81,371 research outputs found
The Gremlin Graph Traversal Machine and Language
Gremlin is a graph traversal machine and language designed, developed, and
distributed by the Apache TinkerPop project. Gremlin, as a graph traversal
machine, is composed of three interacting components: a graph , a traversal
, and a set of traversers . The traversers move about the graph
according to the instructions specified in the traversal, where the result of
the computation is the ultimate locations of all halted traversers. A Gremlin
machine can be executed over any supporting graph computing system such as an
OLTP graph database and/or an OLAP graph processor. Gremlin, as a graph
traversal language, is a functional language implemented in the user's native
programming language and is used to define the of a Gremlin machine.
This article provides a mathematical description of Gremlin and details its
automaton and functional properties. These properties enable Gremlin to
naturally support imperative and declarative querying, host language
agnosticism, user-defined domain specific languages, an extensible
compiler/optimizer, single- and multi-machine execution models, hybrid depth-
and breadth-first evaluation, as well as the existence of a Universal Gremlin
Machine and its respective entailments.Comment: To appear in the Proceedings of the 2015 ACM Database Programming
Languages Conferenc
Creation of blenders in the conservative setting
In this work we prove that each C^r conservative diffeomorphism with a pair
of hyperbolic periodic points of co-index one can be C^1-approximated by C^r
conservative diffeomorphisms having a blender.Comment: 4 figures, 16 figure
-symmetries for discrete equations
Following the usual definition of -symmetries of differential
equations, we introduce the analogous concept for difference equations and
apply it to some examples.Comment: 10 page
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