In this paper, we present a new image regularization method using a rotating smoothing filter. The novelty of this approach resides in the mixing of ideas coming both from pixel classification which determines roughly if a pixel belongs to a homogenous region or an edge and an anisotropic perceptual edge detector which computes two precise diffusion directions. These directions are used by an a...

In this paper, we provide a framework based upon diffusion processes for finding meaningful geometric descriptions of data sets. We show that eigenfunctions of Markov matrices can be used to construct coordinates called diffusion maps that generate efficient representations of complex geometric structures. The associated family of diffusion distances, obtained by iterating the Markov matrix, de...

We study the connections between discrete one-dimensional schemes for nonlinear diffusion and shift-invariant Haar wavelet shrinkage. We show that one step of (stabilised) explicit discretisation of nonlinear diffusion can be expressed in terms of wavelet shrinkage on a single spatial level. This equivalence allows a fruitful exchange of ideas between the two fields. In this paper we derive new...

Diffusion occurs in various contexts and generally involves a network of entities and interactions between entities. Through these interactions, some property, e.g. information, ideas, etc., is spread through the network. This paper presents a general model of diffusion in dynamic networks. We simulate the diffusion of evacuation warnings in multiple network structures under various model setti...

We provide convergence guarantees in Wasserstein distance for a variety of variance-reduction methods: SAGA Langevin diffusion, SVRG Langevin diffusion and control-variate underdamped Langevin diffusion. We analyze these methods under a uniform set of assumptions on the log-posterior distribution, assuming it to be smooth, strongly convex and Hessian Lipschitz. This is achieved by a new proof t...

Political debate concerning moralized issues is increasingly common in online social networks. However, moral psychology has yet to incorporate the study of social networks to investigate processes by which some moral ideas spread more rapidly or broadly than others. Here, we show that the expression of moral emotion is key for the spread of moral and political ideas in online social networks, ...

• Similar policies may be found in different countries. This, in turn, is an indication that policies travel. But why are certain policies imitated while others are not? The author seeks to further our understanding of policy diffusion and its dynamics by investigating how foreign ideas are integrated and translated into new contexts, and how these imported ideas influence national policymaking...