On integrability of Hirota-Kimura type discretizations

We give an overview of the integrability of the Hirota-Kimura discretization method applied to algebraically completely integrable (a.c.i.) systems with quadratic vector fields. Along with the description of the basic mechanism of integrability (Hirota-Kimura bases), we provide the reader with a fairly complete list of the currently available results for concrete a.c.i. systems.Comment: 47 pages, some minor change

Variation of discrete spectra for non-selfadjoint perturbations of selfadjoint operators

Let B=A+K where A is a bounded selfadjoint operator and K is an element of the von Neumann-Schatten ideal S_p with p>1. Let {\lambda_n} denote an enumeration of the discrete spectrum of B. We show that \sum_n \dist(\lambda_n, \sigma(A))^p is bounded from above by a constant multiple of |K|_p^p. We also derive a unitary analog of this estimate and apply it to obtain new estimates on zero-sets of Cauchy transforms.Comment: Differences to previous version: Extended Introduction, new Section 5, additional references. To appear in Int. Eq. Op. Theor

A comparison of methods to adjust for continuous covariates in the analysis of randomised trials

BACKGROUND: Although covariate adjustment in the analysis of randomised trials can be beneficial, adjustment for continuous covariates is complicated by the fact that the association between covariate and outcome must be specified. Misspecification of this association can lead to reduced power, and potentially incorrect conclusions regarding treatment efficacy. METHODS: We compared several methods of adjustment to determine which is best when the association between covariate and outcome is unknown. We assessed (a) dichotomisation or categorisation; (b) assuming a linear association with outcome; (c) using fractional polynomials with one (FP1) or two (FP2) polynomial terms; and (d) using restricted cubic splines with 3 or 5 knots. We evaluated each method using simulation and through a re-analysis of trial datasets. RESULTS: Methods which kept covariates as continuous typically had higher power than methods which used categorisation. Dichotomisation, categorisation, and assuming a linear association all led to large reductions in power when the true association was non-linear. FP2 models and restricted cubic splines with 3 or 5 knots performed best overall. CONCLUSIONS: For the analysis of randomised trials we recommend (1) adjusting for continuous covariates even if their association with outcome is unknown; (2) keeping covariates as continuous; and (3) using fractional polynomials with two polynomial terms or restricted cubic splines with 3 to 5 knots when a linear association is in doubt

On the construction of high-order force gradient algorithms for integration of motion in classical and quantum systems

A consequent approach is proposed to construct symplectic force-gradient algorithms of arbitrarily high orders in the time step for precise integration of motion in classical and quantum mechanics simulations. Within this approach the basic algorithms are first derived up to the eighth order by direct decompositions of exponential propagators and further collected using an advanced composition scheme to obtain the algorithms of higher orders. Contrary to the scheme by Chin and Kidwell [Phys. Rev. E 62, 8746 (2000)], where high-order algorithms are introduced by standard iterations of a force-gradient integrator of order four, the present method allows to reduce the total number of expensive force and its gradient evaluations to a minimum. At the same time, the precision of the integration increases significantly, especially with increasing the order of the generated schemes. The algorithms are tested in molecular dynamics and celestial mechanics simulations. It is shown, in particular, that the efficiency of the new fourth-order-based algorithms is better approximately in factors 5 to 1000 for orders 4 to 12, respectively. The results corresponding to sixth- and eighth-order-based composition schemes are also presented up to the sixteenth order. For orders 14 and 16, such highly precise schemes, at considerably smaller computational costs, allow to reduce unphysical deviations in the total energy up in 100 000 times with respect to those of the standard fourth-order-based iteration approach.Comment: 23 pages, 2 figures; submitted to Phys. Rev.

Core pinning by intragranular nanoprecipitates in polycrystalline MgCNi_3

The nanostructure and magnetic properties of polycrystalline MgCNi_3 were studied by x-ray diffraction, electron microscopy, and vibrating sample magnetometry. While the bulk flux-pinning force curve F_p(H) indicates the expected grain-boundary pinning mechanism just below T_c = 7.2 K, a systematic change to pinning by a nanometer-scale distribution of core pinning sites is indicated by a shift of F_p(H) with decreasing temperature. The lack of scaling of F_p(H) suggests the presence of 10 to 20% of nonsuperconducting regions inside the grains, which are smaller than the diameter of fluxon cores 2xi at high temperature and become effective with decreasing temperature when xi(T) approaches the nanostructural scale. Transmission electron microscopy revealed cubic and graphite nanoprecipitates with 2 to 5 nm size, consistent with the above hypothesis since xi(0) = 6 nm. High critical current densities, more than 10^6 A/cm^2 at 1 T and 4.2 K, were obtained for grain colonies separated by carbon. Dirty-limit behavior seen in previous studies may be tied to electron scattering by the precipitates, indicating the possibility that strong core pinning might be combined with a technologically useful upper critical field if versions of MgCNi_3 with higher T_c can be found.Comment: 5 pages, 6 figures, submitted to PR

A Novel Approach for Ellipsoidal Outer-Approximation of the Intersection Region of Ellipses in the Plane

In this paper, a novel technique for tight outer-approximation of the intersection region of a finite number of ellipses in 2-dimensional (2D) space is proposed. First, the vertices of a tight polygon that contains the convex intersection of the ellipses are found in an efficient manner. To do so, the intersection points of the ellipses that fall on the boundary of the intersection region are determined, and a set of points is generated on the elliptic arcs connecting every two neighbouring intersection points. By finding the tangent lines to the ellipses at the extended set of points, a set of half-planes is obtained, whose intersection forms a polygon. To find the polygon more efficiently, the points are given an order and the intersection of the half-planes corresponding to every two neighbouring points is calculated. If the polygon is convex and bounded, these calculated points together with the initially obtained intersection points will form its vertices. If the polygon is non-convex or unbounded, we can detect this situation and then generate additional discrete points only on the elliptical arc segment causing the issue, and restart the algorithm to obtain a bounded and convex polygon. Finally, the smallest area ellipse that contains the vertices of the polygon is obtained by solving a convex optimization problem. Through numerical experiments, it is illustrated that the proposed technique returns a tighter outer-approximation of the intersection of multiple ellipses, compared to conventional techniques, with only slightly higher computational cost

Containing, embracing and hyper-activating Britishness: British-based foreign-owned firms

There are in the UK ownership forms different to the characteristics of Britishness – British-based foreign-owned firms where dominant owners may have differentiated control interests. These may contain, that is, override, national institutional characteristics embedded in a particular national capitalism. Accordingly, separating the agency of these firms from presumed business system structures may reveal how diverse patterns of firm ownership – those associated with British-based foreign-owned firms – can inform dynamic ownership developments in British capitalism which contain and hyper-activate Britishness. The article theorizes British-based foreign-owned firms and provides empirical detail on how ownership characteristics influence financial commitment and strategic control in 10 of these firms

Climate stories: Why do climate scientists and sceptical voices participate in the climate debate?

Public perceptions of the climate debate predominantly frame the key actors as climate scientists versus sceptical voices; however, it is unclear why climate scientists and sceptical voices choose to participate in this antagonistic and polarised public battle. A narrative interview approach is used to better understand the underlying rationales behind 22 climate scientists’ and sceptical voices’ engagement in the climate debate, potential commonalities, as well as each actor’s ability to be critically self-reflexive. Several overlapping rationales are identified including a sense of duty to publicly engage, agreement that complete certainty about the complex assemblage of climate change is unattainable and that political factors are central to the climate debate. We argue that a focus on potential overlaps in perceptions and rationales as well as the ability to be critically self-reflexive may encourage constructive discussion among actors previously engaged in purposefully antagonistic exchange on climate change

Progress in Classical and Quantum Variational Principles

We review the development and practical uses of a generalized Maupertuis least action principle in classical mechanics, in which the action is varied under the constraint of fixed mean energy for the trial trajectory. The original Maupertuis (Euler-Lagrange) principle constrains the energy at every point along the trajectory. The generalized Maupertuis principle is equivalent to Hamilton's principle. Reciprocal principles are also derived for both the generalized Maupertuis and the Hamilton principles. The Reciprocal Maupertuis Principle is the classical limit of Schr\"{o}dinger's variational principle of wave mechanics, and is also very useful to solve practical problems in both classical and semiclassical mechanics, in complete analogy with the quantum Rayleigh-Ritz method. Classical, semiclassical and quantum variational calculations are carried out for a number of systems, and the results are compared. Pedagogical as well as research problems are used as examples, which include nonconservative as well as relativistic systems