Structure Of Variant Research Articles

Program to generate and evaluate three-phase structure-invariant ω estimates from single-wavelength anomalous dispersion data

A direct-methods computer program for evaluating three-phase structure invariants for single-wavelength anomalous dispersion data is described. The entire program was coded in 570 lines of Fortran, is highly automated and requires a minimal amount of user-supplied input data.

Thiocyanato complexes of the coinage metals: synthesis and crystal structures of the polymeric pyridine complexes [Ag xCuy(SCN)x + y(py)z

From solutions of CuSCN or AgSCN in pyridine, several pyridine complexes of the thiocyanates with varying compositions and crystal structures were isolated depending on the reaction conditions. In CuSCN and in the orthorhombic modification of AgSCN the SCN– anions co-ordinate to four metal atoms as 1,1,1,3-µ4 bridges, whereas the degree of bridging decreases with increasing amounts of pyridine in the polymeric complexes [Cu(SCN)(py)z] and [Ag(SCN)(py)z] (z = 1 or 2). The distorted tetrahedral co-ordination of the metal atoms is preserved by co-ordination of pyridine ligands. Especially in the heteronuclear complexes [AgCu(SCN)2(py)4], [AgCu(SCN)2(py)3] and [Ag2Cu(SCN)3(py)3], interesting variants of structures result from the different possible modes of co-ordination of the SCN– ligand and from the preferred co-ordination of the “soft” S atoms to the “soft” Ag+ ions as defined by Pearson’s hard and soft acid and base principle.

Phasing methods for protein crystallography

The phase problem has been formulated as one of constrained global minimization and it leads to the minimal principle, which is the theoretical basis of ‘Shake-and-Bake’ — an algorithm for the automatic solution of the phase problem, ab initio. A related approach (termed ‘Half-Baked’) that, as in Shake-and-Bake, alternates phase refinement in reciprocal space with density modification in real space, has recently been formulated. The traditional techniques of direct methods have been integrated with isomorphous replacement and anomalous scattering and the first applications have been made. The accurate measurement of a limited number of structure invariants by means of multiple beam X-ray diffraction has become a reality. A feasibility study shows that, in combination with the direct method, the ability to measure the values of the structure invariants experimentally will strengthen existing techniques.

General Expression for Probabilistic Examination of Multiphase Structure Invariants in the Case of a Native Protein and Multiple Derivatives. Application to Estimates of the Three-Phase Structure Invariants

Concise probabilistic formulae with definite crystallographic implications are obtained from the distribution for eight three-phase structure invariants (3PSIs) in the case of a native protein and a heavy-atom derivative [Hauptman (1982). Acta Cryst. A38, 289–294] and from the distribution for 27 3PSIs in the case of a native and two derivatives [Fortier, Weeks & Hauptman (1984). Acta Cryst. A40, 646–651]. The main results of the probabilistic formulae for the four-phase structure invariants are presented and compared with those for the 3PSIs. The analysis directly leads to a general formula of probabilistic estimation for the n-phase structure invariants in the case of a native and m derivatives. The factors affecting the estimated accuracy of the 3PSIs are examined using the diffraction data from a moderate-sized protein. A method to estimate a set of the large-modulus invariants, each corresponding to one of the eight 3PSIs, that has the largest [\Delta] values and relatively large structure-factor moduli between the native and derivative is suggested, which remarkably improves the accuracy, and thus a phasing procedure making full use of all eight 3PSIs is proposed.

Variational Approach to Unsupervised Learning Algorithms of Neural Networks

Variational approach in pattern recognition basing on a mean risk functional is applied to unsupervised learning algorithms for neural networks. The paper summarizes main statements and results of the approach: a structure of mean risk functionals relevant for the problem of grouping the multivariate data; optimum conditions; recurrent algorithms of stochastic approximation type for minimization of the functionals; and conditions ensuring convergence of the algorithms to appropriate solutions. Basing on this theory a general scheme is proposed and it allows to obtain neural networks whose adaptation laws arise as the recurrent unsupervised learning algorithms for suitably selected mean risk functionals. The well known Grossberg networks, counter-propagation networks, and Kohonen self-organizing networks are among them. Moreover the new variants of unsupervised-learning neural structures can be derived as it is demonstrated in the paper. The developed mathematical means can serve for theoretical justification of using such neural networks in data processing systems. © 1997 Elsevier Science Ltd. All Rights Reserved.

On integrating the techniques of direct methods with anomalous dispersion. IV. A simplified perturbation treatment for SAS phasing.

Results from probabilistic theory for the single-wavelength anomalous-scattering (SAS) Friedel pair, two-phase structure invariants, psi H = phi H + phi-H, are used to show that the SAS three-phase structure invariants, psi HK = phi H + phi K + phi-H-K, tend to positive values that are easily estimated. Appropriate averages of the estimates provide SAS perturbation corrections in the form of positive origin shifts for the probability distribution of psi HK values and for the tangent formula. The theoretical probabilistic results are verified by empirical statistical analyses of model-calculated phases and experimentally measured structure-factor magnitudes for a small-molecule and a protein crystal structure.

Direct Methods for Incommensurately Modulated Structures. On the Applicability of Normalized Structure Factors

The recently defined normalized structure factors for incommensurately modulated structures [Lam, Beurskens & van Smaalen (1993). Acta Cryst. A49, 709–721] have been subjected to extensive tests regarding their applicability in direct methods for phase determination. It is shown that the probability distribution associated with the structure invariants E(−H)E(H′)E(H − H′), where H and H′ are reciprocal vectors of main and/or satellite reflections, approximately has the same functional form as the Cochran distribution but triplet phase relations are relatively less reliable when satellites are involved. The use of the multidimensional Sayre equation for the determination of phases of satellite reflections [Hao, Liu & Fan (1987). Acta Cryst. A43, 820–824; Fu & Fan (1994). J. Appl. Cryst. 27, 124–127] is not improved by using normalized structure factors instead of ordinary structure factors.

The SAS Maximal Principle: a New Approach to the Phase Problem

The phase problem, when single-wavelength anomalous scattering (SAS) diffraction data are available, is formulated as a problem in global optimization. Although the objective function has a myriad of local maxima, its global maxima, never more than two, are readily accessible and easily identified by virtue of their isolation. The ability to determine the global maxima of the objective function represents the latest and most successful attempt to go directly from the known probabilistic estimates of the three-phase structure invariants to the values of the individual phases. The relationship between the maxima of the objective function and the solutions of the newly formulated system of SAS tangent equations plays a key role in this development.

Studies on ABX6 Compounds. V. Thermodynamics and kinetics of the high pressure transformations on ABX6 compounds (A = Ca, Dy, Ge, Sn, Pb; B = Th, U; X = I)

AbstractThe results of high pressure experiments with ternary iodides of the general formula ABI6 with A = Ca, Dy, Ge, Sn, Pb and B = Th, U are described. These compounds transform from a β‐ to a γ‐SnThI6‐type structure, both variants of known trihalide structures (BiI3‐ and PuBr3‐type). Trends and pecularities in the values for the minimal transformation pressures and in the velocities of transition are pointed out, and they are discussed in terms of geometric and electronic factors.

Theory of magnetic electron drift modes

The nonlinear theory of two-dimensional magnetic electron drift modes is outlined. A Hamiltonian structure and integral invariants are identified. Spectral and statistical properties are considered and an energy spectrum with several similarity ranges is found. The inhomogeneity of the system is reflected by spectral anisotropy. Stationary localized vortex solutions are given. The linear stability of vortex street solutions with respect to the long wavelength perturbations is established. It is shown that nonlinear stability cannot be proven using Arnol'd's method.

Estimation of the one-phase structure seminvariants in the single isomorphous replacement case: an application of Hauptman's distribution

A method for estimating the one-phase structure seminvariants (OPSSs) having values of 0 or π has been proposed on the basis of the probabilistic theory of the three-phase structure invariants for a pair of isomorphous structures [Hauptman (1982). Acta Cryst. A38, 289–294]. The test calculations using error-free diffraction data of protein cytochrome c550 and its PtCl2−4 derivative show that reliable estimates of a number of the OPSSs can be obtained. The reliability of the estimation increases with the increase of the differences between diffraction intensities of the native protein and its heavy-atom derivative. A means to estimate the parameters of the distribution from the diffraction ratio is suggested.

Probabilistic estimation of the structure seminvariants in the monoclinic and orthorhombic systems when anomalous scatterers are present

The estimate formulas for the two-phase structure seminvariants (TPSSs) in the presence of anomalous scattering are obtained from the estimate of the two-phase structure invariants [Hauptman (1982). Acta Cryst. A38, 632–641; Giacovazzo (1983). Acta Cryst. A39, 585–592] and the conditional probability distribution of the TPSSs is derived from the neighborhood theory [Hauptman (1975). Acta Cryst. A31, 680–687]. A procedure for estimating the one-phase structure seminvariants near 0 or π (OPSSs) is proposed, based on the TPSS estimates. Test results for known structures with error-free data show accurate estimates for the TPSSs, even in the macromolecular case. For the OPSSs, the accuracy is related to the strength of anomalous scattering by heavy atoms in the macromolecular case. The incorporation of the heavy-atom information improves the results.

On integrating the techniques of direct methods with anomalous dispersion. III. Estimation of two-wavelength two-phase structure invariants

For diffraction data at two wavelengths from a crystal with anomalous scatterers, there are six types of two-phase structure invariants for Friedel pairs. Two of the six are single-wavelength invariants; the other four are mixed-wavelength invariants. It is shown that the latter can be estimated by a straightforward extension of results from the probabilistic direct-methods theory for the single-wavelength anomalous scattering case described in paper I [Hauptman (1982). Acta Cryst. A38, 632-641]. Statistical tests of the mixed-wavelength estimates are reported for small-molecule and macro-molecular examples.

Electron crystallography of inorganic compounds. Direct determination of the basic copper chloride structure CuCl2·3Cu(OH)2

Experimental electron diffraction intensity data from basic copper chloride CuCl2·3Cu(OH)2 in its metastable form have been used for a direct structure analysis based on the evaluation of three and four phase structure invariants. The resultant electrostatic potential maps clearly show the correct atomic positions which correspond to those determined earlier by Voronova and Vainshtein (1958) from their interpretation of Patterson maps, and also to the X-ray analysis of the isostructural CuBr2·3Cu(OH)2 carried out by Aebi in 1948.

Epidermal ultrastructure of the adult parasitic phase female and encapsulated larva of Kronborgia isopodicola (Platyhelminthes, Fecampiidae): Phylogenetic implications

The parasitic phase female K. isopodicola possesses a ciliated epidermis of polyhedral cells. Adjacent lateral plasma membranes are separated at intervals creating intercellular spaces. Epidermal cilia are anchored by a horizontal rootlet, opposite which a spur projects from the basal body, and a narrow vertical rootlet. The cytoplasm contains coated vesicles, and coated pits lie between microvilli. Large granular and vesicular bodies (rhabdoids) are scattered through the epidermal epithelium; in the epidermis of the encapsulated larva, granular rhabdoids are densely packed and slender, more compact bodies also occur. The compact, granular and vesicular bodies are probably morphological variants of the same epidermal structures, suggested to undergo sequential changes accomplished in later stages by lysosomal activity. Morphologically similar epidermal bodies are found in triclads. They are also characteristic of the parasitic genus Urastoma, which shares other ultrastructural features with K. isopodicola. The Neodermata may have arisen from parasitic turbellarian forms, at a more “primitive” level of organization than ancestors of the contemporary Rhabdocoela.

Engineering measures to ensure reliable operation of the Tugur tidal power station under the severe ice conditions of the sea of Okhotsk

All three variants of the ice-protecting structures are completely reliable with respect to retaining ice and forming a stable ice barrier (jam) seaward of the dam site of the Tugur TPS. The length of the hummocked ice at the ice-protecting structures will not exceed 0.5 km, its thickness will be about 6 m. The head losses in this stretch of ice will not exceed 10 cm. Standard 50×13×3-m pontoons with an ice-retaining deflector with a height of 2 m (at the top and bottom) are quite stable under the action of ice masses, since their metacenter is 5.1 m above the center of gravity. With consideration of the considerable cost and labor intensity of constructing ice-resistant piers in Tugur Bay, it is recommended to protect the Tugur TPS from ice annually by using an ice-retaining boom consisting of standard pontoons equipped with ice-retaining deflectors and chained together and secured by dead anchors. Thus the use of ice-protecting structures ensures reliable operation of the Tugur TPS during the entire winter under the severe ice conditions of the Sea of Okhotsk. At the same time, the ice-protecting structures developed can be used for retaining ice and forming small artificial ice jams in safe places on river stretches located upstream of the hydraulic structures being built, which makes it possible to prevent the passage of ice during construction on the stretch of the river channel confined by the structures.

Electron Crystallographic Analysis of a Polysaccharide Structure—Direct Phase Determination and Model Refinement for Mannan I

Three-dimensional electron diffraction intensity data from the polysaccharide mannan I, previously published by H. Chanzy et al. (1987; Macromolecules 20, 2407-2413), were used for an ab initio structure determination. The space group is P 2 12 12 1, with unit cell constants a = 8.92, b = 7.21, c = 10.27 Å. After determination of crystallographic phases by evaluation of triplet and quartet structure invariants, 41 values were assigned to 58 unique reflections, 11 linked through a single algebraic unknown a. Two potential maps corresponding to two possible values of a were calculated by a Fourier transformation of the limited 3D data set, combining the phase terms with measured structure factor magnitudes. Either map allowed a monomer model, taken from the crystal structure of methyl α- d-mannopyranoside, to be fit very well in the xy plane, since 24 of 34 hk0 data are accessed by the direct phase determination. Although the limited goniometer tilt range is responsible for an incomplete sampling of the 3D reciprocal net, resulting in a series termination effect, a choice could be made between the two possible maps (permuting the unknown phase term a = ±π/2), since only one is a good envelope to the monomer structure in the chain direction. After optimizing linkage geometry, a structure that is very close to the initial determination was derived based on a conformational refinement.

Identification of Structure and Parameters of the Multivariable Systems

The identification of the ARMAX model and the state space model of the multivariable system is investigated in the presence of coloured noise. Firstly. the optimal input vector design is introduced to identify the Markov parameter matrices. Secondly. in the description of the multi-dimensional ARMAX model. an order recursive algorithm is presented for estimating the order and the parameter matrices of the ARMAX model using the estimated Markov matrices. The aymptotic biases are compensated to achieve higher identification precision. Furthermore. the autocorrelation function matrices of the observation noise are estimated. Finally. the recursive algorithm of the identification of the Kronecker structure invariants and the parameters of the state space model of the multivariable system is suggested.

Frequency statistical method for evaluating cosine invariants of three-phase relationships.

A new variation on the established procedure to evaluate three-phase structure invariants through quadrupole relationships is described. This method differs from earlier algebraic formulations in that the cosine-invariant estimates are based on a conditional observed frequency distribution of magnitude of E magnitudes for the quadrupole, rather than on the values of the magnitudes themselves. Successful applications of this method to a number of structures that ranged in size from 84 to 317 independent non-hydrogen light atoms are given.

On the sign ambiguity of triplet phases in nonsystematic many-beam effects in CBED patterns

The possibility to determine not only the magnitude but also the sign of three-phase structure invariants from nonsystematic many-beam effects in convergent-beam electron diffraction (CBED) patterns is discussed. From the full dynamical many-beam intensity expression it is clear that it is a principal difference between equivalent three-beam cases of opposite sign of the triplet phases. However, the difference and thus the ability to distinguish between the two cases depends strongly both on the relative magnitude of the structure factors involved and the specimen thickness for which the actual CBED discs are obtained. The largest differences are obtained for a weakly coupled three-beam case where the intensity in the line of the primary reflection, which in this case coincides with the kinematical two-beam position, has a distinct maximum or minimum at the three-beam condition depending on the sign of the triplet phase. In a strong coupling case where the intensity in the primary-reflection line near the three-beam condition is split into two individual segments, the differences are generally less and are not so obvious and quantitative measurements are necessary to distinguish the two cases of opposite sign of the triplet phases. Calculated examples with respect to a nonsystematic three-beam example in the noncentrosymmetric InP are given.