Foundational aspects of multiscale digitization

Foundational aspects of multiscale digitization

In this article, we describe the theoretical foundations of the Ω-arithmetization. This method provides a multi-scale discretization of a continuous function that is a solution of a differential equation. This discretization process is based on the Harthong-Reeb line HRω. The HarthongReeb line is a linear space that is both discrete and continuous. This strange line HRω stems from a nonstandard...

Foundational Aspects of Multiscale Digitisation

In this article, we describe the theoretical foundations of the Ω-arithmetization. This method provides a multi-scale discretization of a continuous function that is a solution of a differential equation. This discretization process is based on the Harthong-Reeb line HRω. The HarthongReeb line is a linear space that is both discrete and continuous. This strange line HRω stems from a nonstandard...

Foundational Aspects of

Foundational aspects of nonlocality

Nonlocality refers to correlations between spatially separated parties that are stronger than those explained by the existence of local hidden variables. Quantum mechanics is known to allow some nonlocal correlations between particles in a phenomena known as entanglement. We explore several aspects of nonlocality in general and how they relate to quantum mechanics. First, we construct a hierarc...

Preface Foundational aspects of security

• Joshua Guttman in “Establishing and preserving protocol security goals” proposes a model-theoretic approach to the verification of security properties, where the models are executions, and the security goals are implications over the geometric fragment of predicate logic. This methodology also leads to a new reading of protocol refinement and transformation, and offers the possibility of reas...