59 research outputs found
Ribbon graphs and bialgebra of Lagrangian subspaces
To each ribbon graph we assign a so-called L-space, which is a Lagrangian
subspace in an even-dimensional vector space with the standard symplectic form.
This invariant generalizes the notion of the intersection matrix of a chord
diagram. Moreover, the actions of Morse perestroikas (or taking a partial dual)
and Vassiliev moves on ribbon graphs are reinterpreted nicely in the language
of L-spaces, becoming changes of bases in this vector space. Finally, we define
a bialgebra structure on the span of L-spaces, which is analogous to the
4-bialgebra structure on chord diagrams.Comment: 21 pages, 13 figures. v2: major revision, Sec 2 and 3 completely
rewritten; v3: minor corrections. Final version, to appear in Journal of Knot
Theory and its Ramification
European Journal of Combinatorics Index, Volume 27
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 < 0.001) and haemopexin was higher in type 2 diabetes (p < 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 < 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
Rank functions and invariants of delta-matroids
In this note, we give a rank function axiomatization for delta-matroids and
study the corresponding rank generating function. We relate an evaluation of
the rank generating function to the number of independent sets of the
delta-matroid, and we prove a log-concavity result for that evaluation using
the theory of Lorentzian polynomials
Signed permutohedra, delta-matroids, and beyond
We establish a connection between the algebraic geometry of the type B
permutohedral toric variety and the combinatorics of delta-matroids. Using this
connection, we compute the volume and lattice point counts of type B
generalized permutohedra. Applying tropical Hodge theory to a new framework of
"tautological classes of delta-matroids," modeled after certain vector bundles
associated to realizable delta-matroids, we establish the log-concavity of a
Tutte-like invariant for a broad family of delta-matroids that includes all
realizable delta-matroids. Our results include new log-concavity statements for
all (ordinary) matroids as special cases
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