Refinement of Novikov - Betti numbers and of Novikov homology provided by an angle valued map

To a pair (X,f), X compact ANR and f a continuous angle valued map defined on X, a fixed field and a nonnegative integer one assigns a finite configuration of complex numbers with multiplicities located in the punctured complex plane and a finite configuration of free modules over the ring of Laurent polynomials (with coefficients in the fixed field) indexed by the same complex numbers. This is done in analogy with the configuration of eigenvalues and of generalized eigenspaces of an invertible linear operator in a finite dimensional complex vector space. The configuration of complex numbers refines the Novikov - Betti number and the configuration of free modules refines the Novikov homology associated with the cohomology class defined by f, in the same way the collection of eigenvalues and of generalized eigen-spaces refine the dimension of the vector space and the vector space on which the operator acts. In the case the field is the field of complex numbers the configuration of free modules induces by "von-Neumann completion" a configuration of mutually orthogonal closed Hilbert submodules of the L 2--homology of the infinite cyclic cover of X determined by the map f, which is an Hilbert module over the von-Neumann algebra of complex L-infinity functions on the unit circle in the complex plane

A simplified test of universality in Lattice QCD

A simplified test of universality in Lattice QCD is performed by analytically evaluating the continuous Euclidean time limits of various lattice fermion determinants, both with and without a Wilson term to lift the fermion doubling on the Euclidean time axis, and comparing them with each other and with the zeta-regularised fermion determinant in the continuous time--lattice space setting. The determinant relations expected from universality considerations are found to be violated by a certain gauge field-dependent factor, i.e. we uncover a "universality anomaly". The physical significance, or lack thereof, of this factor is a delicate question which remains to be settled.Comment: 6 pages. v2: Revised to include a further result on the zeta-regularised fermion determinant in the continuous time--lattice space setting which impacts on the conclusions; typos corrected; acknowledgement and reference added; to appear in Phys.Rev.Let

Comparison of Allen Carr's Easyway programme with a specialist behavioural and pharmacological smoking cessation support service: a randomized controlled trial.

BACKGROUND AND AIMS: A combination of behavioural and pharmacological support is judged to be the optimal approach for assisting smoking cessation. Allen Carr's Easyway (ACE) is a single-session pharmacotherapy-free programme that has been in operation internationally for 38 years. We compared the effectiveness of ACE with specialist behavioural and pharmacological support delivered to the national standard in England. DESIGN: A two-arm, parallel-group, single-blind, randomized controlled trial. SETTING: London, UK, between February 2017 and May 2018. PARTICIPANTS: A total of 620 participants (310 in ACE and 310 in the combined behavioural and pharmacological support condition) were included in the analysis. Adult (≥ 18 years) smokers wanting to quit were randomized in a 1 : 1 ratio. Mean age for the total sample was 40.8 years, with 53.4% being male. Participant baseline characteristics (ethnicity, educational level, number of previous quit attempts, nicotine dependence) were evenly balanced between treatment groups. INTERVENTION AND COMPARATOR: The intervention was the ACE method of stopping smoking. This centres on a 4.5-6-hour session of group-based support, alongside subsequent text messages and top-up sessions if needed. It aims to make it easy to stop smoking by convincing smokers that smoking provides no benefits for them. The comparator was a specialist stop smoking service (SSS) providing behavioural and pharmacological support in accordance with national standards. MEASUREMENTS: The primary outcome was self-reported continuous abstinence for 26 weeks from the quit/quit re-set date verified by exhaled breath carbon monoxide measurement < 10 parts per million (p.p.m.). Primary analysis was by intention to treat. Secondary outcomes were: use of pharmacotherapy, adverse events and continuous abstinence up to 4 and 12 weeks. FINDINGS: A total of 468 participants attended treatment (255 ACE versus 213 SSS, P < 0.05). Of those who did attend treatment, 100 completed 6-month measures (23.7% ACE versus 20.7% SSS). Continuous abstinence to 26 weeks was 19.4% (60 of 310) in the ACE intervention and 14.8% (46 of 310) in the SSS intervention [risk difference for ACE versus SSS 4.5% (95% confidence interval (CI) = -1.4 to 10.4%, odds ratio (OR) = 1.38)]. The Bayes factor for superiority of the ACE condition was 1.24. CONCLUSION: There was no clear evidence of a difference in the efficacies of the Allen Carr's Easyway (ACE) and specialist smoking cessation support involving behavioural support and pharmacotherapy

P(phi)_2 quantum field theories and Segal's axioms

We show that P(phi)_2 quantum field theories satisfy axioms of the type advocated by Graeme Segal.Comment: final version; to appear in Comm. Math. Phy