Large collections of music bring new challenges for people to choose the favorite songs. Music genre explicitly defined can help people to solve this problem. However, classifying the music genre automatically is a challenging problem since many genres do not have any special features. This paper presents a new music genre classification method which utilizes hierarchical analysis of the spectrograms features extracted from the audio signals. First support vector machines are used to build the classification tree, then K nearest neighbors are implemented to improve the accuracy of the classification. The GTZAN genre collection music database is used to evaluate the proposed model, and the results show that this model can get comparable results compared with some other existing music genre classification methods.
The common density functionals for the exchange-correlation energy make serious self-interaction errors in the molecular dissociation limit when real or spurious noninteger electron numbers N are found on the dissociation products. An "M-electron self-interaction-free" functional for positive integer M is one that produces a realistic linear variation of total energy with N in the range of M-1<N<or=M, and so can avoid these errors. This desideratum is a natural generalization to all M of the more familiar one of one-electron self-interaction freedom. The intent of this paper is not to advocate for any functional, but to understand what is required for a functional to be M-electron self-interaction-free and thus correct even for highly stretched bonds. The original Perdew-Zunger self-interaction correction (SIC) and our scaled-down variant of it are exactly one- and nearly two-electron self-interaction-free, but only the former is nearly so for atoms with M>2. Thus all these SIC's produce an exact binding energy curve for H2+, and an accurate one for He2+, but only the unscaled Perdew-Zunger SIC produces an accurate one for Ne2+, where there are more than two electrons on each fragment Ne+0.5. We also discuss LiH+, which is relatively free from self-interaction errors. We suggest that the ability of the original and unscaled Perdew-Zunger SIC to be nearly M-electron self-interaction-free for atoms of all M stems in part from its formal resemblance to the Hartree-Fock theory, with which it shares a sum rule on the exchange-correlation hole of an open system.
It is known that the nonempirical generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE) provides a much more realistic description of the short-range part of the van der Waals (vdW) interaction than does the local spin density (LSD) approximation. In the present work, the ability of the higher-level nonempirical meta-GGA of Tao, Perdew, Staroverov, and Scuseria (TPSS) to describe vdW interaction is tested self-consistently in ten rare-gas dimers with Z⩽36. The one-parameter hybrid version (TPSSh) of the TPSS exchange-correlation functional is also included in this test. Calculations show that both TPSS and TPSSh functionals correctly yield vdW bonds in these dimers and significantly improve the prediction of bond lengths, binding energies, and harmonic vibrational frequencies over LSD. The rather close agreement of TPSS with PBE for these dimers confirms a principle of the TPSS construction: preservation of the PBE large-gradient behavior. More importantly, it suggests that TPSS can serve as a platform on which to construct a still-higher level of nonempirical functionals. Compared with the PBE GGA, TPSS, and TPSSh yield a slightly weaker binding. As for normally bonded molecules, TPSSh yields the most accurate vibrational frequencies. The typically too-long bond lengths and too-small binding energies of TPSS meta-GGA suggest the need for some long-range vdW interaction correction even in this class of systems. The effect of basis-set superposition error on the calculated properties of these vdW systems is investigated. We also show that the relatively strong anharmonic effects in the rare-gas dimers are described remarkably well by the Morse potential.
The ionization energy of a large spherical metal cluster of radius R is I(R)=W+(+c)/R, where W is the bulk work function and c\ensuremath{\approx}-0.1 is a material-dependent quantum correction to the electrostatic size effect. We present 'Koopmans' and 'displaced-profile change-in-self-consistent-field' expressions for W and c within the ordinary and stabilized-jellium models. These expressions are shown to be exact and equivalent when the exact density profile of a large neutral cluster is employed; these equivalences generalize the Budd-Vannimenus theorem. With an approximate profile obtained from a restricted variational calculation, the 'displaced-profile' expressions are the more accurate ones. This profile insensitivity is important, because it is not practical to extract c from solutions of the Kohn-Sham equations for small metal clusters.
Received 10 December 2008DOI:https://doi.org/10.1103/PhysRevB.78.239906©2008 American Physical Society
Generalized gradient approximations (GGA's) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential.
In Table II, the meta-GGA energies for the 20-electron jellium spheres should have been Ϫ1.782,Ϫ1.901, and Ϫ1.804 eV for r s ϭ3.25, 4.00, and 5.62, respectively.These corrected energies are very close to the GGA values.The incorrect published values arose from a factor-of-two error in the input kinetic energy density.
The exact solution to the self-consistent field screening problem presented in a previous paper (Moore et al.), reduces in the weak pseudopotential limit to the diffraction model for the electron–phonon matrix element, and in particular to Animalu's expression for the screening of a nonlocal pseudopotential. Systematic corrections to the diffraction model, including local field effects, are presented for a pseudopotential of moderate strength; these corrections are particularly simple when the pseudopotential is local. Local pseudopotential calculations of the anisotropic electron–phonon form factors indicate that corrections to the diffraction model are small in sodium but substantial in lithium.
Unlike the local density approximation (LDA) and the generalized gradient approximation (GGA), calculations with meta-generalized gradient approximations (meta-GGA) are usually done according to the generalized Kohn-Sham (gKS) formalism. The exchange-correlation potential of the gKS equation is nonmultiplicative, which prevents systematic comparison of meta-GGA band structures to those of the LDA and the GGA. We implement the optimized effective potential (OEP) of the meta-GGA for periodic systems, which allows us to carry out meta-GGA calculations in the same KS manner as for the LDA and the GGA. We apply the OEP to several meta-GGAs, including the new SCAN functional [Phys. Rev. Lett. 115, 036402 (2015)]. We find that the KS gaps and KS band structures of meta-GGAs are close to those of GGAs. They are smaller than the more realistic gKS gaps of meta-GGAs, but probably close to the less-realistic gaps in the band structure of the exact KS potential, as can be seen by comparing with the gaps of the EXX+RPA OEP potential. The well-known grid sensitivity of meta-GGAs is much more severe in OEP calculations.
We construct analytic formulas that represent the coupling-constant-averaged pair distribution function $\gxcav(r_s,ζ, k_Fu)$ of a uniform electron gas with density parameter $r_s =(9π/4)^{1/3}/k_F$ and relative spin polarization $ζ$ over the whole range $0
It was shown by J. P. Perdew, R. G. Parr, M. Levy, and J. L. Balduz [Phys. Rev. Lett. 49, 1691 (1982)]; J. P. Perdew and M. Levy [Phys. Rev. Lett. 51, 1884 (1983)]; and L. J. Sham and M. Schl\"uter [Phys. Rev. Lett. 51, 1888 (1983)] that the exact Kohn-Sham exchange-correlation potential ${v}_{\text{xc}}(\stackrel{P\vec}{r})$ of an open system may jump discontinuously as the particle number crosses an integer, with important physical consequences. The original derivations of the size and nature of the discontinuity rely on an implicit assumption that, when $N\ensuremath{\rightarrow}J$ from above and below, the effective potential of the interacting system with particle number $N$ becomes identical (modulo a constant) to the effective potential at an integer particle number $J$ so that the Kohn-Sham orbitals change continuously as $N$ passes through $J$ at fixed external potential. We prove under mild assumptions that the noninteracting kinetic energy of the interacting system is a continuous function of the particle number (as is the density itself), and hence argue that the original assumption is likely correct; if so, then all energy components are continuous. A rigorous proof of the existence and size of the ${v}_{\text{xc}}$ discontinuity is presented in the special case where the particle number crosses 1, by showing that, even when the Levy-Lieb constrained search for a minimum kinetic energy expectation value is taken to go over ensembles instead of wave functions, the noninteracting kinetic energy is still given by the von Weizs\"acker functional for all densities with real particle number $N$ between 0 and 2 inclusive. We also prove that the von Weizs\"acker functional is a lower bound on the ensemble-search noninteracting kinetic energy for all real $N>2$. To illustrate the ${v}_{\text{xc}}$ discontinuity and related results, we construct an analytic model density for the ${\text{H}}^{\ensuremath{-}}$ ion and plot the exchange-correlation potential as the particle number approaches 1 from above and below, and 2 from below. Finally, we discuss the behavior of the free-electron continuum as the particle number crosses an integer and the case where the particle number of a hydrogen or helium atom crosses $J=2$, the maximum number of electrons they can bind.
