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

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

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

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

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

Levodopa medication improves incidental sequence learning in Parkinson’s disease

Empirical evidence suggests that levodopa medication used to treat the motor symptoms of Parkinson’s disease (PD) may either improve, impair or not affect specific cognitive processes. This evidence led to the ‘dopamine overdose’ hypothesis that levodopa medication impairs performance on cognitive tasks if they recruit fronto-striatal circuits which are not yet dopamine-depleted in early PD and as a result the medication leads to an excess of dopamine. This hypothesis has been supported for various learning tasks including conditional associative learning, reversal learning, classification learning and intentional deterministic sequence learning, on all of which PD patients demonstrated significantly worse performance when tested on relative to off dopamine medication. Incidental sequence learning is impaired in PD, but how such learning is affected by dopaminergic therapy remains undetermined. The aim of the current study was to investigate the effect of dopaminergic medication on incidental sequence learning in PD. We used a probabilistic serial reaction time task (SRTT), a sequence learning paradigm considered to make the sequence less apparent and more likely to be learned incidentally rather than intentionally. We compared learning by the same group of PD patients (n = 15) on two separate occasions following oral administration of levodopa medication (on state) and after overnight withdrawal of medication (off state). Our results demonstrate for the first time that levodopa medication enhances incidental learning of a probabilistic sequence on the serial reaction time task in PD. However, neither group significantly differed from performance of a control group without a neurological disease, which indicates the importance of within group comparisons for identifying deficits. Levodopa medication enhanced incidental learning by patients with PD on a probabilistic sequence learning paradigm even though the patients were not aware of the existence of the sequence or their acquired knowledge. The results suggest a role in acquiring incidental motor sequence learning for dorsal striatal areas strongly affected by dopamine depletion in early PD.Mazda Beigi was supported by a 3+1 ESRC PhD studentship (R84003). Leonora Wilkinson was funded by a Career Development Fellowship from Parkinson’s UK

Bounding Average-Energy Games

We consider average-energy games, where the goal is to minimize the long-run average of the accumulated energy. While several results have been obtained on these games recently, decidability of average-energy games with a lower-bound constraint on the energy level (but no upper bound) remained open; in particular, so far there was no known upper bound on the memory that is required for winning strategies. By reducing average-energy games with lower-bounded energy to infinite-state mean-payoff games and analyzing the density of low-energy configurations, we show an almost tight doubly-exponential upper bound on the necessary memory, and prove that the winner of average-energy games with lower-bounded energy can be determined in doubly-exponential time. We also prove EXPSPACE-hardness of this problem. Finally, we consider multi-dimensional extensions of all types of average-energy games: without bounds, with only a lower bound, and with both a lower and an upper bound on the energy. We show that the fully-bounded version is the only case to remain decidable in multiple dimensions.SCOPUS: cp.kinfo:eu-repo/semantics/publishe

A Hidden Markov Model for Analysis of Frontline Veterinary Data for Emerging Zoonotic Disease Surveillance

Surveillance systems tracking health patterns in animals have potential for early warning of infectious disease in humans, yet there are many challenges that remain before this can be realized. Specifically, there remains the challenge of detecting early warning signals for diseases that are not known or are not part of routine surveillance for named diseases. This paper reports on the development of a hidden Markov model for analysis of frontline veterinary sentinel surveillance data from Sri Lanka. Field veterinarians collected data on syndromes and diagnoses using mobile phones. A model for submission patterns accounts for both sentinel-related and disease-related variability. Models for commonly reported cattle diagnoses were estimated separately. Region-specific weekly average prevalence was estimated for each diagnoses and partitioned into normal and abnormal periods. Visualization of state probabilities was used to indicate areas and times of unusual disease prevalence. The analysis suggests that hidden Markov modelling is a useful approach for surveillance datasets from novel populations and/or having little historical baselines

Reduction of Hydrophilic Ubiquinones by the Flavin in Mitochondrial NADH:Ubiquinone Oxidoreductase (Complex I) and Production of Reactive Oxygen Species†

ABSTRACT: NADH:ubiquinone oxidoreductase (complex I) from bovine heart mitochondria is a complicated, energy-transducing, membrane-bound enzyme that contains 45 different subunits, a non-covalently bound flavin mononucleotide, and eight iron-sulfur clusters. The mechanisms of NADH oxidation and intramolecular electron transfer by complex I are gradually being defined, but the mechanism linking ubiquinone reduction to proton translocation remains unknown. Studies of ubiquinone reduction by isolated complex I are problematic because the extremely hydrophobic natural substrate, ubiquinone-10, must be substituted with a relatively hydrophilic analogue (such as ubiquinone-1). Hydrophilic ubiquinones are reduced by an additional, non-energy-transducing pathway (which is insensitive to inhibitors such as rotenone and piericidin A). Here, we show that inhibitor-insensitive ubiquinone reduction occurs by a ping-pong type mechanism, catalyzed by the flavin mononucleotide cofactor in the active site for NADH oxidation. Moreover, semiquinones produced at the flavin site initiate redox cycling reactions with molecular oxygen, producing superoxide radicals and hydrogen peroxide. The ubiquinone reactant is regenerated, so the NADH:Q reaction becomes superstoichiometric. Idebenone, an artificial ubiquinone showing promise in the treatment of Friedreich’s Ataxia, reacts at the flavin site. The factors which determine the balance of reactivity between the two sites of ubiquinone reduction (the energy-transducing site and the flavi