Related papers: Probabilistic tractography, Path Integrals and the…
In this paper we identify the Fokker-Planck equation for (reflected) Sticky Brownian Motion as a Wasserstein gradient flow in the space of probability measures. The driving functional is the relative entropy with respect to a non-standard…
The path integral quantization method is applied to a relativistically covariant version of the Hopfield model, which represents a very interesting mesoscopic framework for the description of the interaction between quantum light and…
The goal of diffusion-weighted magnetic resonance imaging (DWI) is to infer the structural connectivity of an individual subject's brain in vivo. To statistically study the variability and differences between normal and abnormal brain…
We study the impact of the brain tractography false positives in the brain connectivity graphs. The representative input database for the analysis is the set of tractograms from the participants on the ISMRM-2015 Tractography Challenge. We…
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 consider a system of $N$ interacting particles, governed by transport and diffusion, that converges in a mean-field limit to the solution of a McKean-Vlasov equation. From the observation of a trajectory of the system over a fixed time…
Fiber tractography on diffusion imaging data offers rich potential for describing white matter pathways in the human brain, but characterizing the spatial organization in these large and complex data sets remains a challenge. We show that…
Sampling from nonsmooth target probability distributions is essential in various applications, including the Bayesian Lasso. We propose a splitting-based sampling algorithm for the time-implicit discretization of the probability flow for…
Fractional Wiener--Weierstrass bridges are a class of Gaussian processes that arise from replacing the trigonometric function in the construction of classical Weierstrass functions by a fractional Brownian bridge. We investigate the sample…
There is growing interest in understanding how the structural interconnections among brain regions change with the occurrence of neurological diseases. Diffusion weighted MRI imaging has allowed researchers to non-invasively estimate a…
We study path integration on a quantum computer that performs quantum summation. We assume that the measure of path integration is Gaussian, with the eigenvalues of its covariance operator of order j^{-k} with k>1. For the Wiener measure…
Auxiliary-field quantum Monte Carlo (AFQMC) is typically formulated as an open-ended random walk in an overcomplete space of Slater determinants, implemented through a Langevin equation. However, the explicit form of the underlying…
The system of one-dimensional symmetric simple random walks, in which none of walkers have met others in a given time period, is called the vicious walker model. It was introduced by Michael Fisher and applications of the model to various…
This paper considers the Fokker-Planck equation and path integral formulation of the fractional Ornstein-Uhlenbeck process parametrized by two indices. The effective Fokker-Planck equation of this process is derived from the associated…
The truncated Wigner approximation (TWA) enables us to investigate bosonic quantum many-body dynamics, including open quantum systems described by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. In the TWA, the Weyl-Wigner…
Functional connectivity (FC) refers to the investigation of interactions between brain regions to understand integration of neural activity in several regions. FC is often estimated using functional magnetic resonance images (fMRI). There…
For the characterization of surface height profiles we present a new stochastic approach which is based on the theory of Markov processes. With this analysis we achieve a characterization of the complexity of the surface roughness by means…
We consider a continuous random walk model for describing normal as well as anomalous diffusion of particles subjected to an external force when these particles diffuse in a uniformly expanding (or contracting) medium. A general equation…
The construction of transfer functions in theoretical neuroscience plays an important role in determining the spiking rate behavior of neurons in networks. These functions can be obtained through various fitting methods, but the biological…
Wasserstein gradient flows provide a powerful means of understanding and solving many diffusion equations. Specifically, Fokker-Planck equations, which model the diffusion of probability measures, can be understood as gradient descent over…