GEOMVAP - Geometria de Varietats i Aplicacions
http://hdl.handle.net/2117/79732
2024-03-29T10:44:17Z
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Bohr–Sommerfeld quantization of b-symplectic toric manifolds
http://hdl.handle.net/2117/405007
Bohr–Sommerfeld quantization of b-symplectic toric manifolds
Mir Garcia, Pau; Miranda Galcerán, Eva; Weitsman, Jonathan
We define the Bohr-Sommerfeld quantization via T -modules for a b-symplectic toric manifold and show that it coincides with the formal geometric quantization of [Victor W. Guillemin, Eva Miranda, and Jonathan Weitsman. On geometric quantization of b-symplectic
manifolds. Adv. Math., 331:941–951, 2018]. In particular, we prove that its dimension is given by a signed count of the integral points in the moment polytope of the toric action on the manifold
2024-03-20T11:10:34Z
Mir Garcia, Pau
Miranda Galcerán, Eva
Weitsman, Jonathan
We define the Bohr-Sommerfeld quantization via T -modules for a b-symplectic toric manifold and show that it coincides with the formal geometric quantization of [Victor W. Guillemin, Eva Miranda, and Jonathan Weitsman. On geometric quantization of b-symplectic
manifolds. Adv. Math., 331:941–951, 2018]. In particular, we prove that its dimension is given by a signed count of the integral points in the moment polytope of the toric action on the manifold
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Identifiability in robust estimation of tree structured models
http://hdl.handle.net/2117/404727
Identifiability in robust estimation of tree structured models
Casanellas Rius, Marta; Garrote López, Marina; Zwiernik, Piotr
Consider the problem of learning undirected graphical models on trees from corrupted data. Recently Katiyar, Shah, and Caramanis showed that it is possible to recover trees from noisy binary data up to a small equivalence class of possible trees. Another paper by Katiyar, Hoffmann, and Caramanis follows a similar pattern for the Gaussian case. By framing this as a special phylogenetic recovery problem we largely generalize these two settings. Using the framework of linear latent tree models we discuss tree identifiability for binary data under a continuous corruption model (e.g. black/white images with greyscale corruption). For the Ising and the Gaussian tree model we also provide a characterisation of when the Chow-Liu algorithm consistently learns the underlying tree from the noisy data.
2024-03-15T12:20:36Z
Casanellas Rius, Marta
Garrote López, Marina
Zwiernik, Piotr
Consider the problem of learning undirected graphical models on trees from corrupted data. Recently Katiyar, Shah, and Caramanis showed that it is possible to recover trees from noisy binary data up to a small equivalence class of possible trees. Another paper by Katiyar, Hoffmann, and Caramanis follows a similar pattern for the Gaussian case. By framing this as a special phylogenetic recovery problem we largely generalize these two settings. Using the framework of linear latent tree models we discuss tree identifiability for binary data under a continuous corruption model (e.g. black/white images with greyscale corruption). For the Ising and the Gaussian tree model we also provide a characterisation of when the Chow-Liu algorithm consistently learns the underlying tree from the noisy data.
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New slope inequalities for families of complete intersections
http://hdl.handle.net/2117/404717
New slope inequalities for families of complete intersections
Barja Yáñez, Miguel Ángel; Stoppino, Lidia
We prove f-positivity of Ox (1) for arbitrary dimensional fibrations over curves f:X¿B whose general fibre is a complete intersection. In the special case where the family is a global complete intersection, we prove numerical sufficient and necessary conditions for f-positivity of powers of Ox (1) and for the relative canonical sheaf. From these results we also derive a Chow instability condition for the fibres of relative complete intersections in the projective bundle of a µ-unstable bundle.
2024-03-15T11:33:52Z
Barja Yáñez, Miguel Ángel
Stoppino, Lidia
We prove f-positivity of Ox (1) for arbitrary dimensional fibrations over curves f:X¿B whose general fibre is a complete intersection. In the special case where the family is a global complete intersection, we prove numerical sufficient and necessary conditions for f-positivity of powers of Ox (1) and for the relative canonical sheaf. From these results we also derive a Chow instability condition for the fibres of relative complete intersections in the projective bundle of a µ-unstable bundle.
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Reduction theory for singular symplectic manifolds and singular forms on moduli spaces
http://hdl.handle.net/2117/403996
Reduction theory for singular symplectic manifolds and singular forms on moduli spaces
Matveeva, Anastasiia; Miranda Galcerán, Eva
The investigation of symmetries of b-symplectic manifolds and folded-symplectic manifolds is well-understood when the group under consideration is a torus (see, for instance, [25,21, 28] for b-symplectic manifolds and [12,14] for folded symplec-tic manifolds). However, reduction theory has not been set in this realm in full generality. This is fundamental, among other reasons, to advance in the “quantization commutes with reduction” programme for these manifolds initiated in [29,30].
© 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license
2024-03-08T11:32:36Z
Matveeva, Anastasiia
Miranda Galcerán, Eva
The investigation of symmetries of b-symplectic manifolds and folded-symplectic manifolds is well-understood when the group under consideration is a torus (see, for instance, [25,21, 28] for b-symplectic manifolds and [12,14] for folded symplec-tic manifolds). However, reduction theory has not been set in this realm in full generality. This is fundamental, among other reasons, to advance in the “quantization commutes with reduction” programme for these manifolds initiated in [29,30].
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Valuations with an infinite limit-depth
http://hdl.handle.net/2117/402280
Valuations with an infinite limit-depth
Alberich Carramiñana, Maria; Guàrdia Rubies, Jordi; Nart Vinyals, Enric; Roé Vallvé, Joaquim
We construct a field K and a valuation-algebraic valuation on K[x] , whose underlying Maclane–Vaquié chain consists of an infinite (countable) number of limit augmentations.
2024-02-20T08:13:58Z
Alberich Carramiñana, Maria
Guàrdia Rubies, Jordi
Nart Vinyals, Enric
Roé Vallvé, Joaquim
We construct a field K and a valuation-algebraic valuation on K[x] , whose underlying Maclane–Vaquié chain consists of an infinite (countable) number of limit augmentations.
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Morse cell decomposition and parametrization of surfaces from point clouds
http://hdl.handle.net/2117/401639
Morse cell decomposition and parametrization of surfaces from point clouds
Alberich Carramiñana, Maria; Amorós Torrent, Jaume; Coltraro, Franco; Torras, Carme; Verdaguer López, Miquel
An algorithm for the reconstruction of a surface from a point sample is presented. It proceeds directly from the point-cloud to obtain a cellular decomposition of the surface derived from a Morse function. No intermediate triangulation or local implicit equations are used, saving on computation time and reconstruction-induced artifices. No a priori knowledge of surface topology, density or regularity of its point sample is required to run the algorithm. The results are a piecewise parametrization of the surface as a union of Morse cells, suitable for tasks such as noise-filtering or mesh-independent reparametrization, and a cell complex of small rank determining the surface topology. The algorithm can be applied to smooth surfaces with or without boundary, embedded in an ambient space of any dimension.
2024-02-09T13:44:00Z
Alberich Carramiñana, Maria
Amorós Torrent, Jaume
Coltraro, Franco
Torras, Carme
Verdaguer López, Miquel
An algorithm for the reconstruction of a surface from a point sample is presented. It proceeds directly from the point-cloud to obtain a cellular decomposition of the surface derived from a Morse function. No intermediate triangulation or local implicit equations are used, saving on computation time and reconstruction-induced artifices. No a priori knowledge of surface topology, density or regularity of its point sample is required to run the algorithm. The results are a piecewise parametrization of the surface as a union of Morse cells, suitable for tasks such as noise-filtering or mesh-independent reparametrization, and a cell complex of small rank determining the surface topology. The algorithm can be applied to smooth surfaces with or without boundary, embedded in an ambient space of any dimension.
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Multisymplectic constraint analysis of scalar field theories, Chern-Simons gravity, and bosonic string theory
http://hdl.handle.net/2117/400960
Multisymplectic constraint analysis of scalar field theories, Chern-Simons gravity, and bosonic string theory
Gomis Torné, Joaquim; Guerra IV, Arnoldo; Román Roy, Narciso
The (pre)multisymplectic geometry of the De Donder–Weyl formalism for field theories is further developed for a variety of field theories including a scalar field theory from the canonical Klein-Gordon action, the electric and magnetic Carrollian scalar field theories, bosonic string theory from the Nambu-Goto action, and gravity as a Chern-Simons theory. The Lagrangians for the scalar field theories and for Chern-Simons gravity are found to be singular in the De Donder–Weyl sense while the Nambu-Goto Lagrangian is found to be regular. Furthermore, the constraint structure of the premultisymplectic phase spaces of singular field theories is explained and applied to these theories. Finally, it is studied how symmetries are developed on the (pre)multisymplectic phase spaces in the presence of constraints.
© 2023 Elsevier. This manuscript version is made available under the CC BY 4.0 DEED license https://creativecommons.org/licenses/by/4.0/
2024-02-05T10:49:09Z
Gomis Torné, Joaquim
Guerra IV, Arnoldo
Román Roy, Narciso
The (pre)multisymplectic geometry of the De Donder–Weyl formalism for field theories is further developed for a variety of field theories including a scalar field theory from the canonical Klein-Gordon action, the electric and magnetic Carrollian scalar field theories, bosonic string theory from the Nambu-Goto action, and gravity as a Chern-Simons theory. The Lagrangians for the scalar field theories and for Chern-Simons gravity are found to be singular in the De Donder–Weyl sense while the Nambu-Goto Lagrangian is found to be regular. Furthermore, the constraint structure of the premultisymplectic phase spaces of singular field theories is explained and applied to these theories. Finally, it is studied how symmetries are developed on the (pre)multisymplectic phase spaces in the presence of constraints.
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Reconstruction of sampled surfaces with boundary via Morse theory
http://hdl.handle.net/2117/400622
Reconstruction of sampled surfaces with boundary via Morse theory
Coltraro, Franco; Amorós Torrent, Jaume; Alberich Carramiñana, Maria; Torras, Carme
We study the perception problem for garments (e.g. a pair of pants) using tools from computational topology: the identification of their geometry and position from point-cloud samples, as obtained e.g. with 3D scanners. We present a reconstruction algorithm based on Morse theory that proceeds directly from the point-cloud to obtain a cellular decomposition of the surface derived via a Morse function. No intermediate triangulation or local implicit equations are used, avoiding reconstruction-induced artifices. The results are a piecewise parametrization of the surface as a union of Morse cells, suitable for tasks such as noise-filtering or mesh-independent reparametrization, and a cell complex of small rank determining the surface topology. This algorithm can be applied to smooth surfaces with or without boundary, embedded in an ambient space of any dimension.
2024-01-31T11:59:29Z
Coltraro, Franco
Amorós Torrent, Jaume
Alberich Carramiñana, Maria
Torras, Carme
We study the perception problem for garments (e.g. a pair of pants) using tools from computational topology: the identification of their geometry and position from point-cloud samples, as obtained e.g. with 3D scanners. We present a reconstruction algorithm based on Morse theory that proceeds directly from the point-cloud to obtain a cellular decomposition of the surface derived via a Morse function. No intermediate triangulation or local implicit equations are used, avoiding reconstruction-induced artifices. The results are a piecewise parametrization of the surface as a union of Morse cells, suitable for tasks such as noise-filtering or mesh-independent reparametrization, and a cell complex of small rank determining the surface topology. This algorithm can be applied to smooth surfaces with or without boundary, embedded in an ambient space of any dimension.
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Grid equivalent representation of power systems with penetration of power electronics
http://hdl.handle.net/2117/397907
Grid equivalent representation of power systems with penetration of power electronics
Song, Jie; Cheah Mañé, Marc; Prieto Araujo, Eduardo; Amorós Torrent, Jaume; Gomis Bellmunt, Oriol
The Thévenin equivalent is considered as the standard grid equivalent for power system analysis. The integration on power electronics components in the power systems introduces non-linear operation characteristics that cannot be captured by Thévenin equivalent. Therefore, an alternative grid equivalent representation is required. This paper presents a steady-state equivalent representation of power systems with penetration of power electronics, which is suitable for both normal operation studies and short-circuit calculations. This equivalent grid representation is developed based on the voltage-current (U-I) characteristic of a power system to map the relationship between voltages and currents of a specific network node. Such grid equivalent representation has been presented for single-phase, balanced and unbalanced three-phase power systems in this paper. A methodology is presented to identify operation points when the equivalent system under study is connected to any external system. The proposed equivalent grid representation and the methodology for operation points identification have been tested on the Voltage Source Converter (VSC) based test system and are validated through dynamic simulations.
© 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works
2023-12-13T11:06:10Z
Song, Jie
Cheah Mañé, Marc
Prieto Araujo, Eduardo
Amorós Torrent, Jaume
Gomis Bellmunt, Oriol
The Thévenin equivalent is considered as the standard grid equivalent for power system analysis. The integration on power electronics components in the power systems introduces non-linear operation characteristics that cannot be captured by Thévenin equivalent. Therefore, an alternative grid equivalent representation is required. This paper presents a steady-state equivalent representation of power systems with penetration of power electronics, which is suitable for both normal operation studies and short-circuit calculations. This equivalent grid representation is developed based on the voltage-current (U-I) characteristic of a power system to map the relationship between voltages and currents of a specific network node. Such grid equivalent representation has been presented for single-phase, balanced and unbalanced three-phase power systems in this paper. A methodology is presented to identify operation points when the equivalent system under study is connected to any external system. The proposed equivalent grid representation and the methodology for operation points identification have been tested on the Voltage Source Converter (VSC) based test system and are validated through dynamic simulations.
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From 2N to infinitely many escape orbits
http://hdl.handle.net/2117/397018
From 2N to infinitely many escape orbits
Fontana McNally, Josep; Miranda Galcerán, Eva; Oms, Cédric; Peralta Salas, Daniel
—In this short note, we prove that singular Reeb vector fields associated with generic b-contact forms on three dimensional manifolds with compact embedded critical surfaces have either (at least) 2N or an infinite number of escape orbits, where N denotes the number of connected components of the critical set. In case where the first Betti number of a connected component of the critical surface is positive, there exist infinitely many escape orbits. A similar result holds in the case of b-Beltrami vector fields that are not b-Reeb. The proof is based on a more detailed analysis of the main result in [19].
2023-11-24T14:00:02Z
Fontana McNally, Josep
Miranda Galcerán, Eva
Oms, Cédric
Peralta Salas, Daniel
—In this short note, we prove that singular Reeb vector fields associated with generic b-contact forms on three dimensional manifolds with compact embedded critical surfaces have either (at least) 2N or an infinite number of escape orbits, where N denotes the number of connected components of the critical set. In case where the first Betti number of a connected component of the critical surface is positive, there exist infinitely many escape orbits. A similar result holds in the case of b-Beltrami vector fields that are not b-Reeb. The proof is based on a more detailed analysis of the main result in [19].