Departament de Matemàtiques
http://hdl.handle.net/2117/3917
20160505T23:59:55Z

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.

Triangles in random cubic planar graphs
http://hdl.handle.net/2117/86630
Triangles in random cubic planar graphs
Requilé, Clément; Rué Perna, Juan José
In this extended abstract we determine a normal limiting distribution for the number of triangles in a uniformly at random 3connected cubic planar graph, as well as the precise expectation and variance values. Further comments towards the more complicated problem of studying both the limiting distribution of triangles in random cubic planar graphs, and the (asymptotic) number of trianglefree cubic planar graphs are discussed as well.
20160505T10:58:29Z
Requilé, Clément
Rué Perna, Juan José
In this extended abstract we determine a normal limiting distribution for the number of triangles in a uniformly at random 3connected cubic planar graph, as well as the precise expectation and variance values. Further comments towards the more complicated problem of studying both the limiting distribution of triangles in random cubic planar graphs, and the (asymptotic) number of trianglefree cubic planar graphs are discussed as well.

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.

SEPsFLAREs: 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
20160504T17:19:50Z
García Rigo, Alberto
Hernández Pajares, Manuel
Nuñez, Marlon
Qahwaji, Rami
Ashamari, Omar W

SEPsFLAREs: 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
20160504T17:08:46Z
García Rigo, Alberto
Hernández Pajares, Manuel
Nuñez, Marlon
Qahwaji, Rami
Ashamari, Omar W

SEPsFLAREs: Technical Specification
http://hdl.handle.net/2117/86607
SEPsFLAREs: Technical Specification
García Rigo, Alberto; Hernández Pajares, Manuel; Nuñez, Marlon; Qahwaji, Rami; Ashamari, Omar W
20160504T16:56:38Z
García Rigo, Alberto
Hernández Pajares, Manuel
Nuñez, Marlon
Qahwaji, Rami
Ashamari, Omar W

SEPsFLAREs: Migration File (MFv2)
http://hdl.handle.net/2117/86605
SEPsFLAREs: Migration File (MFv2)
Pérez, Gustau; García Rigo, Alberto; Hernández Pajares, Manuel
20160504T16:41:17Z
Pérez, Gustau
García Rigo, Alberto
Hernández Pajares, Manuel

SEPsFLAREs: Final Report
http://hdl.handle.net/2117/86604
SEPsFLAREs: Final Report
Nuñez, Marlon; Qahwaji, Rami; Ashamari, Omar W; García Rigo, Alberto; Hernández Pajares, Manuel
20160504T16:24:00Z
Nuñez, Marlon
Qahwaji, Rami
Ashamari, Omar W
García Rigo, Alberto
Hernández Pajares, Manuel