41,644 research outputs found
Online Tensor Methods for Learning Latent Variable Models
We introduce an online tensor decomposition based approach for two latent
variable modeling problems namely, (1) community detection, in which we learn
the latent communities that the social actors in social networks belong to, and
(2) topic modeling, in which we infer hidden topics of text articles. We
consider decomposition of moment tensors using stochastic gradient descent. We
conduct optimization of multilinear operations in SGD and avoid directly
forming the tensors, to save computational and storage costs. We present
optimized algorithm in two platforms. Our GPU-based implementation exploits the
parallelism of SIMD architectures to allow for maximum speed-up by a careful
optimization of storage and data transfer, whereas our CPU-based implementation
uses efficient sparse matrix computations and is suitable for large sparse
datasets. For the community detection problem, we demonstrate accuracy and
computational efficiency on Facebook, Yelp and DBLP datasets, and for the topic
modeling problem, we also demonstrate good performance on the New York Times
dataset. We compare our results to the state-of-the-art algorithms such as the
variational method, and report a gain of accuracy and a gain of several orders
of magnitude in the execution time.Comment: JMLR 201
Restrictions on the Material Coefficients in the Constitutive Theories for Non-Classical Viscous Fluent Continua
This paper considers conservation and balance laws and the constitutive theo-ries for non-classical viscous fluent continua without memory, in which in-ternal rotation rates due to the velocity gradient tensor are incorporated in the thermodynamic framework. The constitutive theories for the deviatoric part of the symmetric Cauchy stress tensor and the Cauchy moment tensor are de-rived based on integrity. The constitutive theories for the Cauchy moment tensor are considered when the balance of moments of moments 1) is not a balance law and 2) is a balance law. The constitutive theory for heat vector based on integrity is also considered. Restrictions on the material coefficients in the constitutive theories for the stress tensor, moment tensor, and heat vector are established using the conditions resulting from the entropy inequa-lity, keeping in mind that the constitutive theories derived here based on inte-grity are in fact nonlinear constitutive theories. It is shown that in the case of the simplest linear constitutive theory for stress tensor used predominantly for compressible viscous fluids, Stokes’ hypothesis or Stokes’ assumption has no thermodynamic basis, hence may be viewed incorrect. Thermodynamically consistent derivations of the restrictions on various material coefficients are presented for non-classical as well as classical theories that are applicable to nonlinear constitutive theories, which are inevitable if the constitutive theo-ries are derived based on integrity
Operational Markov condition for quantum processes
We derive a necessary and sufficient condition for a quantum process to be
Markovian which coincides with the classical one in the relevant limit. Our
condition unifies all previously known definitions for quantum Markov processes
by accounting for all potentially detectable memory effects. We then derive a
family of measures of non-Markovianity with clear operational interpretations,
such as the size of the memory required to simulate a process, or the
experimental falsifiability of a Markovian hypothesis.Comment: 5+3 pages, 4 figures; split off from earlier version of
arXiv:1512.0058
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