Tensor LRR and sparse coding-based subspace clustering

Subspace clustering groups a set of samples from a union of several linear subspaces into clusters, so that the samples in the same cluster are drawn from the same linear subspace. In the majority of the existing work on subspace clustering, clusters are built based on feature information, while sample correlations in their original spatial structure are simply ignored. Besides, original high-dimensional feature vector contains noisy/redundant information, and the time complexity grows exponentially with the number of dimensions. To address these issues, we propose a tensor low-rank representation (TLRR) and sparse coding-based (TLRRSC) subspace clustering method by simultaneously considering feature information and spatial structures. TLRR seeks the lowest rank representation over original spatial structures along all spatial directions. Sparse coding learns a dictionary along feature spaces, so that each sample can be represented by a few atoms of the learned dictionary. The affinity matrix used for spectral clustering is built from the joint similarities in both spatial and feature spaces. TLRRSC can well capture the global structure and inherent feature information of data, and provide a robust subspace segmentation from corrupted data. Experimental results on both synthetic and real-world data sets show that TLRRSC outperforms several established state-of-the-art methods.

Heterogeneous tensor decomposition for clustering via manifold optimization

Tensor clustering is an important tool that exploits intrinsically rich structures in real-world multiarray or Tensor datasets. Often in dealing with those datasets, standard practice is to use subspace clustering that is based on vectorizing multiarray data. However, vectorization of tensorial data does not exploit complete structure information. In this paper, we propose a subspace clustering algorithm without adopting any vectorization process. Our approach is based on a novel heterogeneous Tucker decomposition model taking into account cluster membership information. We propose a new clustering algorithm that alternates between different modes of the proposed heterogeneous tensor model. All but the last mode have closed-form updates. Updating the last mode reduces to optimizing over the multinomial manifold for which we investigate second order Riemannian geometry and propose a trust-region algorithm. Numerical experiments show that our proposed algorithm compete effectively with state-of-the-art clustering algorithms that are based on tensor factorization.

Energy-momentum tensor in thermal strong-field QED with unstable vacuum

Themean value of the one-loop energy-momentum tensor in thermal QED with an electric-like background that creates particles from vacuum is calculated. The problem is essentially different from calculations of effective actions ( similar to the action of Heisenberg-Euler) in backgrounds that respect the stability of vacuum. The role of a constant electric background in the violation of both the stability of vacuum and the thermal character of particle distribution is investigated. Restrictions on the electric field and the duration over which one can neglect the back-reaction of created particles are established.

Abnormal Corpus Callosum Integrity in Bipolar Disorder: A Diffusion Tensor Imaging Study

Objective: Abnormalities in the anterior interhemispheric connections provided by the corpus callosum (CC) have long been implicated in bipolar disorder (BID). In this study, we used complementary diffusion tensor imaging methods to study the structural integrity of the CC and localization of potential abnormalities in BD. Methods: Subjects included 33 participants with BID and 40 healthy comparison participants. Fractional anisotropy (FA) measures were compared between groups with region of interest (ROD methods to investigate the anterior, middle, and posterior CC and voxel-based methods to further localize abnormalities. Results: In ROI-based analyses, FA was significantly decreased in the anterior and middle CC in the BID group (p <.05). Voxel-based analyses similarly localized group differences to the genu, rostral body, and anterior midbody of CC (p <.05, corrected). Conclusion: The findings demonstrate abnormalities in the structural integrity of the anterior CC in BID that might contribute to altered interhemispheric connectivity in this disorder.

Abnormal anterior cingulum integrity in bipolar disorder determined through diffusion tensor imaging

Background Convergent evidence implicates white matter abnormalities in bipolar disorder. The cingulum is an important candidate structure for study in bipolar disorder as it provides substantial white matter connections within the corticolimbic neural system that subserves emotional regulation involved in the disorder. Aims To test the hypothesis that bipolar disorder is associated with abnormal white matter integrity in the cingulum. Method Fractional anisotropy in the anterior and posterior cingulum was compared between 42 participants with bipolar disorder and 42 healthy participants using diffusion tensor imaging. Results Fractional anisotropy was significantly decreased in the anterior cingulum in the bipolar disorder group compared with the healthy group (P=0.003); however, fractional anisotropy in the posterior cingulum did not differ significantly between groups. Conclusions Our findings demonstrate abnormalities in the structural integrity of the anterior cingulum in bipolar disorder. They extend evidence that supports involvement of the neural system comprising the anterior cingulate cortex and its corticolimbic gray matter connection sites in bipolar disorder to implicate abnormalities in the white matter connections within the system provided by the cingulum.

Corpus callosum in maltreated children with posttraumatic stress disorder: A diffusion tensor imaging study

Contrary to expectations derived from preclinical studies of the effects of stress, and imaging studies of adults with posttraumatic stress disorder (PTSD), there is no evidence of hippocampus atrophy in children with PTSD. Multiple pediatric studies have reported reductions in the corpus callosum - the primary white matter tract in the brain. Consequently, in the present study, diffusion tensor imaging was used to assess white matter integrity in the corpus callosum in 17 maltreated children with PTSD and 15 demographically matched normal controls. Children with PTSD had reduced fractional anisotropy in the medial and posterior corpus, a region which contains interhemispheric projections from brain structures involved in circuits that mediate the processing of emotional stimuli and various memory functions - core disturbances associated with a history of trauma. Further exploration of the effects of stress on the corpus callosum and white matter development appears a promising strategy to better understand the pathophysiology of PTSD in children. (C) 2007 Elsevier Ireland Ltd. All rights reserved.

Absence of gluonic components in axial and tensor mesons

A quarkonium-gluonium mixing scheme previously developed to describe the characteristic of the pseudoscalar mesons is applied to axial and tensor mesons. The parameters of the model are determined by fitting the eigenvalues of a mass matrix. The corresponding eigenvectors give the proportion of light quarks, strange quarks and glueball in each meson. However, the predictions of the model for the branching ratios and electromagnetic decays are incompatible with the experimental results. These results suggest the absence of gluonic components in the states of axial and tensor isosinglet mesons analyzed here.

Tensor coupling and pseudospin symmetry in nuclei

In this work we study the contribution of the isoscalar tensor coupling to the realization of pseudospin symmetry in nuclei. Using realistic values for the tensor coupling strength, we show that this coupling reduces noticeably the pseudospin splittings, especially for single-particle levels near the Fermi surface. By using an energy. decomposition of the pseudospin energy splittings, we show that the changes in these splittings come mainly through the changes induced in the lower radial wave function for the low-lying pseudospin partners and through changes in the expectation value of the pseudospin-orbit coupling term for surface partners. This allows us to confirm the conclusion already reached in previous studies, namely that the pseudospin symmetry in nuclei is of a dynamical nature.

Mass generation for Abelian spin-1 particles via a symmetric tensor

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Model to localize gauge and tensor fields on thick branes

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Nonuniqueness of the Fierz-Pauli mass term for a nonsymmetic tensor

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Force and displacement transmissibility of a nonlinear isolator with high-static-low-dynamic-stiffness

Engineers often face the challenge of reducing the level of vibrations experienced by a given payload or those transmitted to the support structure to which a vibrating source is attached. In order to increase the range over which vibrations are isolated, soft mounts are often used in practice. The drawback of this approach is the static displacement may be too large for reasons of available space for example. Ideally, a vibration isolator should have a high-static stiffness, to withstand static loads without too large a displacement, and at the same time, a low dynamic stiffness so that the natural frequency of the system is as low as possible which will result in an increased isolation region. These two effects are mutually exclusive in linear isolators but can be overcome if properly configured nonlinear isolators are used. This paper is concerned with the characterisation of such a nonlinear isolator comprising three springs, two of which are configured to reduce the dynamic stiffness of the isolator. The dynamic behaviour of the isolator supporting a lumped mass is investigated using force and displacement transmissibility, which are derived by modelling the dynamic system as a single-degree-of-freedom system. This results in the system dynamics being approximately described by the Duffing equation. For a linear isolator, the dynamics of the system are the same regardless if the source of the excitation is a harmonic force acting on the payload (force transmissibility) or a harmonic motion of the base (displacement transmissibility) on which the payload is mounted. In this paper these two expressions are compared for the nonlinear isolator and it is shown that they differ. A particular feature of the displacement transmissibility is that the response is unbounded at the nonlinear resonance frequency unless the damping in the isolator is greater than some threshold value, which is not the case for force transmissibility. An explanation for this is offered in the paper. (C) 2011 Elsevier Ltd. All rights reserved.

An experimental switchable stiffness device for shock isolation

The development of an experimental switching stiffness device fcr shock isolation is presented. The system uses magnetic forces to exert a restoring force, which results in an effective stiffness that is used to isolate a payload. When the magnetic force is turned on and off, a switchable stiffness is obtained. Characterization of the physical properties of the device is presented. They are estimated in terms of the percentage stiffness change and effective damping ratio when switched between two constant stiffness states. Additionally, the setup is used to implement a control strategy to reduce the shock response and minimize residual vibration. The system was found to be very effective for shock isolation. The response is reduced by around 50 percent compared with passive isolation showing good correlation with theoretical predictions, and the effective damping ratio in the system following the shock was increased from about 4.5 percent to 13 percent. (c) 2012 Elsevier Ltd. All rights reserved.