Reduction of amplitude equations by the renormalization group approach

This article elucidates and analyzes the fundamental underlying structure of the renormalization group (RG) approach as it applies to the solution of any differential equation involving multiple scales. The amplitude equation derived through the elimination of secular terms arising from a naive perturbation expansion of the solution to these equations by the RG approach is reduced to an algebraic equation which is expressed in terms of the Thiele semi-invariants or cumulants of the eliminant sequence { Zi } i=1 . Its use is illustrated through the solution of both linear and nonlinear perturbation problems and certain results from the literature are recovered as special cases. The fundamental structure that emerges from the application of the RG approach is not the amplitude equation but the aforementioned algebraic equation. © 2008 The American Physical Society.

Generalized azimuthal shear deformations in compressible isotropic elastic materials

In this article we study the azimuthal shear deformations in a compressible Isotropic elastic material. This class of deformations involves an azimuthal displacement as a function of the radial and axial coordinates. The equilibrium equations are formulated in terms of the Cauchy-Green strain tensors, which form an overdetermined system of partial differential equations for which solutions do not exist in general. By means of a Legendre transformation, necessary and sufficient conditions for the material to support this deformation are obtained explicitly, in the sense that every solution to the azimuthal equilibrium equation will satisfy the remaining two equations. Additionally, we show how these conditions are sufficient to support all currently known deformations that locally reduce to simple shear. These conditions are then expressed both in terms of the invariants of the Cauchy-Green strain and stretch tensors. Several classes of strain energy functions for which this deformation can be supported are studied. For certain boundary conditions, exact solutions to the equilibrium equations are obtained. © 2005 Society for Industrial and Applied Mathematics.

The eight variable homogeneous degree three bent functions

We determine the affine equivalence classes of the eight variable degree three homogeneous bent functions using a new algorithm. Our algorithm applies to general bent functions and can systematically determine the automorphism groups. We provide a partial verification of the enumeration of eight variable degree three homogeneous bent functions obtained by Meng et al. We determine the affine equivalence classes of these functions.

Safety envelope for security

We present an approach for detecting sensor spoofing attacks on a cyber-physical system. Our approach consists of two steps. In the first step, we construct a safety envelope of the system. Under nominal conditions (that is, when there are no attacks), the system always stays inside its safety envelope. In the second step, we build an attack detector: a monitor that executes synchronously with the system and raises an alarm whenever the system state falls outside the safety envelope. We synthesize safety envelopes using a modified machine learning procedure applied on data collected from the system when it is not under attack. We present experimental results that show effectiveness of our approach, and also validate the several novel features that we introduced in our learning procedure.

Depth of anaesthesia monitoring during procedural sedation and analgesia: A systematic review protocol

Background Procedural sedation and analgesia (PSA) is used to attenuate the pain and distress that may otherwise be experienced during diagnostic and interventional medical or dental procedures. As the risk of adverse events increases with the depth of sedation induced, frequent monitoring of level of consciousness is recommended. Level of consciousness is usually monitored during PSA with clinical observation. Processed electroencephalogram-based depth of anaesthesia (DoA) monitoring devices provide an alternative method to monitor level of consciousness that can be used in addition to clinical observation. However, there is uncertainty as to whether their routine use in PSA would be justified. Rigorous evaluation of the clinical benefits of DoA monitors during PSA, including comprehensive syntheses of the available evidence, is therefore required. One potential clinical benefit of using DoA monitoring during PSA is that the technology could improve patient safety by reducing sedation-related adverse events, such as death or permanent neurological disability. We hypothesise that earlier identification of lapses into deeper than intended levels of sedation using DoA monitoring leads to more effective titration of sedative and analgesic medications, and results in a reduction in the risk of adverse events caused by the consequences of over-sedation, such as hypoxaemia. The primary objective of this review is to determine whether using DoA monitoring during PSA in the hospital setting improves patient safety by reducing the risk of hypoxaemia (defined as an arterial partial pressure of oxygen below 60 mmHg or percentage of haemoglobin that is saturated with oxygen [SpO2] less than 90 %). Other potential clinical benefits of using DoA monitoring devices during sedation will be assessed as secondary outcomes. Methods/design Electronic databases will be systematically searched for randomized controlled trials comparing the use of depth of anaesthesia monitoring devices with clinical observation of level of consciousness during PSA. Language restrictions will not be imposed. Screening, study selection and data extraction will be performed by two independent reviewers. Disagreements will be resolved by discussion. Meta-analyses will be performed if suitable. Discussion This review will synthesise the evidence on an important potential clinical benefit of DoA monitoring during PSA within hospital settings.

Visualization tools for high angular resolution diffusion imaging

There is a major effort in medical imaging to develop algorithms to extract information from DTI and HARDI, which provide detailed information on brain integrity and connectivity. As the images have recently advanced to provide extraordinarily high angular resolution and spatial detail, including an entire manifold of information at each point in the 3D images, there has been no readily available means to view the results. This impedes developments in HARDI research, which need some method to check the plausibility and validity of image processing operations on HARDI data or to appreciate data features or invariants that might serve as a basis for new directions in image segmentation, registration, and statistics. We present a set of tools to provide interactive display of HARDI data, including both a local rendering application and an off-screen renderer that works with a web-based viewer. Visualizations are presented after registration and averaging of HARDI data from 90 human subjects, revealing important details for which there would be no direct way to appreciate using conventional display of scalar images.