Guglielmo Libri, matematico e storico della matematica. L’irresitibile ascesa dall’Ateneo pisano all’Institut de France. By Andrea Del Centina and Alessandra Fiocca. Florence (Olschki). 2010. ISBN 978-88-222-6003-1. XXII + 342 pp. + CD-ROM. 39 €

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A Comparison of Biased Simulation Schemes for Stochastic Volatility Models

When using an Euler discretisation to simulate a mean-reverting square root process, one runs into the problem that while the process itself is guaranteed to be nonnegative, the discretisation is not. Although an exact and efficient simulation algorithm exists for this process, at present this is not the case for the Heston stochastic volatility model, where the variance is modelled as a square root process. Consequently, when using an Euler discretisation, one must carefully think about how to fix negative variances. Our contribution is threefold. Firstly, we unify all Euler fixes into a single general framework. Secondly, we introduce the new full truncation scheme, tailored to minimise the upward bias found when pricing European options. Thirdly and finally, we numerically compare all Euler fixes to a recent quasi-second order scheme of Kahl and Jäckel and the exact scheme of Broadie and Kaya. The choice of fix is found to be extremely important. The full truncation scheme by far outperforms all biased schemes in terms of bias, root-mean-squared error, and hence should be the preferred discretisation method for simulation of the Heston model and extensions thereof

The Coulomb phase shift revisited

We investigate the Coulomb phase shift, and derive and analyze new and more precise analytical formulae. We consider next to leading order terms to the Stirling approximation, and show that they are important at small values of the angular momentum $l$ and other regimes. We employ the uniform approximation. The use of our expressions in low energy scattering of charged particles is discussed and some comparisons are made with other approximation methods.Comment: 13 pages, 5 figures, 1 tabl

Reduced dimensionality spin-orbit dynamics of CH3 + HCl reversible arrow CH4 Cl on ab initio surfaces

A reduced dimensionality quantum scattering method is extended to the study of spin-orbit nonadiabatic transitions in the CH3 + HCl reversible arrow CH4 + Cl(P-2(J)) reaction. Three two-dimensional potential energy surfaces are developed by fitting a 29 parameter double-Morse function to CCSD(T)/IB//MP2/cc-pV(T+d)Z-dk ab initio data; interaction between surfaces is described by geometry-dependent spin-orbit coupling functions fit to MCSCF/cc-pV(T+d)Z-dk ab initio data. Spectator modes are treated adiabatically via inclusion of curvilinear projected frequencies. The total scattering wave function is expanded in a vibronic basis set and close-coupled equations are solved via R-matrix propagation. Ground state thermal rate constants for forward and reverse reactions agree well with experiment. Multi-surface reaction probabilities, integral cross sections, and initial-state selected branching ratios all highlight the importance of vibrational energy in mediating nonadiabatic transition. Electronically excited state dynamics are seen to play a small but significant role as consistent with experimental conclusions. (C) 2011 American Institute of Physics. [doi:10.1063/1.3592732

Super-KMS functionals for graded-local conformal nets

Motivated by a few preceding papers and a question of R. Longo, we introduce super-KMS functionals for graded translation-covariant nets over R with superderivations, roughly speaking as a certain supersymmetric modification of classical KMS states on translation-covariant nets over R, fundamental objects in chiral algebraic quantum field theory. Although we are able to make a few statements concerning their general structure, most properties will be studied in the setting of specific graded-local (super-) conformal models. In particular, we provide a constructive existence and partial uniqueness proof of super-KMS functionals for the supersymmetric free field, for certain subnets, and for the super-Virasoro net with central charge c>= 3/2. Moreover, as a separate result, we classify bounded super-KMS functionals for graded-local conformal nets over S^1 with respect to rotations.Comment: 30 pages, revised version (to appear in Ann. H. Poincare

Looking backward: From Euler to Riemann

We survey the main ideas in the early history of the subjects on which Riemann worked and that led to some of his most important discoveries. The subjects discussed include the theory of functions of a complex variable, elliptic and Abelian integrals, the hypergeometric series, the zeta function, topology, differential geometry, integration, and the notion of space. We shall see that among Riemann's predecessors in all these fields, one name occupies a prominent place, this is Leonhard Euler. The final version of this paper will appear in the book \emph{From Riemann to differential geometry and relativity} (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017

Change in the distribution of a member of the strand line community: the seaweed fly (Diptera: Coelopidae)

1. Coastal organisms are predicted to be particularly susceptible to the impact of global warming. In this study the distribution and relative abundance of two coastal invertebrates, Coelopa frigida (Fabricius) and C. pilipes are investigated. 2. Coelopa pilipes has a more southerly distribution than C. frigida , and prefers a warmer climate. Coelopa pilipes is less resistant to sub-zero temperatures than C. frigida and its northerly distribution is probably limited by cold winter days. 3. The most recent distribution map of C. frigida and C. pilipes in northern Europe was published a decade ago and showed the northerly extent of the distribution of C. pilipes reaching the north coast of mainland Scotland but its complete absence from the Western and Northern Isles. 4. C. pilipes has now spread throughout the Western Isles and the Orkney Islands but is still absent from Shetland. There has also been an increase in the relative frequency of C. pilipes at sites harbouring coelopids on the British mainland. A similar pattern of distribution change along the west coast of Sweden is reported. 5. It is proposed that these changes have occurred primarily as a result of global warming and in particular due to the recent increase in winter temperatures. A number of other indirect effects may have also contributed to these changes, including a probable change in macroalgae distribution. The implications of these changes for the wrack bed ecosystem and at higher trophic levels are considered

The Phyre2 web portal for protein modeling, prediction and analysis

Phyre2 is a suite of tools available on the web to predict and analyze protein structure, function and mutations. The focus of Phyre2 is to provide biologists with a simple and intuitive interface to state-of-the-art protein bioinformatics tools. Phyre2 replaces Phyre, the original version of the server for which we previously published a paper in Nature Protocols. In this updated protocol, we describe Phyre2, which uses advanced remote homology detection methods to build 3D models, predict ligand binding sites and analyze the effect of amino acid variants (e.g., nonsynonymous SNPs (nsSNPs)) for a user's protein sequence. Users are guided through results by a simple interface at a level of detail they determine. This protocol will guide users from submitting a protein sequence to interpreting the secondary and tertiary structure of their models, their domain composition and model quality. A range of additional available tools is described to find a protein structure in a genome, to submit large number of sequences at once and to automatically run weekly searches for proteins that are difficult to model. The server is available at http://www.sbg.bio.ic.ac.uk/phyre2. A typical structure prediction will be returned between 30 min and 2 h after submission