http://hdl.handle.net/2117/3549 Wed, 19 Jun 2013 06:48:20 GMT 2013-06-19T06:48:20Z webmaster.bupc@upc.edu Universitat Politècnica de Catalunya. Servei de Biblioteques i Documentació no http://hdl.handle.net/2117/17663 Title: Exploiting symmetry on the Universal Polytope Authors: Pfeifle, Julián Abstract: The most successful method to date for finding lower bounds on the number of simplices needed to triangulate a given polytope P involves optimizing a linear functional over the associated Universal Polytope U(P). However, as the dimension of P grows, these linear programs become increasingly difficult to formulate and solve. Here we present a method to algorithmically construct the quotient of U(P) by the symmetry group Aut(P) of P, which leads to dramatic reductions in the size of the linear program. We compare the power of our approach with older computations by Orden and Santos, indicate the influence of the combinatorial complexity barrier on these computations, and sketch some future applications. Tue, 12 Feb 2013 13:49:09 GMT http://hdl.handle.net/2117/17663 2013-02-12T13:49:09Z Pfeifle, Julián no The most successful method to date for finding lower bounds on the number of simplices needed to triangulate a given polytope P involves optimizing a linear functional over the associated Universal Polytope U(P). However, as the dimension of P grows, these linear programs become increasingly difficult to formulate and solve. Here we present a method to algorithmically construct the quotient of U(P) by the symmetry group Aut(P) of P, which leads to dramatic reductions in the size of the linear program. We compare the power of our approach with older computations by Orden and Santos, indicate the influence of the combinatorial complexity barrier on these computations, and sketch some future applications. http://hdl.handle.net/2117/15220 Title: On two distributions of subgroups of free groups Authors: Bassino, Frédérique; Martino, Armando; Nicaud, Cyril; Ventura Capell, Enric; Weil, Pascal Abstract: We study and compare two natural distributions of finitely generated subgroups of free groups. One is based on the random generation of tuples of reduced words; that is the one classically used by group theorists. The other relies on Stallings’ graphical representation of subgroups and in spite of its naturality, it was only recently considered. The combinatorial structures underlying both distributions are studied in this paper with methods of analytic combinatorics. We use these methods to point out the differences between these distributions. It is particularly interesting that certain important properties of subgroups that are generic in one distribution, turn out to be negligible in the other. Fri, 17 Feb 2012 14:39:00 GMT http://hdl.handle.net/2117/15220 2012-02-17T14:39:00Z Bassino, Frédérique; Martino, Armando; Nicaud, Cyril; Ventura Capell, Enric; Weil, Pascal no We study and compare two natural distributions of finitely generated subgroups of free groups. One is based on the random generation of tuples of reduced words; that is the one classically used by group theorists. The other relies on Stallings’ graphical representation of subgroups and in spite of its naturality, it was only recently considered. The combinatorial structures underlying both distributions are studied in this paper with methods of analytic combinatorics. We use these methods to point out the differences between these distributions. It is particularly interesting that certain important properties of subgroups that are generic in one distribution, turn out to be negligible in the other. http://hdl.handle.net/2117/11523 Title: On the evaluation of the Tutte polynomial at the points (1,-1) and (2,-1) Authors: Goodall, Andrew; Merino, Criel; Mier Vinué, Anna de; Noy Serrano, Marcos Abstract: C. Merino proved recently the following identity between evaluations of the Tutte polynomial of complete graphs: t($K_{n+2}$; 1,−1) = t($K_n$;2,−1). In this work we extend this result by giving a large class of graphs with this property, that is, graphs G such that there exist two vertices u and v with t(G;1,−1) = t(G−{u,v};2,−1). The class is described in terms of forbidden induced subgraphs and it contains in particular threshold graphs. Thu, 24 Feb 2011 12:39:38 GMT http://hdl.handle.net/2117/11523 2011-02-24T12:39:38Z Goodall, Andrew; Merino, Criel; Mier Vinué, Anna de; Noy Serrano, Marcos no C. Merino proved recently the following identity between evaluations of the Tutte polynomial of complete graphs: t($K_{n+2}$; 1,−1) = t($K_n$;2,−1). In this work we extend this result by giving a large class of graphs with this property, that is, graphs G such that there exist two vertices u and v with t(G;1,−1) = t(G−{u,v};2,−1). The class is described in terms of forbidden induced subgraphs and it contains in particular threshold graphs. http://hdl.handle.net/2117/8718 Title: Rotational and dihedral symmetries in Steinhaus and Pascal binary triangles Authors: Brunat Blay, Josep Maria; Maureso Sánchez, Montserrat Abstract: We give explicit formulae for obtaining the binary sequences which produce Steinhaus triangles and generalized Pascal triangles with rotational and dihedral symmetries. Thu, 02 Sep 2010 10:25:11 GMT http://hdl.handle.net/2117/8718 2010-09-02T10:25:11Z Brunat Blay, Josep Maria; Maureso Sánchez, Montserrat no We give explicit formulae for obtaining the binary sequences which produce Steinhaus triangles and generalized Pascal triangles with rotational and dihedral symmetries. http://hdl.handle.net/2117/8428 Title: An algorithm to design prescribed length codes for single-tracked shaft encoders Authors: Balle Pigem, Borja de; Ventura Capell, Enric; Fuertes Armengol, José Mª Abstract: Abstract-Maximal-length binary shift register sequences have been known for a long time. They have many interesting properties, one of them is that when taken in blocks of n consecutive positions they form 2n - 1 different codes in a closed circular sequence. This property can be used for measuring absolute angular positions as the circle can be divided in as many parts as different codes can be retrieved. This paper describes how a closed binary sequence with arbitrary length can be effectively designed with the minimal possible block-length, using linear feedback shift registers (LFSR). Such sequences can be used for measuring a specified exact number of angular positions, using the minimal possible number of detectors allowed by linear methods. Tue, 27 Jul 2010 12:04:47 GMT http://hdl.handle.net/2117/8428 2010-07-27T12:04:47Z Balle Pigem, Borja de; Ventura Capell, Enric; Fuertes Armengol, José Mª no Abstract-Maximal-length binary shift register sequences have been known for a long time. They have many interesting properties, one of them is that when taken in blocks of n consecutive positions they form 2n - 1 different codes in a closed circular sequence. This property can be used for measuring absolute angular positions as the circle can be divided in as many parts as different codes can be retrieved. This paper describes how a closed binary sequence with arbitrary length can be effectively designed with the minimal possible block-length, using linear feedback shift registers (LFSR). Such sequences can be used for measuring a specified exact number of angular positions, using the minimal possible number of detectors allowed by linear methods. http://hdl.handle.net/2117/8200 Title: On polytopality of Cartesian products of graphs Authors: Pfeifle, Julián; Pilaud, Vincent; Santos Pérez, Francisco Javier Abstract: We study the polytopality of Cartesian products of non-polytopal graphs. On the one hand, we prove that a product of graphs is the graph of a simple polytope if and only if its factors are. On the other hand, we provide a general construction of polytopal products of a polytopal graph by a non-polytopal graph. Fri, 16 Jul 2010 09:44:24 GMT http://hdl.handle.net/2117/8200 2010-07-16T09:44:24Z Pfeifle, Julián; Pilaud, Vincent; Santos Pérez, Francisco Javier no We study the polytopality of Cartesian products of non-polytopal graphs. On the one hand, we prove that a product of graphs is the graph of a simple polytope if and only if its factors are. On the other hand, we provide a general construction of polytopal products of a polytopal graph by a non-polytopal graph. http://hdl.handle.net/2117/8198 Title: Graph operations and Laplacian eigenpolytopes Authors: Padrol Sureda, Arnau; Pfeifle, Julián Abstract: We introduce the Laplacian eigenpolytopes ("L-polytopes") associated to a simple undirected graph G, investigate how they change under basic operations such as taking the union, join, complement, line graph and cartesian product of graphs, and show how several "famous" polytopes arise as L-polytopes of "famous" graphs. Eigenpolytopes have been previously introduced by Godsil, who studied them in detail in the context of distance-regular graphs. Our focus on the Laplacian matrix, as opposed to the adjacency matrix of G, permits simpler proofs and descriptions of the result of operations on not necessarily distance-regular graphs. Additionally, it motivates the study of new operations on polytopes, such as the Kronecker product. Thus, we open the door to a detailed study of how combinatorial properties of G are reflected in its L-polytopes. Subsequent papers will use these tools to construct interesting polytopes from interesting graphs, and vice versa. Fri, 16 Jul 2010 09:29:16 GMT http://hdl.handle.net/2117/8198 2010-07-16T09:29:16Z Padrol Sureda, Arnau; Pfeifle, Julián no We introduce the Laplacian eigenpolytopes ("L-polytopes") associated to a simple undirected graph G, investigate how they change under basic operations such as taking the union, join, complement, line graph and cartesian product of graphs, and show how several "famous" polytopes arise as L-polytopes of "famous" graphs. Eigenpolytopes have been previously introduced by Godsil, who studied them in detail in the context of distance-regular graphs. Our focus on the Laplacian matrix, as opposed to the adjacency matrix of G, permits simpler proofs and descriptions of the result of operations on not necessarily distance-regular graphs. Additionally, it motivates the study of new operations on polytopes, such as the Kronecker product. Thus, we open the door to a detailed study of how combinatorial properties of G are reflected in its L-polytopes. Subsequent papers will use these tools to construct interesting polytopes from interesting graphs, and vice versa. http://hdl.handle.net/2117/7797 Title: Overlapping community search for social networks Authors: Padrol Sureda, Arnau; Perarnau Llobet, Guillem; Pfeifle, Julián; Muntés Mulero, Víctor Abstract: Finding decompositions of a graph into a family of clusters is crucial to understanding its underlying structure. While most existing approaches focus on partitioning the nodes, real-world datasets suggest the presence of overlapping communities. We present OCA, a novel algorithm to detect overlapped communities in large data graphs. It outperforms previous proposals in terms of execution time, and efficiently handles large graphs containing more than 108 nodes and edges. Tue, 22 Jun 2010 14:08:12 GMT http://hdl.handle.net/2117/7797 2010-06-22T14:08:12Z Padrol Sureda, Arnau; Perarnau Llobet, Guillem; Pfeifle, Julián; Muntés Mulero, Víctor no Finding decompositions of a graph into a family of clusters is crucial to understanding its underlying structure. While most existing approaches focus on partitioning the nodes, real-world datasets suggest the presence of overlapping communities. We present OCA, a novel algorithm to detect overlapped communities in large data graphs. It outperforms previous proposals in terms of execution time, and efficiently handles large graphs containing more than 108 nodes and edges. http://hdl.handle.net/2117/7626 Title: Búsqueda de comunidades en grafos grandes mediante configuraciones implícitas de vectores Authors: Muntés Mulero, Víctor; Padrol Sureda, Arnau; Perarnau Llobet, Guillem; Pfeifle, Julián Abstract: Presentamos el algoritmo OCA para buscar comunidades solapadas en grafos grandes, como por ejemplo la Wikipedia con 1,6×107 nodos y 1,8×108 aristas. OCA se basa en la búsqueda iterativa de subconjuntos localmente óptimos para una función objetivo, representando los subconjuntos como vectores suma de una configuración virtual de vectores. Analizamos el comportamiento de dos funciones objetivo, la Laplaciana asociada a la longitud del vector suma, y la conductividad. Fri, 11 Jun 2010 15:23:22 GMT http://hdl.handle.net/2117/7626 2010-06-11T15:23:22Z Muntés Mulero, Víctor; Padrol Sureda, Arnau; Perarnau Llobet, Guillem; Pfeifle, Julián no Presentamos el algoritmo OCA para buscar comunidades solapadas en grafos grandes, como por ejemplo la Wikipedia con 1,6×107 nodos y 1,8×108 aristas. OCA se basa en la búsqueda iterativa de subconjuntos localmente óptimos para una función objetivo, representando los subconjuntos como vectores suma de una configuración virtual de vectores. Analizamos el comportamiento de dos funciones objetivo, la Laplaciana asociada a la longitud del vector suma, y la conductividad. http://hdl.handle.net/2117/7623 Title: Complejos de homomorfismos y disecciones de polígonos Authors: Pfeifle, Julián Abstract: Encontramos realizaciones canónicas de los complejos politopales Hom(G,H)formados por homomorfismos de grafos y estudiados por Babson y Kozlov. Si G es un grafo completo, caracterizamos en qué casos cierta proyección canónica de esta realización es a su vez un complejo, y mostramos que multitud de objetos interesantes aparecen como subestructuras de estas proyecciones: las disecciones de un polígono convexo en k- ágonos, los permutaedros generalizados de Postnikov, triangulaciones escalera y el grafo de composiciones de un entero en un número fijo de sumandos no negativos. Fri, 11 Jun 2010 15:01:37 GMT http://hdl.handle.net/2117/7623 2010-06-11T15:01:37Z Pfeifle, Julián no Encontramos realizaciones canónicas de los complejos politopales Hom(G,H)formados por homomorfismos de grafos y estudiados por Babson y Kozlov. Si G es un grafo completo, caracterizamos en qué casos cierta proyección canónica de esta realización es a su vez un complejo, y mostramos que multitud de objetos interesantes aparecen como subestructuras de estas proyecciones: las disecciones de un polígono convexo en k- ágonos, los permutaedros generalizados de Postnikov, triangulaciones escalera y el grafo de composiciones de un entero en un número fijo de sumandos no negativos.