Reliability for linear differential equations with noisy coefficients

AbstractSuppose Ẋ = (A + W)X is a system of stochastic differential equations, where A is a matrix of constants and W is a matrix of white noises. We say the system is reliable if the variance-covariance matrix of the states asymptotically approaches zero. We give conditions in terms of measures of the coefficient matrix and a matrix whose entries are standard deviation parameters of the coefficient noises which will insure that the system is reliable

Fecal Coliform Release Studies and Development of a Preliminary Nonpoint Source Transport Model for Indicator Bacteria

The effect of grazing on water quality has been documented by bacteriological studies of streams adjacent to grazed areas. Bacterial release from fecal deposits is a parameter of the pollution transport mechanism that is poorly understood. The objective of this study was to determine a fecal coliform release function for cattle fecal deposits. Standard cowpies were rained on with a rainfall simulator, and the fecal coliform counts were determined using the most probably number (MPN) method of enumeration. The fecal deposits were rained on at ages 2 through 100 days. The effects of rainfall intensity and recurrent rainfall were tested. Naturally occurring fecal deposits were also tested to compare their results with the results from the standard cowpies. A log-log regression was found to describe the decline in peak fecal coliform release with fecal deposit age. The 100-day-old fecal deposits produced peak counts of 4,200 fecal coliforms per 100 milliliters of water. This quantity of release is insignificant compared to the release from fresher fecal material. Rainfall intensity had little effect on peak fecal coliform release from fecal deposits that ere 2 or 10 days old. At age 20 days the effect of rainfall intensity was significant; the highest intensity gave the lowest peak counts, and the lowest intensity gave the highest peak counts. The effect of rainfall intensity appears to be related to the dryness of the fecal deposits. Peak fecal coliform counts were significantly lowered by raining on the fecal deposits more than once. This decline was thought to be produced by the loss of bacteria from the fecal deposits during the previous wettings. Standard cowpies produced a peak release regression that was not significantly different from the regression for the natural fecal deposits. Apparently, grossly manipulating the fecal deposits did not significantly change the release patterns

Random Differential Equations in Water Quality Modeling

A probabilistic river water quality model is developed with the capability of determinging the joint and marginal probability density function of biochemical oxygen demand (BOD) and dissolved oxygen (DO) at any point in a river. The one dimensional steady-state model can be applied to a river system with any reasonable number of point loads and diversions and lateral surface and subsurface inflow. The model can simultaneously consider randomness in the intital conditions, inputs, and coefficients of the water quality equations. Any empirical or known distribution can be used for the initial condition. The randomness in the water quality equation inputs and coefficients is modeled as a Gaussian white noise process. The joint probability density function (pdf) of BOD and DO is determined by numerically solving the Fokker-Plank equation. Moment equations are developed which allow the mean and variance of the marginal distrubution of BOD and DO to be calculated independently of the joint pdf. An upper limit on the coefficient noise variance parameter is presented for which the BOD-DO covariance matrix will be asymptotically stable. The probabilistic river water quality model is applied to two problems, a sensitivity problem and a hypothetical problem. The sensitivity problem and a hypothetical problem. The sensitivity problem is used to gain familiarity with the simulation model and determine the sensitivity of the model responses to changes in the standard deviation parameter of the input and coefficient noise. The standard deviation parameter of the input noise if varied between zero and 30 percent of the respective input, while the standard deviation parameter of the coefficient noise is varied between zero and 50 percent of the respective coefficeitn. The model responses are foind to be fairly sensitive to changes in the standard deviation parameter of the coefficient noise but relatively insensitive to changes in the standard deviation parameter of the input noise. The possibility of using the moment equations and a normal approximation in lieu of calculating the joint pdf of BOD and DO is discussed. The accuracy of the numerical solution technique for the Fokker-Plank equation is also discussed. The hypothetical problem is used to evaluate the performance of the model in simulating a more complex river system (which included two point loads) and to evaluate the numerical quandrature algorithm used to determine the joint pdf of BOD and DO immediately downstream of a point load. The numerical solution technique used to determine the joing pdf of BOD and DO remained stable throughout the simulation and the computational costs are judged to be reasonable for a problem of this complexity. The quadrature algorithm was judged to have performed adequately for both the pont loads

Stochastic Analysis for Water Quality

This report demonstrates the feasibility of applying stochastic techniques to linear water quality models. The Monte Carlo, First Order, and Generation of Moment Equation techniques are applied to a long term phosphorus model of Lake Washington. The effect of uncertainty of the phosphours loading term on simulated phosphous levels is analyzed. All three stochastic techniques produced the same results. The simulated concentrations of phosphorus in the water column are very responsive to uncertainty in annual phosphorus loading, the sediment concentrations relatively insensitive. The Monte Carlo technique is shown to require the most computation time of the three stochastic techniques applied. The First Order and Generation of Moment Equation techniques are shown to be precise and efficent methods of stochastic analysis. In this application they required less than one thousandth the computation time of the Monte Carlo technique. The Generation of Moment Equations technique is also applied to a steady state salinity model of the Colorado River system. Two sources of uncertainty are considered: 1) the estimation of steady state values of salinity loading from a limited historic data base and 2) the estimation of salinity loading from irrigated land by a semi-empirical approach. Six stochastic simulations of the Colorado River system are presented. Coefficients of variations of simulated salinities at Imperial Dam are shown to vary from 5.7 to 10.3 percent. The major source of uncertainty in all simulations is the estimation of the steady state salinity loading with the agricultural loading term becoming important in some simulated management alternatives

Orthostatic Hypotension in Middle-Age and Risk of Falls

One-third of older adults fall each year. Orthostatic hypotension (OH) has been hypothesized as an important risk factor for falls, but findings from prior studies have been inconsistent

Horizontal transfer of an adaptive chimeric photoreceptor from bryophytes to ferns

Ferns are well known for their shade-dwelling habits. Their ability to thrive under low-light conditions has been linked to the evolution of a novel chimeric photoreceptor-neochrome-that fuses red-sensing phytochrome and blue-sensing phototropin modules into a single gene, thereby optimizing phototropic responses. Despite being implicated in facilitating the diversification of modern ferns, the origin of neochrome has remained a mystery. We present evidence for neochrome in hornworts (a bryophyte lineage) and demonstrate that ferns acquired neochrome from hornworts via horizontal gene transfer (HGT). Fern neochromes are nested within hornwort neochromes in our large-scale phylogenetic reconstructions of phototropin and phytochrome gene families. Divergence date estimates further support the HGT hypothesis, with fern and hornwort neochromes diverging 179 Mya, long after the split between the two plant lineages (at least 400 Mya). By analyzing the draft genome of the hornwort Anthoceros punctatus, we also discovered a previously unidentified phototropin gene that likely represents the ancestral lineage of the neochrome phototropin module. Thus, a neochrome originating in hornworts was transferred horizontally to ferns, where it may have played a significant role in the diversification of modern ferns

Determinants of Aortic Stiffness: 16-Year Follow-Up of the Whitehall II Study

Aortic stiffness is a strong predictor of cardiovascular disease endpoints. Cross-sectional studies have shown associations of various cardiovascular risk factors with aortic pulse wave velocity, a measure of aortic stiffness, but the long-term impact of these factors on aortic stiffness is unknown.In 3,769 men and women from the Whitehall II cohort, a wide range of traditional and novel cardiovascular risk factors were determined at baseline (1991-1993) and aortic pulse wave velocity was measured at follow-up (2007-2009). The prospective associations between each baseline risk factor and aortic pulse wave velocity at follow-up were assessed through sex stratified linear regression analysis adjusted for relevant confounders. Missing data on baseline determinants were imputed using the Multivariate Imputation by Chained Equations.Among men, the strongest predictors were waist circumference, waist-hip ratio, heart rate and interleukin 1 receptor antagonist, and among women, adiponectin, triglycerides, pulse pressure and waist-hip ratio. The impact of 10 centimeter increase in waist circumference on aortic pulse wave velocity was twice as large for men compared with women (men: 0.40 m/s (95%-CI: 0.24;0.56); women: 0.17 m/s (95%-CI: -0.01;0.35)), whereas the opposite was true for the impact of a two-fold increase in adiponectin (men: -0.30 m/s (95%-CI: -0.51;-0.10); women: 0.61 m/s (95%-CI: -0.86;-0.35)).In this large prospective study, central obesity was a strong predictor of aortic stiffness. Additionally, heart rate in men and adiponectin in women predicted aortic pulse wave velocity suggesting that strategies to prevent aortic stiffening should be focused differently by sex

The importance of organizational characteristics for improving outcomes in patients with chronic disease: a systematic review of congestive heart failure

Luci K. Leykum, Jacqueline Pugh, Valerie Lawrence, and Polly H. Noel are with the South Texas Veterans Health Care System and Department of Medicine, University of Texas Health Science Center at San Antonio, San Antonio TX, 78229, USA -- Michael Parchman is with the South Texas Veterans Health Care System and Department of Family and Community Medicine, University of Texas Health Science Center at San Antonio, San Antonio TX, 78229, USA -- Reuben R. McDaniel Jr. is with the McComb's School of Business, University of Texas at Austin, Austin TX, USABackground: Despite applications of models of care and organizational or system-level interventions to improve patient outcomes for chronic disease, consistent improvements have not been achieved. This may reflect a mismatch between the interventions and the nature of the settings in which they are attempted. The application of complex adaptive systems (CAS) framework to understand clinical systems and inform efforts to improve them may lead to more successful interventions. We performed a systematic review of interventions to improve outcomes of patients with congestive heart failure (CHF) to examine whether interventions consistent with CAS are more likely to be effective. We then examine differences between interventions that are most effective for improving outcomes for patients with CHF versus previously published data for type 2 diabetes to explore the potential impact of the nature of the disease on the types of interventions that are more likely to be effective. Methods: We conducted a systematic review of the literature between 1998 and 2008 of organizational interventions to improve care of patients with CHF. Two independent reviewers independently assessed studies that met inclusion criteria to determine whether each reported intervention reflected one or more CAS characteristics. The effectiveness of interventions was rated as either 0 (no effect), 0.5 (mixed effect), or 1.0 (effective) based on the type, number, and significance of reported outcomes. Fisher's exact test was used to examine the association between CAS characteristics and intervention effectiveness. Specific CAS characteristics associated with intervention effectiveness for CHF were contrasted with previously published data for type 2 diabetes. Results and discussion: Forty-four studies describing 46 interventions met eligibility criteria. All interventions utilized at least one CAS characteristic, and 85% were either 'mixed effect' or 'effective' in terms of outcomes. The number of CAS characteristics present in each intervention was associated with effectiveness (p < 0.001), supporting the idea that interventions consistent with CAS are more likely to be effective. The individual CAS characteristics associated with CHF intervention effectiveness were learning, self-organization, and co-evolution, a finding different from our previously published analysis of interventions for diabetes. We suggest this difference may be related to the degree of uncertainty involved in caring for patients with diabetes versus CHF. Conclusion: These results suggest that for interventions to be effective, they must be consistent with the CAS nature of clinical systems. The difference in specific CAS characteristics associated with intervention effectiveness for CHF and diabetes suggests that interventions must also take into account attributes of the disease.McCombs School of [email protected]