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Modern recording techniques enable neuroscientists to simultaneously study neural activity across large populations of neurons, with capturing predictor-dependent correlations being a fundamental challenge in neuroscience. Moreover, the…
Developing a unified small-signal model for modern, large-scale power systems that remains accurate across a wide range of operating ranges presents a formidable challenge. Traditional methods, spanning mechanistic modeling, modal…
Background: Transcranial magnetic stimulation (TMS) is a powerful tool to investigate neurophysiology of the human brain and treat brain disorders. Traditionally, therapeutic TMS has been applied in a one-size-fits-all approach,…
There remains an important need for the development of image reconstruction methods that can produce diagnostically useful images from undersampled measurements. In magnetic resonance imaging (MRI), for example, such methods can facilitate…
Mobile technology enables unprecedented continuous monitoring of an individual's behavior, social interactions, symptoms, and other health conditions, presenting an enormous opportunity for therapeutic advancements and scientific…
It is well known that numerical simulations of high-speed reacting flows, in the framework of state-to-state formulations, are the most detailed but also often prohibitively computationally expensive. In this work, we start to investigate…
Public health data are often spatially dependent, but standard spatial regression methods can suffer from bias and invalid inference when the independent variable is associated with spatially-correlated residuals. This could occur if, for…
State-space models (SSMs) are a popular tool for modeling animal abundances. Inference difficulties for simple linear SSMs are well known, particularly in relation to simultaneous estimation of process and observation variances. Several…
Subspace segmentation or subspace learning is a challenging and complicated task in machine learning. This paper builds a primary frame and solid theoretical bases for the minimal subspace segmentation (MSS) of finite samples. Existence and…
The recent wide adoption of Electronic Medical Records (EMR) presents great opportunities and challenges for data mining. The EMR data is largely temporal, often noisy, irregular and high dimensional. This paper constructs a novel ordinal…
We develop a general framework for state estimation in systems modeled with noise-polluted continuous time dynamics and discrete time noisy measurements. Our approach is based on maximum likelihood estimation and employs the calculus of…
Electroencephalography (EEG) is shown to be a valuable data source for evaluating subjects' mental states. However, the interpretation of multi-modal EEG signals is challenging, as they suffer from poor signal-to-noise-ratio, are highly…
Multimode Gaussian states are a versatile resource for quantum information technologies and have been realized across a wide range of physical platforms. Recent progress in the large-scale generation of such states provides a key ingredient…
Distribution System State Estimation (DSSE) plays an increasingly-important role in modern power grids due to the integration of distributed energy resources (DERs). The inherent characteristics of distribution systems make classical…
Recent advances in deep learning have had a methodological and practical impact on brain-computer interface research. Among the various deep network architectures, convolutional neural networks have been well suited for…
The resting-state brain networks (RSNs) reflects the functional connectivity patterns between brain modules, providing essential foundations for decoding intrinsic neural information within the brain. It serves as one of the primary tools…
In this paper we introduce a covariance framework for the analysis of EEG and MEG data that takes into account observed temporal stationarity on small time scales and trial-to-trial variations. We formulate a model for the covariance…
An inverse elastic source problem with sparse measurements is of concern. A generic mathematical framework is proposed which incorporates a low- dimensional manifold regularization in the conventional source reconstruction algorithms…
We consider the problem of localization of sources of brain electrical activity from electroencephalographic (EEG) and magnetoencephalographic (MEG) measurements using spatial filtering techniques. We propose novel reduced-rank activity…
The Normal Means problem plays a fundamental role in many areas of modern high-dimensional statistics, both in theory and practice. And the Empirical Bayes (EB) approach to solving this problem has been shown to be highly effective, again…