Related papers: Information Geometry of Dynamics on Graphs and Hyp…
We study the statistical geometry of random chords on n-dimensional spheres by deriving explicit analytical expressions for the chord length distribution and its associated structural properties. A critical threshold emerges at dimension…
A new conceptual foundation for the notion of "information" is proposed, based on the concept of a "distinction graph": a graph in which two nodes are connected iff they cannot be distinguished by a particular observer. The "graphtropy" of…
In this paper we: 1) show how the smooth geometry of spaces of normal quantum states over W*-algebras (generalised spaces of density matrices) may be used to substantially enrich the description of quantum dynamics in the algebraic and path…
This work presents a complete geometrical characterisation of divisible and indivisible time-evolution at the level of probabilities for systems with two configurations, open or closed. Our new geometrical construction in the space of…
We study the growth of London's street-network in its dual representation, as the city has evolved over the last 224 years. The dual representation of a planar graph is a content-based network, where each node is a set of edges of the…
We propose a novel node embedding of directed graphs to statistical manifolds, which is based on a global minimization of pairwise relative entropy and graph geodesics in a non-linear way. Each node is encoded with a probability density…
We introduce the category of information structures, whose objects are suitable diagrams of measurable sets that encode the possible outputs of a given family of observables and their mutual relationships of refinement; they serve as…
In this paper, we introduce \emph{$\ell^p$-information geometry}, an infinite-dimensional framework that shares key features with the geometry of the space of probability densities \( \mathrm{Dens}(M) \) on a closed manifold, while also…
Information based thermodynamic logic is revisited. It consists of two parts: Part A applies the modern theory of probability in which an arbitrary convex function \phi is employed as an analytic "device" to express information as…
Galilean and Carrollian algebras acting on two-dimensional Newton-Cartan and Carrollian manifolds are isomorphic. A consequence of this property is a duality correspondence between one-dimensional Galilean and Carrollian fluids. We describe…
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…
We describe recent links between two topics: geometric structures on manifolds in the sense of Ehresmann and Thurston, and dynamics "at infinity" for representations of discrete groups into Lie groups.
We study properties of a non equilibrium steady state generated when two heat baths are initially in contact with one another. The dynamics of the system we study are governed by holographic duality in a large number of dimensions. We…
We study random graphs with latent geometric structure, where the probability of each edge depends on the underlying random positions corresponding to the two endpoints. We focus on the setting where this conditional probability is a…
We introduce a general framework for analysing general probabilistic theories, which emphasises the distinction between the dynamical and probabilistic structures of a system. The dynamical structure is the set of pure states together with…
In 4-dimensional supergravity theories, covariant under symplectic electric-magnetic duality rotations, a significant role is played by the symplectic matrix M({\phi}), related to the coupling of scalars {\phi} to vector field-strengths. In…
The four dimensional gauged supergravities descending from non-geometric string compactifications involve a wide class of flux objects which are needed to make the theory invariant under duality transformations at the effective level.…
Morphology and dynamics at the meso-scale play crucial roles in the overall macro- or system-scale flow of heterogeneous materials. In a multi-scale framework, closure models upscale unresolved sub-grid (meso-scale) physics and therefore…
Multiplex graphs, characterised by their layered structure, exhibit informative interdependencies within layers that are crucial for understanding complex network dynamics. Quantifying the interaction and shared information among these…
We consider a gravity dual description of time dependent, strongly interacting large-Nc N=4 SYM. We regard the gauge theory system as a fluid with shear viscosity. Our fluid is expanding in one direction following the Bjorken's picture that…