相关论文: Dual formulation of spin network evolution

A new approach to quantum gravity is described which joins the loop representation formulation of the canonical theory to the causal set formulation of the path integral. The theory assigns quantum amplitudes to special classes of causal…

The original models of causal dynamical triangulations construct space-time by arranging a set of simplices in layers separated by a fixed time-like distance. The importance of the foliation structure in the 2+1 dimensional model is studied…

Spin networks, the quantum states of discrete geometry in loop quantum gravity, are directed graphs whose links are labeled by irreducible representations of SU(2), or spins. Cosmic strings are 1-dimensional topological defects carrying…

We revisit the topic of self-organized criticality (SOC) in simple statistical graph models, with the purpose of capturing essential processes leading to the emergence of macroscopic spacetime from the microscopic dynamics in loop quantum…

The spacetime discreteness of causal set theory has enabled the formulation of novel spacetime dynamics. In these so-called "growth" dynamics, a causal set spacetime is generated probabilistically by means of a random walk on certain tree…

We consider causal 3-dimensional triangulations with the topology of $S^2\times [0,1]$ or $D^2\times [0,1]$ where $S^2$ and $D^2$ are the two-dimensional sphere and disc, respectively. These triangulations consist of slices and we show that…

The Lagrangian constraint analysis of the selfdual massive spin 2 theory in a 2+1 dimensional flat space-time and its extension to a curved one, are performed. Demanding consistence of degrees of freedom in the model with gravitational…

An alternative framework underlying connection between tensor ${\rm sl}_2$-calculus and spin networks is suggested. New sign convention for the inner product in the dual spinor space leads to a simpler and direct set of initial rules for…

The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a…

We perform a non-perturbative sum over geometries in a (2+1)-dimensional quantum gravity model given in terms of Causal Dynamical Triangulations. Inspired by the concept of triangulations of product type introduced previously, we impose an…

The intuitiveness of the tensor network graphical language is becoming well known through its use in numerical simulations using methods from tensor network algorithms. Recent times have also seen rapid progress in developing equations of…

Disentangling the mechanisms underlying the social network evolution is one of social science's unsolved puzzles. Preferential attachment is a powerful mechanism explaining social network dynamics, yet not able to explain all scaling-laws…

Prediction and control of the dynamics of complex networks is a central problem in network science. Structural and dynamical similarities of different real networks suggest that some universal laws might accurately describe the dynamics of…

Link prediction is central to unraveling social network evolution and node relationships, as well as understanding the characteristic mechanisms of complex networks. Currently, research on link prediction for complex dynamic networks…

Can the direction of time and the causal structure of space-time be inferred from operational principles? Causal models and tensor networks offer complementary perspectives: the former encodes cause-effect relations via directed graphs,…

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 compute Teitelboim's causal propagator in the context of canonical loop quantum gravity. For the Lorentzian signature, we find that the resultant power series can be expressed as a sum over branched, colored two-surfaces with an…

Phylogenetic networks are an important way to represent evolutionary histories that involve reticulations such as hybridization or horizontal gene transfer, yet fundamental questions such as how many networks there are that satisfy certain…

Majorana-Weyl spacetimes offer a rich algebraic setup and new types of space-time dualities besides those discussed by Hull. The triality automorphisms of Spin(8) act non-trivially on Majorana-Weyl representations and Majorana-Weyl…

Citation networks represent the flow of information between agents. They are constrained in time and so form directed acyclic graphs which have a causal structure. Here we provide novel quantitative methods to characterise that structure by…