Pair Of Coordinates Research Articles

Electron-proton free-energy surfaces for proton transfer reaction in polar solvents: test calculations for carbon-carbon reaction centres

The proton transfer reaction R− + HR → RH + R− of benzyl-type compounds in a polar solvent has been studied theoretically in terms of a proton adiabatic dynamical treatment of a mixed quantum-classical reacting system. The gas phase potentials were obtained using the PM3 method and then approximated by appropriate (LEPS type) quasi-analytical functions. Polar medium degrees of freedom were introduced, similar to the Marcus electron transfer theory, in terms of a two-state electronic Hamiltonian. At this level, three-dimensional free energy surfaces were obtained, including a pair of intrasolute coordinates, the CH stretch and heavy-atom vibrational mode of the reaction centre, together with the collective medium polarization mode. At the next stage, two-dimensional electron-proton free energy surfaces (EP FESs) corresponding to the adiabatic approximation with respect to CH stretch were generated for the two lowest proton levels. Their main features are described. The reaction with R = benzyl proved to be proton-adiabatic. Its rate constant transmission factor calculated in terms of the Kramers-Grote-Hynes theory is significantly less than unity (∼0.4–0.6) because the reaction coordinate at the transition state of the ground state EP FES coincides with the medium mode. The reaction with R = fluorenyl does not obey the proton-adiabaticity condition and needs a special kinetic treatment. A remarkable observation is that the double adiabatic electron-proton approximation is incapable of providing sufficiently high classical barriers (> 10 kcal/mol) on ground-state two-dimensional EP FESs for proton transfer reactions in polar solvents.

A multi-ASIC real-time implementation of the two dimensional affine transform with a bilinear interpolation scheme

Some image processing applications (e.g. computer graphics and robot vision) require the rotation, scaling and translation of digitized images in real-time (25---30 images per second). Today's standard image processors can not meet this timing constraint so other solutions have to be considered. This paper describes a multi-ASIC solution which is capable of doing the image processing tasks in real-time. The first ASIC is a so-called affine transformer which calculates a one-dimensional coordinate every 25 ns. The second ASIC is a bilinear interpolator which calculates an interpolated value from four known surrounding values, again every 25 ns. This ASIC is designed in a modular setup which results in a flexible accuracy of the interpolation. If more accurate interpolation is required, another ASIC (containing an interpolation stage) is used. In this way for each application a proper accuracy is implemented, reaching optimal silicon area utilization and desired accuracy of interpolation. Using two affine transformers (for obtaining a two dimensional coordinate pair) and an interpolator, one can build a system which can translate, rotate and scale an image of size 1024 * 1024 in real-time (25---30 images per second). In this paper the system as well as the design of the ASICs are presented.

Application of 2-D Statistical Theory of Overlap to Three Separation Types: 2-D Thin-Layer Chromatography, 2-D Gas Chromatography, and Liquid Chromatography/Capillary Electrophoresis

A modified statistical theory of overlap for two-dimensional (2-D) separations was applied to three types of 2-D separations : 2-D thin-layer chromatography (2-D TLC), 2-D gas chromatography (2-D GC), and liquid chromatography/capillary electrophoresis (LC/CE). The 2-D TLCs were developed in this laboratory on two adsorbents by overpressure layer chromatography and ascending TLC from a standard solution containing 30 polynuclear aromatic hydrocarbons. The other separations were given to us for interpretation by colleagues. The coordinate pairs of maxima in these separations were determined and interpreted using procedures that predict from them the number of mixture components. For 2-D TLCs developed on one adsorbent, this number agreed to within 5% of the known number of mixture components. For 2-D TLCs developed on another adsorbent, this number was incorrect but was shown to be incorrect by simulation. The numbers calculated from the other separations were internally consistent and also were consistent with simulations developed to mimic the separations. In particular, a portion of a 2-D GC of kerosene containing compounds of nine carbon atoms had modest overlap, and LC/CEs of tryptic digests of thyroglobulin and cytochrome c appeared to have virtually no overlap.

On substructure synthesis with FRF data

A new physically and mathematically generalized receptance coupling method is presented in this paper. This new method overcomes some shortcomings of the commonly used receptance coupling methods. There are two modified formulae: one completes the substructure synthesis in a single step, and the other couples two joint co-ordinates at each step, and implements the coupling process in several steps. The second formula is of more interest. It is computationally efficient and very simple to program. It is also very effective in detecting the linearly dependent co-ordinate pairs. This is particularly attractive, because if these linearly dependent coordinate pairs are not deleted in the coupling process, the accuracy of the substructure synthesis can deteriorate.

Comparison of Some Neural Network and Scattered Data Approximations: The Inverse Manipulator Kinematics Example

This paper compares the application of five different methods for the approximation of the inverse kinematics of a manipulator arm from a number of joint angle/Cartesian coordinate training pairs. The first method is a standard feedforward neural network with error backpropagation learning. The next two methods are derived from an extended Kohonen Map algorithm that we combine with Shepard interpolation for the forward computation. We compare the method of Ritter et al. for the learning of the extended Kohonen Map to our own scheme based on gradient descent optimization. We also study three scattered data approximation algorithms. They include two variants of the Radial Basis Function (RBF) method: Hardy's multiquadrics and gaussian RBF. We further develop our own Local Polynomial Fit method that could be considered as a modification of McLain's method. We propose extensions to the considered scattered data approximation algorithms to make them suitable for vector-valued multivariable functions, such as the mapping of Cartesian coordinates into joint angle coordinates.

Arnold diffusion and adiabatic invariants

The evolution of any pair of canonical coordinates of an arbitrary Hamiltonian is given by a Hamiltonian of one and a half degrees of freedom H( p, q, t). An arbitrary action evolves stochastically if its Hamiltonian H is aperiodic in time. If H is periodic, the action can be bounded for all time.

Evaluation of standardized methods for registration of time-dependent orthodontic tooth movements

An in vitro study was conducted to compare reproducibility of repeated recordings obtained from devices constructed for standardized registrations. An existing radiographic method and a new photographic technique were employed. On five in vitro models, half of the maxilla from dry skulls, special designed splints with a Troll-biten film holder were constructed. A stiff metal bar attached to the splints and to either an X-ray apparatus or a standard photographic camera made it possible to obtain standardized registrations. For each model 10 radiographs and photographs were taken before and after the canine was moved. Subtracting the values from well defined points for these pictures, 10 pairs of coordinates were available for each of the models with both methods. The findings showed very similar reproducibility for the two methods with 95 per cent of the discrepancies within a magnitude of 0.12 mm for the radiographic method and 0.14 mm for the photographic method. When evaluating the canine movements, similar results were observed. No significant difference could be detected in the five in vitro models. In addition, the results showed that a splint can be used as a stable reference for registration of tooth movements. Because of ethical objections to unnecessary radiation, the photographic registration technique might substitute the radiographs in future investigations where standardized periodic records are necessary for the description of tooth movement.

Majorization and Schur Convexity with Respect to Partial Orders

Majorization and Schur convexity constitute an important tool for establishing inequalities, in particular, due to the Schur-Ostrowski Theorem which provides a simple characterization of Schur convex functions through local two-coordinate conditions. However, the usefulness of the approach is limited by two stringent requirements. First, every Schur convex function must be symmetric. Second, the necessary and sufficient conditions for Schur convexity involve every pair of coordinates on its (symmetric) domain. Several attempts have been made to relax these two requirements. In particular, a more general concept of “majorization with respect to partial orders” was introduced to prepare for such tasks, but it did not capture the classic theory for symmetric functions. In the current paper we obtain the desired generalization by developing a theory of majorization and Schur convexity with respect to partial orders over subsets of Euclidean spaces. Our results are used in Hwang, Rothblum and Shepp (1993) to address some optimal assembly problems.

DGPS, Doppler, datums and discrepancies - your positions explained

It is still quite commonly believed that latitude and longitude coordinate pairs uniquely define points on the earth's surface. Witness the general neglect of any qualifying geodetic information when exploration and production licence boundaries are defined and its continuing omission from many medium- and large-scale maps depicting exploration data.

Real Birkhoff normal forms and complex coordinates

When dealing with Birkhoff normal forms, one can often simplify notations and computations by interpreting pairs of real coordinates as complex coordinates. In the present paper we try to establish an adequate frame for this old and useful trick: Starting with an embedding of a real vector space in a complex one, we construct the respective embedding of the vector fields and the analogue of the homological operator. The construction offers a systematic technique of introducing complex coordinates; in the last section we show how it applies to some well-known examples.

The non‐N‐representability of the Colle–Salvetti second‐order reduced density matrix

AbstractThe Colle–Salvetti second‐order reduced density matrix (2‐matrix) is an approximation to the 2‐matrix obtained from a wave function that is a product of a reference wave function containing little or no correlation times a product of correlation factors that are functions of the coordinates of pairs of electrons. A formal proof is given for the non‐N‐representability for the Colle–Salvetti 2‐matrix using the nonnegativity condition of the 2‐matrix. The nonnegativity condition of the particle‐hole overlap matrix (G matrix) is also not satisfied. The proof is valid for Colle–Salvetti 2‐matrices obtained from both the Hartree–Fock and small multiconfigurational‐self‐consistent‐field wave functions. Even though the Colle–Salvetti 2‐matrix is not N‐representable, it does satisfy the Pauli principle component of the G‐matrix condition because it reduces to an N‐representable first‐order reduced density matrix. © 1993 John Wiley & Sons, Inc.

The spatial amplitude mapping method for estimation of time delay using adaptive filtering

Uniform and multiple delays/advances were estimated under heavy noisy conditions [signal-to-noise-ratio (SNR=signal energy/noise energy) below 0 dB]. The technique introduced, called the spatialamplitudemapping (SAM) method, isolates a data segment from each of the channels in a multichannel system by using a suitable window. When two matched segments are plotted on an x–y plane, the distribution of every pair of windowed coordinates will remain near a straight 45° line that passes through the origin. The distribution of two nonmatched segments or two matched segments containing noise will scatter around this line; hence, a pair of matching windowed segments can be found by searching for the distribution closest to the 45° line. This information is then used to estimate the segment delays. Under very noisy conditions, however, multiple delays can be detected. A recursive least-squares (RLS) filter is then used to adaptively estimate the correct delay. The technique was implemented in the delay estimation of synthetic (stationary) data and neurophysiological (nonstationary) data with satisfying results. Compared to the window correlation technique (WCT) [Callison etal., J. Acoust. Soc. Am. 81, 1000–1006 (1987)], SAM can estimate delays down to a SNR of −17.1 dB while the lower bound for the WCT is −2 dB.

Acquiring taxonomic relations in lexical memory: The role of superordinate category labels

Two experiments tested predictions based on Nelson's (e.g., Nelson, 1985; Lucariello & Nelson, 1985) theory of taxonomic development. In Nelson's view, children relate slot-fillers (e.g., cereal - egg) in memory because they are substitutable within the same scripts. Coordinates (e.g., cereal - hamburger), members of the same superordinate category that are part of different scripts, are related through knowledge of a shared superordinate label (e.g., food). In these experiments, we tested whether knowledge of a superordinate label is associated with stronger relations between coordinates but not between slot-fillers. In Experiment 1, preschoolers' reaction times were measured during a triad sorting task. Matching picture pairs within the triads were either slot-filler familiar (slot-fillers with a familiar superordinate label), slot-filler unfamiliar (slot-fillers with an unfamiliar superordinate label), coordinate familiar, or coordinate unfamiliar. In Experiment 2, subjects were given a cued recall task. Lists consisted of either slot-filler or coordinate word pairs. Half the word pairs had familiar superordinate labels and half had unfamiliar labels. In both studies, superordinate label familiarity had no effects, although children's performance was better on slot-filler pairs overall. Because these results do not support Nelson's theory, we propose an alternative account of taxonomic development.

Nonparametric Estimation of Nonstationary Spatial Covariance Structure

Abstract Estimation of the covariance structure of spatial processes is a fundamental prerequisite for problems of spatial interpolation and the design of monitoring networks. We introduce a nonparametric approach to global estimation of the spatial covariance structure of a random function Z(x, t) observed repeatedly at times ti (i = 1, …, T) at a finite number of sampling stations xi (i = 1, 2, …, N) in the plane. Our analyses assume temporal stationarity but do not assume spatial stationarity (or isotropy). We analyze the spatial dispersions var(Z(xi, t) − Z(xj, t)) as a natural metric for the spatial covariance structure and model these as a general smooth function of the geographic coordinates of station pairs (xi, xj ). The model is constructed in two steps. First, using nonmetric multidimensional scaling (MDS) we compute a two-dimensional representation of the sampling stations for which a monotone function of interpoint distances δij approximates the spatial dispersions. MDS transforms the problem into one for which the covariance structure, expressed in terms of spatial dispersions, is stationary and isotropic. Second, we compute thin-plate splines to provide smooth mappings of the geographic representation of the sampling stations into their MDS representation. The composition of this mapping f and a monotone function g derived from MDS yields a nonparametric estimator of var(Z(xa, t) − Z(xb, t)) for any two geographic locations xa and xb (monitored or not) of the form g(|f(xa ) − f(xb )|). By restricting the monotone function g to a class of conditionally nonpositive definite variogram functions, we ensure that the resulting nonparametric model corresponds to a nonnegative definite covariance model. We use biorthogonal grids, introduced by Bookstein in the field of morphometrics, to depict the thin-plate spline mappings that embody the nature of the anisotropy and nonstationarity in the sample covariance matrix. An analysis of mesoscale variability in solar radiation monitored in southwestern British Columbia demonstrates this methodology.

Nonparametric Estimation of Nonstationary Spatial Covariance Structure

Abstract Estimation of the covariance structure of spatial processes is a fundamental prerequisite for problems of spatial interpolation and the design of monitoring networks. We introduce a nonparametric approach to global estimation of the spatial covariance structure of a random function Z(x, t) observed repeatedly at times ti (i = 1, …, T) at a finite number of sampling stations xi (i = 1, 2, …, N) in the plane. Our analyses assume temporal stationarity but do not assume spatial stationarity (or isotropy). We analyze the spatial dispersions var(Z(xi, t) − Z(xj, t)) as a natural metric for the spatial covariance structure and model these as a general smooth function of the geographic coordinates of station pairs (xi, xj ). The model is constructed in two steps. First, using nonmetric multidimensional scaling (MDS) we compute a two-dimensional representation of the sampling stations for which a monotone function of interpoint distances δij approximates the spatial dispersions. MDS transforms the problem...

Unified models from gauged supergroups. II. Exceptional series D(2,1;α), G(3), F(4)

Previously elaborated principles [J. Math. Phys. 31, 1783 (1990)] for dimensional reduction of models of gauged supergroups over supercoset spaces are applied to the exceptional superalgebras. The superspace is parametrized by a pair of Grassmann coordinates.

A partial ordering of rank densities

A function f( π) on the set of permutations of {1, 2, …, n} is called arrangement increasing (AI) if it increases each time we transpose a pair of coordinates in descending order, i < j and π i > π j , putting them in ascending order. We define and develop a partial ordering ≤ AI on densities of rank vectors in terms of expectations of AI functions. Specially, one density g is defined to be AI-larger than another density f( f≤ AI g) if the expectation under g of any AI function is at least as large as its expectation under f. We show that the uniform density is the AI-smallest AI density, and this leads to power results for tests of agreement of two rank vectors. The extreme points of the convex set of AI densities are determined, from which additional results concerning the minimum power of rank tests are shown to follow. We also give applications to ranking and selection problems.

Nonequilibrium effects in kinetics of cycloaddition reactions under high pressure

A Diels-Alder condensation reaction in liquid phase under varying pressure conditions is modeled as a pair of coordinates, one associated with a chemical reactive motion and the other describing the accompanying contraction of the medium cavity which surrounds the chemical subsystem. A two-dimensional enthalpy surface with a pressure-dependent activation barrier is constructed

Critical potentials and correlation functions in the minus two dimensional matrix model

We review the construction and exact solution of the critical points of the matrix model with a pair of anti-commuting coordinates. The generic critical point describes c = −2 matter coupled to two-dimensional quantum gravity, while other critical points do not obey KPZ-DDK scaling, and have not yet been identified. We define scaling operators which perturb each of the critical points towards others, and find their correlation functions to all orders in the genus expansion. We also discuss other operators, which perturb the c = −2 matrix model towards K = 2, 3,… critical points of the one-matrix model. Some of their correlation functions diverge, and these divergent amplitudes are proportional to the correlation functions of the topological gravity.

GEOBASE: a simple geographical information system on a personal computer

Spatially distributed data are often encountered in the biological sciences. Representation and analysis of such data requires specific tools. A simple geographical information system is presented, which allows representation and elementary analysis of geographically coded information. The system handles two kinds of data: maps and facts, where map data describe the basis on which the fact data are located. Maps consist of objects described through a set of coordinates, while for facts a coordinate pair is associated with an unlimited number of data records containing five fields: a date, an element from a list, a two-character code, an integer number and a real number. The input data can be displayed interactively on screen by logically combining selection criteria for each field. The facts corresponding to the selected criteria are either displayed as such, or are clustered and displayed as polygons or pies. A short example showing a possible application of the program is presented and advantages as well as limitations are discussed.