Approximate well-supported Nash equilibria in symmetric bimatrix games

The $\varepsilon$-well-supported Nash equilibrium is a strong notion of approximation of a Nash equilibrium, where no player has an incentive greater than $\varepsilon$ to deviate from any of the pure strategies that she uses in her mixed strategy. The smallest constant $\varepsilon$ currently known for which there is a polynomial-time algorithm that computes an $\varepsilon$-well-supported Nash equilibrium in bimatrix games is slightly below $2/3$. In this paper we study this problem for symmetric bimatrix games and we provide a polynomial-time algorithm that gives a $(1/2+\delta)$-well-supported Nash equilibrium, for an arbitrarily small positive constant $\delta$

Novel flavanones with anti-trypanosomal activity isolated from Zambian and Tanzanian propolis samples

A bioassay-guided phytochemical investigation of propolis samples from Tanzania and Zambia that screened for activity against Trypanosoma brucei has led to the isolation of two novel flavanones with promising antitrypanosomal activity. The compounds were characterized based on their spectral and physical data and identified as 6-(1,1-dimethylallyl) pinocembrin and 5-hydroxy-4″,4″-dimethyl-5″-methyl-5″-H-dihydrofuranol [2″,3″,6,7] flavanone. The two compounds, together with the propolis extracts and fractions, were assayed against a standard drug-sensitive strain of T. b. brucei (s427 wild-type), multi-drug resistant-resistant T. b. brucei (B48), drug-sensitive T. congolense (1L300) and a derived diminazene-resistant T. congolense strain (6C3), and for toxicity against U947 human cells and RAW 246.7 murine cells. Activity against T. b. brucei was higher than against T. congolense. Interestingly, the Tanzanian propolis extract was found to be more active than its fractions and purified compounds in these assays, with an IC of 1.20 μg/mL against T. b. brucei. The results of a cytotoxicity assay showed that the propolis extracts were less toxic than the purified compounds with mean IC values > 165.0 μg/mL

Tick paralysis of dogs in Victoria due to Ixodes cornuatus

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The Antiprotozoal Activity of Papua New Guinea Propolis and Its Triterpenes

Profiling a propolis sample from Papua New Guinea (PNG) using high-resolution mass spectrometry indicated that it contained several triterpenoids. Further fractionation by column chromatography and medium-pressure liquid chromatography (MPLC) followed by nuclear magnetic resonance spectroscopy (NMR) identified 12 triterpenoids. Five of these were obtained pure and the others as mixtures of two or three compounds. The compounds identified were: mangiferonic acid, ambonic acid, isomangiferolic acid, ambolic acid, 27-hydroxyisomangiferolic acid, cycloartenol, cycloeucalenol, 24-methylenecycloartenol, 20-hydroxybetulin, betulin, betulinic acid and madecassic acid. The fractions from the propolis and the purified compounds were tested in vitro against Crithidia fasciculata, Trypanosoma congolense, drug-resistant Trypanosoma congolense, Trypanosoma b. brucei and multidrug-resistant Trypanosoma b. brucei (B48). They were also assayed for their toxicity against U947 cells. The compounds and fractions displayed moderate to high activity against parasitic protozoa but only low cytotoxicity against the mammalian cells. The most active isolated compound, 20-hydroxybetulin, was found to be trypanostatic when different concentrations were tested against T. b. brucei growth

Isolation of a novel flavanonol and an alkylresorcinol with highly potent anti-trypanosomal activity from Libyan propolis

Twelve propolis samples from different parts of Libya were investigated for their phytochemical constituents. Ethanol extracts of the samples and some purified compounds were tested against Trypanosoma brucei, Plasmodium falciparum and against two helminth species, Trichinella spiralis and Caenorhabditis elegans, showing various degrees of activity. Fourteen compounds were isolated from the propolis samples, including a novel compound Taxifolin-3-acetyl-4’-methyl ether (4), a flavanonol derivative. The crude extracts showed moderate activity against T. spiralis and C. elegans, while the purified compounds had low activity against P. falciparum. Anti-trypanosomal activity (EC50 = 0.7 µg/mL) was exhibited by a fraction containing a cardol identified as bilobol (10) and this fraction had no effect on Human Foreskin Fibroblasts (HFF), even at 2.0 mg/mL, thus demonstrating excellent selectivity. A metabolomics study was used to explore the mechanism of action of the fraction and it revealed significant disturbances in trypanosomal phospholipid metabolism, especially the formation of choline phospholipids. We conclude that a potent and highly selective new trypanocide may be present in the fraction

Ten Misconceptions from the History of Analysis and Their Debunking

The widespread idea that infinitesimals were "eliminated" by the "great triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d'Alembert, Cauchy, and others.Comment: 46 pages, 4 figures; Foundations of Science (2012). arXiv admin note: text overlap with arXiv:1108.2885 and arXiv:1110.545

The highly rearranged mitochondrial genomes of the crabs Maja crispata and Maja squinado (Majidae) and gene order evolution in Brachyura

Abstract We sequenced the mitochondrial genomes of the spider crabs Maja crispata and Maja squinado (Majidae, Brachyura). Both genomes contain the whole set of 37 genes characteristic of Bilaterian genomes, encoded on both \u3b1- and \u3b2-strands. Both species exhibit the same gene order, which is unique among known animal genomes. In particular, all the genes located on the \u3b2-strand form a single block. This gene order was analysed together with the other nine gene orders known for the Brachyura. Our study confirms that the most widespread gene order (BraGO) represents the plesiomorphic condition for Brachyura and was established at the onset of this clade. All other gene orders are the result of transformational pathways originating from BraGO. The different gene orders exhibit variable levels of genes rearrangements, which involve only tRNAs or all types of genes. Local homoplastic arrangements were identified, while complete gene orders remain unique and represent signatures that can have a diagnostic value. Brachyura appear to be a hot-spot of gene order diversity within the phylum Arthropoda. Our analysis, allowed to track, for the first time, the fully evolutionary pathways producing the Brachyuran gene orders. This goal was achieved by coupling sophisticated bioinformatic tools with phylogenetic analysis

Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond

Many historians of the calculus deny significant continuity between infinitesimal calculus of the 17th century and 20th century developments such as Robinson's theory. Robinson's hyperreals, while providing a consistent theory of infinitesimals, require the resources of modern logic; thus many commentators are comfortable denying a historical continuity. A notable exception is Robinson himself, whose identification with the Leibnizian tradition inspired Lakatos, Laugwitz, and others to consider the history of the infinitesimal in a more favorable light. Inspite of his Leibnizian sympathies, Robinson regards Berkeley's criticisms of the infinitesimal calculus as aptly demonstrating the inconsistency of reasoning with historical infinitesimal magnitudes. We argue that Robinson, among others, overestimates the force of Berkeley's criticisms, by underestimating the mathematical and philosophical resources available to Leibniz. Leibniz's infinitesimals are fictions, not logical fictions, as Ishiguro proposed, but rather pure fictions, like imaginaries, which are not eliminable by some syncategorematic paraphrase. We argue that Leibniz's defense of infinitesimals is more firmly grounded than Berkeley's criticism thereof. We show, moreover, that Leibniz's system for differential calculus was free of logical fallacies. Our argument strengthens the conception of modern infinitesimals as a development of Leibniz's strategy of relating inassignable to assignable quantities by means of his transcendental law of homogeneity.Comment: 69 pages, 3 figure

A Burgessian critique of nominalistic tendencies in contemporary mathematics and its historiography

We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of Cantor, Dedekind, and Weierstrass; to the reconstruction of Cauchy's foundational work associated with the work of Boyer and Grabiner; and to Bishop's constructivist reconstruction of classical analysis. We examine the effects of a nominalist disposition on historiography, teaching, and research.Comment: 57 pages; 3 figures. Corrected misprint