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.     

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.     

Quinazolines. VII. Synthesis of 1,3-Diamino-5,6-dihydrobenzo[f]quinazolines

Eighteen new 1,3-diamino-5,6-dihydrobenzo[f] quinazolines ( 6 , R. = alkyl, Cl, MeO) were synthesized via the condensation of appropriate 2-tetralones with cyanoguanidine under fusion conditions. Methods were developed for the preparation of a number of heretofore undescribed 2-tetralones as precursors. The final products can be viewed as conformationally rigid analogs of pyrimethamine ( 2 ), and are of interest as inhibitors of dihydrofolate reductase and as potential antimalarial and antitumor agents.     

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.     

Non self-consistent field theory — A new approach in quantum mechanical calculations

An R ^o-independent electronic repulsion matrix is constructed, replacing the R ^o-dependent Hamiltonian matrix (R ^o is the density matrix). A non-SCF theory is developed to solve the eigenequation without using an iterative procedure. Three methods are proposed to solve for the eigenvectors and eigenvalues. Illustrative calculations are reported comparing the non-SCF and SCF theories. The calculated results are as expected: the ground state energies are nearly unchanged while the orbital energies are nearer to the experimental results. Other physical properties and spectral quantities are also compared. It is found that the ZDO assumption is applicable in the non-SCF theory if it is applicable in SCF theory.

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Zusammenfassung Eine R ^o-unabhängige Elektronenabstoßungsmatrix wird eingeführt, die die R ^o-abhängige Hamiltonmatrix ersetzt (R ^o ist die Dichtematrix). Zur Lösung der Eigenwertgleichung ohne iterative Prozeduren wird eine sog. Nicht-SCF-Theorie aufgestellt. An Beispielen werden die Ergebnisse von SCF- und Nicht-SCF-Rechnungen verglichen; dabei erweisen sich die Energien des Grundzustandes als nahezu unverändert, während die Energien der Orbitale näher bei den experimentellen Werten liegen. Die zero-differential-overlap-Näherung ist immer dann in der neuen Theorie anwendbar, wenn sie in der SCF-Theorie anwendbar ist.

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Résumé Une matrice de répulsion électronique indépendante de R ^o est construite, remplaçant la matrice hamiltonienne dépendant de R ^o (R ^o matrice de densité). Une théorie non SCF est développée afin de résoudre l'équation aux valeurs propres sans itérations. Trois méthodes de résolution du problème aux valeurs propres sont proposées. Des calculs illustrent la comparaison entre les théories SCF et non SCF. Les résultats des calculs sont comme prévus: l'énergie de l'état fondamental varie peu alors que les énergies orbitales sont plus proches des résultats expérimentaux. D'autres propriétés physiques ainsi que des grandeurs spectrales sont comparées. On trouve que l'approximation du recouvrement différentiel nul est applicable dans la théorie non SCF si elle est applicable dans la théorie SCF.

     

Shaping the density to fit one-electron properties: Constrained RHF calculations on N2, FH,CO, and LiH

The molecular density required to give the correct values for one-electron properties is rarely given by wave functions obtained from variation methods based on the total energy or the eigenvalues. Perhaps if we knew how the density should be shaped in any particular volume to fit a particular property, the whole molecular density might then be properly described to fit the whole volume. The secant-parametrization procedure is used to constrain minimum basis set RHF wave functions for N₂, FH, CO, and LiH to determine the effects of different constraints on RHF wave functions, and to see how constraints improve the quality of small basis set RHF wave functions. One-electron property expectation values, energies, and unweighted and property weighted populations and electron density difference profiles are used to analyze the constrained wavefunctions. With the information from the constrained wave functions it should be possible to select a LCAO -CI basis and states to give the correct density for all properties. This should map onto the constrained wave function in the region of the constraint and at the same time minimize the energy of the total molecular wave function. Such a density would be suitable for the density analyses favored by Bader and Nguyen-Dang [Adv. Quantum Chem. 14 , 113 (1981)], Mezey [Theor. Chim. Acta 54 , 95 (1980); 58 , 309 (1981); 59 , 321 (1981)], and March [Theoretical Chemistry (Royal Society of Chemistry, London, 1981), Vol. 4, p. 158], and show the real atom needed to generate the molecule.