7363283
Self-adapting software for numerical linear algebra and LAPACK for clusters
This article describes the context, design, and recent development of the LAPACK for clusters (LFC) project. It has been developed in the framework of Self-Adapting Numerical Software (SANS) since we believe such an approach can deliver the convenience and ease of use of existing sequential environments bundled with the power and versatility of highly tuned parallel codes that execute on clusters. Accomplishing this task is far from trivial as we argue in the paper by presenting pertinent case studies and possible usage scenarios.
1479535
Self Adaptive Application Level Fault Tolerance for Parallel and Distributed Computing
Most application level fault tolerance schemes in literature are non-adaptive in the sense that the fault tolerance schemes incorporated in applications are usually designed without incorporating information from system environments such as the amount of available memory and the local or network I/O bandwidth. However, from an application point of view, it is often desirable for fault tolerant high performance applications to be able to achieve high performance under whatever system environment it executes with as low fault tolerance overhead as possible In this paper, we demonstrate that, in order to achieve high reliability with as low performance penalty as possible, fault tolerant schemes in applications need to be able to adapt themselves to different system environments. We propose a framework under which different fault tolerant schemes can be incorporated in applications using an adaptive method. Under this framework, applications are able to choose near optimal fault tolerance schemes at run time according to the specific characteristics of the platform on which the application is executing.
5809396
Self-adapting numerical software (SANS) effort
The challenge for the development of next-generation software is the successful management of the complex computational environment while delivering to the scientist the full power of flexible compositions of the available algorithmic alternatives. Self-adapting numerical software (SANS) systems are intended to meet this significant challenge. The process of arriving at an efficient numerical solution of problems in computational science involves numerous decisions by a numerical expert. Attempts to automate such decisions distinguish three levels: algorithmic decision, management of the parallel environment, and processor-specific tuning of kernels. Additionally, at any of these levels we can decide to rearrange the user's data. In this paper we look at a number of efforts at the University of Tennessee to investigate these areas.
1853937
Numerically Stable Real Number Codes Based on Random Matrices
Error correction codes defined over real-number field have been studied and recognized as useful in many applications. However, most real-number codes in literature are quite suspect in their numerical stability. In this paper, we introduce a class of real-number codes based on random generator matrices over real-number fields. Codes over complex-number field are also discussed. Experiment results demonstrate our codes are numerically much more stable than existing codes in literature.
18029622
The Bounded Injury Priority Method and the Learnability of Unions of Rectangles
Abstract We develop a bounded version of the finite injury priority method in recursion theory. We use this to study the learnability of unions of rectangles over the domain {0, …, n − 1}d with only equivalence queries. Applying this method, we show three main results: 1. (1)The class of unions of rectangles is polynomial time learnable for constant dimension d. 2. (2)The class of unions of rectangles whose projections at some unknown dimension are pairwise-disjoint is polynomial time learnable. 3. (3)The class of unions of two disjoint rectangles is polynomial time learnable with unions of two rectangles as hypotheses.
7380429
A BLAS based C library for exact linear algebra on integer matrices
Algorithms for solving linear systems of equations over the integers are designed and implemented. The implementations are based on the highly optimized and portable ATLAS/BLAS library for numerical linear algebra and the GNU Multiple Precision library (GMP) for large integer arithmetic.
19262472
Relevance Feedback and Learning in Content-Based Image Search
A major bottleneck in content-based image retrieval (CBIR) systems or search engines is the large gap between low-level image features used to index images and high-level semantic contents of images. One solution to this bottleneck is to apply relevance feedback to refine the query or similarity measures in image search process. In this paper, we first address the key issues involved in relevance feedback of CBIR systems and present a brief overview of a set of commonly used relevance feedback algorithms. Almost all of the previously proposed methods fall well into such framework. We present a framework of relevance feedback and semantic learning in CBIR. In this framework, low-level features and keyword annotations are integrated in image retrieval and in feedback processes to improve the retrieval performance. We have also extended framework to a content-based web image search engine in which hosting web pages are used to collect relevant annotations for images and users' feedback logs are used to refine annotations. A prototype system has developed to evaluate our proposed schemes, and our experimental results indicated that our approach outperforms traditional CBIR system and relevance feedback approaches.
40322419
A Quadratic Lower Bound for Rocchio's Similarity-Based Relevance Feedback Algorithm
It is shown in [4] that Rocchio's similarity-based relevance feedback algorithm makes Ωn mistakes in searching for a collection of documents represented by a monotone disjunction of at most k relevant features or terms over the n-dimensional binary vector space {0, 1}n. In practice, Rocchio's algorithm often uses a fixed query updating factor and a fixed classification threshold. When this is the case, we strengthen the work in [4] in this paper and prove that Rocchio's algorithm makes Ωkn---k mistakes in searching for the same collection of documents over the binary vector space {0, 1}n. A quadratic lower bound is obtained when k is proportional to n. An Okn---k2 upper bound is also obtained.
8613420
Degenerate Two-Phase Incompressible Flow IV: Local Refinement and Domain Decomposition
This is the fourth paper of a series in which we analyze mathematical properties and develop numerical methods for a degenerate elliptic-parabolic partial differential system which describes the flow of two incompressible, immiscible fluids in porous media. In this paper we describe a finite element approximation for this system on locally refined grids. This adaptive approximation is based on a mixed finite element method for the elliptic pressure equation and a Galerkin finite element method for the degenerate parabolic saturation equation. Both discrete stability and sharp a priori error estimates are established for this approximation. Iterative techniques of domain decomposition type for solving it are discussed, and numerical results are presented.