Optimal linear interpolation of multiple missing values

Statistical Inference for Stochastic Processes - The problem of linear interpolation in the context of a multivariate time series having multiple (possibly non-consecutive) missing values is...     

Particle production from signature change

We consider the (massless) scalar field on 2-dimensional manifolds whose metric changes signature and which admit a spacelike isometry. Choosing the wave equation so that there will be a conserved Klein-Gordon product implicitly determines the junction conditions one needs to impose in order to obtain global solutions. The resulting mix of positive and negative frequencies produced by the presence of Euclidean regions depends only on the total width of the regions, and not on the detailed form of the metric.This essay received honorable mention in the 1991 competition of the Gravity Research Foundation.     

Minimum audible movement angle as a function of signal frequency and the velocity of the source

Thresholds for the detection of the direction of travel of a moving sound source were determined in a single-interval, forced-choice paradigm. Both the rate at which the sound source is displaced (8 degrees-128 degrees/s) and the frequency of the signal to be localized (500-3700 Hz) affect dynamic spatial resolution. There is an inverse relationship between spatial resolution and the rate of travel, a finding that replicates an earlier observation on performance with sources displaced at high velocities [Perrott and Musicant, J. Acoust. Soc. Am. 62, 1463-1466 (1977)]. However, the magnitude of this effect depends on the actual velocities employed. Relatively small changes in spatial resolution are apparent for velocities below approximately 32 degrees/s. The significant frequency effect can be summarized as follows: Dynamic spatial resolution is better for signals below 1000 Hz than for signals above this value (within the range tested). Particularly poor resolution is evident for signals between 1300-2000 Hz. The present results indicate that signal frequency affects dynamic spatial resolution in a fashion similar to that which has been observed in the more common "static" localization test situation. There is no indication of an interaction between these two variables. These results provide additional support for the hypothesis that both static and dynamic spatial discrimination functions are dependent upon the same underlying mechanisms. The effects of velocity upon the spatial resolution problem, a unique aspect of the dynamic paradigm, can probably be explained without the necessity of additional hypothetical mechanisms in the auditory system (e.g., a specialized motion detector).     

How to choose one-dimensional basis functions so that a very efficient multidimensional basis may be extracted from a direct product of the one-dimensional functions: energy levels of coupled systems with as many as 16 coordinates

In this paper we propose a scheme for choosing basis functions for quantum dynamics calculations. Direct product bases are frequently used. The number of direct product functions required to converge a spectrum, compute a rate constant, etc., is so large that direct product calculations are impossible for molecules or reacting systems with more than four atoms. It is common to extract a smaller working basis from a huge direct product basis by removing some of the product functions. We advocate a build and prune strategy of this type. The one-dimensional (1D) functions from which we build the direct product basis are chosen to satisfy two conditions: (1) they nearly diagonalize the full Hamiltonian matrix; (2) they minimize off-diagonal matrix elements that couple basis functions with diagonal elements close to those of the energy levels we wish to compute. By imposing these conditions we increase the number of product functions that can be removed from the multidimensional basis without degrading the accuracy of computed energy levels. Two basic types of 1D basis functions are in common use: eigenfunctions of 1D Hamiltonians and discrete variable representation (DVR) functions. Both have advantages and disadvantages. The 1D functions we propose are intermediate between the 1D eigenfunction functions and the DVR functions. If the coupling is very weak, they are very nearly 1D eigenfunction functions. As the strength of the coupling is increased they resemble more closely DVR functions. We assess the usefulness of our basis by applying it to model 6D, 8D, and 16D Hamiltonians with various coupling strengths. We find approximately linear scaling.     

Sulfoalkyl Ether β-Cyclodextrin Derivatives: Synthesis and Characterizations

A series of sulfoalkyl ether -cyclodextrin derivatives, including sulfoethyl, sulfopropyl and sulfobutyl ethyl -cyclodextrins, have been synthesized and characterized. Each sulfoalkyl ether -cyclodextrin is a mixture of various degrees of substitution and different positional isotherms. Elemental analysis, ¹H NMR, MS, and Differential Scanning Calorimetry analysis were used to determine the average degree of substitution for each -cyclodextrin derivative. The average degrees of substitution are 3.4, 1.6 and 2.5 for sulfoethyl, sulfopropyl and sulfobutyl ether -cyclodextrin, respectively. The water solubility of these derivatives is substantially higher than that of -cyclodextrin. ¹H NMR indicates thatsulfoethyl ether -cyclodextrin may have major substitution on the secondaryhydroxyl group while the major substitution in sulfopropyl and sulfobutyl ether-cyclodextrin could be on the primary hydroxyl group. MS spectra showthat no more than one substitution occurred on a single glucose unit.     

A comparison of SCF-Xα and extended Hückel methods for metal clusters

A comparison of some results from Xα-scattered wave (Xα-SW) and extended Hückel (EH) calculations for metal clusters is given. It is found that small clusters of atoms (≈ 13 atoms) using the Xα-SW method reproduce many of the features of the electronic structure of the bulk metals, whereas this is not the case for the same clusters using the EH method. A more systematic approach to EH parametrizations is suggested in order to make this method a more viable approach to treating metal clusters.     

Contracted basis Lanczos methods for computing numerically exact rovibrational levels of methane

We present a numerically exact calculation of rovibrational levels of a five-atom molecule. Two contracted basis Lanczos strategies are proposed. The first and preferred strategy is a two-stage contraction. Products of eigenfunctions of a four-dimensional (4D) stretch problem and eigenfunctions of 5D bend-rotation problems, one for each K, are used as basis functions for computing eigenfunctions and eigenvalues (for each K) of the Hamiltonian without the Coriolis coupling term, denoted H0. Finally, energy levels of the full Hamiltonian are calculated in a basis of the eigenfunctions of H0. The second strategy is a one-stage contraction in which energy levels of the full Hamiltonian are computed in the product contracted basis (without first computing eigenfunctions of H0). The two-stage contraction strategy, albeit more complicated, has the crucial advantage that it is trivial to parallelize the calculation so that the CPU and memory costs are independent of J. For the one-stage contraction strategy the CPU and memory costs of the difficult part of the calculation scale linearly with J. We use the polar coordinates associated with orthogonal Radau vectors and spherical harmonic type rovibrational basis functions. A parity-adapted rovibrational basis suitable for a five-atom molecule is proposed and employed to obtain bend-rotation eigenfunctions in the first step of both contraction methods. The effectiveness of the two methods is demonstrated by calculating a large number of converged J = 1 rovibrational levels of methane using a global potential energy surface.