Articles de revista
http://hdl.handle.net/2117/184705
Tue, 27 Oct 2020 10:39:04 GMT
20201027T10:39:04Z

Embeddability of Kimura 3ST Markov matrices
http://hdl.handle.net/2117/192336
Embeddability of Kimura 3ST Markov matrices
Roca Lacostena, Jordi; Fernández Sánchez, Jesús
In this note, we characterize the embeddability of generic Kimura 3ST Markov matrices in terms of their eigenvalues. As a consequence, we are able to compute the volume of such matrices relative to the volume of all Markov matrices within the model. We also provide examples showing that, in general, mutation rates are not identifiable from substitution probabilities. These examples also illustrate that symmetries between mutation probabilities do not necessarily arise from symmetries between the corresponding mutation rates.
Thu, 02 Jul 2020 15:50:17 GMT
http://hdl.handle.net/2117/192336
20200702T15:50:17Z
Roca Lacostena, Jordi
Fernández Sánchez, Jesús
In this note, we characterize the embeddability of generic Kimura 3ST Markov matrices in terms of their eigenvalues. As a consequence, we are able to compute the volume of such matrices relative to the volume of all Markov matrices within the model. We also provide examples showing that, in general, mutation rates are not identifiable from substitution probabilities. These examples also illustrate that symmetries between mutation probabilities do not necessarily arise from symmetries between the corresponding mutation rates.

The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability
http://hdl.handle.net/2117/185418
The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability
Pérez Cervera, Alberto; Ashwin, Peter; Huguet Casades, Gemma; Rankin, James; MartínezSeara Alonso, M. Teresa
We study the dynamics arising when two identical oscillators are coupled near a Hopfbifurcation where we assume a parameter uncouples the system at = 0. Using anormal form forN= 2 identical systems undergoing Hopf bifurcation, we explore thedynamical properties. Matching the normal form coefficients to a coupledWilson–Cowan oscillator network gives an understanding of different types ofbehaviour that arise in a model of perceptual bistability. Notably, we find bistabilitybetween inphase and antiphase solutions that demonstrates the feasibility forsynchronisation to act as the mechanism by which periodic inputs can be segregated(rather than via strong inhibitory coupling, as in the existing models). Using numericalcontinuation we confirm our theoretical analysis for small coupling strength andexplore the bifurcation diagrams for large coupling strength, where the normal formapproximation breaks down.
Tue, 28 Apr 2020 09:58:09 GMT
http://hdl.handle.net/2117/185418
20200428T09:58:09Z
Pérez Cervera, Alberto
Ashwin, Peter
Huguet Casades, Gemma
Rankin, James
MartínezSeara Alonso, M. Teresa
We study the dynamics arising when two identical oscillators are coupled near a Hopfbifurcation where we assume a parameter uncouples the system at = 0. Using anormal form forN= 2 identical systems undergoing Hopf bifurcation, we explore thedynamical properties. Matching the normal form coefficients to a coupledWilson–Cowan oscillator network gives an understanding of different types ofbehaviour that arise in a model of perceptual bistability. Notably, we find bistabilitybetween inphase and antiphase solutions that demonstrates the feasibility forsynchronisation to act as the mechanism by which periodic inputs can be segregated(rather than via strong inhibitory coupling, as in the existing models). Using numericalcontinuation we confirm our theoretical analysis for small coupling strength andexplore the bifurcation diagrams for large coupling strength, where the normal formapproximation breaks down.

Some properties for bisemivalues on bicooperative games
http://hdl.handle.net/2117/185232
Some properties for bisemivalues on bicooperative games
Domènech Blázquez, Margarita; Giménez Pradales, José Miguel; Puente del Campo, María Albina
In this work, we focus on bicooperative games, a variation of the classic cooperative games, and investigate the conditions for the coefficients of the bisemivalues—a generalization of semivalues for cooperative games—necessary and / or sufficient in order to satisfy some properties, including among others, desirability relation, balanced contributions, null player exclusion property and block property. Moreover, a computational procedure to calculate bisemivalues in terms of the multilinear extension of the game is given.
This is a postpeerreview, precopyedit version of an article published in Journal of Optimization Theory and Applications. The final authenticated version is available online at: http://dx.doi.org/10.1007%2Fs1095702001640x.
Mon, 27 Apr 2020 10:41:47 GMT
http://hdl.handle.net/2117/185232
20200427T10:41:47Z
Domènech Blázquez, Margarita
Giménez Pradales, José Miguel
Puente del Campo, María Albina
In this work, we focus on bicooperative games, a variation of the classic cooperative games, and investigate the conditions for the coefficients of the bisemivalues—a generalization of semivalues for cooperative games—necessary and / or sufficient in order to satisfy some properties, including among others, desirability relation, balanced contributions, null player exclusion property and block property. Moreover, a computational procedure to calculate bisemivalues in terms of the multilinear extension of the game is given.

Fixed subgroups and computation of autofixed closures in freeabelian times free groups
http://hdl.handle.net/2117/184934
Fixed subgroups and computation of autofixed closures in freeabelian times free groups
Roy, Mallika; Ventura Capell, Enric
The classical result by Dyer–Scott about fixed subgroups of finite order automorphisms of Fnbeing free factors of Fn is no longer true inZm×Fn. Within this more generalcontext, we prove a relaxed version in the spirit of Bestvina–Handel Theorem: the rank of fixed subgroups of finite order automorphisms is uniformly bounded in terms of m, n. We also studyperiodic points of endomorphisms of Zm×Fn, and give an algorithm to compute autofixed closures of finitely generated subgroups of Zm×Fn. On the way, we prove the analog of Day’sTheorem for real elements in Zm×Fn, contributing a modest step into the project of doing sofor any right angled Artin group (as McCool did with respect to Whitehead’s Theorem in the free context).
Fri, 24 Apr 2020 10:12:43 GMT
http://hdl.handle.net/2117/184934
20200424T10:12:43Z
Roy, Mallika
Ventura Capell, Enric
The classical result by Dyer–Scott about fixed subgroups of finite order automorphisms of Fnbeing free factors of Fn is no longer true inZm×Fn. Within this more generalcontext, we prove a relaxed version in the spirit of Bestvina–Handel Theorem: the rank of fixed subgroups of finite order automorphisms is uniformly bounded in terms of m, n. We also studyperiodic points of endomorphisms of Zm×Fn, and give an algorithm to compute autofixed closures of finitely generated subgroups of Zm×Fn. On the way, we prove the analog of Day’sTheorem for real elements in Zm×Fn, contributing a modest step into the project of doing sofor any right angled Artin group (as McCool did with respect to Whitehead’s Theorem in the free context).

Vibrationbased detection and classification of structural changes using principal component analysis and tdistributed stochastic neighbor embedding
http://hdl.handle.net/2117/183436
Vibrationbased detection and classification of structural changes using principal component analysis and tdistributed stochastic neighbor embedding
Agis Cherta, David; Tibaduiza Burgos, Diego Alexander; Pozo Montero, Francesc
This paper describes a structural health monitoring strategy to detect and classify structural changes in structures that can be equipped with sensors. The proposed approach is based on the tdistributed stochastic neighbor embedding (tSNE), a nonlinear technique that can represent the local structure of highdimensional data collected from multiple sensors in a plane or spatial representation. We propose the following basic steps for the detection and classification. First, the raw data are preprocessed: We scale the data using the meancentered group scaling and apply principal component analysis to reduce the dimensionality of the scaled data. Second, tSNE is applied to represent the scaled and reduced data as points in a plane, defining a cluster for each structural state. Finally, the current structure to be diagnosed is associated with a cluster (or structural state) using three different strategies: (a) the smallest pointcentroid distance; (b) the majority voting; and (c) the sum of the inverse distances. The combination of tSNE with our preprocessing and the three proposed classification strategies signif icantly improves the quality of the clusters that represent different structural states. We evaluate the performance of our method using experimental data from an aluminum plate instrumented with piezoelectric transducers. Results are presented in the time domain, and they reveal the high classification accuracy and strong performance of this method, with a percentage of correct decisions close to 100% in several scenarios.
Wed, 15 Apr 2020 10:19:43 GMT
http://hdl.handle.net/2117/183436
20200415T10:19:43Z
Agis Cherta, David
Tibaduiza Burgos, Diego Alexander
Pozo Montero, Francesc
This paper describes a structural health monitoring strategy to detect and classify structural changes in structures that can be equipped with sensors. The proposed approach is based on the tdistributed stochastic neighbor embedding (tSNE), a nonlinear technique that can represent the local structure of highdimensional data collected from multiple sensors in a plane or spatial representation. We propose the following basic steps for the detection and classification. First, the raw data are preprocessed: We scale the data using the meancentered group scaling and apply principal component analysis to reduce the dimensionality of the scaled data. Second, tSNE is applied to represent the scaled and reduced data as points in a plane, defining a cluster for each structural state. Finally, the current structure to be diagnosed is associated with a cluster (or structural state) using three different strategies: (a) the smallest pointcentroid distance; (b) the majority voting; and (c) the sum of the inverse distances. The combination of tSNE with our preprocessing and the three proposed classification strategies signif icantly improves the quality of the clusters that represent different structural states. We evaluate the performance of our method using experimental data from an aluminum plate instrumented with piezoelectric transducers. Results are presented in the time domain, and they reveal the high classification accuracy and strong performance of this method, with a percentage of correct decisions close to 100% in several scenarios.

Sufficient conditions for a digraph to admit a (1,=l)identifying code
http://hdl.handle.net/2117/182027
Sufficient conditions for a digraph to admit a (1,=l)identifying code
Balbuena Martínez, Maria Camino Teófila; Dalfó Simó, Cristina; Martínez Barona, Berenice
A (1, = `)identifying code in a digraph D is a subset C of vertices of D such that all distinct subsets of vertices of cardinality at most ` have distinct closed inneighbourhoods within C. In this paper, we give some sufficient conditions for a digraph of minimum indegree d  = 1 to admit a (1, = `) identifying code for ` ¿ {d , d + 1}. As a corollary, we obtain the result by Laihonen that states that a graph of minimum degree d = 2 and girth at least 7 admits a (1, = d)identifying code. Moreover, we prove that every 1inregular digraph has a (1, = 2)identifying code if and only if the girth of the digraph is at least 5. We also characterize all the 2inregular digraphs admitting a (1, = `)identifying code for ` ¿ {2, 3}.
Fri, 27 Mar 2020 11:45:31 GMT
http://hdl.handle.net/2117/182027
20200327T11:45:31Z
Balbuena Martínez, Maria Camino Teófila
Dalfó Simó, Cristina
Martínez Barona, Berenice
A (1, = `)identifying code in a digraph D is a subset C of vertices of D such that all distinct subsets of vertices of cardinality at most ` have distinct closed inneighbourhoods within C. In this paper, we give some sufficient conditions for a digraph of minimum indegree d  = 1 to admit a (1, = `) identifying code for ` ¿ {d , d + 1}. As a corollary, we obtain the result by Laihonen that states that a graph of minimum degree d = 2 and girth at least 7 admits a (1, = d)identifying code. Moreover, we prove that every 1inregular digraph has a (1, = 2)identifying code if and only if the girth of the digraph is at least 5. We also characterize all the 2inregular digraphs admitting a (1, = `)identifying code for ` ¿ {2, 3}.

An immersed boundary hierarchical Bspline method for flexoelectricity
http://hdl.handle.net/2117/181221
An immersed boundary hierarchical Bspline method for flexoelectricity
Codony Gisbert, David; Marco Alacid, Onofre; Fernández Méndez, Sonia; Arias Vicente, Irene
This paper develops a computational framework with unfitted meshes to solve linear piezoelectricity and flexoelectricity electromechanical boundary value problems including strain gradient elasticity at infinitesimal strains. The highorder nature of the coupled PDE system is addressed by a sufficiently smooth hierarchical Bspline approximation on a background Cartesian mesh. The domain of interest is embedded into the background mesh and discretized in an unfitted fashion. The immersed boundary approach allows us to use Bsplines on arbitrary domain shapes, regardless of their geometrical complexity, and could be directly extended, for instance, to shape and topology optimization. The domain boundary is represented by NURBS, and exactly integrated by means of the NEFEM mapping. Local adaptivity is achieved by hierarchical refinement of Bspline basis, which are efficiently evaluated and integrated thanks to their piecewise polynomial definition. Nitsche's formulation is derived to weakly enforce essential boundary conditions, accounting also for the nonlocal conditions on the nonsmooth portions of the domain boundary (i.e. edges in 3D or corners in 2D) arising from Mindlin's strain gradient elasticity theory. Boundary conditions modeling sensing electrodes are formulated and enforced following the same approach. Optimal error convergence rates are reported using highorder Bspline approximations. The method is verified against available analytical solutions and wellknown benchmarks from the literature.
© 2019. This manuscript version is made available under the CCBYNCND 4.0 license http://creativecommons.org/licenses/byncnd/4.0/
Wed, 25 Mar 2020 08:30:15 GMT
http://hdl.handle.net/2117/181221
20200325T08:30:15Z
Codony Gisbert, David
Marco Alacid, Onofre
Fernández Méndez, Sonia
Arias Vicente, Irene
This paper develops a computational framework with unfitted meshes to solve linear piezoelectricity and flexoelectricity electromechanical boundary value problems including strain gradient elasticity at infinitesimal strains. The highorder nature of the coupled PDE system is addressed by a sufficiently smooth hierarchical Bspline approximation on a background Cartesian mesh. The domain of interest is embedded into the background mesh and discretized in an unfitted fashion. The immersed boundary approach allows us to use Bsplines on arbitrary domain shapes, regardless of their geometrical complexity, and could be directly extended, for instance, to shape and topology optimization. The domain boundary is represented by NURBS, and exactly integrated by means of the NEFEM mapping. Local adaptivity is achieved by hierarchical refinement of Bspline basis, which are efficiently evaluated and integrated thanks to their piecewise polynomial definition. Nitsche's formulation is derived to weakly enforce essential boundary conditions, accounting also for the nonlocal conditions on the nonsmooth portions of the domain boundary (i.e. edges in 3D or corners in 2D) arising from Mindlin's strain gradient elasticity theory. Boundary conditions modeling sensing electrodes are formulated and enforced following the same approach. Optimal error convergence rates are reported using highorder Bspline approximations. The method is verified against available analytical solutions and wellknown benchmarks from the literature.

Adaptive refinement for phasefield models of brittle fracture based on Nitsche's method
http://hdl.handle.net/2117/180978
Adaptive refinement for phasefield models of brittle fracture based on Nitsche's method
Muixí Ballonga, Alba; Fernández Méndez, Sonia; Rodríguez Ferran, Antonio
A new adaptive refinement strategy for phasefield models of brittle fracture is proposed. The approach provides a computationally efficient solution to the high demand in spatial resolution of phasefield models. The strategy is based on considering two types of elements: hrefined elements along cracks, where more accuracy is needed to capture the solution, and standard elements in the rest of the domain. Continuity between adjacent elements of different type is imposed in weak form by means of Nitsche's method. The weakly imposition of continuity leads to a very local refinement in a simple way, for any degree of approximation and both in 2D and 3D. The performance of the strategy is assessed for several scenarios in the quasistatic regime, including coalescence and branching of cracks in 2D and a twisting crack in 3D.
“This is a postpeerreview, precopyedit version of an article published in Computational mechanics. The final authenticated version is available online at:
http://dx.doi.org/10.1007/s00466020018411”.
Tue, 24 Mar 2020 08:09:54 GMT
http://hdl.handle.net/2117/180978
20200324T08:09:54Z
Muixí Ballonga, Alba
Fernández Méndez, Sonia
Rodríguez Ferran, Antonio
A new adaptive refinement strategy for phasefield models of brittle fracture is proposed. The approach provides a computationally efficient solution to the high demand in spatial resolution of phasefield models. The strategy is based on considering two types of elements: hrefined elements along cracks, where more accuracy is needed to capture the solution, and standard elements in the rest of the domain. Continuity between adjacent elements of different type is imposed in weak form by means of Nitsche's method. The weakly imposition of continuity leads to a very local refinement in a simple way, for any degree of approximation and both in 2D and 3D. The performance of the strategy is assessed for several scenarios in the quasistatic regime, including coalescence and branching of cracks in 2D and a twisting crack in 3D.

Monomial generators of complete planar ideals
http://hdl.handle.net/2117/180848
Monomial generators of complete planar ideals
Alberich Carramiñana, Maria; Álvarez Montaner, Josep; Blanco Fernández, Guillem
We provide an algorithm that computes a set of generators for any complete ideal in a smooth complex surface. More interestingly, these generators admit a presentation as monomials in a set of maximal contact elements associated to the minimal logresolution of the ideal. Furthermore, the monomial expression given by our method is an equisingularity invariant of the ideal. As an outcome, we provide a geometric method to compute the integral closure of a planar ideal and we apply our algorithm to some families of complete ideals
Mon, 23 Mar 2020 09:58:32 GMT
http://hdl.handle.net/2117/180848
20200323T09:58:32Z
Alberich Carramiñana, Maria
Álvarez Montaner, Josep
Blanco Fernández, Guillem
We provide an algorithm that computes a set of generators for any complete ideal in a smooth complex surface. More interestingly, these generators admit a presentation as monomials in a set of maximal contact elements associated to the minimal logresolution of the ideal. Furthermore, the monomial expression given by our method is an equisingularity invariant of the ideal. As an outcome, we provide a geometric method to compute the integral closure of a planar ideal and we apply our algorithm to some families of complete ideals

VibrationBased structural health monitoring using piezoelectric transducers and parametric tSNE
http://hdl.handle.net/2117/180633
VibrationBased structural health monitoring using piezoelectric transducers and parametric tSNE
Agis Cherta, David; Pozo Montero, Francesc
In this paper, we evaluate the performance of the socalled parametric tdistributed stochastic neighbor embedding (PtSNE), comparing it to the performance of the tSNE, the nonparametric version. The methodology used in this study is introduced for the detection and classification of structural changes in the field of structural health monitoring. This method is based on the combination of principal component analysis (PCA) and PtSNE, and it is applied to an experimental case study of an aluminum plate with four piezoelectric transducers. The basic steps of the detection and classification process are: (i) the raw data are scaled using meancentered group scaling and then PCA is applied to reduce its dimensionality; (ii) PtSNE is applied to represent the scaled and reduced data as 2dimensional points, defining a cluster for each structural state; and (iii) the current structure to be diagnosed is associated with a cluster employing two strategies: (a) majority voting; and (b) the sum of the inverse distances. The results in the frequency domain manifest the strong performance of PtSNE, which is comparable to the performance of tSNE but outperforms tSNE in terms of computational cost and runtime. When the method is based on PtSNE, the overall accuracy fluctuates between 99.5% and 99.75%.
Fri, 20 Mar 2020 08:11:11 GMT
http://hdl.handle.net/2117/180633
20200320T08:11:11Z
Agis Cherta, David
Pozo Montero, Francesc
In this paper, we evaluate the performance of the socalled parametric tdistributed stochastic neighbor embedding (PtSNE), comparing it to the performance of the tSNE, the nonparametric version. The methodology used in this study is introduced for the detection and classification of structural changes in the field of structural health monitoring. This method is based on the combination of principal component analysis (PCA) and PtSNE, and it is applied to an experimental case study of an aluminum plate with four piezoelectric transducers. The basic steps of the detection and classification process are: (i) the raw data are scaled using meancentered group scaling and then PCA is applied to reduce its dimensionality; (ii) PtSNE is applied to represent the scaled and reduced data as 2dimensional points, defining a cluster for each structural state; and (iii) the current structure to be diagnosed is associated with a cluster employing two strategies: (a) majority voting; and (b) the sum of the inverse distances. The results in the frequency domain manifest the strong performance of PtSNE, which is comparable to the performance of tSNE but outperforms tSNE in terms of computational cost and runtime. When the method is based on PtSNE, the overall accuracy fluctuates between 99.5% and 99.75%.