446 research outputs found

    Lean Tree-Cut Decompositions: Obstructions and Algorithms

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    The notion of tree-cut width has been introduced by Wollan in [The structure of graphs not admitting a fixed immersion, Journal of Combinatorial Theory, Series B, 110:47 - 66, 2015]. It is defined via tree-cut decompositions, which are tree-like decompositions that highlight small (edge) cuts in a graph. In that sense, tree-cut decompositions can be seen as an edge-version of tree-decompositions and have algorithmic applications on problems that remain intractable on graphs of bounded treewidth. In this paper, we prove that every graph admits an optimal tree-cut decomposition that satisfies a certain Menger-like condition similar to that of the lean tree decompositions of Thomas [A Menger-like property of tree-width: The finite case, Journal of Combinatorial Theory, Series B, 48(1):67 - 76, 1990]. This allows us to give, for every k in N, an upper-bound on the number immersion-minimal graphs of tree-cut width k. Our results imply the constructive existence of a linear FPT-algorithm for tree-cut width

    Tangle-tree duality in abstract separation systems

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    We prove a general width duality theorem for combinatorial structures with well-defined notions of cohesion and separation. These might be graphs and matroids, but can be much more general or quite different. The theorem asserts a duality between the existence of high cohesiveness somewhere local and a global overall tree structure. We describe cohesive substructures in a unified way in the format of tangles: as orientations of low-order separations satisfying certain consistency axioms. These axioms can be expressed without reference to the underlying structure, such as a graph or matroid, but just in terms of the poset of the separations themselves. This makes it possible to identify tangles, and apply our tangle-tree duality theorem, in very diverse settings. Our result implies all the classical duality theorems for width parameters in graph minor theory, such as path-width, tree-width, branch-width or rank-width. It yields new, tangle-type, duality theorems for tree-width and path-width. It implies the existence of width parameters dual to cohesive substructures such as kk-blocks, edge-tangles, or given subsets of tangles, for which no width duality theorems were previously known. Abstract separation systems can be found also in structures quite unlike graphs and matroids. For example, our theorem can be applied to image analysis by capturing the regions of an image as tangles of separations defined as natural partitions of its set of pixels. It can be applied in big data contexts by capturing clusters as tangles. It can be applied in the social sciences, e.g. by capturing as tangles the few typical mindsets of individuals found by a survey. It could also be applied in pure mathematics, e.g. to separations of compact manifolds.Comment: We have expanded Section 2 on terminology for better readability, adding explanatory text, examples, and figures. This paper replaces the first half of our earlier paper arXiv:1406.379

    A Hierarchical Core Reference Ontology for New Technology Insertion Design in Long Life Cycle, Complex Mission Critical Systems

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    Organizations, including government, commercial and others, face numerous challenges in maintaining and upgrading long life-cycle, complex, mission critical systems. Maintaining and upgrading these systems requires the insertion and integration of new technology to avoid obsolescence of hardware software, and human skills, to improve performance, to maintain and improve security, and to extend useful life. This is particularly true of information technology (IT) intensive systems. The lack of a coherent body of knowledge to organize new technology insertion theory and practice is a significant contributor to this difficulty. This research organized the existing design, technology road mapping, obsolescence, and sustainability literature into an ontology of theory and application as the foundation for a technology design and technology insertion design hierarchical core reference ontology and laid the foundation for body of knowledge that better integrates the new technology insertion problem into the technology design architecture

    Ecological Kinds and the Units of Conservation

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    Conservation has often been conducted with the implicit internalization of Aldo Leopold’s claim: “A thing is right when it tends to preserve the integrity, stability and beauty of the biotic community.” This position has been found to be problematic as ecological science has not vindicated the ecological community as an entity which can be stable or coherent. Ecological communities do not form natural kinds, and this has forced ecological scientists to explain ecology in a different manner. Individualist approaches to ecological systems have gained prominence. Individualists claim that ecological systems are better explained at the population level rather than as whole communities. My thesis looks at the implications of the current state of ecological science on conservation biology and emphasizes the importance of biodiversity as assessed at the population level. I defend the position that biodiversity should represent taxonomy and be quantified in reference to phylogenetic structure. This is a defence of biodiversity realism, which conceives of biodiversity as a natural quantity in the world which is measurable, valuable to prudent agents, and causally salient to ecological systems. To address how biodiversity at the population level relates to larger ecological systems I create a methodology designed to identify the relevant ecological system which biodiversity maintains and is maintained by biodiversity. This is done through the context dependent modelling of causal networks indexed to populations. My causal modelling methodology is then utilized to explicate ecological functions. These chapters together provide a framework for conservation science, which can then be applied to novel problems. The final section of the thesis utilises this framework to address whether de-extinction is a worthwhile conservation technique

    Analysis of methods

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    Information is one of an organization's most important assets. For this reason the development and maintenance of an integrated information system environment is one of the most important functions within a large organization. The Integrated Information Systems Evolution Environment (IISEE) project has as one of its primary goals a computerized solution to the difficulties involved in the development of integrated information systems. To develop such an environment a thorough understanding of the enterprise's information needs and requirements is of paramount importance. This document is the current release of the research performed by the Integrated Development Support Environment (IDSE) Research Team in support of the IISEE project. Research indicates that an integral part of any information system environment would be multiple modeling methods to support the management of the organization's information. Automated tool support for these methods is necessary to facilitate their use in an integrated environment. An integrated environment makes it necessary to maintain an integrated database which contains the different kinds of models developed under the various methodologies. In addition, to speed the process of development of models, a procedure or technique is needed to allow automatic translation from one methodology's representation to another while maintaining the integrity of both. The purpose for the analysis of the modeling methods included in this document is to examine these methods with the goal being to include them in an integrated development support environment. To accomplish this and to develop a method for allowing intra-methodology and inter-methodology model element reuse, a thorough understanding of multiple modeling methodologies is necessary. Currently the IDSE Research Team is investigating the family of Integrated Computer Aided Manufacturing (ICAM) DEFinition (IDEF) languages IDEF(0), IDEF(1), and IDEF(1x), as well as ENALIM, Entity Relationship, Data Flow Diagrams, and Structure Charts, for inclusion in an integrated development support environment
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