A dynamic scorecard for monitoring baseline performance with application to tracking a mortgage portfolio

A principled technique for monitoring the performance of a consumer credit scorecard through time is derived from Kalman filtering. Standard approaches sporadically compare certain characteristics of the new applicants with those predicted from the scorecard. The new approach systematically updates the scorecard combining new applicant information with the previous best estimate. The dynamically updated scorecard is tracked through time and compared to limits calculated by sequential simulation from the baseline scorecard. The observation equation of the Kalman filter is tailored to take the results of fitting local scorecards by logistic regression to batches of new clients that arrive in the current time interval. The states in the Kalman filter represent the true or underlying score for each attribute in the card: the parameters of the logistic regression. Their progress in time is modelled by a random walk and the filter provides the best estimate of the scores using past and present information. We illustrate the technique using a commercial mortgage portfolio and the results indicate significant emerging deficiencies in the baseline scorecard.     

Local search algorithms for the min-max loop layout problem

In the min-max loop layout problem, machines are to be arranged around a loop of conveyor belt. The ordering of the machines dictates the number of circuits of the conveyor belt required to manufacture each of several products. The goal is to find an ordering of the machines that minimises the maximum number of circuits required for the manufacture of any of the products. Since the problem is strongly NP-hard, the study of heuristic methods is of interest. This paper proposes iterated descent and tabu search algorithms, and a randomised insertion algorithm. Results of extensive computational tests show that all of our algorithms outperform a previously known algorithm that applies a greedy heuristic to the solution of a linear programming relaxation. The best quality solutions are obtained with iterated descent. This adds further evidence to the belief that iterated descent can produce high quality solutions to a variety of combinatorial optimisation problems. Moreover, unlike some other local search algorithms, iterated descent does not require much tuning in order to be competitive.     

THE ENERGY ASPECT OF THE RECIPROCAL INTERACTIONS OF PAIRS OF TWO DIFFERENT VIBRATION MODES OF A CLAMPED ANNULAR PLATE

The standardized mutual active and reactive sound power of a clamped plate, representing the energy aspect of the reciprocal interactions of two different in vacuo modes, has been computed. It was assumed that the vibrations are axisymmetric, elastic and time harmonic, the plate's transverse deflection is small as compared with the plate's size, and that the vibration velocity is small as compared with the acoustic wavenumber generated. The Kirchhoff-Love theory of a perfectly elastic plate was used. The integral formulae for the mutual sound power were transformed into their Hankel representations which made possible their subsequent computation. A closed path integral was used to express the integral in its Hankel representation to compute the mutual active sound power. The asymptotic stationary phase method was used to compute the two magnitudes, i.e., the mutual active and reactive sound power. The results obtained are the asymptotic formulae valid for the acoustically fast waves. The oscillating as well as the non-oscillating terms have been identified in the formulae to make possible their further separate analysis. The availability of the asymptotic formulae makes possible some fast numerical computations of the mutual sound power. Moreover, the formulae presented herein, together with those for the individual modes known from the literature, make a complete basis for further computations of the total sound power of the plate's damped and forced vibrations in fluid.     

Spatial distribution and formation of nitrate radical NO<Stack><Subscript>3</Subscript><Superscript>2−</Superscript></Stack> in Antarctic calcitic evaporates

Nitrate radical NO₃²⁻ in calcitic evaporate was discovered in Antarctica. The distribution and formation of nitrate radical NO₃²⁻ in the calcite have been studied by pulse and continuous-wave electron spin resonance. In samples that had been annealed to destroy the NO₃²⁻, regeneration of the radical by γ-rays or UV light indicated that the radical was formed by UV light (with wavelengths less than 340 nm) from solar rays, not by environmental radiation. The nonuniform spatial distribution of the nitrate radical, which was deduced from high ratios of local spin density to total spin density, suggests that the nitrate impurity was introduced into the calcium carbonate after carbonate grain formation. Formation of the carbonate-containing nitrate requires the presence of high amounts of nitrate and a dry climate. Formation of the nitrate radical requires sample exposure to UV light. These conditions are satisfied in the environment of Antarctica.     

Atomic Xα calculations based on EHFS(α) = Eexp

The total energies and one-electron energies for first- and second-row atoms were calculated by using the Hartree–Fock and the Hartree–Fock-Slater Hamiltonian with X_α orbitals, u_i(α_exp); α was parametrized from E^HFS (α_exp) = E^exp. The E^HF (α_exp) total energies are always higher than the Hartree–Fock energies for the atoms. The relation of the calculated ionization potential to the experimental ionization potential depends on the α used to define u_i(α), α_exp, or α_HF.     

Ionization potentials,electron affinities,electronegativities, and hardnesses of fractional charged atoms from the density-functional theory

The electron-correlation and self-interaction corrected generalized exchange local-spin-density functional theory with the Gopinathan, Whitehead, and Bogdanovic Fermi-hole parameters has been employed to give self-consistent field calculations for the quark atoms, the first- and second-order positive ions, and the first- and second-order negative ions of the quark atoms with fractional nuclear charges $ Z = N \pm \frac{1}{3} $ and $ Z = N \pm \frac{2}{3} $. A special technique to obtain the converged second-order negative ions is discussed. The first and second ionization potentials and electron affinities are calculated by the differences of the total energies between the ionized and nonionized systems and compared with the empirical inter-extrapolation results. The agreement between the present calculations and the inter-extrapolated results is excellent for the ionization potentials and reasonably good for the electron affinities of the quark atoms. Finally, the calculated ionization potentials and electron affinities are used in obtaining the electronegativities and hardnesses for these quark atoms.