相关论文: Observables in Extended Percolation Models of Caus…

Previously, we showed that computational mechanic's causal states -- predictively-equivalent trajectory classes for a stochastic dynamical system -- can be cast into a reproducing kernel Hilbert space. The result is a widely-applicable…

Percolation is the simplest fundamental model in statistical mechanics that exhibits phase transitions signaled by the emergence of a giant connected component. Despite its very simple rules, percolation theory has successfully been applied…

For two causal structures with the same set of visible variables, one is said to observationally dominate the other if the set of distributions over the visible variables realizable by the first contains the set of distributions over the…

We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding…

The configuration space of causal sets is vast. It is a critical goal to map out this space. Here, we take a practical step towards this goal. We investigate nine classes of causal sets, most of them not studied before. These include…

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…

We propose a manifestly covariant framework for causal set dynamics. The framework is based on a structure, dubbed covtree, which is a partial order on certain sets of finite, unlabeled causal sets. We show that every infinite path in…

This PhD thesis contains several contributions to the field of statistical causal modeling. Statistical causal models are statistical models embedded with causal assumptions that allow for the inference and reasoning about the behavior of…

We discuss the causal set approach to discrete quantum gravity. We begin by describing a classical sequential growth process in which the universe grows one element at a time in discrete steps. At each step the process has the form of a…

We find evidence for a continuum limit of a particular causal set dynamics which depends on only a single ``coupling constant'' $p$ and is easy to simulate on a computer. The model in question is a stochastic process that can also be…

A review is given of recent work aimed at constructing a quantum theory of cosmology in which all observables refer to information measurable by observers inside the universe. At the classical level the algebra of observables should be…

Causal structures give us a way to understand the origin of observed correlations. These were developed for classical scenarios, but quantum mechanical experiments necessitate their generalisation. Here we study causal structures in a broad…

Learning meaningful causal representations from observations has emerged as a crucial task for facilitating machine learning applications and driving scientific discoveries in fields such as climate science, biology, and physics. This…

We present the results of a percolation-like model that has been restricted compared to standard percolation models in the sense that we do not allow finite sized clusters to break up once they have formed. We calculate the critical…

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…

Structural-equations models (SEMs) are perhaps the most commonly used framework for modeling causality. However, as we show, naively extending this framework to infinitely many variables, which is necessary, for example, to model dynamical…

We demonstrate when and how an entire left-infinite orbit of an underlying dynamical system or observations from such left-infinite orbits can be uniquely represented by a pair of elements in a different space, a phenomenon which we call…

A set of discrete individual points located in an embedding continuum space can be seen as percolating or non-percolating, depending on the radius of the discs/spheres associated with each of them. This problem is relevant in theoretical…

In a classical Hamiltonian theory with second class constraints the phase space functions on the constraint surface are observables. We give general formulas for extended observables, which are expressions representing the observables in…

We present a detailed motivation for and definition of the contextual values of an observable, which were introduced by Dressel et al. [Phys. Rev. Lett. 104 240401 (2010)]. The theory of contextual values extends the well-established theory…