Related papers: Spectral Properties of Laplacian and Stochastic Di…
We study the size of nodal sets of Laplacian eigenfunctions on compact Riemannian manifolds without boundary and recover the currently optimal lower bound by comparing the heat flow of the eigenfunction with that of an artifically…
We reconsider the problem of diffusion of particles at constant speed and present a generalization of the Telegrapher process to higher dimensional stochastic media ($d>1$), where the particle can move along $2^d$ directions. We derive the…
In this article, we extend the notion of the Laplacian spread to simple directed graphs (digraphs) using the restricted numerical range. First, we provide Laplacian spread values for several families of digraphs. Then, we prove sharp upper…
We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is…
DragDiffusion is a diffusion-based method for interactive point-based image editing that enables users to manipulate images by directly dragging selected points. The method claims that accurate spatial control can be achieved by optimizing…
Using heterodyne transient grating spectroscopy, we observe a significant enhancement of exciton diffusion within a monolayer WSe$_2$ stacked on top of graphene. We further demonstrate that the diffusion dynamics can be optically tuned on…
For an arbitrary initial configuration of discrete loads over vertices of a distributed graph, we consider the problem of minimizing the {\em discrepancy} between the maximum and minimum loads among all vertices. For this problem, this…
In spite of the fact that efficient compression methods for dense two-dimensional flow fields would be very useful for modern video codecs, hardly any research has been performed in this area so far. Our paper addresses this problem by…
The modeling of diffusion processes on graphs is the basis for many network science and machine learning approaches. Entropic measures of network-based diffusion have recently been employed to investigate the reversibility of these…
This paper presents a novel method designed to enhance the efficiency and accuracy of both image retrieval and pixel retrieval. Traditional diffusion methods struggle to propagate spatial information effectively in conventional graphs due…
This work focuses on exploring the potential benefits of introducing a nonlinear Laplacian in Sheaf Neural Networks for graph-related tasks. The primary aim is to understand the impact of such nonlinearity on diffusion dynamics, signal…
In an ultrasonic array system, increasing the aperture size to achieve a high resolution requires more transmit and receive channels, thus making it essential to have an analysis technique that can reconstruct the shape and physical…
We construct a novel estimator for the diffusion coefficient of the limiting homogenized equation, when observing the slow dynamics of a multiscale model, in the case when the slow dynamics are of bounded variation. Previous research…
By introducing a weight function to the Laplace operator, Bakry and \'Emery defined the "drift Laplacian" to study diffusion processes. Our first main result is that, given a Bakry-\'Emery manifold, there is a naturally associated family of…
Excitable media, ranging from bioelectric tissues and chemical oscillators to forest fires and competing populations, are nonlinear, spatially extended systems capable of spiking. Most investigations of excitable media consider situations…
We present a method based on acoustic wavenumber imaging algorithms to quantify the spectral content of strongly nonlinear energy scattering of a propagating wavefront across the discrete-continuum interface of a 2D hybrid system composed…
We consider a generalization of the diffusion equation on graphs. This generalized diffusion equation gives rise to both normal and superdiffusive processes on infinite one-dimensional graphs. The generalization is based on the $k$-path…
Canonical characterization techniques that rely upon mean squared displacement ($\mathrm{MSD}$) break down for non-ergodic processes, making it challenging to characterize anomalous diffusion from an individual time-series measurement.…
Epidemic spreading is well understood when a disease propagates around a contact graph. In a stochastic susceptible-infected-susceptible setting, spectral conditions characterise whether the disease vanishes. However, modelling human…
Graph generative modelling has become an essential task due to the wide range of applications in chemistry, biology, social networks, and knowledge representation. In this work, we propose a novel framework for generating graphs by adapting…