Related papers: Probabilistic tractography, Path Integrals and the…
White matter structures composed of myelinated axons in the living human brain are primarily studied by diffusion-weighted MRI (dMRI). These long-range projections are typically characterized in a two-step process: dMRI is used to estimate…
In the present work, we use information theory to understand the empirical convergence rate of tractography, a widely-used approach to reconstruct anatomical fiber pathways in the living brain. Based on diffusion MRI data, tractography is…
Diffusion magnetic resonance imaging (dMRI) tractography is an advanced imaging technique that enables in vivo mapping of the brain's white matter connections at macro scale. Over the last two decades, the study of brain connectivity using…
In structural brain networks the connections of interest consist of white-matter fibre bundles between spatially segregated brain regions. The presence, location and orientation of these white matter tracts can be derived using diffusion…
We present a framework, which, from the trajectories detailing the spatiotemporal dynamics of a population, simultaneously reconstructs a transport map as well as the Fokker-Planck equation governing the coarse-grained probability…
The transformation of the path integral measure under the reduction procedure in the dynamical systems with a symmetry is considered. The investigation is carried out in the case of the Wiener--type path integrals that are used for…
We study Fokker--Planck equations with symmetric, positive definite mobility matrices capturing diffusion in heterogeneous environments. A weighted Wasserstein metric is introduced for which these equations are gradient flows. This metric…
A Wiener-regularized path integral is presented as an alternative way to formulate Berezin-Toeplitz quantization on a toroidal phase space. Essential to the result is that this quantization prescription for the torus can be constructed as…
Recent progress in diffusion MRI and tractography algorithms as well as the launch of the Human Connectome Project (HCP) have provided brain research with an abundance of structural connectivity data. In this work, we describe and evaluate…
Fokker-Planck equation with the velocity-dependent coefficients is considered for various isotropic systems on the basis of probability transition (PT) approach. This method provides the self-consistent and universal description of friction…
Multi-compartment modeling of diffusion-weighted magnetic resonance imaging measurements is necessary for accurate brain connectivity analysis. Existing methods for estimating the number and orientations of fascicles in an imaging voxel…
The Fokker--Planck Equation can be used in a partially-coherent imaging context to model the evolution of the intensity of a paraxial x-ray wave field with propagation. This forms a natural generalisation of the transport-of-intensity…
Score-based diffusion models have proven effective in image generation and have gained widespread usage; however, the underlying factors contributing to the performance disparity between stochastic and deterministic (i.e., the probability…
We present DeepTract, a deep-learning framework for estimating white matter fibers orientation and streamline tractography. We adopt a data-driven approach for fiber reconstruction from diffusion weighted images (DWI), which does not assume…
We propose a novel and efficient algorithm to model high-level topological structures of neuronal fibers. Tractography constructs complex neuronal fibers in three dimensions that exhibit the geometry of white matter pathways in the brain.…
We propose a gate-based quantum algorithm for the prediction step of Bayesian state estimation based on the Fokker-Planck equation on a discretized position-velocity state space. The probability density is encoded in the amplitudes of a…
The computation of the probability of the first-passage time through a given threshold of a stochastic process is a classic problem that appears in many branches of physics. When the stochastic dynamics is markovian, the probability admits…
The Fokker-Planck equation is a partial differential equation that describes the evolution of a probability distribution over time. It is used to model a wide range of physical and biological phenomena, such as diffusion, chemical…
The transport-of-intensity equation (TIE) has been very widely employed for phase retrieval. In particular, the TIE is an elliptic second-order partial differential equation which may be solved for the phase of a coherent paraxial field…
We study the effective diffusion constant of a Brownian particle linearly coupled to a thermally fluctuating scalar field. We use a path integral method to compute the effective diffusion coefficient perturbatively to lowest order in the…