Generalized information functions
TL;DR: The concept of information functions of type β (β > 0) is introduced and by means of these information functions the entropies of typeβ are defined, which have a number of interesting algebraic and analytic properties similar to Shannon's entropy.
Abstract: The concept of information functions of type β ( β > 0) is introduced and discussed. By means of these information functions the entropies of type β are defined. These entropies have a number of interesting algebraic and analytic properties similar to Shannon's entropy. The capacity of type β ( β > 1) of a discrete constant channel is defined by means of the entropy of type β . Examples are given for the computation of the capacity of type β , from which the Shannon's capacity can be derived as the limiting case β = 1.
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TL;DR: This paper discusses properties of entropy, as well as related concepts such as relative entropy, skew entropy, dynamical entropy, etc, in detail with reference to their implications in statistical mechanics, to get a glimpse of systems with infinitely many degrees of freedom.
Abstract: It is rather paradoxical that, although entropy is one of the most important quantities in physics, its main properties are rarely listed in the usual textbooks on statistical mechanics. In this paper we try to fill this gap by discussing these properties, as, for instance, invariance, additivity, concavity, subadditivity, strong subadditivity, continuity, etc., in detail, with reference to their implications in statistical mechanics. In addition, we consider related concepts such as relative entropy, skew entropy, dynamical entropy, etc. Taking into account that statistical mechanics deals with large, essentially infinite systems, we finally will get a glimpse of systems with infinitely many degrees of freedom.
1,712 citations
TL;DR: The recent generalization by Tsallis (1988) of the Boltzmann-Gibbs statistics becomes consistent with a generalized thermodynamics preserving the Legendre-transformation framework of standard thermodynamics as discussed by the authors.
Abstract: The authors show the manner through which the recent generalization by Tsallis (1988) of the Boltzmann-Gibbs statistics becomes consistent with a generalized thermodynamics preserving the Legendre-transformation framework of standard thermodynamics. In addition to that they generalize the Shannon additivity.
644 citations
TL;DR: It is shown that gain and loss of predicted ubiquitination sites may likely represent a molecular mechanism behind a number of disease‐associatedmutations.
Abstract: Ubiquitination plays an important role in many cellular processes and is implicated in many diseases. Experimental identification of ubiquitination sites is challenging due to rapid turnover of ubiquitinated proteins and the large size of the ubiquitin modifier. We identified 141 new ubiquitination sites using a combination of liquid chromatography, mass spectrometry, and mutant yeast strains. Investigation of the sequence biases and structural preferences around known ubiquitination sites indicated that their properties were similar to those of intrinsically disordered protein regions. Using a combined set of new and previously known ubiquitination sites, we developed a random forest predictor of ubiquitination sites, UbPred. The class-balanced accuracy of UbPred reached 72%, with the area under the ROC curve at 80%. The application of UbPred showed that high confidence Rsp5 ubiquitin ligase substrates and proteins with very short half-lives were significantly enriched in the number of predicted ubiquitination sites. Proteome-wide prediction of ubiquitination sites in Saccharomyces cerevisiae indicated that highly ubiquitinated substrates were prevalent among transcription/enzyme regulators and proteins involved in cell cycle control. In the human proteome, cytoskeletal, cell cycle, regulatory, and cancer-associated proteins display higher extent of ubiquitination than proteins from other functional categories. We show that gain and loss of predicted ubiquitination sites may likely represent a molecular mechanism behind a number of disease-associatedmutations. UbPred is available at http://www.ubpred.org.
538 citations
TL;DR: This work provides a unified method of decomposing these diversities and constructing normalized taxonomic, phylogenetic, and functional similarity and differentiation measures, including N-assemblage phylogenetic or functional generalizations of species diversity.
Abstract: Hill numbers or the effective number of species are increasingly used to quantify species diversity of an assemblage. Hill numbers were recently extended to phylogenetic diversity, which incorporates species evolutionary history, as well as to functional diversity, which considers the differences among species traits. We review these extensions and integrate them into a framework of attribute diversity (the effective number of entities or total attribute value) based on Hill numbers of taxonomic entities (species), phylogenetic entities (branches of unit-length), or functional entities (species-pairs with unit-distance between species). This framework unifies ecologists' measures of species diversity, phylogenetic diversity, and distance-based functional diversity. It also provides a unified method of decomposing these diversities and constructing normalized taxonomic, phylogenetic, and functional similarity and differentiation measures, including N-assemblage phylogenetic or functional generalizations of...
521 citations
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...F o r p er so n al u se o n ly . different disciplines (Havrdra & Charvát 1967, Daróczy 1970, Patil & Taillie 1979, Tsallis 1988, Keylock 2005)....
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TL;DR: It is suggested that Renyi's diversity index family and Logarithmic dominance ordering are the most useful methods for diversity ordering of communities of all sizes.
Abstract: . The measurement of diversity, one of the most important concepts in present-day ecology, can be improved by methods of diversity ordering which have recently been developed. This ordering is achieved by a D(α) diversity index family. Indices of this family show varying sensitivities to the rare and abundant species as the scale parameter, α, changes. The aim of this paper is to review and assess 12 methods of diversity ordering and discuss their relationships in detail. Two of the methods are new to the ecological literature.
The diversity ordering methods are compared as to their effectiveness in graphically displaying the differences of community structure and demonstrating the (non-)comparability of communities. Small, medium and large data sets were used to evaluate the methods. A small artificial data set (five to seven species) and a large semi-artificial data set (31 — 141 species) are used in this paper.
The results suggest that Renyi's diversity index family and Logarithmic dominance ordering are the most useful methods for diversity ordering of communities of all sizes. Right-tailsum diversity ordering performs well for small communities.
457 citations
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01 Jan 1961
TL;DR: A warning device associated with arotatable body comprising means on the rotatable body for creating a magnetic field, a receiving coil on a relatively stationary member arranged such that a warning is given upon occurrence of a predetermined condition, such as pressure of a vehicle wheel deviating outside a predetermined limit.
Abstract: A warning device associated with a rotatable body comprising means on the rotatable body for creating a magnetic field, a receiving coil on a relatively stationary member arranged such that upon rotation of the rotatable body interaction with the magnetic field causes electrical pulses to be generated in the receiving coil and an electronic switching circuit operated by the pulses such that a warning is given upon occurrence of a predetermined condition, such as pressure of a vehicle wheel deviating outside a predetermined limit.
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