Efficient solvers for incompressible fluid flows in geosciences

Saddle point problems involving large systems of linear equations arise in a wide variety of applications in computational science and engineering. A variety of solvers have been developed for these type of problems typically with specific applications in mind. In this paper we will focus on saddle point problems as they arise from incompressible fluid flow problems in applications in geosciences. They are characterized through a spatially variable viscosity when modeling temperature dependencies (e.g. in Earth mantel convection models) or moving material interfaces (e.g. in subduction zones simulation and numerical volcano models). In this paper we will give an overview on some of the iterative techniques that can be used and discuss suitable preconditioning techniques. We will discuss the implementation of the schemes using the python module Escript and compare the efficiency of these schemes when applied to convection models on a parallel computer

Slepian functions and their use in signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and on the surface of a sphere.Comment: Submitted to the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verla

Scalar and vector Slepian functions, spherical signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and, particularly for applications in the geosciences, for scalar and vectorial signals defined on the surface of a unit sphere.Comment: Submitted to the 2nd Edition of the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verlag. This is a slightly modified but expanded version of the paper arxiv:0909.5368 that appeared in the 1st Edition of the Handbook, when it was called: Slepian functions and their use in signal estimation and spectral analysi

Spectral and spatial decomposition of lithospheric magnetic field models using spherical Slepian functions

Global magnetic field models are typically expressed as spherical-harmonic expansion coefficients. Slepian functions are linear combinations of spherical harmonics that produce new basis functions, which vanish approximately outside chosen geographical boundaries but also remain orthogonal within the spatial region of interest. Hence, they are suitable for decomposing spherical-harmonic models into portions that have significant magnetic field strength only in selected areas. Slepian functions are spatio-spectrally concentrated, balancing spatial bias and spectral leakage. Here, we employ them as a basis to decompose the global lithospheric magnetic field model MF7 up to degree and order 72, into two distinct regions. One of the resultant fields is concentrated within the ensemble of continental domains, and the other is localized over its complement, the oceans. Our procedure neatly divides the spectral power at each harmonic degree into two parts. The field over the continents dominates the overall crustal magnetic field, and each region has a distinct power-spectral signature. The oceanic power spectrum is approximately flat, while that of the continental region shows increasing power as the spherical-harmonic degree increases.We provide a further breakdown of the field into smaller, non-overlapping continental and oceanic regions, and speculate on the source of the variability in their spectral signatures

The privacy of k-NN retrieval for horizontal partitioned data - new methods and applications

Recently, privacy issues have become important in clustering analysis, especially when data is horizontally partitioned over several parties. Associative queries are the core retrieval operation for many data mining algorithms, especially clustering and k-NN classification. The algorithms that effciently support k-NN queries are of special interest. We show how to adapt well-known data structures to the privacy preserving context and what is the overhead of this adaptation. We present an algorithm for k-NN in secure multiparty computation. This is based on presenting private computation of several metrics. As a result, we can offer three approaches to associative queries over horizontally partitioned data with progressively less security. We show privacy preserving algorithms for data structures that induce a partition on the space; such as KD-Trees. Our next preference is our Privacy Preserving SASH. However, we demonstrate that the most effective approach to achieve privacy is separate data structures for parties, where associative queries work separately, followed by secure combination to produce the overall output. This idea not only enhances security but also reduces communication cost between data holders. Our results and protocols also enable us to improve on previous approaches for k-NN classification

HERS: Modeling Influential Contexts with Heterogeneous Relations for Sparse and Cold-Start Recommendation

Classic recommender systems face challenges in addressing the data sparsity and cold-start problems with only modeling the user-item relation. An essential direction is to incorporate and understand the additional heterogeneous relations, e.g., user-user and item-item relations, since each user-item interaction is often influenced by other users and items, which form the user’s/item’s influential contexts. This induces important yet challenging issues, including modeling heterogeneous relations, interactions, and the strength of the influence from users/items in the influential contexts. To this end, we design Influential-Context Aggregation Units (ICAU) to aggregate the user-user/item-item relations within a given context as the influential context embeddings. Accordingly, we propose a Heterogeneous relations-Embedded Recommender System (HERS) based on ICAUs to model and interpret the underlying motivation of user-item interactions by considering user-user and item-item influences. The experiments on two real-world datasets show the highly improved recommendation quality made by HERS and its superiority in handling the cold-start problem. In addition, we demonstrate the interpretability of modeling influential contexts in explaining the recommendation results

Design, Synthesis, and Binding Affinity Evaluation of Hoechst 33258 Derivatives for the Development of Sequence-Specific DNA-Based Asymmetric Catalysts

We thank the Ministere de l ̀ ’Enseignement Superieur et de la ́ Recherche, the Agence Nationale de la Recherche (D-CYSIV Project; ANR-2015-CE29-0021-01) and the Erasmus Mundus Backis Program for their support