Related papers: Structural coarse-graining enables noise-robust fu…
This paper introduces an Algebraic MultiScale method for simulation of flow in heterogeneous porous media with embedded discrete Fractures (F-AMS). First, multiscale coarse grids are independently constructed for both porous matrix and…
Neural-network models of high-level brain functions such as memory recall and reasoning often rely on the presence of stochasticity. The majority of these models assumes that each neuron in the functional network is equipped with its own…
In the face of the stupefying complexity of the human brain, network analysis is a most useful tool that allows one to greatly simplify the problem, typically by approximating the billions of neurons comprising the brain by means of a…
Functional data analysis offers a diverse toolkit of statistical methods tailored for analyzing samples of real-valued random functions. Recently, samples of time-varying random objects, such as time-varying networks, have been increasingly…
Multiscale molecular modeling is widely applied in scientific research of molecular properties over large time and length scales. Two specific challenges are commonly present in multiscale modeling, provided that information between the…
In recent years, it has become increasingly popular to construct coarse-grained models with non-Markovian dynamics to account for an incomplete separation of time scales. One challenge of a systematic coarse-graining procedure is the…
Can complex engineered and biological networks be coarse-grained into smaller and more understandable versions in which each node represents an entire pattern in the original network? To address this, we define coarse-graining units (CGU)…
Functional magnetic resonance (fMRI) is an invaluable tool in studying cognitive processes in vivo. Many recent studies use functional connectivity (FC), partial correlation connectivity (PC), or fMRI-derived brain networks to predict…
Coarse graining is an important ingredient in many multi-scale continuum-discrete solvers such as CFD--DEM (computational fluid dynamics--discrete element method) solvers for dense particle-laden flows. Although CFD--DEM solvers have become…
Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…
We consider the challenges in extracting stimulus-related neural dynamics from other intrinsic processes and noise in naturalistic functional magnetic resonance imaging (fMRI). Most studies rely on inter-subject correlations (ISC) of…
Lossy data transformations by definition lose information. Yet, in modern machine learning, methods like data pruning and lossy data augmentation can help improve generalization performance. We study this paradox using a solvable model of…
We introduce an RG-inspired coarse-graining for extracting the collective features of data. The key to successful coarse-graining lies in finding appropriate pairs of data sets. We coarse-grain the two closest data in a regular real-space…
Diffusion MRI tractography technique enables non-invasive visualization of the white matter pathways in the brain. It plays a crucial role in neuroscience and clinical fields by facilitating the study of brain connectivity and neurological…
Diffusion magnetic resonance imaging (dMRI) is a crucial non-invasive technique for exploring the microstructure of the living human brain. Traditional hand-crafted and model-based tissue microstructure reconstruction methods often require…
Diffusion weighted MRI (dMRI) provides a non invasive virtual reconstruction of the brain's white matter structures through tractography. Analyzing dMRI measures along the trajectory of white matter bundles can provide a more specific…
Real time application of deep learning algorithms is often hindered by high computational complexity and frequent memory accesses. Network pruning is a promising technique to solve this problem. However, pruning usually results in irregular…
Fiber tracking based on diffusion weighted Magnetic Resonance Imaging (dMRI) allows for noninvasive reconstruction of fiber bundles in the human brain. In this chapter, we discuss sources of error and uncertainty in this technique, and…
We implemented a coarse-graining procedure to construct mesoscopic models of complex molecules. The final aim is to obtain better results on properties depending on slow modes of the molecules. Therefore the number of particles considered…
Mapping from functional connectivity (FC) to structural connectivity (SC) can facilitate multimodal brain network fusion and discover potential biomarkers for clinical implications. However, it is challenging to directly bridge the reliable…