Running surface couplings

We discuss the renormalization group improved effective action and running surface couplings in curved spacetime with boundary. Using scalar self-interacting theory as an example, we study the influence of the boundary effects to effective equations of motion in spherical cap and the relevance of surface running couplings to quantum cosmology and symmetry breaking phenomenon. Running surface couplings in the asymptotically free SU(2) gauge theory are found.Comment: 11 pages, Latex fil

Phases of supersymmetric O(N) theories

We perform a global renormalization group study of O(N) symmetric Wess-Zumino theories and their phases in three euclidean dimensions. At infinite N the theory is solved exactly. The phases and phase transitions are worked out for finite and infinite short-distance cutoffs. A distinctive new feature arises at strong coupling, where the effective superfield potential becomes multi-valued, signalled by divergences in the fermion-boson interaction. Our findings resolve the long-standing puzzle about the occurrence of degenerate O(N) symmetric phases. At finite N, we find a strongly-coupled fixed point in the local potential approximation and explain its impact on the phase transition. We also examine the possibility for a supersymmetric Bardeen-Moshe-Bander phenomenon, and relate our findings with the spontaneous breaking of supersymmetry in other models.Comment: 23 pages, 18 figure

Relaxation measurements in the regime of the second magnetization peak in Nb films

We report on magnetic measurements as a function of field, temperature and time (relaxation) in superconducting Nb films of critical temperature Tc = 9.25 K. The magnetic measurements as a function of field exhibited a second magnetization peak (SMP) which in general is accompanied by thermomagnetic instabilities (TMIs). The lines where the SMP occurs and where the first flux jump in the virgin magnetization curves is observed, end at a characteristic point (To,Ho)=(7.2 K,80 Oe). Relaxation measurements showed that for T<To=7.2 K the activation energy Uo and the normalized relaxation rate S exhibit non-monotonic behavior as a function either of temperature or field. The extrema observed in Uo and S coincide with the onset and the maximum points of the SMP. In the regime T>To=7.2 K both Uo and S present a conventional monotonic behavior. These results indicate that the SMP behavior observed in our Nb films is promoted by the anomalous relaxation of the magnetization.Comment: To appear in Physica

Tomographic readout of an opto-mechanical interferometer

The quantum state of light changes its nature when being reflected off a mechanical oscillator due to the latter's susceptibility to radiation pressure. As a result, a coherent state can transform into a squeezed state and can get entangled with the motion of the oscillator. The complete tomographic reconstruction of the state of light requires the ability to readout arbitrary quadratures. Here we demonstrate such a readout by applying a balanced homodyne detector to an interferometric position measurement of a thermally excited high-Q silicon nitride membrane in a Michelson-Sagnac interferometer. A readout noise of \unit{1.9 \cdot 10^{-16}}{\metre/\sqrt{\hertz}} around the membrane's fundamental oscillation mode at \unit{133}{\kilo\hertz} has been achieved, going below the peak value of the standard quantum limit by a factor of 8.2 (9 dB). The readout noise was entirely dominated by shot noise in a rather broad frequency range around the mechanical resonance.Comment: 7 pages, 5 figure

An all-optical trap for a gram-scale mirror

We report on a stable optical trap suitable for a macroscopic mirror, wherein the dynamics of the mirror are fully dominated by radiation pressure. The technique employs two frequency-offset laser fields to simultaneously create a stiff optical restoring force and a viscous optical damping force. We show how these forces may be used to optically trap a free mass without introducing thermal noise; and we demonstrate the technique experimentally with a 1 gram mirror. The observed optical spring has an inferred Young's modulus of 1.2 TPa, 20% stiffer than diamond. The trap is intrinsically cold and reaches an effective temperature of 0.8 K, limited by technical noise in our apparatus.Comment: Major revision. Replacement is version that appears in Phy. Rev. Lett. 98, 150802 (2007

Exploiting the convex-concave penalty for tracking: A novel dynamic reweighted sparse Bayesian learning algorithm

We propose a novel dynamic reweighted ℓ2 (DRℓ2) algorithm in the regime of dynamic compressive sensing. Our analysis shows that aiming to solve a Type II optimization problem, DRℓ2 is effectively minimizing a `convex-concave' penalty in the coefficients that transitions from a convex region to a concave function using knowledge of past estimations. DRℓ2 thus provides superior reconstruction performance compared with state-of-the-art dynamic CS algorithms.This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/ICASSP.2014.685422

Simultaneous Bayesian Sparse Approximation with Structured Sparse Models

Sparse approximation is key to many signal processing, image processing and machine learning applications. If multiple signals maintain some degree of dependency, for example the support sets are statistically related, then it will generally be advantageous to jointly estimate the sparse representation vectors from the measurements vectors as opposed to solving for each signal individually. In this paper, we propose simultaneous sparse Bayesian learning (SBL) for joint sparse approximation with two structured sparse models (SSMs), where one is row-sparse with embedded element-sparse, and the other one is row-sparse plus element-sparse. While SBL has attracted much attention as a means to deal with a single sparse approximation problem, it is not obvious how to extend SBL to SSMs. By capitalizing on a dual-space view of existing convex methods for SMs, we showcase the precision component model and covariance component model for SSMs, where both models involve a common hyperparameter and an innovation hyperparameter that together control the prior variance for each coefficient. The statistical perspective of precision component vs. covariance component models unfolds the intrinsic mechanism in SSMs, and also leads to our development of SBL-inspired cost functions for SSMs. Centralized algorithms, that include ℓ1 and ℓ2 reweighting algorithms, and consensus based decentralized algorithms are developed for simultaneous sparse approximation with SSMs. In addition, theoretical analysis is conducted to provide valuable insights into the proposed approach, which includes global minima analysis of the SBLinspired nonconvex cost functions and convergence analysis of the proposed ℓ1 reweighting algorithms for SSMs. Superior performance of the proposed algorithms is demonstrated by numerical experiments.This is the author accepted manuscript. The final version is available from IEEE at http://dx.doi.org/10.1109/TSP.2016.2605067

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