Related papers: A test of weak separability for multi-way function…
The anatomical structure of the brain can be observed via non-invasive techniques such as diffusion imaging. However, these are imperfect because they miss connections that are actually known to exist, especially long range…
The paper analyzes four classical signal-plus-noise models: the factor model, spiked sample covariance matrices, the sum of a Wigner matrix and a low-rank perturbation, and canonical correlation analysis with low-rank dependencies. The…
Many studies collect functional data from multiple subjects that have both multilevel and multivariate structures. An example of such data comes from popular neuroscience experiments where participants' brain activity is recorded using…
We propose an estimation approach to analyse correlated functional data which are observed on unequal grids or even sparsely. The model we use is a functional linear mixed model, a functional analogue of the linear mixed model. Estimation…
Functional magnetic resonance imaging (fMRI) data contain complex spatiotemporal dynamics, thus researchers have developed approaches that reduce the dimensionality of the signal while extracting relevant and interpretable dynamics. Models…
The idea to estimate the statistical interdependence among (interacting) brain regions has motivated numerous researchers to investigate how the resulting connectivity patterns and networks may organize themselves under any conceivable…
In this work we focus on examination and comparison of whole-brain functional connectivity patterns measured with fMRI across experimental conditions. Direct examination and comparison of condition-specific matrices is challenging due to…
Studies in recent years have demonstrated that neural organization and structure impact an individual's ability to perform a given task. Specifically, individuals with greater neural efficiency have been shown to outperform those with less…
Brain-computer interface uses brain signals to communicate with external devices without actual control. Many studies have been conducted to classify motor imagery based on machine learning. However, classifying imagery data with sparse…
Weakly coupled oscillators are used throughout the physical sciences, particularly in mathematical neuroscience to describe the interaction of neurons in the brain. Systems of weakly coupled oscillators have a well-known decomposition to a…
Whole-brain network analyses remain the vanguard in neuroimaging research, coming to prominence within the last decade. Network science approaches have facilitated these analyses and allowed examining the brain as an integrated system.…
A large body of literature has shown the substantial inter-regional functional connectivity in the mammal brain. One important property remaining un-studied is the cross-time interareal connection. This paper serves to provide a tool to…
Matrix factorizations and their extensions to tensor factorizations and decompositions have become prominent techniques for linear and multilinear blind source separation (BSS), especially multiway Independent Component Analysis (ICA),…
Functional decomposition of logic circuits has profound influence on all quality aspects of the cost-effective implementation of modern digital systems. In this paper, a relational approach to the decomposition of logic circuits is…
Most brain disorders are very heterogeneous in terms of their underlying biology and developing analysis methods to model such heterogeneity is a major challenge. A promising approach is to use probabilistic regression methods to estimate…
This paper is motivated by medical studies in which the same patients with multiple sclerosis are examined at several successive visits and described by fractional anisotropy tract profiles, which can be represented as functions. Since the…
Penalized likelihood models are widely used to simultaneously select variables and estimate model parameters. However, the existence of weak signals can lead to inaccurate variable selection, biased parameter estimation, and invalid…
Objective: Multimodal measurements of the same phenomena provide complementary information and highlight different perspectives, albeit each with their own limitations. A focus on a single modality may lead to incorrect inferences, which is…
The problem of covariance estimation for replicated surface-valued processes is examined from the functional data analysis perspective. Considerations of statistical and computational efficiency often compel the use of separability of the…
In recent years, there has been strong interest in neuroscience studies to investigate brain organization through networks of brain regions that demonstrate strong functional connectivity (FC). These networks are extracted from observed…