Reports de recerca
http://hdl.handle.net/2117/3919
Sat, 30 Apr 2016 15:18:40 GMT2016-04-30T15:18:40ZSEPsFLAREs: Executive Summary
http://hdl.handle.net/2117/86424
SEPsFLAREs: Executive Summary
Nuñez, Marlon; Qahwaji, Rami; Ashamari, Omar W; García Rigo, Alberto; Hernández Pajares, Manuel
Fri, 29 Apr 2016 11:08:39 GMThttp://hdl.handle.net/2117/864242016-04-29T11:08:39ZNuñez, MarlonQahwaji, RamiAshamari, Omar WGarcía Rigo, AlbertoHernández Pajares, ManuelMinimal representations for majority games
http://hdl.handle.net/2117/86215
Minimal representations for majority games
Freixas Bosch, Josep; Molinero Albareda, Xavier; Roura Ferret, Salvador
This paper presents some new results about majority games. Isbell (1959) was the first to find a majority game without a minimum normalized representation; he needed 12 voters to construct such a game. Since then, it has been an open problem to find the minimum number of voters of a majority game without a minimum normalized representation. Our main new results are: 1. All majority games with less than 9 voters have a minimum representation. 2. For 9 voters there are 14 majority games without a minimum integer representation, but these games admit a minimal normalized integer representation. 3. For 10 voters exist majority games with neither a minimum integer representation nor a minimal normalized integer representation.
Wed, 27 Apr 2016 07:22:54 GMThttp://hdl.handle.net/2117/862152016-04-27T07:22:54ZFreixas Bosch, JosepMolinero Albareda, XavierRoura Ferret, SalvadorThis paper presents some new results about majority games. Isbell (1959) was the first to find a majority game without a minimum normalized representation; he needed 12 voters to construct such a game. Since then, it has been an open problem to find the minimum number of voters of a majority game without a minimum normalized representation. Our main new results are: 1. All majority games with less than 9 voters have a minimum representation. 2. For 9 voters there are 14 majority games without a minimum integer representation, but these games admit a minimal normalized integer representation. 3. For 10 voters exist majority games with neither a minimum integer representation nor a minimal normalized integer representation.Higher education in Spain
http://hdl.handle.net/2117/86167
Higher education in Spain
Romero Sánchez, Jesús; Juan Zornoza, José Miguel; Sanz Subirana, Jaume
Mon, 25 Apr 2016 17:08:07 GMThttp://hdl.handle.net/2117/861672016-04-25T17:08:07ZRomero Sánchez, JesúsJuan Zornoza, José MiguelSanz Subirana, JaumeExponentially small splitting of separatrices and transversality associated to whiskered tori with quadratic frequency ratio
http://hdl.handle.net/2117/85283
Exponentially small splitting of separatrices and transversality associated to whiskered tori with quadratic frequency ratio
Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere
The splitting of invariant manifolds of whiskered (hyperbolic) tori with two frequencies in a nearly-integrable
Hamiltonian system, whose hyperbolic part is given by a pendulum, is studied.
Wed, 06 Apr 2016 10:18:30 GMThttp://hdl.handle.net/2117/852832016-04-06T10:18:30ZDelshams Valdés, AmadeuGonchenko, MarinaGutiérrez Serrés, PereThe splitting of invariant manifolds of whiskered (hyperbolic) tori with two frequencies in a nearly-integrable
Hamiltonian system, whose hyperbolic part is given by a pendulum, is studied.Examples of integrable and non-integrable systems on singular symplectic manifolds
http://hdl.handle.net/2117/85177
Examples of integrable and non-integrable systems on singular symplectic manifolds
Delshams Valdés, Amadeu; Miranda Galcerán, Eva; Kiesenhofer, Anna
We present a collection of examples borrowed from celes- tial mechanics and projective dynamics. In these examples symplectic structures with singularities arise naturally from regularization trans- formations, Appell's transformation or classical changes like McGehee coordinates, which end up blowing up the symplectic structure or lower- ing its rank at certain points. The resulting geometrical structures that model these examples are no longer symplectic but symplectic with sin- gularities which are mainly of two types: b m -symplectic and m -folded symplectic structures. These examples comprise the three body prob- lem as non-integrable exponent and some integrable reincarnations such as the two xed-center problem. Given that the geometrical and dy- namical properties of b m -symplectic manifolds and folded symplectic manifolds are well-understood [GMP, GMP2, GMPS, KMS, Ma, CGP, GL, GLPR, MO, S, GMW], we envisage that this new point of view in this collection of examples can shed some light on classical long-standing problems concerning the study of dynamical properties of these systems seen from the Poisson viewpoint.
Tue, 05 Apr 2016 09:58:51 GMThttp://hdl.handle.net/2117/851772016-04-05T09:58:51ZDelshams Valdés, AmadeuMiranda Galcerán, EvaKiesenhofer, AnnaWe present a collection of examples borrowed from celes- tial mechanics and projective dynamics. In these examples symplectic structures with singularities arise naturally from regularization trans- formations, Appell's transformation or classical changes like McGehee coordinates, which end up blowing up the symplectic structure or lower- ing its rank at certain points. The resulting geometrical structures that model these examples are no longer symplectic but symplectic with sin- gularities which are mainly of two types: b m -symplectic and m -folded symplectic structures. These examples comprise the three body prob- lem as non-integrable exponent and some integrable reincarnations such as the two xed-center problem. Given that the geometrical and dy- namical properties of b m -symplectic manifolds and folded symplectic manifolds are well-understood [GMP, GMP2, GMPS, KMS, Ma, CGP, GL, GLPR, MO, S, GMW], we envisage that this new point of view in this collection of examples can shed some light on classical long-standing problems concerning the study of dynamical properties of these systems seen from the Poisson viewpoint.Self-organization and evolution on large computer data structures
http://hdl.handle.net/2117/84913
Self-organization and evolution on large computer data structures
Gabarró Vallès, Joaquim; Roselló Saurí, Llorenç
We study the long time evolution of a large data structure
while inserting new items.
It is implemented using a well
known computer science approach based on 2-3 trees.
We have seen self-organized critical behavior on this data structure.
To tackle this problem we have introduced and
studied experimentally three statistical magnitudes: the stress of a
tree, the sequence of jump points and the distribution of subtrees
inside a tree.
The stress measures the amount of free space inside the 2-3 tree. When
the stress increases some part of the tree is restructured in a way
close to an avalanche. Experimentally we obtain a potential law for
stress distribution. When the tree does not have more free space in
any internal node, needs to grow up. When this happens, the height of
the whole tree increases by one and we have a jump
point. Experimentally these points have good expected behavior.A 2-3
tree is composed from a great number of other 2-3 trees called their
subtrees. We have studied experimentally the distribution of the
different subtrees inside the tree.
Finally we analyze these results using simple theoretical models
based on fringe analysis, Markov and branching processes.
These models give us a quite good description of the long term
process.
Wed, 30 Mar 2016 16:51:44 GMThttp://hdl.handle.net/2117/849132016-03-30T16:51:44ZGabarró Vallès, JoaquimRoselló Saurí, LlorençWe study the long time evolution of a large data structure
while inserting new items.
It is implemented using a well
known computer science approach based on 2-3 trees.
We have seen self-organized critical behavior on this data structure.
To tackle this problem we have introduced and
studied experimentally three statistical magnitudes: the stress of a
tree, the sequence of jump points and the distribution of subtrees
inside a tree.
The stress measures the amount of free space inside the 2-3 tree. When
the stress increases some part of the tree is restructured in a way
close to an avalanche. Experimentally we obtain a potential law for
stress distribution. When the tree does not have more free space in
any internal node, needs to grow up. When this happens, the height of
the whole tree increases by one and we have a jump
point. Experimentally these points have good expected behavior.A 2-3
tree is composed from a great number of other 2-3 trees called their
subtrees. We have studied experimentally the distribution of the
different subtrees inside the tree.
Finally we analyze these results using simple theoretical models
based on fringe analysis, Markov and branching processes.
These models give us a quite good description of the long term
process.El Producte lexicogràfic i el producte boustrofedònic
http://hdl.handle.net/2117/84385
El Producte lexicogràfic i el producte boustrofedònic
Molinero Albareda, Xavier
Given a class of combinatorial structures A, a fixed
size n and considering a total order previously defined,
the unrank function gives us the i-th object of
A of size n. We are going to study the average cost of
unrank function when we use the lexicographic or boustrophedonic
product. We will prove that the boustrophedonic product is
theoretically and experimentally better in average cost than
the lexicographic product.
Tue, 15 Mar 2016 13:41:31 GMThttp://hdl.handle.net/2117/843852016-03-15T13:41:31ZMolinero Albareda, XavierGiven a class of combinatorial structures A, a fixed
size n and considering a total order previously defined,
the unrank function gives us the i-th object of
A of size n. We are going to study the average cost of
unrank function when we use the lexicographic or boustrophedonic
product. We will prove that the boustrophedonic product is
theoretically and experimentally better in average cost than
the lexicographic product.Homotopy linear algebra
http://hdl.handle.net/2117/84108
Homotopy linear algebra
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew
By homotopy linear algebra we mean the study of linear functors between slices of the 8-category of 8-groupoids, subject to certain finiteness conditions. After some standard definitions and results, we assemble said slices into 8-categories to model the duality between vector spaces and profinite-dimensional vector spaces, and set up a global notion of homotopy cardinality \`a la Baez-Hoffnung-Walker compatible with this duality. We needed these results to support our work on incidence algebras and M\
arXiv:1602.05082 [math.CT]
Thu, 10 Mar 2016 09:34:54 GMThttp://hdl.handle.net/2117/841082016-03-10T09:34:54ZGálvez Carrillo, Maria ImmaculadaKock, JoachimTonks, AndrewBy homotopy linear algebra we mean the study of linear functors between slices of the 8-category of 8-groupoids, subject to certain finiteness conditions. After some standard definitions and results, we assemble said slices into 8-categories to model the duality between vector spaces and profinite-dimensional vector spaces, and set up a global notion of homotopy cardinality \`a la Baez-Hoffnung-Walker compatible with this duality. We needed these results to support our work on incidence algebras and M\Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals
http://hdl.handle.net/2117/84104
Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew
Decomposition spaces are simplicial 8-groupoids subject to a certain exactness condition, needed to induce a coalgebra structure on the space of arrows. Conservative ULF functors between decomposition spaces induce coalgebra homomorphisms. Suitable added finiteness conditions define the notion of Möbius decomposition space, a far-reaching generalisation of the notion of Möbius category of Leroux. In this paper, we show that the Lawvere-Menni Hopf algebra of Möbius intervals, which contains the universal Möbius function (but is not induced by a Möbius category), can be realised as the homotopy cardinality of a Möbius decomposition space U of all Möbius intervals, and that in a certain sense U is universal
Thu, 10 Mar 2016 09:18:11 GMThttp://hdl.handle.net/2117/841042016-03-10T09:18:11ZGálvez Carrillo, Maria ImmaculadaKock, JoachimTonks, AndrewDecomposition spaces are simplicial 8-groupoids subject to a certain exactness condition, needed to induce a coalgebra structure on the space of arrows. Conservative ULF functors between decomposition spaces induce coalgebra homomorphisms. Suitable added finiteness conditions define the notion of Möbius decomposition space, a far-reaching generalisation of the notion of Möbius category of Leroux. In this paper, we show that the Lawvere-Menni Hopf algebra of Möbius intervals, which contains the universal Möbius function (but is not induced by a Möbius category), can be realised as the homotopy cardinality of a Möbius decomposition space U of all Möbius intervals, and that in a certain sense U is universalDecomposition spaces, incidence algebras and Möbius inversion II: completeness, length filtration, and finiteness
http://hdl.handle.net/2117/84103
Decomposition spaces, incidence algebras and Möbius inversion II: completeness, length filtration, and finiteness
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew
This is part 2 of a trilogy of papers introducing and studying the notion of decomposition space as a general framework for incidence algebras and Möbius inversion, with coefficients in 8-groupoids. A decomposition space is a simplicial 8-groupoid satisfying an exactness condition weaker than the Segal condition. Just as the Segal condition expresses up-to-homotopy composition, the new condition expresses decomposition.
In this paper, we introduce various technical conditions on decomposition spaces. The first is a completeness condition (weaker than Rezk completeness), needed to control non-degeneracy. For complete decomposition spaces we establish a general Möbius inversion principle, expressed as an explicit equivalence of 8-groupoids.
Next we analyse two finiteness conditions on decomposition spaces. The first, that of locally finite length, guarantees the existence of the important length filtration on the associated incidence coalgebra. We show that a decomposition space of locally finite length is actually the left Kan extension of a semi-simplicial space. The second condition, local finiteness, ensures we can take homotopy cardinality to pass from the level of 8-groupoids to the level of vector spaces.
These three conditions - completeness, locally finite length and local finiteness - together define our notion of Möbius decomposition space, which extends Leroux's notion of Möbius category (in turn a common generalisation of the locally finite posets of Rota et al. and of the finite decomposition monoids of Cartier-Foata), but which also covers many coalgebra constructions which do not arise from Möbius categories, such as the Fa\`a di Bruno and Connes-Kreimer bialgebras.
Thu, 10 Mar 2016 09:06:55 GMThttp://hdl.handle.net/2117/841032016-03-10T09:06:55ZGálvez Carrillo, Maria ImmaculadaKock, JoachimTonks, AndrewThis is part 2 of a trilogy of papers introducing and studying the notion of decomposition space as a general framework for incidence algebras and Möbius inversion, with coefficients in 8-groupoids. A decomposition space is a simplicial 8-groupoid satisfying an exactness condition weaker than the Segal condition. Just as the Segal condition expresses up-to-homotopy composition, the new condition expresses decomposition.
In this paper, we introduce various technical conditions on decomposition spaces. The first is a completeness condition (weaker than Rezk completeness), needed to control non-degeneracy. For complete decomposition spaces we establish a general Möbius inversion principle, expressed as an explicit equivalence of 8-groupoids.
Next we analyse two finiteness conditions on decomposition spaces. The first, that of locally finite length, guarantees the existence of the important length filtration on the associated incidence coalgebra. We show that a decomposition space of locally finite length is actually the left Kan extension of a semi-simplicial space. The second condition, local finiteness, ensures we can take homotopy cardinality to pass from the level of 8-groupoids to the level of vector spaces.
These three conditions - completeness, locally finite length and local finiteness - together define our notion of Möbius decomposition space, which extends Leroux's notion of Möbius category (in turn a common generalisation of the locally finite posets of Rota et al. and of the finite decomposition monoids of Cartier-Foata), but which also covers many coalgebra constructions which do not arise from Möbius categories, such as the Fa\`a di Bruno and Connes-Kreimer bialgebras.