Order conditions of stochastic Runge-Kutta methods by B-series

In this paper, general order conditions and a global convergence proof are given for stochastic Runge Kutta methods applied to stochastic ordinary differential equations ( SODEs) of Stratonovich type. This work generalizes the ideas of B-series as applied to deterministic ordinary differential equations (ODEs) to the stochastic case and allows a completely general formalism for constructing high order stochastic methods, either explicit or implicit. Some numerical results will be given to illustrate this theory.

General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems

In many modeling situations in which parameter values can only be estimated or are subject to noise, the appropriate mathematical representation is a stochastic ordinary differential equation (SODE). However, unlike the deterministic case in which there are suites of sophisticated numerical methods, numerical methods for SODEs are much less sophisticated. Until a recent paper by K. Burrage and P.M. Burrage (1996), the highest strong order of a stochastic Runge-Kutta method was one. But K. Burrage and P.M. Burrage (1996) showed that by including additional random variable terms representing approximations to the higher order Stratonovich (or Ito) integrals, higher order methods could be constructed. However, this analysis applied only to the one Wiener process case. In this paper, it will be shown that in the multiple Wiener process case all known stochastic Runge-Kutta methods can suffer a severe order reduction if there is non-commutativity between the functions associated with the Wiener processes. Importantly, however, it is also suggested how this order can be repaired if certain commutator operators are included in the Runge-Kutta formulation. (C) 1998 Elsevier Science B.V. and IMACS. All rights reserved.

Socioeconomic inequalities in cardiovascular mortality and the role of childhood socioeconomic conditions and adulthood risk factors : a prospective cohort study with 17-years of follow up

Background The mechanisms underlying socioeconomic inequalities in mortality from cardiovascular diseases (CVD) are largely unknown. We studied the contribution of childhood socioeconomic conditions and adulthood risk factors to inequalities in CVD mortality in adulthood. Methods The prospective GLOBE study was carried out in the Netherlands, with baseline data from 1991, and linked with the cause of death register in 2007. At baseline, participants reported on adulthood socioeconomic position (SEP) (own educational level), childhood socioeconomic conditions (occupational level of respondent’s father), and a broad range of adulthood risk factors (health behaviours, material circumstances, psychosocial factors). This present study is based on 5,395 men and 6,306 women, and the data were analysed using Cox regression models and hazard ratios (HR). Results A low adulthood SEP was associated with increased CVD mortality for men (HR 1.84; 95% CI: 1.41-2.39) and women (HR 1.80; 95%CI: 1.04-3.10). Those with poorer childhood socioeconomic conditions were more likely to die from CVD in adulthood, but this reached statistical significance only among men with the poorest childhood socioeconomic circumstances. About half of the investigated adulthood risk factors showed significant associations with CVD mortality among both men and women, namely renting a house, experiencing financial problems, smoking, physical activity and marital status. Alcohol consumption and BMI showed a U-shaped relationship with CVD mortality among women, with the risk being significantly greater for both abstainers and heavy drinkers, and among women who were underweight or obese. Among men, being single or divorced and using sleep/anxiety drugs increased the risk of CVD mortality. In explanatory models, the largest contributor to adulthood CVD inequalities were material conditions for men (42%; 95% CI: −73 to −20) and behavioural factors for women (55%; 95% CI: -191 to −28). Simultaneous adjustment for adulthood risk factors and childhood socioeconomic conditions attenuated the HR for the lowest adulthood SEP to 1.34 (95% CI: 0.99-1.82) for men and 1.19 (95% CI: 0.65-2.15) for women. Conclusions Adulthood material, behavioural and psychosocial factors played a major role in the explanation of adulthood SEP inequalities in CVD mortality. Childhood socioeconomic circumstances made a modest contribution, mainly via their association with adulthood risk factors. Policies and interventions to reduce health inequalities are likely to be most effective when considering the influence of socioeconomic circumstances across the entire life course and in particular, poor material conditions and unhealthy behaviours in adulthood.

Carbohydrate gel ingestion and immunoendocrine responses to cycling in temperate and hot conditions

PURPOSE: Heat stress might attenuate the effects of carbohydrate on immunoendocrine responses to exercise by increasing endogenous glucose production and reducing the rate of exogenous carbohydrate oxidation. The authors compared the efficacy of carbohydrate consumption on immune responses to exercise in temperate vs. hot conditions. METHODS: Ten male cyclists exercised on 2 separate occasions in temperate (18.1 +/- 0.4 degrees C, 58% +/- 8% relative humidity) and on another 2 occasions in hot conditions (32.2 +/- 0.7 degrees C, 55% +/- 2% relative humidity). On each occasion, the cyclists exercised in a fed state for 90 min at approximately 60% VO2max and then completed a 16.1-km time trial. Every 15 min during the first 90 min of exercise, they consumed 0.24 g/kg body mass of a carbohydrate or placebo gel. RESULTS: Neutrophil counts increased during exercise in all trials (p < .05) and were significantly lower (40%, p = .006) after the carbohydrate than after the placebo trial in 32 degrees C. The concentrations of serum interleukin (IL)-6, IL-8, and IL-10 and plasma granulocyte-colony-stimulating factor, myeloperoxidase, and calprotectin also increased during exercise in all trials but did not differ significantly between the carbohydrate and placebo trials. Plasma norepinephrine concentration increased during exercise in all trials and was significantly higher (50%, p = .01) after the carbohydrate vs. the placebo trial in 32 degrees C. CONCLUSION: Carbohydrate ingestion attenuated neutrophil counts during exercise in hot conditions, whereas it had no effect on any other immune variables in either temperate or hot conditions.

Effect of driving conditions and suspension parameters on dynamic load-sharing of longitudinal-connected air suspensions

The objective of this research was to investigate the effects of driving conditions and suspension parameters on dynamic load-sharing of longitudinal-connected air suspensions of a tri-axle semi-trailer. A novel nonlinear model of a multi-axle semi-trailer with longitudinal-connected air suspension was formulated based on fluid mechanics and thermodynamics and was validated through test results. The effects of driving conditions and suspension parameters on dynamic load-sharing and road-friendliness of the semi-trailer were analyzed. Simulation results indicate that the road-friendliness metric-DLC (dynamic load coefficient) is not always in accordance with the load-sharing metric-DLSC (dynamic load-sharing coefficient). The effect of employing larger air lines and connectors on the DLSC optimization ratio gives varying results as road roughness increases and as driving speed increases. When the vehicle load reduces, or the static pressure increases, the DLSC optimization ratio declines monotonically. The results also indicate that if the air line diameter is always assumed to be larger than the connector diameter, the influence of air line diameter on load-sharing is more significant than that of the connector.

Changes in profit as market conditions change : an historical study of a building firm

This paper analyses the profits from 221 construction projects undertaken by an Australian building firm in the period 1910–1938 and examines the factors that influence the firm's profit levels. This involves a series of multiple regression analyses with three dependent variables representing profit and 26 independent variables representing economic conditions and project characteristics. From these, 11 models are derived of which two are chosen as having the best explanatory power in explaining approximately 72% of the variability in profit levels movements. The results show that unemployment, interest rates, level of construction activity in the state, change of wage level, inflation rate of building material and project value significantly influenced the firm's profit level during the period.

Effect of environmental conditions on degree of hoof wall hydration in horses

Objective: To determine the effect of various environmental conditions on the degree of hydration in hoof wall horn tissue from feral horses and investigate the effect of short-term foot soaking on moisture content in hoof wall and sole tissue in domestic horses. Animals: 40 feral horses from 3 environments (wet and boggy [n = 10], partially flooded [20], and constantly dry desert [10]) and 6 nonferal Quarter Horses. Procedures: The percentage of moisture content of hoof wall samples from feral horses was measured in vitro. In a separate evaluation, the percentage of moisture content of hoof wall and sole tissue was measured in the dry and soaked forefeet of Quarter Horses. Results: Mean ± SD percentage of moisture content was 29.6 ± 5.1%, 29.5 ± 5.8%, and 29.5 ± 2.9% for feral horses from the wet and boggy, partially flooded, and constantly dry desert environments, respectively. Moisture content did not differ among the 3 groups, nor did it differ between dry and soaked hoof wall samples from nonferal horses. However, soaking in water for 2 hours resulted in a significant increase in the percentage of moisture content of the sole. Conclusions and Clinical Relevance: Environmental conditions do not appear to affect moisture content in the hoof wall horn. Soaking horses' feet regularly in water would be unlikely to change the degree of hydration in the hoof wall horn but may further hydrate the sole.

Influence of drying conditions on the moisture diffusion during single stage and two stage fluidized bed drying of bovine intestine for pet food

Bovine intestine samples were heat pump fluidized bed dried at atmospheric pressure and at temperatures below and above the material freezing points equipped with a continuous monitoring system. The investigation of the drying characteristics has been conducted in the temperature range -10~25oC and the airflow in the range 1.5~2.5 m/s. Some experiments were conducted as a single temperature drying experiments and others as two stage drying experiments employing two temperatures. An Arrhenius-type equation was used to interpret the influence of the drying air parameters on the effective diffusivity, calculated with the method of slopes in terms of energy activation, and this was found to be sensitivity of the temperature. The effective diffusion coefficient of moisture transfer was determined by Fickian method using uni-dimensional moisture movement in both moisture, removal by evaporation and combined sublimation and evaporation. Correlations expressing the effective moisture diffusivity and drying temperature are reported.

Diurnal variation of ocular biometrics under natural and defocused conditions

It is well known that a broad range of ocular anatomical and physiological parameters undergo significant diurnal variation. However, the natural diurnal variations that occur in the length of the human eye (axial length) and their underlying causes have been less well studied. Improvements in optical methods for the measurement of ocular biometrics now allow more precise and comprehensive measurements of axial length to be performed than has previously been possible. Research from animal models also suggests a link between diurnal axial length variations and longer term myopic eye growth, and that retinal image defocus can disrupt these diurnal rhythms in axial length. This research programme has examined the diurnal variations in axial length in young normal eyes, the contributing components and the influence of optical stimuli on these changes. In the first experiment, the normal pattern and consistency of the diurnal variations in axial length were examined at 10 different times (5 measurements each day, at ~ 3-hour intervals from ~ 9 am to ~ 9 pm) over 2 consecutive days on 30 young adult subjects (15 myopes, 15 emmetropes). Additionally, variations in a range of other ocular biometric measurements such as choroidal thickness, intraocular pressure, and other ocular biometrics were also explored as potential factors that may be associated with the observed variations in axial length. To investigate the potential influence of refractive error on diurnal axial length variations, the differences in the magnitude and pattern of diurnal variations in axial length between the myopic and emmetropic subjects were examined. Axial length underwent significant diurnal variation that was consistently observed over the 2 consecutive days of measurements, with the longest axial length typically occurring during the day, and the shortest at night. Significant diurnal variations were also observed in choroidal thickness, IOP and other ocular biometrics (such as central corneal thickness, anterior chamber depth and vitreous chamber depth) of the eye. Diurnal variations in vitreous chamber depth, IOP (positive associations) and choroidal thickness (negative association) were all significantly correlated with the diurnal changes in axial length. Choroidal thickness was found to fluctuate approximately in antiphase to the axial length changes, with the average timing of the longest axial length coinciding with the thinnest choroid and vice versa. There were no significant differences in the ocular diurnal variations associated with refractive error. Given that the diurnal changes in axial length could be associated with the changes in the eye’s optical quality, whether the optical quality of the eye also undergoes diurnal variation in the same cohort of young adult myopes and emmetropes over 2 consecutive days was also examined. Significant diurnal variations were observed only in the best sphere refraction (power vector M) and in the spherical aberration of the eye over two consecutive days of testing. The changes in the eyes lower and higher order ocular optics were not significantly associated with the diurnal variations in axial length and the other measured ocular biometric parameters. No significant differences were observed in the magnitude and timing of diurnal variations in lower-order and higher-order optics associated with refractive error. Since the small natural fluctuations in the eye’s optical quality did not appear to be sufficient to influence the natural diurnal fluctuations in ocular biometric parameters, in the next experiment, the influence of monocular myopic defocus (+1.50 DS) upon the normal diurnal variations in axial length and choroidal thickness of young adult emmetropic human subjects (n=13) imposed over a 12 hour period was examined. A series of axial length and choroidal thickness measurements (collected at ~3 hourly intervals, with the first measurement at ~9 am and the final measurement at ~9 pm) were obtained over three consecutive days. The natural diurnal rhythms (Day 1, no defocus), diurnal rhythms with monocular myopic defocus (Day 2, +1.50 DS spectacle lens over the right eye), and the recovery from any defocus induced changes (Day 3, no defocus) were examined. Significant diurnal variations over the course of the day were observed in both axial length and choroidal thickness on each of the three measurement days. The introduction of monocular myopic defocus led to significant reductions in the mean amplitude of diurnal change, and phase shifts in the peak timing of the diurnal rhythms in axial length and choroidal thickness. These defocus induced changes were found to be transient in nature and returned to normal the day following removal of the defocus. To further investigate the influence of optical stimuli on human diurnal rhythms, in the final experiment, the influence of monocular hyperopic defocus on the normal diurnal rhythms in axial length and choroidal thickness was examined in young adult emmetropic subjects (n=15). Similar to the previous experiment, the natural diurnal rhythms (Day 1, no defocus), diurnal rhythms with monocular hyperopic defocus (Day 2, -2.00 DS spectacle lens over the right eye), and the recovery from any defocus induced changes (Day 3, no defocus) were examined over three consecutive days. Both axial length and choroidal thickness underwent significant diurnal variations on each of the three days. The introduction of monocular hyperopic defocus resulted in a significant increase in the amplitude of diurnal change, but no change in the peak timing of diurnal rhythms in both parameters. The ocular changes associated with hyperopic defocus returned to normal, the day following removal of the defocus. This research has shown that axial length undergoes significant diurnal variation in young adult human eyes, and has shown that the natural diurnal variations in choroidal thickness and IOP are significantly associated, and may underlie these diurnal fluctuations in axial length. This work also demonstrated for the first time that exposing young human eyes to monocular myopic and hyperopic defocus leads to a significant disruption in the normal diurnal rhythms of axial length and choroidal thickness. These changes in axial length with defocus may reflect underlying mechanisms in the human eye that are involved in the regulation of longer term eye growth.

Fire safety of buildings based on realistic fire time-temperature curves

In recent times, fire has become a major disaster in buildings due to the increase in fire loads, as a result of modern furniture and light weight construction. This has caused problems for safe evacuation and rescue activities, and in some instances lead to the collapse of buildings (Lewis, 2008 and Nyman, 2002). Recent research has shown that the actual fire resistance of building elements exposed to building fires can be less than their specified fire resistance rating (Lennon and Moore, 2003, Jones, 2002, Nyman, 2002 and Abecassis-Empis et al. 2008). Conventionally the fire rating of building elements is determined using fire tests based on the standard fire time-temperature curve given in ISO 834. This ISO 834 curve was developed in the early 1900s, where wood was the basic fuel source. In reality, modern buildings make use of thermoplastic materials, synthetic foams and fabrics. These materials are high in calorific values and increase both the speed of fire growth and heat release rate, thus increasing the fire severity beyond that of the standard fire curve. Hence it suggests the need to use realistic fire time-temperature curves in tests. Real building fire temperature profiles depend on the fuel load representing the combustible building contents, ventilation openings and thermal properties of wall lining materials. Fuel load is selected based on a review and suitable realistic fire time-temperature curves were developed. Fire tests were then performed for plasterboard lined light gauge steel framed walls for the developed realistic fire curves. This paper presents the details of the development of suitable realistic building fire curves, and the fire tests using them. It describes the fire performance of tested walls in comparison to the standard fire tests and highlights the differences between them. This research has shown the need to use realistic fire exposures in assessing the fire resistance rating of building elements.

In situ imaging of catalytic etching on silver during methanol oxidation conditions by environmental scanning electron microscopy

Polycrystalline silver is used to catalytically oxidise methanol to formaldehyde. This paper reports the results of extensive investigations involving the use of environmental scanning electron microscopy (ESEM) to monitor structural changes in silver during simulated industrial reaction conditions. The interaction of oxygen, nitrogen, and water, either singly or in combination, with a silver catalyst at temperatures up to 973 K resulted in the appearance of a reconstructed silver surface. More spectacular was the effect an oxygen/methanol mixture had on the silver morphology. At a temperature of ca. 713 K pinholes were created in the vicinity of defects as a consequence of subsurface explosions. These holes gradually increased in size and large platelet features were created. Elevation of the catalyst temperature to 843 K facilitated the wholescale oxygen induced restructuring of the entire silver surface. Methanol reacted with subsurface oxygen to produce subsurface hydroxyl species which ultimately formed water in the subsurface layers of silver. The resultant hydrostatic pressure forced the silver surface to adopt a "hill and valley" conformation in order to minimise the surface free energy. Upon approaching typical industrial operating conditions widespread explosions occurred on the catalyst and it was also apparent that the silver surface was extremely mobile under the applied conditions. The interaction of methanol alone with silver resulted in the initial formation of pinholes primarily in the vicinity of defects, due to reaction with oxygen species incorporated in the catalyst during electrochemical synthesis. However, dramatic reduction in the hole concentration with time occurred as all the available oxygen became consumed. A remarkable correlation between formaldehyde production and hole concentration was found.

Influence of oxidation and reduction conditions upon the morphology of silica-supported polycrystalline silver catalysts

The effect of oxidation and reduction conditions upon the morphology of polycrystalline silver catalysts has been investigated by means of in situ Fourier-transform infrared (FTIR) spectroscopy. Characterization of the sample was achieved by inspection of the νas(COO) band profile of adsorbed formate, recorded after dosing with formic acid at ambient temperature. Evidence was obtained for the existence of a silver surface reconstructed by the presence of subsurface oxygen in addition to the conventional family of Ag(111) and Ag(110) crystal faces. Oxidation at 773 K facilitated the reconstruction of silver planes due to the formation of subsurface oxygen species. Prolonged oxygen treatment at 773 K also caused particle fragmentation as a consequence of excessive oxygen penetration of the silver catalyst at defect sites. It was also deduced that the presence of oxygen in the gas phase stabilized the growth of silver planes which could form stronger bonds with oxygen. In contrast, high-temperature thermal treatment in vacuum induced significant sintering of the silver catalyst. Reduction at 773 K resulted in substantial quantities of dissolved hydrogen (and probably hydroxy species) in the bulk silver structure. Furthermore, enhanced defect formation in the catalyst was also noted, as evidenced by the increased concentration of formate species associated with oxygen-reconstructed silver faces.

Predicting posttraumatic growth and posttraumatic stress in fire-fighters

Emergency service workers (e.g., fire-fighters, police and paramedics) are exposed to elevated levels of potentially traumatising events through the course of their work. Such exposure can have lasting negative consequences (e. g., Post Traumatic Stress Disorder; PTSD) and/or positive outcomes (e. g., Posttraumatic Growth; PTG). Research had implicated trauma, occupational and personal variables that account for variance in post-trauma outcomes yet at this stage no research has investigated these factors and their relative influence on both PTSD and PTG in a single study. Based in Calhoun and Tedeschi’s (2013) model of PTG and previous research, in this study regression models of PTG and PTSD symptoms among 218 fire-fighters were tested. Results indicated organisational factors predicted symptoms of PTSD, while there was partial support for the hypothesis that coping and social support would be predictors of PTG. Experiencing multiple sources of trauma, higher levels of organisational and operational stress, and utilising cognitive reappraisal coping, were all significant predictors of PTSD symptoms. Increases in PTG were predicted by experiencing trauma from multiple sources and the use of self-care coping. Results highlight the importance of organisational factors in the development of PTSD symptoms, and of individual factors for promoting PTG.

Feasibility of ranking articular cartilage conditions with non-destructive near-infrared spectroscopy with extension to the Mankin grading system

Grading osteoarthritic tissue has, until now, been a laboratory process confined to research activities. This thesis establishes a scientific protocol that extends osteoarthritic tissue ranking to surgical practice. The innovative protocol, which now incorporates the structural degeneration of collagen, enhances the traditional Modified Mankin ranking system, enabling its application to real time decision during surgery. Because it is fast and without time consuming laboratory process, it would potentially enable the cataloguing of tissues in osteoarthritic joints in all compartments of diseased joints during surgery for epistemological study and insight into the manifestation of osteoarthritis across age, gender, occupation, physical activities and race.