Inductive Sparse Subspace Clustering

Sparse Subspace Clustering (SSC) has achieved state-of-the-art clustering quality by performing spectral clustering over a $\ell^{1}$-norm based similarity graph. However, SSC is a transductive method which does not handle with the data not used to construct the graph (out-of-sample data). For each new datum, SSC requires solving $n$ optimization problems in O(n) variables for performing the algorithm over the whole data set, where $n$ is the number of data points. Therefore, it is inefficient to apply SSC in fast online clustering and scalable graphing. In this letter, we propose an inductive spectral clustering algorithm, called inductive Sparse Subspace Clustering (iSSC), which makes SSC feasible to cluster out-of-sample data. iSSC adopts the assumption that high-dimensional data actually lie on the low-dimensional manifold such that out-of-sample data could be grouped in the embedding space learned from in-sample data. Experimental results show that iSSC is promising in clustering out-of-sample data.Comment: 2 page

Towards a sound massive cosmology

It is known that de Rham-Gabadadze-Tolley (dRGT) massive gravity does not permit a homogeneous and isotropic universe with flat or spherical spatial metrics. We demonstrate that a singular reference metric solves this problem in an economic and straightforward way. In the dRGT massive gravity with a singular reference metric, there are sound homogeneous and isotropic cosmological solutions. We investigate cosmologies with the static and dynamical singular reference metrics, respectively. The term like dark energy appears naturally and the universe accelerates itself in some late time evolution. The term simulating dark matter also naturally emerges. We make a preliminary constraint on the parameters in the dRGT massive gravity in frame of the present cosmological model by using the data of supernovae, cosmic microwave back ground radiations, and baryonic acoustic oscillations.Comment: 21 pages, 3 figures, version accepted by Physics of the Dark Univers

Locally linear representation for image clustering

It is a key to construct a similarity graph in graph-oriented subspace learning and clustering. In a similarity graph, each vertex denotes a data point and the edge weight represents the similarity between two points. There are two popular schemes to construct a similarity graph, i.e., pairwise distance based scheme and linear representation based scheme. Most existing works have only involved one of the above schemes and suffered from some limitations. Specifically, pairwise distance based methods are sensitive to the noises and outliers compared with linear representation based methods. On the other hand, there is the possibility that linear representation based algorithms wrongly select inter-subspaces points to represent a point, which will degrade the performance. In this paper, we propose an algorithm, called Locally Linear Representation (LLR), which integrates pairwise distance with linear representation together to address the problems. The proposed algorithm can automatically encode each data point over a set of points that not only could denote the objective point with less residual error, but also are close to the point in Euclidean space. The experimental results show that our approach is promising in subspace learning and subspace clustering

Inner structure of Gauss-Bonnet-Chern Theorem and the Morse theory

We define a new one form H^A based on the second fundamental tensor H^abA, the Gauss-Bonnet-Chern form can be novelly expressed with this one-form. Using the phi-mapping theory we find that the Gauss-Bonnet-Chern density can be expressed in terms of the delta-function and the relationship between the Gauss-Bonnet-Chern theorem and Hopf-Poincare theorem is given straightforwardly. The topological current of the Gauss-Bonnet-Chern theorem and its topological structure are discussed in details. At last, the Morse theory formula of the Euler characteristic is generalized.Comment: 10 page

Magnetic-induced condensate, vortices and vortons in color-flavor-locked-type matter

By considering Higgs modes within the Ginzburg-Landau framework, we study influences of a rotated magnetic field on the color-flavor-locked-type matter of dense QCD. We demonstrate, in a model-independent way, that a diquark condensate may be triggered by the magnetic response of rotated-charged Higgs modes, in addition to the known color-flavor-locked condensate. Moreover, the condensate is applied to explore formations of vortices in the presence of external magnetic fields. The superfluid-like vortices are constructed for the magnetic-induced condensate. In the situation including both kinds of condensates, the theoretical possibility of vortons is suggested and the formation condition and the energy stability are investigated semi-classically.Comment: 3 figure

Learning Locality-Constrained Collaborative Representation for Face Recognition

The model of low-dimensional manifold and sparse representation are two well-known concise models that suggest each data can be described by a few characteristics. Manifold learning is usually investigated for dimension reduction by preserving some expected local geometric structures from the original space to a low-dimensional one. The structures are generally determined by using pairwise distance, e.g., Euclidean distance. Alternatively, sparse representation denotes a data point as a linear combination of the points from the same subspace. In practical applications, however, the nearby points in terms of pairwise distance may not belong to the same subspace, and vice versa. Consequently, it is interesting and important to explore how to get a better representation by integrating these two models together. To this end, this paper proposes a novel coding algorithm, called Locality-Constrained Collaborative Representation (LCCR), which improves the robustness and discrimination of data representation by introducing a kind of local consistency. The locality term derives from a biologic observation that the similar inputs have similar code. The objective function of LCCR has an analytical solution, and it does not involve local minima. The empirical studies based on four public facial databases, ORL, AR, Extended Yale B, and Multiple PIE, show that LCCR is promising in recognizing human faces from frontal views with varying expression and illumination, as well as various corruptions and occlusions.Comment: 16 pages, v

An X-ray periodicity of ∼\sim1.8 hours in a narrow-line Seyfert 1 galaxy Mrk 766

In the narrow-line Seyfert 1 galaxy Mrk 766, a Quasi-Periodic Oscillation (QPO) signal with a period of $\sim6450$ s is detected in the \emph{XMM-Newton} data collected on 2005 May 31. This QPO signal is highly statistical significant at the confidence level at $\sim5\sigma$ with the quality factor of $Q=f/\Delta f>13.6$. The X-ray intensity changed by a factor of 3 with root mean square fractional variability of $14.3\%$. Furthermore, this QPO signal presents in the data of all three EPIC detectors and two RGS cameras and its frequency follows the $f_{\rm QPO}$-$M_{\rm BH}$ relation spanning from stellar-mass to supermassive black holes. Interestingly, a possible QPO signal with a period of $\sim4200$ s had been reported in the literature. The frequency ratio of these two QPO signals is $\sim$ 3:2. Our result is also in support of the hypothesis that the QPO signals can be just transient. The spectral analysis reveals that the contribution of the soft excess component below $\sim$ 1 keV is different between epochs with and without QPO, this property as well as the former frequency-ratio are well detected in X-ray BH binaries, which may have shed some lights on the physical origin of our event.Comment: 7 pages, 5 figures, 1 table. Accepted for publication in Ap

Rebuilding of destroyed spin squeezing in noisy environments

We investigate the process of spin squeezing in a ferromagnetic dipolar spin-1 Bose-Einstein condensate under the driven oneaxis twisting scheme, with emphasis on the detrimental effect of noisy environments (stray magnetic fields) which completely destroy the spin squeezing. By applying concatenated dynamical decoupling pulse sequences with a moderate bias magnetic field to suppress the effect of the noisy environments, we faithfully reconstruct the spin squeezing process under realistic experimental conditions. Our noise-resistant method is ready to be employed to generate the spin squeezed state in a dipolar spin-1 Bose-Einstein condensate and paves a feasible way to the Heisenberg-limit quantum metrologyComment: 11 pages, 3 figure

Two-body bound state of ultracold Fermi atoms with two-dimensional spin-orbit coupling

In a recent experiment, a two-dimensional spin-orbit coupling (SOC) was realized for fermions in the continuum [Nat. Phys. 12, 540 (2016)], which represents an important step forward in the study of synthetic gauge field using cold atoms. In the experiment, it was shown that a Raman-induced two-dimensional SOC exists in the dressed-state basis close to a Dirac point of the single-particle spectrum. By contrast, the short-range inter-atomic interactions of the system are typically expressed in the hyperfine-spin basis. The interplay between synthetic SOC and interactions can potentially lead to interesting few- and many-body phenomena but has so far eluded theoretical attention. Here we study in detail properties of two-body bound states of such a system. We find that, due to the competition between SOC and interaction, the stability region of the two-body bound state is in general reduced. Particularly, the threshold of the lowest two-body bound state is shifted to a positive, SOC-dependent scattering length. Furthermore, the center-of-mass momentum of the lowest two-body bound state becomes nonzero, suggesting the emergence of Fulde-Ferrell pairing states in a many-body setting. Our results reveal the critical difference between the experimentally realized two-dimensional SOC and the more symmetric Rashba or Dresselhaus SOCs in an interacting system, and paves the way for future characterizations of topological superfluid states in the experimentally relevant systems.Comment: 10 pages, 7 figure

Connections Between Nuclear Norm and Frobenius Norm Based Representations

A lot of works have shown that frobenius-norm based representation (FNR) is competitive to sparse representation and nuclear-norm based representation (NNR) in numerous tasks such as subspace clustering. Despite the success of FNR in experimental studies, less theoretical analysis is provided to understand its working mechanism. In this paper, we fill this gap by building the theoretical connections between FNR and NNR. More specially, we prove that: 1) when the dictionary can provide enough representative capacity, FNR is exactly NNR even though the data set contains the Gaussian noise, Laplacian noise, or sample-specified corruption, 2) otherwise, FNR and NNR are two solutions on the column space of the dictionary.Comment: IEEE Trans. on Neural Networks and Learning Systems, 201