Departament de Matemàtiques
http://hdl.handle.net/2117/3917
2018-03-23T03:47:04ZReheating constraints in quintessential inflation
http://hdl.handle.net/2117/115509
Reheating constraints in quintessential inflation
Haro Cases, Jaume; Aresté Saló, Llibert
We study the consequences of reheating in quintessential inflation. From simple inflationary quintessential models introduced by de Haro, Amorós, and Pan in [Phys. Rev. D 93, 084018 (2016)] and [Phys. Rev. D 94, 064060 (2016)], we show that when the reheating is due to the production of heavy massive particles conformally coupled with gravity, a viable model which matches with the current observational data is only possible for reheating temperatures that range between 1 GeV and 10^4¿GeV. On the other hand, when the Universe reheats via the production of massless particles, viability of the model is only possible when those particles are nearly conformally coupled with gravity, leading to a reheating temperature between 1 MeV and 10^4 GeV.
2018-03-21T11:10:17ZHaro Cases, JaumeAresté Saló, LlibertWe study the consequences of reheating in quintessential inflation. From simple inflationary quintessential models introduced by de Haro, Amorós, and Pan in [Phys. Rev. D 93, 084018 (2016)] and [Phys. Rev. D 94, 064060 (2016)], we show that when the reheating is due to the production of heavy massive particles conformally coupled with gravity, a viable model which matches with the current observational data is only possible for reheating temperatures that range between 1 GeV and 10^4¿GeV. On the other hand, when the Universe reheats via the production of massless particles, viability of the model is only possible when those particles are nearly conformally coupled with gravity, leading to a reheating temperature between 1 MeV and 10^4 GeV.New algebraic conditions for the identification of the relative position of two coplanar ellipses
http://hdl.handle.net/2117/115506
New algebraic conditions for the identification of the relative position of two coplanar ellipses
Alberich Carramiñana, Maria; Elizalde, Borja; Thomas, Federico
The identification of the relative position of two real coplanar ellipses can be reduced to the identification of the nature of the singular conics in the pencil they define and, in general, their location with respect to these singular conics in the pencil. This latter problem reduces to find the relative location of the roots of univariate polynomials. Since it is usually desired that all generated expressions are algebraic to simplify further analysis, including the case in which the ellipses undergone temporal variations, all recent methods available in the literature rely mathematical tools such as Sturm–Habicht sequences or subresultant sequences. This paper presents an alternative based on more elementary tools which results in a binary decision tree to classify the relative location of two ellipses in 12 different classes. The decision at each node is taken based on the sign of a set of algebraic/rational expressions on the ellipses coefficients, the most complex of them being third and second order polynomial discriminants.
2018-03-21T10:41:01ZAlberich Carramiñana, MariaElizalde, BorjaThomas, FedericoThe identification of the relative position of two real coplanar ellipses can be reduced to the identification of the nature of the singular conics in the pencil they define and, in general, their location with respect to these singular conics in the pencil. This latter problem reduces to find the relative location of the roots of univariate polynomials. Since it is usually desired that all generated expressions are algebraic to simplify further analysis, including the case in which the ellipses undergone temporal variations, all recent methods available in the literature rely mathematical tools such as Sturm–Habicht sequences or subresultant sequences. This paper presents an alternative based on more elementary tools which results in a binary decision tree to classify the relative location of two ellipses in 12 different classes. The decision at each node is taken based on the sign of a set of algebraic/rational expressions on the ellipses coefficients, the most complex of them being third and second order polynomial discriminants.Study of the transfer between libration point orbits and lunar orbits in Earth–Moon system
http://hdl.handle.net/2117/115496
Study of the transfer between libration point orbits and lunar orbits in Earth–Moon system
Cheng, Yu; Gómez Muntané, Gerard; Masdemont Soler, Josep; Yuan, Jianping
This paper is devoted to the study of the transfer problem from a libration point orbit of the Earth–Moon system to an orbit around the Moon. The transfer procedure analysed has two legs: the first one is an orbit of the unstable manifold of the libration orbit and the second one is a transfer orbit between a certain point on the manifold and the final lunar orbit. There are only two manoeuvres involved in the method and they are applied at the beginning and at the end of the second leg. Although the numerical results given in this paper correspond to transfers between halo orbits around the L1 point (of several amplitudes) and lunar polar orbits with altitudes varying between 100 and 500 km, the procedure we develop can be applied to any kind of lunar orbits, libration orbits around the L1 or L2 points of the Earth–Moon system, or to other similar cases with different values of the mass ratio.
2018-03-21T08:13:48ZCheng, YuGómez Muntané, GerardMasdemont Soler, JosepYuan, JianpingThis paper is devoted to the study of the transfer problem from a libration point orbit of the Earth–Moon system to an orbit around the Moon. The transfer procedure analysed has two legs: the first one is an orbit of the unstable manifold of the libration orbit and the second one is a transfer orbit between a certain point on the manifold and the final lunar orbit. There are only two manoeuvres involved in the method and they are applied at the beginning and at the end of the second leg. Although the numerical results given in this paper correspond to transfers between halo orbits around the L1 point (of several amplitudes) and lunar polar orbits with altitudes varying between 100 and 500 km, the procedure we develop can be applied to any kind of lunar orbits, libration orbits around the L1 or L2 points of the Earth–Moon system, or to other similar cases with different values of the mass ratio.An analogue of Vosper's theorem for extension fields
http://hdl.handle.net/2117/115387
An analogue of Vosper's theorem for extension fields
Bachoc, Christine; Serra Albó, Oriol; Zemor, Gilles
We are interested in characterising pairs S, T of F-linear subspaces in a field extension L/F such that the linear span ST of the set of products of elements of S and of elements of T has small dimension. Our central result is a linear analogue of Vosper's Theorem, which gives the structure of vector spaces S, T in a prime extension L of a finite field F for which \begin{linenomath}$$ \dim_FST =\dim_F S+\dim_F T-1, $$\end{linenomath} when dim FS, dim FT ¿ 2 and dim FST ¿ [L : F] - 2.
2018-03-19T10:51:16ZBachoc, ChristineSerra Albó, OriolZemor, GillesWe are interested in characterising pairs S, T of F-linear subspaces in a field extension L/F such that the linear span ST of the set of products of elements of S and of elements of T has small dimension. Our central result is a linear analogue of Vosper's Theorem, which gives the structure of vector spaces S, T in a prime extension L of a finite field F for which \begin{linenomath}$$ \dim_FST =\dim_F S+\dim_F T-1, $$\end{linenomath} when dim FS, dim FT ¿ 2 and dim FST ¿ [L : F] - 2.Colored spanning graphs for set visualization
http://hdl.handle.net/2117/115386
Colored spanning graphs for set visualization
Hurtado Díaz, Fernando Alfredo; Korman, Matias; Van Kreveld, Matias; Löffler, Maarten; Sacristán Adinolfi, Vera; Shioura, Akiyoshi; Silveira, Rodrigo Ignacio; Speckmann, Bettina; Tokuyama, Takeshi
We study an algorithmic problem that is motivated by ink minimization for sparse set visualizations. Our input is a set of points in the plane which are either blue, red, or purple. Blue points belong exclusively to the blue set, red points belong exclusively to the red set, and purple points belong to both sets. A red-blue-purple spanning graph (RBP spanning graph) is a set of edges connecting the points such that the subgraph induced by the red and purple points is connected, and the subgraph induced by the blue and purple points is connected.We study the geometric properties of minimum RBP spanning graphs and the algorithmic problems associated with computing them. Specifically, we show that the general problem can be solved in polynomial time using matroid techniques. In addition, we discuss more efficient algorithms for the case in which points are located on a line or a circle, and also describe a fast (12¿+1)-approximation algorithm, where ¿ is the Steiner ratio.
2018-03-19T10:28:12ZHurtado Díaz, Fernando AlfredoKorman, MatiasVan Kreveld, MatiasLöffler, MaartenSacristán Adinolfi, VeraShioura, AkiyoshiSilveira, Rodrigo IgnacioSpeckmann, BettinaTokuyama, TakeshiWe study an algorithmic problem that is motivated by ink minimization for sparse set visualizations. Our input is a set of points in the plane which are either blue, red, or purple. Blue points belong exclusively to the blue set, red points belong exclusively to the red set, and purple points belong to both sets. A red-blue-purple spanning graph (RBP spanning graph) is a set of edges connecting the points such that the subgraph induced by the red and purple points is connected, and the subgraph induced by the blue and purple points is connected.We study the geometric properties of minimum RBP spanning graphs and the algorithmic problems associated with computing them. Specifically, we show that the general problem can be solved in polynomial time using matroid techniques. In addition, we discuss more efficient algorithms for the case in which points are located on a line or a circle, and also describe a fast (12¿+1)-approximation algorithm, where ¿ is the Steiner ratio.Hamilton-Jacobi theory in multisymplectic classical field theories
http://hdl.handle.net/2117/115384
Hamilton-Jacobi theory in multisymplectic classical field theories
De León, Manuel; Prieto Martínez, Pedro Daniel; Román Roy, Narciso; Vilariño Fernández, Silvia
The geometric framework for the Hamilton-Jacobi theory developed in the studies of Carinena et al. [Int. J. Geom. Methods Mod. Phys. 3(7), 1417-1458 (2006)], Carinena et al. [Int. J. Geom. Methods Mod. Phys. 13(2), 1650017 (2015)], and de Léon et al. [Variations, Geometry and Physics (Nova Science Publishers, New York, 2009)] is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problem is stated for the Lagrangian and the Hamiltonian formalisms of these theories as a particular case of a more general problem, and the classical Hamilton-Jacobi equation for field theories is recovered from this geometrical setting. Particular and complete solutions to these problems are defined and characterized in several equivalent ways in both formalisms, and the equivalence between them is proved. The use of distributions in jet bundles that represent the solutions to the field equations is the fundamental tool in this formulation. Some examples are analyzed and, in particular, the Hamilton-Jacobi equation for non-autonomous mechanical systems is obtained as a special case of our results.
2018-03-19T10:04:33ZDe León, ManuelPrieto Martínez, Pedro DanielRomán Roy, NarcisoVilariño Fernández, SilviaThe geometric framework for the Hamilton-Jacobi theory developed in the studies of Carinena et al. [Int. J. Geom. Methods Mod. Phys. 3(7), 1417-1458 (2006)], Carinena et al. [Int. J. Geom. Methods Mod. Phys. 13(2), 1650017 (2015)], and de Léon et al. [Variations, Geometry and Physics (Nova Science Publishers, New York, 2009)] is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problem is stated for the Lagrangian and the Hamiltonian formalisms of these theories as a particular case of a more general problem, and the classical Hamilton-Jacobi equation for field theories is recovered from this geometrical setting. Particular and complete solutions to these problems are defined and characterized in several equivalent ways in both formalisms, and the equivalence between them is proved. The use of distributions in jet bundles that represent the solutions to the field equations is the fundamental tool in this formulation. Some examples are analyzed and, in particular, the Hamilton-Jacobi equation for non-autonomous mechanical systems is obtained as a special case of our results.Fostering the classroom attention using collective intelligence education tools
http://hdl.handle.net/2117/115285
Fostering the classroom attention using collective intelligence education tools
Simó Mezquita, Ester; Monguet Fierro, José María; Meza, Jaime
Keeping students' attention in class remains a challenge in the teaching-learning process. The consumption of time trying to focus the attention of the student on the tasks of the class generates fatigue to both teacher and students. Several researchers conclude that using technology in the classroom has proven to be a distraction element of care rather than becoming a supportive element. From the scenario raised emerges the question: Could the ICT tools be used to improve attention and learning in class?
This research explores the application of a web tool called Flash Learning (FL) using Problem Based Learning approach (PBL) . Flash Learning allowed implement a strategy with a real-time learning activity that helps in the process of concentrating student attention during a class.
Flash Learning was designed with the aim of integrating classroom management with the attention of its students and allowing self-reflective analysis of students in front of their classmates. On the other hand, the teacher allows him to obtain real-time clues about the tendencies of understanding and learning of the subject matter.
Based on the results, we consider that the use of new forms of teaching and learning based on the emerging paradigms is necessary. Therefore, the combination of Flash Learning could become an effective way to keeping students' attention in class and fostering the collective intelligence.
2018-03-16T12:33:31ZSimó Mezquita, EsterMonguet Fierro, José MaríaMeza, JaimeKeeping students' attention in class remains a challenge in the teaching-learning process. The consumption of time trying to focus the attention of the student on the tasks of the class generates fatigue to both teacher and students. Several researchers conclude that using technology in the classroom has proven to be a distraction element of care rather than becoming a supportive element. From the scenario raised emerges the question: Could the ICT tools be used to improve attention and learning in class?
This research explores the application of a web tool called Flash Learning (FL) using Problem Based Learning approach (PBL) . Flash Learning allowed implement a strategy with a real-time learning activity that helps in the process of concentrating student attention during a class.
Flash Learning was designed with the aim of integrating classroom management with the attention of its students and allowing self-reflective analysis of students in front of their classmates. On the other hand, the teacher allows him to obtain real-time clues about the tendencies of understanding and learning of the subject matter.
Based on the results, we consider that the use of new forms of teaching and learning based on the emerging paradigms is necessary. Therefore, the combination of Flash Learning could become an effective way to keeping students' attention in class and fostering the collective intelligence.Combinatorics in the Art of the Twentieth Century
http://hdl.handle.net/2117/115282
Combinatorics in the Art of the Twentieth Century
Barrière Figueroa, Eulalia
This paper is motivated by a question I asked myself: How can combinatorial structures be used in a work of art? Immediately, other questions arose: Whether there are artists that work or think combinatorially? If so, what works have they produced in this way? What are the similarities and differences between art works produced using
combinatorics? This paper presents the first results of the attempt to answer these questions, being a survey of a selection of works that use or contain combinatorics in some way, including music, literature and visual arts, focusing on the twentieth century.
2018-03-16T11:52:11ZBarrière Figueroa, EulaliaThis paper is motivated by a question I asked myself: How can combinatorial structures be used in a work of art? Immediately, other questions arose: Whether there are artists that work or think combinatorially? If so, what works have they produced in this way? What are the similarities and differences between art works produced using
combinatorics? This paper presents the first results of the attempt to answer these questions, being a survey of a selection of works that use or contain combinatorics in some way, including music, literature and visual arts, focusing on the twentieth century.Measuring the collective intelligence education index
http://hdl.handle.net/2117/115281
Measuring the collective intelligence education index
Simó Mezquita, Ester; Monguet Fierro, José María; Meza, Jaime
War games and sports games always seek glory and excellence in an environment where participants enjoy what they do. Success is guaranteed in the degree of effective collaboration and coordination within the team members, as well as the strategy used by teams, such games or war strategies are generated since the birth of humanity. In this sense, the following questions emerge in the field of education: Is it possible to design learning activities that use this principle applied to collaborative work in the classroom? Which are the conditions of application of team competition strategy using ICT tools and how to measure it?
This research explores the application of a web tool called Choose the Best (CTB). CTB implements a strategy that fosters competitiveness among the teams of a class, as well as the coordination and collaboration within the same, these types of strategies contribute to the development of Collective Intelligence levels. It's measured through a group of implemented metrics.
Based on the results, we consider that the use of new forms of teaching and learning based on the emerging paradigms is necessary. Therefore, CTB is a tool that could become an effective way to measuring the group's performance according to Collective Intelligence paradigms.
2018-03-16T11:49:26ZSimó Mezquita, EsterMonguet Fierro, José MaríaMeza, JaimeWar games and sports games always seek glory and excellence in an environment where participants enjoy what they do. Success is guaranteed in the degree of effective collaboration and coordination within the team members, as well as the strategy used by teams, such games or war strategies are generated since the birth of humanity. In this sense, the following questions emerge in the field of education: Is it possible to design learning activities that use this principle applied to collaborative work in the classroom? Which are the conditions of application of team competition strategy using ICT tools and how to measure it?
This research explores the application of a web tool called Choose the Best (CTB). CTB implements a strategy that fosters competitiveness among the teams of a class, as well as the coordination and collaboration within the same, these types of strategies contribute to the development of Collective Intelligence levels. It's measured through a group of implemented metrics.
Based on the results, we consider that the use of new forms of teaching and learning based on the emerging paradigms is necessary. Therefore, CTB is a tool that could become an effective way to measuring the group's performance according to Collective Intelligence paradigms.Toward a collective intelligence recommender system for education
http://hdl.handle.net/2117/115279
Toward a collective intelligence recommender system for education
Meza, Jaime; Simó Mezquita, Ester; Monguet Fierro, José María
The development of Information and Communication Technology (ICT), have revolutionized the world and have moved us into the information age, however the access and handling of this large amount of information is causing valuable time losses. Teachers in Higher Education especially use the Internet as a tool to consult materials and content for the development of the subjects. The internet has very broad services, and sometimes it is difficult for users to find the contents in an easy and fast way. This problem is increasing at the time, causing that students spend a lot of time in search information rather than in synthesis, analysis and construction of new knowledge. In this context, several questions have emerged: Is it possible to design learning activities that allow us to value the information search and to encourage collective participation?. What are the conditions that an ICT tool that supports a process of information search has to have to optimize the student's time and learning?
This article presents the use and application of a Recommender System (RS) designed on paradigms of Collective Intelligence (CI). The RS designed encourages the collective learning and the authentic participation of the students.
The research combines the literature study with the analysis of the ICT tools that have emerged in the field of the CI and RS. Also, Design-Based Research (DBR) was used to compile and summarize collective intelligence approaches and filtering techniques reported in the literature in Higher Education as well as to incrementally improving the tool.
Several are the benefits that have been evidenced as a result of the exploratory study carried out. Among them the following stand out:
• It improves student motivation, as it helps you discover new content of interest in an easy way.
• It saves time in the search and classification of teaching material of interest.
• It fosters specialized reading, inspires competence as a means of learning.
• It gives the teacher the ability to generate reports of trends and behaviors of their students, real-time assessment of the quality of learning material.
The authors consider that the use of ICT tools that combine the paradigms of the CI and RS presented in this work, are a tool that improves the construction of student knowledge and motivates their collective development in cyberspace, in addition, the model of Filltering Contents used supports the design of models and strategies of collective intelligence in Higher Education.
2018-03-16T11:32:37ZMeza, JaimeSimó Mezquita, EsterMonguet Fierro, José MaríaThe development of Information and Communication Technology (ICT), have revolutionized the world and have moved us into the information age, however the access and handling of this large amount of information is causing valuable time losses. Teachers in Higher Education especially use the Internet as a tool to consult materials and content for the development of the subjects. The internet has very broad services, and sometimes it is difficult for users to find the contents in an easy and fast way. This problem is increasing at the time, causing that students spend a lot of time in search information rather than in synthesis, analysis and construction of new knowledge. In this context, several questions have emerged: Is it possible to design learning activities that allow us to value the information search and to encourage collective participation?. What are the conditions that an ICT tool that supports a process of information search has to have to optimize the student's time and learning?
This article presents the use and application of a Recommender System (RS) designed on paradigms of Collective Intelligence (CI). The RS designed encourages the collective learning and the authentic participation of the students.
The research combines the literature study with the analysis of the ICT tools that have emerged in the field of the CI and RS. Also, Design-Based Research (DBR) was used to compile and summarize collective intelligence approaches and filtering techniques reported in the literature in Higher Education as well as to incrementally improving the tool.
Several are the benefits that have been evidenced as a result of the exploratory study carried out. Among them the following stand out:
• It improves student motivation, as it helps you discover new content of interest in an easy way.
• It saves time in the search and classification of teaching material of interest.
• It fosters specialized reading, inspires competence as a means of learning.
• It gives the teacher the ability to generate reports of trends and behaviors of their students, real-time assessment of the quality of learning material.
The authors consider that the use of ICT tools that combine the paradigms of the CI and RS presented in this work, are a tool that improves the construction of student knowledge and motivates their collective development in cyberspace, in addition, the model of Filltering Contents used supports the design of models and strategies of collective intelligence in Higher Education.