Algebraic Manipulation of Polynomial Matrices: A Survey

A concise review is given of some recent methods for performingalgebraic operations on polynominal matrices. The problems addressedare division, inversion, and extraction of greatest common divisorof a pair of matrices. Based on a presentation at the International Symposium on theMathematical theory of Networks and Systems, Amsterdam, June1989.     

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 PHOTOREACTION OF A RHODAMINE 6G MONOLAYER ADSORBED ON QUARTZ STUDIED BY SURFACE SECOND HARMONIC GENERATION

Abstract— A monolayer of rhodamine 6G on quartz in air exhibited photochemistry upon laser irradiation in the first absorption band. The course of the reaction was followed in real time by the surface second harmonic generation method. It was observed that the photoproduct had an enhanced non-linear coefficient, relative to rhodamine 6G. Absorption spectra showed that this was not a result of a stronger resonance enhancement of the signal by the photoproduct. Consideration of the factors to which the surface second harmonic signal is sensitive suggested that the enhancement arose from an increased charge transfer character of the photoproduct's electronic transitions, and a reorientation of its transition dipole.     

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.