Self-organizing

S. Weber, editor. Solvent and Polymer Self-Organization, NATO ASI, Kluwer, 1995. 

The importance of numerical treatments, however, caimot be overemphasized in this context. Over the decades enonnous progress has been made in the numerical treatment of differential equations of complex gas-phase reactions [8, 70, 71], Complex reaction systems can also be seen in the context of nonlinear and self-organizing reactions, which are separate subjects in this encyclopedia (see chapter A3,14. chapter C3.6). 

Nicolis G and Prigogine I 1977 Self-organization in Nonequilibrium Systems (New York Wiley)... 

Rovinsky A B and Menzinger M 1993 Self-organization induoed by the differential flow of aotivator and inhibitor Phys. Rev. Lett. 70 778-81... 

Anderson P Wand Stein D 1987 Broken symmetry, emergent properties, dissipative structures, life Self-Organizing Systems ed F E Yates (New York Plenum) pp 445-57... 

Motte L and Pileni M P 1998 Influenoe of length of alkyl ohain used to passivate silver sulfide nanopartioles on two-and three-dimensional self-organization J. Phys. Chem. B 102 4104... 

Taleb A, Petit C and Pileni M P 1997 Synthesis of highly monodisperse silver nanopartioles from AOT reverse mioelles a way to 2D and 3D self-organization Chem. Mater. 9 950... 

Murray C B, Kagan C R and Bawendi M G 1995 Self-organization of CdSe nanoorystallites into three-dimensional quantum dot superlattioes Science 270 1335... 

Abstract. A model of the conformational transitions of the nucleic acid molecule during the water adsorption-desorption cycle is proposed. The nucleic acid-water system is considered as an open system. The model describes the transitions between three main conformations of wet nucleic acid samples A-, B- and unordered forms. The analysis of kinetic equations shows the non-trivial bifurcation behaviour of the system which leads to the multistability. This fact allows one to explain the hysteresis phenomena observed experimentally in the nucleic acid-water system. The problem of self-organization in the nucleic acid-water system is of great importance for revealing physical mechanisms of the functioning of nucleic acids and for many specific practical fields. 

Nicolis, G., Prigogine, I. Self-organization in nonequilibrium systems. John Willey Sons, New York (1977) 512... 

Tolstorukov, M.Ye., Gatash, S.V., Maleev, V.Ya. Self-organization and non-iinear dynamics of nucleic acid-water system. Special Issue of Int. J. Bif. Chaos (in press)... 

Previous work in our group had shown the power of self-organizing neural networks for the projection of high-dimensional datasets into two dimensions while preserving clusters present in the high-dimensional space even after projection [27]. In effect, 2D maps of the high-dimensional data are obtained that can show clusters of similar objects. 

An observation of the results of cross-validation revealed that all but one of the compounds in the dataset had been modeled pretty well. The last (31st) compound behaved weirdly. When we looked at its chemical structure, we saw that it was the only compound in the dataset which contained a fluorine atom. What would happen if we removed the compound from the dataset The quahty ofleaming became essentially improved. It is sufficient to say that the cross-vahdation coefficient in-CTeased from 0.82 to 0.92, while the error decreased from 0.65 to 0.44. Another learning method, the Kohonen s Self-Organizing Map, also failed to classify this 31st compound correctly. Hence, we had to conclude that the compound containing a fluorine atom was an obvious outlier of the dataset. 

This format was developed in our group and is used fruitfully in SONNIA, software for producing Kohonen Self Organizing Maps (KSOM) and Coimter-Propaga-tion (CPG) neural networks for chemical application [6]. This file format is ASCII-based, contains the entire information about patterns and usually comes with the extension "dat . 

Now, one may ask, what if we are going to use Feed-Forward Neural Networks with the Back-Propagation learning rule Then, obviously, SVD can be used as a data transformation technique. PCA and SVD are often used as synonyms. Below we shall use PCA in the classical context and SVD in the case when it is applied to the data matrix before training any neural network, i.e., Kohonen s Self-Organizing Maps, or Counter-Propagation Neural Networks. 

Initially the dataset contained 818 compounds, among which 31 were active (high TA, low USE), 157 inactive (low TA, high USE), and the rest intermediate. When the complete dataset was employed, none of the active compounds and 47 of the inactives were correctly classified by using Kohonen self-organizing maps (KSOM). 

The Kohonen Self-Organizing Maps can be used in a. similar manner. Suppose Xj., k = 1,. Nis the set of input (characteristic) vectors, Wy, 1 = 1,. l,j = 1,. J is that of the trained network, for each (i,j) cell of the map N is the number of objects in the training set, and 1 and j are the dimensionalities of the map. Now, we can compare each with the Wy of the particular cell to which the object was allocated. This procedure will enable us to detect the maximal (e max) minimal ( min) errors of fitting. Hence, if the error calculated in the way just mentioned above is beyond the range between e and the object probably does not belong to the training population. 

Kohonen networks, also known as self-organizing maps (SOMs), belong to the large group of methods called artificial neural networks. Artificial neural networks (ANNs) are techniques which process information in a way that is motivated by the functionality of biological nervous systems. For a more detailed description see Section 9.5. 

The Kohonen network or self-organizing map (SOM) was developed by Teuvo Kohonen [11]. It can be used to classify a set of input vectors according to their similarity. The result of such a network is usually a two-dimensional map. Thus, the Kohonen network is a method for projecting objects from a multidimensional space into a two-dimensional space. This projection keeps the topology of the multidimensional space, i.e., points which are close to one another in the multidimensional space are neighbors in the two-dimensional space as well. An advantage of this method is that the results of such a mapping can easily be visualized. 

Tools SONNIA [12] (Self-Organizing Neural Network for Information Analysis)... 

SONNIA is a self-organizing neural network for data analysis and visualization. 

SONNIA (Self Organizing Neural Network for Information Analysis), http //uww2.chende.uni-eTiangen.de/ softwarefkmap/ and http //www.mol-net.de/... 

Figure 10.1-4. Distribution of compounds from two data sets in the same KNN (Kohonen s self-organizing neural network) map by using 18 topological descriptors as input descriptors, where 1 represents the 1588 compounds in the Merck data set (excluding those compounds that are also in the Huuskonen data set) 2 represents the 799 compounds in the Huuskonen data set (excluding those compounds that are also in the Merck data set), and 3 represents the overlapping part of the Huuskonen data set and the Merck data set.

Til most cases, only one of the two regioisomers is preferentially formed. Wc will show here how reaction classification by a self-organizing neural network can be used for the prediction of the preferred regioisomer in a pyrazole synthesis. 

More elaborate scheme.s can he envisaged. Thus, a. self-organizing neural network as obtained by the classification of a set of chemical reactions as outlined in Section 3,5 can be interfaced with the EROS system to select the reaction that acmaliy occurs from among various reaction alternatives. In this way, knowledge extracted from rcaetion databases can be interfaced with a reaction prediction system,... 

Syntheses of sterically modified biopolymers can clearly yield insights into the presuppositions and possibilities of biological self-organization processes of biopolymers far beyond general thermodynamic and kinetic descriptions of natural systems. 

A typical biomembrane consists largely of amphiphilic lipids with small hydrophilic head groups and long hydrophobic fatty acid tails. These amphiphiles are insoluble in water (<10 ° mol L ) and capable of self-organization into uitrathin bilaycr lipid membranes (BLMs). Until 1977 only natural lipids, in particular phospholipids like lecithins, were believed to form spherical and related vesicular membrane structures. Intricate interactions of the head groups were supposed to be necessary for the self-organization of several ten thousands of... 

Fullerenes can be considered as a molecular full stop to organic synthesis highly complex and possibly very useful molecules are formed by self-organization of carbon atoms in the vapor phase. Sometimes synthetic chemists are not needed. 

The size-exclusion and ion-exchange properties of zeoHtes have been exploited to cause electroactive species to align at a zeoHte—water interface (233—235). The zeoHte thus acts as a template for the self-organization of electron transfer (ET) chains that may find function as biomimetic photosynthetic systems, current rectifiers, and photodiodes. An example is the three subunit ET chain comprising Fe(CN)g anion (which is charge-excluded from the anionic zeoHte pore stmcture), Os(bipyridine)3 (which is an interfacial cation due to size exclusion of the bipyridine ligand), and an intrazeoHte cation (trimethylamino)methylferrocene (F J ). A cationic polymer bound to the (CN) anion holds the self-assembled stmcture at an... 

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