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Maximal-#rho#-extensions and irreducibilityMcGrath, J. D. January 1988 (has links)
No description available.
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The Order Topology on a Linearly Ordered SetCongleton, Carol A. 06 1900 (has links)
The purpose of this paper is to investigate from two viewpoints an order-induced topology on a set X.
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Linear OrderGipson, John Samuel 08 1900 (has links)
This paper will be concerned with some fundamental properties of a line. In particular, fundamental ordering properties of a line segment are covered.
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Deriving Consensus Rankings from Benchmarking ExperimentsHornik, Kurt, Meyer, David January 2006 (has links) (PDF)
Whereas benchmarking experiments are very frequently used to investigate the performance of statistical or machine learning algorithms for supervised and unsupervised learning tasks, overall analyses of such experiments are typically only carried out on a heuristic basis, if at all. We suggest to determine winners, and more generally, to derive a consensus ranking of the algorithms, as the linear order on the algorithms which minimizes average symmetric distance (Kemeny-Snell distance) to the performance relations on the individual benchmark data sets. This leads to binary programming problems which can typically be solved reasonably efficiently. We apply the approach to a medium-scale benchmarking experiment to assess the performance of Support Vector Machines in regression and classification problems, and compare the obtained consensus ranking with rankings obtained by simple scoring and Bradley-Terry modeling. / Series: Research Report Series / Department of Statistics and Mathematics
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Parcijalna uredjenja izomorfnih podstruktura relacijskih stuktura / Partial orders of isomorphic substructures of relational structuresKuzeljević Boriša 02 June 2014 (has links)
<p>Cilj ove teze je da se ispitaju lanci u parcijalnim uredjenjima (P(X), ⊂), pri čemu je P(X) skup domena izomorfnih podstruktura relacijske strukture X. Pošto se svaki lanac u parcijalnom uredjenju može produžiti do maksimalnog lanca, dovoljno je ispitati maksimalne lance u P(X). Dokazano je da, ako je X ultrahomogena relacijska struktura koja ima netrivijalne izomorfne podstrukture, onda je svaki maksimalan lanac u (P(X) ∪ {∅} , ⊂) kompletno linearno uredjenje koje se utapa u R i ima neizolovan minimum. Ako je X relacijska struktura, dat je dovoljan uslov da za svako kompletno linearno uredjenje L koje se utapa u R i ima neizolovan minimum, postoji maksimalan lanac u (P(X) ∪ {∅} , ⊂) izomorfan L. Dokazano je i da ako je X neka od sledećih relacijskih struktura: Rado graf, Hensonov graf, random poset, ultrahomogeni poset Bn ili ultrahomogeni poset Cn; onda je L izomorfno maksimalnom lancu u (P(X) ∪ {∅} , ⊂) ako i samo ako je L kompletno, utapa se u R i ima neizolovan minimum. Ako je X prebrojiv antilanac ili disjunktna unija µ kompletnih grafova sa ν tačaka za µν = ω, onda je L izomorfno maksimalnom lancu u (P(X) ∪ {∅} , ⊂) ako i samo ako je bulovsko, utapa se u R i ima neizolovan minimum.</p> / <p>The purpose of this thesis is to investigate chains in partial orders (P(X), ⊂), where P(X) is the set of domains of isomorphic substructures of a relational structure X. Since each chain in a partial order can be extended to a maximal one, it is enough to describe maximal chains in P(X). It is proved that, if X is an ultrahomogeneous relational structure with non-trivial isomorphic substructures, then each maximal chain in (P(X)∪ {∅} , ⊂) is a complete, R-embeddable linear order with minimum non-isolated. If X is a relational structure, a condition is given for X, which is sufficient for (P(X) ∪ {∅} , ⊂) to embed each complete, R-embeddable linear order with minimum non-isolated as a maximal chain. It is also proved that if X is one of the follow- ing relational structures: Rado graph, Henson graph, random poset, ultrahomogeneous poset Bn or ultrahomogeneous poset Cn; then L is isomorphic to a maximal chain in (P(X) ∪ {∅} , ⊂) if and only if L is complete, R-embeddable with minimum non-isolated. If X is a countable antichain or disjoint union of µ complete graphs with ν points where µν = ω, then L is isomorphic to a maximal chain in (P(X) ∪ {∅} , ⊂) if and only if L is Boolean, R-embeddable with minimum non-isolated.</p>
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