Jiri Pospichal

Application of recurrent neural networks in chemistry. Prediction and classification of carbon-13 NMR chemical shifts in a series of monosubstituted benzenes

The recurrent neural network is a feed-forward network ascribed to a parent neural network with feed-back connections (or in another term, oriented cycles). Its adaptation is performed by an analog of the standard back-propagation adaptation method. The recurrent neural network approach is illustrated by prediction and classification of 13C NMR chemical shifts in a series of monosubstituted benzenes. The descriptors (input activities) of functional groups are determined by 11 nonnegative integers that correspond to numbers of appearance of some substructural features in the corresponding molecular graphs. The obtained results indicate that these descriptors properly describe the basic physical and chemical nature of functional groups.

NEURAL NETWORK PREDICTION OF CARBON-13 NMR CHEMICAL SHIFTS OF ALKANES

Three-layer feed-forward neural networks for the prediction of I3C NMR chemical shifts of alkanes through nine carbon atoms are used. Carbon atoms in alkanes are determined by 13 descriptors that correspond to the so-called embedding frequencies of rooted subtrees. These descriptors are equal to numbers of appearance of smaller structural skeletons composed of two through five carbon atoms. It is demonstrated that the used descriptors offer a very useful formal tool for the proper and adequate description of environment of carbon atoms in alkanes. Neural networks with different numbers of hidden neurons have been examined. Best results are given by the neural network composed of three hidden neurons. Simultaneous calculations carried out by the standard linear regression analysis are compared with our neural network calculations.

Canonical indexing and constructive enumeration of molecular graphs

A canonical indexing of molecular graphs based on the maximal digital code corresponding to the lower triangle part of the adjacency matrix is suggested. Graph-theoretical properties of this indexing make possible formulation of an exhaustive and nonredundant constructive enumeration of connected graphs with prescribed numbers of vertices and edges. The correctness of the concept is confirmed by a series of theorems

SIMULATED ANNEALING CONSTRUCTION OF MOLECULAR GRAPHS WITH REQUIRED PROPERTIES

The method of simulated annealing for the construction of molecular graphs with required properties was studied. The method depends on the already available functional relationship that transforms molecular structural features into a numerical value of a property. The simulated annealing was initialized by a randomly generated molecular graph. A molecular graph was perturbed onto another molecular graph so that starting from a randomly selected point the rest of the numerical code of the current graph was replaced by a randomly generated code. The acceptance of the generated code to the next process of simulated annealing was solved by the Metropolis criterion. After the prescribed number of steps the temperature was multiplicatively decreased. Two types of molecular graphs were studied. The first type of molecular graphs was acyclic graphs (trees) that are simply represented by a numerical code composed of the same number of entries as the number of vertices in molecular graphs. Perturbation operations c...

Simple Construction of Embedding Frequencies of Trees and Rooted Trees

A unified approach for the calculation of embedding frequencies of trees as well as rooted trees is suggested. It consists of a simple pruning process when marginal vertices are successively removed. The problem of isomorphism between (rooted) trees is solved by making use of Read’s linear canonical code. Simple criteria, based on the concept of valence vectors, for verification whether a (rooted) tree can be a subtree of a (rooted) tree are proved. Tables of embedding frequencies of trees and rooted trees through ten and eight vertices, respectively, are presented. The embedding frequencies of rooted trees are useful for construction of descriptors of molecular graphs when the so-called local properties are studied.

Artificial Chemistry and Molecular Darwinian Evolution of DNA/RNA-Like Systems I - Typogenetics and Chemostat

Summary: Two simplified models of Darwinian evolution at the molecular level are studied by applying the methods of artificial chemistry. First, a metaphor of a chemical reactor (chemostat) is considered. It contains molecules that are represented by binary strings, the strings being capable of replication with a probability proportional to their fitness. Moreover, the process of replication is not fully precise, sporadic mutations may produce new offspring strings, which are slightly different from their parent templates. In the framework of this approach we postulate a folding of binary strings into a secondary 2D structure. The proposed chemostat method offers a detailed view of mechanisms of the molecular Darwinian evolution, in particular of the meaning and importance of neutral mutations. Second, a simplified formal system Typogenetics, introduced by Hofstadter, is discussed. Concepts of replicators and hypercycles, defined within Typogenetics, belong to the basic entities in current perception of artificial life. A metaphor of chemical reactions is applied to study an emergence of replicators and hypercycles.

Multistage decision-making using simulated annealing applied to a fuzzy automaton

Abstract A new optimization method that stochastically builds up a solution step-by-step in combination with simulated annealing is used for multistage decision-making of finite-state automaton. The quality of the new algorithm for larger scale problems was tested by two tasks: (1) maximizing the probability of goal satisfaction with fuzzy goals subject to fuzzy constraints and (2) minimizing the length of decision sequence leading to a specified termination state. The new method required a number of evaluations of solutions, which was smaller by orders of magnitude in comparison with a “classical” genetic algorithm.