A divide and conquer method for polynomial zeros

AbstractThe problem of factorising an nth-degree polynomial Pn(x) = xn + a1xn−1 + ⋯ + an−1x + an, where the coefficients ai are real, into two polynomials Q(x) and R(x) of degrees nQ and nR can be posed as a system of n quadratic equations. An efficient implementation of Newton's method for the solution of these equations is achieved by exploiting the block Toeplitz structure of the Jacobian matrix which arises when nQ and nR are restricted to {m − 1, m, m + 1∣m = [12n]}, where [x] is the largest integer ⩽x. This polynomial factorisation permits the development of a divide and conquer method for the simultaneous calculation of all the zeros of a polynomial

Granular dynamics of a vibrated bed of dumbbells

A two-dimensional vibrated bed of dumbbells was investigated using experiment and numerical simulation. Experimentally, high speed photography in combination with image analysis and tracking software was used to determine the location of the centre of mass and the locations and direction of motion of the component particles of the dumbbells. Numerically, a geometry analogous to that used experimentally was employed and the equations of motion for each of the particles were solved using the distinct element method. It was found that, despite some differences, the numerical simulations agreed reasonably well with the experimental results. Subsequently, the simulation method was used to explore the behaviour of the bed over a range of densities. The moments of the velocity distributions were determined as a function of height for a range of numbers of particles, and it was found that a normal distribution of velocities is a good approximation, except close to the vibrating base where there were suggestions that the distribution of the vertical component of the velocities is a composite of two sets of particles, one pre-collision with the base, and the other post-collision

Steady non-ideal detonations in cylindrical sticks of expolsives

Numerical simulations of detonations in cylindrical rate-sticks of highly non-ideal explosives are performed, using a simple model with a weakly pressure dependent rate law and a pseudo-polytropic equation of state. Some numerical issues with such simulations are investigated, and it is shown that very high resolution (hundreds of points in the reaction zone) are required for highly accurate (converged) solutions. High resolution simulations are then used to investigate the qualitative dependences of the detonation driving zone structure on the diameter and degree of confinement of the explosive charge. The simulation results are used to show that, given the radius of curvature of the shock at the charge axis, the steady detonation speed and the axial solution are accurately predicted by a quasi-one-dimensional theory, even for cases where the detonation propagates at speeds significantly below the Chapman-Jouguet speed. Given reaction rate and equation of state models, this quasi-one-dimensional theory offers a significant improvement to Wood-Kirkwood theories currently used in industry

BRST Analysis of Physical States for 2D (Super) Gravity Coupled to (Super) Conformal Matter

We summarize some recent results on the BRST analysis of physical states of 2D gravity coupled to c<=1 conformal matter and the supersymmetric generalization.Comment: 11 page

Attentive Learning of Sequential Handwriting Movements: A Neural Network Model

Defense Advanced research Projects Agency and the Office of Naval Research (N00014-95-1-0409, N00014-92-J-1309); National Science Foundation (IRI-97-20333); National Institutes of Health (I-R29-DC02952-01)

Evolution of the nuclear spin-orbit splitting explored via the ³²Si<i>(d,p)</i>³³Si reaction using SOLARIS

The spin-orbit splitting between neutron 1p orbitals at 33Si has been deduced using the single-neutron-adding (d,p) reaction in inverse kinematics with a beam of 32Si, a long-lived radioisotope. Reaction products were analyzed by the newly implemented SOLARIS spectrometer at the reaccelerated-beam facility at the National Superconducting Cyclotron Laboratory. The measurements show reasonable agreement with shell-model calculations that incorporate modern cross-shell interactions, but they contradict the prediction of proton density depletion based on relativistic mean-field theory. The evolution of the neutron 1p-shell orbitals is systematically studied using the present and existing data in the isotonic chains of = 17, 19, and 21. In each case, a smooth decrease in the separation of the - orbitals is seen as the respective p-orbitals approach zero binding, suggesting that the finite nuclear potential strongly influences the evolution of nuclear structure in this region

Configurations and decay hindrances of high- K states in Hf 180

Multi-quasiparticle high-K states, several of which are isomeric, were observed in Hf180 with the Gammasphere array. Lifetimes in the ns-μs range were determined using centroid-shift and decay measurements within a μs coincidence time window. The configurations of high-K states involve two and four quasiparticles, with states up to Kπ=(18-) established. High-K excitations are found to be progressively more favored with increasing excitation energy. The K quantum number is quite robust up to the highest spins observed, as evidenced by the large values of the reduced hindrance for isomeric decays. Rotational bands built on three high-K states are identified, and the measured branching ratios in these sequences enable the assignment of underlying configurations. Multi-quasiparticle calculations using the Lipkin-Nogami approach for pairing, with blocking included, reproduce the observed high-K energies quite well

Democracy and governance networks: compatible or not?

The relationship between representative democracy and governance networks is investigated at a theoretical level. Four conjectures about the relationship are defined. The incompatibility conjectures rests on the primacy of politics and sees governance networks as a threat. The complementarity conjecture presents governance networks as a means of enabling greater participation in the policy process and sensitivity in programme implementation. The transitional conjecture posits a wider evolution of governance forms towards network relationships. The instrumental conjecture views governance networks as a powerful means through which dominant interests can achieve their goals. Illustrative implications for theory and practice are identified, in relation to power in the policy process, the public interest, and the role of public managers. The heuristic potential of the conjectures is demonstrated through the identification of an outline research agenda

Star clusters near and far; tracing star formation across cosmic time

© 2020 Springer-Verlag. The final publication is available at Springer via https://doi.org/10.1007/s11214-020-00690-x.Star clusters are fundamental units of stellar feedback and unique tracers of their host galactic properties. In this review, we will first focus on their constituents, i.e.\ detailed insight into their stellar populations and their surrounding ionised, warm, neutral, and molecular gas. We, then, move beyond the Local Group to review star cluster populations at various evolutionary stages, and in diverse galactic environmental conditions accessible in the local Universe. At high redshift, where conditions for cluster formation and evolution are more extreme, we are only able to observe the integrated light of a handful of objects that we believe will become globular clusters. We therefore discuss how numerical and analytical methods, informed by the observed properties of cluster populations in the local Universe, are used to develop sophisticated simulations potentially capable of disentangling the genetic map of galaxy formation and assembly that is carried by globular cluster populations.Peer reviewedFinal Accepted Versio

Fine-mapping of prostate cancer susceptibility loci in a large meta-analysis identifies candidate causal variants

Prostate cancer is a polygenic disease with a large heritable component. A number of common, low-penetrance prostate cancer risk loci have been identified through GWAS. Here we apply the Bayesian multivariate variable selection algorithm JAM to fine-map 84 prostate cancer susceptibility loci, using summary data from a large European ancestry meta-analysis. We observe evidence for multiple independent signals at 12 regions and 99 risk signals overall. Only 15 original GWAS tag SNPs remain among the catalogue of candidate variants identified; the remainder are replaced by more likely candidates. Biological annotation of our credible set of variants indicates significant enrichment within promoter and enhancer elements, and transcription factor-binding sites, including AR, ERG and FOXA1. In 40 regions at least one variant is colocalised with an eQTL in prostate cancer tissue. The refined set of candidate variants substantially increase the proportion of familial relative risk explained by these known susceptibility regions, which highlights the importance of fine-mapping studies and has implications for clinical risk profiling. © 2018 The Author(s).Prostate cancer is a polygenic disease with a large heritable component. A number of common, low-penetrance prostate cancer risk loci have been identified through GWAS. Here we apply the Bayesian multivariate variable selection algorithm JAM to fine-map 84 prostate cancer susceptibility loci, using summary data from a large European ancestry meta-analysis. We observe evidence for multiple independent signals at 12 regions and 99 risk signals overall. Only 15 original GWAS tag SNPs remain among the catalogue of candidate variants identified; the remainder are replaced by more likely candidates. Biological annotation of our credible set of variants indicates significant enrichment within promoter and enhancer elements, and transcription factor-binding sites, including AR, ERG and FOXA1. In 40 regions at least one variant is colocalised with an eQTL in prostate cancer tissue. The refined set of candidate variants substantially increase the proportion of familial relative risk explained by these known susceptibility regions, which highlights the importance of fine-mapping studies and has implications for clinical risk profiling. © 2018 The Author(s).Peer reviewe