MM3 parametrization of four‐ and five‐coordinated rhenium complexes by a genetic algorithm—Which factors influence the optimization performance?

Genetic algorithms (GA) were used to solve one of the multidimensional problems in computational chemistry, the optimization of force field parameters. The correlation between the composition of the GA, its parameters (p(c), p(m)) and the quality of the results were investigated. The composition was studied for all combinations of a Simple GA/Steady State GA with a Roulette Wheel/Tournament Selector using different values each for crossover (0.5, 0.7, 0.9) and mutation rates (0.01, 0.02, 0.05, 0.10, 0.20). The results show that the performance is strongly dependent on the GA scheme, where the Simple GA/Tournament Selector yields the best results. Two new MM3 parameters were introduced for rhenium compounds with coordination number four (204) and coordination number five (205), the formal oxidation states of rhenium ranging from +V to +VII. A manifold of parameters (Re-C, N, O, S) was obtained by using a diverse set of CSD structures. The advantage of the GA vs. UFF calculations is shown by comparison of several examples. The GA optimized parameters were able to reproduce the geometrical data of the X-ray structures.     

The electronic structure of small sodium clusters

Ab initio molecular orbital calculations using the STO3-21G basis set has been carried out for the cluster series Na _n ⁺ , Na _n , and Na _n ^– (wheren=2–7). The basis set is shown to be reliable compared with more extensive basis sets at the Hartree-Fock level. Thirty-one optimized structures are reported and discussed, many of which (especially for the anions) have not been considered. The STO3-21G//STO3-21G calculations suggest that for most of the species the optimum geometries are planar. In particular, the optimized structures for the anionic species should provide a starting point for more sophisticated configuration interaction calculations.     

Selecting variables for k-means cluster analysis by using a genetic algorithm that optimises the silhouettes

The goal of present work is to analyse the effect of having non-informative variables (NIV) in a data set when applying cluster analysis and to propose a method computationally capable of detecting and removing these variables. The method proposed is based on the use of a genetic algorithm to select those variables important to make the presence of groups in data clear. The procedure has been implemented to be used with k-means and using the cluster silhouettes as fitness function for the genetic algorithm.The main problem that can appear when applying the method to real data is the fact that, in general, we do not know a priori what the real cluster structure is (number and composition of the groups).The work explores the evolution of the silhouette values computed from the clusters built by using k-means when non-informative variables are added to the original data set in both a literature data set as well as some simulated data in higher dimension. The procedure has also been applied to real data sets.     

Complete graph conjecture for inner-core electrons: homogeneous index case

The complete graph conjecture that encodes the inner-core electrons of atoms with principal quantum number n >or= 2 with complete graphs, and especially with odd complete graphs, is discussed. This conjecture is used to derive new values for the molecular connectivity and pseudoconnectivity basis indices of hydrogen-suppressed chemical pseudographs. For atoms with n = 2 the new values derived with this conjecture are coincident with the old ones. The modeling ability of the new homogeneous basis indices, and of the higher-order terms, is tested and compared with previous modeling studies, which are centered on basis indices that are either based on quantum concepts or partially based on this new conjecture for the inner-core electrons. Two similar algorithms have been proposed with this conjecture, and they parallel the two "quantum" algorithms put forward by molecular connectivity for atoms with n > 2. Nine properties of five classes of compounds have been tested: the molecular polarizabilities of a class of organic compounds, the dipole moment, molar refraction, boiling points, ionization energies, and parachor of a series of halomethanes, the lattice enthalpy of metal halides, the rates of hydrogen abstraction of chlorofluorocarbons, and the pED(50) of phenylalkylamines. The two tested algorithms based on the odd complete graph conjecture give rise to a highly interesting model of the nine properties, and three of them can even be modeled by the same set of basis indices. Interesting is the role of some basis indices all along the model.     

A comparison of two algorithms for warping of analytical signals

The alignment of analytical signals is an important preprocessing step when further analysis (e.g. PCA) requires the same lengths of all of them. Two techniques for alignment of profiles, namely dynamic time warping (DTW) and correlation optimized warping (COW) were tested and compared. The attention was focused on chromatographic and spectroscopic profiles. Simulated and two sets of real data were studied in this study.     

On affine scaling algorithms for nonconvex quadratic programming

We investigate the use of interior algorithms, especially the affine-scaling algorithm, to solve nonconvex — indefinite or negative definite — quadratic programming (QP) problems. Although the nonconvex QP with a polytope constraint is a hard problem, we show that the problem with an ellipsoidal constraint is easy. When the hard QP is solved by successively solving the easy QP, the sequence of points monotonically converge to a feasible point satisfying both the first and the second order optimality conditions.Research supported in part by NSF Grant DDM-8922636 and the College Summer Grant, College of Business Administration, The University of Iowa.     

Numerical solution of minimax problems of optimal control,part 1

This paper contains general transformation techniques useful to convert minimax problems of optimal control into the Mayer-Bolza problem of the calculus of variations [Problem (P)]. We consider two types of minimax problems: minimax problems of Type (Q), in which the minimax function depends on the state and does not depend on the control; and minimax problems of Type (R), in which the minimax function depends on both the state and the control. Both Problem (Q) and Problem (R) can be reduced to Problem (P).For Problem (Q), we exploit the analogy with a bounded-state problem in combination with a transformation of the Jacobson type. This requires the proper augmentation of the state vectorx(t), the control vectoru(t), and the parameter vector , as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized.For Problem (R), we exploit the analogy with a bounded-control problem in combination with a transformation of the Valentine type. This requires the proper augmentation of the control vectoru(t) and the parameter vector , as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized.In a subsequent paper (Part 2), the transformation techniques presented here are employed in conjunction with the sequential gradient-restoration algorithm for solving optimal control problems on a digital computer; both the single-subarc approach and the multiple-subarc approach are discussed.This research was supported by the National Science Foundation, Grant No. ENG-79-18667, and by Wright-Patterson Air Force Base, Contract No. F33615-80-C3000. This paper is a condensation of the investigations reported in Refs. 1–7. The authors are indebted to E. M. Coker and E. M. Sims for analytical and computational assistance.     

Efficient clustering algorithms for self-organizing wireless sensor networks

Self-organization of wireless sensor networks, which involves network decomposition into connected clusters, is a challenging task because of the limited bandwidth and energy resources available in these networks. In this paper, we make contributions towards improving the efficiency of self-organization in wireless sensor networks. We first present a novel approach for message-efficient clustering, in which nodes allocate local “growth budgets” to neighbors. We introduce two algorithms that make use of this approach. We analyze the message complexity of these algorithms and provide performance results from simulations. The algorithms produce clusters of bounded size and low diameter, using significantly fewer messages than the earlier, commonly used, Expanding Ring approach. Next, we present a new randomized methodology for designing the timers of cluster initiators. This methodology provides a probabilistic guarantee that initiators will not interfere with each other. We derive an upper bound on the expected time for network decomposition that is logarithmic in the number of nodes in the network. We also present a variant that optimistically allows more concurrency among initiators and significantly reduces the network decomposition time. However, it produces slightly more clusters than the first method. Extensive simulations over different topologies confirm the analytical results and demonstrate that our proposed methodology scales to large networks.     

秩排序非线性滤波器的自适应优化算法

在图像处理中，秩排序非线性滤波器具有非常重要的作用。本文从加权顺序统计滤波器的自适应优化算法出发，导出了加权中值滤波器、秩选择滤波器和置换滤波器等几种重要的秩排序非线性滤波器的自适应优化设计算法，这些算法采用迭代计算实现，并可以在MAE、MSE和／Z准则下得到最优解。模拟实验表明，这些算法具有非常好的收敛效果，并可以很好地用于类似图像的非平稳信号的处理。