QR Factorization of Tall and Skinny Matrices in a Grid Computing Environment

Previous studies have reported that common dense linear algebra operations do not achieve speed up by using multiple geographical sites of a computational grid. Because such operations are the building blocks of most scientific applications, conventional supercomputers are still strongly predominant in high-performance computing and the use of grids for speeding up large-scale scientific problems is limited to applications exhibiting parallelism at a higher level. We have identified two performance bottlenecks in the distributed memory algorithms implemented in ScaLAPACK, a state-of-the-art dense linear algebra library. First, because ScaLAPACK assumes a homogeneous communication network, the implementations of ScaLAPACK algorithms lack locality in their communication pattern. Second, the number of messages sent in the ScaLAPACK algorithms is significantly greater than other algorithms that trade flops for communication. In this paper, we present a new approach for computing a QR factorization -- one of the main dense linear algebra kernels -- of tall and skinny matrices in a grid computing environment that overcomes these two bottlenecks. Our contribution is to articulate a recently proposed algorithm (Communication Avoiding QR) with a topology-aware middleware (QCG-OMPI) in order to confine intensive communications (ScaLAPACK calls) within the different geographical sites. An experimental study conducted on the Grid'5000 platform shows that the resulting performance increases linearly with the number of geographical sites on large-scale problems (and is in particular consistently higher than ScaLAPACK's).Comment: Accepted at IPDPS10. (IEEE International Parallel & Distributed Processing Symposium 2010 in Atlanta, GA, USA.

The knowledge that shapes the city:the human city beneath the social city

In the Atlanta Symposium (Hillier, 2001, 2003a) a theory of the social constructionof the city was presented. In this paper it is proposed that underlying the variouskinds of social city there is a deeper, more generic human city, which arises from thepervasive intervention of the human cognitive subject in the shaping and workingof the city. This intervention is explored at two critical stages in the forming of thecity: in the 'vertical' form-creating process by which the accumulation of built formscreates an emergent spatial pattern; and in the 'lateral' form-function process bywhich the emergent spatial pattern shapes movement and sets off the process bywhich an aggregate of buildings becomes a living city. The nature of these cognitiveinterventions is investigated by asking a question: how do human beings 'synchronise'diachronically acquired (and diachronically created) spatial information into asynchronic picture of ambient urban spatial patterns, since it is such synchronicpictures which seem to mediate both interventions? A possible answer is sought bydeveloping the concept of 'description retrieval', originally proposed in 'The SocialLogic of Space' as the means by which human beings retrieve abstract informationfrom patterns of relations in the real world. Our ability to retrieve such descriptionhappens, it is argued, at more than one level, and can includes the high-level notionsof the grid which seems to plays a key role in cognitive intervention in the city.Finally we ask what the ubiquity of the human cognitive subject in the formation ofthe city implies for how we should see cities as complex systems. It is argued that,as with language, there is a 'objective subject' at the heart of the processes by whichcities come into existence, and that this provides us both with the need and themeans to mediate between the social physics paradigm of the city, with its focus onthe mathematics of the generation of the physical city and phenomenologicalparadigm with its - too often anti-mathematical - focus on the human experience ofthe city. Since the intervention of the cognitive subject involves formal ideas andhas formal consequences for the structure of the city, we cannot, it is argued, explaineither without the other

Domain Wall Junctions in Supersymmetric Field Theories in D=4

We study the possible BPS domain wall junction configurations for general polynomial superpotentials of N=1 supersymmetric Wess-Zumino models in D=4. We scan the parameter space of the superpotential and find different possible BPS states for different values of the deformation parameters and present our results graphically. We comment on the domain walls in F/M/IIA theories obtained from the Calabi-Yau fourfolds with isolated singularities and a background flux.Comment: 26 pages, 4 figure

Random geometric graphs with general connection functions

In the original (1961) Gilbert model of random geometric graphs, nodes are placed according to a Poisson point process, and links formed between those within a fixed range. Motivated by wireless ad-hoc networks "soft" or "probabilistic" connection models have recently been introduced, involving a "connection function" H(r) that gives the probability that two nodes at distance r are linked (directly connect). In many applications (not only wireless networks), it is desirable that the graph is connected, that is every node is linked to every other node in a multihop fashion. Here, the connection probability of a dense network in a convex domain in two or three dimensions is expressed in terms of contributions from boundary components, for a very general class of connection functions. It turns out that only a few quantities such as moments of the connection function appear. Good agreement is found with special cases from previous studies and with numerical simulations.Comment: 16 pages; improved figures and minor edit

Isogeometric FEM-BEM coupled structural-acoustic analysis of shells using subdivision surfaces

We introduce a coupled finite and boundary element formulation for acoustic scattering analysis over thin shell structures. A triangular Loop subdivision surface discretisation is used for both geometry and analysis fields. The Kirchhoff-Love shell equation is discretised with the finite element method and the Helmholtz equation for the acoustic field with the boundary element method. The use of the boundary element formulation allows the elegant handling of infinite domains and precludes the need for volumetric meshing. In the present work the subdivision control meshes for the shell displacements and the acoustic pressures have the same resolution. The corresponding smooth subdivision basis functions have the $C^1$ continuity property required for the Kirchhoff-Love formulation and are highly efficient for the acoustic field computations. We validate the proposed isogeometric formulation through a closed-form solution of acoustic scattering over a thin shell sphere. Furthermore, we demonstrate the ability of the proposed approach to handle complex geometries with arbitrary topology that provides an integrated isogeometric design and analysis workflow for coupled structural-acoustic analysis of shells

Unsupervised Sparse Dirichlet-Net for Hyperspectral Image Super-Resolution

In many computer vision applications, obtaining images of high resolution in both the spatial and spectral domains are equally important. However, due to hardware limitations, one can only expect to acquire images of high resolution in either the spatial or spectral domains. This paper focuses on hyperspectral image super-resolution (HSI-SR), where a hyperspectral image (HSI) with low spatial resolution (LR) but high spectral resolution is fused with a multispectral image (MSI) with high spatial resolution (HR) but low spectral resolution to obtain HR HSI. Existing deep learning-based solutions are all supervised that would need a large training set and the availability of HR HSI, which is unrealistic. Here, we make the first attempt to solving the HSI-SR problem using an unsupervised encoder-decoder architecture that carries the following uniquenesses. First, it is composed of two encoder-decoder networks, coupled through a shared decoder, in order to preserve the rich spectral information from the HSI network. Second, the network encourages the representations from both modalities to follow a sparse Dirichlet distribution which naturally incorporates the two physical constraints of HSI and MSI. Third, the angular difference between representations are minimized in order to reduce the spectral distortion. We refer to the proposed architecture as unsupervised Sparse Dirichlet-Net, or uSDN. Extensive experimental results demonstrate the superior performance of uSDN as compared to the state-of-the-art.Comment: Accepted by The IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2018, Spotlight

Deep Learning for Image Recognition

Neuronové sítě jsou dnes jeden z nejúspěšnějších modelů pro strojové učení. Můžeme je nalézt v autonomínch robotických systémech, v rozpoznávání objektů i řeči, predikci a mnoha jiných odvětvích umělé inteligence. Tato práce seznámí čtenáře s tímto modelem a jeho rozšířením, které se používá pro rozpoznávání objektů. Posléze popisuje aplikaci těchto konvolučních neuronových sítí(CNNs) pro klasifikaci obrazků na datasetech Caltech101 a Cifar-10. Na příkladu této aplikace diskutuje a měří efektivnost různých technik používaných v CNNs. Výsledky ukazují, že tyto sítě jsou bez dalších rozšíření schopné dosáhnout 80\% přesnosti na datasetu Cifar-10 a 37\% přesnosti na datasetu Caltech101.Neural networks are one of the state-of-the-art models for machine learning today. One may found them in autonomous robot systems, object and speech recognition, prediction and many others AI tasks. The thesis describes this model and its extension which is used in an object recognition. Then explains an application of a convolutional neural networks(CNNs) in an image recognition on Caltech101 and Cifar10 datasets. Using this exemplar application, the thesis discusses and measures efficiency of techniques used in CNNs. Results show that the convolutional networks without advanced extensions are able to reach a 80\% recognition accuracy on Cifar-10 and a 37\% accuracy on Caltech101.