Numerical methods for second-order stochastic differential equations

We seek numerical methods for second‐order stochastic differential equations that reproduce the stationary density accurately for all values of damping. A complete analysis is possible for scalar linear second‐order equations (damped harmonic oscillators with additive noise), where the statistics are Gaussian and can be calculated exactly in the continuous‐time and discrete‐time cases. A matrix equation is given for the stationary variances and correlation for methods using one Gaussian random variable per timestep. The only Runge–Kutta method with a nonsingular tableau matrix that gives the exact steady state density for all values of damping is the implicit midpoint rule. Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case.

Studies of granulosa cell maturation in dominant and subordinate bovine follicles : novel extracellular matrix focimatrix is co-ordinately regulated with cholesterol side-chain cleavage CYP11A1

During growth of antral ovarian follicles granulosa cells first become associated with a novel type of extracellular matrix, focimatrix, and at larger sizes follicles become either subordinate or dominant. To examine this, bovine subordinate (9.0±s.e.m. 0.4 mm; n=16), partially dominant (12.0±0.6 mm; n=18) and fully dominant (15.0±0.4 mm; n=14) follicles were examined by real time RT-PCR analyses of granulosa cells and by immunohistochemistry of focimatrix. Changes in the expression of FSH receptor, LH receptor, cholesterol side-chain cleavage (CYP11A1), 3β-hydroxysteroid dehydrogenase, aromatase (CYP19A1) and inhibin-α and β-B were observed as expected for follicle sizes examined. After adjusting for size differences, only CYP11A1 was significantly different between the groups, and elevated in dominant follicles. Also after adjusting for differences in size there were no significant differences in expression of focimatrix components collagen type IV α-1 (COL4A1), laminin β-2, nidogen 1 (NID1), and perlecan (HSPG2) or the volume density of NID1 and -2 and HSPG2. The volume density of focimatrix components in laminin 111 was significantly elevated in dominant follicles. Adjusting for analysis of more than one follicle per animal and for multiple correlations, CYP11A1 mRNA levels were highly correlated with the focimatrix genes COL4A1, NID1 and -2 and HSPG2. Thus, focimatrix may potentially regulate CYP11A1 expression, and the regulation of both could be important in follicular dominance.

‘Spotty Dick’ : a research experiment to test design suitability for the use of jewelled spot matrix patterns for UV aware men’s swimwear

The great male Aussie cossie is growing spots. The ‘dick’ tog, as it is colloquially referred to, is linked to Australia’s national identify with overtly masculine bronzed Aussie bodies clothed in this iconic apparel. Yet the reality is our hunger for worshiping the sun and the addiction to a beach lifestyle is tempered by the pragmatic need for neck-to-knee, or more apt head-to-toe, swimwear. Spotty Dick is an irreverent play on male swimwear – it experiments with alternate modes to sheath the body with Lyrca in order to protect it from searing UV’s and at the same time light-heartedly fools around with texture and pattern; to be specific, black Scharovsky crystals, jewelled in spot patterns - jewelled clothing is not characteristically aligned to menswear and even less so to the great Aussie cossie. The crystals form a matrix of spots that attempt to provoke a sense of mischievousness aligned to the Aussie beach larrikin. Ironically, spot patterns are in itself a form of a parody, as prolonged sun exposure ages the skin and sun spots can occur if appropriate sun protection is not used. ‘Spotty Dick’ – a research experiment to test design suitability for the use of jewelled spot matrix patterns for UV aware men’s swimwear. The creative work was paraded at 56 shows, over a 2 week period, and an estimated 50,000 people viewed the work.

Fast detection of exact clones in business process model repositories

As organizations reach higher levels of business process management maturity, they often find themselves maintaining very large process model repositories, representing valuable knowledge about their operations. A common practice within these repositories is to create new process models, or extend existing ones, by copying and merging fragments from other models. We contend that if these duplicate fragments, a.k.a. ex- act clones, can be identified and factored out as shared subprocesses, the repository’s maintainability can be greatly improved. With this purpose in mind, we propose an indexing structure to support fast detection of clones in process model repositories. Moreover, we show how this index can be used to efficiently query a process model repository for fragments. This index, called RPSDAG, is based on a novel combination of a method for process model decomposition (namely the Refined Process Structure Tree), with established graph canonization and string matching techniques. We evaluated the RPSDAG with large process model repositories from industrial practice. The experiments show that a significant number of non-trivial clones can be efficiently found in such repositories, and that fragment queries can be handled efficiently.

New exact solutions for Hele-Shaw flow in doubly connected regions

Radial Hele-Shaw flows are treated analytically using conformal mapping techniques. The geometry of interest has a doubly-connected annular region of viscous fluid surrounding an inviscid bubble that is either expanding or contracting due to a pressure difference caused by injection or suction of the inviscid fluid. The zero-surface-tension problem is ill-posed for both bubble expansion and contraction, as both scenarios involve viscous fluid displacing inviscid fluid. Exact solutions are derived by tracking the location of singularities and critical points in the analytic continuation of the mapping function. We show that by treating the critical points, it is easy to observe finite-time blow-up, and the evolution equations may be written in exact form using complex residues. We present solutions that start with cusps on one interface and end with cusps on the other, as well as solutions that have the bubble contracting to a point. For the latter solutions, the bubble approaches an ellipse in shape at extinction.

Sensitivity of the NMR density matrix to pulse sequence parameters : a simplified analytic approach

We present a formalism for the analysis of sensitivity of nuclear magnetic resonance pulse sequences to variations of pulse sequence parameters, such as radiofrequency pulses, gradient pulses or evolution delays. The formalism enables the calculation of compact, analytic expressions for the derivatives of the density matrix and the observed signal with respect to the parameters varied. The analysis is based on two constructs computed in the course of modified density-matrix simulations: the error interrogation operators and error commutators. The approach presented is consequently named the Error Commutator Formalism (ECF). It is used to evaluate the sensitivity of the density matrix to parameter variation based on the simulations carried out for the ideal parameters, obviating the need for finite-difference calculations of signal errors. The ECF analysis therefore carries a computational cost comparable to a single density-matrix or product-operator simulation. Its application is illustrated using a number of examples from basic NMR spectroscopy. We show that the strength of the ECF is its ability to provide analytic insights into the propagation of errors through pulse sequences and the behaviour of signal errors under phase cycling. Furthermore, the approach is algorithmic and easily amenable to implementation in the form of a programming code. It is envisaged that it could be incorporated into standard NMR product-operator simulation packages.

The developmental and acute phases of insulin-induced laminitis involve minimal metalloproteinase activity

Metalloproteinases have been implicated in the pathogenesis of equine laminitis and other inflammatory conditions, through their role in the degradation and remodelling of the extracellular matrix environment. Matrix metalloproteinases (MMPs) and their inhibitors are present in normal equine lamellae, with increased secretion and activation of some metalloproteinases reported in horses with laminitis associated with systemic inflammation. It is unknown whether these enzymes are involved in insulin-induced laminitis, which occurs without overt systemic inflammation. In this study, gene expression of MMP-2, MMP-9, MT1-MMP, ADAMTS-4 and TIMP-3 was determined in the lamellar tissue of normal control horses (n = 4) and horses that developed laminitis after 48 h of induced hyperinsulinaemia (n = 4), using quantitative Real Time-Polymerase Chain Reaction (qRT-PCR). Protein concentrations of MMP-2 and MMP-9 were also examined using gelatin zymography in horses subject to prolonged hyperinsulinaemia for 6 h (n = 4), 12 h (n = 4), 24 h (n = 4) and 48 h (n = 4), and in normal control horses (n = 4). The only change in gene expression observed was an upregulation of MMP-9 (p < 0.05) in horses that developed insulin-induced laminitis (48 h). Zymographical analysis showed an increase (p < 0.05) in pro MMP-9 during the acute phase of laminitis (48 h), whereas pro MMP-2 was present in similar concentration in the tissue of all horses. Thus, MMP-2, MT1-MMP, TIMP-3 and ADAMTS-4 do not appear to play a significant role in the pathogenesis of insulin-induced laminitis. The increased expression of MMP-9 may be associated with the infiltration of inflammatory leukocytes, or may be a direct result of hyperinsulinaemia. The exact role of MMP-9 in basement membrane degradation in laminitis is uncertain as it appears to be present largely in the inactive form.