This paper contains two main results. The first is a variational representation for the expectation of a measurable function of a Hilbert space valued Brownian motion, when the function is uniformly positive and bounded from above and the Brownian motion has a trace class covariance. This representation is then applied to derive the second main result, which is the large deviation principle for...

Characterizing brain connectivity between neural signals is key to understanding brain function. Current measures such as coherence heavily rely on Fourier or wavelet transform, which inevitably assume the signal stationarity and place severe limits on its time-frequency resolution. Here we addressed these issues by introducing a noise-assisted instantaneous coherence (NAIC) measure based on mu...

Consider a closed subgroup H of a locally compact group G together with a strongly continuous unitary representation u of H on a Hilbert space K. The construction of the induced representation uses these three ingredients to supply a new strongly continuous unitary representation ρ of the larger group G on a new Hilbert space K. Induced group representations for finite groups where first introd...

A new Time-Frequency (TF) representation of speech signal is introduced and used for speech enhancement. TF representation and speech enhancement algorithm are both based on perceptual properties of human auditory system in which the concept of band analysis is exploited. TF representation is carried out by the means of analytic decomposition of speech signal in the hearing Critical Bands (CB) ...

The purpose of this paper is to present a consistent mathematical framework that shows how the EPR (Einstein. Podolsky, Rosen) phenomenon fits into our view of space time. To resolve the differences between the Hilbert space structure of quantum theory and the manifold structure of classical physics, the manifold is taken as a partial representation of the Hilbert space. It is the partial natur...

The Holo-Hilbert spectral analysis (HHSA) method is introduced to cure the deficiencies of traditional spectral analysis and to give a full informational representation of nonlinear and non-stationary data. It uses a nested empirical mode decomposition and Hilbert-Huang transform (HHT) approach to identify intrinsic amplitude and frequency modulations often present in nonlinear systems. Compari...

BACKGROUND Compared to the waveform or spectrum analysis of event-related potentials (ERPs), time-frequency representation (TFR) has the advantage of revealing the ERPs time and frequency domain information simultaneously. As the human brain could be modeled as a complicated nonlinear system, it is interesting from the view of psychological knowledge to study the performance of the nonlinear an...

seismic attribute is a quantitative measure of an interested seismic characteristic. there are several seismic attributes. in recent years, time-frequency (tf) attributes have been developed which to reach them, tf analyzing of seismic data is required. a high resolution tf representation (tfr) can yield more accurate tf attributes. there are several tfr methods including short-time fourier tra...