Related papers: Network Gravity
Spatio-temporal network dynamics is an emergent property of many complex systems which remains poorly understood. We suggest a new approach to its study based on the analysis of dynamical motifs -- small subnetworks with periodic and…
Symmetries and transformations are explored in the framework of entropic quantum dynamics. Two conditions arise that are required for any transformation to qualify as a symmetry. The heart of this work lies in the application of these…
On the path towards quantum gravity, we find friction between temporal relations in quantum mechanics (QM) (where they are fixed and field-independent), and in general relativity (where they are field-dependent and dynamic). This paper aims…
We review an approach that uses binary relations as the fundamental constituents of the universe, utilizing them as building blocks for both space and matter. The model is defined by an ultraviolet continuous fixed point of a statistical…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
Spatial curvature is one of the fundamental cosmological parameters that is routinely constrained from observations. The forward modelling of observations, in particular of large-scale structure, often relies on large cosmological…
We propose a simple adaptive-network model describing recent swarming experiments. Exploiting an analogy with human decision making, we capture the dynamics of the model by a low-dimensional system of equations permitting analytical…
We derive the sampling properties of random networks based on weights whose pairwise products parameterize independent Bernoulli trials. This enables an understanding of many degree-based network models, in which the structure of realized…
We study complex networks formed by triangulations and higher-dimensional simplicial complexes representing closed evolving manifolds. In particular, for triangulations, the set of possible transformations of these networks is restricted by…
We investigate the quantum geometry of $2d$ surface $S$ bounding the Cauchy slices of 4d gravitational system. We investigate in detail and for the first time the symplectic current that naturally arises boundary term in the first order…
We give a combinatorial characterization of generic frameworks that are minimally rigid under the additional constraint of maintaining symmetry with respect to a finite order rotation or a reflection. To establish these results we develop a…
Determining whether two graphs are isomorphic is a fundamental problem with practical applications in areas such as molecular chemistry or social network analysis, yet it remains a challenging task, with exact solutions often being…
In this essay we marshal evidence suggesting that Einstein gravity may be an emergent phenomenon, one that is not ``fundamental'' but rather is an almost automatic low-energy long-distance consequence of a wide class of theories.…
We analyse a collection of empirical networks in a wide spectrum of disciplines and show that strong non-normality is ubiquitous in network science. Dynamical processes evolving on non-normal networks exhibit a peculiar behaviour, as…
The two surprising features of gravity are (a) the principle of equivalence and (b) the connection between gravity and thermodynamics. Using principle of equivalence and special relativity in the {\it local inertial frame}, one could obtain…
We exploit an arbitrary extrinsic time foliation of spacetime to solve the constraints in spherically symmetric general relativity. Among such foliations there is a one parameter family, linear and homogeneous in the extrinsic curvature,…
We describe gauge theories which allow to retrieve a large class of gravitational theories, including, MacDowell-Mansouri gravity and its topological extension to Loop Quantum Gravity via the Pontrjagin characteristic class involving the…
Spin networks are at the core of quantum gravity. Our aim is to plug the mathematical community at large into the procedures turn to create a finite quantum theory of general relativity. For this, because of the different cultural…
We explore models with emergent gravity and metric by means of numerical simulations. A particular type of two-dimensional non-linear sigma-model is regularized and discretized on a quadratic lattice. It is characterized by lattice…
In this paper, we have outlined the development of an autonomous dynamical system within a general scalar-tensor gravity framework. This framework encompasses the overall structure of the non-minimally coupled scalar field functions for…