225,320 research outputs found
P Systems and Topology: Some Suggestions for Research
Lately, some studies linked the computational power of abstract computing
systems based on multiset rewriting to Petri nets and the computation power of these
nets to their topology. In turn, the computational power of these abstract computing
devices can be understood just looking at their topology, that is, information flow.
This line of research is very promising for several aspects:
its results are valid for a broad range of systems based on multiset rewriting;
it allows to know the computational power of abstract computing devices without tedious
proofs based on simulations;
it links computational power to topology and, in this way, it opens a broad range of
questions.
In this note we summarize the known result on this topic and we list a few suggestions
for research together with the relevance of possible outcomes
Optimal rates of convergence for persistence diagrams in Topological Data Analysis
Computational topology has recently known an important development toward
data analysis, giving birth to the field of topological data analysis.
Topological persistence, or persistent homology, appears as a fundamental tool
in this field. In this paper, we study topological persistence in general
metric spaces, with a statistical approach. We show that the use of persistent
homology can be naturally considered in general statistical frameworks and
persistence diagrams can be used as statistics with interesting convergence
properties. Some numerical experiments are performed in various contexts to
illustrate our results
Quantum Gravity from Causal Dynamical Triangulations: A Review
This topical review gives a comprehensive overview and assessment of recent
results in Causal Dynamical Triangulations (CDT), a modern formulation of
lattice gravity, whose aim is to obtain a theory of quantum gravity
nonperturbatively from a scaling limit of the lattice-regularized theory. In
this manifestly diffeomorphism-invariant approach one has direct, computational
access to a Planckian spacetime regime, which is explored with the help of
invariant quantum observables. During the last few years, there have been
numerous new and important developments and insights concerning the theory's
phase structure, the roles of time, causality, diffeomorphisms and global
topology, the application of renormalization group methods and new observables.
We will focus on these new results, primarily in four spacetime dimensions, and
discuss some of their geometric and physical implications.Comment: 64 pages, 28 figure
Dynamics of Randomly Constructed Computational Systems
We studied Petri nets with five places constructed in a pseudo-random way:
their underlying net is composed of join and fork. We report initial results linking the
dynamical properties of these systems to the topology of their underlying net.
The obtained results can be easily related to the computational power of some abstract models of computation
- …