Transformation As Search

In model-driven engineering, model transformations are con- sidered a key element to generate and maintain consistency between re- lated models. Rule-based approaches have become a mature technology and are widely used in different application domains. However, in var- ious scenarios, these solutions still suffer from a number of limitations that stem from their injective and deterministic nature. This article pro- poses an original approach, based on non-deterministic constraint-based search engines, to define and execute bidirectional model transforma- tions and synchronizations from single specifications. Since these solely rely on basic existing modeling concepts, it does not require the intro- duction of a dedicated language. We first describe and formally define this model operation, called transformation as search, then describe a proof-of-concept implementation and discuss experiments on a reference use case in software engineering

A definition of the ARCA notation

ARCA is a programming notation intended for interactive specification and manipulation of combinatorial graphs. The main body of this report is a technical description of ARCA sufficiently detailed to allow an interpreter to be developed. Some simple illustrative programs are included. ARCA incorporates variables for denoting primitive data elements (essentially vertices, edges and scalars), and diagrams (essentially embedded graphs). A novel feature is the use of two kinds of variable: the one storing values (as in conventional procedural languages), the other functional definitions (as in nonprocedural languages). By means of such variables, algebraic expressions over the algebra of primitive data elements may represent either explicit values or formulae. The potential applications and limitations of ARCA, and more general "algebraic notations" defined using similar principles, are briefly discussed

Signals on Graphs: Uncertainty Principle and Sampling

In many applications, the observations can be represented as a signal defined over the vertices of a graph. The analysis of such signals requires the extension of standard signal processing tools. In this work, first, we provide a class of graph signals that are maximally concentrated on the graph domain and on its dual. Then, building on this framework, we derive an uncertainty principle for graph signals and illustrate the conditions for the recovery of band-limited signals from a subset of samples. We show an interesting link between uncertainty principle and sampling and propose alternative signal recovery algorithms, including a generalization to frame-based reconstruction methods. After showing that the performance of signal recovery algorithms is significantly affected by the location of samples, we suggest and compare a few alternative sampling strategies. Finally, we provide the conditions for perfect recovery of a useful signal corrupted by sparse noise, showing that this problem is also intrinsically related to vertex-frequency localization properties.Comment: This article is the revised version submitted to the IEEE Transactions on Signal Processing on May, 2016; first revision was submitted on January, 2016; original manuscript was submitted on July, 2015. The work includes 16 pages, 8 figure

Combining Relational Algebra, SQL, Constraint Modelling, and Local Search

The goal of this paper is to provide a strong integration between constraint modelling and relational DBMSs. To this end we propose extensions of standard query languages such as relational algebra and SQL, by adding constraint modelling capabilities to them. In particular, we propose non-deterministic extensions of both languages, which are specially suited for combinatorial problems. Non-determinism is introduced by means of a guessing operator, which declares a set of relations to have an arbitrary extension. This new operator results in languages with higher expressive power, able to express all problems in the complexity class NP. Some syntactical restrictions which make data complexity polynomial are shown. The effectiveness of both extensions is demonstrated by means of several examples. The current implementation, written in Java using local search techniques, is described. To appear in Theory and Practice of Logic Programming (TPLP)Comment: 30 pages, 5 figure

Unbounded Orbits for Outer Billiards

Outer billiards is a basic dynamical system, defined relative to a planar convex shape. This system was introduced in the 1950's by B.H. Neumann and later popularized in the 1970's by J. Moser. All along, one of the central questions has been: is there an outer billiards system with an unbounded orbit. We answer this question by proving that outer billiards defined relative to the Penrose Kite has an unbounded orbit. The Penrose kite is the quadrilateral that appears in the famous Penrose tiling. We also analyze some of the finer orbit structure of outer billiards on the penrose kite. This analysis shows that there is an uncountable set of unbounded orbits. Our method of proof relates the problem to self-similar tilings, polygon exchange maps, and arithmetic dynamics.Comment: 65 pages, computer-aided proof. Auxilliary program, Billiard King, available from author's website. Latest version is essentially the same as earlier versions, but with minor improvements and many typos fixe