Teoria del Mac Guffin (i II)

Abstract not availabl

Accurate and efficient linear scaling DFT calculations with universal applicability

Density Functional Theory calculations traditionally suffer from an inherent cubic scaling with respect to the size of the system, making big calculations extremely expensive. This cubic scaling can be avoided by the use of so-called linear scaling algorithms, which have been developed during the last few decades. In this way it becomes possible to perform ab-initio calculations for several tens of thousands of atoms or even more within a reasonable time frame. However, even though the use of linear scaling algorithms is physically well justified, their implementation often introduces some small errors. Consequently most implementations offering such a linear complexity either yield only a limited accuracy or, if one wants to go beyond this restriction, require a tedious fine tuning of many parameters. In our linear scaling approach within the BigDFT package, we were able to overcome this restriction. Using an ansatz based on localized support functions expressed in an underlying Daubechies wavelet basis -- which offers ideal properties for accurate linear scaling calculations -- we obtain an amazingly high accuracy and a universal applicability while still keeping the possibility of simulating large systems with only a moderate demand of computing resources

Daubechies Wavelets for Linear Scaling Density Functional Theory

We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized contracted basis functions in which the Kohn-Sham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energies and the forces acting on the ions can be calculated in this basis with the same accuracy as if they were calculated directly in a Daubechies wavelets basis, provided that the amplitude of these contracted basis functions is sufficiently small on the surface of the localization region, which is guaranteed by the optimization procedure described in this work. This approach reduces the computational costs of DFT calculations, and can be combined with sparse matrix algebra to obtain linear scaling with respect to the number of electrons in the system. Calculations on systems of 10,000 atoms or more thus become feasible in a systematic basis set with moderate computational resources. Further computational savings can be achieved by exploiting the similarity of the contracted basis functions for closely related environments, e.g. in geometry optimizations or combined calculations of neutral and charged systems

Discriminant random field and patch-based redundancy analysis for image change detection

International audienceTo develop better image change detection algorithms, new models able to capture all the spatio-temporal regularities and geometries seen in an image pair are needed. In con- trast to the usual pixel-wise methods, we propose a patch- based formulation for modeling semi-local interactions and detecting occlusions and other local or regional changes in an image pair. To this end, the image redundancy property is exploited to detect unusual spatio-temporal patterns in the scene. We first define adaptive detectors of changes between two given image patches and combine locally in space and scale such detectors. The resulting score at a given loca- tion is exploited within a discriminant Markov random field (DRF) whose global optimization flags out changes with no optical flow computation. Experimental results on several applications demonstrate that the method performs well at detecting occlusions and meaningful regional changes and is especially robust in the case of low signal-to-noise ratios