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.

Harmonic elimination technique for a single-phase multilevel converter with unequal DC link voltage levels

Multilevel converters, because of the benefits they attract in generating high quality output voltage, are used in several applications. Various modulation and control techniques are introduced by several researchers to control the output voltage of the multilevel converters like space vector modulation and harmonic elimination (HE) methods. Multilevel converters may have a DC link with equal or unequal DC voltages. In this study a new HE technique based on the HE method is proposed for multilevel converters with unequal DC link voltage. The DC link voltage levels are considered as additional variables for the HE method and the voltage levels are defined based on the HE results. Increasing the number of voltage levels can reduce lower order harmonic content because of the fact that more variables are created. In comparison to previous methods, this new technique has a positive effect on the output voltage quality by reducing its total harmonic distortion, which must take into consideration for some applications such as uninterruptable power supply, motor drive systems and piezoelectric transducer excitation. In order to verify the proposed modulation technique, MATLAB simulations and experimental tests are carried out for a single-phase four-level diode-clamped converter.

Mechanism of dehydroxylation temperature decrease and high temperature phase transition of coal-bearing strata kaolinite intercalated by potassium acetate

The thermal decomposition and dehydroxylation process of coal-bearing strata kaolinite–potassium acetate intercalation complex (CSKK) has been studied using X-ray diffraction (XRD), infrared spectroscopy (IR), thermal analysis, mass spectrometric analysis and infrared emission spectroscopy. The XRD results showed that the potassium acetate (KAc) have been successfully intercalated into coal-bearing strata kaolinite with an obvious basal distance increase of the first basal peak, and the positive correlation was found between the concentration of intercalation regent KAc and the degree of intercalation. As the temperature of the system is raised, the formation of KHCO3, KCO3 and KAlSiO4, which is derived from the thermal decomposition or phase transition of CSKK, is observed in sequence. The IR results showed that new bands appeared, the position and intensities shift can also be found when the concentration of intercalation agent is raised. The thermal analysis and mass spectrometric analysis results revealed that CSKK is stable below 300 °C, and the thermal decomposition products (H2O and CO2) were further proved by the mass spectrometric analysis. A comparison of thermal analysis results of original coal-bearing strata kaolinite and its intercalation complex gives new discovery that not only a new mass loss peak is observed at 285 °C, but also the temperature of dehydroxylation and dehydration of coal bearing strata kaolinite is decreased about 100 °C. This is explained on the basis of the interlayer space of the kaolinite increased obviously after being intercalated by KAc, which led to the interlayer hydrogen bonds weakened, enables the dehydroxylation from kaolinite surface more easily. Furthermore, the possible structural model for CSKK has been proposed, with further analysis required in order to prove the most possible structures.

Time-varying bispectral analysis of visually evoked multi-channel EEG

Theoretical foundations of higher order spectral analysis are revisited to examine the use of time-varying bicoherence on non-stationary signals using a classical short-time Fourier approach. A methodology is developed to apply this to evoked EEG responses where a stimulus-locked time reference is available. Short-time windowed ensembles of the response at the same offset from the reference are considered as ergodic cyclostationary processes within a non-stationary random process. Bicoherence can be estimated reliably with known levels at which it is significantly different from zero and can be tracked as a function of offset from the stimulus. When this methodology is applied to multi-channel EEG, it is possible to obtain information about phase synchronization at different regions of the brain as the neural response develops. The methodology is applied to analyze evoked EEG response to flash visual stimulii to the left and right eye separately. The EEG electrode array is segmented based on bicoherence evolution with time using the mean absolute difference as a measure of dissimilarity. Segment maps confirm the importance of the occipital region in visual processing and demonstrate a link between the frontal and occipital regions during the response. Maps are constructed using bicoherence at bifrequencies that include the alpha band frequency of 8Hz as well as 4 and 20Hz. Differences are observed between responses from the left eye and the right eye, and also between subjects. The methodology shows potential as a neurological functional imaging technique that can be further developed for diagnosis and monitoring using scalp EEG which is less invasive and less expensive than magnetic resonance imaging.

Histological and morphometric lesions in the pre-clinical, developmental phase of insulin-induced laminitis in Standardbred horses

Lamellar pathology in experimentally-induced equine laminitis associated with euglycaemic hyperinsulinaemia is substantial by the acute, clinical phase (∼48 h post-induction). However, lamellar pathology of the developmental, pre-clinical phase requires evaluation. The aim of this study was to analyse lamellar lesions both qualitatively and quantitatively, 6, 12 and 24 h after the commencement of hyperinsulinaemia. Histological and histomorphometrical analyses of lamellar pathology at each time-point included assessment of lamellar length and width, epidermal cell proliferation and death, basement membrane (BM) pathology and leucocyte infiltration. Archived lamellar tissue from control horses and those with acute, insulin-induced laminitis (48 h) was also assessed for cellular proliferative activity by counting the number of cells showing positive nuclear immuno labelling for TPX2. Decreased secondary epidermal lamellar (SEL) width and increased histomorphological evidence of SEL epidermal basal (and supra-basal) cell death occurred early in disease progression (6 h). Increased cellular proliferation in SELs, infiltration of the dermis with small numbers of leucocytes and BM damage occurred later (24 and 48 h). Some lesions, such as narrowing of the SELs, were progressive over this time period (6–48 h). Cellular pathology preceded leucocyte infiltration and BM pathology, indicating that the latter changes may be secondary or downstream events in hyperinsulinaemic laminitis.

Advanced practice nursing role development : factor analysis of a modified role delineation tool

Aim his study reports the use of exploratory factor analysis to determine construct validity of a modified advanced practice role delineation tool. Background Little research exists on specific activities and domains of practice within advanced practice nursing roles, making it difficult to define service parameters of this level of nursing practice. A valid and reliable tool would assist those responsible for employing or deploying advanced practice nurses by identifying and defining their service profile. This is the third paper from a multi-phase Australian study aimed at assigning advanced practice roles. Methods A postal survey was conducted of a random sample of state government employed Registered nurses and midwives, across various levels and grades of practice in the state of Queensland, Australia, using the modified Advanced Practice Role Delineation tool. Exploratory factor analysis, using principal axis factoring was undertaken to examine factors in the modified tool. Cronbach’s alpha coefficient determined reliability of the overall scale and identified factors. Results There were 658 responses (42% response rate). The five factors found with loadings of ≥.400 for 40 of the 41 APN activities were similar to the five domains in the Strong model. Cronbach’s alpha coefficient was .94 overall and for the factors ranged from 0.83 to 0.95. Conclusion Exploratory factor analysis of the modified tool supports validity of the five domains of the original tool. Further investigation will identify use of the tool in a broader healthcare environment.

Exponential integrators and a dual-scale model for wood drying

For the timber industry, the ability to simulate the drying of wood is invaluable for manufacturing high quality wood products. Mathematically, however, modelling the drying of a wet porous material, such as wood, is a diffcult task due to its heterogeneous and anisotropic nature, and the complex geometry of the underlying pore structure. The well{ developed macroscopic modelling approach involves writing down classical conservation equations at a length scale where physical quantities (e.g., porosity) can be interpreted as averaged values over a small volume (typically containing hundreds or thousands of pores). This averaging procedure produces balance equations that resemble those of a continuum with the exception that effective coeffcients appear in their deffnitions. Exponential integrators are numerical schemes for initial value problems involving a system of ordinary differential equations. These methods differ from popular Newton{Krylov implicit methods (i.e., those based on the backward differentiation formulae (BDF)) in that they do not require the solution of a system of nonlinear equations at each time step but rather they require computation of matrix{vector products involving the exponential of the Jacobian matrix. Although originally appearing in the 1960s, exponential integrators have recently experienced a resurgence in interest due to a greater undertaking of research in Krylov subspace methods for matrix function approximation. One of the simplest examples of an exponential integrator is the exponential Euler method (EEM), which requires, at each time step, approximation of φ(A)b, where φ(z) = (ez - 1)/z, A E Rnxn and b E Rn. For drying in porous media, the most comprehensive macroscopic formulation is TransPore [Perre and Turner, Chem. Eng. J., 86: 117-131, 2002], which features three coupled, nonlinear partial differential equations. The focus of the first part of this thesis is the use of the exponential Euler method (EEM) for performing the time integration of the macroscopic set of equations featured in TransPore. In particular, a new variable{ stepsize algorithm for EEM is presented within a Krylov subspace framework, which allows control of the error during the integration process. The performance of the new algorithm highlights the great potential of exponential integrators not only for drying applications but across all disciplines of transport phenomena. For example, when applied to well{ known benchmark problems involving single{phase liquid ow in heterogeneous soils, the proposed algorithm requires half the number of function evaluations than that required for an equivalent (sophisticated) Newton{Krylov BDF implementation. Furthermore for all drying configurations tested, the new algorithm always produces, in less computational time, a solution of higher accuracy than the existing backward Euler module featured in TransPore. Some new results relating to Krylov subspace approximation of '(A)b are also developed in this thesis. Most notably, an alternative derivation of the approximation error estimate of Hochbruck, Lubich and Selhofer [SIAM J. Sci. Comput., 19(5): 1552{1574, 1998] is provided, which reveals why it performs well in the error control procedure. Two of the main drawbacks of the macroscopic approach outlined above include the effective coefficients must be supplied to the model, and it fails for some drying configurations, where typical dual{scale mechanisms occur. In the second part of this thesis, a new dual{scale approach for simulating wood drying is proposed that couples the porous medium (macroscale) with the underlying pore structure (microscale). The proposed model is applied to the convective drying of softwood at low temperatures and is valid in the so{called hygroscopic range, where hygroscopically held liquid water is present in the solid phase and water exits only as vapour in the pores. Coupling between scales is achieved by imposing the macroscopic gradient on the microscopic field using suitably defined periodic boundary conditions, which allows the macroscopic ux to be defined as an average of the microscopic ux over the unit cell. This formulation provides a first step for moving from the macroscopic formulation featured in TransPore to a comprehensive dual{scale formulation capable of addressing any drying configuration. Simulation results reported for a sample of spruce highlight the potential and flexibility of the new dual{scale approach. In particular, for a given unit cell configuration it is not necessary to supply the effective coefficients prior to each simulation.

Social signal processing for pain monitoring using a hidden conditional random field

utomatic pain monitoring has the potential to greatly improve patient diagnosis and outcomes by providing a continuous objective measure. One of the most promising methods is to do this via automatically detecting facial expressions. However, current approaches have failed due to their inability to: 1) integrate the rigid and non-rigid head motion into a single feature representation, and 2) incorporate the salient temporal patterns into the classification stage. In this paper, we tackle the first problem by developing a “histogram of facial action units” representation using Active Appearance Model (AAM) face features, and then utilize a Hidden Conditional Random Field (HCRF) to overcome the second issue. We show that both of these methods improve the performance on the task of pain detection in sequence level compared to current state-of-the-art-methods on the UNBC-McMaster Shoulder Pain Archive.

Preparation and thermal energy storage properties of paraffin/calcined diatomite composites as form-stable phase change materials

A composite paraffin-based phase change material (PCM) was prepared by blending composite paraffin and calcined diatomite through the fusion adsorption method. In this study, raw diatomite was purified by thermal treatment in order to improve the adsorption capacity of diatomite, which acted as a carrier material to prepare shape-stabilized PCMs. Two forms of paraffin (paraffin waxes and liquid paraffin) with different melting points were blended together by the fusion method, and the optimum mixed proportion with a suitable phase-transition temperature was obtained through differential scanning calorimetry (DSC) analysis. Then the prepared composite paraffin was adsorbed in calcined diatomite. The prepared paraffin/calcined diatomite composites were characterized by the scanning electron microscope (SEM) and Fourier transformation infrared (FT-IR) analysis techniques. Thermal energy storage properties of the composite PCMs were determined by DSC method. DSC results showed that there was an optimum adsorption ratio between composite paraffin and calcined diatomite and the phase-transition temperature and the latent heat of the composite PCMs were 33.04 ◦C and 89.54 J/g, respectively. Thermal cycling test of composite PCMs showed that the prepared material is thermally reliable and chemically stable. The obtained paraffin/calcined diatomite composites have proper latent heat and melting temperatures, and show practical significance and good potential application value.

Interpersonal coordination tendencies shape 1-vs-1 sub-phase performance outcomes in youth soccer

This study investigated the influence of interpersonal coordination tendencies on performance outcomes of 1-vs-1 subphases in youth soccer. Eight male developing soccer players (age: 11.8+0.4 years; training experience: 3.6+1.1 years) performed an in situ simulation of a 1-vs-1 sub-phase of soccer. Data from 82 trials were obtained with motion-analysis techniques, and relative phase used to measure the space-time coordination tendencies of attacker-defender dyads. Approximate entropy (ApEn) was then used to quantify the unpredictability of interpersonal interactions over trials. Results revealed how different modes of interpersonal coordination emerging from attacker-defender dyads influenced the 1-vs-1 performance outcomes. High levels of space-time synchronisation (47%) and unpredictability in interpersonal coordination processes (ApEn: 0.91+0.34) were identified as key features of an attacking player’s success. A lead-lag relation attributed to a defending player (34% around 7308 values) and a more predictable coordination mode (ApEn: 0.65+0.27, P50.001), demonstrated the coordination tendencies underlying the success of defending players in 1-vs-1 sub-phases. These findings revealed how the mutual influence of each player on the behaviour of dyadic systems shaped emergent performance outcomes. More specifically, the findings showed that attacking players should be constrained to exploit the space-time synchrony with defenders in an unpredictable and creative way, while defenders should be encouraged to adopt postures and behaviours that actively constrain the attacker’s actions.

Sex discrimination and non-random sampling in the Australian labour market

Historically a significant gap between male and female wages has existed in the Australian labour market. Indeed this wage differential was institutionalised in the 1912 arbitration decision which determined that the basic female wage would be set at between 54 and 66 per cent of the male wage. More recently however, the 1969 and 1972 Equal Pay Cases determined that male/female wage relativities should be based upon the premise of equal pay for work of equal value. It is important to note that the mere observation that average wages differ between males and females is not sine qua non evidence of sex discrimination. Economists restrict the definition of wage discrimination to cases where two distinct groups receive different average remuneration for reasons unrelated to differences in productivity characteristics. This paper extends previous studies of wage discrimination in Australia (Chapman and Mulvey, 1986; Haig, 1982) by correcting the estimated male/female wage differential for the existence of non-random sampling. Previous Australian estimates of male/female human capital basedwage specifications together with estimates of the corresponding wage differential all suffer from a failure to address this issue. If the sample of females observed to be working does not represent a random sample then the estimates of the male/female wage differential will be both biased and inconsistent.

Experimental and computer simulation validation of ultrasound phase interference created by lateral inhomogeneity of transit time in replica bone marrow composite models

Purpose: The measurement of broadband ultrasonic attenuation (BUA) in cancellous bone for the assessment of osteoporosis follows a parabolic-type dependence with bone volume fraction; having minima values corresponding to both entire bone and entire marrow. Langton has recently proposed that the primary BUA mechanism may be significant phase interference due to variations in propagation transit time through the test sample as detected over the phase-sensitive surface of the receive ultrasound transducer. This fundamentally simple concept assumes that the propagation of ultrasound through a complex solid : liquid composite sample such as cancellous bone may be considered by an array of parallel ‘sonic rays’. The transit time of each ray is defined by the proportion of bone and marrow propagated, being a minimum (tmin) solely through bone and a maximum (tmax) solely through marrow. A Transit Time Spectrum (TTS), ranging from tmin to tmax, may be defined describing the proportion of sonic rays having a particular transit time, effectively describing lateral inhomogeneity of transit time over the surface of the receive ultrasound transducer. Phase interference may result from interaction of ‘sonic rays’ of differing transit times. The aim of this study was to test the hypothesis that there is a dependence of phase interference upon the lateral inhomogenity of transit time by comparing experimental measurements and computer simulation predictions of ultrasound propagation through a range of relatively simplistic solid:liquid models exhibiting a range of lateral inhomogeneities. Methods: A range of test models was manufactured using acrylic and water as surrogates for bone and marrow respectively. The models varied in thickness in one dimension normal to the direction of propagation, hence exhibiting a range of transit time lateral inhomogeneities, ranging from minimal (single transit time) to maximal (wedge; ultimately the limiting case where each sonic ray has a unique transit time). For the experimental component of the study, two unfocused 1 MHz ¾” broadband diameter transducers were utilized in transmission mode; ultrasound signals were recorded for each of the models. The computer simulation was performed with Matlab, where the transit time and relative amplitude of each sonic ray was calculated. The transit time for each sonic ray was defined as the sum of transit times through acrylic and water components. The relative amplitude considered the reception area for each sonic ray along with absorption in the acrylic. To replicate phase-sensitive detection, all sonic rays were summed and the output signal plotted in comparison with the experimentally derived output signal. Results: From qualtitative and quantitative comparison of the experimental and computer simulation results, there is an extremely high degree of agreement of 94.2% to 99.0% between the two approaches, supporting the concept that propagation of an ultrasound wave, for the models considered, may be approximated by a parallel sonic ray model where the transit time of each ray is defined by the proportion of ‘bone’ and ‘marrow’. Conclusions: This combined experimental and computer simulation study has successfully demonstrated that lateral inhomogeneity of transit time has significant potential for phase interference to occur if a phase-sensitive ultrasound receive transducer is implemented as in most commercial ultrasound bone analysis devices.

Breast cancer detection from thermal images using bispectral invariant features

Highly sensitive infrared (IR) cameras provide high-resolution diagnostic images of the temperature and vascular changes of breasts. These images can be processed to emphasize hot spots that exhibit early and subtle changes owing to pathology. The resulting images show clusters that appear random in shape and spatial distribution but carry class dependent information in shape and texture. Automated pattern recognition techniques are challenged because of changes in location, size and orientation of these clusters. Higher order spectral invariant features provide robustness to such transformations and are suited for texture and shape dependent information extraction from noisy images. In this work, the effectiveness of bispectral invariant features in diagnostic classification of breast thermal images into malignant, benign and normal classes is evaluated and a phase-only variant of these features is proposed. High resolution IR images of breasts, captured with measuring accuracy of ±0.4% (full scale) and temperature resolution of 0.1 °C black body, depicting malignant, benign and normal pathologies are used in this study. Breast images are registered using their lower boundaries, automatically extracted using landmark points whose locations are learned during training. Boundaries are extracted using Canny edge detection and elimination of inner edges. Breast images are then segmented using fuzzy c-means clustering and the hottest regions are selected for feature extraction. Bispectral invariant features are extracted from Radon projections of these images. An Adaboost classifier is used to select and fuse the best features during training and then classify unseen test images into malignant, benign and normal classes. A data set comprising 9 malignant, 12 benign and 11 normal cases is used for evaluation of performance. Malignant cases are detected with 95% accuracy. A variant of the features using the normalized bispectrum, which discards all magnitude information, is shown to perform better for classification between benign and normal cases, with 83% accuracy compared to 66% for the original.

The structured phase of concurrency

This extended abstract summarizes the state-of-the-art solution to the structuring problem for models that describe existing real world or envisioned processes. Special attention is devoted to models that allow for the true concurrency semantics. Given a model of a process, the structuring problem deals with answering the question of whether there exists another model that describes the process and is solely composed of structured patterns, such as sequence, selection, option for simultaneous execution, and iteration. Methods and techniques for structuring developed by academia as well as products and standards proposed by industry are discussed. Expectations and recommendations on the future advancements of the structuring problem are suggested.