Vladimír Kvasnička

Introduction to multi-layer feed-forward neural networks

Abstract Basic definitions concerning the multi-layer feed-forward neural networks are given. The back-propagation training algorithm is explained. Partial derivatives of the objective function with respect to the weight and threshold coefficients are derived. These derivatives are valuable for an adaptation process of the considered neural network. Training and generalisation of multi-layer feed-forward neural networks are discussed. Improvements of the standard back-propagation algorithm are reviewed. Example of the use of multi-layer feed-forward neural networks for prediction of carbon-13 NMR chemical shifts of alkanes is given. Further applications of neural networks in chemistry are reviewed. Advantages and disadvantages of multilayer feed-forward neural networks are discussed.

A HYBRID OF SIMPLEX METHOD AND SIMULATED ANNEALING

Abstract One of basic concepts of the well-known simplex optimization method is that from the current simplex set of points (solutions) a new point – reflection is constructed. The reflection point is used for a conditional updating of the simplex set. This simple and efficient idea is applied in the simulated annealing to suggest a new version of this stochastic optimization method. As a forerunner of the presented simulated annealing is the controlled random search invented by Price in the middle of seventies. He proposed the very important idea that a population of points is considered and from this population the simplex set is randomly selected. Reflection points update the population so that they conditionally substitute points with highest values of objective function. The simplex simulated annealing enhances further stronger stochastic and evolution character of this method. The construction of reflection points is randomized and their returning to the population is solved by the Metropolis criterion. A parallel version of simplex simulated annealing uses a decomposition of the whole population into disjoint subpopulations for which independent simulated annealings are done. The subpopulations randomly interact so that between two subpopulations their best points are exchanged and worst ones are eliminated.

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.

Coupled-cluster approach for open-shell systems

Abstract The coupled-cluster approach is generalized for open-shell systems, resulting in a model interaction of hermitean form. This theory represents a recursive method for the simultaneous construction and evaluation of all possible diagrammatic terms appearing in a pertinent many-body perturbation formalism.

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

Neural Network Prediction of the Solvatochromic Polarity/Polarizability Parameter

A three-layer feed-forward neural network was used for the prediction of the polarity/polarizability parameter . A simulated annealing algorithm was used to minimize the error at the neural network output. Descriptors related to the structure of the compounds were calculated as the input vector. The Kohonen neural network was used to split the data set into training and testing sets. The results obtained from the neural network were compared with the MLRA results.

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...

Synthon model of organic chemistry and synthesis design

1. Introduction.- References.- 2. The Molecular Graphs.- 2.1 Basic Concepts.- 2.2 Chemical Distance.- 2.3 Reaction Graphs.- 2.4 Reaction Distance.- 2.4.1 Illustrative Example.- 2.4.2 Bilateral Approach for Evaluation of Reaction Distances.- 2.4.3 Construction of Precursors and Successors of a Graph.- References.- 3. S-Graphs and Synthons.- 3.1 Basic Concepts.- 3.2 Chemical Distance.- 3.3 Reaction Graphs.- 3.4 Reaction Distance.- 3.5 Stable S-Graphs.- References.- 4. The Applied Synthon Model.- 4.1 The Matrix Model of the Synthon.- 4.2 The Graph Model of the Synthon.- 4.3 One-Atom Synthons - Valence States of Atoms.- References.- 5. Mathematical Model of Synthon Reactions.- 5.1 Isomerism of Synthons.- 5.2 The Matrix Model of Synthon Reactions.- 5.3 The Graph Model of Synthon Reactions.- 5.3.1 The Internal SR-Graph.- 5.3.2 The External SR-Graph.- 5.3.3 Construction of SR-Graphs.- 5.4 Elementary Electron Processes and Isomerisation of Synthons.- 5.5 The Reaction Distance.- 5.5.1 The Graph of Reaction Distances.- 5.5.2 The Chemical Interpretation of Reaction Distance.- 5.6 The Synthon Model and Reaction Mechanisms.- References.- 6. The Synthon Model and Organic Synthesis.- 6.1 Solution of the Precursor-Successor Problem in Computer Programs for Organic Synthesis Design.- 6.2 Deductive Prediction of SPS by the Synthon Model.- 6.2.1 Definition of SPS.- 6.2.2 The Concept of Stabilization and Construction of S (S(A/X)).- 6.2.3 Reduced Set of SPS and Order of SPS.- 6.3 The Synthon Model and Construction of the Tree of Synthesis/Retrosynthesis.- References.- 7. Conclusion.- 8. Index.

Wigner's (2n + 1) rule in MBPT

Wigners (2n + 1) rule (stating that the 2nth and/or (2n + 1)th order perturbation contributions to a non-degenerate energy can be evaluated from a knowledge of the wavefunction through nth order) is applied to many-body perturbation theory (MBPT). This approach essentially simplifies the calculation of correlation energy to an order higher than the third and reduces the number of required diagrams.