Supersymmetric KdV equation: Darboux transformation and discrete systems

For the supersymmetric KdV equation, a proper Darboux transformation is presented. This Darboux transformation leads to the B\"{a}cklund transformation found early by Liu and Xie \cite{liu2}. The Darboux transformation and the related B\"{a}cklund transformation are used to construct integrable super differential-difference and difference-difference systems. The continuum limits of these discrete systems and of their Lax pairs are also considered.Comment: 13pages, submitted to Journal of Physics

TimeMachine: Timeline Generation for Knowledge-Base Entities

We present a method called TIMEMACHINE to generate a timeline of events and relations for entities in a knowledge base. For example for an actor, such a timeline should show the most important professional and personal milestones and relationships such as works, awards, collaborations, and family relationships. We develop three orthogonal timeline quality criteria that an ideal timeline should satisfy: (1) it shows events that are relevant to the entity; (2) it shows events that are temporally diverse, so they distribute along the time axis, avoiding visual crowding and allowing for easy user interaction, such as zooming in and out; and (3) it shows events that are content diverse, so they contain many different types of events (e.g., for an actor, it should show movies and marriages and awards, not just movies). We present an algorithm to generate such timelines for a given time period and screen size, based on submodular optimization and web-co-occurrence statistics with provable performance guarantees. A series of user studies using Mechanical Turk shows that all three quality criteria are crucial to produce quality timelines and that our algorithm significantly outperforms various baseline and state-of-the-art methods.Comment: To appear at ACM SIGKDD KDD'15. 12pp, 7 fig. With appendix. Demo and other info available at http://cs.stanford.edu/~althoff/timemachine

Multi-task learing for subspace segmentation

Subspace segmentation is the process of clustering a set of data points that are assumed to lie on the union of multiple linear or affine subspaces, and is increasingly being recognized as a fundamental tool for data analysis in high dimensional settings. Arguably one of the most successful approaches is based on the observation that the sparsest representation of a given point with respect to a dictionary formed by the others involves nonzero coefficients associated with points originating in the same subspace. Such sparse representations are computed independently for each data point via ℓ1-norm minimization and then combined into an affinity matrix for use by a final spectral clustering step. The downside of this procedure is two-fold. First, unlike canonical compressive sensing scenarios with ideally-randomized dictionaries, the data-dependent dictionaries here are unavoidably highly structured, disrupting many of the favorable properties of the ℓ1 norm. Secondly, by treating each data point independently, we ignore useful relationships between points that can be leveraged for jointly computing such sparse representations. Consequently, we motivate a multi-task learning-based framework for learning coupled sparse representations leading to a segmentation pipeline that is both robust against correlation structure and tailored to generate an optimal affinity matrix. Theoretical analysis and empirical tests are provided to support these claims.Y. Wang is sponsored by the University of Cambridge Overseas Trust. Y. Wang and Q. Ling are partially supported by sponsorship from Microsoft Research Asia. Q. Ling is also supported in part by NSFC grant 61004137. W. Chen is supported by EPSRC Research Grant EP/K033700/1 and the Natural Science Foundation of China 61401018.This is the final version of the article. It first appeared from JMLR via http://jmlr.org/proceedings/papers/v37/wangc15.htm

Demonstrating Additional Law of Relativistic Velocities based on Squeezed Light

Special relativity is foundation of many branches of modern physics, of which theoretical results are far beyond our daily experience and hard to realized in kinematic experiments. However, its outcomes could be demonstrated by making use of convenient substitute, i.e. squeezed light in present paper. Squeezed light is very important in the field of quantum optics and the corresponding transformation can be regarded as the coherent state of SU(1; 1). In this paper, the connection between the squeezed operator and Lorentz boost is built under certain conditions. Furthermore, the additional law of relativistic velocities and the angle of Wigner rotation are deduced as well

Reexamining the "finite-size" effects in isobaric yield ratios using a statistical abrasion-ablation model

The "finite-size" effects in the isobaric yield ratio (IYR), which are shown in the standard grand-canonical and canonical statistical ensembles (SGC/CSE) method, is claimed to prevent obtaining the actual values of physical parameters. The conclusion of SGC/CSE maybe questionable for neutron-rich nucleus induced reaction. To investigate whether the IYR has "finite-size" effects, the IYR for the mirror nuclei [IYR(m)] are reexamined using a modified statistical abrasion-ablation (SAA) model. It is found when the projectile is not so neutron-rich, the IYR(m) depends on the isospin of projectile, but the size dependence can not be excluded. In reactions induced by the very neutron-rich projectiles, contrary results to those of the SGC/CSE models are obtained, i.e., the dependence of the IYR(m) on the size and the isospin of the projectile is weakened and disappears both in the SAA and the experimental results.Comment: 5 pages and 4 figure

Coherent Backscattering of light in a magnetic field

This paper describes how coherent backscattering is altered by an external magnetic field. In the theory presented, magneto-optical effects occur inside Mie scatterers embedded in a non-magnetic medium. Unlike previous theories based on point-like scatterers, the decrease of coherent backscattering is obtained in leading order of the magnetic field using rigorous Mie theory. This decrease is strongly enhanced in the proximity of resonances, which cause the path length of the wave inside a scatterer to be increased. Also presented is a novel analysis of the shape of the backscattering cone in a magnetic field.Comment: 27 pages, 5 figures, Revtex, to appear in Phys. Rev.

Glass Transition in the Polaron Dynamics of CMR Manganites

Neutron scattering measurements on a bilayer manganite near optimal doping show that the short-range polarons correlations are completely dynamic at high T, but then freeze upon cooling to a temperature T* 310 K. This glass transition suggests that the paramagnetic/insulating state arises from an inherent orbital frustration that inhibits the formation of a long range orbital- and charge-ordered state. Upon further cooling into the ferromagnetic-metallic state (Tc=114 K), where the polarons melt, the diffuse scattering quickly develops into a propagating, transverse optic phonon.Comment: 4 pages, 4 figures. Physical Review Letters (in Press

Vertically Aligned Gold Nanorod Monolayer on Arbitrary Substrates: Self-Assembly and Femtomolar Detection of Food Contaminants

Cataloged from PDF version of article.Public attention to the food scandals raises an urgent need to develop effective and reliable methods to detect food contaminants. The current prevailing detections are primarily based upon liquid chromatography, mass spectroscopy, or colorimetric methods, which usually require sophisticated and time-consuming steps or sample preparation. Herein, we develop a facile strategy to assemble the vertically aligned monolayer of Au nanorods with a nominal 0.8 nm gap distance and demonstrate their applications in the rapid detection of plasticizers and melamine contamination at femtomolar level by surface-enhanced Raman scattering spectroscopy (SERS). The SERS signals of plasticizers are sensitive down to 0.9 fM concentrations in orange juices. It is the lowest detection limit reported to date, which is 7 orders of magnitude lower than the standard of United States (6 ppb). The highly organized vertical arrays generate the reproducible "SERS-active sites" and can be achieved on arbitrary substrates, ranging from silicon, gallium nitride, glass to flexible poly(ethylene naphthalate) substrates

Inhomogeneous magnetism in La-doped CaMnO3. (I) Nanometric-scale spin clusters and long-range spin canting

Neutron measurements on Ca{1-x}La{x}MnO3 (0.00 <= x <= 0.20) reveal the development of a liquid-like spatial distribution of magnetic droplets of average size ~10 Angstroms, the concentration of which is proportional to x (one cluster per ~60 doped electrons). In addition, a long-range ordered ferromagnetic component is observed for ~0.05 < x < ~0.14. This component is perpendicularly coupled to the simple G-type antiferromagnetic (G-AFM) structure of the undoped compound, which is a signature of a G-AFM + FM spin-canted state. The possible relationship between cluster formation and the stabilization of a long-range spin-canting for intermediate doping is discussed.Comment: Submitted to Physical Review