A comparison of low-storage strategies for spectral analysis in dissipative systems: filter diagonalisation in the Lanczos representation and harmonic inversion of the Chebychev-order-domain autocorrelation function

We compare the performance of two different low-storage filter diagonalisation (LSFD) strategies in the calculation of complex resonance energies of the HO2, radical. The first is carried out within a complex-symmetric Lanczos subspace representation [H. Zhang, S.C. Smith, Phys. Chem. Chem. Phys. 3 (2001) 2281]. The second involves harmonic inversion of a real autocorrelation function obtained via a damped Chebychev recursion [V.A. Mandelshtam, H.S. Taylor, J. Chem. Phys. 107 (1997) 6756]. We find that while the Chebychev approach has the advantage of utilizing real algebra in the time-consuming process of generating the vector recursion, the Lanczos, method (using complex vectors) requires fewer iterations, especially for low-energy part of the spectrum. The overall efficiency in calculating resonances for these two methods is comparable for this challenging system. (C) 2001 Elsevier Science B.V. All rights reserved.

A Desigualdade De Chebychev

Quando se pretende calcular a probabilidade de poder ocorrer determinado acontecimento e se conhece a distribuição probabilística que está em causa no problema, não se colocam dificuldades particulares.

Quadraturformeln für das Qualokationsverfahren

Im Mittelpunkt dieser Arbeit steht Beweis der Existenz- und Eindeutigkeit von Quadraturformeln, die für das Qualokationsverfahren geeignet sind. Letzteres ist ein von Sloan, Wendland und Chandler entwickeltes Verfahren zur numerischen Behandlung von Randintegralgleichungen auf glatten Kurven (allgemeiner: periodische Pseudodifferentialgleichungen). Es erreicht die gleichen Konvergenzordnungen wie das Petrov-Galerkin-Verfahren, wenn man durch den Operator bestimmte Quadraturformeln verwendet. Zunächst werden die hier behandelten Pseudodifferentialoperatoren und das Qualokationsverfahren vorgestellt. Anschließend wird eine Theorie zur Existenz und Eindeutigkeit von Quadraturformeln entwickelt. Ein wesentliches Hilfsmittel hierzu ist die hier bewiesene Verallgemeinerung eines Satzes von Nürnberger über die Existenz und Eindeutigkeit von Quadraturformeln mit positiven Gewichten, die exakt für Tschebyscheff-Räume sind. Es wird schließlich gezeigt, dass es stets eindeutig bestimmte Quadraturformeln gibt, welche die in den Arbeiten von Sloan und Wendland formulierten Bedingungen erfüllen. Desweiteren werden 2-Punkt-Quadraturformeln für so genannte einfache Operatoren bestimmt, mit welchen das Qualokationsverfahren mit einem Testraum von stückweise konstanten Funktionen eine höhere Konvergenzordnung hat. Außerdem wird gezeigt, dass es für nicht-einfache Operatoren im Allgemeinen keine Quadraturformel gibt, mit der die Konvergenzordnung höher als beim Petrov-Galerkin-Verfahren ist. Das letzte Kapitel beinhaltet schließlich numerische Tests mit Operatoren mit konstanten und variablen Koeffizienten, welche die theoretischen Ergebnisse der vorangehenden Kapitel bestätigen.

Unimolecular Rovibrational Bound and Resonance States for Large Angular Momentum: J=20 Calculations for HO2

We explore the calculation of unimolecular bound states and resonances for deep-well species at large angular momentum using a Chebychev filter diagonalization scheme incorporating doubling of the autocorrelation function as presented recently by Neumaier and Mandelshtam [Phys. Rev. Lett. 86, 5031 (2001)]. The method has been employed to compute the challenging J=20 bound and resonance states for the HO2 system. The methodology has firstly been tested for J=2 in comparison with previous calculations, and then extended to J=20 using a parallel computing strategy. The quantum J-specific unimolecular dissociation rates for HO2-> H+O-2 in the energy range from 2.114 to 2.596 eV have been reported for the first time, and comparisons with the results of Troe and co-workers [J. Chem. Phys. 113, 11019 (2000) Phys. Chem. Chem. Phys. 2, 631 (2000)] from statistical adiabatic channel method/classical trajectory calculations have been made. For most of the energies, the reported statistical adiabatic channel method/classical trajectory rate constants agree well with the average of the fluctuating quantum-mechanical rates. Near the dissociation threshold, quantum rates fluctuate more severely, but their average is still in agreement with the statistical adiabatic channel method/classical trajectory results.

A novel signal processing method for intraoperative neurophysiological monitoring in spinal surgeries

Intraoperative neurophysiologic monitoring is an integral part of spinal surgeries and involves the recording of somatosensory evoked potentials (SSEP). However, clinical application of IONM still requires anywhere between 200 to 2000 trials to obtain an SSEP signal, which is excessive and introduces a significant delay during surgery to detect a possible neurological damage. The aim of this study is to develop a means to obtain the SSEP using a much less, twelve number of recordings. The preliminary step involved was to distinguish the SSEP with the ongoing brain activity. We first establish that the brain activity is indeed quasi-stationary whereas an SSEP is expected to be identical every time a trial is recorded. An algorithm was developed using Chebychev time windowing for preconditioning of SSEP trials to retain the morphological characteristics of somatosensory evoked potentials (SSEP). This preconditioning was followed by the application of a principal component analysis (PCA)-based algorithm utilizing quasi-stationarity of EEG on 12 preconditioned trials. A unique Walsh transform operation was then used to identify the position of the SSEP event. An alarm is raised when there is a 10% time in latency deviation and/or 50% peak-to-peak amplitude deviation, as per the clinical requirements. The algorithm shows consistency in the results in monitoring SSEP in up to 6-hour surgical procedures even under this significantly reduced number of trials. In this study, the analysis was performed on the data recorded in 29 patients undergoing surgery during which the posterior tibial nerve was stimulated and SSEP response was recorded from scalp. This method is shown empirically to be more clinically viable than present day approaches. In all 29 cases, the algorithm takes 4sec to extract an SSEP signal, as compared to conventional methods, which take several minutes. The monitoring process using the algorithm was successful and proved conclusive under the clinical constraints throughout the different surgical procedures with an accuracy of 91.5%. Higher accuracy and faster execution time, observed in the present study, in determining the SSEP signals provide a much improved and effective neurophysiological monitoring process.