Large Chiral Diffeomorphisms on Riemann Surfaces and W-algebras

The diffeomorphism action lifted on truncated (chiral) Taylor expansion of a complex scalar field over a Riemann surface is presented in the paper under the name of large diffeomorphisms. After an heuristic approach, we show how a linear truncation in the Taylor expansion can generate an algebra of symmetry characterized by some structure functions. Such a linear truncation is explicitly realized by introducing the notion of Forsyth frame over the Riemann surface with the help of a conformally covariant algebraic differential equation. The large chiral diffeomorphism action is then implemented through a B.R.S. formulation (for a given order of truncation) leading to a more algebraic set up. In this context the ghost fields behave as holomorphically covariant jets. Subsequently, the link with the so called W-algebras is made explicit once the ghost parameters are turned from jets into tensorial ghost ones. We give a general solution with the help of the structure functions pertaining to all the possible truncations lower or equal to the given order. This provides another contribution to the relationship between KdV flows and W-diffeomorphimsComment: LaTeX file, 31 pages, no figure. Version to appear in J. Math. Phys. Work partly supported by Region PACA and INF

Motor deficits in schizophrenia quantified by nonlinear analysis of postural sway.

Motor dysfunction is a consistently reported but understudied aspect of schizophrenia. Postural sway area was examined in individuals with schizophrenia under four conditions with different amounts of visual and proprioceptive feedback: eyes open or closed and feet together or shoulder width apart. The nonlinear complexity of postural sway was assessed by detrended fluctuation analysis (DFA). The schizophrenia group (n = 27) exhibited greater sway area compared to controls (n = 37). Participants with schizophrenia showed increased sway area following the removal of visual input, while this pattern was absent in controls. Examination of DFA revealed decreased complexity of postural sway and abnormal changes in complexity upon removal of visual input in individuals with schizophrenia. Additionally, less complex postural sway was associated with increased symptom severity in participants with schizophrenia. Given the critical involvement of the cerebellum and related circuits in postural stability and sensorimotor integration, these results are consistent with growing evidence of motor, cerebellar, and sensory integration dysfunction in the disorder, and with theoretical models that implicate cerebellar deficits and more general disconnection of function in schizophrenia

Parameterization invariance and shape equations of elastic axisymmetric vesicles

The issue of different parameterizations of the axisymmetric vesicle shape addressed by Hu Jian-Guo and Ou-Yang Zhong-Can [ Phys.Rev. E {\bf 47} (1993) 461 ] is reassesed, especially as it transpires through the corresponding Euler - Lagrange equations of the associated elastic energy functional. It is argued that for regular, smooth contours of vesicles with spherical topology, different parameterizations of the surface are equivalent and that the corresponding Euler - Lagrange equations are in essence the same. If, however, one allows for discontinuous (higher) derivatives of the contour line at the pole, the differently parameterized Euler - Lagrange equations cease to be equivalent and describe different physical problems. It nevertheless appears to be true that the elastic energy corresponding to smooth contours remains a global minimum.Comment: 10 pages, latex, one figure include

The complex multiferroic phase diagram of Mn1−x_{1-x}Cox_xWO4_4

The complete magnetic and multiferroic phase diagram of Mn$_{1-x}$Co$_{x}$WO$_4$ single crystals is investigated by means of magnetic, heat capacity, and polarization experiments. We show that the ferroelectric polarization $\overrightarrow{P}$ in the multiferroic state abruptly changes its direction twice upon increasing Co content, x. At x$_{c1}$=0.075, $\overrightarrow{P}$ rotates from the $b-$axis into the $a-c$ plane and at x$_{c2}$=0.15 it flips back to the $b-$axis. The origin of the multiple polarization flops is identified as an effect of the Co anisotropy on the orientation and shape of the spin helix leading to thermodynamic instabilities caused by the decrease of the magnitude of the polarization in the corresponding phases. A qualitative description of the ferroelectric polarization is derived by taking into account the intrachain ($c-$axis) as well as the interchain ($a-$axis) exchange pathways connecting the magnetic ions. In a narrow Co concentration range (0.1$\leq$x$\leq$0.15), an intermediate phase, sandwiched between the collinear high-temperature and the helical low-temperature phases, is discovered. The new phase exhibits a collinear and commensurate spin modulation similar to the low-temperature magnetic structure of MnWO$_4$.Comment: 18 pages, 6 figure

Characterization of erbium doped photonic crystal fiber

Photonic crystal fibers (PCFs) are a new emerging research area, and have been undergoing rapid development in recent years due to their unique and excellent optical properties and features. Studies on the characteristics of various types of PCFs have been reported. However, characterization on erbium-doped PCF has not previously been investigated. Therefore, in this paper, we have modeled an erbium-doped core PCF which has 7 rings of hexagonal air holes. The PCF structure, with a perfectly matched layer (PML), is modeled and simulated using Finite Element Method (FEM) via COMSOL software. The PML is optimized by varying the radius and thickness of the layer. Modal properties of the PCF have been investigated in terms of its effective index of the supported fundamental mode, confinement loss and thickness of the perfectly matched layer. This erbium-doped PCF has a confinement loss of 1.0E-6 at 1500 nm and a maximum effective refractive index of 1.476. This paper gathers useful data, which could be used for studying the characteristics of a PCF

Social isolation in mental health: a conceptual and methodological review

PURPOSE: Social isolation and related concepts have been discussed increasingly in the field of mental health. Despite this, there is a lack of conceptual clarity and consistency in the definition and operationalisation of these terms. This review aimed to provide a clear framework for social isolation and related concepts, and to identify well-established measures in the field of mental health for each conceptual domain discussed. METHODS: We used an iterative strategy of expert consultation and literature searching. A multi-disciplinary group of senior academics was consulted both before and after the literature searching to identify relevant terms, conceptual papers, or recommended measures. Our conceptual framework was also validated through expert consultation. We searched the Web of Science database using terms suggested by experts and subsequently identified further relevant studies through review articles and by reading full texts and reference lists of included studies. A narrative synthesis was conducted. RESULTS: We developed a model with five domains incorporating all the concepts relevant to social isolation in regular use in the mental health research literature. These five domains are: social network—quantity; social network—structure; social network—quality; appraisal of relationships—emotional; and appraisal of relationships—resources. We also identified well-developed measures suitable for assessing each of the five conceptual domains or covering multi-domains. CONCLUSIONS: Our review proposes a conceptual model to encompass and differentiate all terms relating to social isolation. Potential uses are in allowing researchers and intervention developers to identify precisely the intended outcomes of interventions, and to choose the most appropriate measures to use in mental health setting

Flux-area operator and black hole entropy

We show that, for space-times with inner boundaries, there exists a natural area operator different from the standard one used in loop quantum gravity. This new flux-area operator has equidistant eigenvalues. We discuss the consequences of substituting the standard area operator in the Ashtekar-Baez-Corichi-Krasnov definition of black hole entropy by the new one. Our choice simplifies the definition of the entropy and allows us to consider only those areas that coincide with the one defined by the value of the level of the Chern-Simons theory describing the horizon degrees of freedom. We give a prescription to count the number of relevant horizon states by using spin components and obtain exact expressions for the black hole entropy. Finally we derive its asymptotic behavior, discuss several issues related to the compatibility of our results with the Bekenstein-Hawking area law and the relation with Schwarzschild quasi-normal modes.Comment: 25 page

Polyhedral Cosmic Strings

Quantum field theory is discussed in M\"obius corner kaleidoscopes using the method of images. The vacuum average of the stress-energy tensor of a free field is derived and is shown to be a simple sum of straight cosmic string expressions, the strings running along the edges of the corners. It does not seem possible to set up a spin-half theory easily.Comment: 15 pages, 4 text figures not include