Related papers: Discrete mechanics: a sequential growth dynamics f…
An important question that discrete approaches to quantum gravity must address is how continuum features of spacetime can be recovered from the discrete substructure. Here, we examine this question within the causal set approach to quantum…
Quantum geometry on a discrete set means a directed graph with a weight associated to each arrow defining the quantum metric. However, these `lattice spacing' weights do not have to be independent of the direction of the arrow. We use this…
It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum…
A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…
The logistic equation is ubiquitous in applied mathematics as a minimal model of saturating growth. Here, we examine a broad generalisation of the logistic growth model to discretely structured populations, motivated by examples that range…
The goal of this paper is to propose an approach to the formulation of dynamics for causal sets and coupled matter fields. We start from the continuum version of the action for a Klein-Gordon field coupled to gravity, and rewrite it first…
A temporally varying discretization often features in discrete gravitational systems and appears in lattice field theory models subject to a coarse graining or refining dynamics. To better understand such discretization changing dynamics in…
We show that if a discrete quantum gravity is not classical, then it cannot be generated by an isometric dynamics. In particular, we show that if the quantum measure {\mu} (or equivalently the decoherence functional) is generated by an…
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…
In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…
A quantum causal topology is presented. This is modeled after a non-commutative scheme type of theory for the curved finitary spacetime sheaves of the non-abelian incidence Rota algebras that represent `gravitational quantum causal sets'.…
This article presents a sequential growth model for the universe that acts like a quantum computer. The basic constituents of the model are a special type of causal set (causet) called a $c$-causet. A $c$-causet is defined to be a causet…
Classical sequential growth models for causal sets provide an important step towards the formulation of a quantum causal set dynamics. The covariant observables in a class of these models known as generalised percolation have been…
This paper provides a thorough introduction to the causal set hypothesis aimed at students, and other interested persons, with some knowledge of general relativity and nonrelativistic quantum mechanics. I elucidate the arguments for why the…
Identifying an appropriate set of ``observables'' is a nontrivial task for most approaches to quantum gravity. We describe how it may be accomplished in the context of a recently proposed family of stochastic (but classical) dynamical laws…
Causal set theory provides a model of discrete spacetime in which spacetime events are represented by elements of a causal set---a locally finite, partially ordered set in which the partial order represents the causal relationships between…
We consider a preferential growth model where particles are added one by one to the system consisting of clusters of particles. A new particle can either form a new cluster (with probability q) or join an already existing cluster with a…
Set prediction is about learning to predict a collection of unordered variables with unknown interrelations. Training such models with set losses imposes the structure of a metric space over sets. We focus on stochastic and underdefined…
A probabilistic model describes a system in its observational state. In many situations, however, we are interested in the system's response under interventions. The class of structural causal models provides a language that allows us to…
This paper analyzes a stochastic logistic difference equation under the assumption that the population distribution follows a normal distribution. Our focus is on the mathematical relationship between the average growth rate and a newly…