Reports de recerca
http://hdl.handle.net/2117/3919
Thu, 30 Mar 2017 22:35:36 GMT2017-03-30T22:35:36ZReport on the EGNSS competition after Y1
http://hdl.handle.net/2117/102717
Report on the EGNSS competition after Y1
Sanz Subirana, Jaume; Juan Zornoza, José Miguel; Alonso Alonso, María Teresa
Tue, 21 Mar 2017 10:30:26 GMThttp://hdl.handle.net/2117/1027172017-03-21T10:30:26ZSanz Subirana, JaumeJuan Zornoza, José MiguelAlonso Alonso, María TeresaDecomposition spaces in combinatorics
http://hdl.handle.net/2117/102202
Decomposition spaces in combinatorics
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew
A decomposition space (also called unital 2-Segal space) is a simplicial object satisfying an exactness condition weaker than the Segal condition: just as the Segal condition expresses (up to homotopy) composition, the new condition expresses decomposition. It is a general framework for incidence (co)algebras. In the present contribution, after establishing a formula for the section coefficients, we survey a large supply of examples, emphasising the notion's firm roots in classical combinatorics. The first batch of examples, similar to binomial posets, serves to illustrate two key points: (1) the incidence algebra in question is realised directly from a decomposition space, without a reduction step, and reductions are often given by CULF functors; (2) at the objective level, the convolution algebra is a monoidal structure of species. Specifically, we encounter the usual Cauchy product of species, the shuffle product of L-species, the Dirichlet product of arithmetic species, the Joyal-Street external product of q-species and the Morrison `Cauchy' product of q-species, and in each case a power series representation results from taking cardinality. The external product of q-species exemplifies the fact that Waldhausen's S-construction on an abelian category is a decomposition space, yielding Hall algebras. The next class of examples includes Schmitt's chromatic Hopf algebra, the Fa\`a di Bruno bialgebra, the Butcher-Connes-Kreimer Hopf algebra of trees and several variations from operad theory. Similar structures on posets and directed graphs exemplify a general construction of decomposition spaces from directed restriction species. We finish by computing the M\
Thu, 09 Mar 2017 13:10:06 GMThttp://hdl.handle.net/2117/1022022017-03-09T13:10:06ZGálvez Carrillo, Maria ImmaculadaKock, JoachimTonks, AndrewA decomposition space (also called unital 2-Segal space) is a simplicial object satisfying an exactness condition weaker than the Segal condition: just as the Segal condition expresses (up to homotopy) composition, the new condition expresses decomposition. It is a general framework for incidence (co)algebras. In the present contribution, after establishing a formula for the section coefficients, we survey a large supply of examples, emphasising the notion's firm roots in classical combinatorics. The first batch of examples, similar to binomial posets, serves to illustrate two key points: (1) the incidence algebra in question is realised directly from a decomposition space, without a reduction step, and reductions are often given by CULF functors; (2) at the objective level, the convolution algebra is a monoidal structure of species. Specifically, we encounter the usual Cauchy product of species, the shuffle product of L-species, the Dirichlet product of arithmetic species, the Joyal-Street external product of q-species and the Morrison `Cauchy' product of q-species, and in each case a power series representation results from taking cardinality. The external product of q-species exemplifies the fact that Waldhausen's S-construction on an abelian category is a decomposition space, yielding Hall algebras. The next class of examples includes Schmitt's chromatic Hopf algebra, the Fa\`a di Bruno bialgebra, the Butcher-Connes-Kreimer Hopf algebra of trees and several variations from operad theory. Similar structures on posets and directed graphs exemplify a general construction of decomposition spaces from directed restriction species. We finish by computing the M\Three Hopf algebras and their common simplicial and categorical background
http://hdl.handle.net/2117/102199
Three Hopf algebras and their common simplicial and categorical background
Gálvez Carrillo, Maria Immaculada; Kaufmann, Ralph L.; Tonks, Andrew
We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebras of Goncharov for multiple zeta values, that of Connes--Kreimer for renormalization, and a Hopf algebra constructed by Baues to study double loop spaces. We show that these examples can be successively unified by considering simplicial objects, cooperads with multiplication and Feynman categories at the ultimate level. These considerations open the door to new constructions and reinterpretation of known constructions in a large common framework
Thu, 09 Mar 2017 12:51:30 GMThttp://hdl.handle.net/2117/1021992017-03-09T12:51:30ZGálvez Carrillo, Maria ImmaculadaKaufmann, Ralph L.Tonks, AndrewWe consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebras of Goncharov for multiple zeta values, that of Connes--Kreimer for renormalization, and a Hopf algebra constructed by Baues to study double loop spaces. We show that these examples can be successively unified by considering simplicial objects, cooperads with multiplication and Feynman categories at the ultimate level. These considerations open the door to new constructions and reinterpretation of known constructions in a large common frameworkMeasuring satisfaction in societies with opinion leaders and mediators
http://hdl.handle.net/2117/101810
Measuring satisfaction in societies with opinion leaders and mediators
Molinero Albareda, Xavier; Riquelme Csori, F.; Serna Iglesias, María José
An opinion leader-follower model (OLF) is a two-action collective decision-making model for societies, in which three kinds of actors are considered:
Wed, 01 Mar 2017 16:19:14 GMThttp://hdl.handle.net/2117/1018102017-03-01T16:19:14ZMolinero Albareda, XavierRiquelme Csori, F.Serna Iglesias, María JoséAn opinion leader-follower model (OLF) is a two-action collective decision-making model for societies, in which three kinds of actors are considered:Sullivan minimal models of operad algebras
http://hdl.handle.net/2117/101791
Sullivan minimal models of operad algebras
Roig Martí, Agustín; Cirici, Joana
We prove the existence of Sullivan minimal models of operad algebras, for a quite wide family of operads in the category of complexes of vector spaces over a field of characteristic zero. Our construction is an adaptation of Sullivan’s original step by step construction to the setting of operad algebras. The family of operads that we consider includes all operads concentrated in degree 0 as well as their minimal models. In particular, this gives Sullivan minimal models for algebras over Com, Ass and Lie, as well as over their minimal models Com8, Ass8 and Lie8. Other interesting operads, such as the operad Ger encoding Gerstenhaber algebras, also fit in our study.
preprint
Wed, 01 Mar 2017 12:38:54 GMThttp://hdl.handle.net/2117/1017912017-03-01T12:38:54ZRoig Martí, AgustínCirici, JoanaWe prove the existence of Sullivan minimal models of operad algebras, for a quite wide family of operads in the category of complexes of vector spaces over a field of characteristic zero. Our construction is an adaptation of Sullivan’s original step by step construction to the setting of operad algebras. The family of operads that we consider includes all operads concentrated in degree 0 as well as their minimal models. In particular, this gives Sullivan minimal models for algebras over Com, Ass and Lie, as well as over their minimal models Com8, Ass8 and Lie8. Other interesting operads, such as the operad Ger encoding Gerstenhaber algebras, also fit in our study.On (non-)exponential decay in generalized thermoelasticity with two temperatures
http://hdl.handle.net/2117/98756
On (non-)exponential decay in generalized thermoelasticity with two temperatures
Leseduarte Milán, María Carme; Quintanilla de Latorre, Ramón; Racke, Reinhard
We study solutions for the one-dimensional problem of the Green-Lindsay and the Lord-Shulman theories with two temperatures. First, existence and uniqueness of weakly regular solutions are obtained. Second, we prove the exponential stability in the Green-Lindsay model, but the nonexponential
stability for the Lord-Shulman model
Konstanzer Schriften in Mathematik ; 355
Thu, 22 Dec 2016 11:55:43 GMThttp://hdl.handle.net/2117/987562016-12-22T11:55:43ZLeseduarte Milán, María CarmeQuintanilla de Latorre, RamónRacke, ReinhardWe study solutions for the one-dimensional problem of the Green-Lindsay and the Lord-Shulman theories with two temperatures. First, existence and uniqueness of weakly regular solutions are obtained. Second, we prove the exponential stability in the Green-Lindsay model, but the nonexponential
stability for the Lord-Shulman modelConnected and internal graph searching
http://hdl.handle.net/2117/97422
Connected and internal graph searching
Barrière Figueroa, Eulalia; Fraigniaud, Pierre; Santoro, Nicola; Thilikos Touloupas, Dimitrios
This paper is concerned with the graph searching game. The search number es(G) of a graph G is the smallest number of searchers required to clear G. A search strategy is monotone (m) if no recontamination ever occurs. It is connected (c) if the set of clear edges always forms a connected subgraph. It is internal (i) if the removal of searchers is not allowed. The difficulty of the connected version and of the monotone internal version of the graph searching problem comes from the fact that, as shown in the paper, none of these problems is minor closed for arbitrary graphs, as opposed to all known variants of the graph searching problem. Motivated by the fact that connected graph searching, and monotone internal graph searching are both minor closed in trees, we provide a complete characterization of the set of trees that can be cleared by a given number of searchers. In fact, we show that, in trees, there is only one obstruction for monotone internal search, as well as for connected search, and this obstruction is the same for the two problems. This allows us to prove that, for any tree T, mis(T)= cs(T). For arbitrary graphs, we prove that there is a unique chain of inequalities linking all the search numbers above. More precisely, for any graph G, es(G)= is(G)= ms(G)leq mis(G)leq cs(G)= ics(G)leq mcs(G)=mics(G). The first two inequalities can be strict. In the case of trees, we have mics(G)leq 2 es(T)-2, that is there are exactly 2 different search numbers in trees, and these search numbers differ by a factor of 2 at most.
Tue, 29 Nov 2016 13:30:39 GMThttp://hdl.handle.net/2117/974222016-11-29T13:30:39ZBarrière Figueroa, EulaliaFraigniaud, PierreSantoro, NicolaThilikos Touloupas, DimitriosThis paper is concerned with the graph searching game. The search number es(G) of a graph G is the smallest number of searchers required to clear G. A search strategy is monotone (m) if no recontamination ever occurs. It is connected (c) if the set of clear edges always forms a connected subgraph. It is internal (i) if the removal of searchers is not allowed. The difficulty of the connected version and of the monotone internal version of the graph searching problem comes from the fact that, as shown in the paper, none of these problems is minor closed for arbitrary graphs, as opposed to all known variants of the graph searching problem. Motivated by the fact that connected graph searching, and monotone internal graph searching are both minor closed in trees, we provide a complete characterization of the set of trees that can be cleared by a given number of searchers. In fact, we show that, in trees, there is only one obstruction for monotone internal search, as well as for connected search, and this obstruction is the same for the two problems. This allows us to prove that, for any tree T, mis(T)= cs(T). For arbitrary graphs, we prove that there is a unique chain of inequalities linking all the search numbers above. More precisely, for any graph G, es(G)= is(G)= ms(G)leq mis(G)leq cs(G)= ics(G)leq mcs(G)=mics(G). The first two inequalities can be strict. In the case of trees, we have mics(G)leq 2 es(T)-2, that is there are exactly 2 different search numbers in trees, and these search numbers differ by a factor of 2 at most.Unranking of combinatorial structures
http://hdl.handle.net/2117/97301
Unranking of combinatorial structures
Molinero Albareda, Xavier
The present work is a study of the deterministic generation of
combinatorial structures. We generate classes of combinatorial
structures formally specifiable by grammars involving unlabelled
sequence, unlabelled set, unlabelled multiset, unlabelled pointing,
unlabelled unpointing, unlabelled substitution, labelled sequence,
labelled set, labelled multiset, labelled cycle, labelled pointing,
labelled unpointing and labelled substitution constructions.
It consists of some basic preliminaries about classes
of combinatorial structures and three chapters. The first
one, Unlabelled Unranking , solves the unranking of unlabelled
structures. The second one, Labelled
Unranking, solves the unranking of labelled
structures. The third one, Product of labellings,
explains the order of the labellings in the structures. Appendix
contains the libraries developed in this work.
Mon, 28 Nov 2016 10:45:06 GMThttp://hdl.handle.net/2117/973012016-11-28T10:45:06ZMolinero Albareda, XavierThe present work is a study of the deterministic generation of
combinatorial structures. We generate classes of combinatorial
structures formally specifiable by grammars involving unlabelled
sequence, unlabelled set, unlabelled multiset, unlabelled pointing,
unlabelled unpointing, unlabelled substitution, labelled sequence,
labelled set, labelled multiset, labelled cycle, labelled pointing,
labelled unpointing and labelled substitution constructions.
It consists of some basic preliminaries about classes
of combinatorial structures and three chapters. The first
one, Unlabelled Unranking , solves the unranking of unlabelled
structures. The second one, Labelled
Unranking, solves the unranking of labelled
structures. The third one, Product of labellings,
explains the order of the labellings in the structures. Appendix
contains the libraries developed in this work.The Plogi and ACi-1 operators on the polynomial time hierarchy
http://hdl.handle.net/2117/97278
The Plogi and ACi-1 operators on the polynomial time hierarchy
Castro Rabal, Jorge; Seara Ojea, Carlos
In a previous paper ([CS-92]) we studied the agreement of operators P_{log^i} and AC^{i-1} acting on NP. In this article we extend this work to other classes of the polynomial time hierarchy. We show that on Sigma_k^p, Pi_k^p, Delta_k^P and Theta_k^P-classes both operators have the same behaviour, but this coincidence does not seem to be true on other classes included in the PH hierarchy: we give a set A such that, relativized to A, P_{log^i}(P_{log^j}(NP)) is different from AC^{i-1}(P_{log^j}(NP)). As a result of these characterizations we show P_{log}(Theta_k^p) = Theta_k^p, an equality that is useful to show lowness properties. In fact, we get easily the Theta-lowness results given by Long and Sheu in their paper [LS-91]. Besides, we clarify the situation of the classes in L_2^{p,Delta} for which their membership to L_2^{p,Theta} was not clear.
Mon, 28 Nov 2016 09:01:43 GMThttp://hdl.handle.net/2117/972782016-11-28T09:01:43ZCastro Rabal, JorgeSeara Ojea, CarlosIn a previous paper ([CS-92]) we studied the agreement of operators P_{log^i} and AC^{i-1} acting on NP. In this article we extend this work to other classes of the polynomial time hierarchy. We show that on Sigma_k^p, Pi_k^p, Delta_k^P and Theta_k^P-classes both operators have the same behaviour, but this coincidence does not seem to be true on other classes included in the PH hierarchy: we give a set A such that, relativized to A, P_{log^i}(P_{log^j}(NP)) is different from AC^{i-1}(P_{log^j}(NP)). As a result of these characterizations we show P_{log}(Theta_k^p) = Theta_k^p, an equality that is useful to show lowness properties. In fact, we get easily the Theta-lowness results given by Long and Sheu in their paper [LS-91]. Besides, we clarify the situation of the classes in L_2^{p,Delta} for which their membership to L_2^{p,Theta} was not clear.Generic algorithms for the generation of combinatorial objects
http://hdl.handle.net/2117/97031
Generic algorithms for the generation of combinatorial objects
Molinero Albareda, Xavier; Martínez Parra, Conrado
This report briefly describes our generic approach to the exhaustive generation of unlabelled and labelled combinatorial classes. Our algorithms receive a size n and a finite description of a combinatorial class A using combinatorial operators such as union, product, set or sequence, in order to list all objects of size n in A. The algorithms work in constant amortized time per generated object and thus they are suitable for rapid prototyping or for inclusion in general libraries.
Tue, 22 Nov 2016 14:37:57 GMThttp://hdl.handle.net/2117/970312016-11-22T14:37:57ZMolinero Albareda, XavierMartínez Parra, ConradoThis report briefly describes our generic approach to the exhaustive generation of unlabelled and labelled combinatorial classes. Our algorithms receive a size n and a finite description of a combinatorial class A using combinatorial operators such as union, product, set or sequence, in order to list all objects of size n in A. The algorithms work in constant amortized time per generated object and thus they are suitable for rapid prototyping or for inclusion in general libraries.