Related papers: On the connection between evolution algebras, rand…
We study a one-dimensional random walk with memory in which the step lengths to the left and to the right evolve at each step in order to reduce the wandering of the walker. The feedback is quite efficient and lead to a non-diffusive walk.…
Quantum walks on graphs are ubiquitous in quantum computing finding a myriad of applications. Likewise, random walks on graphs are a fundamental building block for a large number of algorithms with diverse applications. While the…
We develop a general theory of random walks on hypergraphs which includes, as special cases, the different models that are found in literature. In particular, we introduce and analyze general random walk Laplacians for hypergraphs, and we…
We study the evolution of graphs densifying by adding edges: Two vertices are chosen randomly, and an edge is (i) established if each vertex belongs to a tree; (ii) established with probability $p$ if only one vertex belongs to a tree;…
We study a broad class of random labelled trees in which integer-valued labels evolve along the edges according to increments in $\{-1, 0, 1\}$. These models include e.g. branching random walks, embedded complete and incomplete binary…
We consider, following the work of S. Kerov, random walks which are continuous-space generalizations of the Hook Walks defined by Greene-Nijenhuis-Wilf, performed under the graph of a continual Young diagram. The limiting point of these…
We introduce a notion of chain of evolution algebras. The sequence of matrices of the structural constants for this chain of evolution algebras satisfies an analogue of Chapman-Kolmogorov equation. We give several examples (time homogenous,…
We study the interplay between evolutionary game and network structure and show how the dynamics of the game affect the growth pattern of the network and how the evolution of the network influence the cooperative behavior in the game.…
Genetic and evolution algebras arise naturally from applied probability and stochastic processes. Gibbs measures describe interacting systems commonly studied in thermodynamics and statistical mechanics with applications in several fields.…
Accurately analyzing graph properties of social networks is a challenging task because of access limitations to the graph data. To address this challenge, several algorithms to obtain unbiased estimates of properties from few samples via a…
One of the most influential recent results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent…
Working withing the framework of Hopf algebras, a random walk and the associated diffusion equation are constructed on a space that is algebraically described as the merging of the real line algebra with the anyonic line algebra.…
Message-passing graph neural networks (GNNs) excel at capturing local relationships but struggle with long-range dependencies in graphs. In contrast, graph transformers (GTs) enable global information exchange but often oversimplify the…
Graphs are used to represent a plethora of phenomena, from the Web and social networks, to biological pathways, to semantic knowledge bases. Arguably the most interesting and important questions one can ask about graphs have to do with…
We consider a finite structured population of mobile individuals that strategically explore a network using a Markov movement model and interact with each other via a public goods game. We extend the model of Erovenko et al. (2019) from…
A random graph evolution based on the interactions of N vertices is studied. During the evolution both the preferential attachment method and the uniform choice of vertices are allowed. The weight of a vertex means the number of its…
Locally Markov walks are natural generalizations of classical Markov chains, where instead of a particle moving independently of the past, it decides where to move next depending on the last action performed at the current location. We…
We show how to construct discrete-time quantum walks on directed, Eulerian graphs. These graphs have tails on which the particle making the walk propagates freely, and this makes it possible to analyze the walks in terms of scattering…
Graph theory is a branch of mathematics in which pair-wise relations between objects are studied. My PhD thesis, supervised by David R. Wood, introduces and investigates a new family of graphs, called link graphs, that generalises the…
In this note, we discuss a general definition of quantum random walks on graphs and illustrate with a simple graph the possibility of very different behavior between a classical random walk and its quantum analogue. In this graph,…