7,293 research outputs found
Block CUR: Decomposing Matrices using Groups of Columns
A common problem in large-scale data analysis is to approximate a matrix
using a combination of specifically sampled rows and columns, known as CUR
decomposition. Unfortunately, in many real-world environments, the ability to
sample specific individual rows or columns of the matrix is limited by either
system constraints or cost. In this paper, we consider matrix approximation by
sampling predefined \emph{blocks} of columns (or rows) from the matrix. We
present an algorithm for sampling useful column blocks and provide novel
guarantees for the quality of the approximation. This algorithm has application
in problems as diverse as biometric data analysis to distributed computing. We
demonstrate the effectiveness of the proposed algorithms for computing the
Block CUR decomposition of large matrices in a distributed setting with
multiple nodes in a compute cluster, where such blocks correspond to columns
(or rows) of the matrix stored on the same node, which can be retrieved with
much less overhead than retrieving individual columns stored across different
nodes. In the biometric setting, the rows correspond to different users and
columns correspond to users' biometric reaction to external stimuli, {\em
e.g.,}~watching video content, at a particular time instant. There is
significant cost in acquiring each user's reaction to lengthy content so we
sample a few important scenes to approximate the biometric response. An
individual time sample in this use case cannot be queried in isolation due to
the lack of context that caused that biometric reaction. Instead, collections
of time segments ({\em i.e.,} blocks) must be presented to the user. The
practical application of these algorithms is shown via experimental results
using real-world user biometric data from a content testing environment.Comment: shorter version to appear in ECML-PKDD 201
Dimerized and trimerized phases for spin-2 Bosons in a one-dimensional optical lattice
We study the phase diagram for spin-2 bosons loaded in a one-dimensional
optical lattice. By using non-Abelian density matrix renormalization group
(DMRG) method we identify three possible phases: ferromagnetic, dimerized, and
trimerized phases. We sketch the phase boundaries based on DMRG. We illustrate
two methods for identifying the phases. The first method is based on the
spin-spin correlation function while in the second method one observes the
excitation gap as a dimerization or a trimerization superlattice is imposed.
The advantage of the second method is that it can also be easily implemented in
experiments. By using the scattering lengths in the literature we estimate that
Rb, Na, and Rb be ferromagnetic, dimerized, and trimerized
respectively.Comment: 4 pages, 3 figures. Add acknowledgemen
Multiple Correspondence and Typological Convergence in Contact-Induced Grammaticalization: Evidence from Cantonese-English Bilingual Development
This paper examines the emergence of perfective aspect in Cantonese-English bilingual children from the perspective of contact-induced grammaticalization, focusing on the novel use of already. Although the adverbial already seems to serve a function similar to that of the Cantonese perfective marker zo2 in the bilingual children, other model constructions suggest that the function of already may combine those of several Cantonese particles such as the sentence-final particle laa3. The results suggest that in contact-induced grammaticalization, it is possible to develop a new category in the replica language based on multiple different but related categories in the model language. Adopting an evolutionary approach to language transmission (Mufwene, 2001), we discuss why grammaticalization in the Cantonese-English bilingual children does not seem to involve coevolution of form and meaning, why the grammaticalization phenomena in the bilingual children are only transient, and how the study of bilingual acquisition can contribute to contact linguistics
Dissipation of the 3^He A-B Transition
A rigorous hydrodynamic theory of the A-B transition is presented. All
dissipative processes are considered. At low interface velocities, those
occurring on hydrodynamic length scales, not considered hitherto, are most
probably the dominant ones.Comment: 13 pages, REVTeX, 2 figures, ITP-UH 13/9
Quantum Critical Spin-2 Chain with Emergent SU(3) Symmetry
We study the quantum critical phase of a SU(2) symmetric spin-2 chain
obtained from spin-2 bosons in a one-dimensional lattice. We obtain the scaling
of the entanglement entropy and finite-size energies by exact diagonalization
and density-matrix renormalization group methods. From the numerical results of
the energy spectrum, central charge, and scaling dimension we identify the
conformal field theory describing the whole critical phase to be the SU(3)
Wess-Zumino-Witten model. We find that while in the whole critical phase the
Hamiltonian is only SU(2) invariant, there is an emergent SU(3) symmetry in the
thermodynamic limit
Bubble Growth in Superfluid 3-He: The Dynamics of the Curved A-B Interface
We study the hydrodynamics of the A-B interface with finite curvature. The
interface tension is shown to enhance both the transition velocity and the
amplitudes of second sound. In addition, the magnetic signals emitted by the
growing bubble are calculated, and the interaction between many growing bubbles
is considered.Comment: 20 pages, 3 figures, LaTeX, ITP-UH 11/9
Internal Vortex Structure of a Trapped Spinor Bose-Einstein Condensate
The internal vortex structure of a trapped spin-1 Bose-Einstein condensate is
investigated. It is shown that it has a variety of configurations depending on,
in particular, the ratio of the relevant scattering lengths and the total
magnetization.Comment: replacement; minor grammatical corrections but with additional
figure
Supercurrent tunneling between conventional and unconventional superconductors: A Ginzburg-Landau approach
We investigate the Josephson tunneling between a conventional and an unconventional superconductor via a Ginzburg-Landau theory. This approach allows us to write down the general form of the Josephson coupling between the two superconductors, and to see which terms are forbidden or allowed by spatial symmetries. The time-reversal symmetry is also considered. We discuss the current-phase relationships, magnetic, and ac effects if we just include this direct coupling to the unconventional superconductor. In addition we consider the Josephson coupling between two short-coherence-length superconductors, extending the work of Deutscher and Müller (DM) to a finite-current calculation. We find that the critical current is suppressed below the DM value due to the fact that the coupling between the two superconductors across the junction depends on the phase difference and hence the current itself. Finally we investigate the possibility of the proximity effect, in particular the possibility that the conventional-type pairing is induced and hence coexists with the unconventional pairing near the junction. This would give the dominant contribution to the tunneling current if the direct tunneling to the unconventional pairs are suppressed for some reason. We point out that there is no possibility of dissipationless tunneling above the transition temperature of the unconventional superconductor. Even in the case in which the unconventional superconductor is below its transition temperature, we find that, for the possibility of a dissipationless current, it is crucial to have a coupling between the induced s wave and the unconventional superconductor that depends on their phase difference, which allows the conversion of the supercurrent from one type to the other. The behavior of this current, in particular as a function of temperature, is discussed. We also discuss the magnetic and time-dependent effects of the junction in the presence of this proximity effect. We see that, while some of these remain unaffected, some, in particular the time-dependent processes, are affected in a rather nontrivial manner
Symmetry and inert states of spin Bose Condensates
We construct the list of all possible inert states of spin Bose condensates
for . In doing so, we also obtain their symmetry properties. These
results are applied to classify line defects of these spin condensates at zero
magnetic field.Comment: an error in Sec III C correcte
Stationary Josephson effect in a weak-link between nonunitary triplet superconductors
A stationary Josephson effect in a weak-link between misorientated nonunitary
triplet superconductors is investigated theoretically. The non-self-consistent
quasiclassical Eilenberger equation for this system has been solved
analytically. As an application of this analytical calculation, the
current-phase diagrams are plotted for the junction between two nonunitary
bipolar wave superconducting banks. A spontaneous current parallel to the
interface between superconductors has been observed. Also, the effect of
misorientation between crystals on the Josephson and spontaneous currents is
studied. Such experimental investigations of the current-phase diagrams can be
used to test the pairing symmetry in the above-mentioned superconductors.Comment: 6 pages and 6 figure
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