35077963
A Combinatorial Relationship between Eulerian Maps and Hypermaps in Orientable Surfaces
Abstract There is a remarkable relationship between the genus series for rooted maps and rooted quadrangulations that has been obtained by a character theoretic argument. Hitherto no combinatorial explanation for this has been given. In this paper we generalize this relationship to a larger set of maps for which such a relationship can be found and we ascertain some of the properties that a putative bijection must possess. Several examples of images of sets under this bijection are given. We give them in detail since they may contain useful information about the bijection.
40941890
The Quadrangulation Conjecture for Orientable Surfaces
By means of character theory and symmetric functions, D. M. Jackson and T. I. Visentin (1990, Trans. Amer. Math. Soc. 322, (343-363)) proved the existence of certain bijections between the set of quadrangulations in orientable surfaces and decorated maps (with marked edges and coloured vertices) in orientable surfaces. The bijections preserve a weight function consisting of a pair (g,n) of integer parameters. For quadrangulations, g is the genus and n is the number of faces. For decorated maps, g is the genus plus half the number of white vertices and n is the number of edges. The Quadrangulation Conjecture concerns the problem of finding a natural bijection of this type. Tutte's medial construction is a solution in the special case g = 0 of planar maps. We give a construction of a bijection ??Ξ which both extends Tutte's medial construction to non-planar maps and preserves the parameter n of the Quadrangulation Conjecture. (The parameter g is not generally preserved, except when g = 0.) Non-orientable surfaces play an important part in the construction of ??Ξ. As part of the construction, we introduce a bijection between orientable rooted quadrangulations and locally orientable, bipartite, rooted quadrangulations.
10058409
Hierarchical Analysis of Dependency in Metabolic Networks
MOTIVATION
Elucidation of metabolic networks for an increasing number of organisms reveals that even small networks can contain thousands of reactions and chemical species. The intimate connectivity between components complicates their decomposition into biologically meaningful sub-networks. Moreover, traditional higher-order representations of metabolic networks as metabolic pathways, suffers from the lack of rigorous definition, yielding pathways of disparate content and size.


RESULTS
We introduce a hierarchical representation that emphasizes the gross organization of metabolic networks in largely independent pathways and sub-systems at several levels of independence. The approach highlights the coupling of different pathways and the shared compounds responsible for those couplings. By assessing our results on Escherichia coli (E.coli metabolic reactions, Genetic Circuits Research Group, University of California, San Diego, http://gcrg.ucsd.edu/organisms/ecoli.html, 'model v 1.01. reactions') against accepted biochemical annotations, we provide the first systematic synopsis of an organism's metabolism. Comparison with operons of E.coli shows that low-level clusters are reflected in genome organization and gene regulation.


AVAILABILITY
Source code, data sets and supplementary information are available at http://www.mas.ecp.fr/labo/equipe/gagneur/hierarchy/hierarchy.html
7746968
Faster fractal image compression using quadtree recomposition
In this paper, we present a fractal image compression algorithm employing a new quadtree recomposition (QR) approach. In this approach, quadtree subblocks of an image are iteratively recombined into larger blocks for fractal coding. For complex images, this approach exhibits superior runtime performance, when compared to a classical quadtree decomposition (QD) scheme, while maintaining high fidelity for reconstructed images. Quantitative results include an evaluation of attained compression ratios, runtime performance, and signal-to-noise ratios (SNR) for reconstructed images.
44859424
Lightweight Extraction of Object Models from Bytecode
14356359
Decision and Separability Problems for Baumslag-Solitar Semigroups
We show that the semigroups Sk,l having semigroup presentations are residually finite and finitely separable. Generally, these semigroups have finite separating images which are finite groups and other finite separating images which are semigroups of order-increasing transformations on a finite partially ordered set. These semigroups thus have vastly different residual and separability properties than the Baumslag–Solitar groups which contain them.
946209
A new model of program dependences for reverse engineering
A dependence model for reverse engineering should treat procedures in a modular fashion and should be fine-grained, distinguishing dependences that are due to different variables. The program dependence graph (PDG) satisfies neither of these criteria. We present a new form of dependence graph that satisfies both, while retaining the advantages of the PDG: it is easy to construct and allows program slicing to be implemented as a simple graph traversal. We define 'chopping', a generalization of slicing that can express most of its variants, and show that, using our dependence graph, it produces more accurate results than algorithms based directly on the PDG.