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

Some Variations on Maxwell's Equations

In the first sections of this article, we discuss two variations on Maxwell's equations that have been introduced in earlier work--a class of nonlinear Maxwell theories with well-defined Galilean limits (and correspondingly generalized Yang-Mills equations), and a linear modification motivated by the coupling of the electromagnetic potential with a certain nonlinear Schroedinger equation. In the final section, revisiting an old idea of Lorentz, we write Maxwell's equations for a theory in which the electrostatic force of repulsion between like charges differs fundamentally in magnitude from the electrostatic force of attraction between unlike charges. We elaborate on Lorentz' description by means of electric and magnetic field strengths, whose governing equations separate into two fully relativistic Maxwell systems--one describing ordinary electromagnetism, and the other describing a universally attractive or repulsive long-range force. If such a force cannot be ruled out {\it a priori} by known physical principles, its magnitude should be determined or bounded experimentally. Were it to exist, interesting possibilities go beyond Lorentz' early conjecture of a relation to (Newtonian) gravity.Comment: 26 pages, submitted to a volume in preparation to honor Gerard Emch v. 2: discussion revised, factors of 4\pi corrected in some equation

Children’s spontaneous comparisons from 26 to 58 months predict performance in verbal and non-verbal analogy tests in 6th grade

Comparison supports the development of children’s analogical reasoning. The evidence for this claim comes from laboratory studies. We describe spontaneous comparisons produced by 24 typically developing children from 26 to 58 months. Children tend to express similarity before expressing difference. They compare objects from the same category before objects from different categories, make global comparisons before specific comparisons, and specify perceptual features of similarity/difference before non-perceptual features. We then investigate how a theoretically interesting subset of children’s comparisons – those expressing a specific feature of similarity or difference – relates to analogical reasoning as measured by verbal and non-verbal tests in 6th grade. The number of specific comparisons children produce before 58 months predicts their scores on both tests, controlling for vocabulary at 54 months. The results provide naturalistic support for experimental findings on comparison development, and demonstrate a strong relationship between children’s early comparisons and their later analogical reasoning

CLARREO: Reference Inter-Calibration on Orbit With Reflected Solar Spectrometer

The CLARREO approach for reference intercalibration is based on obtaining coincident highly accurate spectral reflectance and reflected radiance measurements, and establish an on-orbit reference for existing Earth viewing reflected solar radiation sensors: CERES and VIIRS on JPSS satellites, AVHRR and follow-on imagers on MetOp, and imagers on GEO platforms. The mission goal is to be able to provide CLARREO RS reference observations that are matched in space, time, and viewing angles with measurements from the aforementioned instruments, with sampling sufficient to overcome the random error sources from imperfect data matching and instrument noise. The intercalibration method is to monitor over time changes in targeted sensor response function parameters: effective offset, gain, nonlinearity, spectral degradation, and sensitivity to polarization of optics

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

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

Gesture analysis for physics education researchers

Systematic observations of student gestures can not only fill in gaps in students' verbal expressions, but can also offer valuable information about student ideas, including their source, their novelty to the speaker, and their construction in real time. This paper provides a review of the research in gesture analysis that is most relevant to physics education researchers and illustrates gesture analysis for the purpose of better understanding student thinking about physics.Comment: 14 page

Cognitive demands of face monitoring: Evidence for visuospatial overload

Young children perform difficult communication tasks better face to face than when they cannot see one another (e.g., Doherty-Sneddon & Kent, 1996). However, in recent studies, it was found that children aged 6 and 10 years, describing abstract shapes, showed evidence of face-to-face interference rather than facilitation. For some communication tasks, access to visual signals (such as facial expression and eye gaze) may hinder rather than help children’s communication. In new research we have pursued this interference effect. Five studies are described with adults and 10- and 6-year-old participants. It was found that looking at a face interfered with children’s abilities to listen to descriptions of abstract shapes. Children also performed visuospatial memory tasks worse when they looked at someone’s face prior to responding than when they looked at a visuospatial pattern or at the floor. It was concluded that performance on certain tasks was hindered by monitoring another person’s face. It is suggested that processing of visual communication signals shares certain processing resources with the processing of other visuospatial information

Vector coherent state representations, induced representations, and geometric quantization: II. Vector coherent state representations

It is shown here and in the preceeding paper (quant-ph/0201129) that vector coherent state theory, the theory of induced representations, and geometric quantization provide alternative but equivalent quantizations of an algebraic model. The relationships are useful because some constructions are simpler and more natural from one perspective than another. More importantly, each approach suggests ways of generalizing its counterparts. In this paper, we focus on the construction of quantum models for algebraic systems with intrinsic degrees of freedom. Semi-classical partial quantizations, for which only the intrinsic degrees of freedom are quantized, arise naturally out of this construction. The quantization of the SU(3) and rigid rotor models are considered as examples.Comment: 31 pages, part 2 of two papers, published versio