相关论文: Causal Relations and their applications

The recently introduced model of representations has been defined and motivated somewhat ex-nihilo. In this document, I will show that representations are related to a more ''classical'' model through a 2-adjunction. The target model is…

In this work we provide the full description of the upper levels of the classical causal ladder for spacetimes in the context of Lorenztian length spaces, thus establishing the hierarchy between them. We also show that global hyperbolicity,…

Discovery of causal relations is fundamental for understanding the dynamics of complex systems. While causal interactions are well defined for acyclic systems that can be separated into causally effective subsystems, a mathematical…

We propose a new definition of actual causes, using structural equations to model counterfactuals.We show that the definitions yield a plausible and elegant account ofcausation that handles well examples which have caused problems forother…

Causal world models are systems that can answer counterfactual questions about an environment of interest, i.e. predict how it would have evolved if an arbitrary subset of events had been realized differently. It requires understanding the…

The mathematics of a 4-dimensional renormalizable generally covariant lagrangian model (with first order derivatives) is reviewed. The lorentzian CR manifolds are totally real submanifolds of 4(complex)-dimensional complex manifolds…

To a significant extent, the metrical and topological properties of spacetime can be described purely order-theoretically. The $K^+$ relation has proven to be useful for this purpose, and one could wonder whether it could serve as the…

Recent research has severely constrained the standard ``defect'' models of cosmic structure formation. Here I discuss the nature of the problems with defect models, and place this discussion in the context of the big picture of cosmic…

In this work we revisit the notion of the (future) causal completion of a globally hyperbolic spacetime and endow it with the structure of a Lorentzian pre-length space. We further carry out this construction for a certain class of…

A new technique for the study of geodesic connectedness in a class of Lorentzian manifolds is introduced. It is based on arguments of Brouwer's topological degree for the solution of functional equations. It is shown to be very useful for…

Dual structures on causal sets called timelets are introduced, being discrete analogs of global time coordinates. Algebraic and geometrical features of the set of timelets on a causal set are studied. A characterization of timelets in terms…

The discovery of causal relationships is a fundamental problem in science and medicine. In recent years, many elegant approaches to discovering causal relationships between two variables from observational data have been proposed. However,…

We address the problem of causal interpretation of the graphical structure of Bayesian belief networks (BBNs). We review the concept of causality explicated in the domain of structural equations models and show that it is applicable to…

In this paper a systematic study of the causal structure and global causality properties of multiwarped spacetimes is developed. This analysis is used to make a detailed description of the causal boundary of these spacetimes. Some…

We study groups of formal diffeomorphisms in several complex variables. For abelian, metabelian or nilpotent groups we investigate the existence of suitable formal vector fields and closed differential forms which exhibit an invariance…

We look more carefully at the modeling of causality using structural equations. It is clear that the structural equations can have a major impact on the conclusions we draw about causality. In particular, the choice of variables and their…

Recent advances in artificial intelligence reveal the limits of purely predictive systems and call for a shift toward causal and collaborative reasoning. Drawing inspiration from the revolution of Grothendieck in mathematics, we introduce…

In causal graphical models based on directed acyclic graphs (DAGs), directed paths represent causal pathways between the corresponding variables. The variable at the beginning of such a path is referred to as an ancestor of the variable at…

We study the relation between representations of certain infinite-dimensional Lie groups and those of the associated conformal nets. For a chiral conformal net extending the net generated by the vacuum representation of a loop group or…

Diophantine approximation is the problem of approximating a real number by rational numbers. We propose a version of this in which the numerators are approximately related to the denominators by a Laurent polynomial. Our definition is…