Discrete Morse theory for the collapsibility of supremum sections

The Dushnik-Miller dimension of a poset $\le$ is the minimal number $d$ of linear extensions $\le_1, \ldots , \le_d$ of $\le$ such that $\le$ is the intersection of $\le_1, \ldots , \le_d$. Supremum sections are simplicial complexes introduced by Scarf and are linked to the Dushnik-Miller as follows: the inclusion poset of a simplicial complex is of Dushnik-Miller dimension at most $d$ if and only if it is included in a supremum section coming from a representation of dimension $d$. Collapsibility is a topoligical property of simplicial complexes which has been introduced by Whitehead and which resembles to shellability. While Ossona de Mendez proved in that a particular type of supremum sections are shellable, we show in this article that supremum sections are in general collapsible thanks to the discrete Morse theory developped by Forman

Planar graphs as L-intersection or L-contact graphs

The L-intersection graphs are the graphs that have a representation as intersection graphs of axis parallel shapes in the plane. A subfamily of these graphs are {L, |, --}-contact graphs which are the contact graphs of axis parallel L, |, and -- shapes in the plane. We prove here two results that were conjectured by Chaplick and Ueckerdt in 2013. We show that planar graphs are L-intersection graphs, and that triangle-free planar graphs are {L, |, --}-contact graphs. These results are obtained by a new and simple decomposition technique for 4-connected triangulations. Our results also provide a much simpler proof of the known fact that planar graphs are segment intersection graphs

Industrial Ecology's Hidden Philosophy of Nature. Fundamental Underpinning to Use Nature as Model

In its scientific sense, industrial ecology represents an emerging transdisciplinary field of studying industrial systems and their fundamental linkage with natural ecosystems. As a short form, industrial ecology is called the "science of sustainability". At the bottom of industrial ecology there is a refreshingly different perspective of understanding nature as model in comparison with other scientific disciplines and concepts of understanding nature e.g. in terms of "sack of resources", "biophysical limit", "something outside", "surrounding", or just "environment" as opposed to industrial systems. The keynote of industrial ecology's specific perspective of understanding nature is to balance the development of industrial systems with the constraints of natural eco-systems, analogous to an "industrial symbiosis". The goal is to contribute for laying a fundamental underpinning for industrial ecology in its scientific sense, in this case especially for its use of nature as model. Therefore an impressive battery of philosophical arguments is provided bringing to bear against the sort of probably raised fallacies and facile or hasty proclaimed critics by sceptics, hard-liners, and mainstream-scientists who often overlook industrial ecology's stimulating role towards sustainability

The Rural Older Adult Population and Transportation Services

OAT . incorporated provide transportation service throughout the state of Missouri. OATS initially began serving the rural population of older adults. OATS now provides transportation for non-emergency Medicaid patients. Head Start, and other organizations. Demographics, mobility, gender differences, normal age related changes. cognitive and physical impairments and disabilities are discussed in relation with driving and mobility needs Transportation affects all aspects of the older adult\u27s life. The White House Conference on Aging and the OIder Americans Act were influential in legislation which began funding transportation services tor older adults. Federal. state and local governments. and private agencies are responsible for funding transportation services. An in depth literature review and evaluation of OATS is compared with a few other transportation systems and used to determine the adequacy of service delivery to the rural, older adult population in Missouri

On the Distance Identifying Set Meta-Problem and Applications to the Complexity of Identifying Problems on Graphs

Numerous problems consisting in identifying vertices in graphs using distances are useful in domains such as network verification and graph isomorphism. Unifying them into a meta-problem may be of main interest. We introduce here a promising solution named Distance Identifying Set. The model contains Identifying Code (IC), Locating Dominating Set (LD) and their generalizations $r$-IC and $r$-LD where the closed neighborhood is considered up to distance $r$. It also contains Metric Dimension (MD) and its refinement $r$-MD in which the distance between two vertices is considered as infinite if the real distance exceeds $r$. Note that while IC = 1-IC and LD = 1-LD, we have MD = $\infty$-MD; we say that MD is not local In this article, we prove computational lower bounds for several problems included in Distance Identifying Set by providing generic reductions from (Planar) Hitting Set to the meta-problem. We mainly focus on two families of problem from the meta-problem: the first one, called bipartite gifted local, contains $r$-IC, $r$-LD and $r$-MD for each positive integer $r$ while the second one, called 1-layered, contains LD, MD and $r$-MD for each positive integer $r$. We have: - the 1-layered problems are NP-hard even in bipartite apex graphs, - the bipartite gifted local problems are NP-hard even in bipartite planar graphs, - assuming ETH, all these problems cannot be solved in $2^{o(\sqrt{n})}$ when restricted to bipartite planar or apex graph, respectively, and they cannot be solved in $2^{o(n)}$ on bipartite graphs, - even restricted to bipartite graphs, they do not admit parameterized algorithms in $2^{O(k)}.n^{O(1)}$ except if W[0] = W[2]. Here $k$ is the solution size of a relevant identifying set. In particular, Metric Dimension cannot be solved in $2^{o(n)}$ under ETH, answering a question of Hartung in 2013

Umweltberichterstattung von Unternehmen im Internet. Der aktuelle Stand für Deutschland

Von den Umweltberichten deutscher Unternehmen werden bisher erst unter 3% im Internet veröffentlicht. Die Tendenz ist steigend. Hier werden die im Internet verfügbaren Umweltberichte ausgewertet und Gründe für die Nutzung des Internet für die Umweltberichterstattung vorgetragen. Der Beitrag ist in fünf Abschnitte gegliedert: Zur thematischen Einführung werden betriebliche Umweltberichte durch eine Morphologie charakterisiert (Abschnitt 2). Es schließen sich die IKT-spezifischen Herausforderungen an umweltberichterstattende Unternehmen als Ansatzpunkte für Umweltberichte im Internet an (Abschnitt 3). Damit ist die Basis für eine Systematisierung der internetbasierten Unterstützungspotenziale zur Umweltberichterstattung gelegt (Abschnitt 4). Der Systematik folgt eine detaillierte Bestandsaufnahme der Umweltberichte deutscher Unternehmen im Internet in fünffacher Hinsicht (Abschnitt 5): Die zugrunde gelegte Untersuchungsmethodik zur Bestandsaufnahme wird erläutert (Abschnitt 5.1). Die ergänzend herangezogenen empirischen Studien zu Umweltberichten im Internet werden ausgewertet (Abschnitt 5.2). Die Ergebnisse bzgl. Inhalt und Darstellung von Umweltberichten im Internet werden ausführlicher beschrieben (Abschnitt 5.3) und durch Erklärungsansätze interpretiert (Abschnitt 5.4). Abschließend werden auf der Grundlage der konzeptionell erschließbaren Unterstützungspotenziale einerseits und der empirischen Studien andererseits zentrale Tendenzen zur zukünftigen Entwicklung von Umweltberichten im Internet vorgetragen (Abschnitt 5.5)

Technologie-Roadmap Lithium-Ionen-Batterien 2030

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Knowledge Cartography for Controversies: The Iraq Debate

In analysing controversies and debates—which would include reviewing a literature in order to plan research, or assessing intelligence to formulate policy—there is no one worldview which can be mapped, for instance as a single, coherent concept map. The cartographic challenge is to show which facts are agreed and contested, and the different kinds of narrative links that use facts as evidence to define the nature of the problem, what to do about it, and why. We will use the debate around the invasion of Iraq to demonstrate the methodology of using a knowledge mapping tool to extract key ideas from source materials, in order to classify and connect them within and across a set of perspectives of interest to the analyst. We reflect on the value that this approach adds, and how it relates to other argument mapping approaches