Related papers: Dynamics of weighted shifts on directed trees
This is a survey article on trees, with a modest number of proofs to give a flavor of the way these topologies can be efficiently handled. Trees are defined in set-theorist fashion as partially ordered sets in which the elements below each…
Transport networks are crucial to the functioning of natural systems and technological infrastructures. For flow networks in many scenarios, such as rivers or blood vessels, acyclic networks (i.e., trees) are optimal structures when…
Hardly any real self-propelling or actively driven object is perfect. Thus, undisturbed motion will generally not follow straight lines but rather circular trajectories. We here address self-propelled or actively driven objects that move in…
We consider directed weighted graphs and define various families of path counting functions. Our main results are explicit formulas for the main term of the asymptotic growth rate of these counting functions, under some irrationality…
We study a class of nonlocal, energy-driven dynamical models that govern the motion of closed, embedded curves from both an energetic and dynamical perspective. Our energetic results provide a variety of ways to understand physically…
We study the dynamical response of a circularly-driven rigid body, focusing on the description of intrinsic rotational behavior (reverse rotations). The model system we address is integrable but nontrivial, allowing for qualitative and…
I give a short review of the theory of twisted symmetries of differential equations, emphasizing geometrical aspects. Some open problems are also mentioned.
We study the long-term behavior of weighted multi-type branching processes, focusing on extending classical laws of large numbers and martingale convergence to settings with infinitely many weighted particles, arbitrary type spaces and…
We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces…
The tribology of a sliding elastic continuum in contact with a disordered substrate is investigated analytically and numerically via a bead-spring model. The deterministic dynamics of this system exhibits a depinning transition at a finite…
We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks…
This paper concerns the dynamical behaviors of acoustic wave motion driven by a force acting through the boundary. If the boundary force is a suitable control, we show that the dynamical system associated to the acoustic wave motion is…
In this paper, we characterize mixing unilateral backward shifts on barrelled and ultrabarrelled topological sequence spaces respectively, which extend several well-known results in the existing literature. We present some nontrivial…
In this paper, we provide novel definitions of clustering coefficient for weighted and directed multilayer networks. We extend in the multilayer theoretical context the clustering coefficients proposed in the literature for weighted…
We define a potential-weighted connective constant that measures the effective strength of a repulsive pair potential of a Gibbs point process modulated by the geometry of the underlying space. We then show that this definition leads to…
Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning. In this work, we propose a theoretical framework to analyze learning dynamics through the lens of dynamical…
Predictive models that generalize well under distributional shift are often desirable and sometimes crucial to building robust and reliable machine learning applications. We focus on distributional shift that arises in causal inference from…
For most technical networks, the interplay of dynamics, traffic and topology is assumed crucial to their evolution. In this paper, we propose a traffic-driven evolution model of weighted technological networks. By introducing a general…
Understanding how cooperation evolves in structured populations remains a fundamental question across diverse disciplines. The problem of cooperation typically involves pairwise or group interactions among individuals. While prior studies…
In weighted trees, all edges are endowed with positive integral weight. We enumerate weighted bicolored plane trees according to their weight and number of edges.