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

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

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

A Total Evidence Approach to Understanding Phylogenetic Relationships and Ecological Diversity in Selanginella subg. Tetragonostachys

• Premise of the Study: Several members of Selaginella are renowned for their ability to survive extreme drought and “resurrect” when conditions improve. Many of these belong to subgenus Tetragonostachys , a group of ~45 species primarily found in North and Central America, with substantial diversity in the Sonoran and Chihuahuan Deserts. We evaluated the monophyly and the age of subgenus Tetragonostachys and assess how drought tolerance contributed to the evolution of this clade. • Methods: Our study included most Tetragonostachys species, using plastid and nuclear sequences, fossil and herbarium records, and climate variables to describe the species diversity, phylogenetic relationships, divergence times, and climatic niche evolution in the subgenus. • Key Results: We found that subgenus Tetragonostachys forms a monophyletic group sister to Selaginella lepidophylla and may have diverged from other Selaginella because of a Gondwanan–Laurasian vicariance event ca. 240 mya. The North American radiation of Tetragonostachys appears to be much more recent and to have occurred during the Early Cretaceous–late Paleocene interval. We identifi ed two signifi cant and nested ecological niche shifts during the evolution of Tetragonostachys associated with extreme drought tolerance and a more recent shift to cold climates. Our analyses suggest that drought tolerance evolved in the warm deserts of southwest North America and may have been advantageous for colonization of cold and dry boreal climates. • Conclusions: Our investigation provides a foundation for future research addressing the genomics of ecological niche evolution and the potential role of reticulate evolution in Selaginella subgenus Tetragonostachys .The authors thank P. Korall for sharing data. S. Buerki, N. Alvarez, and B. Marazzi provided technical assistance and valuable comments on the manuscript. N.A. was funded by the Swiss National Science Foundation (grant no. PBNEP3-132747). C.L.A. was funded by the Swedish Research Council

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

Rare Manifestation of a Rare Disease, Acute Liver Failure in Adult Onset Still’s Disease: Dramatic Response to Methylprednisolone Pulse Therapy—A Case Report and Review

Adult onset Still’s disease (AOSD) is a rare systemic inflammatory disorder of unknown etiology. It is characterized by daily fevers, arthralgias or arthritis, typical skin rash, and leukocytosis. Hepatic involvement is frequently observed in the course of AOSD with mildly elevated transaminases and/or hepatomegaly. Fulminant hepatic failure, occasionally requiring urgent liver transplantation, is a rare manifestation of AOSD. Here, we present a case of 22-year-old woman with no significant medical history who initially came with fever, arthralgias, myalgias, generalized weakness, and sore throat. Laboratory data showed mildly elevated transaminases and markedly elevated ferritin levels. She was diagnosed with AOSD based on Yamaguchi diagnostic criteria and was started on prednisone. Three months later, while she was on tapering dose of steroid, she presented with fever, abdominal pain, jaundice, and markedly elevated transaminases. Extensive workup excluded all potential causes of liver failure. She was diagnosed with AOSD associated acute liver failure (ALF). Intravenous (IV) methylprednisolone pulse therapy was started, with dramatic improvement in liver function. Our case demonstrated that ALF can present as a complication of AOSD and IV mega dose pulse methylprednisolone therapy can be employed as a first-line treatment in AOSD associated ALF with favorable outcome

Interview with Michael Joslin Gordon - OH 539

In his May 18, 2017 interview with Alex Windham, Michael Joslin Gordon detailed his thoughts and memories of his time at the Rock Hill Printing and Finishing Company referred to locals as the Bleachery. Gordon spoke of the time of the 1960s through 2017 and on the following topics: Race relations, Archie Joslin, day-to-day job responsibilities and actions, technology changes, the buyout of the Bleachery by Springs, the decline of the Bleachery, his work as a salesmen and businessman to the year 2017.https://digitalcommons.winthrop.edu/oralhistoryprogram/1616/thumbnail.jp

Arkansas Agriculture Situation and Outlook 2002

Many farmers in Arkansas and other parts of the United States are experiencing financial stress. The purpose of this special report is to highlight the situation of Arkansas farmers and to offer an outlook for 2002. The report emphasizes the production, price, income, policy, financial, farmland value, and interest rate outlook for Arkansas farmers and considers the impact of the macro economy on agriculture. In addition, a summary of commercial rowcrop farm characteristics and production practices is presented

Arkansas Agriculture Situation and Outlook 2003

The purpose of this research series is to highlight the situation of Arkansas farmers and to offer an outlook for 2003. The research emphasizes the production, price, income, policy, financial, farmland value, and interest rate outlook for Arkansas farmers and considers the impact of the macro economy on agriculture. In addition, the advantages and disadvantages of biodiesel as an alternative to petroleum diesel are discussed