Supplement : Efficient weak second-order stochastic Runge-Kutta methods for non-commutative Stratonvich stochastic differential equations

This paper gives a modification of a class of stochastic Runge–Kutta methods proposed in a paper by Komori (2007). The slight modification can reduce the computational costs of the methods significantly.

Higher order spectral analysis of Chua's circuit

Higher order spectral analysis is used to investigate nonlinearities in time series of voltages measured from a realization of Chua's circuit. For period-doubled limit cycles, quadratic and cubic nonlinear interactions result in phase coupling and energy exchange between increasing numbers of triads and quartets of Fourier components as the nonlinearity of the system is increased. For circuit parameters that result in a chaotic Rossler-type attractor, bicoherence and tricoherence spectra indicate that both quadratic and cubic nonlinear interactions are important to the dynamics. When the circuit exhibits a double-scroll chaotic attractor the bispectrum is zero, but the tricoherences are high, consistent with the importance of higher-than-second order nonlinear interactions during chaos associated with the double scroll.

Higher-order spectral analysis of nonlinear ocean surface gravity waves

Higher-order spectral analysis is used to detect the presence of secondary and tertiary forced waves associated with the nonlinearity of energetic swell observed in 8- and 13-m water depths. Higher-order spectral analysis techniques are first described and then applied to the field data, followed by a summary of the results.

On the behaviour of higher-order spectral features for object recognition in the presence of various types of noise

This paper presents results on the robustness of higher-order spectral features to Gaussian, Rayleigh, and uniform distributed noise. Based on cluster plots and accuracy results for various signal to noise conditions, the higher-order spectral features are shown to be better than moment invariant features.

Diurnal Variation of Retinal Thickness with Spectral Domain OCT

Purpose. To investigate whether diurnal variation occurs in retinal thickness measures derived from spectral domain optical coherence tomography (SD-OCT). Methods. Twelve healthy adult subjects had retinal thickness measured with SD-OCT every 2 h over a 10 h period. At each measurement session, three average B-scan images were derived from a series of multiple B-scans (each from a 5 mm horizontal raster scan along the fovea, containing 1500 A-scans/B-scan) and analyzed to determine the thickness of the total retina, as well as the thickness of the outer retinal layers. Average thickness values were calculated at the foveal center, at the 0.5 mm diameter foveal region, and for the temporal parafovea (1.5 mm from foveal center) and nasal parafovea (1.5 mm from foveal center). Results. Total retinal thickness did not exhibit significant diurnal variation in any of the considered retinal regions (p > 0.05). Evidence of significant diurnal variation was found in the thickness of the outer retinal layers (p < 0.05), with the most prominent changes observed in the photoreceptor layers at the foveal center. The photoreceptor inner and outer segment layer thickness exhibited mean amplitude (peak to trough) of daily change of 7 ± 3 μm at the foveal center. The peak in thickness was typically observed at the third measurement session (mean measurement time, 13:06). Conclusions. The total retinal thickness measured with SD-OCT does not exhibit evidence of significant variation over the course of the day. However, small but significant diurnal variation occurs in the thickness of the foveal outer retinal layers.

The lived experience of post-traumatic stress disorder as described by motor vehicle accident victims in Jordan

Aim: To explore the lived experience of post-traumatic stress disorder (PTSD) as described by individuals who have been involved in a motor vehicle accident (MVA) in Jordan. Background: Motor vehicle accident (MVA) survivors who develop post-traumatic stress disorder (PTSD) have become an important health issue. The World Health Organisation (WHO) states that trauma resulting from MVAs is a phenomenon of increasing concern, with death from injuries projected to rise from 5.1 million in 1990 to 8.4 million in 2020 particularly in developing countries such as Jordan (WHO, 2002). The impact of trauma from MVAs inevitably compromises the victim’s quality of life (WHO, 2002; Blanchard & Hickling, 2007) resulting in psychological and emotional distress, occupational disability, family disintegration, and socio-economic difficulty (Jordan Ministry of Health, 2005). The development of PTSD as a result of an MVA is not limited to the individual, but also extends to the family, friends, and the health care team involved in the person's care and rehabilitation. Design: A descriptive phenomenological approach was used for this study. Method: This study was conducted in an orthopaedic unit in Amera Basma Hospital in Irbid Jordan. Fifteen (15) participants were voluntary recruited through the process of purposeful sampling. Data was collected by face-to-face in depth-interviews. Interviews were digitally recorded and transcribed verbatim. The process of analysis was undertaken using Colaizzi’s (1978) eight step approach with the addition of two extra steps. Findings: The process of analysis identified seven themes explicated from the participants’ transcripts of interview. The seven themes were: 1. Feeling frustrated at a diminishing health status 2. Struggling to maintain a sense of independence 3. Harbouring feelings of not being able to recover 4. Feeling discriminated against and marginalised by society 5. Feeling ignored and neglected by health care professionals 6. Feeling abandoned by family, and 7. Moving toward acceptance through having faith in Allah. Conclusion: The findings of this study have the potential to make a significant contribution to extant knowledge on the topic which can inform future nursing practice, education, policy development, and research initiatives in Jordan and internationally.

Gene duplication is an evolutionary mechanism for expanding spectral diversity in the long-wavelength photopigments of butterflies

Butterfly long-wavelength (L) photopigments are interesting for comparative studies of adaptive evolution because of the tremendous phenotypic variation that exists in their wavelength of peak absorbance (lambda(max) value). Here we present a comprehensive survey of L photopigment variation by measuring lambda(max) in 12 nymphalid and 1 riodinid species using epi-microspectrophotometry. Together with previous data, we find that L photopigment lambda(max) varies from 510-565 nm in 22 nymphalids, with an even broader 505- to 600-nm range in riodinids. We then surveyed the L opsin genes for which lambda(max) values are available as well as from related taxa and found 2 instances of L opsin gene duplication within nymphalids, in Hermeuptychia hermes and Amathusia phidippus, and 1 instance within riodinids, in the metalmark butterfly Apodemia mormo. Using maximum parsimony and maximum likelihood ancestral state reconstructions to map the evolution of spectral shifts within the L photopigments of nymphalids, we estimate the ancestral pigment had a lambda(max) = 540 nm +/- 10 nm standard error and that blueshifts in wavelength have occurred at least 4 times within the family. We used ancestral state reconstructions to investigate the importance of several amino acid substitutions (Ile17Met, Ala64Ser, Asn70Ser, and Ser137Ala) previously shown to have evolved under positive selection that are correlated with blue spectral shifts. These reconstructions suggest that the Ala64Ser substitution has indeed occurred along the newly identified blueshifted L photopigment lineages. Substitutions at the other 3 sites may also be involved in the functional diversification of L photopigments. Our data strongly suggest that there are limits to the evolution of L photopigment spectral shifts among species with only one L opsin gene and that opsin gene duplication broadens the potential range of lambda(max) values.

High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula

In recent years considerable attention has been paid to the numerical solution of stochastic ordinary differential equations (SODEs), as SODEs are often more appropriate than their deterministic counterparts in many modelling situations. However, unlike the deterministic case numerical methods for SODEs are considerably less sophisticated due to the difficulty in representing the (possibly large number of) random variable approximations to the stochastic integrals. Although Burrage and Burrage [High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations, Applied Numerical Mathematics 22 (1996) 81-101] were able to construct strong local order 1.5 stochastic Runge-Kutta methods for certain cases, it is known that all extant stochastic Runge-Kutta methods suffer an order reduction down to strong order 0.5 if there is non-commutativity between the functions associated with the multiple Wiener processes. This order reduction down to that of the Euler-Maruyama method imposes severe difficulties in obtaining meaningful solutions in a reasonable time frame and this paper attempts to circumvent these difficulties by some new techniques. An additional difficulty in solving SODEs arises even in the Linear case since it is not possible to write the solution analytically in terms of matrix exponentials unless there is a commutativity property between the functions associated with the multiple Wiener processes. Thus in this present paper first the work of Magnus [On the exponential solution of differential equations for a linear operator, Communications on Pure and Applied Mathematics 7 (1954) 649-673] (applied to deterministic non-commutative Linear problems) will be applied to non-commutative linear SODEs and methods of strong order 1.5 for arbitrary, linear, non-commutative SODE systems will be constructed - hence giving an accurate approximation to the general linear problem. Secondly, for general nonlinear non-commutative systems with an arbitrary number (d) of Wiener processes it is shown that strong local order I Runge-Kutta methods with d + 1 stages can be constructed by evaluated a set of Lie brackets as well as the standard function evaluations. A method is then constructed which can be efficiently implemented in a parallel environment for this arbitrary number of Wiener processes. Finally some numerical results are presented which illustrate the efficacy of these approaches. (C) 1999 Elsevier Science B.V. All rights reserved.

Electron paramagnetic resonance, optical absorption and Raman spectral studies on a pyrite/chalcopyrite mineral

Pyrite and chalcopyrite mineral samples from Mangampet barite mine, Kadapa, Andhra Pradesh, India are used in the present study. XRD data indicate that the pyrite mineral has a face centered cubic lattice structure with lattice constant 5.4179 Å. Also it possesses an average particle size of 91.9 nm. An EPR study on the powdered samples confirms the presence of iron in pyrite and iron and Mn(II) in chalcopyrite. The optical absorption spectrum of chalcopyrite indicates presence of copper which is in a distorted octahedral environment. NIR results confirm the presence of water fundamentals and Raman spectrum reveals the presence of water and sulfate ions.

Spectral approximations to the fractional integral and derivative

In this paper, the spectral approximations are used to compute the fractional integral and the Caputo derivative. The effective recursive formulae based on the Legendre, Chebyshev and Jacobi polynomials are developed to approximate the fractional integral. And the succinct scheme for approximating the Caputo derivative is also derived. The collocation method is proposed to solve the fractional initial value problems and boundary value problems. Numerical examples are also provided to illustrate the effectiveness of the derived methods.

Bearing Fault Diagnostics Using the Spectral Pattern Recognition

In the field of diagnostics of rolling element bearings, the development of sophisticated techniques, such as Spectral Kurtosis and 2nd Order Cyclostationarity, extended the capability of expert users to identify not only the presence, but also the location of the damage in the bearing. Most of the signal-analysis methods, as the ones previously mentioned, result in a spectrum-like diagram that presents line frequencies or peaks in the neighbourhood of some theoretical characteristic frequencies, in case of damage. These frequencies depend only on damage position, bearing geometry and rotational speed. The major improvement in this field would be the development of algorithms with high degree of automation. This paper aims at this important objective, by discussing for the first time how these peaks can draw away from the theoretical expected frequencies as a function of different working conditions, i.e. speed, torque and lubrication. After providing a brief description of the peak-patterns associated with each type of damage, this paper shows the typical magnitudes of the deviations from the theoretical expected frequencies. The last part of the study presents some remarks about increasing the reliability of the automatic algorithm. The research is based on experimental data obtained by using artificially damaged bearings installed in a gearbox.

Flexible IBE and beyond in the commutative-blinding framework

The cryptographic community has, of late, shown much inventiveness in the creation of powerful new IBE-like primitives that go beyond the basic IBE notion and extend it in many new directions. Virtually all of these “super-IBE” schemes rely on bilinear pairings for their implementation, which they tend to use in a surprisingly small number of different ways: three of them as of this writing. What is interesting is that, among the three main frameworks that we know of so far, one has acted as a veritable magnet for the construction of many of these “generalized IBE” primitives, whereas the other two have not been nearly as fruitful in that respect. This refers to the Commutative Blinding framework defined by the Boneh-Boyen [Bscr ][Bscr ]1 IBE scheme from 2004. The aim of this chapter is to try to shed some light on this approach's popularity, first by comparing its key properties with those of the competing frameworks, and then by providing a number of examples that illustrate how those properties have been used.