798 research outputs found
Truck Component Simulation Meshes and Synthetic LiDAR Measurements
No full textThis is the synthetic dataset from the paper: Jochen Garcke, Sara Hahner, and Rodrigo Iza-Teran. "Alignment of Highly Resolved Time-Dependent Experimental and Simulated Crash Test Data". In: International Journal of Crashworthiness.
The work compares highly resolved experimental data with corresponding simulation data. The dataset contains one component from several completed frontal crash simulations of a Chevrolet C2500 pick-up truck model (from National Crash Analysis Center (NCAC)). Additionally, we provide our LiDAR measurements of the component. The data, which is provided here, is described in detail in section 5.3 of the paper
A dimension adaptive sparse grid combination technique for machine learning
No full textWe introduce a dimension adaptive sparse grid combination technique for the machine learning problems of classification and regression. A function over a -dimensional space, which assumedly describes the relationship between the features and the response variable, is reconstructed using a linear combination of partial functions that possibly depend only on a subset of all features. The partial functions are adaptively chosen during the computational procedure. This approach (approximately) identifies the \textsc{anova} decomposition of the underlying problem. Experiments on synthetic data, where the structure is known, show the advantages of a dimension adaptive combination technique in run time behaviour, approximation errors, and interpretability.
References M. Griebel, M. Schneider, and C. Zenger. A combination technique for the solution of sparse grid problems. In P. de Groen and R. Beauwens, editors, Iterative Methods in Linear Algebra, pages 263--281. IMACS, Elsevier, North Holland, 1992. http://wissrech.ins.uni-bonn.de/research/pub/griebel/griesiam.ps.gz. M. Hegland. Adaptive sparse grids. In K. Burrage and Roger B. Sidje, editors, Proc. of 10th Computational Techniques and Applications Conference CTAC-2001, volume 44 of ANZIAM J., pages C335--C353, 2003. http://anziamj.austms.org.au/V44/CTAC2001/Hegl. M. Hegland, J. Garcke, and V. Challis. The combination technique and some generalisations. Linear Algebra and its Applications, 420(2--3):249--275, 2007. doi:10.1016/j.laa.2006.07.014. Ian H. Sloan, Xiaoqun Wang, and Henryk Wozniakowski. Finite-order weights imply tractability of multivariate integration. Journal of Complexity, 20:46--74, 2004. doi:10.1016/j.jco.2003.11.003. Jerome H. Friedman. Multivariate adaptive regression splines. Ann. Statist., 19(1):1--141, 1991. http://projecteuclid.org/euclid.aos/1176347963. J. Garcke. Regression with the optimised combination technique. In W. Cohen and A. Moore, editors, Proceedings of the 23rd ICML, pages 321--328, 2006. doi:10.1007/s006070170007. J. Garcke, M. Griebel, and M. Thess. Data mining with sparse grids. Computing, 67(3):225--253, 2001. doi:10.1007/s006070170007. T. Gerstner and M. Griebel. Dimension-Adaptive Tensor-Product Quadrature. Computing, 71(1):65--87, 2003. doi:10.1007/s00607-003-0015-5
Gene loss and lineage specific restriction-modification systems associated with niche differentiation in the Campylobacter jejuni Sequence Type 403 clonal complex
No full textCampylobacter jejuni is a highly diverse species of bacteria commonly associated with infectious intestinal disease of humans and zoonotic carriage in poultry, cattle, pigs, and other animals. The species contains a large number of distinct clonal complexes that vary from host generalist lineages commonly found in poultry, livestock, and human disease cases to host-adapted specialized lineages primarily associated with livestock or poultry. Here, we present novel data on the ST403 clonal complex of C. jejuni, a lineage that has not been reported in avian hosts. Our data show that the lineage exhibits a distinctive pattern of intralineage recombination that is accompanied by the presence of lineage-specific restriction-modification systems. Furthermore, we show that the ST403 complex has undergone gene decay at a number of loci. Our data provide a putative link between the lack of association with avian hosts of C. jejuni ST403 and both gene gain and gene loss through nonsense mutations in coding sequences of genes, resulting in pseudogene formation
Die Römische Republik /
No full textWer sich für antike Geschichte interessiert, greift zu dieser knappen und gut lesbaren Geschichte der Römischen Republik, geschrieben von einem der bekanntesten Althistoriker Deutschlands. Jochen Bleicken (1926-2005) führt den Leser von der Zeit der Etrusker bis zum Ende der Republik, das die Herrschaft Caesars besiegelte. Alle wichtigen Phasen der republikanischen Geschichte entfalten sich: die Ständekämpfe, Aufstieg Roms zur Weltherrschaft - und die zugehörigen ungeheuren kriegerischen Auseinandersetzungen -, Ursachen und Beginn der inneren Krise seit den Gracchen, die Restauration unter Sulla und schließlich: die Auflösung der Republik und die Begründung der Monarchie. Aloys Winterling Jochen Bleicken, 1926-2005, war Professor für Alte Geschichte an der Universität Göttingen und u.a. Mitherausgeber von "Oldenbourg Grundriss der Geschichte" und der HISTORISCHEN ZEITSCHRIFT.Wer sich für antike Geschichte interessiert, greift zu dieser knappen und gut lesbaren Geschichte der Römischen Republik, geschrieben von einem der bekanntesten Althistoriker Deutschlands. Jochen Bleicken (1926-2005) führt den Leser von der Zeit der Etrusker bis zum Ende der Republik, das die Herrschaft Caesars besiegelte. Alle wichtigen Phasen der republikanischen Geschichte entfalten sich: die Ständekämpfe, Aufstieg Roms zur Weltherrschaft - und die zugehörigen ungeheuren kriegerischen Auseinandersetzungen -, Ursachen und Beginn der inneren Krise seit den Gracchen, die Restauration unter Sulla und schließlich: die Auflösung der Republik und die Begründung der Monarchie. Aloys Winterling Jochen Bleicken, 1926-2005, war Professor für Alte Geschichte an der Universität Göttingen und u.a. Mitherausgeber von "Oldenbourg Grundriss der Geschichte" und der HISTORISCHEN ZEITSCHRIFT.Mode of access: Internet via World Wide Web.Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019
The Signature Transform in Numerics and Machine Learning
No full textIn this work we study the signature transform from the viewpoint of applied and numerical mathematics. The theoretical background is established in the first part, where the signature is defined as a map going from continuous paths of bounded variations to ordered tensor algebras. Approximation theorems and computational considerations are clarified, together with explicit and well commented examples. Only selected essential properties are pointed out, useful for non-linear approximation of functionals, dimension reduction and extension to the probabilistic setting. In the second part we use all the previously introduced theory to design numerical experiments of interest in data science and machine learning, targeting problems like time series classification, clustering, correlation detection and generation of artificial samples. A small section on agents classification for reinforcement learning is also included. Finally, the reader is given a list of possible connections to other areas of mathematics like PDE, kernel theory, jump processes and even algebraic geometry. We did our best to keep the exposition clear and compact
Combination technique based second moment analysis for elliptic PDEs on random domains
No full textIn this article, we propose the sparse grid combination technique for the second moment analysis of elliptic partial differential equations on random domains. By employing shape sensitivity analysis, we linearize the influence of the random domain perturbation on the solution. We derive deterministic partial differential equations to approximate the random solution’s mean and its covariance with leading order in the amplitude of the random domain perturbation. The partial differential equation for the covariance is a tensor product Dirichlet problem which can efficiently be determined by Galerkin’s method in the sparse tensor product space. We show that this Galerkin approximation coincides with the solution derived from the combination technique if the detail spaces in the related multiscale hierarchy are constructed with respect to Galerkin projections. This means that the combination technique does not impose an additional error in our construction. Numerical experiments quantify and qualify the proposed method
An Adaptive Sparse Grid Algorithm for Elliptic PDEs with Lognormal Diffusion Coefficient
No full textIn this work we build on the classical adaptive sparse grid algorithm (T. Gerstner and M. Griebel, Dimension-adaptive tensor-product quadrature), obtaining an enhanced version capable of using non-nested collocation points, and supporting quadrature and interpolation on unbounded sets. We also consider several profit indicators that are suitable to drive the adaptation process. We then use such algorithm to solve an important test case in Uncertainty Quantification problem, namely the Darcy equation with lognormal permeability random field, and compare the results with those obtained with the quasi-optimal sparse grids based on profit estimates, which we have proposed in our previous works (cf. e.g. Convergence of quasi-optimal sparse grids approximation of Hilbert-valued functions: application to random elliptic PDEs). To treat the case of rough permeability fields, in which a sparse grid approach may not be suitable, we propose to use the adaptive sparse grid quadrature as a control variate in a Monte Carlo simulation. Numerical results show that the adaptive sparse grids have performances similar to those of the quasi-optimal sparse grids and are very effective in the case of smooth permeability fields. Moreover, their use as control variate in a Monte Carlo simulation allows to tackle efficiently also problems with rough coefficients, significantly improving the performances of a standard Monte Carlo scheme.CSQ
Interpretable deep learning for studying the Earth system : Soil-moisture-precipitation coupling across Europe
No full textThe Earth system is a highly complex dynamical system. While considerable process understanding has been achieved in past research, many processes and relations in the Earth system remain poorly understood due to this complexity. A better understanding of these processes and relations can improve weather and climate predictions and eventually help make decisions that protect life and property. In this thesis, I evolve the recently proposed approach of using interpretable deep learning to gain new scientific insights into the Earth system. In the approach, a deep learning model is trained to predict one Earth system variable (referred to as target variable) given some others as input. After training the model, the relations between input and target variables that the model learned are analyzed to gain new scientific insights. The major challenge to the approach is that the model may learn spurious correlations rather than actual causal relations. This is a challenge, not only because the scientist cannot gain new scientific insights from a model that learned spurious correlations, but also because detecting whether a given model learned spurious or causal relations is difficult in complex systems. Here, I propose a variant approach to identify spurious correlations that any given statistical model learned. Furthermore, I develop a methodology of causal deep learning models, which combines the approach of using interpretable deep learning to gain new scientific insights with findings from causality research to actually obtain a causal deep learning model, i.e. a model that learns the causal relations between input and target variables. Applied to several examples from hydrometeorology, the variant approach is superior to other commonly applied approaches for identifying spurious correlations that statistical models learn. Moreover, results obtained with causal deep learning models differ entirely from results obtained with a simple linear correlation analysis, which stresses the importance of considering non-linear effects and the difference between correlation and causation. Finally, I apply both methodologies to gain new insights into soil-moisture-precipitation coupling, i.e. the question how soil moisture affects precipitation. Improving our understanding of soil-moisture-precipitation coupling can help to better understand and mitigate extreme events like droughts and floods, and the effects of land management and climate change. The developed methodology of causal deep learning models overcomes several common limitations of previous studies on soil-moisture-precipitation coupling and reveals that an increase in local soil moisture leads to a subsequent increase in precipitation locally, and a simultaneous decrease in precipitation in a surrounding area. The non-local coupling strength exceeds the local coupling strength. These findings contribute to our understanding of soil-moisture-precipitation coupling and stress the importance of non-local effects, which have commonly been neglected in previous studies
Error analysis of regularized and unregularized least-squares regression on discretized function spaces
No full textIn this thesis, we analyze a variant of the least-squares regression method which operates on subsets of finite-dimensional vector spaces. In the first part, we focus on a regression problem which is constrained to a ball of finite radius in the search space. We derive an upper bound on the overall error by coupling the ball radius to the resolution of the search space. In the second part, the corresponding penalized Lagrangian dual problem is considered to establish probabilistic results on the well-posedness of the underlying minimization problem. Furthermore, we have a look at the limit case, where the penalty term vanishes and we improve on our error estimates from the first part for the special case of noiseless function reconstruction. Subsequently, our theoretical foundation is used to obtain novel convergence results for regression algorithms based on sparse grids with linear splines and Fourier polynomial spaces on hyperbolic crosses. We conclude the thesis by giving several numerical examples and comparing the observed error behavior to our theoretical results
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