Articles de revista
http://hdl.handle.net/2117/3918
Mon, 20 Jan 2020 06:57:28 GMT2020-01-20T06:57:28ZArcs and tensors
http://hdl.handle.net/2117/175074
Arcs and tensors
Ball, Simeon Michael; Lavrauw, Michel
To an arc A of PG(k-1,q) of size q+k-1-t we associate a tensor in ¿¿k,t(A)¿¿k-1 , where ¿k,t denotes the Veronese map of degree t defined on PG(k-1,q) . As a corollary we prove that for each arc A in PG(k-1,q) of size q+k-1-t , which is not contained in a hypersurface of degree t, there exists a polynomial F(Y1,…,Yk-1) (in k(k-1) variables) where Yj=(Xj1,…,Xjk) , which is homogeneous of degree t in each of the k-tuples of variables Yj , which upon evaluation at any (k-2) -subset S of the arc A gives a form of degree t on PG(k-1,q) whose zero locus is the tangent hypersurface of A at S, i.e. the union of the tangent hyperplanes of A at S. This generalises the equivalent result for planar arcs ( k=3 ), proven in [2], to arcs in projective spaces of arbitrary dimension. A slightly weaker result is obtained for arcs in PG(k-1,q) of size q+k-1-t which are contained in a hypersurface of degree t. We also include a new proof of the Segre–Blokhuis–Bruen–Thas hypersurface associated to an arc of hyperplanes in PG(k-1,q) .
This is a post-peer-review, pre-copyedit version of an article published in Designs, Codes, and Cryptography. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10623-019-00668-z
Thu, 16 Jan 2020 13:26:05 GMThttp://hdl.handle.net/2117/1750742020-01-16T13:26:05ZBall, Simeon MichaelLavrauw, MichelTo an arc A of PG(k-1,q) of size q+k-1-t we associate a tensor in ¿¿k,t(A)¿¿k-1 , where ¿k,t denotes the Veronese map of degree t defined on PG(k-1,q) . As a corollary we prove that for each arc A in PG(k-1,q) of size q+k-1-t , which is not contained in a hypersurface of degree t, there exists a polynomial F(Y1,…,Yk-1) (in k(k-1) variables) where Yj=(Xj1,…,Xjk) , which is homogeneous of degree t in each of the k-tuples of variables Yj , which upon evaluation at any (k-2) -subset S of the arc A gives a form of degree t on PG(k-1,q) whose zero locus is the tangent hypersurface of A at S, i.e. the union of the tangent hyperplanes of A at S. This generalises the equivalent result for planar arcs ( k=3 ), proven in [2], to arcs in projective spaces of arbitrary dimension. A slightly weaker result is obtained for arcs in PG(k-1,q) of size q+k-1-t which are contained in a hypersurface of degree t. We also include a new proof of the Segre–Blokhuis–Bruen–Thas hypersurface associated to an arc of hyperplanes in PG(k-1,q) .Matching points with disks with a common intersection
http://hdl.handle.net/2117/175020
Matching points with disks with a common intersection
Huemer, Clemens; Pérez Lantero, Pablo; Seara Ojea, Carlos; Silveira, Rodrigo Ignacio
We consider matchings with diametral disks between two sets of points R and B. More precisely, for each pair of matched points p ¿ R and q ¿ B, we consider the disk through p and q with the smallest diameter. We prove that for any R and B such that |R| = |B|, there exists a perfect matching such that the diametral disks of the matched point pairs have a common intersection. In fact, our result is stronger, and shows that a maximum weight perfect matching has this property.
Thu, 16 Jan 2020 12:07:53 GMThttp://hdl.handle.net/2117/1750202020-01-16T12:07:53ZHuemer, ClemensPérez Lantero, PabloSeara Ojea, CarlosSilveira, Rodrigo IgnacioWe consider matchings with diametral disks between two sets of points R and B. More precisely, for each pair of matched points p ¿ R and q ¿ B, we consider the disk through p and q with the smallest diameter. We prove that for any R and B such that |R| = |B|, there exists a perfect matching such that the diametral disks of the matched point pairs have a common intersection. In fact, our result is stronger, and shows that a maximum weight perfect matching has this property.Rainbow matchings in Dirac bipartite graphs
http://hdl.handle.net/2117/174992
Rainbow matchings in Dirac bipartite graphs
Coulson, Matthew John; Perarnau Llobet, Guillem
We show the existence of rainbow perfect matchings in µn-bounded edge colorings of Dirac bipartite graphs, for a sufficiently small µ¿>¿0. As an application of our results, we obtain several results on the existence of rainbow k-factors in Dirac graphs and rainbow spanning subgraphs of bounded maximum degree on graphs with large minimum degree.
This is the peer reviewed version of the following article: Coulson, M, Perarnau, G. Rainbow matchings in Dirac bipartite graphs. Random Struct Alg. 2019; 55: 271– 289., which has been published in final form at https://doi.org/10.1002/rsa.20835. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions
Thu, 16 Jan 2020 11:07:55 GMThttp://hdl.handle.net/2117/1749922020-01-16T11:07:55ZCoulson, Matthew JohnPerarnau Llobet, GuillemWe show the existence of rainbow perfect matchings in µn-bounded edge colorings of Dirac bipartite graphs, for a sufficiently small µ¿>¿0. As an application of our results, we obtain several results on the existence of rainbow k-factors in Dirac graphs and rainbow spanning subgraphs of bounded maximum degree on graphs with large minimum degree.Non-crossing paths with geographic constraints
http://hdl.handle.net/2117/174889
Non-crossing paths with geographic constraints
Silveira, Rodrigo Ignacio; Speckmann, Bettina; Verbeek, Kevin
A geographic network is a graph whose vertices are restricted to lie in a prescribed region in the plane. In this paper we begin to study the following fundamental problem for geographic networks: can a given geographic network be drawn without crossings? We focus on the seemingly simple setting where each region is a unit length vertical segment, and one wants to connect pairs of segments with a path that lies inside the convex hull of the two segments. We prove that when paths must be drawn as straight line segments, it is NP-complete to determine if a crossing-free solution exists. In contrast, we show that when paths must be monotone curves, the question can be answered in polynomial time. In the more general case of paths that can have any shape, we show that the problem is polynomial under certain assumptions.
Wed, 15 Jan 2020 12:13:37 GMThttp://hdl.handle.net/2117/1748892020-01-15T12:13:37ZSilveira, Rodrigo IgnacioSpeckmann, BettinaVerbeek, KevinA geographic network is a graph whose vertices are restricted to lie in a prescribed region in the plane. In this paper we begin to study the following fundamental problem for geographic networks: can a given geographic network be drawn without crossings? We focus on the seemingly simple setting where each region is a unit length vertical segment, and one wants to connect pairs of segments with a path that lies inside the convex hull of the two segments. We prove that when paths must be drawn as straight line segments, it is NP-complete to determine if a crossing-free solution exists. In contrast, we show that when paths must be monotone curves, the question can be answered in polynomial time. In the more general case of paths that can have any shape, we show that the problem is polynomial under certain assumptions.Electron density retrieval from truncated Radio Occultation GNSS data
http://hdl.handle.net/2117/174869
Electron density retrieval from truncated Radio Occultation GNSS data
Lyu, Haixia; Hernández Pajares, Manuel; Monte Moreno, Enrique; Cardellach Galí, Estel
This paper summarizes the definition and validation of two complementary new strategies, to invert incomplete Global Navigation Satellite System Radio-Occultation (RO) ionospheric measurements, such as the ones to be provided by the future EUMETSAT Polar System Second Generation. It will provide RO measurements with impact parameter much below the Low Earth Orbiters' height (817 km): from 500 km down approximately. The first presented method to invert truncated RO data is denoted as Abel-VaryChap Hybrid modeling from topside Incomplete Global Navigation Satellite System RO data, based on simple First Principles, very precise, and well suited for postprocessing. And the second method is denoted as Simple Estimation of Electron density profiles from topside Incomplete RO data, is less precise, but yields very fast estimations, suitable for Near Real-Time determination. Both techniques will be described and assessed with a set of 546 representative COSMIC/FORMOSAT-3 ROs, with relative errors of 7% and 11% for Abel-VaryChap Hybrid modeling from topside Incomplete Global Navigation Satellite System RO data and Simple Estimation of Electron density profiles from topside Incomplete RO data, respectively, with 20 min and 15 s, respectively, of computational time per occultation in our Intel I7 PC.
Wed, 15 Jan 2020 11:29:34 GMThttp://hdl.handle.net/2117/1748692020-01-15T11:29:34ZLyu, HaixiaHernández Pajares, ManuelMonte Moreno, EnriqueCardellach Galí, EstelThis paper summarizes the definition and validation of two complementary new strategies, to invert incomplete Global Navigation Satellite System Radio-Occultation (RO) ionospheric measurements, such as the ones to be provided by the future EUMETSAT Polar System Second Generation. It will provide RO measurements with impact parameter much below the Low Earth Orbiters' height (817 km): from 500 km down approximately. The first presented method to invert truncated RO data is denoted as Abel-VaryChap Hybrid modeling from topside Incomplete Global Navigation Satellite System RO data, based on simple First Principles, very precise, and well suited for postprocessing. And the second method is denoted as Simple Estimation of Electron density profiles from topside Incomplete RO data, is less precise, but yields very fast estimations, suitable for Near Real-Time determination. Both techniques will be described and assessed with a set of 546 representative COSMIC/FORMOSAT-3 ROs, with relative errors of 7% and 11% for Abel-VaryChap Hybrid modeling from topside Incomplete Global Navigation Satellite System RO data and Simple Estimation of Electron density profiles from topside Incomplete RO data, respectively, with 20 min and 15 s, respectively, of computational time per occultation in our Intel I7 PC.Critical issues in ionospheric data quality and implications for scientific studies
http://hdl.handle.net/2117/174746
Critical issues in ionospheric data quality and implications for scientific studies
Araujo-Pradere, E.; Weatherhead, E. C.; Dandenault, P. B.; Bilitza, D.; Wilkinson, P.; Hernández Pajares, Manuel
Ionospheric data are valuable records of the behavior of the ionosphere, solar activity, and the entire Sun-Earth system. The data are critical for both societally important services and scientific investigations of upper atmospheric variability. This work investigates some of the difficulties and pitfalls in maintaining long-term records of geophysical measurements. This investigation focuses on the ionospheric parameters contained in the historical data sets within the National Oceanic and Atmospheric Administration National Geophysical Data Center and Space Physics Interactive Data Resource databases. These archives include data from approximately 100 ionosonde stations worldwide, beginning in the early 1940s. Our study focuses on the quality and consistency of ionosonde data accessible via the primary Space Physics Interactive Data Resource node located within the National Oceanic and Atmospheric Administration National Geophysical Data Center and the World Data Center for Solar-Terrestrial Physics located in Boulder, Colorado. We find that, although the Space Physics Interactive Data Resource archives contained an impressive amount of high-quality data, specific problems existed involving missing and noncontiguous data sets, long-term variations or changes in methodologies and analysis procedures used, and incomplete documentation. The important lessons learned from this investigation are that the data incorporated into an archive must have clear traceability back to the primary source, including scientific validation by the contributors, and that the historical records must have associated metadata that describe relevant nuances in the observations. Although this report only focuses on historical ionosonde data in National Oceanic and Atmospheric Administration databases, we feel that these findings have general applicability to environmental scientists interested in using long-term geophysical data sets for climate and global change research.
Tue, 14 Jan 2020 09:13:31 GMThttp://hdl.handle.net/2117/1747462020-01-14T09:13:31ZAraujo-Pradere, E.Weatherhead, E. C.Dandenault, P. B.Bilitza, D.Wilkinson, P.Hernández Pajares, ManuelIonospheric data are valuable records of the behavior of the ionosphere, solar activity, and the entire Sun-Earth system. The data are critical for both societally important services and scientific investigations of upper atmospheric variability. This work investigates some of the difficulties and pitfalls in maintaining long-term records of geophysical measurements. This investigation focuses on the ionospheric parameters contained in the historical data sets within the National Oceanic and Atmospheric Administration National Geophysical Data Center and Space Physics Interactive Data Resource databases. These archives include data from approximately 100 ionosonde stations worldwide, beginning in the early 1940s. Our study focuses on the quality and consistency of ionosonde data accessible via the primary Space Physics Interactive Data Resource node located within the National Oceanic and Atmospheric Administration National Geophysical Data Center and the World Data Center for Solar-Terrestrial Physics located in Boulder, Colorado. We find that, although the Space Physics Interactive Data Resource archives contained an impressive amount of high-quality data, specific problems existed involving missing and noncontiguous data sets, long-term variations or changes in methodologies and analysis procedures used, and incomplete documentation. The important lessons learned from this investigation are that the data incorporated into an archive must have clear traceability back to the primary source, including scientific validation by the contributors, and that the historical records must have associated metadata that describe relevant nuances in the observations. Although this report only focuses on historical ionosonde data in National Oceanic and Atmospheric Administration databases, we feel that these findings have general applicability to environmental scientists interested in using long-term geophysical data sets for climate and global change research.Stress relaxation in epithelial monolayers is controlled by the actomyosin cortex
http://hdl.handle.net/2117/174696
Stress relaxation in epithelial monolayers is controlled by the actomyosin cortex
Khalilgharibi, Nargess; Fouchard, Jonathan; Asadipour, Nina; Barrientos, Ricardo; Duda, Maria; Bonfanti, Alessandra; Yonis, Amina; Harris, Andrew; Mosaffa, Payman; Fujita, Yasuyuki; Kabla, Alexandre; Mao, Yanlan; Baum, Buzz; Muñoz Romero, José; Miodownik, Mark; Charras, Guillaume
Epithelial monolayers are one-cell thick tissue sheets that separate internal and external environments. As part of their function, they have to withstand extrinsic mechanical stresses applied at high strain rates. However, little is known about how monolayers respond to mechanical deformations. Here, by subjecting suspended epithelial monolayers to stretch, we find that they dissipate stresses on a minute time-scale in a process that involves an increase in monolayer length, pointing to active remodelling of cell architecture during relaxation. Strikingly, monolayers consisting of tens of thousands of cells relax stress with similar dynamics to single rounded cells and both respond similarly to perturbations of actomyosin. By contrast, cell-cell junctional complexes and intermediate filaments do not relax tissue stress, but form stable connections between cells, allowing monolayers to behave rheologically as single cells. Taken together our data show that actomyosin dynamics governs the rheological properties of epithelial monolayers, dissipating applied stresses, and enabling changes in monolayer length.
Mon, 13 Jan 2020 13:11:25 GMThttp://hdl.handle.net/2117/1746962020-01-13T13:11:25ZKhalilgharibi, NargessFouchard, JonathanAsadipour, NinaBarrientos, RicardoDuda, MariaBonfanti, AlessandraYonis, AminaHarris, AndrewMosaffa, PaymanFujita, YasuyukiKabla, AlexandreMao, YanlanBaum, BuzzMuñoz Romero, JoséMiodownik, MarkCharras, GuillaumeEpithelial monolayers are one-cell thick tissue sheets that separate internal and external environments. As part of their function, they have to withstand extrinsic mechanical stresses applied at high strain rates. However, little is known about how monolayers respond to mechanical deformations. Here, by subjecting suspended epithelial monolayers to stretch, we find that they dissipate stresses on a minute time-scale in a process that involves an increase in monolayer length, pointing to active remodelling of cell architecture during relaxation. Strikingly, monolayers consisting of tens of thousands of cells relax stress with similar dynamics to single rounded cells and both respond similarly to perturbations of actomyosin. By contrast, cell-cell junctional complexes and intermediate filaments do not relax tissue stress, but form stable connections between cells, allowing monolayers to behave rheologically as single cells. Taken together our data show that actomyosin dynamics governs the rheological properties of epithelial monolayers, dissipating applied stresses, and enabling changes in monolayer length.Planar differential growth rates initiate precise fold positions in complex epithelia
http://hdl.handle.net/2117/174693
Planar differential growth rates initiate precise fold positions in complex epithelia
Muñoz Romero, José
Tissue folding is a fundamental process that shapes epithelia into complex 3D organs. The initial positioning of folds is the foundation for the emergence of correct tissue morphology. Mechanisms forming individual folds have been studied, but the precise positioning of folds in complex, multi-folded epithelia is less well understood. We present a computational model of morphogenesis, encompassing local differential growth and tissue mechanics, to investigate tissue fold positioning. We use the Drosophila wing disc as our model system, and show that there is spatial-temporal heterogeneity in its planar growth rates. This differential growth, especially at the early stages of development, is the main driver for fold positioning. Increased apical layer stiffness and confinement by the basement membrane drive fold formation, but influence positioning to a lesser degree. The model successfully predicts the in vivo morphology of overgrowth clones and wingless mutants via perturbations solely on planar differential growth in silico.
Mon, 13 Jan 2020 12:58:02 GMThttp://hdl.handle.net/2117/1746932020-01-13T12:58:02ZMuñoz Romero, JoséTissue folding is a fundamental process that shapes epithelia into complex 3D organs. The initial positioning of folds is the foundation for the emergence of correct tissue morphology. Mechanisms forming individual folds have been studied, but the precise positioning of folds in complex, multi-folded epithelia is less well understood. We present a computational model of morphogenesis, encompassing local differential growth and tissue mechanics, to investigate tissue fold positioning. We use the Drosophila wing disc as our model system, and show that there is spatial-temporal heterogeneity in its planar growth rates. This differential growth, especially at the early stages of development, is the main driver for fold positioning. Increased apical layer stiffness and confinement by the basement membrane drive fold formation, but influence positioning to a lesser degree. The model successfully predicts the in vivo morphology of overgrowth clones and wingless mutants via perturbations solely on planar differential growth in silico.Differentiable families of traceless matrix triples
http://hdl.handle.net/2117/174673
Differentiable families of traceless matrix triples
García Planas, María Isabel; Klymchuk, Tetiana
Analysis of spectra of families of sets of matrices verifying certain properties is not simple because phenomena as singularities and bifurcations appear. An excellent tool for the analysis can be making use of versal deformations because of the spectrum of the family coincides with the spectrum of its versal deformation. Disposing of a versal deformation is advantageous since any perturbation of an element can be described up to equivalence by its versal deformation, and it gives the possibility to calculate bifurcation diagrams of families of elements in general position. V.I. Arnold constructed versal deformations, of a differentiable family of square matrices under conjugation and his techniques have been generalised to different cases as to matrix pencils under the strict equivalence, for example.
In this paper, we present versal deformations of elements of the Lie algebra consisting of triples of traceless matrices to coefficients on $\mathbb{F} =\mathbb{ C}$ or $\mathbb{R}$, which are simultaneously diagonalizable.
Study families of traceless matrix triples have great interest because the Lie algebra is related to gauge fields because they appear in the Lagrangian describing the dynamics of the field, then they are associated to 1-forms that take values on a certain Lie algebra. It is also of interest to note that triples of traceless matrices have some relevance for supergravity theories. Another application is found when we must give the instanton solution of Yang-Mills field can be presented in an octonion form, and it can be represented by triples of traceless matrices.
Montse Pallàs <mpallasm@gmail.com>
4 de nov. 2019 13:31
“This is a post-peer-review, pre-copyedit version of an article published in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas (Online). The final authenticated version is available online at: http://dx.doi.org/10.1007/s13398-019-00754-w
Mon, 13 Jan 2020 09:42:33 GMThttp://hdl.handle.net/2117/1746732020-01-13T09:42:33ZGarcía Planas, María IsabelKlymchuk, TetianaAnalysis of spectra of families of sets of matrices verifying certain properties is not simple because phenomena as singularities and bifurcations appear. An excellent tool for the analysis can be making use of versal deformations because of the spectrum of the family coincides with the spectrum of its versal deformation. Disposing of a versal deformation is advantageous since any perturbation of an element can be described up to equivalence by its versal deformation, and it gives the possibility to calculate bifurcation diagrams of families of elements in general position. V.I. Arnold constructed versal deformations, of a differentiable family of square matrices under conjugation and his techniques have been generalised to different cases as to matrix pencils under the strict equivalence, for example.
In this paper, we present versal deformations of elements of the Lie algebra consisting of triples of traceless matrices to coefficients on $\mathbb{F} =\mathbb{ C}$ or $\mathbb{R}$, which are simultaneously diagonalizable.
Study families of traceless matrix triples have great interest because the Lie algebra is related to gauge fields because they appear in the Lagrangian describing the dynamics of the field, then they are associated to 1-forms that take values on a certain Lie algebra. It is also of interest to note that triples of traceless matrices have some relevance for supergravity theories. Another application is found when we must give the instanton solution of Yang-Mills field can be presented in an octonion form, and it can be represented by triples of traceless matrices.Minor loops of the Dahl and LuGre models
http://hdl.handle.net/2117/174597
Minor loops of the Dahl and LuGre models
Ikhouane, Fayçal; Mañosa Fernández, Víctor; Pujol Vázquez, Gisela
Hysteresis is a special type of behavior encountered in physical systems: in a hysteretic system, when the input is periodic and varies slowly, the steady-state part of the output- versus-input graph becomes a loop called hysteresis loop . In the presence of perturbed in- puts, this hysteresis loop presents small lobes called minor loops that are located inside a larger curve called major loop. The study of minor loops is becoming increasingly popular since it leads to a quantification of the loss of energy. The aim of the present paper is to give an explicit analytic expression of the minor loops of the LuGre and the Dahl models of dynamic dry friction.
Fri, 10 Jan 2020 13:58:09 GMThttp://hdl.handle.net/2117/1745972020-01-10T13:58:09ZIkhouane, FayçalMañosa Fernández, VíctorPujol Vázquez, GiselaHysteresis is a special type of behavior encountered in physical systems: in a hysteretic system, when the input is periodic and varies slowly, the steady-state part of the output- versus-input graph becomes a loop called hysteresis loop . In the presence of perturbed in- puts, this hysteresis loop presents small lobes called minor loops that are located inside a larger curve called major loop. The study of minor loops is becoming increasingly popular since it leads to a quantification of the loss of energy. The aim of the present paper is to give an explicit analytic expression of the minor loops of the LuGre and the Dahl models of dynamic dry friction.