Related papers: Fractional Diffusion on Graphs: Superposition of L…

Representing and exploiting multivariate signals requires capturing relations between variables, which we can represent by graphs. Graph dictionaries allow to describe complex relational information as a sparse sum of simpler structures,…

Spatiotemporal forecasting has various applications in neuroscience, climate and transportation domain. Traffic forecasting is one canonical example of such learning task. The task is challenging due to (1) complex spatial dependency on…

We present a method to extract temporal hypergraphs from sequences of 2-dimensional functions obtained as solutions to Optimal Transport problems. We investigate optimality principles exhibited by these solutions from the point of view of…

This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation…

Diffusion in a multidimensional energy surface with minima and barriers is a problem of importance in statistical mechanics and also has wide applications, such as protein folding. To understand it in such a system, we carry out theory and…

We present Fractional Diffusion Bridge Models (FDBM), a novel generative diffusion bridge framework driven by an approximation of the rich and non-Markovian fractional Brownian motion (fBM). Real stochastic processes exhibit a degree of…

We study the time scales associated to diffusion processes that take place on multiplex networks, i.e. on a set of networks linked through interconnected layers. To this end, we propose the construction of a supra-Laplacian matrix, which…

We all depend on mobility, and vehicular transportation affects the daily lives of most of us. Thus, the ability to forecast the state of traffic in a road network is an important functionality and a challenging task. Traffic data is often…

Employing a phase space which includes the (Riemann-Liouville) fractional derivative of curves evolving on real space, we develop a restricted variational principle for Lagrangian systems yielding the so-called restricted fractional…

We introduce a novel diffusion-based spectral algorithm to tackle regression analysis on high-dimensional data, particularly data embedded within lower-dimensional manifolds. Traditional spectral algorithms often fall short in such…

Diffusion is a fundamental graph procedure and has been a basic building block in a wide range of theoretical and empirical applications such as graph partitioning and semi-supervised learning on graphs. In this paper, we study…

Diffusion Transformer, the backbone of Sora for video generation, successfully scales the capacity of diffusion models, pioneering new avenues for high-fidelity sequential data generation. Unlike static data such as images, sequential data…

There has been considerable recent study in "sub-diffusion" models that replace the standard parabolic equation model by a one with a fractional derivative in the time variable. There are many ways to look at this newer approach and one…

The capability of generalization is a cornerstone for the success of modern learning systems. For non-Euclidean data, e.g., graphs, that particularly involves topological structures, one important aspect neglected by prior studies is how…

Spatial-temporal data forecasting of traffic flow is a challenging task because of complicated spatial dependencies and dynamical trends of temporal pattern between different roads. Existing frameworks typically utilize given spatial…

We consider issues associated with the Lagrangian characterisation of flow structures arising in aperiodically time-dependent vector fields that are only known on a finite time interval. A major motivation for the consideration of this…

In this paper we investigate the application of non-local graph entropy to evolving and dynamical graphs. The measure is based upon the notion of Markov diffusion on a graph, and relies on the entropy applied to trajectories originating at…

Temporal graphs represent the dynamic relationships among entities and occur in many real life application like social networks, e commerce, communication, road networks, biological systems, and many more. They necessitate research beyond…

Since the dawn of the space age, observations of energetic particles in planetary radiation belts have been interpreted within a diffusive transport framework, even though the processes that populate and deplete these belts produce highly…

For irreducible, time-homogeneous Markov networks, mutual linearity has recently been established for both occupation probabilities and network currents in the stationary regime as well as in the non-stationary regime in Laplace space. The…