3,290 research outputs found

    Isomorphisms in co-TT graphs

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    2019 Spring.Includes bibliographical references.A threshold tolerance graph is a graph where each vertex v is assigned a weight wv and a tolerance tv, and there is an edge between two vertices vx and vy if and only if wx + wy ≥ min(tx,ty). A co-TT graph is the complement of a threshold tolerance graph. Recognition of these graphs can be done in O(n2) time; however no polynomial-time algorithm to identify isomorphisms between pairs of TT or co-TT graphs was previously known. We give an algorithm to identify these isomorphisms, which takes O(n2) time

    tt*-geometry and pluriharmonic maps

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    International audienceIn this paper we use the real differential geometric definition of a metric (an unimodular oriented metric) tt*-bundle of Cortés and the author to define a map Φ\Phi from the space of metric (unimodular oriented metric) tt*-bundles of rank r over a complex manifold M to the space of pluriharmonic maps from M to GL(r)/O(p,q)GL(r)/O(p,q) (respectively SL(r)/SO(p,q)SL(r)/SO(p,q)), where (p,q) is the signature of the metric. In the sequel the image of the map Φ\Phi is characterized. It follows, that in signature (r,0) the image of Φ.\Phi. is the whole space of pluriharmonic maps. This generalizes a result of Dubrovin

    performance of the low-rank TT-SVD for large dense tensors on modern multicore CPUs

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    There are several factorizations of multidimensional tensors into lower-dimensional components, known as ``tensor networks."" We consider the popular ``tensor-train"" (TT) format and ask, How efficiently can we compute a low-rank approximation from a full tensor on current multicore CPUs? Compared to sparse and dense linear algebra, kernel libraries for multilinear algebra are rare and typically not as well optimized. Linear algebra libraries like BLAS and LAPACK may provide the required operations in principle but often at the cost of additional data movements for rearranging memory layouts. Furthermore, these libraries are typically optimized for the compute-bound case (e.g., square matrix operations), whereas low-rank tensor decompositions lead to memory bandwidth limited operations. We propose a ``TT singular value decomposition"" (TT-SVD) algorithm based on two building blocks: a ``Q-less tall-skinny QR"" factorization and a fused tall-skinny matrix-matrix multiplication and reshape operation. We analyze the performance of the resulting TT-SVD algorithm using the roofline performance model. In addition, we present performance results for different algorithmic variants for shared-memory as well as distributed-memory architectures. Our experiments show that commonly used TT-SVD implementations suffer severe performance penalties. We conclude that a dedicated library for tensor factorization kernels would benefit the community: Computing a low-rank approximation can be as cheap as reading the data twice from main memory. As a consequence, an implementation that achieves realistic performance will move the limit at which one has to resort to randomized methods that only process part of the data.Numerical Analysi

    "_Pst-tt!", circa 1962

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    A dark figure marked "Merchants" opens a door labeled "Back Door Deals". Written on recto: "_Pst-tt!".Crim
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