Articles de revista
http://hdl.handle.net/2117/3918
20160506T03:54:45Z

Dynamic programming for graphs on surfaces
http://hdl.handle.net/2117/86631
Dynamic programming for graphs on surfaces
Rué Perna, Juan José; Sau, Ignasi; Thilikos, Dimitrios
We provide a framework for the design and analysis of dynamic programming algorithms for surfaceembedded graphs on n vertices and branchwidth at most k. Our technique applies to general families of problems where standard dynamic programming runs in 2O(k·log k) · n steps. Our approach combines tools from topological graph theory and analytic combinatorics. In particular, we introduce a new type of branch decomposition called surface cut decomposition, generalizing sphere cut decompositions of planar graphs, which has nice combinatorial properties. Namely, the number of partial solutions that can be arranged on a surface cut decomposition can be upperbounded by the number of noncrossing partitions on surfaces with boundary. It follows that partial solutions can be represented by a singleexponential (in the branchwidth k) number of configurations. This proves that, when applied on surface cut decompositions, dynamic programming runs in 2O(k) · n steps. That way, we considerably extend the class of problems that can be solved in running times with a singleexponential dependence on branchwidth and unify/improve most previous results in this direction.
20160505T11:09:58Z
Rué Perna, Juan José
Sau, Ignasi
Thilikos, Dimitrios
We provide a framework for the design and analysis of dynamic programming algorithms for surfaceembedded graphs on n vertices and branchwidth at most k. Our technique applies to general families of problems where standard dynamic programming runs in 2O(k·log k) · n steps. Our approach combines tools from topological graph theory and analytic combinatorics. In particular, we introduce a new type of branch decomposition called surface cut decomposition, generalizing sphere cut decompositions of planar graphs, which has nice combinatorial properties. Namely, the number of partial solutions that can be arranged on a surface cut decomposition can be upperbounded by the number of noncrossing partitions on surfaces with boundary. It follows that partial solutions can be represented by a singleexponential (in the branchwidth k) number of configurations. This proves that, when applied on surface cut decompositions, dynamic programming runs in 2O(k) · n steps. That way, we considerably extend the class of problems that can be solved in running times with a singleexponential dependence on branchwidth and unify/improve most previous results in this direction.

Viability of the matter bounce scenario in F(T) gravity and Loop Quantum Cosmology forgeneral potentials
http://hdl.handle.net/2117/86625
Viability of the matter bounce scenario in F(T) gravity and Loop Quantum Cosmology forgeneral potentials
Haro Cases, Jaume; Amorós Torrent, Jaume
We consider the matter bounce scenario in F (T) gravity and Loop Quantum Cosmology (LQC) for phenomenological potentials that at early times provide a nearly matter dominated Universe in the contracting phase, having a reheating mechanism in the expanding or contracting phase, i.e., being able to release the energy of the scalar field creating particles that thermalize in order to match with the hot Friedmann Universe, and finally at late times leading to the current cosmic acceleration. For these potentials, numerically solving the dynamical perturbation equations we have seen that, for the particular F (T) model that we will name tele parallelversion of LQC, and whose modified Friedmann equation coincides with the corresponding one in holonomy corrected LQC when one deals with the flat FriedmannLemai treRobertsonWalker (FLRW) geometry, the corresponding equations obtained from the well know perturbed equations in F (T) gravity lead to theoretical results that fit well with current observational data. More precisely, in this teleparallelversion of LQC there is a set of solutions which leads to theoretical results that match correctly with last BICEP2 data, and there is another set whose theoretical results fit well with Planck's experimental data. On the other hand, in the standard holonomy corrected LQC, using the perturbed equations obtained replacing the Ashtekar connection by a suitable sinus function and inserting some counterterms in order to preserve the algebra of constrains, the theoretical value of the tensor/scalar ratio is smaller than in the teleparallel version, which means that there is always a set of solutions that matches with Planck's data, but for some potentials BICEP2 experimental results disfavours holonomy corrected LQC.
20160505T10:27:44Z
Haro Cases, Jaume
Amorós Torrent, Jaume
We consider the matter bounce scenario in F (T) gravity and Loop Quantum Cosmology (LQC) for phenomenological potentials that at early times provide a nearly matter dominated Universe in the contracting phase, having a reheating mechanism in the expanding or contracting phase, i.e., being able to release the energy of the scalar field creating particles that thermalize in order to match with the hot Friedmann Universe, and finally at late times leading to the current cosmic acceleration. For these potentials, numerically solving the dynamical perturbation equations we have seen that, for the particular F (T) model that we will name tele parallelversion of LQC, and whose modified Friedmann equation coincides with the corresponding one in holonomy corrected LQC when one deals with the flat FriedmannLemai treRobertsonWalker (FLRW) geometry, the corresponding equations obtained from the well know perturbed equations in F (T) gravity lead to theoretical results that fit well with current observational data. More precisely, in this teleparallelversion of LQC there is a set of solutions which leads to theoretical results that match correctly with last BICEP2 data, and there is another set whose theoretical results fit well with Planck's experimental data. On the other hand, in the standard holonomy corrected LQC, using the perturbed equations obtained replacing the Ashtekar connection by a suitable sinus function and inserting some counterterms in order to preserve the algebra of constrains, the theoretical value of the tensor/scalar ratio is smaller than in the teleparallel version, which means that there is always a set of solutions that matches with Planck's data, but for some potentials BICEP2 experimental results disfavours holonomy corrected LQC.

How can holonomy corrections be introduced in f(R) gravity?
http://hdl.handle.net/2117/86623
How can holonomy corrections be introduced in f(R) gravity?
Haro Cases, Jaume
We study the introduction of holonomy corrections in f(R) gravity. We will show that there are infinitely many ways, as many as canonical transformations, to introduce this kind of corrections, depending on the canonical variables (two coordinates and its conjugate momenta) used to obtain the Hamiltonian. In each case, these corrections lead, at effective level, to different modified holonomycorrected Friedmann equations in f(R) gravity, which are in practice analytically unworkable, i.e. only numerical analysis can be used to understand its dynamics. In fact, there are infinitely many quantum theories, as many as canonical transformations, leading to different quantum cosmologies. Then, the problem is to know which of these quantum theories apply correctly to our Universe. We do not have an answer to this problem, and we could only give the following argument in favour of one preferred set of variables: the one that conformally maps f(R) to Einstein gravity, because for these variables the Hamiltonian of the system has the same form as in standard Loop Quantum Cosmology, which provides a map between the dynamics obtained in holonomycorrected f(R) gravity and the one of standard Loop Quantum Cosmology. © CopyrightEPLA, 2014.
20160505T10:19:37Z
Haro Cases, Jaume
We study the introduction of holonomy corrections in f(R) gravity. We will show that there are infinitely many ways, as many as canonical transformations, to introduce this kind of corrections, depending on the canonical variables (two coordinates and its conjugate momenta) used to obtain the Hamiltonian. In each case, these corrections lead, at effective level, to different modified holonomycorrected Friedmann equations in f(R) gravity, which are in practice analytically unworkable, i.e. only numerical analysis can be used to understand its dynamics. In fact, there are infinitely many quantum theories, as many as canonical transformations, leading to different quantum cosmologies. Then, the problem is to know which of these quantum theories apply correctly to our Universe. We do not have an answer to this problem, and we could only give the following argument in favour of one preferred set of variables: the one that conformally maps f(R) to Einstein gravity, because for these variables the Hamiltonian of the system has the same form as in standard Loop Quantum Cosmology, which provides a map between the dynamics obtained in holonomycorrected f(R) gravity and the one of standard Loop Quantum Cosmology. © CopyrightEPLA, 2014.

AARbased decomposition method for lowerbound limit analysis
http://hdl.handle.net/2117/86620
AARbased decomposition method for lowerbound limit analysis
Muñoz Romero, José; Rabiei, Syednima
Despite the recent progress in optimisation techniques, finiteelement stability analysis of realistic threedimensional problems is still hampered by the size of the resulting optimisation problem. Current solvers may take a prohibitive computational time, if they give a solution at all. The possible remedies to this are the design of adaptive deremeshing techniques, decomposition of the system of equations or of the optimisation problem. This paper concentrates on the last approach, and presents an algorithm especially suited for limit analysis. Optimisation problems in limit analysis are in general convex but nonlinear. This fact renders the design of decomposition techniques specially challenging. The efficiency of general approaches such as Benders or Dantzig–Wolfe is not always satisfactory, and strongly depends on the structure of the optimisation problem. This work presents a new method that is based on rewriting the feasibility region of the global optimisation problem as the intersection of two subsets. By resorting to the averaged alternating reflections (AAR) method in order to find the distance between the sets, the optimisation problem is successfully solved in a decomposed manner. Some representative examples illustrate the application of the method and its efficiency with respect to other wellknown decomposition algorithms.
20160505T08:50:31Z
Muñoz Romero, José
Rabiei, Syednima
Despite the recent progress in optimisation techniques, finiteelement stability analysis of realistic threedimensional problems is still hampered by the size of the resulting optimisation problem. Current solvers may take a prohibitive computational time, if they give a solution at all. The possible remedies to this are the design of adaptive deremeshing techniques, decomposition of the system of equations or of the optimisation problem. This paper concentrates on the last approach, and presents an algorithm especially suited for limit analysis. Optimisation problems in limit analysis are in general convex but nonlinear. This fact renders the design of decomposition techniques specially challenging. The efficiency of general approaches such as Benders or Dantzig–Wolfe is not always satisfactory, and strongly depends on the structure of the optimisation problem. This work presents a new method that is based on rewriting the feasibility region of the global optimisation problem as the intersection of two subsets. By resorting to the averaged alternating reflections (AAR) method in order to find the distance between the sets, the optimisation problem is successfully solved in a decomposed manner. Some representative examples illustrate the application of the method and its efficiency with respect to other wellknown decomposition algorithms.

Entrevista a Nuno Freitas, Premio José Luis Rubio de Francia 2014
http://hdl.handle.net/2117/86577
Entrevista a Nuno Freitas, Premio José Luis Rubio de Francia 2014
Alsina Aubach, Montserrat
20160504T14:09:14Z
Alsina Aubach, Montserrat

Perfect and quasiperfect domination in trees
http://hdl.handle.net/2117/86561
Perfect and quasiperfect domination in trees
Cáceres, José; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas, Maria Luz
A k quasip erfect dominating set of a connected graph G is a vertex subset S such that every vertex not in S is adjacent to at least one and at most k vertices in S . The cardinality of a minimum kquasip erfect dominating set in G is denoted by 1 k ( G ) . These graph parameters were rst intro duced by Chellali et al. (2013) as a generalization of b oth the p erfect domination numb er 11 ( G ) and the domination numb er ( G ) . The study of the socalled quasip erfect domination chain 11 ( G ) 12 ( G ) 1 ( G ) = ( G ) enable us to analyze how far minimum dominating sets are from b eing p erfect. In this pap er, we provide, for any tree T and any p ositive integer k , a tight upp er b ound of 1 k ( T ) . We also prove that there are trees satisfying all p ossible equalities and inequalities in this chain. Finally a linear algorithm for computing 1 k ( T ) in any tree T is presente
20160504T10:50:08Z
Cáceres, José
Hernando Martín, María del Carmen
Mora Giné, Mercè
Pelayo Melero, Ignacio Manuel
Puertas, Maria Luz
A k quasip erfect dominating set of a connected graph G is a vertex subset S such that every vertex not in S is adjacent to at least one and at most k vertices in S . The cardinality of a minimum kquasip erfect dominating set in G is denoted by 1 k ( G ) . These graph parameters were rst intro duced by Chellali et al. (2013) as a generalization of b oth the p erfect domination numb er 11 ( G ) and the domination numb er ( G ) . The study of the socalled quasip erfect domination chain 11 ( G ) 12 ( G ) 1 ( G ) = ( G ) enable us to analyze how far minimum dominating sets are from b eing p erfect. In this pap er, we provide, for any tree T and any p ositive integer k , a tight upp er b ound of 1 k ( T ) . We also prove that there are trees satisfying all p ossible equalities and inequalities in this chain. Finally a linear algorithm for computing 1 k ( T ) in any tree T is presente

Secular instability in the threebody problem
http://hdl.handle.net/2117/86530
Secular instability in the threebody problem
Fejoz, J.; Guàrdia Munarriz, Marcel
© 2016 European Union Consider the threebody problem, in the regime where one body revolves far away around the other two, in space, the masses of the bodies being arbitrary but fixed; in this regime, there are no resonances in mean motions. The socalled secular dynamics governs the slow evolution of the Keplerian ellipses. We show that it contains a horseshoe and all the chaotic dynamics which goes along with it, corresponding to motions along which the eccentricity of the inner ellipse undergoes large, random excursions. The proof goes through the surprisingly explicit computation of the homoclinic solution of the first order secular system, its complex singularities and the Melnikov potential.
20160503T11:49:55Z
Fejoz, J.
Guàrdia Munarriz, Marcel
© 2016 European Union Consider the threebody problem, in the regime where one body revolves far away around the other two, in space, the masses of the bodies being arbitrary but fixed; in this regime, there are no resonances in mean motions. The socalled secular dynamics governs the slow evolution of the Keplerian ellipses. We show that it contains a horseshoe and all the chaotic dynamics which goes along with it, corresponding to motions along which the eccentricity of the inner ellipse undergoes large, random excursions. The proof goes through the surprisingly explicit computation of the homoclinic solution of the first order secular system, its complex singularities and the Melnikov potential.

Oscillatory motions for the restricted planar circular three body problem
http://hdl.handle.net/2117/86502
Oscillatory motions for the restricted planar circular three body problem
Guàrdia Munarriz, Marcel; Martín, Pau; MartínezSeara Alonso, M. Teresa
© 2015, SpringerVerlag Berlin Heidelberg. The restricted three body problem models the motion of a massless body under the influence of the Newtonian gravitational force caused by two other bodies called the primaries. When they move along circular Keplerian orbits and the third body moves in the same plane, one has the restricted planar circular three body problem (RPC3BP). In suitable coordinates, it is a Hamiltonian system of two degrees of freedom. The conserved energy is usually called the Jacobi constant. Llibre and Simó [Math Ann 248(2):153–184, 1980] proved the existence of oscillatory motions for this system. That is, orbits which leave every bounded region but which return infinitely often to some fixed bounded region. To prove their existence they had to assume the ratio between the masses of the primaries to be small enough. In this paper we prove the existence of such motions for any value of the mass ratio(Formula presented.) closing the problem of existence of oscillatory motions in the RPC3BP. To obtain such motions, we restrict ourselves to the level sets of the Jacobi constant. We show that, for any value of the mass ratio and for large values of the Jacobi constant, there exist transversal intersections between the stable and unstable manifolds of infinity in these level sets. These transversal intersections guarantee the existence of a symbolic dynamics that creates the oscillatory orbits. The main achievement is to prove the existence of these orbits without assuming the mass ratio (Formula presented.) small. When (Formula presented.) is not small, this transversality can not be checked by means of classical perturbation theory. Since our method is valid for all values of v, we are able to detect a curve in the parameter space, formed by (Formula presented.) and the Jacobi constant, where cubic homoclinic tangencies between the invariant manifolds of infinity appear.
20160502T17:44:48Z
Guàrdia Munarriz, Marcel
Martín, Pau
MartínezSeara Alonso, M. Teresa
© 2015, SpringerVerlag Berlin Heidelberg. The restricted three body problem models the motion of a massless body under the influence of the Newtonian gravitational force caused by two other bodies called the primaries. When they move along circular Keplerian orbits and the third body moves in the same plane, one has the restricted planar circular three body problem (RPC3BP). In suitable coordinates, it is a Hamiltonian system of two degrees of freedom. The conserved energy is usually called the Jacobi constant. Llibre and Simó [Math Ann 248(2):153–184, 1980] proved the existence of oscillatory motions for this system. That is, orbits which leave every bounded region but which return infinitely often to some fixed bounded region. To prove their existence they had to assume the ratio between the masses of the primaries to be small enough. In this paper we prove the existence of such motions for any value of the mass ratio(Formula presented.) closing the problem of existence of oscillatory motions in the RPC3BP. To obtain such motions, we restrict ourselves to the level sets of the Jacobi constant. We show that, for any value of the mass ratio and for large values of the Jacobi constant, there exist transversal intersections between the stable and unstable manifolds of infinity in these level sets. These transversal intersections guarantee the existence of a symbolic dynamics that creates the oscillatory orbits. The main achievement is to prove the existence of these orbits without assuming the mass ratio (Formula presented.) small. When (Formula presented.) is not small, this transversality can not be checked by means of classical perturbation theory. Since our method is valid for all values of v, we are able to detect a curve in the parameter space, formed by (Formula presented.) and the Jacobi constant, where cubic homoclinic tangencies between the invariant manifolds of infinity appear.

El impacto de las políticas de evaluación del profesorado en la posición en los ránquines universitarios: el caso de la Universidad Politécnica de Cataluña
http://hdl.handle.net/2117/86427
El impacto de las políticas de evaluación del profesorado en la posición en los ránquines universitarios: el caso de la Universidad Politécnica de Cataluña
GarcíaBerro Montilla, Enrique; Roca Martín, Santiago; Navallas Ramos, Francisco Javier; Soriano Ibáñez, Miguel; Ras Sabido, Antoni
La universidad española ha afrontado con éxito el tránsito entre una universidad clásica, eminentemente docente, y una universidad moderna, en la que la investigación juega un papel esencial. Gran parte de este éxito reside en la instauración de sistemas de evaluación. No obstante, a pesar de los indiscutibles logros, aún queda un camino importante por recorrer para situarla en los lugares que le corresponden en las clasificaciones internacionales por el lugar que ocupamos dentro de los países de nuestro entorno. La Universidad Politécnica de Cataluña dispone de un modelo de evaluación docente, así como de información sobre la actividad investigadora del profesorado. Ello ha permitido implementar un modelo de evaluación global, que presentamos en este artículo. Asimismo, usando una muestra de 4.996 evaluaciones individuales de unos 1.700 profesores, analizamos la evolución temporal de las evaluaciones de los años 2011, 2012 y 2013, estudiamos si existen diferencias entre los ámbitos de conocimiento y examinamos si existe una relación entre la productividad académica así evaluada y la posición de la universidad en los ránquines universitarios. Los datos de este estudio corroboran que el modelo ha tenido éxito, al haber permitido que la universidad progresara en el ranquin Quacquarelli Symonds del puesto 350 al 337.
Spanish universities have moved from a classical model, a teaching university, to a modern one, in which research is essential. Part of this success is due to the implementation of quality assessment policies. Nonetheless, and in spite of this, there is still a long way to place it at the level of similar countries in university rankings. The Universidad Politécnica de Cataluña has an evaluation model of the teaching performance of its staff, and also abundant information of their research. This has allowed implementing a global evaluation model. Here we present the evaluation model. Also, using 4,996 individual evaluations corresponding to about 1,700 academic staff members we analyze the evolution of the results of the evaluations of years 2011, 2012 and 2013, we study if there are differences among the various academic fields, and we examine if there exists a correlation between the evolution of the academic productivity measured using this model and the position of the university in the university rankings. We show that this model has allowed the university to improve its classification in the Quacquarelli Symonds Top University Ranking, from position 350 to 337.
20160429T12:32:32Z
GarcíaBerro Montilla, Enrique
Roca Martín, Santiago
Navallas Ramos, Francisco Javier
Soriano Ibáñez, Miguel
Ras Sabido, Antoni
La universidad española ha afrontado con éxito el tránsito entre una universidad clásica, eminentemente docente, y una universidad moderna, en la que la investigación juega un papel esencial. Gran parte de este éxito reside en la instauración de sistemas de evaluación. No obstante, a pesar de los indiscutibles logros, aún queda un camino importante por recorrer para situarla en los lugares que le corresponden en las clasificaciones internacionales por el lugar que ocupamos dentro de los países de nuestro entorno. La Universidad Politécnica de Cataluña dispone de un modelo de evaluación docente, así como de información sobre la actividad investigadora del profesorado. Ello ha permitido implementar un modelo de evaluación global, que presentamos en este artículo. Asimismo, usando una muestra de 4.996 evaluaciones individuales de unos 1.700 profesores, analizamos la evolución temporal de las evaluaciones de los años 2011, 2012 y 2013, estudiamos si existen diferencias entre los ámbitos de conocimiento y examinamos si existe una relación entre la productividad académica así evaluada y la posición de la universidad en los ránquines universitarios. Los datos de este estudio corroboran que el modelo ha tenido éxito, al haber permitido que la universidad progresara en el ranquin Quacquarelli Symonds del puesto 350 al 337.
Spanish universities have moved from a classical model, a teaching university, to a modern one, in which research is essential. Part of this success is due to the implementation of quality assessment policies. Nonetheless, and in spite of this, there is still a long way to place it at the level of similar countries in university rankings. The Universidad Politécnica de Cataluña has an evaluation model of the teaching performance of its staff, and also abundant information of their research. This has allowed implementing a global evaluation model. Here we present the evaluation model. Also, using 4,996 individual evaluations corresponding to about 1,700 academic staff members we analyze the evolution of the results of the evaluations of years 2011, 2012 and 2013, we study if there are differences among the various academic fields, and we examine if there exists a correlation between the evolution of the academic productivity measured using this model and the position of the university in the university rankings. We show that this model has allowed the university to improve its classification in the Quacquarelli Symonds Top University Ranking, from position 350 to 337.

Polygons as sections of higherdimensional polytopes
http://hdl.handle.net/2117/86389
Polygons as sections of higherdimensional polytopes
Padrol Sureda, Arnau; Pfeifle, Julián
We show that every heptagon is a section of a 3polytope with 6 vertices. This implies that every ngon with n >= 7 can be obtained as a section of a (2 + [n/7])dimensional polytope with at most [6n/7] vertices; and provides a geometric proof of the fact that every nonnegative n x rn matrix of rank 3 has nonnegative rank not larger than [6min(n,m)/7]. This result has been independently proved, algebraically, by Shitov (J. Combin. Theory Ser. A 122, 2014).
20160428T14:55:10Z
Padrol Sureda, Arnau
Pfeifle, Julián
We show that every heptagon is a section of a 3polytope with 6 vertices. This implies that every ngon with n >= 7 can be obtained as a section of a (2 + [n/7])dimensional polytope with at most [6n/7] vertices; and provides a geometric proof of the fact that every nonnegative n x rn matrix of rank 3 has nonnegative rank not larger than [6min(n,m)/7]. This result has been independently proved, algebraically, by Shitov (J. Combin. Theory Ser. A 122, 2014).