Related papers: Observables are glocal
Change and local spatial variation are missing in canonical General Relativity's observables as usually defined, part of the problem of time. Definitions can be tested using equivalent formulations, non-gauge and gauge, because they must…
The questions of describing observables and observation in quantum gravity appear to be centrally important to its physics. A relational approach holds significant promise, and a classification of different types of relational observables…
The history of general relativity suggests that in absence of experimental data, constructing a theory on philosophical first principles can lead to a very useful theory as well as to ground-breaking insights about physical reality. The two…
We define totally-isotropic polynomials of alternating matrix spaces over finite fields, by analogy with independence polynomials of graphs. Our main result shows that totally-isotropic polynomials of graphical alternating matrix spaces…
Given a graph $G$, the (graph theory) general position problem is to find the maximum number of vertices such that no three vertices lie on a common geodesic. This graph invariant is called the general position number (gp-number for short)…
We study linear cosmological perturbations in the most general teleparallel gravity setting, where gravity is mediated by the torsion and nonmetricity of a flat connection alongside the metric. For a general linear perturbation of this…
Many optimization, inference and learning tasks can be accomplished efficiently by means of decentralized processing algorithms where the network topology (i.e., the graph) plays a critical role in enabling the interactions among…
We investigate graphs that can be disconnected into small components by removing a vanishingly small fraction of their vertices. We show that when a quantum network is described by such a graph, the network is efficiently controllable, in…
Quantum gravity is extended to include purely virtual "cloud sectors", which allow us to define a complete set of point-dependent observables, including a gauge invariant metric and gauge invariant matter fields, and calculate their…
Suppose we are given two graphs on $n$ vertices. We define an observable in the Hilbert space $\Co[(S_n \wr S_2)^m]$ which returns the answer ``yes'' with certainty if the graphs are isomorphic and ``no'' with probability at least…
A recent proposal for gauge-invariant observables in inflation [R. Brunetti et al., JHEP 1608 (2016) 032] is examined. We give a generalisation of their construction to general background spacetimes. In flat space, we calculate one-loop…
Spin networks are natural generalization of Wilson loops functionals. They have been extensively studied in the case where the gauge group is compact and it has been shown that they naturally form a basis of gauge invariant observables.…
Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a…
In this paper we study the algebra of graph invariants, focusing mainly on the invariants of simple graphs. All other invariants, such as sorted eigenvalues, degree sequences and canonical permutations, belong to this algebra. In fact,…
In this paper, we study the graph classification problem from the graph homomorphism perspective. We consider the homomorphisms from $F$ to $G$, where $G$ is a graph of interest (e.g. molecules or social networks) and $F$ belongs to some…
Finding classical canonical observables consists of taking a function space over phase space. For constrained theories, these functions must form zero brackets with a closed algebraic structure of first-class constraints. This brackets…
Invariant graph representation learning aims to learn the invariance among data from different environments for out-of-distribution generalization on graphs. As the graph environment partitions are usually expensive to obtain, augmenting…
We define a GL-variety to be a (typically infinite dimensional) algebraic variety equipped with an action of the infinite general linear group under which the coordinate ring forms a polynomial representation. Such varieties have been used…
Fractional graph isomorphism is the linear relaxation of an integer programming formulation of graph isomorphism. It preserves some invariants of graphs, like degree sequences and equitable partitions, but it does not preserve others like…
We provide the full classification, in arbitrary even and odd dimensions, of global conformal invariants, i.e., scalar densities in the spacetime metric and its derivatives that are invariant, possibly up to a total derivative, under local…