Prox-regular functions in variational analysis

The class of prox-regular functions covers all l.s.c., proper, convex functions, lower- functions and strongly amenable functions, hence a large core of functions of interest in variational analysis and optimization. The subgradient mappings associated with prox-regular functions have unusually rich properties, which are brought to light here through the study of the associated Moreau envelope functions and proximal mappings. Connections are made between second-order epi-derivatives of the functions and proto-derivatives of their subdifferentials. Conditions are identified under which the Moreau envelope functions are convex or strongly convex, even if the given functions are not.

     

Nonmonotone bundle-type scheme for convex nonsmooth minimization

In this paper, we present a general scheme for bundle-type algorithms which includes a nonmonotone line search procedure and for which global convergence can be proved. Some numerical examples are reported, showing that the nonmonotonicity can be beneficial from a computational point of view.This work was partially supported by the National Research Program on Metodi di ottimizzazione per le decisioni, Ministero dell' Universitá e della Ricerca Scientifica e Tecnologica and by ASI: Agenzia Spaziale Italiana.     

The application of the genetic algorithm to the minimization of potential energy functions

We adapted the genetic algorithm to minimize the AMBER potential energy function. We describe specific recombination and mutation operators for this task. Next we use our algorithm to locate low energy conformation of three polypeptides (AGAGAGAGA, A9, and [Met]-enkephalin) which are probably the global minimum conformations. Our potential energy minima are –94.71, –98.50, and –48.94 kcal/mol respectively. Next, we applied our algorithm to the 46 amino acid protein crambin and located a non-native conformation which had an AMBER potential energy 150 kcal/mol lower than the native conformation. This is not necessarily the global minimum conformation, but it does illustrate problems with the AMBER potential energy function. We believe this occurred because the AMBER potential energy function does not account for hydration.     

Analysis of grid file algorithms

Grid file algorithms were suggested in [12] to provide multi-key access to records in a dynamically growing file. We specify here two algorithms and derive the average sizes of the corresponding directories. We provide an asymptotic analysis. The growth of the indexes appears to be non-linear for uniform distributions:O(v ^c ) orO(v ), wherec=1+b^–1, =1+(s-1)/(sb+1),s is the number of attributes being used,v the file size, andb the page capacity of the system. Finally we give corresponding results for biased distributions and compare transient phases.     

Lattice models of peptide aggregation: evaluation of conformational search algorithms

We present a series of conformational search calculations on the aggregation of short peptide fragments that form fibrils similar to those seen in many protein mis-folding diseases. The proteins were represented by a face-centered cubic lattice model with the conformational energies calculated using the Miyazawa-Jernigan potential. The searches were performed using algorithms based on the Metropolis Monte Carlo method, including simulated annealing and replica exchange. We also present the results of searches using the tabu search method, an algorithm that has been used for many optimization problems, but has rarely been used in protein conformational searches. The replica exchange algorithm consistently found more stable structures then the other algorithms, and was particularly effective for the octamers and larger systems.     

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.     

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.     

基于遗传算法的波长选择方法在绿茶近红外光谱分析模型中的应用

利用遗传算法(GA)提取茶叶的近红外吸收特征波长的方法,研究建立了绿茶水分和氨基酸的近红外分析模型,并对波长选择前后两种成分的模型进行了比较分析。结果表明,经遗传算法波长选择后,简化了分析模型,同时模型的稳健性增强。氨基酸预测集的均方根误差(SEP)减小82.1%,水分预测集的均方根误差减小(SEP)76.6%,它们在波长选择前后对应的分析波长数之比分别为995∶7和1990∶33。