DSpace Collection:
http://hdl.handle.net/2117/3549
Tue, 16 Sep 2014 13:44:59 GMT2014-09-16T13:44:59Zwebmaster.bupc@upc.eduUniversitat Politècnica de Catalunya. Servei de Biblioteques i DocumentaciónoExploiting symmetry on the Universal Polytope
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 GMThttp://hdl.handle.net/2117/176632013-02-12T13:49:09ZPfeifle, JuliánnoThe 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.On two distributions of subgroups of free groups
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 GMThttp://hdl.handle.net/2117/152202012-02-17T14:39:00ZBassino, Frédérique; Martino, Armando; Nicaud, Cyril; Ventura Capell, Enric; Weil, PascalnoWe 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.On the evaluation of the Tutte polynomial at the points (1,-1) and (2,-1)
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 GMThttp://hdl.handle.net/2117/115232011-02-24T12:39:38ZGoodall, Andrew; Merino, Criel; Mier Vinué, Anna de; Noy Serrano, MarcosnoC. 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.Rotational and dihedral symmetries in Steinhaus and Pascal binary triangles
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 GMThttp://hdl.handle.net/2117/87182010-09-02T10:25:11ZBrunat Blay, Josep Maria; Maureso Sánchez, MontserratnoWe give explicit formulae for obtaining the binary sequences which produce Steinhaus triangles and generalized Pascal triangles with rotational and dihedral symmetries.An algorithm to design prescribed length codes for single-tracked shaft encoders
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 GMThttp://hdl.handle.net/2117/84282010-07-27T12:04:47ZBalle Pigem, Borja de; Ventura Capell, Enric; Fuertes Armengol, José MªnoAbstract-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.On polytopality of Cartesian products of graphs
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 GMThttp://hdl.handle.net/2117/82002010-07-16T09:44:24ZPfeifle, Julián; Pilaud, Vincent; Santos Pérez, Francisco JaviernoWe 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.Graph operations and Laplacian eigenpolytopes
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 GMThttp://hdl.handle.net/2117/81982010-07-16T09:29:16ZPadrol Sureda, Arnau; Pfeifle, JuliánnoWe 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.Overlapping community search for social networks
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 GMThttp://hdl.handle.net/2117/77972010-06-22T14:08:12ZPadrol Sureda, Arnau; Perarnau Llobet, Guillem; Pfeifle, Julián; Muntés Mulero, VíctornoFinding 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.Búsqueda de comunidades en grafos grandes mediante configuraciones implícitas de vectores
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 GMThttp://hdl.handle.net/2117/76262010-06-11T15:23:22ZMuntés Mulero, Víctor; Padrol Sureda, Arnau; Perarnau Llobet, Guillem; Pfeifle, JuliánnoPresentamos 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.Complejos de homomorfismos y disecciones de polígonos
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 GMThttp://hdl.handle.net/2117/76232010-06-11T15:01:37ZPfeifle, JuliánnoEncontramos 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.