DSpace Collection:
http://hdl.handle.net/2117/3919
Mon, 01 Sep 2014 19:14:39 GMT2014-09-01T19:14:39Zwebmaster.bupc@upc.eduUniversitat Politècnica de Catalunya. Servei de Biblioteques i DocumentaciónoDecomposition 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/2117/231302014-06-03T08:45:51ZGálvez 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/2117/230402014-05-23T18:17:49ZJuan 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/2117/230392014-05-23T17:48:23ZJuan 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 convidant-lo
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 físico-matemàtics que han
participat, Tullio Levi-Civita 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/2117/229952014-05-15T09:07:35ZRoca Rosell, Antoni Maria ClaretnoHermann Weyl, WeylEl 30 de març de 1921 Esteve Terradas escriví Hermann Weyl a Zúric convidant-lo
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 físico-matemàtics que han
participat, Tullio Levi-Civita 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 2-dimensional 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/2117/226872014-04-24T09:32:24ZDelshams 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 2-dimensional 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/2117/225432014-04-07T14:05:21ZGómez 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 Hamilton-Jacobi theory for higher-order autonomous systems
http://hdl.handle.net/2117/22509
Title: Geometric Hamilton-Jacobi theory for higher-order autonomous systems
Authors: Colombo, Leonardo; de León, Manuel; Prieto Martínez, Pedro Daniel; Román Roy, Narciso
Abstract: The geometric framework for the Hamilton-Jacobi theory is used to study this theory in the ambient of higher-order mechanical systems, both in the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding Hamilton-Jacobi 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/2117/225092014-04-03T17:26:58ZColombo, 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 Hamilton-Jacobi theory is used to study this theory in the ambient of higher-order mechanical systems, both in the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding Hamilton-Jacobi equations in these formalisms and apply our results to analyze some particular physical examples.Generalized Clifford-Severi inequality and the volume of irregular varieties
http://hdl.handle.net/2117/22384
Title: Generalized Clifford-Severi 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 Clifford-Severi 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/2117/223842014-03-25T20:15:26ZBarja 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 Clifford-Severi 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 group-based models
http://hdl.handle.net/2117/22383
Title: Local description of phylogenetic group-based 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 group-based 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
3-parameter 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/2117/223832014-03-25T19:26:25ZCasanellas Rius, Marta; Fernández Sánchez, Jesús; Michalek, Mateusznogroup-based 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 group-based 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
3-parameter 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, Watson-Crick, 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, Watson-Crick, 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) Watson-Crick 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 time-inhomogeneous scenarios, unlike models that are not closed, such
as the general time-reversible 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/2117/223822014-03-25T17:59:41ZWoodhams, 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) Watson-Crick 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 time-inhomogeneous scenarios, unlike models that are not closed, such
as the general time-reversible 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: Continuous-time Markov chains are a standard tool in phylogenetic inference. If homogeneity is assumed, the chain is formulated by specifying time-independent 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 time-dependent 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/2117/223812014-03-25T17:13:58ZFernández Sánchez, Jesús; Sumner, Jeremy; Jarvis, Peter; Woodhams, Michael D.noevolutionary model, group representation theory, Lie algebraContinuous-time Markov chains are a standard tool in phylogenetic inference. If homogeneity is assumed, the chain is formulated by specifying time-independent 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 time-dependent 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.ICASES scenarios Final Report
http://hdl.handle.net/2117/22332
Title: ICASES scenarios Final Report
Authors: Juan Zornoza, José Miguel; Sanz Subirana, JaumeFri, 21 Mar 2014 14:17:23 GMThttp://hdl.handle.net/2117/223322014-03-21T14:17:23ZJuan Zornoza, José Miguel; Sanz Subirana, JaumenoUnified formalism for the generalized kth-order Hamilton-Jacobi problem
http://hdl.handle.net/2117/21964
Title: Unified formalism for the generalized kth-order Hamilton-Jacobi problem
Authors: Colombo, Leonardo; León, Manuel de; Prieto Martínez, Pedro Daniel; Román Roy, Narciso
Abstract: The geometric formulation of the Hamilton-Jacobi theory enables u
s to generalize it to
systems of higher-order ordinary differential equations. In this w
ork we introduce the unified
Lagrangian-Hamiltonian formalism for the geometric Hamilton-Jacob
i theory on higher-order
autonomous dynamical systems described by regular Lagrangian f
unctions.Mon, 10 Mar 2014 13:07:34 GMThttp://hdl.handle.net/2117/219642014-03-10T13:07:34ZColombo, Leonardo; León, Manuel de; Prieto Martínez, Pedro Daniel; Román Roy, NarcisonoThe geometric formulation of the Hamilton-Jacobi theory enables u
s to generalize it to
systems of higher-order ordinary differential equations. In this w
ork we introduce the unified
Lagrangian-Hamiltonian formalism for the geometric Hamilton-Jacob
i theory on higher-order
autonomous dynamical systems described by regular Lagrangian f
unctions.Periodic orbits of planar integrable birational maps
http://hdl.handle.net/2117/21748
Title: Periodic orbits of planar integrable birational maps
Authors: Gálvez Carrillo, Maria Immaculada; Mañosa Fernández, Víctor
Abstract: A birational planar map F possessing a rational ﬁrst integral preserves a
foliation of the plane given by algebraic curves which, if F is not globally periodic,
is given by a foliation of curves that have generically genus 0 or 1. In the genus 1
case, the group structure of the foliation characterizes the dynamics of any birational
map preserving it. We will see how to take advantage of this structure to ﬁnd periodic
orbits of such maps.Tue, 25 Feb 2014 12:09:41 GMThttp://hdl.handle.net/2117/217482014-02-25T12:09:41ZGálvez Carrillo, Maria Immaculada; Mañosa Fernández, VíctornoDiscrete dynamical systems, Algebraic geometry, Birational maps, Integrable maps, Elliptic curves, Periodic orbits.A birational planar map F possessing a rational ﬁrst integral preserves a
foliation of the plane given by algebraic curves which, if F is not globally periodic,
is given by a foliation of curves that have generically genus 0 or 1. In the genus 1
case, the group structure of the foliation characterizes the dynamics of any birational
map preserving it. We will see how to take advantage of this structure to ﬁnd periodic
orbits of such maps.Symplectic topology of b-symplectic manifolds
http://hdl.handle.net/2117/21516
Title: Symplectic topology of b-symplectic manifolds
Authors: Miranda Galcerán, Eva; Martinez Torres, David; Frejlich, Pedro
Abstract: A Poisson manifold (M2n; ) is b-symplectic if
Vn is transverse
to the zero section. In this paper we apply techniques of Symplectic Topology
to address global questions pertaining to b-symplectic manifolds. The main
results provide constructions of: b-symplectic submanifolds a la Donaldson,
b-symplectic structures on open manifolds by Gromov's h-principle, and of
b-symplectic manifolds with a prescribed singular locus, by means of surgeries.Tue, 11 Feb 2014 13:34:06 GMThttp://hdl.handle.net/2117/215162014-02-11T13:34:06ZMiranda Galcerán, Eva; Martinez Torres, David; Frejlich, PedronoA Poisson manifold (M2n; ) is b-symplectic if
Vn is transverse
to the zero section. In this paper we apply techniques of Symplectic Topology
to address global questions pertaining to b-symplectic manifolds. The main
results provide constructions of: b-symplectic submanifolds a la Donaldson,
b-symplectic structures on open manifolds by Gromov's h-principle, and of
b-symplectic manifolds with a prescribed singular locus, by means of surgeries.