60 research outputs found

    Positroids are 3-colorable

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    We show that every positroid of rank r3r \geq 3 has a positive coline. Using the definition of the chromatic number of oriented matroid introduced by J.\ Ne\v{s}et\v{r}il, R.\ Nickel, and W.~Hochst\"{a}ttler, this shows that every orientation of a positroid is 3-colorable

    European Journal of Combinatorics Index, Volume 27

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    BACKGROUND: Diabetes is an inflammatory condition associated with iron abnormalities and increased oxidative damage. We aimed to investigate how diabetes affects the interrelationships between these pathogenic mechanisms. METHODS: Glycaemic control, serum iron, proteins involved in iron homeostasis, global antioxidant capacity and levels of antioxidants and peroxidation products were measured in 39 type 1 and 67 type 2 diabetic patients and 100 control subjects. RESULTS: Although serum iron was lower in diabetes, serum ferritin was elevated in type 2 diabetes (p = 0.02). This increase was not related to inflammation (C-reactive protein) but inversely correlated with soluble transferrin receptors (r = - 0.38, p = 0.002). Haptoglobin was higher in both type 1 and type 2 diabetes (p &lt; 0.001) and haemopexin was higher in type 2 diabetes (p &lt; 0.001). The relation between C-reactive protein and haemopexin was lost in type 2 diabetes (r = 0.15, p = 0.27 vs r = 0.63, p &lt; 0.001 in type 1 diabetes and r = 0.36, p = 0.001 in controls). Haemopexin levels were independently determined by triacylglycerol (R(2) = 0.43) and the diabetic state (R(2) = 0.13). Regarding oxidative stress status, lower antioxidant concentrations were found for retinol and uric acid in type 1 diabetes, alpha-tocopherol and ascorbate in type 2 diabetes and protein thiols in both types. These decreases were partially explained by metabolic-, inflammatory- and iron alterations. An additional independent effect of the diabetic state on the oxidative stress status could be identified (R(2) = 0.5-0.14). CONCLUSIONS: Circulating proteins, body iron stores, inflammation, oxidative stress and their interrelationships are abnormal in patients with diabetes and differ between type 1 and type 2 diabetes</p

    An extensive English language bibliography on graph theory and its applications, supplement 1

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    Graph theory and its applications - bibliography, supplement

    Using Grassmann calculus in combinatorics: Lindstr\"om-Gessel-Viennot lemma and Schur functions

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    Grassmann (or anti-commuting) variables are extensively used in theoretical physics. In this paper we use Grassmann variable calculus to give new proofs of celebrated combinatorial identities such as the Lindstr\"om-Gessel-Viennot formula for graphs with cycles and the Jacobi-Trudi identity. Moreover, we define a one parameter extension of Schur polynomials that obey a natural convolution identity.Comment: 10 pages, contribution to GASCom 2016; v2: minor correction

    Pseudodeterminants and perfect square spanning tree counts

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    The pseudodeterminant pdet(M)\textrm{pdet}(M) of a square matrix is the last nonzero coefficient in its characteristic polynomial; for a nonsingular matrix, this is just the determinant. If \partial is a symmetric or skew-symmetric matrix then pdet(t)=pdet()2\textrm{pdet}(\partial\partial^t)=\textrm{pdet}(\partial)^2. Whenever \partial is the kthk^{th} boundary map of a self-dual CW-complex XX, this linear-algebraic identity implies that the torsion-weighted generating function for cellular kk-trees in XX is a perfect square. In the case that XX is an \emph{antipodally} self-dual CW-sphere of odd dimension, the pseudodeterminant of its kkth cellular boundary map can be interpreted directly as a torsion-weighted generating function both for kk-trees and for (k1)(k-1)-trees, complementing the analogous result for even-dimensional spheres given by the second author. The argument relies on the topological fact that any self-dual even-dimensional CW-ball can be oriented so that its middle boundary map is skew-symmetric.Comment: Final version; minor revisions. To appear in Journal of Combinatoric

    Graph Theory

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    Highlights of this workshop on structural graph theory included new developments on graph and matroid minors, continuous structures arising as limits of finite graphs, and new approaches to higher graph connectivity via tree structures

    Negative circuits for flows and submodular flows

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    AbstractFor solving minimum cost flow problems Goldberg and Tarjan [7] prove strongly polynomial bounds on the negative circuit method of Klein [9] which previously was not even known to be finite. Following the proposal of Goldberg and Tarjan, Cui and Fujishige [1] discuss the use of minimum mean circuits for solving the much more general minimum cost submodular flow problem and prove finiteness where the minimum mean circuit is chosen using a secondary criterium. We introduce certain additional positive weights on negative circuits and propose selecting a negative circuit with minimum ration of cost and weight. The resulting method for solving minimum cost submodular flow problems is pseudopolynomial. In fact, it terminates after at most m·U minimum ratio computations where m denotes the number of arcs and U the maximum capacity of an arc
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