2,449 research outputs found

    Multilevel Quasi-Monte Carlo Methods for Lognormal Diffusion Problems

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    In this paper we present a rigorous cost and error analysis of a multilevel estimator based on randomly shifted Quasi-Monte Carlo (QMC) lattice rules for lognormal diffusion problems. These problems are motivated by uncertainty quantification problems in subsurface flow. We extend the convergence analysis in [Graham et al., Numer. Math. 2014] to multilevel Quasi-Monte Carlo finite element discretizations and give a constructive proof of the dimension-independent convergence of the QMC rules. More precisely, we provide suitable parameters for the construction of such rules that yield the required variance reduction for the multilevel scheme to achieve an ε\varepsilon-error with a cost of O(ε−θ)\mathcal{O}(\varepsilon^{-\theta}) with θ<2\theta < 2, and in practice even θ≈1\theta \approx 1, for sufficiently fast decaying covariance kernels of the underlying Gaussian random field inputs. This confirms that the computational gains due to the application of multilevel sampling methods and the gains due to the application of QMC methods, both demonstrated in earlier works for the same model problem, are complementary. A series of numerical experiments confirms these gains. The results show that in practice the multilevel QMC method consistently outperforms both the multilevel MC method and the single-level variants even for non-smooth problems.Comment: 32 page

    Product recognition in store shelves as a sub-graph isomorphism problem

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    The arrangement of products in store shelves is carefully planned to maximize sales and keep customers happy. However, verifying compliance of real shelves to the ideal layout is a costly task routinely performed by the store personnel. In this paper, we propose a computer vision pipeline to recognize products on shelves and verify compliance to the planned layout. We deploy local invariant features together with a novel formulation of the product recognition problem as a sub-graph isomorphism between the items appearing in the given image and the ideal layout. This allows for auto-localizing the given image within the aisle or store and improving recognition dramatically.Comment: Slightly extended version of the paper accepted at ICIAP 2017. More information @project_page --> http://vision.disi.unibo.it/index.php?option=com_content&view=article&id=111&catid=7

    POD for optimal control of the Cahn-Hilliard system using spatially adapted snapshots

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    The present work considers the optimal control of a convective Cahn-Hilliard system, where the control enters through the velocity in the transport term. We prove the existence of a solution to the considered optimal control problem. For an efficient numerical solution, the expensive high-dimensional PDE systems are replaced by reduced-order models utilizing proper orthogonal decomposition (POD-ROM). The POD modes are computed from snapshots which are solutions of the governing equations which are discretized utilizing adaptive finite elements. The numerical tests show that the use of POD-ROM combined with spatially adapted snapshots leads to large speedup factors compared with a high-fidelity finite element optimization

    Interactions between environment, wild animals and human leptospirosis

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    Leptospirosis, a worldwide distributed zoononis caused by bacteria of the genus Leptospira (antigenically classified into serovars), may be direct or indirectly transmitted through infected urine or environment. Several domestic and wild animals are leptospirosis reservoirs. The disease presents occupational character since it is widely reported in professionals that work in humid environments - such as sewage workers and fishermen - and in places where rodents or susceptible animals are found, like slaughterhouses and veterinary clinics. In developing countries, outbreaks are related to lack of sanitation, overcrowding in inadequate housing and climatic conditions. In developed countries, sporadic cases occur in aquatic recreational activities including swimming and triathlon. The diagnosis of leptospirosis is complex due to the variety of symptoms, disease severity and the lack of techniques that are able to early detect the infection. Thus, leptospirosis causes numerous public health problems and educational activities are very important to its control

    CGHPRO – A comprehensive data analysis tool for array CGH

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    BACKGROUND: Array CGH (Comparative Genomic Hybridisation) is a molecular cytogenetic technique for the genome wide detection of chromosomal imbalances. It is based on the co-hybridisation of differentially labelled test and reference DNA onto arrays of genomic BAC clones, cDNAs or oligonucleotides, and after correction for various intervening variables, loss or gain in the test DNA can be indicated from spots showing aberrant signal intensity ratios. Now that this technique is no longer confined to highly specialized laboratories and is entering the realm of clinical application, there is a need for a user-friendly software package that facilitates estimates of DNA dosage from raw signal intensities obtained by array CGH experiments, and which does not depend on a sophisticated computational environment. RESULTS: We have developed a user-friendly and versatile tool for the normalization, visualization, breakpoint detection and comparative analysis of array-CGH data. CGHPRO is a stand-alone JAVA application that guides the user through the whole process of data analysis. The import option for image analysis data covers several data formats, but users can also customize their own data formats. Several graphical representation tools assist in the selection of the appropriate normalization method. Intensity ratios of each clone can be plotted in a size-dependent manner along the chromosome ideograms. The interactive graphical interface offers the chance to explore the characteristics of each clone, such as the involvement of the clones sequence in segmental duplications. Circular Binary Segmentation and unsupervised Hidden Markov Model algorithms facilitate objective detection of chromosomal breakpoints. The storage of all essential data in a back-end database allows the simultaneously comparative analysis of different cases. The various display options facilitate also the definition of shortest regions of overlap and simplify the identification of odd clones. CONCLUSION: CGHPRO is a comprehensive and easy-to-use data analysis tool for array CGH. Since all of its features are available offline, CGHPRO may be especially suitable in situations where protection of sensitive patient data is an issue. It is distributed under GNU GPL licence and runs on Linux and Windows

    Multilevel quasi-Monte Carlo methods for lognormal diffusion problems

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