Efficient Localization of Discontinuities in Complex Computational Simulations

Surrogate models for computational simulations are input-output approximations that allow computationally intensive analyses, such as uncertainty propagation and inference, to be performed efficiently. When a simulation output does not depend smoothly on its inputs, the error and convergence rate of many approximation methods deteriorate substantially. This paper details a method for efficiently localizing discontinuities in the input parameter domain, so that the model output can be approximated as a piecewise smooth function. The approach comprises an initialization phase, which uses polynomial annihilation to assign function values to different regions and thus seed an automated labeling procedure, followed by a refinement phase that adaptively updates a kernel support vector machine representation of the separating surface via active learning. The overall approach avoids structured grids and exploits any available simplicity in the geometry of the separating surface, thus reducing the number of model evaluations required to localize the discontinuity. The method is illustrated on examples of up to eleven dimensions, including algebraic models and ODE/PDE systems, and demonstrates improved scaling and efficiency over other discontinuity localization approaches

A continuous analogue of the tensor-train decomposition

We develop new approximation algorithms and data structures for representing and computing with multivariate functions using the functional tensor-train (FT), a continuous extension of the tensor-train (TT) decomposition. The FT represents functions using a tensor-train ansatz by replacing the three-dimensional TT cores with univariate matrix-valued functions. The main contribution of this paper is a framework to compute the FT that employs adaptive approximations of univariate fibers, and that is not tied to any tensorized discretization. The algorithm can be coupled with any univariate linear or nonlinear approximation procedure. We demonstrate that this approach can generate multivariate function approximations that are several orders of magnitude more accurate, for the same cost, than those based on the conventional approach of compressing the coefficient tensor of a tensor-product basis. Our approach is in the spirit of other continuous computation packages such as Chebfun, and yields an algorithm which requires the computation of "continuous" matrix factorizations such as the LU and QR decompositions of vector-valued functions. To support these developments, we describe continuous versions of an approximate maximum-volume cross approximation algorithm and of a rounding algorithm that re-approximates an FT by one of lower ranks. We demonstrate that our technique improves accuracy and robustness, compared to TT and quantics-TT approaches with fixed parameterizations, of high-dimensional integration, differentiation, and approximation of functions with local features such as discontinuities and other nonlinearities

antioxidant and anticandidal activities of the tunisian haplophyllum tuberculatum forssk a juss essential oils

Abstract Haplophyllum tuberculatum Forssk. is a medicinal plant growing in Tunisia. It is widely used in traditional medicine against gastro-intestinal problems, fevers, ear infections and rheumatisms. The present investigation evaluated the effects of leaves, stems and leaves + stems essential oils of Haplophyllum tuberculatum Forssk. and of their pure compounds on free radicals as well as their anticandidal activities. Screening for the antioxidant activity of the oils, R-(+)-limonene, S-(−)-limonene and 1-octanol was conducted by DPPH, ABTS and β-carotene/linoleic acid radical scavenging assays. The essentials oils and their compounds were screened for antifungal activity against four Candida species: Candida albicans ATCC 90028; Candida glabrata ATCC 90030; Candida parapsilosis ATCC 27853 and Candida krusei ATCC 6258. When compared with ascorbic acid as standard, it was found that the essential oils have a significant inhibition in scavenging free radicals, resulting in an important IC50. The pure compounds were inactive against the free radicals. The anticandidal test results showed that leaves, stems and leaves + stems oils strongly inhibited the growth of Candida krusei at 30 μg/mL leaves oils and 70 μg/mL for other oils and that moderately of the 3 other Candida species. The pure compound, 1-octanol, was active one against the candida species, with MIC-values between 0.07 and 1.25 mg/mL. In all in vitro assays, a significant correlation existed between the concentrations of the essential oils, the percentage inhibition of free radicals and of the growth inhibitory of tested candida species. The results indicate the essential oils may be applied for treating diseases related to free radicals, potentially to prevent cancer development and as an antifungal agent against Candida

Bayesian inference with optimal maps

We present a new approach to Bayesian inference that entirely avoids Markov chain simulation, by constructing a map that pushes forward the prior measure to the posterior measure. Existence and uniqueness of a suitable measure-preserving map is established by formulating the problem in the context of optimal transport theory. We discuss various means of explicitly parameterizing the map and computing it efficiently through solution of an optimization problem, exploiting gradient information from the forward model when possible. The resulting algorithm overcomes many of the computational bottlenecks associated with Markov chain Monte Carlo. Advantages of a map-based representation of the posterior include analytical expressions for posterior moments and the ability to generate arbitrary numbers of independent posterior samples without additional likelihood evaluations or forward solves. The optimization approach also provides clear convergence criteria for posterior approximation and facilitates model selection through automatic evaluation of the marginal likelihood. We demonstrate the accuracy and efficiency of the approach on nonlinear inverse problems of varying dimension, involving the inference of parameters appearing in ordinary and partial differential equations.United States. Dept. of Energy. Office of Advanced Scientific Computing Research (Grant DE-SC0002517)United States. Dept. of Energy. Office of Advanced Scientific Computing Research (Grant DE-SC0003908

Inhibitory Activity of Leaves Extracts of Citrullus colocynthis Schrad. on HT29 Human Colon Cancer Cells

Aims: Citrullus colocynthis is a plant endemic in Asia, Africa and in the Mediterranean basin. It is used in folk medicine against infections, inflammations and cardiovascular and immune-related diseases. There are further evidences of the use of Citrullus colocynthis Schrad in the treatment of cancer in traditional practices. The present study aimed to determine the potential antiproliferative effects of different Citrullus colocynthis leaf extracts on human cancer cells. Methodology: Antiproliferative and antioxidant effects on HT-29 human colon cancer cells were detected by MTS assay and a modified protocol of the alkaline Comet assay. In vitro antioxidant activities of different leaf extracts were evaluated through DPPH, \u3b2-carotene/linoleic acid and reducing power assays. Results: The leaf chloroform extract exhibited the higher cell growth inhibitory activity without induction of DNA damage; it showed to be able to significantly decrease DNA damage induced by H2O2 (100 M). This antioxidant activity seems to be comparable to that of vitamin C (1 mM). Ethyl acetate, acetone and methanol leaf extracts showed to be the most effective in reducing the stable free DPPH radical (IC50 =113 g/ml), in transforming the Fe3+ to Fe2+ (IC50 = 134 \ub5g/ml) and in inducing linoleic acid oxidation with an inhibition of 31.9 %. Conclusion: Our results confirm the antiproliferative potential of Citrullus colocynthis Schrad. on human cancer cells

14-Bromo-12-chloro-2,16-dioxapentacyclohenicosa-3(8),10,12,14-tetraene-7,20-dione

In the title compound, C19H16BrClO4, both the fused xanthene rings and one of the cyclohexane rings adopt envelope conformations, while the other cyclohexane ring is in a chair conformation. In the crystal, molecules are linked by C-H...O hydrogen bonds, forming infinite chains running along [10-1] incorporating R22(16) ring motifs. In addition, C-H...[pi] interactions and weak [pi]-[pi] stacking interactions [centroid-centroid distance = 3.768 (3) Å] help to consolidate the packing