Indices Based on Information Theory

Information theory 71,72) is a convenient basis for the quantitative characterization of structures. It introduces simple structural indices called information content (total or mean) of any structured system. For such a system having N elements distributed into classes of equivalence Nls N2. Nk a probability distribution P pi, p2. pk is constructed (p = Nj/N). The entropy of this distribution, calculated 71) by the Shannon formula1  

The equations (49) and (50) can also be used for the case when N is a non-integer quantity partitioned into different contributions N,. 

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Topological information indices are graph invariants, based on information theory and calculated as - information content of specified equivalence relationships on the molecular graph. 

One of the most widely used indexes of community structure has been species diversity. Many measures for diversity are used, from such elementary forms as species number to measures based on information theory. A decrease in species diversity is usually taken as an indication of stress or impact upon a particular ecosystem. Diversity indexes, however, hide the dynamic nature of the system and the effects of island biogeography and seasonal state. As demonstrated in microcosm experiments, diversity is often insensitive to toxicant impacts. 

Information-Theoretical Indices Information theory has been employed to define topological indices based on the Shannon equation [17] ... 

Pyka and Sliwiok separated a-tocopherols, p-tocopherols, y-tocopherols, and 8-tocopherols by normal-phase high-performance liquid chromatography (NP-HPLC) and RP-Cig-HPLC. The selected topological indices based on connectivity (M, x ")> distance matrix W, MTI), and information theory (Zac, Tag) were... 

The refractive indices of polymers provide fundamental physical property information that can be used in characterization, processing, and usage analyses. In-depth description of refractive indices based on classic electromagnetic theory can be found in basic texts (1,2). The purpose of this monograph is to provide a convenient reference of values and some general remarks in approximating and utilizing refractive indices of polymers. 

This flexibility is not without a price, however, as learners need to keep track of where they are and pace themselves. To address this, we examine the situation from the psychological perspective of cognitive load theory. Cognitive load theory is based on the premise that people have a limited working memory capacity and that information must flow through before it can be stored in long-term memory (Sweller 2005). The basis for this is Miller s work, which indicated most people had a working memory capacity of 7 2 items (Miller 1956). 

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