Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution

The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.

A taxonomy for wavelet neural networks applied to nonlinear modelling

This article presents a novel classification of wavelet neural networks based on the orthogonality/non-orthogonality of neurons and the type of nonlinearity employed. On the basis of this classification different network types are studied and their characteristics illustrated by means of simple one-dimensional nonlinear examples. For multidimensional problems, which are affected by the curse of dimensionality, the idea of spherical wavelet functions is considered. The behaviour of these networks is also studied for modelling of a low-dimension map.

Coherent X-ray production via pulse reflection from laser-driven dense electron sheets

A scheme to obtain brilliant x-ray sources by coherent reflection of a counter-propagating pulse from laser-driven dense electron sheets is theoretically and numerically investigated in a self-consistent manner. A radiation pressure acceleration model for the dynamics of the electron sheets blown out from laser-irradiated ultrathin foils is developed and verified by PIC simulations. The first multidimensional and integral demonstration of the scheme by 2D PIC simulations is presented. It is found that the reflected pulse undergoes Doppler-upshift by a factor 4?z2, where ?z = (1- vz2/c2)-1/2 is the effective Lorentz factor of the electron sheet al ong its normal direction. Meanwhile the pulse electric field is intensified by a factor depending on the electron density of the sheet in its moving frame ne/?, where ? is the full Lorentz factor.

Compactness properties of operator multipliers

We continue the study of multidimensional operator multipliers initiated in~cite{jtt}. We introduce the notion of the symbol of an operator multiplier. We characterise completely compact operator multipliers in terms of their symbol as well as in terms of approximation by finite rank multipliers. We give sufficient conditions for the sets of compact and completely compact multipliers to coincide and characterise the cases where an operator multiplier in the minimal tensor product of two C*-algebras is automatically compact. We give a description of multilinear modular completely compact completely bounded maps defined on the direct product of finitely many copies of the C*-algebra of compact operators in terms of tensor products, generalising results of Saar

Length of Stay-Based Patient Flow Models: Recent Developments and Future Directions

Modelling patient flow in health care systems is vital in understanding the system activity and may therefore prove to be useful in improving their functionality. An extensively used measure is the average length of stay which, although easy to calculate and quantify, is not considered appropriate when the distribution is very long-tailed. In fact, simple deterministic models are generally considered inadequate because of the necessity for models to reflect the complex, variable, dynamic and multidimensional nature of the systems. This paper focuses on modelling length of stay and flow of patients. An overview of such modelling techniques is provided, with particular attention to their impact and suitability in managing a hospital service.

Nationalism, Ethnicity and Self-Determination: A Paradigm Shift?

An ongoing paradigm shift is giving birth to a more multidimensional understanding of the relationship between nationalism, sovereignty, self determination and democratic governance. A common element across the various versions of the new paradigm is the dispersal of democratic governance across multiple and overlapping jurisdictions. Governmental processes are no longer seen as discrete, centralised and homogenous as in the old nation-state model, but as asymmetrical, multilayered and multicultural, with devolution into multiple jurisdictions. These changes have hardly affected the two main conceptual frameworks that dominate the study of nationalism, Modernism and Ethnosymbolism. As a result, they risk becoming irrelevant to the new forms of national self determination, asymmetrical governance and shared sovereignty. Modernism and Ethnosymbolism insist that nationalism seeks to equate the nation with a sovereign state, while in reality the overwhelming majority of nations are stateless and unable to build nation states, as they often inhabit territories shared with other nations. The paradigm shift occurs precisely with the realisation that nation state sovereignty is no longer a feasible solution to the demands of stateless nations. Ethnosymbolism is in a much better position to adapt to the paradigm shift provided it abandons the claim that the nation state is the best shell for the nation.

Modeling Frequency-Dependent Boundaries as Digital Impedance Filters in FDTD and K-DWM Room Acoustics Simulations

A new method for modeling-frequency-dependent boundaries in finite-difference time-domain (FDTD) and Kirchhoff variable digital waveguide mesh (K-DWM) room acoustics simulations is presented. The proposed approach allows the direct incorporation of a digital impedance filter (DIF) in the Multidimensional (2D or 3D) FDTD boundary model of a locally reacting surface. An explicit boundary update equation is obtained by carefully constructing a Suitable recursive formulation. The method is analyzed in terms of pressure wave reflectance for different wall impedance filters and angles of incidence. Results obtained from numerical experiments confirm the high accuracy of the proposed digital impedance filter boundary model, the reflectance of which matches locally reacting surface (LRS) theory closely. Furthermore a numerical boundary analysis (NBA) formula is provided as a technique for an analytic evaluation of the numerical reflectance of the proposed digital impedance filter boundary formulation.

Alternative Factor Models and Heritability of the Short Leyton Obsessional Inventory-Children's Version

An alternative models framework was used to test three confirmatory factor analytic models for the Short Leyton Obsessional Inventory-Children's Version (Short LOI-CV) in a general population sample of 517 young adolescent twins (11-16 years). A one-factor model as implicit in current classification systems of Obsessive-Compulsive Disorder (OCD), a two-factor obsessions and compulsions model, and a multidimensional model corresponding to the three proposed subscales of the Short LOI-CV (labelled Obsessions/Incompleteness, Numbers/Luck and Cleanliness) were considered. The three-factor model was the only model to provide an adequate explanation of the data. Twin analyses suggested significant quantitative sex differences in heritability for both the Obsessions/Incompleteness and Numbers/Luck dimensions with these being significantly heritable in males only (heritability of 60% and 65% respectively). The correlation between the additive genetic effects for these two dimensions in males was 0.95 suggesting they largely share the same genetic risk factors.

Transonic Aeroelastic Stability Analysis Using a Kriging-Based Schur Complement Formulation

A method is described to allow searches for transonic aeroelastic instability of realistically sized aircraft models in multidimensional parameter spaces when computational fluid dynamics are used to model the aerodynamics. Aeroelastic instability is predicted from a small nonlinear eigenvalue problem. The approximation of the computationally expensive interaction term modeling the fluid response is formulated to allow the automated and blind search for aeroelastic instability. The approximation uses a kriging interpolation of exact numerical samples covering the parameter space. The approach, demonstrated for the Goland wing and the multidisciplinary optimization transport wing, results in stability analyses over whole flight envelopes at an equivalent cost of several steady-state simulations.

Prospective study of workplace social capital and depression: are vertical and horizontal components equally important?

Background Recent studies have emphasised the multidimensional nature of the social capital concept, but it is not known whether the health effects of social capital vary by dimension. The objective of this study was to examine the vertical component (ie, respectful and trusting relationships across power differentials at work) and the horizontal component of workplace social capital (trust and reciprocity between employees at the same hierarchical level) as risk factors for subsequent depression.

Scaling of proton acceleration driven by petawatt-laser-plasma interactions

The possibility of using high-power lasers to generate high-quality beams of energetic ions is attracting large global interest. The prospect of using laser-accelerated protons in medicine attracts particular interest, as these schemes may lead to compact and relatively low-cost sources. Among the challenges remaining before these sources can be used in medicine is to increase the numbers and energies of the ions accelerated. Here, we extend the energy and intensity range over which proton scaling is experimentally investigated, up to 400 J and 6 x 10(20) W cm(-2) respectively, and find a slower proton scaling than previously predicted. With the aid of plasma-expansion simulation tools, our results suggest the importance of time-dependent and multidimensional effects in predicting the maximum proton energy in this ultrahigh-intensity regime. The implications of our new understanding of proton scaling for potential medical applications are discussed.

Acquired deafness: A multi-dimensional experience

The aim of this study was to investigate the subjective experience of acquired deafness using quantitative (questionnaire) and qualitative (interview) methods. This paper presents findings from the questionnaire data. Eighty-seven people (of whom 38 had acquired a profound loss) participated in the study. The questionnaire contained items designed to examine both audiological and non-audiological aspects of deafened people's experiences. It also sought to measure the extent to which those aspects affect their quality of life. The questionnaire included three variables (i.e. reported frequency and impact of depression, and overall effect of deafness on one's life) as broad indicators of adjustment. Seventy-three respondents (including all but one of the profound group) completed the questionnaire. Factor analysis of the questionnaire data identified six major themes (with variance >10%) underlying the personal experience of acquired deafness. Three themes-communicative deprivation, restriction, and malinteraction by hearing people-dealt with observable aspects of respondents' experience. Multiple regression found that these factor themes associated with biomedical variables. The remaining three themes dealt with less tangible aspects of the deafness experience. These themes-feelings of distress in interaction, feelings of abandonment and benefit from positive experiences-did not associate with biomedical variables. Finally, multiple regression indicates that respondents' factor scores predict the impact of deafness at least as strongly as their audiological and social characteristics.

Thalidomide for managing cancer cachexia [review paper]

Cancer cachexia is a multidimensional syndrome characterised by wasting, loss of weight, loss of appetite, metabolic alterations, fatigue and reduced performance status. A significant number of patients with advanced cancer develop cachexia before death. There is no identified optimum treatment for cancer cachexia. While the exact mechanism of the action of thalidomide is unclear, it is known to have immunomodulatory and anti-inflammatory properties, which are thought to help reduce the weight loss associated with cachexia. Preliminary studies of thalidomide have demonstrated encouraging results. This review aimed to (1) evaluate the effectiveness of thalidomide, and (2) identify and assess adverse effects from thalidomide for cancer cachexia. Electronic searches were undertaken in CENTRAL, MEDLINE, EMBASE, Web of Science and CINAHL (from inception to April 2011). Reference lists from reviewed articles, trial registers, relevant conference documents and thalidomide manufacturers identified additional literature. This review included randomised controlled trials (RCTs) and non-RCTs. Participants were adults diagnosed with advanced or incurable cancer and weight loss or a clinical diagnosis of cachexia who were administered thalidomide. All titles and abstracts retrieved by electronic searching were downloaded to a reference management database. Duplicates were removed and the remaining citations were read by two review authors and checked for eligibility. Studies that were deemed ineligible for inclusion had clear reasons for exclusion documented. Data were extracted independently by two review authors for all eligible studies. While a meta-analysis was planned for this review, this was not possible due to the small number of studies included and high heterogeneity among them. Thus a narrative synthesis of the findings is presented. The literature search revealed a dearth of large, well conducted trials in this area. This has hindered the review authors' ability to make an informed decision about thalidomide for the management of cancer cachexia. At present, there is insufficient evidence to refute or support the use of thalidomide for the management of cachexia in advanced cancer patients. The review authors cannot confirm or refute previous literature on the use of thalidomide for patients with advanced cancer who have cachexia and there is inadequate evidence to recommend it for clinical practice. Additional, well conducted, large RCTs are needed to test thalidomide both singularly and in combination with other treatment modalities to ascertain its true benefit, if any, for this population. Furthermore, one study (out of the three reviewed) highlighted that thalidomide was poorly tolerated and its use needs to be explored further in light of the frailty of this population

On the dimensionality of ecological stability

Ecological stability is touted as a complex and multifaceted concept, including components such as variability, resistance, resilience, persistence and robustness. Even though a complete appreciation of the effects of perturbations on ecosystems requires the simultaneous measurement of these multiple components of stability, most ecological research has focused on one or a few of those components analysed in isolation. Here, we present a new view of ecological stability that recognises explicitly the non-independence of components of stability. This provides an approach for simplifying the concept of stability. We illustrate the concept and approach using results from a field experiment, and show that the effective dimensionality of ecological stability is considerably lower than if the various components of stability were unrelated. However, strong perturbations can modify, and even decouple, relationships among individual components of stability. Thus, perturbations not only increase the dimensionality of stability but they can also alter the relationships among components of stability in different ways. Studies that focus on single forms of stability in isolation therefore risk underestimating significantly the potential of perturbations to destabilise ecosystems. In contrast, application of the multidimensional stability framework that we propose gives a far richer understanding of how communities respond to perturbations.