Related papers: Structural Balance via Gradient Flows over Signed …
We give a twistorial interpretation of geometric structures on a Riemannian manifold, as sections of homogeneous fibre bundles, following an original insight by Wood (2003). The natural Dirichlet energy induces an abstract harmonicity…
Heider's Balance Theory in signed networks, which consists of friendship or enmity relationships, is a model that relates the type of relationship between two people to the third person. In this model, there is an assumption of the…
Families of hypersurfaces that are level-set families of harmonic functions free of critical points are characterized by a local differential-geometric condition. Harmonic functions with a specified level-set family are constructed from…
This article serves to concisely review the link between gradient flow systems on hypergraphs and information geometry which has been established within the last five years. Gradient flow systems describe a wealth of physical phenomena and…
The modeling of networks, specifically generative models, have been shown to provide a plethora of information about the underlying network structures, as well as many other benefits behind their construction. Recently there has been a…
Our modern life has grown to depend on many and nearly ubiquitous large complex engineering systems. Many disciplines now seemingly ask the same question: ``In the face of assumed disruption, to what degree will these systems continue to…
Throughout the history of science, physics-based modeling has relied on judiciously approximating observed dynamics as a balance between a few dominant processes. However, this traditional approach is mathematically cumbersome and only…
The frustration index is a key measure for analysing signed networks, which has been underused due to its computational complexity. We use an exact optimisation-based method to analyse frustration as a global structural property of signed…
We develop a theoretical framework that explains how discrete symbolic structures can emerge naturally from continuous neural network training dynamics. By lifting neural parameters to a measure space and modeling training as Wasserstein…
The time evolution of physical systems is described by differential equations, which depend on abstract quantities like energy and force. Traditionally, these quantities are derived as functionals based on observables such as positions and…
Understanding the relationship between the dynamics of neural processes and the anatomical substrate of the brain is a central question in neuroscience. On the one hand, modern neuroimaging technologies, such as diffusion tensor imaging,…
The recently introduced structured input-output analysis is a powerful method for capturing nonlinear phenomena associated with incompressible flows, and this paper extends that method to the compressible regime. The proposed method relies…
Where graphs are used for modelling and specifying systems, consistency is an important concern. To be a valid model of a system, the graph structure must satisfy a number of constraints. To date, consistency has primarily been viewed as a…
Tracking of reference signals is addressed in the context of a class of nonlinear controlled systems modelled by $r$-th order functional differential equations, encompassing inter alia systems with unknown "control direction" and dead-zone…
Social networks inherently exhibit complex relationships that can be positive or negative, as well as directional. Understanding balance in these networks is crucial for unraveling social dynamics, yet traditional theories struggle to…
Causal structure learning has been a challenging task in the past decades and several mainstream approaches such as constraint- and score-based methods have been studied with theoretical guarantees. Recently, a new approach has transformed…
How do networks of relationships evolve over time? We analyse a dataset tracking the social interactions of 900 individuals over four years. Despite continuous shifts in individual relationships, the macroscopic structural properties of the…
Hierarchy significantly shapes interactions in social structures by organizing individuals or groups based on status, power, or privilege. This study investigates how hierarchy affects structural balance as temperature variations, which…
Three one-body profiles that correspond to local fluctuations in energy, in entropy, and in particle number are used to describe the equilibrium properties of inhomogeneous classical many-body systems. Local fluctuations are obtained from…
Classical Heider balance theory models the evolution of social networks towards balanced states with stress minimization. Triad relationships are classically either balanced or imbalanced. However, real-world relationships often exhibit…