9,969 research outputs found
DFacTo: Distributed Factorization of Tensors
We present a technique for significantly speeding up Alternating Least
Squares (ALS) and Gradient Descent (GD), two widely used algorithms for tensor
factorization. By exploiting properties of the Khatri-Rao product, we show how
to efficiently address a computationally challenging sub-step of both
algorithms. Our algorithm, DFacTo, only requires two sparse matrix-vector
products and is easy to parallelize. DFacTo is not only scalable but also on
average 4 to 10 times faster than competing algorithms on a variety of
datasets. For instance, DFacTo only takes 480 seconds on 4 machines to perform
one iteration of the ALS algorithm and 1,143 seconds to perform one iteration
of the GD algorithm on a 6.5 million x 2.5 million x 1.5 million dimensional
tensor with 1.2 billion non-zero entries.Comment: Under review for NIPS 201
KMS states on Nica-Toeplitz algebras of product systems
We investigate KMS states of Fowler's Nica-Toeplitz algebra
associated to a compactly aligned product system over a semigroup of
Hilbert bimodules. This analysis relies on restrictions of these states to the
core algebra which satisfy appropriate scaling conditions. The concept of
product system of finite type is introduced. If is a lattice ordered
group and is a product system of finite type over satisfying certain
coherence properties, we construct KMS states of \NT(X) associated to
a scalar dynamics from traces on the coefficient algebra of the product system.
Our results were motivated by, and generalize some of the results of Laca and
Raeburn obtained for the Toeplitz algebra of the affine semigroup over the
natural numbers.Comment: Changes to Proposition 3.1 and Theorem 4.10. Major changes to section
5 starting from (and including) new Lemma 5.4 to new Example 5.1
The Cuntz Algebra Q_N and C*-Algebras of Product Systems
We consider a product system over the multiplicative semigroup N^x of Hilbert
bimodules which is implicit in work of S. Yamashita and of the second named
author. We prove directly, using universal properties, that the associated
Nica-Toeplitz algebra is an extension of the C^*-algebra Q_N introduced
recently by Cuntz.Comment: 13 page
D-type Conformal Matter and SU/USp Quivers
We discuss the four dimensional models obtained by compactifying a single M5
brane probing singularity (minimal D-type conformal matter in
six dimensions) on a torus with flux for abelian subgroups of the
flavor symmetry. We derive the resulting quiver field theories in four
dimensions by first compactifying on a circle and relating the flux to duality
domain walls in five dimensions. This leads to novel dualities in
4 dimensions which arise from distinct five dimensional realizations of the
circle compactifications of the D-type conformal matter.Comment: 38 pages, 13 figure
A complete FFT-based decomposition formalism for the redshift-space bispectrum
To fully extract cosmological information from nonlinear galaxy distribution
in redshift space, it is essential to include higher-order statistics beyond
the two-point correlation function. In this paper, we propose a new
decomposition formalism for computing the anisotropic bispectrum in redshift
space and for measuring it from galaxy samples. Our formalism uses tri-polar
spherical harmonic decomposition with zero total angular momentum to compress
the 3D modes distribution in the redshift-space bispectrum. This approach
preserves three fundamental properties of the Universe: statistical
homogeneity, isotropy, and parity-symmetry, allowing us to efficiently separate
the anisotropic signal induced by redshift-space distortions (RSDs) and the
Alcock-Paczy\'{n}ski (AP) effect from the isotropic bispectrum. The relevant
expansion coefficients in terms of the anisotropic signal are reduced to one
multipole index , and the modes are induced only by the RSD or AP
effects. Our formalism has two advantages: (1) we can make use of Fast Fourier
Transforms (FFTs) to measure the bispectrum; (2) it gives a simple expression
to correct for the survey geometry, i.e., the survey window function. As a
demonstration, we measure the decomposed bispectrum from the Baryon Oscillation
Spectroscopic Survey (BOSS) Data Release 12, and, for the first time, present a
detection of the anisotropic bispectrum in the mode.Comment: 23 pages, 13 figure
[Review of] Charles V. Willie. Race, Ethnicity, and Socioeconomic Status
The author examines the interrelations of race, ethnicity, and socioeconomic status through the presentation of a collection of his writings about blacks which have been reprinted from various sources. By reprinting this collection of works, Willie seeks to gain the opportunity to take theoretical stock of what he has learned through his involvements as a planner, student, teacher, researcher, administrator, policy maker, consultant, and concerned citizen. His aim is to link his work with others in the field, hoping to benefit from their clarification and correction. Willie\u27s main objective is to articulate his theoretical conceptions about the field of race relations
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