Generalized causal set d’Alembertians

Causal set topology

The Causal Set Theory (CST) approach to quantum gravity is motivated by the observation that, associated with any causal spacetime (M,g) is a poset (M,≺), with the order relation ≺ corresponding to the spacetime causal relation. Spacetime in CST is assumed to have a fundamental atomicity or discreteness, and is replaced by a locally finite poset, the causal set. In order to obtain a well define...

A Causal Set Black Hole

We explicitly compute the causal structure of the Schwarzschild black hole spacetime, by providing an algorithm to decide if any pair of events is causally related. The primary motivation for this study comes from discrete quantum gravity, in particular the causal set approach, in which the fundamental variables can be thought of as the causal ordering of randomly selected events in spacetime. ...

Indications of Causal Set Cosmology *

Within the context of a recently proposed family of stochastic dynamical laws for causal sets, one can ask whether the universe might have emerged from the quantum-gravity era with a large enough size and with sufficient homogeneity to explain its present-day large-scale structure. In general, such a scenario would be expected to require the introduction of very large or very small fundamental ...

Generalized Rough Set Models

Generalized Index-Set Splitting

This paper introduces Index-Set Splitting (ISS), a technique that splits a loop containing several conditional statements into several loops with less complex control flow. Contrary to the classic loop unswitching technique, ISS splits loops when the conditional is loop variant. ISS uses an Index Sub-range Tree (IST) to identify the structure of the conditionals in the loop and to select which ...