Heavy-tailed distributions have been studied in statistics, random matrix theory, physics, and econometrics as models of correlated systems, among other domains. Further, heavy-tail distributed eigenvalues of the covariance matrix of the weight matri
ces in neural networks have been shown to empirically correlate with test set accuracy in several works (e.g. arXiv:1901.08276), but a formal relationship between heavy-tail distributed parameters and generalization bounds was yet to be demonstrated. In this work, the compression framework of arXiv:1802.05296 is utilized to show that matrices with heavy-tail distributed matrix elements can be compressed, resulting in networks with sparse weight matrices. Since the parameter count has been reduced to a sum of the non-zero elements of sparse matrices, the compression framework allows us to bound the generalization gap of the resulting compressed network with a non-vacuous generalization bound. Further, the action of these matrices on a vector is discussed, and how they may relate to compression and resilient classification is analyzed.
The quasi-static strain (QSS) is the product generated by the lattice thermal expansion after ultrafast photo-excitation and the effects of thermal and QSS are inextricable. Nevertheless, the two phenomena with the same relaxation timescale should be
treated separately because of their different fundamental actions to the ultrafast spin dynamics. By employing ultrafast Sagnac interferometry and magneto-optical Kerr effect, we quantitatively prove the existence of QSS, which has been disregarded, and decouple two effects counter-acting each other. Through the magnetoelastic energy analysis, rather we show that QSS in ferromagnets plays a governing role on ultrafast spin dynamics, which is opposite to what have been known on the basis of thermal effect. Our demonstration provides an essential way of analysis on ultrafast photo-induced phenomena.
Graph neural networks are a popular variant of neural networks that work with graph-structured data. In this work, we consider combining graph neural networks with the energy-based view of Grathwohl et al. (2019) with the aim of obtaining a more robu
st classifier. We successfully implement this framework by proposing a novel method to ensure generation over features as well as the adjacency matrix and evaluate our method against the standard graph convolutional network (GCN) architecture (Kipf & Welling (2016)). Our approach obtains comparable discriminative performance while improving robustness, opening promising new directions for future research for energy-based graph neural networks.
We study the spatial distributions of the spin and mass currents generated by a moving Gaussian magnetic obstacle in a symmetric, two-component Bose-Einstein condensate in two dimensions. We analytically describe the current distributions for a slow
obstacle and show that the spin and the mass currents exhibit characteristic spatial structures resembling those of electromagnetic fields around dipole moments. When the obstacles velocity increases, we numerically observe that the flow pattern maintains its overall structure while the spin polarization induced by the obstacle is enhanced with an increased spin current. We investigate the critical velocity of the magnetic obstacle based on the local criterion of Landau energetic instability and find that it decreases almost linearly as the magnitude of the obstacles potential increases, which can be directly tested in current experiments.
Spectropolarimetry is a powerful technique for investigating the physical properties of gas and solid materials in cometary comae without mutual contamination, but there have been few spectropolarimetric studies to extract each component. We attempt
to derive the continuum polarization degree of comet 2P/Encke, free from influence of molecular emissions. The target is unique in that it has an orbit dynamically decoupled from Jupiter like main-belt asteroids, while ejecting gas and dust like ordinary comets. We observed the comet using the Higashi-Hiroshima Optical and Near-Infrared Camera attached to the Cassegrain focus of the 150-cm Kanata telescope on UT 2017 February 21 when the comet was at the solar phase angle of 75.7 deg. We find that the continuum polarization degree with respect to the scattering plane is 33.8+/-2.7 % at the effective wavelength of 0.815 um, which is significantly higher than those of cometary dust in a high-Pmax group at similar phase angles. Assuming that an ensemble polarimetric response of 2P/Enckes dust as a function of phase angle is morphologically similar with those of other comets, its maximum polarization degree is estimated to > 40 % at the phase angle of ~100 deg. In addition, we obtain the polarization degrees of the C2 swan bands (0.51-0.56 um), the NH2 alpha bands (0.62-0.69 um) and the CN-red system (0.78-0.94 um) in a range of 3-19 %, which depend on the molecular species and rotational quantum numbers of each branch. The polarization vector aligns nearly perpendicularly to the scattering plane with the average of 0.4 deg over a wavelength range of 0.50-0.97 um. From the observational evidence, we conjecture that the large polarization degree of 2P/Encke would be attributable to a dominance of large dust particles around the nucleus, which have remained after frequent perihelion passages near the Sun.
Modern high-resolution microscopes, such as the scanning tunneling microscope, are commonly used to study specimens that have dense and aperiodic spatial structure. Extracting meaningful information from images obtained from such microscopes remains
a formidable challenge. Fourier analysis is commonly used to analyze the underlying structure of fundamental motifs present in an image. However, the Fourier transform fundamentally suffers from severe phase noise when applied to aperiodic images. Here, we report the development of a new algorithm based on nonconvex optimization, applicable to any microscopy modality, that directly uncovers the fundamental motifs present in a real-space image. Apart from being quantitatively superior to traditional Fourier analysis, we show that this novel algorithm also uncovers phase sensitive information about the underlying motif structure. We demonstrate its usefulness by studying scanning tunneling microscopy images of a Co-doped iron arsenide superconductor and prove that the application of the algorithm allows for the complete recovery of quasiparticle interference in this material. Our phase sensitive quasiparticle interference imaging results indicate that the pairing symmetry in optimally doped NaFeAs is consistent with a sign-changing s+- order parameter.
We report a Keldysh-like model for the electron transition rate in dielectrics under an intense circularly polarized laser. We assume a parabolic two-band system and the Houston function as the time-dependent wave function of the valence and conducti
on bands. Our formula reproduces the experimental result for the ratio of the excitation rate between linear and circular polarizations for $alpha$-quartz. This formula can be easily introduced into simulations of nanofabrication using an intense circularly polarized laser.
We present the first experimental realization of an $S=2$ ferromagnetic-antiferromagnetic (F-AF) alternating chain in a new Mn-verdazyl complex [Mn(hfac)$_2$]$cdot$($o$-Py-V) [hfac=1,1,1,5,5,5-hexafluoroacetylacetonate; $o$-Py-V=3-(2-pyridyl)-1,5-dip
henylverdazyl]. Through the $ab$ $initio$ molecular orbital calculation, magnetization, and ESR measurements, this compound is confirmed to form an $S=2$ F-AF alternating chain with Ising anisotropy below about 100 K. Furthermore, we find an anomalous change in magnetization at 1/4 of the saturation value, which is probably a manifestation of the quantum nature of the system.
We apply the coupled dynamics of time-dependent density functional theory and Maxwell equations to the interaction of intense laser pulses with crystalline silicon. As a function of electromagnetic field intensity, we see several regions in the respo
nse. At the lowest intensities, the pulse is reflected and transmitted in accord with the dielectric response, and the characteristics of the energy deposition is consistent with two-photon absorption. The absorption process begins to deviate from that at laser intensities ~ 10^13 W/cm^2, where the energy deposited is of the order of 1 eV per atom. Changes in the reflectivity are seen as a function of intensity. When it passes a threshold of about 3 times 1012 W/cm2, there is a small decrease. At higher intensities, above 2 times 10^13 W/cm^2, the reflectivity increases strongly. This behavior can be understood qualitatively in a model treating the excited electron-hole pairs as a plasma.
Diffraction measurements performed via transmission electron microscopy and high resolution X-ray scattering reveal two distinct charge density wave transitions in Gd$_2$Te$_5$ at $T_{c1}$ = 410(3) and $T_{c2}$ = 532(3) K, associated with the textit{
on}-axis incommensurate lattice modulation and textit{off}-axis commensurate lattice modulation respectively. Analysis of the temperature dependence of the order parameters indicates a non-vanishing coupling between these two distinct CDW states.
