The Erd\H{o}s-Szekeres problem for non-crossing convex sets

We show an equivalence between a conjecture of Bisztriczky and Fejes T{\'o}th about arrangements of planar convex bodies and a conjecture of Goodman and Pollack about point sets in topological affine planes. As a corollary of this equivalence we improve the upper bound of Pach and T\'{o}th on the Erd\H{o}s-Szekeres theorem for disjoint convex bodies, as well as the recent upper bound obtained by Fox, Pach, Sudakov and Suk, on the Erd\H{o}s-Szekeres theorem for non-crossing convex bodies. Our methods also imply improvements on the positive fraction Erd\H{os}-Szekeres theorem for disjoint (and non-crossing) convex bodies, as well as a generalization of the partitioned Erd\H{o}s-Szekeres theorem of P\'{o}r and Valtr to arrangements of non-crossing convex bodies

Regular systems of paths and families of convex sets in convex position

In this paper we show that every sufficiently large family of convex bodies in the plane has a large subfamily in convex position provided that the number of common tangents of each pair of bodies is bounded and every subfamily of size five is in convex position. (If each pair of bodies have at most two common tangents it is enough to assume that every triple is in convex position, and likewise, if each pair of bodies have at most four common tangents it is enough to assume that every quadruple is in convex position.) This confirms a conjecture of Pach and Toth, and generalizes a theorem of Bisztriczky and Fejes Toth. Our results on families of convex bodies are consequences of more general Ramsey-type results about the crossing patterns of systems of graphs of continuous functions $f:[0,1] \to \mathbb{R}$. On our way towards proving the Pach-Toth conjecture we obtain a combinatorial characterization of such systems of graphs in which all subsystems of equal size induce equivalent crossing patterns. These highly organized structures are what we call regular systems of paths and they are natural generalizations of the notions of cups and caps from the famous theorem of Erdos and Szekeres. The characterization of regular systems is combinatorial and introduces some auxiliary structures which may be of independent interest

Lack of influence of the COX inhibitors metamizol and diclofenac on platelet GPIIb/IIIa and P-selectin expression in vitro

BACKGROUND: The effect of non-steroidal anti-inflammatory drugs (NSAIDs) for reduced platelet aggregation and thromboxane A(2 )synthesis has been well documented. However, the influence on platelet function is not fully explained. Aim of this study was to examine the influence of the COX-1 inhibiting NSAIDs, diclofenac and metamizol on platelet activation and leukocyte-platelet complexes, in vitro. Surface expression of GPIIb/IIIa and P-selectin on platelets, and the percentage of platelet-leukocyte complexes were investigated. METHODS: Whole blood was incubated with three different concentrations of diclofenac and metamizol for 5 and 30 minutes, followed by activation with TRAP-6 and ADP. Rates of GPIIb/IIIa and P-selectin expression, and the percentage of platelet-leukocyte complexes were analyzed by a flow-cytometric assay. RESULTS: There were no significant differences in the expression of GPIIb/IIIa and P-selectin, and in the formation of platelet-leukocyte complexes after activation with ADP and TRAP-6, regarding both the time of incubation and the concentrations of diclofenac and metamizol. CONCLUSIONS: Accordingly, the inhibitory effect of diclofenac and metamizol on platelet aggregation is not related to a reduced surface expression of P-selectin and GPIIb/IIIa on platelets

In thrombin stimulated human platelets Citalopram, Promethazine, Risperidone, and Ziprasidone, but not Diazepam, may exert their pharmacological effects also through intercalation in membrane phospholipids in a receptor-independent manner

Intercalation of drugs in the platelet membrane affects phospholipid-requiring enzymatic processes according to the drugs’ intercalation capability. We investigated effects of Promethazine, Citalopram, Ziprasidone, Risperidone, and Diazepam on phospholipase A2 (PLA2) and polyphosphoinositide (PPI) metabolism in thrombin-stimulated human platelets. We also examined effects of the drugs on monolayers of glycerophospholipids using the Langmuir technique. Diazepam did not influence PLA2 activity, had no effects on PPI cycle, and caused no change in mean molecular area of phospholipid monolayers. The remaining psychotropic drugs affected these parameters in different ways and levels of potency suggesting that they act by being intercalated between the molecules of adjacent membrane phospholipids, thus causing changes in substrate availability for phospholipid-hydrolyzing enzymes (PLA2 and Phospholipase C). We show that several psychotropic drugs can also have other cellular effects than receptor antagonism. These effects may be implicated in the psychotropic effects of the drugs and/or their side effects

Loss of estrogen receptor β decreases mitochondrial energetic potential and increases thrombogenicity of platelets in aged female mice

Platelets derived from aged (reproductively senescent) female mice with genetic deletion of estrogen receptor beta (βER) are more thrombogenic than those from age-matched wild-type (WT) mice. Intracellular processes contributing to this increased thrombogenicity are not known. Experiments were designed to identify subcellular localization of estrogen receptors and evaluate both glycolytic and mitochondrial energetic processes which might affect platelet activation. Platelets and blood from aged (22–24 months) WT and estrogen receptor β knockout (βERKO) female mice were used in this study. Body, spleen weight, and serum concentrations of follicle-stimulating hormone and 17β-estradiol were comparable between WT and βERKO mice. Number of spontaneous deaths was greater in the βERKO colony (50% compared to 30% in WT) over the course of 24 months. In resting (nonactivated) platelets, estrogen receptors did not appear to colocalize with mitochondria by immunostaining. Lactate production and mitochondrial membrane potential of intact platelets were similar in both groups of mice. However, activities of NADH dehydrogenase, cytochrome bc1 complex, and cytochrome c oxidase of the electron transport chain were reduced in mitochondria isolated from platelets from βERKO compared to WT mice. There were a significantly higher number of phosphatidylserine-expressing platelet-derived microvesicles in the plasma and a greater thrombin-generating capacity in βERKO compared to WT mice. These results suggest that deficiencies in βER affect energy metabolism of platelets resulting in greater production of circulating thrombogenic microvesicles and could potentially explain increased predisposition to thromboembolism in some elderly females

Receptor Activation and Inositol Lipid Hydrolysis in Neural Tissues

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66228/1/j.1471-4159.1987.tb05618.x.pd