The stochastic counterpart of conservation laws with heterogeneous conductivity fields: application to deterministic problems and uncertainty quantification

Conservation laws in the form of elliptic and parabolic partial differential equations (PDEs) are fundamental to the modeling of many problems such as heat transfer and flow in porous media. Many of such PDEs are stochastic due to the presence of uncertainty in the conductivity field. Based on the relation between stochastic diffusion processes and PDEs, Monte Carlo (MC) methods are available to solve these PDEs. These methods are especially relevant for cases where we are interested in the solution in a small subset of the domain. The existing MC methods based on the stochastic formulation require restrictively small time steps for high variance conductivity fields. Moreover, in many applications the conductivity is piecewise constant and the existing methods are not readily applicable in these cases. Here we provide an algorithm to solve one-dimensional elliptic problems that bypasses these two limitations. The methodology is demonstrated using problems governed by deterministic and stochastic PDEs. It is shown that the method provides an efficient alternative to compute the statistical moments of the solution to a stochastic PDE at any point in the domain. A variance reduction scheme is proposed for applying the method for efficient mean calculations

Hypothesis-based Restoration Study For Mitigation of a Damaged SE Florida Coral Reef: A Work in Progress

The United States Submarine Memphis (Figure 1) ran aground in approximately 10 meter depth on a coral reef off southeast Florida (Figure 2) February 25, 1993. Extensive physical damage to the reef substrate and injury to the coral community were attributed to the initial grounding and subsequent attempts to free the submarine from the impacted reef (Figures 3 and 4). The impact of the grounding was assessed, and the area of damage was determined through field and photographic studies. An impacted area of 2,310 m2 was assessed with 1,205 m2 having been totally destroyed (Figures 3 and 4). In 1997, the State of Florida was awarded a settlement of $750,000 by the Federal government for environmental damages caused by the submarine grounding. A plan to perform hypothesis testing of restoration techniques was developed and initiated. Using artificial reefs as experimental platforms, we are examining three restoration strategies: 1) the potential of enhancing coral recruitment through the use of coral larval attractants, 2) the effect of reef structure on the associated fish assemblages, and 3) the interaction between fish assemblages and coral recruitment and survival

Growth and Survivorship of Scleractinian Coral Transplants and the Effectiveness of Plugging Core Holes in Transplant Donor Colonies

Replicate scleractinian coral transplants were obtained from the species Meandrina meandrites and Montastrea cavernosa on a natural reef, off Dania Beach, Florida, using a hydraulic drill fitted with a 4 in. (~10 cm) core barrel. The transplants were fixed to Reef Ball™ substrates using an adhesive marine epoxy. Drill holes in the donor corals (core holes) were filled with concrete plugs. Control corals, of comparable size to both donor colonies and transplant corals, were monitored for comparison. Transplant corals, donor corals, and controls on the natural reef were monitored for growth and survivorship. Core holes were monitored for tissue regrowth over the surface of concrete plugs. Growth during the transplantation project was defined as an increase in surface area of tissue and skeleton. Growth was monitored on a quarterly basis using photographic techniques. Meandrina meandrites transplants experienced greater mortality and significantly less growth than M. cavernosa transplants. No significant difference in the change in percent tissue coverage between both species of donor corals or between their respective controls was determined. The process of filling core holes in donor colonies with concrete plugs was effective, however, tissue did not completely regenerate over the surface of plugs in either species over the relatively short 15-month observation period. Results of this study indicate that species selection is an important factor in the success of coral transplantation

Growth and Survivorship of Stony Coral Meandrina meandrites and Montastrea cavernosa Transplants to an Artificial Reef Environment: A Work in Progress

Reef Ball Deployment: In November of 2000, 160 concrete Reef BallTM modules (1.22m wide x 0.9m high) were deployed, at a depth of approximately 15 meters, between the Second and Third Reef tracts off Dania Beach, FL (Figures 1 and 2). The Reef Balls were grouped into 40 quads, with each quad containing four individual Reef Balls. One modified Reef Ball from each quad was designated as the ‘transplant’ ball, and was used as the receptacle for the coral transplants. The other three balls in each quad are part of a more comprehensive study. This multifactorial study is examining the effects of reef structure on fish assemblages, the effects of coral larval attractants on coral recruitment, and the interaction between fish assemblages and coral recruitment. The coral transplants are one such ‘coral larval attractant’ being examined. Coral transplants, and the donor colonies from which they were obtained, are being monitored for growth and survivorshi

Recurrent Cellulitis Associated with Long-Term Intrathecal Opioid Infusion Therapy: A Case Report and Review of the Literature

Lower-limb edema is recognized as an untoward side effect of intrathecal opioid therapy. Cellulitis, an acute, spreading pyogenic inflammation of the dermis and subcutaneous tissue, predisposed by persistent leg edema, can become problematic in patients on intraspinal opioid infusion therapy.To present a case of recurrent cellulitis in an elderly lady with persistent leg edema associated with intrathecal morphine/hydromorphone infusion therapy.Sixty-one-year-old woman with intractable chronic low back pain and bilateral leg pain treated with an intrathecal infusion of morphine up to 5 mg/day over 3 months with satisfactory pain control developed progressive lower extremity edema, complicated by recurrent cellulitis, requiring repeated hospitalization and intravenous antibiotic treatment. Switching to intrathecal hydromorphone helped minimally. Intrathecal baclofen and clonidine infusion resulted in complete resolution of leg edema and pain relief over the following 12 months.Intrathecal Baclofen and Clonidine may be used as alternatives to provide spinally mediated antinociception when intraspinal opioid fails due to pharmacological side effects such as persistent edema.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/79174/1/j.1526-4637.2010.00854.x.pd

Utility of repeat cytological assessment of thyroid nodules initially classified as benign: clinical insights from multidisciplinary care in an Irish tertiary referral centre.

BACKGROUND: Fine needle aspiration biopsy (FNAB) is the tool of choice for evaluating thyroid nodules with the majority classified as benign following initial assessment. However, concern remains about false negative results and some guidelines have recommended routine repeat aspirates. We aimed to assess the utility of routine repeat FNAB for nodules classified as benign on initial biopsy and to examine the impact of establishing a multidisciplinary team for the care of these patients. METHODS: We performed a retrospective review of 400 consecutive patients (413 nodules) who underwent FNAB of a thyroid nodule at our hospital between July 2008 and July 2011. Data recorded included demographic, clinical, histological and radiological variables. RESULTS: Three hundred and fifty seven patients (89 %) were female. Median follow-up was 5.5 years. Two hundred and fifty eight (63 %) nodules were diagnosed as benign. The rate of routine repeat biopsy increased significantly over the time course of the study (p for trend = 0.012). Nine Thy 2 nodules were classified differently on the basis of routine repeat biopsy; one patient was classified as malignant on repeat biopsy and was diagnosed with papillary thyroid carcinoma. Eight were classified as a follicular lesions on repeat biopsy-six diagnosed as benign following lobectomy; two declined lobectomy and were followed radiologically with no nodule size increase. CONCLUSIONS: The false negative rate of an initial benign cytology result, from a thyroid nodule aspirate, is low. In the setting of an experienced multidisciplinary thyroid team, routine repeat aspiration is not justified