Related papers: Network Gravity
We introduce Forman-Ricci curvature and its corresponding flow as characteristics for complex networks attempting to extend the common approach of node-based network analysis by edge-based characteristics. Following a theoretical…
We undertake first steps in making a class of discrete models of quantum gravity, spin foams, accessible to a large scale analysis by numerical and computational methods. In particular, we apply Migdal-Kadanoff and Tensor Network…
Overparameterized shallow neural networks admit substantial parameter redundancy: distinct parameter vectors may represent the same predictor due to hidden-unit permutations, rescalings, and related symmetries. As a result, geometric…
Newtonian gravity arises as the nonrelativistic, static, weak-field limit of some Lorentzian spacetime geometry solving the generally covariant Einstein equations for a given matter field configuration. Spacetime geometry has a local…
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face is to find the discrete protoforms of…
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face in this enterprise is to find the…
A novel field theoretical approach towards modelling dynamic networking in complex systems is presented. An equilibrium networking formalism which utilises Gaussian fields is adapted to model the dynamics of particles that can bind and…
A spinfoam model of 3D gravity non-minimally coupled with a scalar field is studied. By discretization of the scalar field, the model is worked out precisely in a purely combinational way. It is shown that the quantum physics of the scalar…
We propose a computation of curvature of arbitrary two-dimensional surfaces of three-dimensional objects, which is a contribution to discrete gravity with potential applications in network geometry. We begin by linking each point of the…
We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement…
A possible way out of the conundrum of quantum gravity is the proposal that general relativity (GR) is not a fundamental theory but emerges from an underlying microscopic description. Despite recent interest in the emergent gravity program…
A new numerical framework, based on the use of a simple first order strongly hyperbolic evolution equations, is introduced and tested in case of 4-dimensional spherically symmetric gravitating systems. The analytic setup is chosen such that…
Cellular structures must organize themselves within strict physical constraints, operating with finite resources and well-defined boundaries. Classical systems demonstrate only passive responses to boundaries, from surface energy…
We show that hypernetworks can be regarded as posets which, in their turn, have a natural interpretation as simplicial complexes and, as such, are endowed with an intrinsic notion of curvature, namely the Forman Ricci curvature, that…
A goal in network science is the geometrical characterization of complex networks. In this direction, we (arXiv:1603.00386; J. Stat. Mech. (2016) P063206) have recently introduced the Forman's discretization of Ricci curvature to the realm…
This paper extends a recently proposed robust computational framework for constructing the boundary representation (brep) of the volume swept by a given smooth solid moving along a one parameter family $h$ of rigid motions. Our extension…
I describe several conceptual aspects of a particular paradigm which treats the field equations of gravity as emergent. These aspects are related to the features of classical gravitational theories which defy explanation within the…
We discuss the possibility that spacetime geometry may be an emergent phenomenon. This idea has been motivated by the Analogue Gravity programme. These are systems where the kinematics of small perturbations are dominated by an effective…
We extend a model of four-dimensional simplicial quantum gravity to include degenerate triangulations in addition to combinatorial triangulations traditionally used. Relaxing the constraint that every 4-simplex is uniquely defined by a set…
In this paper and a companion paper, we show how the framework of information geometry, a geometry of discrete probability distributions, can form the basis of a derivation of the quantum formalism. The derivation rests upon a few…