In this paper we propose guaranteed spectral methods for learning a broad range of topic models, which generalize the popular Latent Dirichlet Allocation (LDA). We overcome the limitation of LDA to incorporate arbitrary topic correlations, by assuming that the hidden topic proportions are drawn from a flexible class of Normalized Infinitely Divisible (NID) distributions. NID distributions are g...

We show that polynomials do not belong to the reproducing kernel Hilbert space of infinitely differentiable translation-invariant kernels whose spectral measures have moments corresponding a det...

A new approach to recognize and predict succedent epileptic seizure by using single channel electroencephalogram (EEG) analysis is proposed. Spectral analysis of a brain time series of the left frontal FP1-F7 (LF) scalp location signal is devoted for seizure prediction and analysis. Important findings showing the presence of preictal spectral changes in studied brain signal are described. Spect...

We investigate the equivalence between spectral characteristics of the Laplace operator on a metric graph, and the associated unitary scattering operator. We prove that the statistics of level spacings, and moments of observations in the eigenbases coincide in the limit that all bond lengths approach a positive constant value.

A combination of spectral and moments analysis of the continuous X-ray flux data is used to show consistency of statistical properties of the powerful solar flares with 2D BTW prototype model of self-organized criticality. PACS. 05.65.+b Self-organized systems – 05.45.Tp Time series analysis – 96.60.Rd Flares, bursts, and related phenomena

The noise characteristics of supercontinuum generation are characterized using higherorder statistical moments. Measures of skew and kurtosis, and the coefficient of variation allow quantitative identification of spectral regions dominated by rogue wave like behaviour. OCIS codes: (030.1640) Coherence; (190.4370) Nonlinear optics, fibers; (320.6629) Supercontinuum generation.

The paper presents a new method that enables us to construct direct routines to estimate spectral moments of any orders. Accuracy analysis confirms high efficiency of the estimates. The feasibility of the method is tested for signal fading data acquired during observations of ionosphere multipath propagation.

This paper determines how to define a discretely implemented Fourier transform when analysing an observed spatial point process. To develop this we answer four questions; first what is the natural definition of transform, and are its spectral moments, second calculate fourth order moments using Campbell’s theorem. Third determine implement tapering, important component for analysis other stocha...

A review of the basic ideas and techniques of the spectral density-functional theory is presented. This method is currently used for electronic structure calculations of strongly correlated materials where the one-electron description breaks down. The method is illustrated with several examples where interactions play a dominant role: systems near metal-insulator transitions, systems near volum...