scholarly journals Object and image indexing based on region connection calculus and oriented matroid theory

2005 ◽  
Vol 147 (2-3) ◽  
pp. 345-361 ◽  
Author(s):  
Ernesto Staffetti ◽  
Antoni Grau ◽  
Francesc Serratosa ◽  
Alberto Sanfeliu
Keyword(s):  
Image Indexing ◽  
Oriented Matroid ◽  
Matroid Theory ◽  
Region Connection Calculus

Oriented Matroids

10.37236/25 ◽  
2002 ◽  
Vol 1000 ◽  
Author(s):  
Günter M. Ziegler
Keyword(s):  
Oriented Matroids ◽  
Entry Point ◽  
Oriented Matroid ◽  
Matroid Theory

This dynamic survey offers an “entry point” for current research in oriented matroids. For this, it provides updates on the 1993 monograph “Oriented Matroids” by Bjö̈rner, Las Vergnas, Sturmfels, White & Ziegler [85], in three parts: 1. a sketch of a few “Frontiers of Research” in oriented matroid theory, 2. an update of corrections, comments and progress as compared to [85], and 3. an extensive, complete and up-to-date bibliography of oriented matroids, comprising and extending the bibliography of [85].

scholarly journals Dyck path triangulations and extendability (extended abstract)

2015 ◽  
Vol DMTCS Proceedings, 27th... (Proceedings) ◽  
Author(s):  
Cesar Ceballos ◽  
Arnau Padrol ◽  
Camilo Sarmiento
Keyword(s):  
Cartesian Product ◽  
Explicit Construction ◽  
Oriented Matroids ◽  
Oriented Matroid ◽  
Dyck Path ◽  
Matroid Theory ◽  
Dyck Paths ◽  
Nous Montrons ◽  
International Audience

International audience We introduce the Dyck path triangulation of the cartesian product of two simplices $\Delta_{n-1}\times\Delta_{n-1}$. The maximal simplices of this triangulation are given by Dyck paths, and its construction naturally generalizes to produce triangulations of $\Delta_{r\ n-1}\times\Delta_{n-1}$ using rational Dyck paths. Our study of the Dyck path triangulation is motivated by extendability problems of partial triangulations of products of two simplices. We show that whenever$m\geq k>n$, any triangulations of $\Delta_{m-1}^{(k-1)}\times\Delta_{n-1}$ extends to a unique triangulation of $\Delta_{m-1}\times\Delta_{n-1}$. Moreover, with an explicit construction, we prove that the bound $k>n$ is optimal. We also exhibit interpretations of our results in the language of tropical oriented matroids, which are analogous to classical results in oriented matroid theory. Nous introduisons la triangulation par chemins de Dyck du produit cartésien de deux simplexes $\Delta_{n-1}\times\Delta_{n-1}$. Les simplexes maximaux de cette triangulation sont donnés par des chemins de Dyck, et cette construction se généralise de façon naturelle pour produire des triangulations $\Delta_{r\ n-1}\times\Delta_{n-1}$ qui utilisent des chemins de Dyck rationnels. Notre étude de la triangulation par chemins de Dyck est motivée par des problèmes de prolongement de triangulations partielles de produits de deux simplexes. On montre que $m\geq k>n$ alors toute triangulation de $\Delta_{m-1}^{(k-1)}\times\Delta_{n-1}$ se prolonge en une unique triangulation de $\Delta_{m-1}\times\Delta_{n-1}$. De plus, avec une construction explicite, nous montrons que la borne $k>n$ est optimale. Nous présentons aussi des interprétations de nos résultats dans le langage des matroïdes orientés tropicaux, qui sont analogues aux résultats classiques de la théorie des matroïdes orientés.

A LINK BETWEEN p-BRANES, NAMBU–POISSON STRUCTURE AND MATROIDS

2004 ◽  
Vol 01 (06) ◽  
pp. 795-811 ◽  
Author(s):  
PARTHA GUHA
Keyword(s):  
Poisson Structure ◽  
Canonical Transformation ◽  
Local Condition ◽  
Oriented Matroid ◽  
Matroid Theory ◽  
Yang Mills ◽  
Degenerate Form ◽  
Nambu Bracket ◽  
Nambu Brackets

Recently Nieto has proposed a link between oriented matroid theory and the Schild type action of p-branes. This particular matroid theory satisfies the local condition, i.e., the degenerate form must be closed. This allows us to explain the dynamics of p-branes in terms of Nambu–Poisson structure. In this paper using an infinitesimal canonical transformation of Nambu brackets we show that the helicity is conserved in the dynamics of p-branes. Applying Filippov algebra (or quantum Nambu bracket) we define a generalized Yang–Mills action in 4k space. We show that this action is equivalent to Dolan–Tchrakian type action.

Computing irreversible minimal cut sets in genome-scale metabolic networks via flux cone projection

2018 ◽  
Vol 35 (15) ◽  
pp. 2618-2625 ◽  
Author(s):  
Annika Röhl ◽  
Tanguy Riou ◽  
Alexander Bockmayr
Keyword(s):  
Metabolic Networks ◽  
Supplementary Information ◽  
Oriented Matroid ◽  
Matroid Theory ◽  
Supplementary Data ◽  
Large Genome ◽  
Minimal Cut Sets ◽  
Minimal Cut ◽  
Genome Scale ◽  
Target Reaction

Abstract Motivation Minimal cut sets (MCSs) for metabolic networks are sets of reactions which, if they are removed from the network, prevent a target reaction from carrying flux. To compute MCSs different methods exist, which may fail to find sufficiently many MCSs for larger genome-scale networks. Results Here we introduce irreversible minimal cut sets (iMCSs). These are MCSs that consist of irreversible reactions only. The advantage of iMCSs is that they can be computed by projecting the flux cone of the metabolic network on the set of irreversible reactions, which usually leads to a smaller cone. Using oriented matroid theory, we show how the projected cone can be computed efficiently and how this can be applied to find iMCSs even in large genome-scale networks. Availability and implementation Software is freely available at https://sourceforge.net/projects/irreversibleminimalcutsets/. Supplementary information Supplementary data are available at Bioinformatics online.

Euclideaness and final polynomials in oriented matroid theory

COMBINATORICA ◽  
1993 ◽  
Vol 13 (3) ◽  
pp. 259-268 ◽  
Author(s):  
J�rgen Richter-Gebert
Keyword(s):  
Oriented Matroid ◽  
Matroid Theory

scholarly journals SEARCH FOR A "GRAVITOID" THEORY

2003 ◽  
Vol 18 (28) ◽  
pp. 5261-5276 ◽  
Author(s):  
J. A. NIETO ◽  
M. C. MARÍN
Keyword(s):  
Mathematical Structure ◽  
Gravitational Theory ◽  
Oriented Matroid ◽  
Matroid Theory ◽  
M Theory

By combining the concepts of graviton and matroid, we outline a new gravitational theory which we call gravitoid theory. The idea of this theory emerged as an attempt to link the mathematical structure of matroid theory with M theory. Our observations are essentially based on the formulation of matroid bundle due to MacPherson and Anderson–Davis. Also, by considering the oriented matroid theory, we add new observations about the link between the Fano matroid and D=11 supergravity which was discussed in some of our recent papers. In particular we find a connection between the affine matroid AG(3, 2) and the G2-symmetry of D=11 supergravity.

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