Related papers: Structural Balance via Gradient Flows over Signed …
The present research is devoted to the problem of stability of the fluid flow moving in a channel with flexible walls and interacting with the walls, which are subject to traveling waves. Experimental data shows that the energy of the…
Continuous graph neural models based on differential equations have expanded the architecture of graph neural networks (GNNs). Due to the connection between graph diffusion and message passing, diffusion-based models have been widely…
On signed social networks, balanced and unbalanced triangles are a critical motif due to their role as the foundations of Structural Balance Theory. The uses for these motifs have been extensively explored in networks with known edge signs,…
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
Interacting systems are prevalent in nature. It is challenging to accurately predict the dynamics of the system if its constituent components are analyzed independently. We develop a graph-based model that unveils the systemic interactions…
We discuss a link between graph theory and geometry that arises when considering graph dynamical systems with odd interactions. The equilibrium set in such systems is not a collection of isolated points, but rather a union of manifolds,…
We investigate hydrodynamic fluctuations in a 2D granular fluid excited by a vibrating base and in the presence of gravity, focusing on the transverse velocity modes. Since the system is inhomogeneous, we measure fluctuations in horizontal…
Understanding the structure of weighted signed networks is essential for analysing social systems in which relationships vary both in sign and strength. Despite significant advances in statistical network analysis, there is still a lack of…
Transition to turbulence is due to the instability of a laminar flow subject to a disturbance. This complicated problem can be explained using a new proposed energy gradient theory in our previous study. This theory is extended to the…
The Gardner transition in structural glasses is characterized by full-replica symmetry breaking of the free-energy landscape and the onset of anomalous aging dynamics due to marginal stability. Here we show that this transition also has a…
In this paper, we provide an overview of the research conducted in the context of structural systems since the latest survey by Dion et al. in 2003. We systematically consider all the papers that cite this survey as well as the seminal work…
For networks of coupled dynamical systems we characterize admissible functions, that is, functions whose gradient is an admissible vector field. The schematic representation of a gradient network dynamical system is of an undirected cell…
Inhomogeneity generated waves, discovered more than a decade ago, play an important role in processes like energy transfer, turbulence generation, heating, etc. To understand the nature of these waves we developed the formalism that looks…
When a fluid is subject to an external field, as is the case near an interface or under spatial confinement, then the density becomes spatially inhomogeneous. Although the one-body density provides much useful information, a higher level of…
Diffusion and flow-based generative models have achieved remarkable success in domains such as image synthesis, video generation, and natural language modeling. In this work, we extend these advances to weight space learning by leveraging…
Many dynamical systems can be described in terms of structured flows combining source/sink behavior, cyclic dynamics, and topology-constrained transport. These features arise across a wide range of domains, including physical, engineered,…
Structural balance has been posited as one of the factors influencing how friendly and hostile relations of social actors evolve over time. This study investigates the behavior of the Heider balance model in Erd\"os-R\'enyi random graphs in…
We compute the rheological properties of inelastic hard spheres in steady shear flow for general shear rates and densities. Starting from the microscopic dynamics we generalise the Integration Through Transients (\textsc{itt}) formalism to…
This paper addresses questions regarding controllability for `generic parameter' dynamical systems, i.e. the question whether a dynamical system is `structurally controllable'. Unlike conventional methods that deal with structural…
The Heider balance is investigated in a chain of actors, with periodic boundary conditions and the neighborhood of range $r$, with $r$ as a parameter. Two model dynamics are applied: a deterministic cellular automaton (Malarz et al, Physica…