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.

Latent factor analysis to discover pathway-associated putative segmental aneuploidies in human cancers.

Tumor microenvironmental stresses, such as hypoxia and lactic acidosis, play important roles in tumor progression. Although gene signatures reflecting the influence of these stresses are powerful approaches to link expression with phenotypes, they do not fully reflect the complexity of human cancers. Here, we describe the use of latent factor models to further dissect the stress gene signatures in a breast cancer expression dataset. The genes in these latent factors are coordinately expressed in tumors and depict distinct, interacting components of the biological processes. The genes in several latent factors are highly enriched in chromosomal locations. When these factors are analyzed in independent datasets with gene expression and array CGH data, the expression values of these factors are highly correlated with copy number alterations (CNAs) of the corresponding BAC clones in both the cell lines and tumors. Therefore, variation in the expression of these pathway-associated factors is at least partially caused by variation in gene dosage and CNAs among breast cancers. We have also found the expression of two latent factors without any chromosomal enrichment is highly associated with 12q CNA, likely an instance of "trans"-variations in which CNA leads to the variations in gene expression outside of the CNA region. In addition, we have found that factor 26 (1q CNA) is negatively correlated with HIF-1alpha protein and hypoxia pathways in breast tumors and cell lines. This agrees with, and for the first time links, known good prognosis associated with both a low hypoxia signature and the presence of CNA in this region. Taken together, these results suggest the possibility that tumor segmental aneuploidy makes significant contributions to variation in the lactic acidosis/hypoxia gene signatures in human cancers and demonstrate that latent factor analysis is a powerful means to uncover such a linkage.

Response decision processes and externalizing behavior problems in adolescents.

Externalizing behavior problems of 124 adolescents were assessed across Grades 7-11. In Grade 9, participants were also assessed across social-cognitive domains after imagining themselves as the object of provocations portrayed in six videotaped vignettes. Participants responded to vignette-based questions representing multiple processes of the response decision step of social information processing. Phase 1 of our investigation supported a two-factor model of the response evaluation process of response decision (response valuation and outcome expectancy). Phase 2 showed significant relations between the set of these response decision processes, as well as response selection, measured in Grade 9 and (a) externalizing behavior in Grade 9 and (b) externalizing behavior in Grades 10-11, even after controlling externalizing behavior in Grades 7-8. These findings suggest that on-line behavioral judgments about aggression play a crucial role in the maintenance and growth of aggressive response tendencies in adolescence.

Control of radiative processes using tunable plasmonic nanopatch antennas.

The radiative processes associated with fluorophores and other radiating systems can be profoundly modified by their interaction with nanoplasmonic structures. Extreme electromagnetic environments can be created in plasmonic nanostructures or nanocavities, such as within the nanoscale gap region between two plasmonic nanoparticles, where the illuminating optical fields and the density of radiating modes are dramatically enhanced relative to vacuum. Unraveling the various mechanisms present in such coupled systems, and their impact on spontaneous emission and other radiative phenomena, however, requires a suitably reliable and precise means of tuning the plasmon resonance of the nanostructure while simultaneously preserving the electromagnetic characteristics of the enhancement region. Here, we achieve this control using a plasmonic platform consisting of colloidally synthesized nanocubes electromagnetically coupled to a metallic film. Each nanocube resembles a nanoscale patch antenna (or nanopatch) whose plasmon resonance can be changed independent of its local field enhancement. By varying the size of the nanopatch, we tune the plasmonic resonance by ∼ 200 nm, encompassing the excitation, absorption, and emission spectra corresponding to Cy5 fluorophores embedded within the gap region between nanopatch and film. By sweeping the plasmon resonance but keeping the field enhancements roughly fixed, we demonstrate fluorescence enhancements exceeding a factor of 30,000 with detector-limited enhancements of the spontaneous emission rate by a factor of 74. The experiments are supported by finite-element simulations that reveal design rules for optimized fluorescence enhancement or large Purcell factors.

Elucidating the Space-Time Structure of Low Level Warm Season Precipitation Processes in the Southern Appalachian Mountains Using Models and Observations

Light rainfall is the baseline input to the annual water budget in mountainous landscapes through the tropics and at mid-latitudes. In the Southern Appalachians, the contribution from light rainfall ranges from 50-60% during wet years to 80-90% during dry years, with convective activity and tropical cyclone input providing most of the interannual variability. The Southern Appalachians is a region characterized by rich biodiversity that is vulnerable to land use/land cover changes due to its proximity to a rapidly growing population. Persistent near surface moisture and associated microclimates observed in this region has been well documented since the colonization of the area in terms of species health, fire frequency, and overall biodiversity. The overarching objective of this research is to elucidate the microphysics of light rainfall and the dynamics of low level moisture in the inner region of the Southern Appalachians during the warm season, with a focus on orographically mediated processes. The overarching research hypothesis is that physical processes leading to and governing the life cycle of orographic fog, low level clouds, and precipitation, and their interactions, are strongly tied to landform, land cover, and the diurnal cycles of flow patterns, radiative forcing, and surface fluxes at the ridge-valley scale. The following science questions will be addressed specifically: 1) How do orographic clouds and fog affect the hydrometeorological regime from event to annual scale and as a function of terrain characteristics and land cover?; 2) What are the source areas, governing processes, and relevant time-scales of near surface moisture convergence patterns in the region?; and 3) What are the four dimensional microphysical and dynamical characteristics, including variability and controlling factors and processes, of fog and light rainfall? The research was conducted with two major components: 1) ground-based high-quality observations using multi-sensor platforms and 2) interpretive numerical modeling guided by the analysis of the in situ data collection. Findings illuminate a high level of spatial – down to the ridge scale - and temporal – from event to annual scale - heterogeneity in observations, and a significant impact on the hydrological regime as a result of seeder-feeder interactions among fog, low level clouds, and stratiform rainfall that enhance coalescence efficiency and lead to significantly higher rainfall rates at the land surface. Specifically, results show that enhancement of an event up to one order of magnitude in short-term accumulation can occur as a result of concurrent fog presence. Results also show that events are modulated strongly by terrain characteristics including elevation, slope, geometry, and land cover. These factors produce interactions between highly localized flows and gradients of temperature and moisture with larger scale circulations. Resulting observations of DSD and rainfall patterns are stratified by region and altitude and exhibit clear diurnal and seasonal cycles.

Multi-View Weighted Network

Extensive investigation has been conducted on network data, especially weighted network in the form of symmetric matrices with discrete count entries. Motivated by statistical inference on multi-view weighted network structure, this paper proposes a Poisson-Gamma latent factor model, not only separating view-shared and view-specific spaces but also achieving reduced dimensionality. A multiplicative gamma process shrinkage prior is implemented to avoid over parameterization and efficient full conditional conjugate posterior for Gibbs sampling is accomplished. By the accommodating of view-shared and view-specific parameters, flexible adaptability is provided according to the extents of similarity across view-specific space. Accuracy and efficiency are tested by simulated experiment. An application on real soccer network data is also proposed to illustrate the model.