Related papers: Harmonic morphisms and dynamical invariants in net…

We introduce a method for fast estimation of data-adapted, spatio-temporally dependent regularization parameter-maps for variational image reconstruction, focusing on total variation (TV)-minimization. Our approach is inspired by recent…

In this paper, we explore different Markovian random walk strategies on networks with transition probabilities between nodes defined in terms of functions of the Laplacian matrix. We generalize random walk strategies with local information…

Metric networks are network-shaped, one-dimensional structures on which one can solve differential equations to simulate a wide range of physical systems including conjugated molecules, photonic crystals, quantum mechanics in waveguide…

Multiple scales coexist in complex networks. However, the small world property makes them strongly entangled. This turns the elucidation of length scales and symmetries a defiant challenge. Here, we define a geometric renormalization group…

We study the statistical properties of the sampled networks by a random walker. We compare topological properties of the sampled networks such as degree distribution, degree-degree correlation, and clustering coefficient with those of the…

We consider random walks in the form of nearest-neighbor hopping on Erdos-Renyi random graphs of finite fixed mean degree c as the number of vertices N tends to infinity. In this regime, using statistical field theory methods, we develop an…

Scale invariance profoundly influences the dynamics and structure of complex systems, spanning from critical phenomena to network architecture. Here, we propose a precise definition of scale-invariant networks by leveraging the concept of a…

The need for large amounts of training data in modern machine learning is one of the biggest challenges of the field. Compared to the brain, current artificial algorithms are much less capable of learning invariance transformations and…

A graph homomorphism is a map between two graphs that preserves adjacency relations. We consider the problem of sampling a random graph homomorphism from a graph into a large network. We propose two complementary MCMC algorithms for…

Magnitude pruning is one of the mainstream methods in lightweight architecture design whose goal is to extract subnetworks with the largest weight connections. This method is known to be successful, but under very high pruning regimes, it…

In this article we study algorithmic synthesis of the class of stabilizing switching signals for discrete-time switched linear systems proposed in [12]. A weighted digraph is associated in a natural way to a switched system, and the…

Pinning control of a complex network aims at forcing the states of all nodes to track an external signal by controlling a small number of nodes in the network. In this paper, an algebraic graph-theoretic condition is introduced to optimize…

We present a novel mechanism to improve the accuracy of the recently-introduced class of graph random features (GRFs). Our method induces negative correlations between the lengths of the algorithm's random walks by imposing antithetic…

Graphs with diverse structural characteristics play a central role in modelling and optimization tasks. The ability to generate different types of graphs that exhibit shared properties is likewise essential for algorithm selection and…

Though commonly found in the real world, directed networks have received relatively less attention from the literature in which concerns their topological and dynamical characteristics. In this work, we develop a magnetic Laplacian-based…

The importance of structured, complex connectivity patterns found in several real-world systems is to a great extent related to their respective effects in constraining and even defining the respective dynamics. Yet, while complex networks…

We consider random walks evolving on two models of connected and undirected graphs and study the exact large deviations of a local dynamical observable. We prove, in the thermodynamic limit, that this observable undergoes a first-order…

Can a graph specifying the pattern of connections of a dynamical network be reconstructed from statistical properties of a signal generated by such a system? In this model study, we present an evolutionary algorithm for reconstruction of…

We address the correspondence search problem among multiple graphs with complex properties while considering the matching consistency. We describe each pair of graphs by combining multiple attributes, then jointly match them in a unified…

Many real-world datasets have an underlying dynamic graph structure, where entities and their interactions evolve over time. Machine learning models should consider these dynamics in order to harness their full potential in downstream…