Gaussian Process Kernels for Cross-Spectrum Analysis in Electrophysiological Time Series

Multi-output Gaussian processes provide a convenient framework for multi-task problems. An illustrative and motivating example of a multi-task problem is multi-region electrophysiological time-series data, where experimentalists are interested in both power and phase coherence between channels. Recently, the spectral mixture (SM) kernel was proposed to model the spectral density of a single task in a Gaussian process framework. This work develops a novel covariance kernel for multiple outputs, called the cross-spectral mixture (CSM) kernel. This new, flexible kernel represents both the power and phase relationship between multiple observation channels. The expressive capabilities of the CSM kernel are demonstrated through implementation of 1) a Bayesian hidden Markov model, where the emission distribution is a multi-output Gaussian process with a CSM covariance kernel, and 2) a Gaussian process factor analysis model, where factor scores represent the utilization of cross-spectral neural circuits. Results are presented for measured multi-region electrophysiological data.

Optimized, unequal pulse spacing in multiple echo sequences improves refocusing in magnetic resonance.

A recent quantum computing paper (G. S. Uhrig, Phys. Rev. Lett. 98, 100504 (2007)) analytically derived optimal pulse spacings for a multiple spin echo sequence designed to remove decoherence in a two-level system coupled to a bath. The spacings in what has been called a "Uhrig dynamic decoupling (UDD) sequence" differ dramatically from the conventional, equal pulse spacing of a Carr-Purcell-Meiboom-Gill (CPMG) multiple spin echo sequence. The UDD sequence was derived for a model that is unrelated to magnetic resonance, but was recently shown theoretically to be more general. Here we show that the UDD sequence has theoretical advantages for magnetic resonance imaging of structured materials such as tissue, where diffusion in compartmentalized and microstructured environments leads to fluctuating fields on a range of different time scales. We also show experimentally, both in excised tissue and in a live mouse tumor model, that optimal UDD sequences produce different T(2)-weighted contrast than do CPMG sequences with the same number of pulses and total delay, with substantial enhancements in most regions. This permits improved characterization of low-frequency spectral density functions in a wide range of applications.

Scale-wise evolution of rainfall probability density functions fingerprints the rainfall generation mechanism

© 2010 by the American Geophysical Union.The cross-scale probabilistic structure of rainfall intensity records collected over time scales ranging from hours to decades at sites dominated by both convective and frontal systems is investigated. Across these sites, intermittency build-up from slow to fast time-scales is analyzed in terms of heavy tailed and asymmetric signatures in the scale-wise evolution of rainfall probability density functions (pdfs). The analysis demonstrates that rainfall records dominated by convective storms develop heavier-Tailed power law pdfs toward finer scales when compared with their frontal systems counterpart. Also, a concomitant marked asymmetry build-up emerges at such finer time scales. A scale-dependent probabilistic description of such fat tails and asymmetry appearance is proposed based on a modified q-Gaussian model, able to describe the cross-scale rainfall pdfs in terms of the nonextensivity parameter q, a lacunarity (intermittency) correction and a tail asymmetry coefficient, linked to the rainfall generation mechanism.

Intraoperative spectral domain optical coherence tomography for vitreoretinal surgery.

We demonstrate in vivo human retinal imaging using an intraoperative microscope-mounted optical coherence tomography system (MMOCT). Our optomechanical design adapts an Oculus Binocular Indirect Ophthalmo Microscope (BIOM3), suspended from a Leica ophthalmic surgical microscope, with spectral domain optical coherence tomography (SD-OCT) scanning and relay optics. The MMOCT enables wide-field noncontact real-time cross-sectional imaging of retinal structure, allowing for SD-OCT augmented intrasurgical microscopy for intraocular visualization. We experimentally quantify the axial and lateral resolution of the MMOCT and demonstrate fundus imaging at a 20Hz frame rate.

Performance metrics of an optical spectral imaging system for intra-operative assessment of breast tumor margins.

As many as 20-70% of patients undergoing breast conserving surgery require repeat surgeries due to a close or positive surgical margin diagnosed post-operatively [1]. Currently there are no widely accepted tools for intra-operative margin assessment which is a significant unmet clinical need. Our group has developed a first-generation optical visible spectral imaging platform to image the molecular composition of breast tumor margins and has tested it clinically in 48 patients in a previously published study [2]. The goal of this paper is to report on the performance metrics of the system and compare it to clinical criteria for intra-operative tumor margin assessment. The system was found to have an average signal to noise ratio (SNR) >100 and <15% error in the extraction of optical properties indicating that there is sufficient SNR to leverage the differences in optical properties between negative and close/positive margins. The probe had a sensing depth of 0.5-2.2 mm over the wavelength range of 450-600 nm which is consistent with the pathologic criterion for clear margins of 0-2 mm. There was <1% cross-talk between adjacent channels of the multi-channel probe which shows that multiple sites can be measured simultaneously with negligible cross-talk between adjacent sites. Lastly, the system and measurement procedure were found to be reproducible when evaluated with repeated measures, with a low coefficient of variation (<0.11). The only aspect of the system not optimized for intra-operative use was the imaging time. The manuscript includes a discussion of how the speed of the system can be improved to work within the time constraints of an intra-operative setting.