The structure of the class of maximum tsallis-havrda-chavat entropy copulas

A maximum entropy copula is the copula associated with the joint distribution, with prescribed marginal distributions on [0, 1], which maximizes the Tsallis-Havrda-Chavat entropy with q = 2. We find necessary and sufficient conditions for each maximum entropy copula to be a copula in the class introduced in Rodriguez-Lallena and Ubeda-Flores (2004), and we also show that each copula in that class is a maximum entropy copula.A maximum entropy copula is the copula associated with the joint distribution, with prescribed marginal distributions on [0, 1], which maximizes the Tsallis-Havrda-Chavat entropy with q = 2. We find necessary and sufficient conditions for each maximum entropy copula to be a copula in the class introduced in Rodriguez-Lallena and Ubeda-Flores (2004), and we also show that each copula in that class is a maximum entropy copula.18

Dependence in probabilistic modeling, Dempster-Shafer theory, and probability bounds analysis.

This report summarizes methods to incorporate information (or lack of information) about inter-variable dependence into risk assessments that use Dempster-Shafer theory or probability bounds analysis to address epistemic and aleatory uncertainty. The report reviews techniques for simulating correlated variates for a given correlation measure and dependence model, computation of bounds on distribution functions under a specified dependence model, formulation of parametric and empirical dependence models, and bounding approaches that can be used when information about the intervariable dependence is incomplete. The report also reviews several of the most pervasive and dangerous myths among risk analysts about dependence in probabilistic models

Ευρετικές προσεγγίσεις του μοναδιάστατου προβλήματος πακετοποίησης

Article 59.1, of the International Code of Nomenclature for Algae, Fungi, and Plants (ICN; Melbourne Code), which addresses the nomenclature of pleomorphic fungi, became effective from 30 July 2011. Since that date, each fungal species can have one nomenclaturally correct name in a particular classification. All other previously used names for this species will be considered as synonyms. The older generic epithet takes priority over the younger name. Any widely used younger names proposed for use, must comply with Art. 57.2 and their usage should be approved by the Nomenclature Committee for Fungi (NCF). In this paper, we list all genera currently accepted by us in Dothideomycetes (belonging to 23 orders and 110 families), including pleomorphic and non-pleomorphic genera. In the case of pleomorphic genera, we follow the rulings of the current ICN and propose single generic names for future usage. The taxonomic placements of 1261 genera are listed as an outline. Protected names and suppressed names for 34 pleomorphic genera are listed separately. Notes and justifications are provided for possible proposed names after the list of genera. Notes are also provided on recent advances in our understanding of asexual and sexual morph linkages in Dothideomycetes. A phylogenetic tree based on four gene analyses supported 23 orders and 75 families, while 35 families still lack molecular data

Nuggets of number theory: a visual approach

Nuggets of Number Theory will attract fans of visual thinking, number theory, and surprising connections. This book contains hundreds of visual explanations of results from elementary number theory. Figurate numbers and Pythagorean triples feature prominently, of course, but there are also proofs of Fermat's Little and Wilson's Theorems. Fibonacci and perfect numbers, Pell's equation, and continued fractions all find visual representation in this charming collection. It will be a rich source of visual inspiration for anyone teaching, or learning, number theory and will provide endless pleasure to those interested in looking at number theory with new eyes. Author Roger Nelsen is a long-time contributor of "Proofs Without Words" in the MAA's Mathematics Magazine and College Mathematics Journal. This is his twelfth book with MAA Press