相关论文: Quantum statistics in Network Geometry with Fracti…
A statistical model M is a family of probability distributions, characterised by a set of continuous parameters known as the parameter space. This possesses natural geometrical properties induced by the embedding of the family of…
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant…
Random shapes arise naturally in many contexts. The topological and geometric structure of such objects is interesting for its own sake, and also for applications. In physics, for example, such objects arise naturally in quantum gravity, in…
A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…
We develop a full characterization of abelian quantum statistics on graphs. We explain how the number of anyon phases is related to connectivity. For 2-connected graphs the independence of quantum statistics with respect to the number of…
The area of networks is very interdisciplinary and exhibits many applications in several fields of science. Nevertheless, there are few studies focusing on geographically located $d$-dimensional networks. In this paper, we study scaling…
We derive an equation for the current of particles in energy space; particles are subject to a mean field effective potential that may represent quantum effects. From the assumption that non-interacting particles imply a free diffusion…
Proximity networks are time-varying graphs representing the closeness among humans moving in a physical space. Their properties have been extensively studied in the past decade as they critically affect the behavior of spreading phenomena…
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
Traditionally, network analysis is based on local properties of vertices, like their degree or clustering, and their statistical behavior across the network in question. This paper develops an approach which is different in two respects. We…
We introduce the construction of a new framework for probing discrete emergent geometry and boundary-boundary observables based on a fundamentally a-dimensional underlying network structure. Using a gravitationally motivated action with…
Fractional revival occurs between two vertices in a graph if a continuous-time quantum walk unitarily maps the characteristic vector of one vertex to a superposition of the characteristic vectors of the two vertices. This phenomenon is…
Quantum many-body systems are characterized by patterns of correlations that define highly-non trivial manifolds when interpreted as data structures. Physical properties of phases and phase transitions are typically retrieved via simple…
Over the last decade, random hyperbolic graphs have proved successful in providing geometric explanations for many key properties of real-world networks, including strong clustering, high navigability, and heterogeneous degree…
In recent years, there has been a growing recognition that higher-order structures are important features in real-world networks. A particular class of structures that has gained prominence is known as a simplicial complex. Despite their…
In the last 15 years, statistical physics has been a very successful framework to model complex networks. On the theoretical side, this approach has brought novel insights into a variety of physical phenomena, such as self-organisation,…
In this work, we investigate an original strategy in order to derive a statistical modeling of the interface in gas-liquid two-phase flows through geometrical variables. The con- tribution is two-fold. First it participates in the…
In this thesis we develop a full characterization of abelian quantum statistics on graphs. We explain how the number of anyon phases is related to connectivity. For 2-connected graphs the independence of quantum statistics with respect to…
Complex networks have recently attracted much attention in diverse areas of science and technology. Many networks such as the WWW and biological networks are known to display spatial heterogeneity which can be characterized by their fractal…
Quantum spin networks overcome the challenges of traditional charge-based electronics by encoding the information into spin degrees of freedom. Although beneficial for transmitting information with minimal losses when compared to their…