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

A note on entropic force and brane cosmology

Recently Verlinde proposed that gravity is an entropic force caused by information changes when a material body moves away from the holographic screen. In this note we apply this argument to brane cosmology, and show that the cosmological equation can be derived from this holographic scenario.Comment: 5 pages, no figures;references adde

Analysis of the Duration of Rising Tone Chorus Elements

AbstractThe duration of chorus elements is an important parameter to understand chorus excitation and to quantify the effects of nonlinear wave‐particle interactions on energetic electron dynamics. In this work, we analyze the duration of rising tone chorus elements statistically using Van Allen Probes data. We present the distribution of chorus element duration (τ) as a function of magnetic local time (MLT) and the geomagnetic activity level characterized by auroral electrojet (AE) index. We show that the typical value of τ for nightside and dawnside is about 0.12 s, smaller than that for dayside and duskside by about a factor of 2 to 4. Using a previously developed hybrid code, DAWN, we suggest that the background magnetic field inhomogeneity might be an important factor in controlling the chorus element duration. We also report that τ is larger during quiet times and shorter during moderate and active periods; this result is consistent with the MLT dependence of τ and the occurrence pattern of chorus waves at different levels of geomagnetic activity. We then investigate the correlation between τ and the frequency chirping rate (Γ). We show that, from observation, τ scales with Γ as , suggesting that statistically the frequency range of chorus elements (τΓ) should be roughly the same for different elements. These findings should be useful to the further development of a theoretical model of chorus excitation and to the quantification of nonlinear wave‐particle interactions on energetic electron dynamics

A Note on Temperature and Energy of 4-dimensional Black Holes from Entropic Force

We investigate the temperature and energy on holographic screens for 4-dimensional black holes with the entropic force idea proposed by Verlinde. We find that the "Unruh-Verlinde temperature" is equal to the Hawking temperature on the horizon and can be considered as a generalized Hawking temperature on the holographic screen outside the horizons. The energy on the holographic screen is not the black hole mass $M$ but the reduced mass $M_0$, which is related to the black hole parameters. With the replacement of the black hole mass $M$ by the reduced mass $M_0$, the entropic force can be written as $F=\frac{GmM_0}{r^2}$, which could be tested by experiments.Comment: V4: 13 pages, 4 figures, title changed, discussions for experiments added, accepted by CQ

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

Study on Evolvement Complexity in an Artificial Stock Market

An artificial stock market is established based on multi-agent . Each agent has a limit memory of the history of stock price, and will choose an action according to his memory and trading strategy. The trading strategy of each agent evolves ceaselessly as a result of self-teaching mechanism. Simulation results exhibit that large events are frequent in the fluctuation of the stock price generated by the present model when compared with a normal process, and the price returns distribution is L\'{e}vy distribution in the central part followed by an approximately exponential truncation. In addition, by defining a variable to gauge the "evolvement complexity" of this system, we have found a phase cross-over from simple-phase to complex-phase along with the increase of the number of individuals, which may be a ubiquitous phenomenon in multifarious real-life systems.Comment: 4 pages and 4 figure

Imaging defects and their evolution in a metal-organic framework at sub-unit-cell resolution

Defect engineering of metal–organic frameworks (MOFs) offers promising opportunities for tailoring their properties to specific functions and applications. However, determining the structures of defects in MOFs—either point defects or extended ones—has proved challenging owing to the difficulty of directly probing local structures in these typically fragile crystals. Here we report the real-space observation, with sub-unit-cell resolution, of structural defects in the catalytic MOF UiO-66 using a combination of low-dose transmission electron microscopy and electron crystallography. Ordered ‘missing linker’ and ‘missing cluster’ defects were found to coexist. The missing-linker defects, reconstructed three-dimensionally with high precision, were attributed to terminating formate groups. The crystallization of the MOF was found to undergo an Ostwald ripening process, during which the defects also evolve: on prolonged crystallization, only the missing-linker defects remained. These observations were rationalized through density functional theory calculations. Finally, the missing-cluster defects were shown to be more catalytically active than their missing-linker counterparts for the isomerization of glucose to fructose

Quantum Non-Demolition Measurement on the Spin Precession of Laser-Trapped 171^{171}Yb Atoms

Quantum non-demolition (QND) measurement enhances the detection efficiency and measurement fidelity, and is highly desired for its applications in precision measurements and quantum information processing. We propose and demonstrate a QND measurement scheme for the spin states of laser-trapped atoms. On $^{171}$Yb atoms held in an optical dipole trap, a transition that is simultaneously cycling, spin-state selective, and spin-state preserving is created by introducing a circularly polarized beam of control laser to optically dress the spin states in the excited level, while leaving the spin states in the ground level unperturbed. We measure the phase of spin precession of $5\times10^{4}$ atoms in a bias magnetic field of 20 mG. This QND approach reduces the optical absorption detection noise by $\sim$19 dB, to a level of 2.3 dB below the atomic quantum projection noise. In addition to providing a general approach for efficient spin-state readout, this all-optical technique allows quick switching and real-time programming for quantum sensing and quantum information processing

Doubly Differential Cross Sections of Low-Energy Electrons Emitted in the Ionization of Molecular Hydrogen by Bare Carbon Ions

We have measured the double differential cross sections (DDCS) (d2σ/dεedΩe) of low-energy electron emission in the ionization of H2 bombarded by bare carbon ions of energy 30 MeV. The energy and angular distributions of the electron DDCS have been obtained for 12 different emission angles and for electron energies varying between 0.1 and 300 eV. We have also deduced the single differential and total ionization cross section from the measured DDCS. The data have been compared with the predictions of first Born approximations and the CDW-EIS (continuum distorted wave–eikonal initial state) model. The CDW-EIS model provides an excellent agreement with the data. [S1050-2947~96!10109-8