustrate our approach with examples drawn from a variety of group-theoretic and topological contexts, such as finitely generated torsion-free nilpotent groups, link groups, and fundamental groups of Seifert fibered manifolds.Comment: 41 pages; accepted for publication in Forum Mathematicu

Model-independent Constraints on the Weak Phase α\alpha (or ϕ2\phi_2) and QCD Penguin Pollution in B→ππB \to \pi\pi Decays

We present an {\it algebraic} isospin approach towards a more straightforward and model-independent determination of the weak phase $\alpha$ (or $\phi_2$) and QCD penguin pollution in $B\to \pi\pi$ decays. The world averages of current experimental data allow us to impose some useful constraints on the isospin parameters of $B\to \pi\pi$ transitions. We find that the magnitude of $\alpha$ (or $\phi_2$) extracted from the indirect CP violation in $\pi^+\pi^-$ mode is in agreement with the standard-model expectation from other indirect measurements, but its four-fold discrete ambiguity has to be resolved in the near future.Comment: 11 pages, 3 figures, 2 table

Setting per-field normalisation hyper-parameters for the named-page finding search task

Per-field normalisation has been shown to be effective for Web search tasks, e.g. named-page finding. However, per-field normalisation also suffers from having hyper-parameters to tune on a per-field basis. In this paper, we argue that the purpose of per-field normalisation is to adjust the linear relationship between field length and term frequency. We experiment with standard Web test collections, using three document fields, namely the body of the document, its title, and the anchor text of its incoming links. From our experiments, we find that across different collections, the linear correlation values, given by the optimised hyper-parameter settings, are proportional to the maximum negative linear correlation. Based on this observation, we devise an automatic method for setting the per-field normalisation hyper-parameter values without the use of relevance assessment for tuning. According to the evaluation results, this method is shown to be effective for the body and title fields. In addition, the difficulty in setting the per-field normalisation hyper-parameter for the anchor text field is explained

Stable Sarma State in Two-band Fermi Systems

We investigate fermionic superconductivity with mismatched Fermi surfaces in a general two-band system. The exchange interaction between the two bands changes significantly the stability structure of the pairing states. The Sarma state with two gapless Fermi surfaces which is always unstable in single-band systems, can be the stable ground state in two-band systems. To realize a visible mismatch window for the stable Sarma state, two conditions should be satisfied: a nonzero inter-band exchange interaction and a large asymmetry between the two bands.Comment: V3: Version published in Physical Review