DSpace Collection:
http://hdl.handle.net/2117/3919
Mon, 20 Oct 2014 11:51:58 GMT20141020T11:51:58Zwebmaster.bupc@upc.eduUniversitat Politècnica de Catalunya. Servei de Biblioteques i DocumentaciónoLyubeznik numbers of local rings and linear strands of graded ideals
http://hdl.handle.net/2117/24185
Title: Lyubeznik numbers of local rings and linear strands of graded ideals
Authors: Álvarez Montaner, Josep; Yanagawa, Kohji
Abstract: n this work we intro duce a new set of invariants asso ciated to the linear
strands of a minimal free resolution of a
Z
graded ideal
I
R
=

[
x
1
;:::;x
n
]
. We
also prove that these invariants satisfy some prop erties analogous to those of Lyub eznik
numb ers of lo cal rings. In particular, they satisfy a consecutiveness prop erty that we
prove rst for Lyub eznik numb ers. For the case of squarefree monomial ideals we get
more insight on the relation b etween Lyub eznik numb ers and the linear strands of their
asso ciated Alexander dual ideals. Finally, we prove that Lyub eznik numb ers of Stanley
Reisner rings are not only an algebraic invariant but also a top ological invariant, meaning
that they dep end on the homeomorphic class of the geometric realization of the asso ciated
simplicial complex and the characteristic of the base fieldTue, 30 Sep 2014 09:46:24 GMThttp://hdl.handle.net/2117/2418520140930T09:46:24ZÁlvarez Montaner, Josep; Yanagawa, Kohjinon this work we intro duce a new set of invariants asso ciated to the linear
strands of a minimal free resolution of a
Z
graded ideal
I
R
=

[
x
1
;:::;x
n
]
. We
also prove that these invariants satisfy some prop erties analogous to those of Lyub eznik
numb ers of lo cal rings. In particular, they satisfy a consecutiveness prop erty that we
prove rst for Lyub eznik numb ers. For the case of squarefree monomial ideals we get
more insight on the relation b etween Lyub eznik numb ers and the linear strands of their
asso ciated Alexander dual ideals. Finally, we prove that Lyub eznik numb ers of Stanley
Reisner rings are not only an algebraic invariant but also a top ological invariant, meaning
that they dep end on the homeomorphic class of the geometric realization of the asso ciated
simplicial complex and the characteristic of the base fieldA methodology for obtaining asymptotic estimates for the exponentially small splitting of separatrices to whiskered tori with quadratic frequencies
http://hdl.handle.net/2117/24155
Title: A methodology for obtaining asymptotic estimates for the exponentially small splitting of separatrices to whiskered tori with quadratic frequencies
Authors: Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, PereThu, 25 Sep 2014 08:12:02 GMThttp://hdl.handle.net/2117/2415520140925T08:12:02ZDelshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, PerenoContinuation of the exponentially small lower bounds for the splitting of separatrices to a whiskered torus with silver ratio
http://hdl.handle.net/2117/24138
Title: Continuation of the exponentially small lower bounds for the splitting of separatrices to a whiskered torus with silver ratio
Authors: Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere
Abstract: We study the exponentially small splitting of invariant manifolds of whiskered (hyperbolic) tori with two fast
frequencies in nearlyintegrable Hamiltonian systems whose hyperbolic part is given by a pendulum. We consider a torus whose frequency ratio is the silver number $\Omega=\sqrt21$. We show that the oincareMelnikov method can be applied to establish the existence of 4 transverse homoclinic orbits to the whiskered torus, and provide
asymptotic estimates for the tranversality of the splitting whose dependence on the perturbation parameter $\varepsilon$ satisffies a periodicity property. We also prove the continuation of the transversality of the homoclinic orbits for all the sufficiently small values of $\varepsilonTue, 23 Sep 2014 09:33:01 GMThttp://hdl.handle.net/2117/2413820140923T09:33:01ZDelshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Perenotransverse homoclinic orbits, splitting of separatrices, Melnikov integrals, silver ratioWe study the exponentially small splitting of invariant manifolds of whiskered (hyperbolic) tori with two fast
frequencies in nearlyintegrable Hamiltonian systems whose hyperbolic part is given by a pendulum. We consider a torus whose frequency ratio is the silver number $\Omega=\sqrt21$. We show that the oincareMelnikov method can be applied to establish the existence of 4 transverse homoclinic orbits to the whiskered torus, and provide
asymptotic estimates for the tranversality of the splitting whose dependence on the perturbation parameter $\varepsilon$ satisffies a periodicity property. We also prove the continuation of the transversality of the homoclinic orbits for all the sufficiently small values of $\varepsilonCàlcul numèric. Manual de pràctiques
http://hdl.handle.net/2117/24072
Title: Càlcul numèric. Manual de pràctiques
Authors: Lázaro Ochoa, José Tomás; Ollé Torner, Mercè; Pacha Andújar, Juan RamónWed, 17 Sep 2014 07:45:15 GMThttp://hdl.handle.net/2117/2407220140917T07:45:15ZLázaro Ochoa, José Tomás; Ollé Torner, Mercè; Pacha Andújar, Juan RamónnoDecomposition spaces, incidence algebras and Möbius inversion
http://hdl.handle.net/2117/23130
Title: Decomposition spaces, incidence algebras and Möbius inversion
Authors: Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, AndrewTue, 03 Jun 2014 08:45:51 GMThttp://hdl.handle.net/2117/2313020140603T08:45:51ZGálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, AndrewnoAlgebraic topology, CombinatoricsConsolidated characterisation of an ionospheric indicator for the definition of EGNOS Ionospheric Conditions
http://hdl.handle.net/2117/23040
Title: Consolidated characterisation of an ionospheric indicator for the definition of EGNOS Ionospheric Conditions
Authors: Juan Zornoza, José Miguel; Sanz Subirana, JaumeFri, 23 May 2014 18:17:49 GMThttp://hdl.handle.net/2117/2304020140523T18:17:49ZJuan Zornoza, José Miguel; Sanz Subirana, JaumenoFeasibility analysis of a methodology to estimate hourly DCBs for Feared Events Characterization
http://hdl.handle.net/2117/23039
Title: Feasibility analysis of a methodology to estimate hourly DCBs for Feared Events Characterization
Authors: Juan Zornoza, José Miguel; Sanz Subirana, Jaume
Abstract: Analysis of Hardware Biases Feared EventsFri, 23 May 2014 17:48:23 GMThttp://hdl.handle.net/2117/2303920140523T17:48:23ZJuan Zornoza, José Miguel; Sanz Subirana, JaumenoAnalysis of Hardware Biases Feared EventsHermann Weyl entre nosaltres. El curs de 1922 i algunes de les seves repercussions
http://hdl.handle.net/2117/22995
Title: Hermann Weyl entre nosaltres. El curs de 1922 i algunes de les seves repercussions
Authors: Roca Rosell, Antoni Maria Claret
Abstract: El 30 de març de 1921 Esteve Terradas escriví Hermann Weyl a Zúric convidantlo
perquè vingués a Barcelona a donar un curs “de 8 lliçons”1. Es tractava molt
probablement del primer contacte que s’establia entre ambdós. Terradas explica que “el
nostre govern local”, és a dir, la Mancomunitat de Catalunya, organitza conferències a
càrrec de professors destacats. Li menciona els primers físicomatemàtics que han
participat, Tullio LeviCivita i Jacques Hadamard, tots dos en el primer trimestre de
1921. També li diu que té la intenció de fer venir Einstein.Thu, 15 May 2014 09:07:35 GMThttp://hdl.handle.net/2117/2299520140515T09:07:35ZRoca Rosell, Antoni Maria ClaretnoHermann Weyl, WeylEl 30 de març de 1921 Esteve Terradas escriví Hermann Weyl a Zúric convidantlo
perquè vingués a Barcelona a donar un curs “de 8 lliçons”1. Es tractava molt
probablement del primer contacte que s’establia entre ambdós. Terradas explica que “el
nostre govern local”, és a dir, la Mancomunitat de Catalunya, organitza conferències a
càrrec de professors destacats. Li menciona els primers físicomatemàtics que han
participat, Tullio LeviCivita i Jacques Hadamard, tots dos en el primer trimestre de
1921. També li diu que té la intenció de fer venir Einstein.Exponentially small lower bounds for the splitting of separatrices to whiskered tori with frequencies of constant type
http://hdl.handle.net/2117/22687
Title: Exponentially small lower bounds for the splitting of separatrices to whiskered tori with frequencies of constant type
Authors: Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere
Abstract: We study the splitting of invariant manifolds of whiskered tori with two frequencies in nearlyintegrable
Hamiltonian systems, such that the hyperbolic part is given by a pendulum. We
consider a 2dimensional torus with a fast frequency vector $\omega/v\epsilon$, with $\epsilon=(1,\Omega)$ where $\Omega$ is an irrational number of constant type, i.e. a number whose continued fraction has bounded
entries. Applying the Poincar´e–Melnikov method, we find exponentially small lower bounds for
the maximal splitting distance between the stable and unstable invariant manifolds associated to
the invariant torus, and we show that these bounds depend strongly on the arithmetic properties
of the frequencies.Thu, 24 Apr 2014 09:32:24 GMThttp://hdl.handle.net/2117/2268720140424T09:32:24ZDelshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Perenosplitting of separatrices, Melnikov integrals, numbers of constant typeWe study the splitting of invariant manifolds of whiskered tori with two frequencies in nearlyintegrable
Hamiltonian systems, such that the hyperbolic part is given by a pendulum. We
consider a 2dimensional torus with a fast frequency vector $\omega/v\epsilon$, with $\epsilon=(1,\Omega)$ where $\Omega$ is an irrational number of constant type, i.e. a number whose continued fraction has bounded
entries. Applying the Poincar´e–Melnikov method, we find exponentially small lower bounds for
the maximal splitting distance between the stable and unstable invariant manifolds associated to
the invariant torus, and we show that these bounds depend strongly on the arithmetic properties
of the frequencies.Review of multivariate survival data
http://hdl.handle.net/2117/22543
Title: Review of multivariate survival data
Authors: Gómez Melis, Guadalupe; Calle Rosingana, M. Luz; Serrat Piè, Carles; Espinal Berenguer, Anna
Abstract: This paper reviews some of the main contributions in the area of multivariate survival data and proposes some possible extensions. In particular, we have concentrated our search and study on those papers that are relevant to the situation where two (or more) consecutive variables are followed until a common day of analysis and subject to informative censoring.
The paper reviews bivariate nonparametric approaches and extend some of them to the case of two nonconsecutive times. We introduce the notation and construct the likelihood for the general problem of more than two consecutive survival times. We formulate the time dependencies and trends via a Bayesian approach. Finally, three regression models for multivariate survival times are discussed together with the differences among them which will be useful when the main interest is on the effect of covariates on the risk of failure.
Description: Document de recerca publicat per la UPC. Departament d'Estadística i Investigació operativaMon, 07 Apr 2014 14:05:21 GMThttp://hdl.handle.net/2117/2254320140407T14:05:21ZGómez Melis, Guadalupe; Calle Rosingana, M. Luz; Serrat Piè, Carles; Espinal Berenguer, AnnanoBivariate distributions, Bivariate survival estimator, Multivariate regression survival models
62N01 Statistics: Survival analysis and censored data: Censored data models
62N02 Statistics: Survival analysis and censored data: EstimationThis paper reviews some of the main contributions in the area of multivariate survival data and proposes some possible extensions. In particular, we have concentrated our search and study on those papers that are relevant to the situation where two (or more) consecutive variables are followed until a common day of analysis and subject to informative censoring.
The paper reviews bivariate nonparametric approaches and extend some of them to the case of two nonconsecutive times. We introduce the notation and construct the likelihood for the general problem of more than two consecutive survival times. We formulate the time dependencies and trends via a Bayesian approach. Finally, three regression models for multivariate survival times are discussed together with the differences among them which will be useful when the main interest is on the effect of covariates on the risk of failure.Geometric HamiltonJacobi theory for higherorder autonomous systems
http://hdl.handle.net/2117/22509
Title: Geometric HamiltonJacobi theory for higherorder autonomous systems
Authors: Colombo, Leonardo; de León, Manuel; Prieto Martínez, Pedro Daniel; Román Roy, Narciso
Abstract: The geometric framework for the HamiltonJacobi theory is used to study this theory in the ambient of higherorder mechanical systems, both in the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding HamiltonJacobi equations in these formalisms and apply our results to analyze some particular physical examples.Thu, 03 Apr 2014 17:26:58 GMThttp://hdl.handle.net/2117/2250920140403T17:26:58ZColombo, Leonardo; de León, Manuel; Prieto Martínez, Pedro Daniel; Román Roy, NarcisonoHamilton–Jacobi equation, Higher–order, Lagrangian and Hamiltonian systems, Symplectic geometryThe geometric framework for the HamiltonJacobi theory is used to study this theory in the ambient of higherorder mechanical systems, both in the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding HamiltonJacobi equations in these formalisms and apply our results to analyze some particular physical examples.Generalized CliffordSeveri inequality and the volume of irregular varieties
http://hdl.handle.net/2117/22384
Title: Generalized CliffordSeveri inequality and the volume of irregular varieties
Authors: Barja Yáñez, Miguel Ángel
Abstract: We give a sharp lower bound for the selfintersection of a nef li
ne bundle L on an irregular variety X in terms of its continuous global sections and the Albanese dim
ension of X, which we call the Generalized CliffordSeveri inequality. We also extend the result to nef
vector bundles and give a slope inequality for fibred irregular varieties. As a byproduct we obtain a lower b
ound for the volume of irregular varieties; when X is of maximal Albanese dimension the bound is vol(X)=2n!¿¿X
and it is sharp.
Description: Preprint. Acceptat per publicar a Duke Math. J.Tue, 25 Mar 2014 20:15:26 GMThttp://hdl.handle.net/2117/2238420140325T20:15:26ZBarja Yáñez, Miguel ÁngelnoSeveri inequality
Slope
maximal Albanese Varieties
VolumeWe give a sharp lower bound for the selfintersection of a nef li
ne bundle L on an irregular variety X in terms of its continuous global sections and the Albanese dim
ension of X, which we call the Generalized CliffordSeveri inequality. We also extend the result to nef
vector bundles and give a slope inequality for fibred irregular varieties. As a byproduct we obtain a lower b
ound for the volume of irregular varieties; when X is of maximal Albanese dimension the bound is vol(X)=2n!¿¿X
and it is sharp.Local description of phylogenetic groupbased models
http://hdl.handle.net/2117/22383
Title: Local description of phylogenetic groupbased models
Authors: Casanellas Rius, Marta; Fernández Sánchez, Jesús; Michalek, Mateusz
Abstract: Motivated by phylogenetics, our aim is to obtain a system of equations that
de ne a phylogenetic variety on an open set containing the biologically meaningful points. In
this paper we consider phylogenetic varieties de ned via groupbased models. For any nite
abelian group G, we provide an explicit construction of codimX phylogenetic invariants
(polynomial equations) of degree at most jGj that de ne the variety X on a Zariski open set
U. The set U contains all biologically meaningful points when G is the group of the Kimura
3parameter model. In particular, our main result con rms [Mic12, Conjecture 7.9] and, on
the set U, Conjectures 29 and 30 of [SS05].Tue, 25 Mar 2014 19:26:25 GMThttp://hdl.handle.net/2117/2238320140325T19:26:25ZCasanellas Rius, Marta; Fernández Sánchez, Jesús; Michalek, Mateusznogroupbased model, phylogenetic invariant, toric varietyMotivated by phylogenetics, our aim is to obtain a system of equations that
de ne a phylogenetic variety on an open set containing the biologically meaningful points. In
this paper we consider phylogenetic varieties de ned via groupbased models. For any nite
abelian group G, we provide an explicit construction of codimX phylogenetic invariants
(polynomial equations) of degree at most jGj that de ne the variety X on a Zariski open set
U. The set U contains all biologically meaningful points when G is the group of the Kimura
3parameter model. In particular, our main result con rms [Mic12, Conjecture 7.9] and, on
the set U, Conjectures 29 and 30 of [SS05].Testing of the three multiplicatively closed (Lie Markov) model heirarchies which respect purine/pyrimidine, WatsonCrick, and amino/keto nucleotide groupings
http://hdl.handle.net/2117/22382
Title: Testing of the three multiplicatively closed (Lie Markov) model heirarchies which respect purine/pyrimidine, WatsonCrick, and amino/keto nucleotide groupings
Authors: Woodhams, Michael D.; Fernández Sánchez, Jesús; Sumner, Jeremy
Abstract: We present three hierarchies of Lie Markov models of DNA sequence evolution. These models are
(locally) “multiplicatively closed,” meaning that the composition of two Markov matrices in the
model results, with some (rare) exceptions, in a third Markov matrix that is still in the model.
Additionally, the models in each hierarchy respectively distinguish between (i) purines and pyrimadines
(RY), (ii) WatsonCrick pairs (WS), and (iii) amino/keto pairs (MK), but otherwise treat
the four nucleotides without distinction. The multiplicative closure property allows mathematically
consistent modeling of timeinhomogeneous scenarios, unlike models that are not closed, such
as the general timereversible model (GTR) and many of its submodels. We derive the nesting
relationships of the three model hierarchies and present software implementing the models. For a
diverse range of biological data sets, we perform Bayesian information criterion model comparision
analogous to that of the ModelTest framework. We find that our models outperform the GTR
model in some (but not all) cases.Tue, 25 Mar 2014 17:59:41 GMThttp://hdl.handle.net/2117/2238220140325T17:59:41ZWoodhams, Michael D.; Fernández Sánchez, Jesús; Sumner, JeremynoLie Markov models, multiplicative closure, DNA evolutionWe present three hierarchies of Lie Markov models of DNA sequence evolution. These models are
(locally) “multiplicatively closed,” meaning that the composition of two Markov matrices in the
model results, with some (rare) exceptions, in a third Markov matrix that is still in the model.
Additionally, the models in each hierarchy respectively distinguish between (i) purines and pyrimadines
(RY), (ii) WatsonCrick pairs (WS), and (iii) amino/keto pairs (MK), but otherwise treat
the four nucleotides without distinction. The multiplicative closure property allows mathematically
consistent modeling of timeinhomogeneous scenarios, unlike models that are not closed, such
as the general timereversible model (GTR) and many of its submodels. We derive the nesting
relationships of the three model hierarchies and present software implementing the models. For a
diverse range of biological data sets, we perform Bayesian information criterion model comparision
analogous to that of the ModelTest framework. We find that our models outperform the GTR
model in some (but not all) cases.Lie Markov models with purine/pyrimidine symmetry
http://hdl.handle.net/2117/22381
Title: Lie Markov models with purine/pyrimidine symmetry
Authors: Fernández Sánchez, Jesús; Sumner, Jeremy; Jarvis, Peter; Woodhams, Michael D.
Abstract: Continuoustime Markov chains are a standard tool in phylogenetic inference. If homogeneity is assumed, the chain is formulated by specifying timeindependent rates of substitutions between states in the chain. In applications, there are usually extra constraints on the rates, depending on the situation. If a model is formulated in this way, it is possible to generalise it and allow for an inhomogeneous process, with timedependent rates satisfying the same constraints. It is then useful to require that there exists a homogeneous average of this inhomogeneous process within the same model. This leads to the definition of "Lie Markov models", which are precisely the class of models where such an average exists. These models form Lie algebras and hence concepts from Lie group theory are central to their derivation. In this paper, we concentrate on applications to phylogenetics and nucleotide evolution, and derive the complete hierarchy of Lie Markov models that respect the grouping of nucleotides into purines and pyrimidines  that is, models with purine/pyrimidine symmetry. We also discuss how to handle the subtleties of applying Lie group methods, most naturally defined over the complex field, to the stochastic case of a Markov process, where parameter values are restricted to be real and positive. In particular, we explore the geometric embedding of the cone of stochastic rate matrices within the ambient space of the associated complex Lie algebra.Tue, 25 Mar 2014 17:13:58 GMThttp://hdl.handle.net/2117/2238120140325T17:13:58ZFernández Sánchez, Jesús; Sumner, Jeremy; Jarvis, Peter; Woodhams, Michael D.noevolutionary model, group representation theory, Lie algebraContinuoustime Markov chains are a standard tool in phylogenetic inference. If homogeneity is assumed, the chain is formulated by specifying timeindependent rates of substitutions between states in the chain. In applications, there are usually extra constraints on the rates, depending on the situation. If a model is formulated in this way, it is possible to generalise it and allow for an inhomogeneous process, with timedependent rates satisfying the same constraints. It is then useful to require that there exists a homogeneous average of this inhomogeneous process within the same model. This leads to the definition of "Lie Markov models", which are precisely the class of models where such an average exists. These models form Lie algebras and hence concepts from Lie group theory are central to their derivation. In this paper, we concentrate on applications to phylogenetics and nucleotide evolution, and derive the complete hierarchy of Lie Markov models that respect the grouping of nucleotides into purines and pyrimidines  that is, models with purine/pyrimidine symmetry. We also discuss how to handle the subtleties of applying Lie group methods, most naturally defined over the complex field, to the stochastic case of a Markov process, where parameter values are restricted to be real and positive. In particular, we explore the geometric embedding of the cone of stochastic rate matrices within the ambient space of the associated complex Lie algebra.