Minimal subtraction and the Callan-Symanzik equation

The usual proof of renormalizability using the Callan-Symanzik equation makes explicit use of normalization conditions. It is shown that demanding that the renormalization group functions take the form required for minimal subtraction allows one to prove renormalizability using the Callan-Symanzik equation, without imposing normalization conditions. Scalar field theory and quantum electrodynamics are treated.Comment: 6 pages, plain Te

Whole family-based physical activity promotion intervention: the Families Reporting Every Step to Health pilot randomised controlled trial protocol

Introduction : Family-based physical activity (PA) interventions present a promising avenue to promote children’s activity, however, high-quality experimental research is lacking. This paper describes the protocol for the FRESH (Families Reporting Every Step to Health) pilot trial, a child-led family-based PA intervention delivered online.  Methods and analysis : FRESH is a three-armed, parallel-group, randomised controlled pilot trial using a 1:1:1 allocation ratio with follow-up assessments at 8- and 52-weeks post-baseline. Families will be eligible if a minimum of one child in school Years 3-6 (aged 7-11 years) and at least one adult responsible for that child are willing to participate. Family members can take part in the intervention irrespective of their participation in the accompanying evaluation and vice versa. Following baseline assessment, families will be randomly allocated to one of three arms: (1) FRESH, (2) pedometer-only, or (3) no-intervention control. All family members in the pedometer-only and FRESH arms receive pedometers and generic PA promotion information. FRESH families additionally receive access to the intervention website; allowing participants to select step challenges to ‘travel’ to target cities around the world, log steps, and track progress as they virtually globetrot. Control families will receive no treatment. All family members will be eligible to participate in the evaluation with two follow-ups (8 and 52 weeks). Physical (e.g., fitness, blood pressure), psychosocial (e.g., social support), and behavioural (e.g., objectively-measured family PA) measures will be collected each time point. At 8-week follow-up, a mixed-methods process evaluation will be conducted (questionnaires and family focus groups) assessing acceptability of the intervention and evaluation. FRESH families’ website engagement will also be explored.  Ethics and dissemination : This study received ethical approval from the Ethics Committee for the School of the Humanities and Social Sciences at the University of Cambridge. Findings will be disseminated via peer-reviewed publications, conferences, and to participating families

Effective and resource-efficient strategies for recruiting families in physical activity, sedentary behavior, nutrition, and obesity prevention research: A systematic review with expert opinion.

We systematically identified effective and resource-efficient strategies for recruiting families into health promoting intervention research. Four databases were searched for reviews. Interventions were extracted from included reviews. Additionally, a Delphi study was conducted with 35 experts in family-based research. We assessed extracted data from our review and Delphi participants' opinions by collating responses into overarching themes based on recruitment setting then recruitment strategies to identify effective and resource-efficient strategies for recruiting families into intervention research. A total of 64 articles (n = 49 studies) were included. Data regarding recruitment duration (33%), target sample size (32%), reach (18%), expressions of interest (33%), and enrollment rate (22%) were scarcely reported. Recruitment settings (84%) and strategies (73%) used were available for most studies. However, the details were vague, particularly regarding who was responsible for recruitment or how recruitment strategies were implemented. The Delphi showed recruitment settings, and strategies fell under six themes: school-based, print/electronic media, community settings-based, primary care-based, employer-based, and referral-based strategies. Underrecruitment in family-based trials is a major issue. Reporting on recruitment can be improved by better adherence to existing guidelines. Our findings suggest a multifaceted recruitment approach targeting adults and children with multiple exposures to study information.This work was supported by the National Institute for Health Research Public Health 16 Research Programme (project number 15/01/19). Funding was also received from the Medical 17 Research Council (project number MC_UU_12015/7) and National Institute for Health Research 18 Biomedical Research Centre Cambridge: Nutrition, Diet, and Lifestyle Research Theme (Grant IS19 BRC-1215-20014)

Renormalization of composite operators

The blocked composite operators are defined in the one-component Euclidean scalar field theory, and shown to generate a linear transformation of the operators, the operator mixing. This transformation allows us to introduce the parallel transport of the operators along the RG trajectory. The connection on this one-dimensional manifold governs the scale evolution of the operator mixing. It is shown that the solution of the eigenvalue problem of the connection gives the various scaling regimes and the relevant operators there. The relation to perturbative renormalization is also discussed in the framework of the $\phi^3$ theory in dimension $d=6$.Comment: 24 pages, revtex (accepted by Phys. Rev. D), changes in introduction and summar

Critical specific heats of the N-vector spin models on the sc and the bcc lattices

We have computed through order $\beta^{21}$ the high-temperature expansions for the nearest-neighbor spin correlation function $G(N,\beta)$ of the classical N-vector model, with general N, on the simple-cubic and on the body-centered-cubic lattices. For this model, also known in quantum field theory as the lattice O(N) nonlinear sigma model, we have presented in previous papers extended expansions of the susceptibility, of its second field derivative and of the second moment of the correlation function. Here we study the internal specific energy and the specific heat $C(N,\beta)$, obtaining new estimates of the critical parameters and therefore a more accurate direct test of the hyperscaling relation $d \nu(N)=2 - \alpha(N)$ on a range of values of the spin dimensionality N, including N=0 [the self-avoiding walk model], N=1 [the Ising spin 1/2 model], N=2 [the XY model], N=3 [the classical Heisenberg model]. By the newly extended series, we also compute the universal combination of critical amplitudes usually denoted by $R^+_{\xi}(N)$, in fair agreement with renormalization group estimates.Comment: 15 pages, latex, no figure

Gawky is a component of cytoplasmic mRNA processing bodies required for early Drosophila development

In mammalian cells, the GW182 protein localizes to cytoplasmic bodies implicated in the regulation of messenger RNA (mRNA) stability, translation, and the RNA interference pathway. Many of these functions have also been assigned to analogous yeast cytoplasmic mRNA processing bodies. We have characterized the single Drosophila melanogaster homologue of the human GW182 protein family, which we have named Gawky (GW). Drosophila GW localizes to punctate, cytoplasmic foci in an RNA-dependent manner. Drosophila GW bodies (GWBs) appear to function analogously to human GWBs, as human GW182 colocalizes with GW when expressed in Drosophila cells. The RNA-induced silencing complex component Argonaute2 and orthologues of LSm4 and Xrn1 (Pacman) associated with 5′–3′ mRNA degradation localize to some GWBs. Reducing GW activity by mutation or antibody injection during syncytial embryo development leads to abnormal nuclear divisions, demonstrating an early requirement for GWB-mediated cytoplasmic mRNA regulation. This suggests that gw represents a previously unknown member of a small group of genes that need to be expressed zygotically during early embryo development

Diluted Networks of Nonlinear Resistors and Fractal Dimensions of Percolation Clusters

We study random networks of nonlinear resistors, which obey a generalized Ohm's law, $V\sim I^r$. Our renormalized field theory, which thrives on an interpretation of the involved Feynman Diagrams as being resistor networks themselves, is presented in detail. By considering distinct values of the nonlinearity r, we calculate several fractal dimensions characterizing percolation clusters. For the dimension associated with the red bonds we show that $d_{\scriptsize red} = 1/\nu$ at least to order {\sl O} (\epsilon^4), with $\nu$ being the correlation length exponent, and $\epsilon = 6-d$, where d denotes the spatial dimension. This result agrees with a rigorous one by Coniglio. Our result for the chemical distance, d_{\scriptsize min} = 2 - \epsilon /6 - [ 937/588 + 45/49 (\ln 2 -9/10 \ln 3)] (\epsilon /6)^2 + {\sl O} (\epsilon^3) verifies a previous calculation by one of us. For the backbone dimension we find D_B = 2 + \epsilon /21 - 172 \epsilon^2 /9261 + 2 (- 74639 + 22680 \zeta (3))\epsilon^3 /4084101 + {\sl O} (\epsilon^4), where $\zeta (3) = 1.202057...$, in agreement to second order in $\epsilon$ with a two-loop calculation by Harris and Lubensky.Comment: 29 pages, 7 figure

The cellular and synaptic architecture of the mechanosensory dorsal horn

The deep dorsal horn is a poorly characterized spinal cord region implicated in processing low-threshold mechanoreceptor (LTMR) information. We report an array of mouse genetic tools for defining neuronal components and functions of the dorsal horn LTMR-recipient zone (LTMR-RZ), a role for LTMR-RZ processing in tactile perception, and the basic logic of LTMR-RZ organization. We found an unexpectedly high degree of neuronal diversity in the LTMR-RZ: seven excitatory and four inhibitory subtypes of interneurons exhibiting unique morphological, physiological, and synaptic properties. Remarkably, LTMRs form synapses on between four and 11 LTMR-RZ interneuron subtypes, while each LTMR-RZ interneuron subtype samples inputs from at least one to three LTMR classes, as well as spinal cord interneurons and corticospinal neurons. Thus, the LTMR-RZ is a somatosensory processing region endowed with a neuronal complexity that rivals the retina and functions to pattern the activity of ascending touch pathways that underlie tactile perception

N-vector spin models on the sc and the bcc lattices: a study of the critical behavior of the susceptibility and of the correlation length by high temperature series extended to order beta^{21}

High temperature expansions for the free energy, the susceptibility and the second correlation moment of the classical N-vector model [also known as the O(N) symmetric classical spin Heisenberg model or as the lattice O(N) nonlinear sigma model] on the sc and the bcc lattices are extended to order beta^{21} for arbitrary N. The series for the second field derivative of the susceptibility is extended to order beta^{17}. An analysis of the newly computed series for the susceptibility and the (second moment) correlation length yields updated estimates of the critical parameters for various values of the spin dimensionality N, including N=0 [the self-avoiding walk model], N=1 [the Ising spin 1/2 model], N=2 [the XY model], N=3 [the Heisenberg model]. For all values of N, we confirm a good agreement with the present renormalization group estimates. A study of the series for the other observables will appear in a forthcoming paper.Comment: Revised version to appear in Phys. Rev. B Sept. 1997. Revisions include an improved series analysis biased with perturbative values of the scaling correction exponents computed by A. I. Sokolov. Added a reference to estimates of exponents for the Ising Model. Abridged text of 19 pages, latex, no figures, no tables of series coefficient