Related papers: If time had no beginning: growth dynamics for past…

The energetic causal set (ECS) program of Cort\^es and Smolin, whose distinguishing feature is the foundational time irreversibility of the evolution equations of quantum gravity, was initiated ten years ago. The model showed the emergence…

We study the cosmological stability of a class of theories with a dynamical preferred frame. For a range of actions, we find cosmological solutions which are compatible with observations of the recent history of the Universe: a matter…

We provide a unified operational framework for the study of causality, non-locality and contextuality, in a fully device-independent and theory-independent setting. Our work has its roots in the sheaf-theoretic framework for contextuality…

The theory of general relativity predicts the existence of closed time-like curves (CTCs), which theoretically would allow an observer to travel back in time and interact with their past self. This raises the question of whether this could…

Causal models capture cause-effect relations both qualitatively - via the graphical causal structure - and quantitatively - via the model parameters. They offer a powerful framework for analyzing and constructing processes. Here, we…

We present a study of dynamical scaling and front motion in a one dimensional system that describes Rayleigh-Benard convection in a rotating cell. We use a model of three competing modes proposed by Busse and Heikes to which spatial…

Time-invariant finite-dimensional systems, under reasonable continuity assumptions, exhibit the property that if solutions exist for all future times, the set of vectors reachable from a bounded set of initial conditions over bounded time…

Models of bacterial growth tend to be `irreversible', allowing for the number of bacteria in a colony to increase but not to decrease. By contrast, models of molecular self-assembly are usually `reversible', allowing for addition and…

We consider a covariant causal set approach to discrete quantum gravity. We first review the microscopic picture of this approach. In this picture a universe grows one element at a time and its geometry is determined by a sequence of…

We extend Robins' theory of causal inference for complex longitudinal data to the case of continuously varying as opposed to discrete covariates and treatments. In particular we establish versions of the key results of the discrete theory:…

This paper discusses how the transactional interpretation of quantum mechanics can provide for a natural account of the emergence of spacetime events from a quantum substratum. In this account, spacetime is not a substantive manifold that…

A group presentation is said to have rational growth if the generating series associated to its growth function represents a rational function. A long-standing open question asks whether the Heisenberg group has rational growth for all…

A new speculative model for the expansion of our universe has been under development by the author for the last two decades, which correctly predicts astronomical measurements with no dark matter or dark energy. This new closed model (no…

Causal discovery is the subfield of causal inference concerned with estimating the structure of cause-and-effect relationships in a system of interrelated variables, as opposed to quantifying the strength or describing the form of causal…

A non-statistical theory of continuous, but irreversible, evolution can be constructed in terms of the Cartan calculus. The fundamental postulate, for an evolutionary theory which admits irreversible processes, is that the topology of the…

The formal relationship between two differing approaches to the description of spacetime as an intrinsically discrete mathematical structure, namely causal set theory and the Wolfram model, is studied, and it is demonstrated that the…

The law of proportionate growth simply states that the time dependent change of a quantity $x$ is proportional to $x$. Its applicability to a wide range of dynamic phenomena is based on various assumptions for the proportionality factor,…

We consider a class of evolution equations describing population dynamics in the presence of a carrying capacity depending on the population with delay. In an earlier work, we presented an exhaustive classification of the logistic equation…

An example of a discrete pregeometry on a microscopic scale is introduced. The model is a directed dyadic acyclic graph. This is the particular case of a causal set. The particles in this model must be self-organized repetitive structures.…

We show a general theorem of existence of temporal foliations in a general causal set, under mild constraints. Then we study automorphisms of infinite causal sets (which satisfy further requirements) and show that they fall under one of two…