A fitted numerical method for singularly perturbed parabolic reaction-diffusion problems

This paper treats a time-dependent singularly perturbed reaction-diffusion problem. We semidiscretize the problem in time by means of the classical backward Euler method. We develop a fitted operator finite difference method (FOFDM) to solve the resulting set of linear problems (one at each time level). We prove that the underlying fitted operator satisfies the maximum principle. This result is then used in the error analysis of the FOFDM. The method is shown to be first order convergent in time and second order convergent in space, uniformly with respect to the perturbation parameter. We test the method on several numerical examples to confirm our theoretical findings.Web of Scienc

Assessment of Chemical Inhibitor Addition to Improve the Gas Production from Biowaste

The coexistence of sulphate-reducing bacteria and methanogenic archaea in the reactors during the anaerobic digestion from sulphate-containing waste could favor the accumulation of sulfide on the biogas, and therefore reduce its quality. In this study, the effect of sulphate-reducing bacteria inhibitor (MoO−2 4 ) addition in a two phase system from sulphate-containing municipal solid waste to improve the quality of the biogas has been investigated. The results showed that although SRB and sulphide production decreased, the use of inhibitor was not effective to improve the anaerobic digestion in a two phase system from sulphate-containing waste, since a significant decrease on biogas and organic matter removal were observed. Before MoO−2 4 addition the average values of volatile solid were around 12 g/kg, after 5 days of inhibitor use, those values did exceed to 28 g/kg. Molybdate caused acidification in the reactor and it was according to decrease in the pH values. In relation to microbial consortia, the effect of inhibitor was a decrease in Bacteria (44%; 60% in sulphate-reducing bacteria) and Archaea (38%) population

Comprehensive characterization of 536 patient-derived xenograft models prioritizes candidatesfor targeted treatment

Development of candidate cancer treatments is a resource-intensive process, with the research community continuing to investigate options beyond static genomic characterization. Toward this goal, we have established the genomic landscapes of 536 patient-derived xenograft (PDX) models across 25 cancer types, together with mutation, copy number, fusion, transcriptomic profiles, and NCI-MATCH arms. Compared with human tumors, PDXs typically have higher purity and fit to investigate dynamic driver events and molecular properties via multiple time points from same case PDXs. Here, we report on dynamic genomic landscapes and pharmacogenomic associations, including associations between activating oncogenic events and drugs, correlations between whole-genome duplications and subclone events, and the potential PDX models for NCI-MATCH trials. Lastly, we provide a web portal having comprehensive pan-cancer PDX genomic profiles and source code to facilitate identification of more druggable events and further insights into PDXs' recapitulation of human tumors

European basket option pricing by maximizing over a subset of lower bounds

In this paper we derive a lower bound for the price of a European basket option under the Black and Scholes framework. The bound is based on the conditioning method of [L.C.G. Rogers and Z. Shi, The value of an Asian option, J. of Appl. Prob. 32  (1995), 1077–1088] and [M. Curran, Valuing Asian and portfolio options by conditioning on the geometric mean, Management Science 40(12) (1994), 1705–1711]. We adapt the method of [K.W. Chen and Y.D. Lyuu, Accurate pricing formulas for Asian options, Applied Mathematics and Computation 188 (2007), 1711–1724] applied for Asian options to the case of the European basket options. Using an improved Monte Carlo method based on the antithetic variates, we benchmark our results. We also calculate the lower bound for various parameters involved, compare these results with those obtained by the improved Monte Carlo simulations and conclude that the proposed bound is indeed optimal.Keywords: European basket option, Monte Carlo simulations, variance reduction, anti-thetic variables, conditioningQuaestiones Mathematicae 35(2012), 507–52