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

We study short-horizon forecasting in financial time series under strict causal constraints, treating the market as a non-stationary stochastic system in which any predictive observable must be computable online from information available…

The well-defined but intricate course of time evolution exhibited by many naturally occurring phenomena suggests some source of dynamic order sustaining it. In spite of its obviousness as a problem, it has remained absent from the…

Requiring that the causal structure between different parties is well-defined imposes constraints on the correlations they can establish, which define so-called causal correlations. Some of these are known to have a "dynamical" causal order…

Modelling growth in student achievement is a significant challenge in the field of education. Understanding how interventions or experiences such as part-time work can influence this growth is also important. Traditional methods like…

We propose an extension of the classical variational theory of evolution equations that accounts for dynamics also in possibly non-reflexive and non-separable spaces. The pivoting point is to establish a novel variational structure, based…

This article studies the estimation of the causal effect of a time-varying treatment on time-to-an-event or on some other continuously distributed outcome. The paper applies to the situation where treatment is repeatedly adapted to…

Rapid growth of constraints is often observed in free evolutions of highly gravitating systems. To alleviate this problem we investigate the effect of adding spatial derivatives of the constraints to the right hand side of the evolution…

Certain Markov processes, or deterministic evolution equations, have the property that they are dual to a stochastic process that exhibits extinction versus unbounded growth, i.e., the total mass in such a process either becomes zero, or…

This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…

Existing work on quantum causal structure assumes that one can perform arbitrary operations on the systems of interest. But this condition is often not met. Here, we extend the framework for quantum causal modelling to situations where a…

We discuss the asymptotic structure of spacetimes, presenting a new construction of ideal points at infinity and introducing useful topologies on the completed space. Our construction is based on structures introduced by Geroch, Kronheimer,…

We give a detailed description in 1-D the growth of Sobolev norms for time dependent linear generalized KdV-type equations on the circle. For most initial data, the growth of Sobolev norms is polynomial in time for fixed analytic potential…

We describe an algebraic way to code the causal information of a discrete spacetime. The causal set C is transformed to a description in terms of the causal pasts of the events in C. This is done by an evolving set, a functor which to each…

Time-dependent driving holds the promise of realizing dynamical phenomenon absent in static systems. Here, we introduce a correlated random driving protocol to realize a spatiotemporal order that cannot be achieved even by periodic driving,…

We introduce a theory of sequential causal inference in which learners in a chain estimate a structural model from their upstream teacher and then pass samples from the model to their downstream student. It extends the population dynamics…

The view that the passage of time is physical finds expression in the classical sequential growth models of Rideout and Sorkin in which a discrete spacetime grows by the partially ordered accretion of new spacetime atoms.

The aim of this paper is to discuss a recent result which shows that probabilistic inference in the presence of (unknown) causal mechanisms can be tractable for models that have traditionally been viewed as intractable. This result was…

Cross-sectional studies are widely prevalent since they are more feasible to conduct compared to longitudinal studies. However, cross-sectional data lack the temporal information required to study the evolution of the underlying processes.…

Non-perturbative theories of quantum gravity inevitably include configurations that fail to resemble physically reasonable spacetimes at large scales. Often, these configurations are entropically dominant and pose an obstacle to obtaining…

Many regenerative arguments in stochastic processes use random times which are akin to stopping times, but which are determined by the future as well as the past behaviour of the process of interest. Such arguments based on "conditioning on…