Solution for underflow problem in linkage and segregation analysis

Finding genes for complex traits is one of the major challenges of modern human genetics. Current developments of molecular techniques facilitated use of large pedigrees and marker sets of thousands of single-nucleotide polymorphisms (SNPs). However, one of the problems occurring in statistical analysis of such large data sets is that the likelihood is very low and underflow may easily occur. In this work we describe a method permitting to avoid underflow during computation of a likelihood function, using different algorithms. Our method makes practically possible analysis of thousands of individuals and thousands of SNPs. The method is easy to implement without major change of the code of existing programs. It also helps to reduce the amount of computer memory used in analysis without noticeable alteration of the program running time. The algorithm was implemented in the software packages for segregation and linkage analysis, which are available from http://mga.bionet.nsc.ru/.     

Graphical representation of a new algorithm for nonorthogonalab initio valence bond calculations

A pictorial representation of the algorithm using successive expansion method for the nonorthogonal VB calculations is given. With the help of this representation and the graph analysis, the efficiency of this algorithm is improved and theN! problem is reduced by a factor of about (N!)^1/2. Anab initio VB program for valence bond self-consistent-field (VBSCF) calculations has been implemented based on this algorithm. Some VBSCF calculations have been performed for systems of up to 14 electrons. The statistics of the CPU time of the calculations indicate that this new group-theoretical approach is quite practical.     

Beta spectra deconvolution for liquid scintillation counting

This study presents the first results of a deconvolution method for Liquid Scintillation complex spectra. The method has been developed by means of the software MATLAB and is based on the utilization of Fourier Transforms. Its main target is to obtain a fast calculation procedure capable to unfold complex spectra without requiring any preliminary knowledge of the peak shapes of the component nuclides. Experimental tests have been carried out by means of a Perkin Elmer Wallac Quantulus 1220. Distinctive features of Quantulus have not been used, the instrument was only utilized to generate spectra in numerical form that subsequently were uploaded to a PC and analyzed by MATLAB. Results show acceptable capabilities of the method both for fitting convoluted spectra and for unfolding single nuclide shapes. Further experimentation is scheduled, in order to take account of quenching effects; it will be carried out by adding to the calculation algorithm another step, capable of performing a self-choice of the number of harmonics. The final aim is to fit any kind of beta spectra also when quenching influences the shape deeply.     

Extension of the fast multipole method for the rectangular cells with an anisotropic partition tree structure

The fast multipole method (FMM) is an order N method for the numerically rigorous calculation of the electrostatic interactions among point charges in a system of interest. The FMM is utilized for massively parallelized software for molecular dynamics (MD) calculations. However, an inconvenient limitation is imposed on the implementation of the FMM: In three-dimensional case, a cubic MD unit cell is hierarchically divided by the octree partitioning under isotropic periodic boundary conditions along three axes. Here, we extended the FMM algorithm adaptive to a rectangular MD unit cell with different periodicity along the axes by applying an anisotropic hierarchical partitioning. The algorithm was implemented into the parallelized general-purpose MD calculation software designed for a system with uniform distribution of point charges in the unit cell. The partition tree can be a mixture of binary and ternary branches, the branches being chosen arbitrarily with respect to the coordinate axes at any levels. Errors in the calculated electrostatic interactions are discussed in detail for a selected partition tree structure. The extension enables us to execute MD calculations under more general conditions for the shape of the unit cell, partition tree, and boundary conditions, keeping the accuracy of the calculated electrostatic interactions as high as that with the conventional FMM. An extension of the present FMM algorithm to other prime number branches, such as 5 and 7, is straightforward.     

Global approach for calculation of minimum miscibility pressure

An algorithm has been developed for calculation of minimum miscibility pressure (MMP) for the displacement of oil by multicomponent gas injection. The algorithm is based on the key tie line identification approach initially addressed by Wang and Orr [Y. Wang and F.M. Orr Jr., Analytical calculation of minimum miscibility pressure, Fluid Phase Equilibria, 139 (1997) 101–124]. In this work a new global approach is introduced. A number of deficiencies of the sequential approach have been eliminated resulting in a robust and highly efficient algorithm. The time consumption for calculation of the MMP in multicomponent displacement processes has been reduced significantly and can now be performed within a few seconds on a PC for a 15-component gas mixture. The algorithm is hence particularly suitable for gas enrichment studies or other case studies where a large number of MMP calculations is required. Predicted results from the key tie line identification approach are shown to be in excellent agreement with slimtube data and with other multicell/slimtube simulators presented in the literature.     

Theory and experiment in concert: templated synthesis of amide rotaxanes, catenanes, and knots

The synthesis of amide rotaxanes, amide catenanes, and trefoil amide knots is based on template effects mediated by hydrogen bonds. While a large body of experimental data is available, in-depth theoretical studies of these template syntheses are virtually unavailable, although they would provide a more profound insight into the exact details of the hydrogen-bonding patterns involved in the formation of these mechanically interlocked species. In this article we present a density functional study of the conformational properties of tetralactam macrocycles and the threading mechanism that produces the immediate precursor for rotaxane and catenane formation. Predictions of the geometries and relative energies made on the basis of semi-empirical AM1 calculations are compared with these results in order to judge the reliability of the simpler approach. Since these calculations yield good agreement with the structural features, they have been used to extend the calculations in order to understand the mechanism of formation of a trefoil dodecaamide knot that has recently been synthesized. The inherent topological chirality of the knot is reflected in the intermediates generated during its formation; these involve helical loops. These loops parallel the rotaxane and catenane wheels with respect to the arrangement of the functional groups that mediate the template effect and may well serve as wheel analogues through which one of the precursor molecules can be threaded. This threading step finally results in the knotted structure. Good agreement between the results of the calculations presented here and experimental findings is achieved.     

A machine learning technique toward generating minimum energy structures of small boron clusters

The search for a global minimum related to molecular electronic structure and chemical bonding has received wide attention based on some theoretical calculations at various levels of theory. Particle swarm optimization (PSO) algorithm and modified PSO have been used to predict the energetically stable/metastable states associated with a given chemical composition. Out of a variety of techniques such as genetic algorithm, basin hopping, simulated annealing, PSO, and so on, PSO is considered to be one of the most suitable methods due to its various advantages over others. We use a swarm‐intelligence based parallel code to improve a PSO algorithm in a multidimensional search space augmented by quantum chemical calculations on gas phase structures at 0 K without any symmetry constraint to obtain an optimal solution. Our currently employed code is interfaced with Gaussian software for single point energy calculations. The code developed here is shown to be efficient. Small population size (small cluster) in the multidimensional space is actually good enough to get better results with low computational cost than the typical larger population. But for larger systems also the analysis is possible. One can try with a large number of particles as well. We have also analyzed how arbitrary and random structures and the local minimum energy structures gravitate toward the target global minimum structure. At the same time, we compare our results with that obtained from other evolutionary techniques.     

Cholesky decomposition of the two-electron integral matrix in electronic structure calculations

A standard Cholesky decomposition of the two-electron integral matrix leads to integral tables which have a huge number of very small elements. By neglecting these small elements, it is demonstrated that the recursive part of the Cholesky algorithm is no longer a bottleneck in the procedure. It is shown that a very efficient algorithm can be constructed when family type basis sets are adopted. For subsequent calculations, it is argued that two-electron integrals represented by Cholesky integral tables have the same potential for simplifications as density fitting. Compared to density fitting, a Cholesky decomposition of the two-electron matrix is not subjected to the problem of defining an auxiliary basis for obtaining a fixed accuracy in a calculation since the accuracy simply derives from the choice of a threshold for the decomposition procedure. A particularly robust algorithm for solving the restricted Hartree-Fock (RHF) equations can be speeded up if one has access to an ordered set of integral tables. In a test calculation on a linear chain of beryllium atoms, the advocated RHF algorithm nicely converged, but where the standard direct inversion in iterative space method converged very slowly to an excited state.     

Interference by second order reactions in activation analysis

Equations to calculate the second order reaction interferences in activation analysis have been derived. A simple approximation as well as the exact solution have been investigated. A new algorithm is proposed for fast and accurate calculations, without the need of a computer with high precision arithmetic. The method can be used for all higher order reaction chains. Aspirant NFWO     

A kinematic view of loop closure

We consider the problem of loop closure, i.e., of finding the ensemble of possible backbone structures of a chain segment of a protein molecule that is geometrically consistent with preceding and following parts of the chain whose structures are given. We reduce this problem of determining the loop conformations of six torsions to finding the real roots of a 16th degree polynomial in one variable, based on the robotics literature on the kinematics of the equivalent rotator linkage in the most general case of oblique rotators. We provide a simple intuitive view and derivation of the polynomial for the case in which each of the three pair of torsional axes has a common point. Our method generalizes previous work on analytical loop closure in that the torsion angles need not be consecutive, and any rigid intervening segments are allowed between the free torsions. Our approach also allows for a small degree of flexibility in the bond angles and the peptide torsion angles; this substantially enlarges the space of solvable configurations as is demonstrated by an application of the method to the modeling of cyclic pentapeptides. We give further applications to two important problems. First, we show that this analytical loop closure algorithm can be efficiently combined with an existing loop-construction algorithm to sample loops longer than three residues. Second, we show that Monte Carlo minimization is made severalfold more efficient by employing the local moves generated by the loop closure algorithm, when applied to the global minimization of an eight-residue loop. Our loop closure algorithm is freely available at http://dillgroup. ucsf.edu/loop_closure/.     

Steepest-descent algorithm for vibrational analysis calculations

In this paper we consider problems concerning the effectiveness of iterational calculations on vibrational analysis. Instead of the widespread least-squares method of force field refinement, another method is proposed based on the steepest-descent algorithm for calculation of the functional minimum of many variables. The new method does not require inverting of a large, poorly conditioned matrix or the introduction of experimental damping coefficients for improving the convergency of the calculations. Test calculations performed for several molecules exhibit a significant “elasticity” of the proposed algorithm allowing more precise reproduction of the molecular vibration frequencies than can be found in recently published works.     

Effect of hydrogen bonds on the axial stiffnes of crystalline native cellulose

Previous theoretical calculations of elastic constants for cellulose based on force constants for bond stretching and bending of valence angles have yielded axial stiffness values admittedly too low. The present analysis accounts for a hitherto unexamined geometrical effect associated with deformation of interchain hydrogen bonds. To do this, most primary bond deformations are neglected so the resulting calculation gives an upper bound for the axial stiffness. By using two different sets of hydrogen bond force constants, values of 24.6 and 31.9 × 10¹¹ dyne/cm² were obtained for Young's modulus in the chain direction. These values are very much larger than earlier calculations and experimental determinations from cellulosic fibers, indicating both the importance of the effect considered here and the likelihood of an exact analysis yielding an acceptable result.     

Reduction of injection variance in flow-injection analysis

In order to achieve maximum sensitivity in flow-injection analysis, sample dispersion must be kept to a minimum. This dispersion process, however, is not well understood. Studies of the dispersion process have concentrated on dispersion within the flow manifold while dispersion due to the injection process has been largely ignored. Here sample injection loops packed with inert glass beads and a Serpentine II (distorted) empty loop were constructed and compared to traditional empty sample loops. Digitization of the response curves and subsequent calculation of the statistical moments were used to compare the contribution of each sample loop type to the total system dispersion. Both packed and Serpentine II sample loops were shown to decrease dispersion and increase throughput in flow-injection systems. Plots of peak variance vs. injection volume show variance increasing 1.67 times faster with traditional open sample loops compared to packed loops. When combined with other peak width minimization techniques, this method should further lower concentration limits of detection.     

Simple method for calculating time dependence of individual radionuclide activities in decay series

A rapid method for calculating the time dependence of activities of individual radionuclides in genetically coupled decay series has been proposed. The method is based on the mathematical procedure, in which the matrix method is used for calculating a set of decay equations given in the vector form. The developed method is computerized and uses the modern Scilab software. This simple method eliminates certain drawbacks of older methods used previously for this purpose and is applicable to even solve calculations which are not easily treatable with the older methods. Some practical examples of such calculations are presented. Moreover, the new method is universal and it also enables a more general approach to the problem of the calculation of decay series in nuclear chemistry.      

Improved strategy in analytic surface calculation for molecular systems: Handling of singularities and computational efficiency

Computer methods for analytic surface calculations of molecular systems suffer from numerical instabilities and are CPU time consuming. In this article, we present proposals toward the solution of both problems. Singularities arise when nearly collinear triples of neighboring atoms or multiple vertices are encountered during the calculation. Topological decisions in analytic surface calculation algorithms (accessibility of vertices and arcs) are based upon the comparison of distances or angles. If two such numbers are nearly equal, then currently used computer programs may not resolve this ambiguity correctly and can subsequently fail. In this article, modifications in the analytic surface calculation algorithm are described that recognize singularities automatically and treat them appropriately without restarting parts of the computation. The computing time required to execute these alterations is minimal. The basic modification consists in defining an accuracy limit within which two values may be assumed as equal. The search algorithm has been reformulated to reduce the computational effort. A new set of formulas makes it possible to avoid mostly the extraction of square roots. Tests for small-and medium-sized intersection circles and for pairs of vertices with small vertex height help recognize fully buried circles and vertex pairs at an early stage. The new program can compute the complete topology of the surface and accessible surface area of the protein crambin in 1.50–4.29 s (on a single R3000 processor of an SGI 4D/480) depending on the compactness of the conformation where the limits correspond to the fully extended or fully folded chain, respectively. The algorithm, implemented in a computer program, will be made available on request. © John Wiley & Sons, Inc.     

Automated drawing of structural molecular formulas under constraints

In this paper, we present a new algorithm for automated drawing of 2D structural formulas of molecules. The algorithm is based on the classical scheme of a drawing queue placing the molecular fragments in a sequential way. We extend the concept of so-called prefabricated units developed for complex ring systems to automatically created drawing units for chains and rings which will then be assembled in a sequential fashion. The approach is fast and can be naturally extended to the problem of drawing molecules with common core structures. Further on, we present an algorithm that allows the drawing of 2D structural formulas under directional constraints assigned to a subset of bonds. Since no numerical optimization is necessary, the algorithm creates drawings of small organic molecules on the order of 500 structures per second. The new algorithm is relevant for all kinds of prediction and analysis software presenting a large number of probably similar molecular structures to the user of the software.     

Ped_Outlier software for automatic identification of within-family outliers

A high-throughput resequencing technology has brought family based studies back into genetic research focus. Within-family outliers (the individuals whose phenotype is very much unlike the phenotype of relatives) may carry rare variants of large effects and thus resequencing of these provides a highly powered strategy for rare variants detection. On the other hand, such outliers may complicate search for common variants of smaller effects, because they may obscure a real linkage signal. We have developed a program Ped_Outlier allowing automatic detection of within-family outliers in a sample of pedigrees of arbitrary structure and size. We tested our program by identification of within-family outliers for adult height and intracranial volume in large pedigree. Results of linkage analysis of these traits demonstrated that identification of within-family outliers is one of the important steps of pedigree analysis. The program Ped_outlier is freely available at http://mga.bionet.nsc.ru/soft/index.html.     

A computationally efficient and reliable bond order measure

Bond order indexes are useful measures that connect quantum mechanical results with chemical understanding. One of these measures, the natural bond order index, based on the natural resonance theory procedure and part of the natural bond orbital analysis tools, has been proved to yield reliable results for many systems. The procedure's computational requirements, nevertheless, scales so highly with the number of functions in the basis set and the delocalization of the system, that the calculation of this bond order is limited to small or medium size molecules. We present in this work a bond order index, the first order perturbation theory bond order (fopBO), which is based on and strongly connected to the natural bond orbital analysis tools. We present the methodology for the calculation of the fopBO index and a number of test calculations that shows that it is as reliable as the natural bond orbital index, with the same weak sensitivity to variations among commonly used basis sets and, as opposed to the natural bond order index, suitable for the study of large systems, such as most of those of biological interest.