A hybrid method for indoor user localisation

In this work we describe an approach to indoor user localisation by combining image-based and RF-based methods and compare this new approach to prior work. This paper details a new algorithm for indoor user localisation, demonstrating more effective user localisation than prior approaches and therefore presents the next step in combining two different technologies for localisation in indoor type environments

I=2I=2 ππ\pi\pi potential in the HAL QCD method with all-to-all propagators

In this paper, we perform the first application of the hybrid method (exact low modes plus stochastically estimated high modes) for all-to-all propagators to the HAL QCD method. We calculate the HAL QCD potentials in the $I=2$ $\pi\pi$ scattering in order to see how statistical fluctuations of the potential behave under the hybrid method. All of the calculations are performed with the 2+1 flavor gauge configurations on $16^3 \times 32$ lattice at the lattice spacing $a \approx 0.12$ fm and $m_{\pi} \approx 870$ MeV. It is revealed that statistical errors for the potential are enhanced by stochastic noises introduced by the hybrid method, which, however, are shown to be reduced by increasing the level of dilutions, in particular, that of space dilutions. From systematic studies, we obtain a guiding principle for a choice of dilution types/levels and a number of eigenvectors to reduce noise contaminations to the potential while keeping numerical costs reasonable. We also confirm that we can obtain the scattering phase shifts for the $I=2$ $\pi\pi$ system by the hybrid method within a reasonable numerical cost, which are consistent with the result obtained with the conventional method. The knowledge we obtain in this study will become useful to investigate hadron resonances which require quark annihilation diagrams such as the $\rho$ meson by the HAL QCD potential with the hybrid method.Comment: 20 pages, 10 figures, published version in PTE

A Hybrid of Darboux's Method and Singularity Analysis in Combinatorial Asymptotics

A ``hybrid method'', dedicated to asymptotic coefficient extraction in combinatorial generating functions, is presented, which combines Darboux's method and singularity analysis theory. This hybrid method applies to functions that remain of moderate growth near the unit circle and satisfy suitable smoothness assumptions--this, even in the case when the unit circle is a natural boundary. A prime application is to coefficients of several types of infinite product generating functions, for which full asymptotic expansions (involving periodic fluctuations at higher orders) can be derived. Examples relative to permutations, trees, and polynomials over finite fields are treated in this way.Comment: 31 page

Investigating a hybrid perturbation-Galerkin technique using computer algebra

A two-step hybrid perturbation-Galerkin method is presented for the solution of a variety of differential equations type problems which involve a scalar parameter. The resulting (approximate) solution has the form of a sum where each term consists of the product of two functions. The first function is a function of the independent field variable(s) x, and the second is a function of the parameter lambda. In step one the functions of x are determined by forming a perturbation expansion in lambda. In step two the functions of lambda are determined through the use of the classical Bubnov-Gelerkin method. The resulting hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Bubnov-Galerkin methods applied separately, while combining some of the good features of each. In particular, the results can be useful well beyond the radius of convergence associated with the perturbation expansion. The hybrid method is applied with the aid of computer algebra to a simple two-point boundary value problem where the radius of convergence is finite and to a quantum eigenvalue problem where the radius of convergence is zero. For both problems the hybrid method apparently converges for an infinite range of the parameter lambda. The results obtained from the hybrid method are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed