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

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

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

Corporate governance and employees in South Africa.

Focusing on employees as stakeholders, we analyse corporate governance initiatives in South Africa encouraging and requiring companies to look beyond their shareholders' interests. Successive non-binding codes and the provisions of the recent Companies Act 2008 promoting this have been lauded by many commentators. The 2008 Act provides certain opportunities for employees and their representatives to exercise influence at the margins. We nevertheless question how far current corporate governance initiatives are adequate to promote employee interests. On the basis of three case studies of how companies have responded to employees as stakeholders, we conclude that in fact more stringent regulation is required

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

Search for CP Violation in the Decay Z -> b (b bar) g

About three million hadronic decays of the Z collected by ALEPH in the years 1991-1994 are used to search for anomalous CP violation beyond the Standard Model in the decay Z -> b \bar{b} g. The study is performed by analyzing angular correlations between the two quarks and the gluon in three-jet events and by measuring the differential two-jet rate. No signal of CP violation is found. For the combinations of anomalous CP violating couplings, ${\hat{h}}_b = {\hat{h}}_{Ab}g_{Vb}-{\hat{h}}_{Vb}g_{Ab}$ and $h^{\ast}_b = \sqrt{\hat{h}_{Vb}^{2}+\hat{h}_{Ab}^{2}}$, limits of \hat{h}_b < 0.59$and$h^{\ast}_{b} < 3.02$ are given at 95\% CL.Comment: 8 pages, 1 postscript figure, uses here.sty, epsfig.st

In silico design and biological evaluation of a dual specificity kinase inhibitor targeting cell cycle progression and angiogenesis

Methodology: We have utilized a rational in silico-based approach to demonstrate the design and study of a novel compound that acts as a dual inhibitor of vascular endothelial growth factor receptor 2 (VEGFR2) and cyclin-dependent kinase 1 (CDK1). This compound acts by simultaneously inhibiting pro-Angiogenic signal transduction and cell cycle progression in primary endothelial cells. JK-31 displays potent in vitro activity against recombinant VEGFR2 and CDK1/cyclin B proteins comparable to previously characterized inhibitors. Dual inhibition of the vascular endothelial growth factor A (VEGF-A)-mediated signaling response and CDK1-mediated mitotic entry elicits anti-Angiogenic activity both in an endothelial-fibroblast co-culture model and a murine ex vivo model of angiogenesis

VEGF-A isoforms differentially regulate ATF-2-dependent VCAM-1 gene expression and endothelial-leukocyte interactions

Vascular endothelial growth factor A (VEGF-A) regulates many aspects of vascular physiology. VEGF-A stimulates signal transduction pathways that modulate endothelial outputs such as cell migration, proliferation, tubulogenesis, and cell-cell interactions. Multiple VEGF-A isoforms exist, but the biological significance of this is unclear. Here we analyzed VEGF-A isoform-specific stimulation of VCAM-1 gene expression, which controls endothelial-leukocyte interactions, and show that this is dependent on both ERK1/2 and activating transcription factor-2 (ATF-2). VEGF-A isoforms showed differential ERK1/2 and p38 MAPK phosphorylation kinetics. A key feature of VEGF-A isoform-specific ERK1/2 activation and nuclear translocation was increased phosphorylation of ATF-2 on threonine residue 71 (T71). Using reverse genetics, we showed ATF-2 to be functionally required for VEGF-A-stimulated endothelial VCAM-1 gene expression. ATF-2 knockdown blocked VEGF-A-stimulated VCAM-1 expression and endothelial-leukocyte interactions. ATF-2 was also required for other endothelial cell outputs, such as cell migration and tubulogenesis. In contrast, VCAM-1 was essential only for promoting endothelial-leukocyte interactions. This work presents a new paradigm for understanding how soluble growth factor isoforms program complex cellular outputs and responses by modulating signal transduction pathways