A Dual Measure of Uncertainty: The Deng Extropy

The extropy has recently been introduced as the dual concept of entropy. Moreover, in the context of the Dempster–Shafer evidence theory, Deng studied a new measure of discrimination, named the Deng entropy. In this paper, we define the Deng extropy and study its relation with Deng entropy, and examples are proposed in order to compare them. The behaviour of Deng extropy is studied under changes of focal elements. A characterization result is given for the maximum Deng extropy and, finally, a numerical example in pattern recognition is discussed in order to highlight the relevance of the new measure

The construction of self in relationships: narratives and references to mental states during picture-book reading interactions between mothers and children

Previous studies showed that mothers vary in the way in which they discuss past experiences with their children, since they can exhibit narrative (elaborative) or paradigmatic (repetitive) styles to different extents. Given this background, the aim of the present study was to analyze differences in the mothers’ use of narrative styles and mental state language (MSL), as a function of children’s age and gender. Thirty dyads consisting of mothers and their 4- to 6-year-old children were observed during a picture-book reading interaction. Maternal utterances were coded according to the categories described by Tessler and Nelson (1994), classifying each mother as Narrative or Paradigmatic. Eight categories of MSL were analyzed: perceptual, emotional (positive and negative), volitional, cognitive, communicative, and moral. The results confirmed the existence of the two maternal styles observed in the earlier studies. Importantly, we found that the mothers of younger children were more narrative than paradigmatic, whereas the opposite pattern occurred for the mothers of older children (they were more paradigmatic than narrative). As concerns MSL, the results indicated that the use of communicative terms was significantly more frequent for narrative than for paradigmatic mothers, and decreased linearly with children’s age. Lastly, the mothers of younger children referred their MSL more frequently to the book characters than to themselves or to the child. Taken together, these results support the idea that mothers adapt their narrative styles and MSL input to the growing abilities of their children, therefore contributing to the development of social understanding

Overexpression of PREP-1 in F9 Teratocarcinoma Cells Leads to a Functionally Relevant Increase of PBX-2 by Preventing Its Degradation

To bind DNA and to be retained in the nucleus, PBX proteins must form heterodimeric complexes with members of the MEINOX family. Therefore the balance between PBX and MEINOX must be an important regulatory feature. We show that overexpression of PREP-1 influences the level of PBX-2 protein maintaining the PREP-1-PBX balance. This effect has important functional consequences. F9 teratocarcinoma cells stably transfected with PREP-1 had an increased DNA binding activity to a PREP-PBX-responsive element. Because PREP-1 binds DNA efficiently only when dimerized to PBX, the increased DNA binding activity suggests that the level of PBX might also have increased. Indeed PREP-1-overexpressing cells had a higher level of PBX-2 and PBX-1b proteins. PBX-2 increase did not depend on increased mRNA level or a higher rate of translation but rather because of a protein stabilization process. Indeed, PBX-2 level drastically decreased after 3 h of cycloheximide treatment in control but not in PREP-1-overexpressing cells and the proteasome inhibitor MG132 prevented PBX-2 decay in control cells. Hence, dimerization with PREP-1 appears to decrease proteasomal degradation of PBX-2. Retinoic acid induces differentiation of F9 teratocarcinoma cells with a cascade synthesis of HOX proteins. In PREP-1-overexpressing cells, HOXb1 induction was more sustained (3 days versus 1 day) and the induced level of MEIS-1b, another TALE (three amino acid loop extension) protein involved in embryonal development, was higher. Thus an increase in PREP-1 leads to changes in the fate-determining HOXb1 and has therefore important functional consequences

On Cumulative Entropies in Terms of Moments of Order Statistics

In this paper, relations between some kinds of cumulative entropies and moments of order statistics are established. By using some characterizations and the symmetry of a non-negative and absolutely continuous random variable $X$, lower and upper bounds for entropies are obtained and illustrative examples are given. By the relations with the moments of order statistics, a method is shown to compute an estimate of cumulative entropies and an application to testing whether data are exponentially distributed is outlined

On cumulative entropies in terms of moments of order statistics

In this paper relations among some kinds of cumulative entropies and moments of order statistics are presented. By using some characterizations and the symmetry of a non negative and absolutely continuous random variable X, lower and upper bounds for entropies are obtained and examples are given.Comment: 13 pages, 1 tabl

On Tsallis extropy with an application to pattern recognition

Recently, a new measure of information called extropy has been introduced by Lad, Sanfilippo and Agr\`o as the dual version of Shannon entropy. In the literature, Tsallis introduced a measure for a discrete random variable, named Tsallis entropy, as a generalization of Boltzmann-Gibbs statistics. In this work, a new measure of discrimination, called Tsallis extropy, is introduced and some of its properties are then discussed. The relation between Tsallis extropy and entropy is given and some bounds are also presented. Finally, an application of this extropy to pattern recognition is demonstrated

On generalized reversed aging intensity functions

The reversed aging intensity function is defined as the ratio of the instantaneous reversed hazard rate to the baseline value of the reversed hazard rate. It analyzes the aging property quantitatively, the higher the reversed aging intensity, the weaker the tendency of aging. In this paper, a family of generalized reversed aging intensity functions is introduced and studied. Those functions depend on a real parameter. If the parameter is positive they characterize uniquely the distribution functions of univariate positive absolutely continuous random variables, in the opposite case they characterize families of distributions. Furthermore, the generalized reversed aging intensity orders are defined and studied. Finally, several numerical examples are given

Direct transition from quantum escape to phase diffusion regime in YBaCuO biepitaxial Josephson Junctions

Dissipation encodes interaction of a quantum system with the environment and regulates the activation regimes of a Brownian particle. We have engineered grain boundary biepitaxial YBaCuO junctions to drive a direct transition from quantum activated running state to phase diffusion regime. The cross-over to the quantum regime is tuned by the magnetic field and dissipation is encoded in a fully consistent set of junction parameters. To unravel phase dynamics in moderately damped systems is of general interest for advances in the comprehension of retrapping phenomena and in view of quantum hybrid technology