Convergence of operators acting on a given Hilbert space is an old and well studied topic in operator theory. The idea of introducing a related notion for operators acting on varying spaces is natural. However, it seems that the first results in this direction have been obtained only recently, to the best of our knowledge. Here we consider sectorial operators on scales of Hilbert spaces. We def...

DCR-2002, 16 July, Bologna Outline: • Motivation: real-time coordination of sensors in a high-latency network • Modeling coordination as graph colouring • Soft graph colouring for real-time responsiveness • A class of distributed anytime algorithms (synchronous) • Convergence • Tightness of constraints: conservative variant • Scalability and robustness • Asynchronous execution • Very high commu...

If L is the combinatorial Laplacian of a graph, exp(−L t) converges to a matrix with identical coefficients. The speed of convergence is measured by the maximal entropy distance. When the graph is the sum of a large number of components, a cut-off phenomenon may occur: before some instant the distance to equilibrium tends to infinity; after that instant it tends to 0. A sufficient condition for...

Belief propagation (BP) is a powerful tool to solve distributed inference problems, though it is limited by short cycles in the corresponding factor graph. Such cycles may lead to incorrect solutions or oscillatory behavior. Only for certain types of problems are convergence properties understood. We extend this knowledge by investigating the use of reweighted BP for likelihood consensus proble...

We study the joint degree counts in linear preferential attachment random graphs and find a simple representation for the limit distribution in infinite sequence space. We show weak convergence with respect to the p-norm topology for appropriate p and also provide optimal rates of convergence of the finite dimensional distributions. The results hold for models with any general initial seed grap...

Graph Convolutional Neural Networks (Graph CNNs) are generalizations of classical CNNs to handle graph data such as molecular data, point could and social networks. Current filters in graph CNNs are built for fixed and shared graph structure. However, for most real data, the graph structures varies in both size and connectivity. The paper proposes a generalized and flexible graph CNN taking dat...

In this article, we discuss a data sharing and knowledge integration framework through autonomous agents with blockchain for implementing Electronic Health Records (EHR). This will enable us to augment existing blockchain-based EHR Systems. We how major concerns in the health industry, i.e., trust, security scalability, can be addressed by transitioning from models convergence of three technolo...

In many areas such as computational biology, finance or social sciences, knowledge of an underlying graph explaining the interactions between agents is paramount importance but still challenging. Considering that these may be based on nonlinear relationships adds further complexity to topology inference problem. Among latest methods respond this need a one proposed by authors, which estimates p...

In this article, first, we introduce a class of proximal-point mapping associated with generalized α i β j - id="M2"> H p . ,., … -accretive mapping. ...