Fast and accurate evaluation of Wigner 3j, 6j, and 9j symbols using prime factorisation and multi-word integer arithmetic

We present an efficient implementation for the evaluation of Wigner 3j, 6j, and 9j symbols. These represent numerical transformation coefficients that are used in the quantum theory of angular momentum. They can be expressed as sums and square roots of ratios of integers. The integers can be very large due to factorials. We avoid numerical precision loss due to cancellation through the use of multi-word integer arithmetic for exact accumulation of all sums. A fixed relative accuracy is maintained as the limited number of floating-point operations in the final step only incur rounding errors in the least significant bits. Time spent to evaluate large multi-word integers is in turn reduced by using explicit prime factorisation of the ingoing factorials, thereby improving execution speed. Comparison with existing routines shows the efficiency of our approach and we therefore provide a computer code based on this work.Comment: 7 pages, 2 figures. Accepted for publication in SIAM Journal on Scientific Computing (SISC

Study of chaos in hamiltonian systems via convergent normal forms

We use Moser's normal forms to study chaotic motion in two-degree hamiltonian systems near a saddle point. Besides being convergent, they provide a suitable description of the cylindrical topology of the chaotic flow in that vicinity. Both aspects combined allowed a precise computation of the homoclinic interaction of stable and unstable manifolds in the full phase space, rather than just the Poincar\'e section. The formalism was applied to the H\'enon-Heiles hamiltonian, producing strong evidence that the region of convergence of these normal forms extends over that originally established by Moser.Comment: 29 pages, REVTEX, 22 postscript figures on reques

From Predators to Icons: Exposing the Myth of the Business Hero

[ Excerpted from Forword by John R. Kimberly] From Predators to Icons takes us on a provocative and nuanced journey through the business practices of a number of individuals and the companies they built and shows how they navigated through this volatile mix to achieve extraordinary success in their undertakings. In an era in which we are obsessed with rankings of everything from colleges and universities to hospitals to tennis players, we tend to focus on the end result—who is number 1?—and much less on the means: how did they get there? In an era when we are fascinated by stories of leaders as heroes and by the lives of the rich and famous, we tend to let the gloss of the material trappings of success blind us to questions of their origins. In the work they report here, Villette and Vuillermot use the lens of social science as a vehicle for unpacking the roots of extraordinary success in business, for analyzing how success was achieved. They have accumulated evidence from a variety of sources, including the myriad biographies—authorized and unauthorized—of business icons, to build their comparative analysis of the practices of thirty-two businessmen from Europe and North America, of how their wealth was built, and of the common threads that characterize the roots of success across geographies, across industries, and across time. Their approach is highly original, and the data they assemble are wide-ranging. They are well aware of both the promise and the limitations of their data and are careful to discuss both. Ultimately, it is up to each of us to judge the credibility of both the empirical foundations on which their analysis is built and the conclusions they reach, the messages they send. But theirs is an impressive undertaking and needs to be taken seriously

Fast Algorithms for the computation of Fourier Extensions of arbitrary length

Fourier series of smooth, non-periodic functions on $[-1,1]$ are known to exhibit the Gibbs phenomenon, and exhibit overall slow convergence. One way of overcoming these problems is by using a Fourier series on a larger domain, say $[-T,T]$ with $T>1$, a technique called Fourier extension or Fourier continuation. When constructed as the discrete least squares minimizer in equidistant points, the Fourier extension has been shown shown to converge geometrically in the truncation parameter $N$. A fast ${\mathcal O}(N \log^2 N)$ algorithm has been described to compute Fourier extensions for the case where $T=2$, compared to ${\mathcal O}(N^3)$ for solving the dense discrete least squares problem. We present two ${\mathcal O}(N\log^2 N )$ algorithms for the computation of these approximations for the case of general $T$, made possible by exploiting the connection between Fourier extensions and Prolate Spheroidal Wave theory. The first algorithm is based on the explicit computation of so-called periodic discrete prolate spheroidal sequences, while the second algorithm is purely algebraic and only implicitly based on the theory

High-growth firms, innovation and the distance to the frontier

This paper studies the differences in the R&D and innovation behaviour of high-growth firms for 16 EU countries. The results confirm that R&D and innovation are important characteristics for high-growth firms in countries close to the technological frontier, but not for high-growth firms in countries further away from the technological frontier.R&D, high-growth firms, innovation, Europe, distance to the frontier, CIS

Automatic differentiation in machine learning: a survey

Derivatives, mostly in the form of gradients and Hessians, are ubiquitous in machine learning. Automatic differentiation (AD), also called algorithmic differentiation or simply "autodiff", is a family of techniques similar to but more general than backpropagation for efficiently and accurately evaluating derivatives of numeric functions expressed as computer programs. AD is a small but established field with applications in areas including computational fluid dynamics, atmospheric sciences, and engineering design optimization. Until very recently, the fields of machine learning and AD have largely been unaware of each other and, in some cases, have independently discovered each other's results. Despite its relevance, general-purpose AD has been missing from the machine learning toolbox, a situation slowly changing with its ongoing adoption under the names "dynamic computational graphs" and "differentiable programming". We survey the intersection of AD and machine learning, cover applications where AD has direct relevance, and address the main implementation techniques. By precisely defining the main differentiation techniques and their interrelationships, we aim to bring clarity to the usage of the terms "autodiff", "automatic differentiation", and "symbolic differentiation" as these are encountered more and more in machine learning settings.Comment: 43 pages, 5 figure

Coordinated balancing of muscle oxidative metabolism through PGC-1α increases metabolic flexibility and preserves insulin sensitivity

The peroxisome proliferator-activated receptor γ coactivator 1α (PGC-1α) enhances oxidative metabolism in skeletal muscle. Excessive lipid oxidation and electron transport chain activity can, however, lead to the accumulation of harmful metabolites and impair glucose homeostasis. Here, we investigated the effect of over-expression of PGC-1α on metabolic control and generation of insulin desensitizing agents in extensor digitorum longus (EDL), a muscle that exhibits low levels of PGC-1α in the untrained state and minimally relies on oxidative metabolism. We demonstrate that PGC-1α induces a strictly balanced substrate oxidation in EDL by concomitantly promoting the transcription of activators and inhibitors of lipid oxidation. Moreover, we show that PGC-1α enhances the potential to uncouple oxidative phosphorylation. Thereby, PGC-1α boosts elevated, yet tightly regulated oxidative metabolism devoid of side products that are detrimental for glucose homeostasis. Accordingly, PI3K activity, an early phase marker for insulin resistance, is preserved in EDL muscle. Our findings suggest that PGC-1α coordinately coactivates the simultaneous transcription of gene clusters implicated in the positive and negative regulation of oxidative metabolism and thereby increases metabolic flexibility. Thus, in mice fed a normal chow diet, over-expression of PGC-1α does not alter insulin sensitivity and the metabolic adaptations elicited by PGC-1α mimic the beneficial effects of endurance training on muscle metabolism in this context

Development of a fast screening method for the direct determination of chlorinated persistent organic pollutants in fish oil by high-resolution continuum source graphite furnace molecular absorption spectrometry

The authors are grateful to the Conselho Nacional de Desenvolvimento Científico and Tecnológico (CNPq); the present research was mostly financed through Project no. CNPq 406877/2013-0. The authors are also grateful to the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) for financial support and scholarships, and to Analytik Jena for financial support and donation of the contrAA 600 high-resolution continuum source atomic absorption spectrometer.Peer reviewedPostprin