A genetic algorithm for structure-based de novo design

Genetic algorithms have properties which make them attractive in de novo drug design. Like other de novo design programs, genetic algorithms require a method to reduce the enormous search space of possible compounds. Most often this is done using information from known ligands. We have developed the ADAPT program, a genetic algorithm which uses molecular interactions evaluated with docking calculations as a fitness function to reduce the search space. ADAPT does not require information about known ligands. The program takes an initial set of compounds and iteratively builds new compounds based on the fitness scores of the previous set of compounds. We describe the particulars of the ADAPT algorithm and its application to three well-studied target systems. We also show that the strategies of enhanced local sampling and re-introducing diversity to the compound population during the design cycle provide better results than conventional genetic algorithm protocols.     

Surface diffusion in reversed-phase liquid chromatography using silica gels bonded with C1 and C18 ligands of different densities

Surface diffusion in reversed-phase liquid chromatography (RPLC) using silica gels bonded with C₁ and C₁₈ alkyl ligands of different densities was studied from the viewpoints of two extrathermodynamic relationships, i.e., enthalpy-entropy compensation (EEC) and linear free energy relationship (LFER). First, according to the four methods proposed by Krug et al., the values of surface diffusion coefficient (D_s) were analyzed to confirm that an actual EEC resulting from substantial physico-chemical effects takes place for surface diffusion. Then, it was also demonstrated that a LFER is observed between surface diffusion and the retention equilibrium. The establishment of EEC and LFER suggests a mechanistic similarity of molecular migration by surface diffusion, irrespective of the alkyl chain length and the densities of C₁ and C₁₈ ligands. Finally, a thermodynamic model for the LFER based on the real EEC was used to estimate D_s values under various RPLC conditions. The D_s values can be estimated with a mean square deviation of about 25–30%. The agreement between the D_s values estimated and those experimentally measured suggests that the total mass flux by surface diffusion consists of the two contributions due to C₁ and C₁₈ ligands and that the contribution of each ligand is proportional to the ligand density.     

两种计算吸光光度法同时测定钙镁

研究了在pH10．5的硼砂-氢氧化钾缓冲溶液和乙醇的增敏作用条件下，偶氮氯膦Ⅰ与钙、镁的吸收特性，建立了多波长光度法同时测定钙和镁的方法。采用两种矩阵算法对试验数据进行处理，并对结果进行比较和分析。钙和镁含量在0～25μg／25ml范围内用计算法Ⅱ能得到准确结果。     

Study of the influence of physical aging on macroradical decay in poly(methyl methacrylate)

The macroradical decay in poly(methyl methacrylate) samples with different thermal histories was investigated in the temperature interval 20–100 °C using ESR spectroscopy and the second order kinetic model. The rate constants exhibit two different regimes with the transitions atT _tr=68±1°C which are independent of thermal treatment. ForT<T _tr andT>T _tr the rate constants as well as the corresponding activation parameters are sensitive to history because of different physical microstructures. The compensation law, i.e., the linear relation between lnk _{o, eff} andE _eff, was analyzed in terms of the so-called compensation quantitiesk _c andT _c and a proximity betweenT _c=T _tr andT _o=53±3 °C — Vogel temperature for -segmental dynamics was found. A comparison of kinetic and dynamic data suggests that the decay of terminal macroradicals in the low-temperature region is controlled by secondary relaxations and that the -mobility contributes to a more rapid decay at higher temperatures belowT _g.     

Critical exponents,hyperscaling, and universal amplitude ratios for two- and three-dimensional self-avoiding walks

We make a high-precision Monte Carlo study of two- and three-dimensional self-avoiding walks (SAWs) of length up to 80,000 steps, using the pivot algorithm and the Karp-Luby algorithm. We study the critical exponentsv and 2 ₄ – as well as several universal amplitude ratios; in particular, we make an extremely sensitive test of the hyperscaling relationdv = 2 ₄ –. In two dimensions, we confirm the predicted exponentv=3/4 and the hyperscaling relation; we estimate the universal ratios <R _g ² >/<R _e ² >=0.14026±0.00007, <R _m ² >/<R _e ² >=0.43961±0.00034, and ^*=0.66296±0.00043 (68% confidence limits). In three dimensions, we estimatev=0.5877±0.0006 with a correctionto-scaling exponent ₁=0.56±0.03 (subjective 68% confidence limits). This value forv agrees excellently with the field-theoretic renormalization-group prediction, but there is some discrepancy for ₁. Earlier Monte Carlo estimates ofv, which were 0.592, are now seen to be biased by corrections to scaling. We estimate the universal ratios <R _g ² >/<R _e ² >=0.1599±0.0002 and ^*=0.2471±0.0003; since ^*>0, hyperscaling holds. The approach to ^* is from above, contrary to the prediction of the two-parameter renormalization-group theory. We critically reexamine this theory, and explain where the error lies. In an appendix, we prove rigorously (modulo some standard scaling assumptions) the hyperscaling relationdv = 2 ₄ – for two-dimensional SAWs.     

并行“冒泡”排序算法的改进

并行“冒泡”排序算法的改进黄干平（武汉大学计算机科学系,武汉,４３００７２）关键词排序,并行算法,冒泡中国法分类号ｗ３０１．６ＰＢＳＭ并行排序算法是对ＫａｚｕｈｉｒｓＳａｄｏ和ＹｏｓｈｉｈｉｄｅＩｇａｒａｓｈ的并行“冒泡’书ｒ序算法’“的改进,其并行...     

A new heuristic algorithm solving the linear ordering problem

The linear ordering problem is an NP-hard combinatorial problem with a large number of applications. Contrary to another very popular problem from the same category, the traveling salesman problem, relatively little space in the literature has been devoted to the linear ordering problem so far. This is particularly true for the question of developing good heuristic algorithms solving this problem.In the paper we propose a new heuristic algorithm solving the linear ordering problem. In this algorithm we made use of the sorting through insertion pattern as well as of the operation of permutation reversal. The surprisingly positive effect of the reversal operation, justified in part theoretically and confirmed in computational examples, seems to be the result of a unique property of the problem, called in the paper the symmetry of the linear ordering problem. This property consists in the fact that if a given permutation is an optimal solution of the problem with the criterion function being maximized, then the reversed permutation is a solution of the problem with the same criterion function being minimized.     

Approximate minimum-cost multicommodity flows in\tilde O(ɛ −2 KNM) timetime

We show that an ε-approximate solution of the cost-constrainedK-commodity flow problem on anN-nodeM-arc network,G can be computed by sequentially solving O(K(? ^?2+logGK) logGM log (G? ^?1 GK)) single-commodity minimum-cost flow problems on the same network. In particular, an approximate minimum-cost multicommodity flow can be computed in $\tilde O$ (G? ^?2 GKNM) running time, where the notation Õ(·) means “up to logarithmic factors”. This result improves the time bound mentioned by Grigoriadis and Khachiyan [4] by a factor ofM/N and that developed more recently by Karger and Plotkin [8] by a factor of? ^?1. We also provide a simple $\tilde O$ (NM)-time algorithm for single-commodity budget-constrained minimum-cost flows which is $\tilde O$ (? ^?3) times faster than the algorithm developed in the latter paper.     

Asymptotic behavior of eigenvalues and random updating schemes

For a stochastic matrix (Q _ij ^T ) _i,j=1 ^M withQ _ij ^T exp(–U(ij)/T) at the off-diagonal positions, we develop an algorithm to evaluate the asymptotic convergence rate of all eigenvalues ofQ _ij ^T asT 0 using Ventcel's optimal graphs. As an application we can compare the convergence rates of some random updating schemes used in image processing.This research was partially supported by the National Science Council, Taiwan and Air Force Office of Scientific Research Contract No. F49620 S5C 0144, and was completed while Tzuu-Shuh Chiang was visiting the Center for Stochastic Processes, Department of Statistics, University of North Carolina, Chapel Hill, NC 27599-3260, USA.