Reports de recerca
http://hdl.handle.net/2117/3919
2016-08-24T12:30:37ZNon-commutative integrable systems on b-symplectic manifolds
http://hdl.handle.net/2117/88884
Non-commutative integrable systems on b-symplectic manifolds
Miranda Galcerán, Eva; Kiesenhofer, Anna
In this paper we study non-commutative integrable systems on
b-Poisson manifolds. One important source of examples (and motiva-
tion) of such systems comes from considering non-commutative systems on manifolds with boundary having the right asymptotics on the boundary. In this paper we describe this and other examples and we prove an action-angle theorem for non-commutative integrable systems on a b-symplectic manifold in a neighbourhood of a Liouville torus inside the critical set of the Poisson structure associated to the b-symplectic structure
2016-07-19T09:30:44ZMiranda Galcerán, EvaKiesenhofer, AnnaIn this paper we study non-commutative integrable systems on
b-Poisson manifolds. One important source of examples (and motiva-
tion) of such systems comes from considering non-commutative systems on manifolds with boundary having the right asymptotics on the boundary. In this paper we describe this and other examples and we prove an action-angle theorem for non-commutative integrable systems on a b-symplectic manifold in a neighbourhood of a Liouville torus inside the critical set of the Poisson structure associated to the b-symplectic structureThe HOM problem is decidable
http://hdl.handle.net/2117/87972
The HOM problem is decidable
Godoy, Guillem; Giménez, Omer; Ramos Garrido, Lander; Álvarez Faura, M. del Carme
We close affirmatively a question which has been open for 35 years: decidability of the HOM problem. The HOM problem consists in deciding, given a tree homomorphism $H$ and a regular tree languagle $L$ represented by a tree automaton, whether $H(L)$ is regular. For deciding the HOM problem, we develop new constructions and techniques which are interesting by themselves, and provide several significant intermediate results. For example, we prove that the universality problem is decidable for languages represented by tree automata with equality constraints, and that the equivalence and inclusion problems are decidable for images of regular languages through tree homomorphisms. Our contributions are based on the following new results. We describe a simple transformation for converting a tree automaton with equality constraints into a tree automaton with disequality constraints recognizing the complementary language. We also define a new class of automaton with arbitrary disequality constraints and a particular kind of equality constraints. This new class essentially recognizes the intersection of a tree automaton with disequality constraints and the image of a regular language through a tree homomorphism. We prove decidability of emptiness and finiteness for this class by a pumping mechanism. The above constructions are combined adequately to provide an algorithm deciding the HOM problem.
2016-06-14T11:51:17ZGodoy, GuillemGiménez, OmerRamos Garrido, LanderÁlvarez Faura, M. del CarmeWe close affirmatively a question which has been open for 35 years: decidability of the HOM problem. The HOM problem consists in deciding, given a tree homomorphism $H$ and a regular tree languagle $L$ represented by a tree automaton, whether $H(L)$ is regular. For deciding the HOM problem, we develop new constructions and techniques which are interesting by themselves, and provide several significant intermediate results. For example, we prove that the universality problem is decidable for languages represented by tree automata with equality constraints, and that the equivalence and inclusion problems are decidable for images of regular languages through tree homomorphisms. Our contributions are based on the following new results. We describe a simple transformation for converting a tree automaton with equality constraints into a tree automaton with disequality constraints recognizing the complementary language. We also define a new class of automaton with arbitrary disequality constraints and a particular kind of equality constraints. This new class essentially recognizes the intersection of a tree automaton with disequality constraints and the image of a regular language through a tree homomorphism. We prove decidability of emptiness and finiteness for this class by a pumping mechanism. The above constructions are combined adequately to provide an algorithm deciding the HOM problem.Some advances in the theory of voting systems based on experimental algorithms
http://hdl.handle.net/2117/87345
Some advances in the theory of voting systems based on experimental algorithms
Freixas Bosch, Josep; Molinero Albareda, Xavier
In voting systems, game theory, switching functions, threshold logic, hypergraphs or coherent structures there is an important problem that consists in determining the weightedness of a voting system by means of trades among voters in sets of coalitions. The fundamental theorem by Taylor and Zwicker cite{TaZw92} establishes the equivalence between weighted voting games and $k$-trade robust games for each positive integer $k$. Moreover, they also construct, in cite{TaZw95}, a succession of games $G_k$ based on magic squares which are $(k-1)$-trade robust but not $k$-trade robust, each one of these games $G_k$ has $k^2$ players. The goal of this paper is to provide improvements by means of different experiments to the problem described above. In particular, we will classify all complete games (a basic class of games) of less than eight players according to they are: a weighted voting game or a game which is $(k-1)$-trade robust but not $k$-trade robust for all values of $k$. As a consequence it will we showed the existence of games with less than $k^2$ players which are $(k-1)$-trade robust but not $k$-trade robust. We want to point out that the classifications obtained in this paper by means of experiments are new in the mentioned fields.
2016-05-26T08:32:43ZFreixas Bosch, JosepMolinero Albareda, XavierIn voting systems, game theory, switching functions, threshold logic, hypergraphs or coherent structures there is an important problem that consists in determining the weightedness of a voting system by means of trades among voters in sets of coalitions. The fundamental theorem by Taylor and Zwicker cite{TaZw92} establishes the equivalence between weighted voting games and $k$-trade robust games for each positive integer $k$. Moreover, they also construct, in cite{TaZw95}, a succession of games $G_k$ based on magic squares which are $(k-1)$-trade robust but not $k$-trade robust, each one of these games $G_k$ has $k^2$ players. The goal of this paper is to provide improvements by means of different experiments to the problem described above. In particular, we will classify all complete games (a basic class of games) of less than eight players according to they are: a weighted voting game or a game which is $(k-1)$-trade robust but not $k$-trade robust for all values of $k$. As a consequence it will we showed the existence of games with less than $k^2$ players which are $(k-1)$-trade robust but not $k$-trade robust. We want to point out that the classifications obtained in this paper by means of experiments are new in the mentioned fields.On the Partition Dimension and the Twin Number of a Graph
http://hdl.handle.net/2117/87267
On the Partition Dimension and the Twin Number of a Graph
Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
A partition of the vertex set of a connected graph G is a locating partition of G if every vertex is uniquely determined by its vector of distances to the elements of . The partition dimension of G is the minimum cardinality of a locating partition of G . A pair of vertices u;v of a graph G are called twins if they have exactly the same set of neighbors other than u and v . A twin class is a maximal set of pairwise twin vertices. The twin number of a graph G is the maximum cardinality of a twin class of G . In this paper we undertake the study of the partition dimension of a graph by also considering its twin number. This approach allows us to obtain the set of connected graphs of order n 9 having partition dimension n
2016-05-24T10:33:18ZHernando Martín, María del CarmenMora Giné, MercèPelayo Melero, Ignacio ManuelA partition of the vertex set of a connected graph G is a locating partition of G if every vertex is uniquely determined by its vector of distances to the elements of . The partition dimension of G is the minimum cardinality of a locating partition of G . A pair of vertices u;v of a graph G are called twins if they have exactly the same set of neighbors other than u and v . A twin class is a maximal set of pairwise twin vertices. The twin number of a graph G is the maximum cardinality of a twin class of G . In this paper we undertake the study of the partition dimension of a graph by also considering its twin number. This approach allows us to obtain the set of connected graphs of order n 9 having partition dimension nSEPsFLAREs: Finalised Design Definition File (DDF)
http://hdl.handle.net/2117/86610
SEPsFLAREs: Finalised Design Definition File (DDF)
García Rigo, Alberto; Hernández Pajares, Manuel; Nuñez, Marlon; Qahwaji, Rami; Ashamari, Omar W
2016-05-04T17:19:50ZGarcía Rigo, AlbertoHernández Pajares, ManuelNuñez, MarlonQahwaji, RamiAshamari, Omar WSEPsFLAREs: AR meeting presentation
http://hdl.handle.net/2117/86609
SEPsFLAREs: AR meeting presentation
García Rigo, Alberto; Hernández Pajares, Manuel; Nuñez, Marlon; Qahwaji, Rami; Ashamari, Omar W
2016-05-04T17:08:46ZGarcía Rigo, AlbertoHernández Pajares, ManuelNuñez, MarlonQahwaji, RamiAshamari, Omar WSEPsFLAREs: Technical Specification
http://hdl.handle.net/2117/86607
SEPsFLAREs: Technical Specification
García Rigo, Alberto; Hernández Pajares, Manuel; Nuñez, Marlon; Qahwaji, Rami; Ashamari, Omar W
2016-05-04T16:56:38ZGarcía Rigo, AlbertoHernández Pajares, ManuelNuñez, MarlonQahwaji, RamiAshamari, Omar WSEPsFLAREs: Migration File (MF-v2)
http://hdl.handle.net/2117/86605
SEPsFLAREs: Migration File (MF-v2)
Pérez, Gustau; García Rigo, Alberto; Hernández Pajares, Manuel
2016-05-04T16:41:17ZPérez, GustauGarcía Rigo, AlbertoHernández Pajares, ManuelSEPsFLAREs: Final Report
http://hdl.handle.net/2117/86604
SEPsFLAREs: Final Report
Nuñez, Marlon; Qahwaji, Rami; Ashamari, Omar W; García Rigo, Alberto; Hernández Pajares, Manuel
2016-05-04T16:24:00ZNuñez, MarlonQahwaji, RamiAshamari, Omar WGarcía Rigo, AlbertoHernández Pajares, ManuelIPRESES. Additional Technical Note #8: Virtual Box and Ciraolo SW (v1.0)
http://hdl.handle.net/2117/86602
IPRESES. Additional Technical Note #8: Virtual Box and Ciraolo SW (v1.0)
García Rigo, Alberto; Hernández Pajares, Manuel; Olivares Pulido, Germán
2016-05-04T16:17:15ZGarcía Rigo, AlbertoHernández Pajares, ManuelOlivares Pulido, Germán