Related papers: Emergent Space-Time via a Geometric Renormalizatio…
We propose that the consistent field renormalization of gravity requires a specific Weyl transformation of the metric tensor. As a consequence, proper length and time, as well as energy and momentum, become functions of scale. We estimate…
Coarse-graining is a molecular modeling technique in which an atomistic system is represented in a simplified fashion that retains the most significant system features that contribute to a target output, while removing the degrees of…
We find a geometrical description from a field theoretical setup based on Wilson's renormalization group in real space. We show that renormalization group equations of coupling parameters encode the metric structure of an emergent curved…
Information theoretic geometry near critical points in classical and quantum systems is well understood for exactly solvable systems. Here we show that renormalization group flow equations can be used to construct the information metric and…
We define a distance analogous to the Gromov-Hausdorff distance that enables the comparison of arbitrary quasi-isometric spaces. We also investigate properties preserved under limits with respect to this distance, as well as properties of…
Multiple scales coexist in complex networks. However, the small world property makes them strongly entangled. This turns the elucidation of length scales and symmetries a defiant challenge. Here, we define a geometric renormalization group…
This work explores the manner in which classical phase space distribution functions converge to the microcanonical distribution. We first prove a theorem about the lack of convergence, then define a generalization of the coarse-graining…
Recent research has tried to extend the concept of renormalization, which is naturally defined for geometric objects, to more general networks with arbitrary topology. The current attempts do not naturally apply to directed networks, for…
We establish the functional Renormalization Group as an exploratory tool to investigate a possible phase transition between a pre-geometric discrete phase and a geometric continuum phase in quantum gravity. In this paper, based on the…
One of the reasons we expect a standard quantum mechanics, which predicts probabilities for alternatives defined on spacelike slices, to be inadequate for quantum gravity is that the notion of ``spacelike'' is ill-defined in a theory where…
We propose that Kreimer's method of Feynman diagram renormalization via a Hopf algebra of rooted trees can be fruitfully employed in the analysis of block spin renormalization or coarse graining of inhomogeneous statistical systems.…
We use information geometry, in which the local distance between models measures their distinguishability from data, to quantify the flow of information under the renormalization group. We show that information about relevant parameters is…
We introduce a hypertopology, induced by an inframetric up to full quantum isometry, on the class of pointed proper quantum metric spaces, which are separable, possibly non-unital, C*-algebras endowed with an analogue of the Lipschitz…
The quest for a consistent theory which describes the quantum microstructure of spacetime seems to require some departure from the paradigms that have been followed in the construction of quantum theories for the other fundamental…
This paper is devoted to study of transformations on metric spaces. It is done in an effort to produce qualitative version of quasi-isometries which takes into account the asymptotic behavior of the Gromov product in hyperbolic spaces. We…
Coarse-grained descriptions of dislocation motion in crystalline metals inherently represent a loss of information regarding dislocation-dislocation interactions. In the present work, we consider a coarse-graining framework capable of…
Recently I proposed a simple dynamical network model for discrete space-time which self-organizes as a graph with Hausdorff dimension d_H=4. The model has a geometric quantum phase transition with disorder parameter (d_H-d_s) where d_s is…
Considering the scale dependent effective spacetimes implied by the functional renormalization group in d-dimensional Quantum Einstein Gravity, we discuss the representation of entire evolution histories by means of a single, (d +…
Learning fine-grained embeddings from coarse labels is a challenging task due to limited label granularity supervision, i.e., lacking the detailed distinctions required for fine-grained tasks. The task becomes even more demanding when…
Emergent modified gravity is a post-Einsteinian gravitational theory where spacetime geometry is not fundamental but rather emerges from the gravitational degrees of freedom in a non-trivial way. The specific relationship between geometry…