On the Fixed-Point Structure of Scalar Fields

In a recent Letter (K.Halpern and K.Huang, Phys. Rev. Lett. 74 (1995) 3526), certain properties of the Local Potential Approximation (LPA) to the Wilson renormalization group were uncovered, which led the authors to conclude that $D>2$ dimensional scalar field theories endowed with {\sl non-polynomial} interactions allow for a continuum of renormalization group fixed points, and that around the Gaussian fixed point, asymptotically free interactions exist. If true, this could herald very important new physics, particularly for the Higgs sector of the Standard Model. Continuing work in support of these ideas, has motivated us to point out that we previously studied the same properties and showed that they lead to very different conclusions. Indeed, in as much as the statements in hep-th/9406199 are correct, they point to some deep and beautiful facts about the LPA and its generalisations, but however no new physics.Comment: Typos corrected. A Comment - to be published in Phys. Rev. Lett. 1 page, 1 eps figure, uses LaTeX, RevTex and eps

Sensitivity of Nonrenormalizable Trajectories to the Bare Scale

Working in scalar field theory, we consider RG trajectories which correspond to nonrenormalizable theories, in the Wilsonian sense. An interesting question to ask of such trajectories is, given some fixed starting point in parameter space, how the effective action at the effective scale, Lambda, changes as the bare scale (and hence the duration of the flow down to Lambda) is changed. When the effective action satisfies Polchinski's version of the Exact Renormalization Group equation, we prove, directly from the path integral, that the dependence of the effective action on the bare scale, keeping the interaction part of the bare action fixed, is given by an equation of the same form as the Polchinski equation but with a kernel of the opposite sign. We then investigate whether similar equations exist for various generalizations of the Polchinski equation. Using nonperturbative, diagrammatic arguments we find that an action can always be constructed which satisfies the Polchinski-like equation under variation of the bare scale. For the family of flow equations in which the field is renormalized, but the blocking functional is the simplest allowed, this action is essentially identified with the effective action at Lambda = 0. This does not seem to hold for more elaborate generalizations.Comment: v1: 23 pages, 5 figures, v2: intro extended, refs added, published in jphy

Scheme Independence to all Loops

The immense freedom in the construction of Exact Renormalization Groups means that the many non-universal details of the formalism need never be exactly specified, instead satisfying only general constraints. In the context of a manifestly gauge invariant Exact Renormalization Group for SU(N) Yang-Mills, we outline a proof that, to all orders in perturbation theory, all explicit dependence of beta function coefficients on both the seed action and details of the covariantization cancels out. Further, we speculate that, within the infinite number of renormalization schemes implicit within our approach, the perturbative beta function depends only on the universal details of the setup, to all orders.Comment: 18 pages, 8 figures; Proceedings of Renormalization Group 2005, Helsinki, Finland, 30th August - 3 September 2005. v2: Published in jphysa; minor changes / refinements; refs. adde

Basic research in wake vortex alleviation using a variable twist wing

The variable twist wing concept was used to investigate the relative effects of lift and turbulence distribution on the rolled up vortex wake. Several methods of reducing the vortex strength behind an aircraft were identified. These involve the redistribution of lift spanwise on the wing and drag distribution along the wing. Initial attempts to use the variable twist wing velocity data to validate the WAKE computer code have shown a strong correlation, although the vorticity levels were not exactly matched

Properties of derivative expansion approximations to the renormalization group

Approximation only by derivative (or more generally momentum) expansions, combined with reparametrization invariance, turns the continuous renormalization group for quantum field theory into a set of partial differential equations which at fixed points become non-linear eigenvalue equations for the anomalous scaling dimension $\eta$. We review how these equations provide a powerful and robust means of discovering and approximating non-perturbative continuum limits. Gauge fields are briefly discussed. Particular emphasis is placed on the r\^ole of reparametrization invariance, and the convergence of the derivative expansion is addressed.Comment: (Minor touch ups of the lingo.) Invited talk at RG96, Dubna, Russia; 14 pages including 2 eps figures; uses LaTeX, epsf and sprocl.st

Epigenetic modification of the oxytocin receptor gene is associated with emotion processing in the infant brain

The neural capacity to discriminate between emotions emerges early in development, though little is known about specific factors that contribute to variability in this vital skill during infancy. In adults, DNA methylation of the oxytocin receptor gene (OXTRm) is an epigenetic modification that is variable, predictive of gene expression, and has been linked to autism spectrum disorder and the neural response to social cues. It is unknown whether OXTRm is variable in infants, and whether it is predictive of early social function. Implementing a developmental neuroimaging epigenetics approach in a large sample of infants (N = 98), we examined whether OXTRm is associated with neural responses to emotional expressions. OXTRm was assessed at 5 months of age. At 7 months of age, infants viewed happy, angry, and fearful faces while functional near-infrared spectroscopy was recorded. We observed that OXTRm shows considerable variability among infants. Critically, infants with higher OXTRm show enhanced responses to anger and fear and attenuated responses to happiness in right inferior frontal cortex, a region implicated in emotion processing through action-perception coupling. Findings support models emphasizing oxytocin's role in modulating neural response to emotion and identify OXTRm as an epigenetic mark contributing to early brain function

Holographic renormalisation group flows and renormalisation from a Wilsonian perspective

From the Wilsonian point of view, renormalisable theories are understood as submanifolds in theory space emanating from a particular fixed point under renormalisation group evolution. We show how this picture precisely applies to their gravity duals. We investigate the Hamilton-Jacobi equation satisfied by the Wilson action and find the corresponding fixed points and their eigendeformations, which have a diagonal evolution close to the fixed points. The relevant eigendeformations are used to construct renormalised theories. We explore the relation of this formalism with holographic renormalisation. We also discuss different renormalisation schemes and show that the solutions to the gravity equations of motion can be used as renormalised couplings that parametrise the renormalised theories. This provides a transparent connection between holographic renormalisation group flows in the Wilsonian and non-Wilsonian approaches. The general results are illustrated by explicit calculations in an interacting scalar theory in AdS space.Comment: 63 pages. Minor changes and references added. Matches JHEP versio

Which diagnostic tests are most useful in a chest pain unit protocol?

Background The chest pain unit (CPU) provides rapid diagnostic assessment for patients with acute, undifferentiated chest pain, using a combination of electrocardiographic (ECG) recording, biochemical markers and provocative cardiac testing. We aimed to identify which elements of a CPU protocol were most diagnostically and prognostically useful. Methods The Northern General Hospital CPU uses 2–6 hours of serial ECG / ST segment monitoring, CK-MB(mass) on arrival and at least two hours later, troponin T at least six hours after worst pain and exercise treadmill testing. Data were prospectively collected over an eighteen-month period from patients managed on the CPU. Patients discharged after CPU assessment were invited to attend a follow-up appointment 72 hours later for ECG and troponin T measurement. Hospital records of all patients were reviewed to identify adverse cardiac events over the subsequent six months. Diagnostic accuracy of each test was estimated by calculating sensitivity and specificity for: 1) acute coronary syndrome (ACS) with clinical myocardial infarction and 2) ACS with myocyte necrosis. Prognostic value was estimated by calculating the relative risk of an adverse cardiac event following a positive result. Results Of the 706 patients, 30 (4.2%) were diagnosed as ACS with myocardial infarction, 30 (4.2%) as ACS with myocyte necrosis, and 32 (4.5%) suffered an adverse cardiac event. Sensitivities for ACS with myocardial infarction and myocyte necrosis respectively were: serial ECG / ST segment monitoring 33% and 23%; CK-MB(mass) 96% and 63%; troponin T (using 0.03 ng/ml threshold) 96% and 90%. The only test that added useful prognostic information was exercise treadmill testing (relative risk 6 for cardiac death, non-fatal myocardial infarction or arrhythmia over six months). Conclusion Serial ECG / ST monitoring, as used in our protocol, adds little diagnostic or prognostic value in patients with a normal or non-diagnostic initial ECG. CK-MB(mass) can rule out ACS with clinical myocardial infarction but not myocyte necrosis(defined as a troponin elevation without myocardial infarction). Using a low threshold for positivity for troponin T improves sensitivity of this test for myocardial infarction and myocardial necrosis. Exercise treadmill testing predicts subsequent adverse cardiac events

A study of the enzymatic hydrolysis of fish frames using model systems

A model system was employed to study the operating conditions and primary parameters of enzymic hydrolysis of cod proteins. Pancreatin, papain, and bromelain were used to hydrolyse minced cod fillets under controlled conditions and with the rate of hydrolysis being continually monitored via both the pH-stat and TNBS method. The two methods were compared and evaluated. The rate of protein solubilisation was plotted against the degree of hydrolysis (DH). Dry fish protein hydrolysate (FPH) powders having short, medium and high degrees of hydrolysis (DH of approximately 8%, 11% and 16% respectively) were produced and analysed for their molecular weight distribution, using size exclusion chromatography. Almost complete protein solubilisation (75 g soluble protein per kg hydrolysis solution) could be achieved within an hour, at 40°C, at 1% enzyme/substrate ratio (w/w) with papain and bromelain. The pH-stat was found capable of continuously following the rate of hydrolysis but only at low DH. The TNBS could be accurately used even at high DH to estimate the percentage of the peptide bonds cleaved, but required chemical analysis of withdrawn samples