Bacterially synthesized c-Ha-ras protein (Ras) was incubated with guanosine triphosphatase (GTPase) activating (GA) protein in the presence of various phospholipids. The stimulation of Ras GTPase activity by GA protein was inhibited in some cases. Among the lipids most active in blocking GA protein activity were lipids that show altered metabolism during mitogenic stimulation. These included phosphatidic acid (containing arachidonic acid), phosphatidylinositol phosphates, and arachidonic acid. Other lipids, including phosphatidic acid with long, saturated side chains, diacylglycerols, and many other common phospholipids, were unable to alter GA protein activity. The interaction of lipids with GA protein might be important in the regulation of Ras activity during mitogenic stimulation.
Bounded treewidth and Monadic Second Order (MSO) logic have proved to be key concepts in establishing fixed-parameter tractability results. Indeed, by Courcelle's Theorem we know: Any property of finite structures, which is expressible by an MSO sentence, can be decided in linear time (data complexity) if the structures have bounded treewidth.In principle, Courcelle's Theorem can be applied directly to construct concrete algorithms by transforming the MSO evaluation problem into a tree language recognition problem. The latter can then be solved via a finite tree automaton (FTA). However, this approach has turned out to be problematical, since even relatively simple MSO formulae may lead to a "state explosion" of the FTA.In this work we propose monadic datalog (i.e., datalog where all intentional predicate symbols are unary) as an alternative method to tackle this class of fixed-parameter tractable problems. We show that if some property of finite structures is expressible in MSO then this property can also be expressed by means of a monadic datalog program over the structure plus the tree decomposition. Moreover, we show that the resulting fragment of datalog can be evaluated in linear time (both w.r.t. the program size and w.r.t. the data size). This new approach is put to work by devising a new algorithm for the PRIMALITY problem (i.e., testing if some attribute in a relational schema is part of a key). We also report on experimental results with a prototype implementation.
Abstract.There exist two new embedded minimal surfaces, asymptotic to the helicoid. One is periodic, with quotient (by orientation-preserving translations) of genus one. The other is nonperiodic of genus one.We have constructed two minimal surfaces of theoretical interest. The first is a complete, embedded, singly periodic minimal surface (SPEMS) that is asymptotic to the helicoid, has infinite genus, and whose quotient by translations has genus one. The quotient of the helicoid by translations has genus zero and the helicoid itself is simply connected. Theorem 1. There exists an embedded singly periodic minimal surface W\, asymptotic to the helicoid and invariant under a translation T. The quotient surface W\¡T has genus equal to one and two ends.W\ contains a vertical axis, as does the helicoid, and W\/T contains two horizontal lines. The second surface is a complete, properly embedded minimal surface of finite topology with infinite total curvature. It is the first such surface to be found since the helicoid, which was discovered in the eighteenth century.
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