Departament de Matemàtiques
http://hdl.handle.net/2117/3917
2017-03-29T21:09:53ZLayer structure of De Bruijn and Kautz digraphs: an application to deflection routing
http://hdl.handle.net/2117/103040
Layer structure of De Bruijn and Kautz digraphs: an application to deflection routing
Fàbrega Canudas, José; Martí Farré, Jaume; Muñoz López, Francisco Javier
In the main part of this paper we present polynomial expressions for the cardinalities of some sets of interest of the nice distance-layer structure of the well-known De Bruijn and Kautz digraphs. More precisely, given a vertex $v$, let $S_{i}^\star(v)$ be the set of vertices at distance $i$ from $v$. We show that $|S_{i}^\star(v)|=d^i-a_{i-1}d^{i-1}-\cdots -a_{1} d-a_{0}$, where $d$ is the degree of the digraph and the coefficients $a_{k}\in\{0,1\}$ are explicitly calculated. Analogously, let $w$ be a vertex adjacent from $v$ such that $S_{i}^\star(v)\cap S_j^{\ast}(w)\neq \emptyset$ for some $j$. We prove that $\big |S_{i}^\star(v) \cap S_j^{\ast}(w) \big |=d^i-b_{i-1}d^{i-1}-\ldots -b_{1} d-b_{0},$ where the coefficients $b_{t}\in\{0,1\}$ are determined from the coefficients $a_k$ of the polynomial expression of $|S_{i}^\star(v)|$. An application to deflection routing in De Bruijn and Kautz networks serves as motivation for our study. It is worth-mentioning that our analysis can be extended to other families of digraphs on alphabet or to general iterated line digraphs.
2017-03-29T12:12:53ZFàbrega Canudas, JoséMartí Farré, JaumeMuñoz López, Francisco JavierIn the main part of this paper we present polynomial expressions for the cardinalities of some sets of interest of the nice distance-layer structure of the well-known De Bruijn and Kautz digraphs. More precisely, given a vertex $v$, let $S_{i}^\star(v)$ be the set of vertices at distance $i$ from $v$. We show that $|S_{i}^\star(v)|=d^i-a_{i-1}d^{i-1}-\cdots -a_{1} d-a_{0}$, where $d$ is the degree of the digraph and the coefficients $a_{k}\in\{0,1\}$ are explicitly calculated. Analogously, let $w$ be a vertex adjacent from $v$ such that $S_{i}^\star(v)\cap S_j^{\ast}(w)\neq \emptyset$ for some $j$. We prove that $\big |S_{i}^\star(v) \cap S_j^{\ast}(w) \big |=d^i-b_{i-1}d^{i-1}-\ldots -b_{1} d-b_{0},$ where the coefficients $b_{t}\in\{0,1\}$ are determined from the coefficients $a_k$ of the polynomial expression of $|S_{i}^\star(v)|$. An application to deflection routing in De Bruijn and Kautz networks serves as motivation for our study. It is worth-mentioning that our analysis can be extended to other families of digraphs on alphabet or to general iterated line digraphs.On the length and area spectrum of analytic convex domains
http://hdl.handle.net/2117/103012
On the length and area spectrum of analytic convex domains
Martín, Pau; Ramírez Ros, Rafael; Tamarit Sariol, A.
Area-preserving twist maps have at least two different (p, q)-periodic orbits and every (p, q)-periodic orbit has its (p, q)-periodic action for suitable couples (p, q). We establish an exponentially small upper bound for the differences of (p, q)-periodic actions when the map is analytic on a (m, n)-resonant rotational invariant curve (resonant RIC) and p/q is 'sufficiently close' to m/n. The exponent in this upper bound is closely related to the analyticity strip width of a suitable angular variable. The result is obtained in two steps. First, we prove a Neishtadt-like theorem, in which the n-th power of the twist map is written as an integrable twist map plus an exponentially small remainder on the distance to the RIC. Second,
we apply the MacKay-Meiss-Percival action principle. We apply our exponentially small upper bound to several billiard problems. The resonant RIC is a boundary of the phase space in almost all of them. For instance, we show that the lengths (respectively, areas) of all the (1, q)-periodic billiard (respectively, dual billiard) trajectories inside (respectively, outside) analytic strictly convex domains are exponentially close in the period q. This improves some classical results of Marvizi, Melrose, Colin de Verdiere, Tabachnikov, and others about the smooth case.
2017-03-29T07:37:50ZMartín, PauRamírez Ros, RafaelTamarit Sariol, A.Area-preserving twist maps have at least two different (p, q)-periodic orbits and every (p, q)-periodic orbit has its (p, q)-periodic action for suitable couples (p, q). We establish an exponentially small upper bound for the differences of (p, q)-periodic actions when the map is analytic on a (m, n)-resonant rotational invariant curve (resonant RIC) and p/q is 'sufficiently close' to m/n. The exponent in this upper bound is closely related to the analyticity strip width of a suitable angular variable. The result is obtained in two steps. First, we prove a Neishtadt-like theorem, in which the n-th power of the twist map is written as an integrable twist map plus an exponentially small remainder on the distance to the RIC. Second,
we apply the MacKay-Meiss-Percival action principle. We apply our exponentially small upper bound to several billiard problems. The resonant RIC is a boundary of the phase space in almost all of them. For instance, we show that the lengths (respectively, areas) of all the (1, q)-periodic billiard (respectively, dual billiard) trajectories inside (respectively, outside) analytic strictly convex domains are exponentially close in the period q. This improves some classical results of Marvizi, Melrose, Colin de Verdiere, Tabachnikov, and others about the smooth case.Structural aspects of Hamilton–Jacobi theory
http://hdl.handle.net/2117/102965
Structural aspects of Hamilton–Jacobi theory
Cariñena Marzo, José F.; Gràcia Sabaté, Francesc Xavier; Marmo, Giuseppe; Martínez Fernandez, Eduardo; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso
In our previous papers [11, 13] we showed that the Hamilton–Jacobi problem can be regarded as a way to describe a given dynamics on a phase space manifold in terms of a family of dynamics on a lower-dimensional manifold. We also showed how constants of the motion help to solve the Hamilton–Jacobi equation. Here we want to delve into this interpretation by considering the most general case: a dynamical system on a manifold that is described in terms of a family of dynamics (‘slicing vector fields’) on lower-dimensional manifolds. We identify the relevant geometric structures that lead from this decomposition of the dynamics to the classical Hamilton– Jacobi theory, by considering special cases like fibred manifolds and Hamiltonian dynamics, in the symplectic framework and the Poisson one. We also show how a set of functions on a tangent bundle can determine a second-order dynamics for which they are constants of the motion.
The final publication is available at Springer via http://dx.doi.org/10.1142/S0219887816500171
2017-03-28T13:13:36ZCariñena Marzo, José F.Gràcia Sabaté, Francesc XavierMarmo, GiuseppeMartínez Fernandez, EduardoMuñoz Lecanda, Miguel CarlosRomán Roy, NarcisoIn our previous papers [11, 13] we showed that the Hamilton–Jacobi problem can be regarded as a way to describe a given dynamics on a phase space manifold in terms of a family of dynamics on a lower-dimensional manifold. We also showed how constants of the motion help to solve the Hamilton–Jacobi equation. Here we want to delve into this interpretation by considering the most general case: a dynamical system on a manifold that is described in terms of a family of dynamics (‘slicing vector fields’) on lower-dimensional manifolds. We identify the relevant geometric structures that lead from this decomposition of the dynamics to the classical Hamilton– Jacobi theory, by considering special cases like fibred manifolds and Hamiltonian dynamics, in the symplectic framework and the Poisson one. We also show how a set of functions on a tangent bundle can determine a second-order dynamics for which they are constants of the motion.Temporal and spatial variations of global ionospheric total electron content under various solar conditions
http://hdl.handle.net/2117/102959
Temporal and spatial variations of global ionospheric total electron content under various solar conditions
Liu, Jingbin; Hernández Pajares, Manuel; Liang, Xinlian; An, Jiachun; Wang, Zemin; Chen, Ruizhi; Sun, Wei; Hyyppä, Juha
By utilizing the numerical technique of principal component analysis (PCA), this work analyses temporal and spatial variations of the ionosphere under various solar conditions during the period 1999–2013. Applying the PCA technique to the time series of the global ionospheric total electron content (TEC) maps provides an efficient method for analyzing the main ionospheric variability on a global scale that is able to decompose periodic variations (e.g., annual and semiannual oscillations) while retaining the asymmetry in the temporal and spatial domains (e.g., seasonal and equator anomalies). The TEC series of different local times are processed separately at two time scales: (1) the whole 15 years of the period of study and (2) the individual years. In contrast with previous studies, the analysis of the dataset of the 15 years shows that dawn (e.g., LT4–6) and late morning (LT10–12) are the more remarkable characteristic times for ionospheric variability. This study also reveals a cyclic trend of the variability with respect to local times. The first two modes, which contain 80–90% of the total variance, represent spatial distributions and temporal variations with respect to the different stages of the solar cycle and local times. Annual and semiannual variations are demodulated from the first two modes, and the results show that these variations evidently have distinct trends for daytime and nighttime. An exception is that, under active solar conditions, extremely strong solar irradiance during the daytime has a residual effect on the variability of the nighttime.
The final publication is available at Springer via http://dx.doi.org/10.1007/s00190-016-0977-7
2017-03-28T12:19:48ZLiu, JingbinHernández Pajares, ManuelLiang, XinlianAn, JiachunWang, ZeminChen, RuizhiSun, WeiHyyppä, JuhaBy utilizing the numerical technique of principal component analysis (PCA), this work analyses temporal and spatial variations of the ionosphere under various solar conditions during the period 1999–2013. Applying the PCA technique to the time series of the global ionospheric total electron content (TEC) maps provides an efficient method for analyzing the main ionospheric variability on a global scale that is able to decompose periodic variations (e.g., annual and semiannual oscillations) while retaining the asymmetry in the temporal and spatial domains (e.g., seasonal and equator anomalies). The TEC series of different local times are processed separately at two time scales: (1) the whole 15 years of the period of study and (2) the individual years. In contrast with previous studies, the analysis of the dataset of the 15 years shows that dawn (e.g., LT4–6) and late morning (LT10–12) are the more remarkable characteristic times for ionospheric variability. This study also reveals a cyclic trend of the variability with respect to local times. The first two modes, which contain 80–90% of the total variance, represent spatial distributions and temporal variations with respect to the different stages of the solar cycle and local times. Annual and semiannual variations are demodulated from the first two modes, and the results show that these variations evidently have distinct trends for daytime and nighttime. An exception is that, under active solar conditions, extremely strong solar irradiance during the daytime has a residual effect on the variability of the nighttime.The Kernel Matrix Diffie-Hellman Assumption
http://hdl.handle.net/2117/102936
The Kernel Matrix Diffie-Hellman Assumption
Morillo Bosch, M. Paz; Rafols Salvador, Carla; Villar Santos, Jorge Luis
We put forward a new family of computational assumptions, the Kernel Matrix Diffie-Hellman Assumption. Given some matrix A sampled from some distribution D, the kernel assumption says that it is hard to find “in the exponent” a nonzero vector in the kernel of A>. This family is a natural computational analogue of the Matrix Decisional Diffie-Hellman Assumption (MDDH), proposed by Escala et al. As such it allows to extend the advantages of their algebraic framework to computational assumptions. The k-Decisional Linear Assumption is an example of a family of decisional assumptions of strictly increasing hardness when k grows. We show that for any such family of MDDH assumptions, the corresponding Kernel assumptions are also strictly increasingly weaker. This requires ruling out the existence of some black-box reductions between flexible problems (i.e., computational problems with a non unique solution).
The final publication is available at link.springer.com
2017-03-28T09:12:06ZMorillo Bosch, M. PazRafols Salvador, CarlaVillar Santos, Jorge LuisWe put forward a new family of computational assumptions, the Kernel Matrix Diffie-Hellman Assumption. Given some matrix A sampled from some distribution D, the kernel assumption says that it is hard to find “in the exponent” a nonzero vector in the kernel of A>. This family is a natural computational analogue of the Matrix Decisional Diffie-Hellman Assumption (MDDH), proposed by Escala et al. As such it allows to extend the advantages of their algebraic framework to computational assumptions. The k-Decisional Linear Assumption is an example of a family of decisional assumptions of strictly increasing hardness when k grows. We show that for any such family of MDDH assumptions, the corresponding Kernel assumptions are also strictly increasingly weaker. This requires ruling out the existence of some black-box reductions between flexible problems (i.e., computational problems with a non unique solution).Integrated design of hybrid interstory-interbuilding multi-actuation schemes for vibration control of adjacent buildings under seismic excitations
http://hdl.handle.net/2117/102918
Integrated design of hybrid interstory-interbuilding multi-actuation schemes for vibration control of adjacent buildings under seismic excitations
Palacios Quiñonero, Francisco; Rubió Massegú, Josep; Rossell Garriga, Josep Maria; Karimi, Hamid Reza
The design of vibration control systems for the seismic protection of closely adjacent buildings is a complex and challenging problem. In this paper, we consider distributed multi-actuation schemes that combine interbuilding linking elements and interstory actuation devices. Using an advanced static output-feedback H 8 approach, active and passive vibration control systems are designed for a multi-story two-building structure equipped with a selected set of linked and unlinked actuation schemes. To validate the effectiveness of the obtained controllers, the corresponding frequency responses are investigated and a proper set of numerical simulations is conducted using the full scale North–South El Centro 1940 seismic record as ground acceleration disturbance. The observed results indicate that using combined interstory-interbuilding multi-actuation schemes is an effective means of mitigating the vibrational response of the individual buildings and, simultaneously, reducing the risk of interbuilding pounding. These results also point out that passive control systems with high-performance characteristics can be designed using damping elements.
2017-03-27T13:39:05ZPalacios Quiñonero, FranciscoRubió Massegú, JosepRossell Garriga, Josep MariaKarimi, Hamid RezaThe design of vibration control systems for the seismic protection of closely adjacent buildings is a complex and challenging problem. In this paper, we consider distributed multi-actuation schemes that combine interbuilding linking elements and interstory actuation devices. Using an advanced static output-feedback H 8 approach, active and passive vibration control systems are designed for a multi-story two-building structure equipped with a selected set of linked and unlinked actuation schemes. To validate the effectiveness of the obtained controllers, the corresponding frequency responses are investigated and a proper set of numerical simulations is conducted using the full scale North–South El Centro 1940 seismic record as ground acceleration disturbance. The observed results indicate that using combined interstory-interbuilding multi-actuation schemes is an effective means of mitigating the vibrational response of the individual buildings and, simultaneously, reducing the risk of interbuilding pounding. These results also point out that passive control systems with high-performance characteristics can be designed using damping elements.The flow and solidification of a thin fluid film on an arbitrary three-dimensional surface
http://hdl.handle.net/2117/102903
The flow and solidification of a thin fluid film on an arbitrary three-dimensional surface
Myers, Timothy; Charpin, Jean P. F.; Chapman, Jonathan S
A model for the flow of a thin film, with and without solidification, on an arbitrary three-dimensional substrate is presented. The problem is reduced to two simultaneous partial differential equations for the film and solid layer thicknesses. The flow model (with the solidification rate set to zero) is the first such model to describe thin film flow on an arbitrary three-dimensional surface. Various limits are investigated to recover previous models for flow on flat, cylindrical and two-dimensional curved surfaces. With solidification a previous model for accretion on a flat substrate is retrieved. It is shown how the model may be reduced to standard forms, such as solidification on a flat surface, circular and non-circular cylinders, aerofoils and spheres. Numerical solutions are obtained by combining an ADI scheme with a shock capturing method. Results are presented for flow and accretion on a flat surface, aerofoil and sphere.
2017-03-27T10:03:32ZMyers, TimothyCharpin, Jean P. F.Chapman, Jonathan SA model for the flow of a thin film, with and without solidification, on an arbitrary three-dimensional substrate is presented. The problem is reduced to two simultaneous partial differential equations for the film and solid layer thicknesses. The flow model (with the solidification rate set to zero) is the first such model to describe thin film flow on an arbitrary three-dimensional surface. Various limits are investigated to recover previous models for flow on flat, cylindrical and two-dimensional curved surfaces. With solidification a previous model for accretion on a flat substrate is retrieved. It is shown how the model may be reduced to standard forms, such as solidification on a flat surface, circular and non-circular cylinders, aerofoils and spheres. Numerical solutions are obtained by combining an ADI scheme with a shock capturing method. Results are presented for flow and accretion on a flat surface, aerofoil and sphere.Multidimensional big data processing for damage detection in real pipelines using a smart pig tool
http://hdl.handle.net/2117/102797
Multidimensional big data processing for damage detection in real pipelines using a smart pig tool
Ruiz Ordóñez, Magda; Mujica Delgado, Luis Eduardo; Alférez Baquero, Edwin Santiago; Quintero, Mario; Villamizar Mejía, Rodolfo
The history of the hydrocarbons business in Colombia dates back to the early twentieth century where mining and energy sector has been one of the principal pillars for the its development. Thus, the pipelines currently in service have over 30 years and most of them are buried and phenomena like metal losses, corrosion, mechanical stress, strike by excavation machinery and other type of damages are presented. Since it can generate social and environmental problems, monitoring tools and programs should be developed in order to prevent catastrophic situations. However, the maintaining of these structures is very expensive and it is normally developed by foreign companies. In order to overcome this situation, recently the native research institute “Research Institute of Corrosion - CIC (Corporación para la Investigación de la Corrosión)” developed an in-line inspection tool to be operated in Colombian pipelines (especially gas) to get valuable information of their current state along of thousand kilometres. The recorded data is of big size and its processing demand a high computational cost and adequate tool analysis to determine a certain pipeline damage condition. On other hand, the author from UPC and UIS have been bringing its expertise in processing and analysing this type of big data by using mainly Principal Component Analysis (PCA) as an effective tool to detect and locate different damages. In previous papers, multidimensional data matrix was used to locate possible damages along the pipeline, however most of activated points were considered false alarms since they corresponded to weld points. Thus, in this paper it is proposed no considering piecewise weld points (tube sections) and an extension of PCA named Multiway PCA (MPCA) is applied for each each one of the tube sections that form the pipeline. Therefore, if a tube section is found outside from overall indices found by using the MPCA model, an alarm activated in that section and a precise location can be obtained by analyzing only data from that specific tube section.
2017-03-22T12:43:59ZRuiz Ordóñez, MagdaMujica Delgado, Luis EduardoAlférez Baquero, Edwin SantiagoQuintero, MarioVillamizar Mejía, RodolfoThe history of the hydrocarbons business in Colombia dates back to the early twentieth century where mining and energy sector has been one of the principal pillars for the its development. Thus, the pipelines currently in service have over 30 years and most of them are buried and phenomena like metal losses, corrosion, mechanical stress, strike by excavation machinery and other type of damages are presented. Since it can generate social and environmental problems, monitoring tools and programs should be developed in order to prevent catastrophic situations. However, the maintaining of these structures is very expensive and it is normally developed by foreign companies. In order to overcome this situation, recently the native research institute “Research Institute of Corrosion - CIC (Corporación para la Investigación de la Corrosión)” developed an in-line inspection tool to be operated in Colombian pipelines (especially gas) to get valuable information of their current state along of thousand kilometres. The recorded data is of big size and its processing demand a high computational cost and adequate tool analysis to determine a certain pipeline damage condition. On other hand, the author from UPC and UIS have been bringing its expertise in processing and analysing this type of big data by using mainly Principal Component Analysis (PCA) as an effective tool to detect and locate different damages. In previous papers, multidimensional data matrix was used to locate possible damages along the pipeline, however most of activated points were considered false alarms since they corresponded to weld points. Thus, in this paper it is proposed no considering piecewise weld points (tube sections) and an extension of PCA named Multiway PCA (MPCA) is applied for each each one of the tube sections that form the pipeline. Therefore, if a tube section is found outside from overall indices found by using the MPCA model, an alarm activated in that section and a precise location can be obtained by analyzing only data from that specific tube section.Embedded piezodiagnostics for online structural damage detection based on PCA algorithm
http://hdl.handle.net/2117/102795
Embedded piezodiagnostics for online structural damage detection based on PCA algorithm
Camacho-Navarro, Jhonatan; Ruiz Ordóñez, Magda; Villamizar Mejía, Rodolfo; Mujica Delgado, Luis Eduardo; Ariza, Fabian
This work discusses a methodology used to implement a data-driven strategy for Structural Health Monitoring. First, the instrumentation of the equipment is detailed by describing the main components to be installed in the test structure in order to produce guide d waves. Specifically, an active piezo active system is used for this purpose , which consists of piezoelectric devices attached to the test structure surface and an ac quisition system. Then, the programming procedure to embed the damage detection algorithm is defined. In particular, the mathematical foundations and software requirements for impleme nting the preprocessing stage, baseline model building, and statistical index computation are specified. As a result, the Odroid-U3 computational core has the capability t o perform online damage assessment. Finally, some validation tests are presented through videos and short real time demonstration. Experimental data are recorded from two test specimens: i.) a lab carbon steel pipe loop built to emulate leak scenarios, and ii.) an aluminum plate, where mass adding is used to emulate reversible damages. The results reported i n this work show the high feasibility of the proposal methodology for obtaining an online embedded monitoring system with several advantages such as low cost, easy configuration, expandability and few computational resources
2017-03-22T12:27:24ZCamacho-Navarro, JhonatanRuiz Ordóñez, MagdaVillamizar Mejía, RodolfoMujica Delgado, Luis EduardoAriza, FabianThis work discusses a methodology used to implement a data-driven strategy for Structural Health Monitoring. First, the instrumentation of the equipment is detailed by describing the main components to be installed in the test structure in order to produce guide d waves. Specifically, an active piezo active system is used for this purpose , which consists of piezoelectric devices attached to the test structure surface and an ac quisition system. Then, the programming procedure to embed the damage detection algorithm is defined. In particular, the mathematical foundations and software requirements for impleme nting the preprocessing stage, baseline model building, and statistical index computation are specified. As a result, the Odroid-U3 computational core has the capability t o perform online damage assessment. Finally, some validation tests are presented through videos and short real time demonstration. Experimental data are recorded from two test specimens: i.) a lab carbon steel pipe loop built to emulate leak scenarios, and ii.) an aluminum plate, where mass adding is used to emulate reversible damages. The results reported i n this work show the high feasibility of the proposal methodology for obtaining an online embedded monitoring system with several advantages such as low cost, easy configuration, expandability and few computational resourcesDifferentiability with respect to parameters in global smooth linearization
http://hdl.handle.net/2117/102779
Differentiability with respect to parameters in global smooth linearization
Rodrigues, Hildebrando M.; Solà-Morales Rubió, Joan de
Let XX be a Banach space and T¿:X¿XT¿:X¿X a family of invertible contractions, T¿=L¿+f¿T¿=L¿+f¿, where L¿L¿ is linear and f¿f¿ is nonlinear with f¿(0)=0f¿(0)=0. We give conditions for the existence of a family of global linearization maps H¿H¿, such that View the MathML sourceH¿°T¿°H¿-1=L¿, with a smooth dependence on ¿. The results depend strongly on the choice of some appropriate spaces of maps, adapted norms and the use of a specific fixed point theorem with smooth dependence on parameters
2017-03-22T09:59:13ZRodrigues, Hildebrando M.Solà-Morales Rubió, Joan deLet XX be a Banach space and T¿:X¿XT¿:X¿X a family of invertible contractions, T¿=L¿+f¿T¿=L¿+f¿, where L¿L¿ is linear and f¿f¿ is nonlinear with f¿(0)=0f¿(0)=0. We give conditions for the existence of a family of global linearization maps H¿H¿, such that View the MathML sourceH¿°T¿°H¿-1=L¿, with a smooth dependence on ¿. The results depend strongly on the choice of some appropriate spaces of maps, adapted norms and the use of a specific fixed point theorem with smooth dependence on parameters