PICOSECOND FLUORESCENCE FROM PHYCOCYANIN 612

The biliprotein, phycocyanin 612, was purified from a cryptomonad, Hemiselmis virescens. The protein, which is an α₂β₂ dimer having four spectrally different tetrapyrrole chromophores, was studied using picosecond fluorescence by exciting the various chromophores at three wavelengths, 565, 585 and 615 nm. These wavelengths were chosen to excite selectively the three highest energy chromophores. Decay times were measured as the excitation energy migrated from each of the three excited chromophores to the lowest-energy chromophore. The ps decay times were found to be 9, 13, and 12 ps for excitations at 565, 585, and 615 nm, respectively. A comparison is made between phycocyanin 612 and phycocyanin 645 with regard to the causes of their differing absorption maxima.     

Local error estimates for radial basis function interpolation of scattered data

Introducing a suitable variational formulation for the localerror of scattered data interpolation by radial basis functions(r), the error can be bounded by a term depending on the Fouriertransform of the interpolated function f and a certain ‘Krigingfunction’, which allows a formulation as an integral involvingthe Fourier transform of . The explicit construction of locallywell-behaving admissible coefficient vectors makes the Krigingfunction bounded by some power of the local density h of datapoints. This leads to error estimates for interpolation of functionsf whose Fourier transform f is ‘dominated’ by thenonnegative Fourier transform of (x) = (||x||) in the sense . Approximation orders are arbitrarily high for interpolationwith Hardy multiquadrics, inverse multiquadrics and Gaussiankernels. This was also proven in recent papers by Madych andNelson, using a reproducing kernel Hilbert space approach andrequiring the same hypothesis as above on f, which limits thepractical applicability of the results. This work uses a differentand simpler analytic technique and allows to handle the casesof interpolation with (r) = r^s for s R, s > 1, s 2N, and(r) = r^s log r for s 2N, which are shown to have accuracy O(h^s/2)     

The Economics of Social Stratification in Premodern Societies

We present a microeconomic model of social stratification, which includes an endogenous fertility component. In the model, egalitarian and stratified societies coexist. The latter are divided into 2 hereditary classes: a warrior elite and a productive class. The model entails that the extra cost warriors must incur to train and equip their children for war determines the relative sizes of both classes and the degree of economic inequality. Higher costs of warrior children imply a greater economic advantage for warriors and a smaller ratio of warriors to producers. These results are consistent with the historical evidence. Finally, we explore conditions under which the social contributions of the warrior elite could discourage a revolution.     

Calculation of the conductance and selectivity of an ion-selective potassium channel (IRK1) from simulation of atomic scale models

We present the equations and methodology for the theoretical prediction of the conductance, permeability and selectivity of a K⁺ channel on the basis of atomic scale models for it. The methodology involves the use of Langevin dynamics and activated trajectories in order to obtain translocation free energies, rate constants and transmission coefficients for an ion going through the channel. The models are for the Inward Rectifier K⁺ channel (IRK1) which is a member of a family of ion-selective K⁺ channels. The IRK1 channel is biologically important because of its role in cardiac pacemaker function. The models we use for the IRK1 channel are developed from a model of the Shaker voltage-gated K⁺ channel. We find that the theoretically predicted conductance is too low by three orders of magnitude. We attribute this underestimate to a specific structural defect in the model used. Perhaps our most significant result is that the computed conductance is tremendously sensitive to the structural details of the so-called ‘P-loop’ that lines the outer half of the permeation pathway of the channel. This sensitivity may be useful in future studies on ion channel proteins for which the structure is not known from X-ray crystallography. In addition, this sensitivity may help determine whether X-ray structures of these proteins correspond to open or closed conformations.     

A scheduling algorithm for open pit mines

An open pit (opencast) mine can be described by a three-dimensionalarray of blocks, each of which is assigned a number of valuesdefining its characteristics. Scheduling an open pit consistsin finding a sequence in which the blocks should be removedfrom the mine in order to maximize the total discounted profitfrom the mine subject to a variety of technical and economicconstraints. This paper proposes to model the mine-schedulingproblem as one of sequential optimization, and develops an algorithmfor its solution. To overcome the difficulty caused by an extremelylarge number of states in the problem at hand, we consider atechnique which is related to dynamic programming but avoidsthe complete enumeration of the state space. Our algorithm isa combination of this technique with powerful heuristics derivedfrom the specific properties of open pit mining.     

On the Differential Equation for the Generation of Frequency Modulation

Representations are presented for the general solution of thelinear differential equation associated with the electronicgeneration of frequency modulated signals. The frequency modulationcomponent is determined explicitly by an orthogonal fundamentalsolution matrix, while the amplitude modulation component, whicharises as an impurity in the generation process, is discussedwith the aid of elementary aspects of the theory of Lie algebras.The Lie algebra thus defined is three dimensional and algebraicallysimple. Asymptotic representations of the amplitude modulationcomponent to the first-order in the absolute frequency deviationare shown to be completely prescribed by the basis vectors chosenfor the Lie algebra.     

Bayesian networks applied to credit scoring

Email: kchang{at}gmu.eduEmail: RobertFung{at}Fairlsaac.comEmail: alan.lucas{at}hotmail.com^¶Email: BobOliver{at}Fairlsaac.com^||Email: NShikaloff{at}Fairlsaac.com The objectives of this paper are to apply the theory and numericalalgorithms of Bayesian networks to risk scoring, and comparethe results with traditional methods for computing scores andposterior predictions of performance variables. Model identification,inference, and prediction of random variables using Bayesiannetworks have been successfully applied in a number of areas,including medical diagnosis, equipment failure, informationretrieval, rare-event prediction, and pattern recognition. Theability to graphically represent conditional dependencies andindependencies among random variables may also be useful incredit scoring. Although several papers have already appearedin the literature which use graphical models for model identification,as far as we know there have been no explicit experimental resultsthat compare a traditionally computed risk score with predictionsbased on Bayesian learning algorithms. In this paper, we examine a database of credit-card applicantsand attempt to ‘learn’ the graphical structure ofthe characteristics or variables that make up the database.We identify representative Bayesian networks in a developmentsample as well as the associated Markov blankets and cliquestructures within the Markov blanket. Once we obtain the structureof the underlying conditional independencies, we are able toestimate the probabilities of each node conditional on its directpredecessor node(s). We then calculate the posterior probabilitiesand scores of a performance variable for the development sample.Finally, we calculate the receiver operating characteristic(ROC) curves and relative profitability of scorecards basedon these identifications. The results of the different modelsand methods are compared with both development and validationsamples. Finally, we report on a statistical entropy calculationthat measures the degree to which cliques identified in theBayesian network are independent of one another.     

Singularities and the Rayleigh Hypothesis for Solutions to the Helmholtz Equation

Possible and actual singularities in the analytic continuationof the solution to the Dirichlet problem for the two-dimensionalHelmholtz equation are studied in order to investigate the Rayleighhypothesis of scattering theory. The procedure uses a representationfor the solution to the analytic Cauchy problem and relatesone type of singularity in the Schwarz function associated withthe boundary curve to singularities in the solution. The resultsprovide confiration of criteria for the validity of the Rayleighhypothesis that have been given by van den Berg and Fokkema.