Self-Similar Random Processes and Infinite-Dimensional Configuration Spaces

We discuss various infinite-dimensional configuration spaces that carry measures quasiinvariant under compactly-supported diffeomorphisms of a manifold M corresponding to a physical space. Such measures allow the construction of unitary representations of the diffeomorphism group, which are important to nonrelativistic quantum statistical physics and to the quantum theory of extended objects in d-dimensional Euclidean space. Special attention is given to measurable structure and topology underlying measures on generalized configuration spaces obtained from self-similar random processes (both for d = 1 and d > 1), which describe infinite point configurations having accumulation points

Indigenous and institutional profile: Limpopo River Basin

River basins / Water resource management / History / Institutions / Social aspects / Legal aspects

Nonlinear Response of a Kondo system: Direct and Alternating Tunneling Currents

Non - equilibrium tunneling current of an Anderson impurity system subject to both constant and alternating electric fields is studied. A time - dependent Schrieffer - Wolff transformation maps the time - dependent Anderson Hamiltonian onto a Kondo one. Perturbation expansion in powers of the Kondo coupling strength is carried out up to third order, yielding a remarkably simple analytical expression for the tunneling current. It is found that the zero - bias anomaly is suppressed by an ac - field. Both dc and the first harmonic are equally enhanced by the Kondo effect, while the higher harmonics are relatively small. These results are shown to be valid also below the Kondo temperature.Comment: 7 pages, RevTeX, 3 PS figures attached, the article has been significantly developed: time - dependent Schrieffer - Wolff transformation is presented in the full form, the results are applied to the change in the direct current induced by an alternating field (2 figures are new

Equivariant cohomology and analytic descriptions of ring isomorphisms

In this paper we consider a class of connected closed $G$-manifolds with a non-empty finite fixed point set, each $M$ of which is totally non-homologous to zero in $M_G$ (or $G$-equivariantly formal), where $G={\Bbb Z}_2$. With the help of the equivariant index, we give an explicit description of the equivariant cohomology of such a $G$-manifold in terms of algebra, so that we can obtain analytic descriptions of ring isomorphisms among equivariant cohomology rings of such $G$-manifolds, and a necessary and sufficient condition that the equivariant cohomology rings of such two $G$-manifolds are isomorphic. This also leads us to analyze how many there are equivariant cohomology rings up to isomorphism for such $G$-manifolds in 2- and 3-dimensional cases.Comment: 20 pages, updated version with two references adde

A Search for Cosmic Microwave Background Anisotropies on Arcminute Scales with Bolocam

We have surveyed two science fields totaling one square degree with Bolocam at 2.1 mm to search for secondary CMB anisotropies caused by the Sunyaev- Zel'dovich effect (SZE). The fields are in the Lynx and Subaru/XMM SDS1 fields. Our survey is sensitive to angular scales with an effective angular multipole of l_eff = 5700 with FWHM_l = 2800 and has an angular resolution of 60 arcseconds FWHM. Our data provide no evidence for anisotropy. We are able to constrain the level of total astronomical anisotropy, modeled as a flat bandpower in C_l, with frequentist 68%, 90%, and 95% CL upper limits of 590, 760, and 830 uKCMB^2. We statistically subtract the known contribution from primary CMB anisotropy, including cosmic variance, to obtain constraints on the SZE anisotropy contribution. Now including flux calibration uncertainty, our frequentist 68%, 90% and 95% CL upper limits on a flat bandpower in C_l are 690, 960, and 1000 uKCMB^2. When we instead employ the analytic spectrum suggested by Komatsu and Seljak (2002), and account for the non-Gaussianity of the SZE anisotropy signal, we obtain upper limits on the average amplitude of their spectrum weighted by our transfer function of 790, 1060, and 1080 uKCMB^2. We obtain a 90% CL upper limit on sigma8, which normalizes the power spectrum of density fluctuations, of 1.57. These are the first constraints on anisotropy and sigma8 from survey data at these angular scales at frequencies near 150 GHz.Comment: 68 pages, 17 figures, 2 tables, accepted for publication in Ap

Generalizations of Yang-Mills Theory with Nonlinear Constitutive Equations

We generalize classical Yang-Mills theory by extending nonlinear constitutive equations for Maxwell fields to non-Abelian gauge groups. Such theories may or may not be Lagrangian. We obtain conditions on the constitutive equations specifying the Lagrangian case, of which recently-discussed non-Abelian Born-Infeld theories are particular examples. Some models in our class possess nontrivial Galilean (c goes to infinity) limits; we determine when such limits exist, and obtain them explicitly.Comment: Submitted to the Proceedings of the 3rd Symposium on Quantum Theory and Symmetries (QTS3) 10-14 September 2003. Preprint 9 pages including reference

Comparing open and minimally invasive surgical procedures for oesophagectomy in the treatment of cancer: the ROMIO (Randomised Oesophagectomy: Minimally Invasive or Open) feasibility study and pilot trial

Localised oesophageal cancer can be curatively treated with surgery (oesophagectomy) but the procedure is complex with a risk of complications, negative effects on quality of life and a recovery period of 6-9 months. Minimal-access surgery may accelerate recovery.The ROMIO (Randomised Oesophagectomy: Minimally Invasive or Open) study aimed to establish the feasibility of, and methodology for, a definitive trial comparing minimally invasive and open surgery for oesophagectomy. Objectives were to quantify the number of eligible patients in a pilot trial; develop surgical manuals as the basis for quality assurance; standardise pathological processing; establish a method to blind patients to their allocation in the first week post surgery; identify measures of postsurgical outcome of importance to patients and clinicians; and establish the main cost differences between the surgical approaches.Pilot parallel three-arm randomised controlled trial nested within feasibility work.Two UK NHS departments of upper gastrointestinal surgery.Patients aged ≥ 18 years with histopathological evidence of oesophageal or oesophagogastric junctional adenocarcinoma, squamous cell cancer or high-grade dysplasia, referred for oesophagectomy or oesophagectomy following neoadjuvant chemo(radio)therapy.Oesophagectomy, with patients randomised to open surgery, a hybrid open chest and minimally invasive abdomen or totally minimally invasive access.The primary outcome measure for the pilot trial was the number of patients recruited per month, with the main trial considered feasible if at least 2.5 patients per month were recruited.During 21 months of recruitment, 263 patients were assessed for eligibility; of these, 135 (51%) were found to be eligible and 104 (77%) agreed to participate, an average of five patients per month. In total, 41 patients were allocated to open surgery, 43 to the hybrid procedure and 20 to totally minimally invasive surgery. Recruitment is continuing, allowing a seamless transition into the definitive trial. Consequently, the database is unlocked at the time of writing and data presented here are for patients recruited by 31 August 2014. Random allocation achieved a good balance between the arms of the study, which, as a high proportion of patients underwent their allocated surgery (69/79, 87%), ensured a fair comparison between the interventions. Dressing patients with large bandages, covering all possible incisions, was successful in keeping patients blind while pain was assessed during the first week post surgery. Postsurgical length of stay and risk of adverse events were within the typical range for this group of patients, with one death occurring within 30 days among 76 patients. There were good completion rates for the assessment of pain at 6 days post surgery (88%) and of the patient-reported outcomes at 6 weeks post randomisation (74%).Rapid recruitment to the pilot trial and the successful refinement of methodology indicated the feasibility of a definitive trial comparing different approaches to oesophagectomy. Although we have shown a full trial of open compared with minimally invasive oesophagectomy to be feasible, this is necessarily based on our findings from the two clinical centres that we could include in this small preliminary study.Current Controlled Trials ISRCTN59036820.This project was funded by the NIHR Health Technology Assessment programme and will be published in full in Health Technology Assessment; Vol. 20, No. 48. See the NIHR Journals Library website for further project information

A Topological String: The Rasetti-Regge Lagrangian, Topological Quantum Field Theory, and Vortices in Quantum Fluids

The kinetic part of the Rasetti-Regge action I_{RR} for vortex lines is studied and links to string theory are made. It is shown that both I_{RR} and the Polyakov string action I_{Pol} can be constructed with the same field X^mu. Unlike I_{NG}, however, I_{RR} describes a Schwarz-type topological quantum field theory. Using generators of classical Lie algebras, I_{RR} is generalized to higher dimensions. In all dimensions, the momentum 1-form P constructed from the canonical momentum for the vortex belongs to the first cohomology class H^1(M,R^m) of the worldsheet M swept-out by the vortex line. The dynamics of the vortex line thus depend directly on the topology of M. For a vortex ring, the equations of motion reduce to the Serret-Frenet equations in R^3, and in higher dimensions they reduce to the Maurer-Cartan equations for so(m).Comment: To appear in Journal of Physics

Representing addition and subtraction : learning the formal conventions

The study was designed to test the effects of a structured intervention in teaching children to represent addition and subtraction. In a post-test only control group design, 90 five-year-olds experienced the intervention entitled Bi-directional Translation whilst 90 control subjects experienced typical teaching. Post-intervention testing showed some significant differences between the two groups both in terms of being able to effect the addition and subtraction operations and in being able to determine which operation was appropriate. The results suggest that, contrary to historical practices, children's exploration of real world situations should precede practice in arithmetical symbol manipulation