With advances in data collection technologies, tensor data is assuming increasing prominence in many applications and the problem of supervised tensor learning has emerged as a topic of critical significance in the data mining and machine learning co
mmunity. Conventional methods for supervised tensor learning mainly focus on learning kernels by flattening the tensor into vectors or matrices, however structural information within the tensors will be lost. In this paper, we introduce a new scheme to design structure-preserving kernels for supervised tensor learning. Specifically, we demonstrate how to leverage the naturally available structure within the tensorial representation to encode prior knowledge in the kernel. We proposed a tensor kernel that can preserve tensor structures based upon dual-tensorial mapping. The dual-tensorial mapping function can map each tensor instance in the input space to another tensor in the feature space while preserving the tensorial structure. Theoretically, our approach is an extension of the conventional kernels in the vector space to tensor space. We applied our novel kernel in conjunction with SVM to real-world tensor classification problems including brain fMRI classification for three different diseases (i.e., Alzheimers disease, ADHD and brain damage by HIV). Extensive empirical studies demonstrate that our proposed approach can effectively boost tensor classification performances, particularly with small sample sizes.
Multiple datasets containing different types of features may be available for a given task. For instance, users profiles can be used to group users for recommendation systems. In addition, a model can also use users historical behaviors and credit hi
story to group users. Each dataset contains different information and suffices for learning. A number of clustering algorithms on multiple datasets were proposed during the past few years. These algorithms assume that at least one dataset is complete. So far as we know, all the previous methods will not be applicable if there is no complete dataset available. However, in reality, there are many situations where no dataset is complete. As in building a recommendation system, some new users may not have a profile or historical behaviors, while some may not have a credit history. Hence, no available dataset is complete. In order to solve this problem, we propose an approach called Collective Kernel Learning to infer hidden sample similarity from multiple incomplete datasets. The idea is to collectively completes the kernel matrices of incomplete datasets by optimizing the alignment of the shared instances of the datasets. Furthermore, a clustering algorithm is proposed based on the kernel matrix. The experiments on both synthetic and real datasets demonstrate the effectiveness of the proposed approach. The proposed clustering algorithm outperforms the comparison algorithms by as much as two times in normalized mutual information.
We suggest a new representation of Maslovs canonical operator in a neighborhood of the caustics using a special class of coordinate systems (eikonal coordinates) on Lagrangian manifolds. The specific features of the two-dimensional case are considere
d. The general case is treated in arXiv:1307.2292 [math-ph].
We suggest a new representation of Maslovs canonical operator in a neighborhood of the caustics using a special class of coordinate systems (eikonal coordinates) on Lagrangian manifolds.
The masses of 68 supermassive black holes (SMBHs) in nearby (z<0.15) active galactic nuclei (AGNs) detected by the INTEGRAL observatory in the hard X-ray energy band (17-60 keV) outside the Galactic plane (|b| > 5 degrees) have been estimated. Well-k
nown relations between the SMBH mass and (1) the infrared luminosity of the stellar bulge (from 2MASS data) and (2) the characteristics of broad emission lines (from RTT-150 data) have been used. A comparison with the more accurate SMBH mass estimates obtained by the reverberation-mapping technique and from direct dynamical measurements is also made for several objects. The SMBH masses derived from the correlation with the bulge luminosity turn out to be systematically higher than the estimates made by other methods. The ratio of the bolometric luminosity to the critical Eddington luminosity has been found for all AGNs. It ranges from 1 to 100% for the overwhelming majority of objects.
We present the numerical simulations for an electron-beam-driven and loss-cone-driven electron-cyclotron maser (ECM) with different plasma parameters and different magnetic field strengths for a relatively small region and short time-scale in an atte
mpt to interpret the recent discovered intense radio emission from ultracool dwarfs. We find that a large amount of electromagnetic field energy can be effectively released from the beam-driven ECM, which rapidly heats the surrounding plasma. A rapidly developed high-energy tail of electrons in velocity space (resulting from the heating process of the ECM) may produce the radio continuum depending on the initial strength of the external magnetic field and the electron beam current. Both significant linear polarization and circular polarization of electromagnetic waves can be obtained from the simulations. The spectral energy distributions of the simulated radio waves show that harmonics may appear from 10 to 70$ u_{rm pe}$ ($ u_{rm pe}$ is the electron plasma frequency) in the non-relativistic case and from 10 to 600$ u_{rm pe}$ in the relativistic case, which makes it difficult to find the fundamental cyclotron frequency in the observed radio frequencies. A wide frequency band should therefore be covered by future radio observations.
Recently, a number of ultracool dwarfs have been found to produce periodic radio bursts with high brightness temperature and polarization degree; the emission properties are similar to the auroral radio emissions of the magnetized planets of the Sola
r System. We simulate the dynamic spectra of radio emission from ultracool dwarfs. The emission is assumed to be generated due to the electron-cyclotron maser instability. We consider two source models: the emission caused by interaction with a satellite and the emission from a narrow sector of active longitudes; the stellar magnetic field is modeled by a tilted dipole. We have found that for the dwarf TVLM 513-46546, the model of the satellite-induced emission is inconsistent with the observations. On the other hand, the model of emission from an active sector is able to reproduce qualitatively the main features of the radio light curves of this dwarf; the magnetic dipole seems to be highly tilted (by about 60 degrees) with respect to the rotation axis.
Recently unanticipated magnetic activity in ultracool dwarfs (UCDs, spectral classes later than M7) have emerged from a number of radio observations. The highly (up to 100%) circularly polarized nature and high brightness temperature of the emission
has been interpreted as an effective amplification mechanism of the high-frequency electromagnetic waves, the electron cyclotron maser instability (ECMI). In order to understand the magnetic topology and the properties of the radio emitting region and associated plasmas in these ultracool dwarfs and interpret the origin of radio pulses and their radiation mechanism, we built an active region model, based on the rotation of the UCD and the ECMI mechanism. ECMI mechanism is responsible for the radio bursts from the magnetic tubes and the rotation of the dwarf can modulate the integral of flux with respect to time. The high degree of variability in the brightness and the diverse profile of pulses can be interpreted in terms of a large-scale hot active region with extended magnetic structure existing in the magnetosphere of TVLM 513-46546. We suggest the time profile of the radio light curve is in the form of power law in the model. The radio emitting region consists of complicated substructure. With this model, we can determine the nature (e.g. size, temperature, density) of the radio emitting region and plasma. The magnetic topology can also be constrained. We compare our predicted X-ray flux with Chandra X-ray observation of TVLM 513-46546. Although the X-ray detection is only marginally significant, our predicted flux is significantly lower than the observed flux. We suggest more observations at multi-wavelength will help us understand the magnetic field structure and plasma behavior on the ultracool dwarf.
We observed a large decrease of Tc by no more than 3 at.% of Zn doped to the optimized superconductor LaFeAsO0.85 (Tc = 26 K), confirmed by measurements of electrical resistivity, magnetic susceptibility, specific heat, Mossbauer spectroscopy, Hall c
oefficient, and an electron probe micro-analysis. The rate ~9 K/% is remarkably higher than observations regarding nonmagnetic impurities. The Tc suppression is likely due to pair-breaking caused by scatterings associated with highly localized electronic state of Zn doped into the Fe2As2 layer. If this is true, the Zn result well accords with the theoretical prediction that suggests a sign reversal s-wave pairing model for the Fe pnictide superconductors, unlike other nonmagnetic impurity results.
The structure of high-lying states in $^{22}$Ne has been studied using the $^{14}$C($^{12}$C,$alpha$)$^{22}$Ne reaction at E($^{12}$C)= 44 MeV. The spins were determined by measuring double ($alpha$,$alpha$) angular correlations. Selective population
of the 9$^-$ and 11$^-$ states at E$_x$=20.1 and 20.7 MeV, respectively, identifies those states as the 9$^-$ and 11$^-$ members of the first $K^{pi}$ = 0$^-$ band, whose lower members were investigated by a method using inverse kinematics and a thick gas target. The spin and parity of four other new levels were determined to be 9$^-$ (21.5 MeV),12$^+$ (22.1 MeV),9$^-$ (25.0 MeV) and 8$^+$ (22.9 MeV). The two levels 9$^-$ and 12$^+$ may belong to the rotational doublets.
