Related papers: Poisson Flow Model of Cortical Folding Pattern
A model polydisperse fluid represents many real fluids such as colloidal suspensions and polymer solutions. In this study, considering a concentrated size-polydisperse hard sphere fluid with size derived from two different distribution…
We present a polar coordinate lattice Boltzmann kinetic model for compressible flows. A method to recover the continuum distribution function from the discrete distribution function is indicated. Within the model, a hybrid scheme being…
In this paper, we review widely used statistical analysis frameworks for data defined along cortical and subcortical surfaces that have been developed in last two decades. The cerebral cortex has the topology of a 2D highly convoluted…
The propagation of gradient flow structures from microscopic to macroscopic models is a topic of high current interest. In this paper we discuss this propagation in a model for the diffusion of particles interacting via hard-core exclusion…
We present the first proof of principle that normalizing flows can accurately learn the Boltzmann distribution of the fermionic Hubbard model - a key framework for describing the electronic structure of graphene and related materials.…
We present a computational technique for modeling the evolution of dynamical systems in a reduced basis, with a focus on the challenging problem of modeling partially-observed partial differential equations (PDEs) on high-dimensional…
In this article we present a system of coupled non-linear PDEs modeling an anisotropic electrokinetic flow. We show the existence of suitable weak solutions in three spatial dimensions, that is weak solutions which fulfill an energy…
In machine learning and neuroscience, certain computational structures and algorithms are known to yield disentangled representations without us understanding why, the most striking examples being perhaps convolutional neural networks and…
Neural or cortical fields are continuous assemblies of mesoscopic models, also called neural masses, of neural populations that are fundamental in the modeling of macroscopic parts of the brain. Neural fields are described by nonlinear…
We introduce a Poissonization method to study the coalescent structure of uniform samples from branching processes. This method relies on the simple observation that a uniform sample of size $k$ taken from a random set with positive…
Sampling from unnormalized densities presents a fundamental challenge with wide-ranging applications, from posterior inference to molecular dynamics simulations. Continuous flow-based neural samplers offer a promising approach, learning a…
The stationary isotropic Poisson line process was used to derive upper bounds on mean excess network geodesic length in Aldous and Kendall [Adv. in Appl. Probab. 40 (2008) 1-21]. The current paper presents a study of the geometry and…
We introduce a class of two-parameter discrete dispersion models, obtained by combining convolution with a factorial tilting operation, similar to exponential dispersion models which combine convolution and exponential tilting. The…
Phase oscillators are a common starting point for the reduced description of many single neuron models that exhibit a strongly attracting limit cycle. The framework for analysing such models in response to weak perturbations is now…
Maintaining cerebral blood flow is critical for adequate neuronal function. Previous computational models of brain capillary networks have predicted that heterogeneous cerebral capillary flow patterns result in lower brain tissue partial…
Different experimental studies have reported anomalous diffusion in brain tissues and notably this anomalous diffusion is expressed through fractional derivatives. Axons are important to understand neurodegenerative diseases such as…
Parkinson disease (PD) is marked by progressive neurodegeneration, yet early and subtle structural alterations in brain tissue remain difficult to detect with conventional imaging and analytical methods. Fractal and multifractal frameworks…
We present a coarse-grid projection (CGP) method for accelerating incompressible flow computations, which is applicable to methods involving Poisson equations as incompressibility constraints. The CGP methodology is a modular approach that…
Cellular electrophysiology is often modeled using the cable equations. The cable model can only be used when ionic concentration effects and three dimensional geometry effects are negligible. The Poisson model, in which the electrostatic…
Large-scale instabilities occurring in the presence of small-scale turbulent fluctuations are frequently observed in geophysical or astrophysical contexts but are difficult to reproduce in the laboratory. Using extensive numerical…