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 $^{83}$Rb, $^{23}$Na, and $^{87}$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)$_1$ 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 $S \le 4$. 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 $f-$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