31,273 research outputs found
Low-distortion Subspace Embeddings in Input-sparsity Time and Applications to Robust Linear Regression
Low-distortion embeddings are critical building blocks for developing random
sampling and random projection algorithms for linear algebra problems. We show
that, given a matrix with and a , with a constant probability, we can construct a low-distortion embedding
matrix \Pi \in \R^{O(\poly(d)) \times n} that embeds \A_p, the
subspace spanned by 's columns, into (\R^{O(\poly(d))}, \| \cdot \|_p);
the distortion of our embeddings is only O(\poly(d)), and we can compute in O(\nnz(A)) time, i.e., input-sparsity time. Our result generalizes the
input-sparsity time subspace embedding by Clarkson and Woodruff
[STOC'13]; and for completeness, we present a simpler and improved analysis of
their construction for . These input-sparsity time embeddings
are optimal, up to constants, in terms of their running time; and the improved
running time propagates to applications such as -distortion
subspace embedding and relative-error regression. For
, we show that a -approximate solution to the
regression problem specified by the matrix and a vector can be
computed in O(\nnz(A) + d^3 \log(d/\epsilon) /\epsilon^2) time; and for
, via a subspace-preserving sampling procedure, we show that a -distortion embedding of \A_p into \R^{O(\poly(d))} can be
computed in O(\nnz(A) \cdot \log n) time, and we also show that a
-approximate solution to the regression problem can be computed in O(\nnz(A) \cdot \log n + \poly(d)
\log(1/\epsilon)/\epsilon^2) time. Moreover, we can improve the embedding
dimension or equivalently the sample size to without increasing the complexity.Comment: 22 page
Maximum thickness of amorphous NiZr interlayers formed by a solid-state reaction technique
Formation of the equilibrium intermetallic compound NiZr in sputter deposited Ni/Zr diffusion couples is suppressed by the formation of a metastable amorphous NiZr alloy until a critical thickness of the amorphous NiZr interlayer is reached. The temperature dependence of this critical thickness is studied experimentally. A phenomenological model based on the premise of interfacial heterogeneous nucleation is proposed to understand the evolution of Ni/Zr diffusion couples
Automatic Classification of Text Databases through Query Probing
Many text databases on the web are "hidden" behind search interfaces, and
their documents are only accessible through querying. Search engines typically
ignore the contents of such search-only databases. Recently, Yahoo-like
directories have started to manually organize these databases into categories
that users can browse to find these valuable resources. We propose a novel
strategy to automate the classification of search-only text databases. Our
technique starts by training a rule-based document classifier, and then uses
the classifier's rules to generate probing queries. The queries are sent to the
text databases, which are then classified based on the number of matches that
they produce for each query. We report some initial exploratory experiments
that show that our approach is promising to automatically characterize the
contents of text databases accessible on the web.Comment: 7 pages, 1 figur
Solid-state interdiffusion reactions in Ni/Ti and Ni/Zr multilayered thin films
We have performed a comparative transmission electron microscopy study of solid-state interdiffusion reactions in multilayered Ni/Zr and Ni/Ti thin films. The Ni-Zr reaction product was amorphous while the Ni-Ti reaction product was a simple intermetallic compound. Because thermodynamic and chemical properties of these two alloy systems are similar, we suggest kinetic origins for this difference in reaction product
Generalized MICZ-Kepler Problems and Unitary Highest Weight Modules
For each integer , we demonstrate that a -dimensional
generalized MICZ-Kepler problem has an \mr{Spin}(2, 2n+2) dynamical symmetry
which extends the manifest \mr{Spin}(2n+1) symmetry. The Hilbert space of
bound states is shown to form a unitary highest weight \mr{Spin}(2,
2n+2)-module which occurs at the first reduction point in the
Enright-Howe-Wallach classification diagram for the unitary highest weight
modules. As a byproduct, we get a simple geometric realization for such a
unitary highest weight \mr{Spin}(2, 2n+2)-module.Comment: 27 pages, Refs. update
Simultaneous planar growth of amorphous and crystalline Ni silicides
We report a solid-state interdiffusion reaction induced by rapid thermal annealing and vacuum furnace annealing in evaporated Ni/Si bilayers. Upon heat treatment of a Ni film overlaid on a film of amorphous Si evaporated from a graphite crucible, amorphous and crystalline silicide layers grow uniformly side by side as revealed by cross-sectional transmission electron microscopy and backscattering spectrometry. This phenomenon contrasts with the silicide formation behavior previously observed in the Ni-Si system, and constitutes an interesting counterpart of the solid-state interdiffusion-induced amorphization in Ni/Zr thin-film diffusion couples. Carbon impurity contained in the amorphous Si film stabilizes the amorphous phase. Kinetic and thermodynamic factors that account for the experimental findings are discussed
Assessment of the Lunar Surface Layer and in Situ Materials to Sustain Construction-related Applications
Present and future technologies to facilitate lunar composition and resource assessment with applications to lunar surface construction are presented. We are particularly interested in the construction activity associated with lunar-based astronomy. We address, as an example, the use of ground-probing radar to help assess subsurface conditions at sites for observatories and other facilities
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