Book Review: Brentidae of the World (Coleoptera: Curculionoidea)

Book Review: SFORZI, A., AND L. BARTOLOZZI. 2004. Brentidae of the World (Coleoptera: Curculionoidea). Monografie XXXIX (39), Museo Regionale di Scienze Naturali, Torino, Italy. 976 pp., 225 figs. Hardcover. ISBN 88-86041-35-7. Price: € 50.00 + postage. May be ordered from the Museo Regionale di Scienze Regionali, via Giolitti, 10123 Torino, Italy. E-mail: [email protected]

Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters

We consider the asymptotic behavior of the incomplete gamma functions gamma(-a,-z) and Gamma(-a,-z) as a goes to infinity. Uniform expansions are needed to describe the transition area z~a in which case error functions are used as main approximants. We use integral representations of the incomplete gamma functions and derive a uniform equation by applying techniques used for the existing uniform expansions for gamma(a,z) and Gamma(a,z). The result is compared with Olver's uniform expansion for the generalized exponential integral. A numerical verification of the expansion is given in a final section

Numerical and Asymptotic Aspects of Parabolic Cylinder Functions

Several uniform asymptotics expansions of the Weber parabolic cylinder functions are considered, one group in terms of elementary functions, another group in terms of Airy functions. Starting point for the discussion are asymptotic expansions given earlier by F.W.J. Olver. Some of his results are modified to improve the asymptotic properties and to enlarge the intervals for using the expansions in numerical algorithms. Olver's results are obtained from the differential equation of the parabolic cylinder functions; we mention how modified expansions can be obtained from integral representations. Numerical tests are given for three expansions in terms of elementary functions. In this paper only real values of the parameters will be considered.Comment: 16 pages, 1 figur

Asymptotics of a 3F2{}_3F_2 polynomial associated with the Catalan-Larcombe-French sequence

The large $n$ behaviour of the hypergeometric polynomial \FFF{-n}{\sfrac12}{\sfrac12}{\sfrac12-n}{\sfrac12-n}{-1} is considered by using integral representations of this polynomial. This ${}_3F_2$ polynomial is associated with the Catalan-Larcombe-French sequence. Several other representations are mentioned, with references to the literature, and another asymptotic method is described by using a generating function of the sequence. The results are similar to those obtained by Clark (2004) who used a binomial sum for obtaining an asymptotic expansion.Comment: 10 pages, 1 figure. Accepted for publication in {\em Analysis and Applications

Remarks on Slater's asymptotic expansions of Kummer functions for large values of the a−a-parameter

In Slater's 1960 standard work on confluent hypergeometric functions, also called Kummer functions, a number of asymptotic expansions of these functions can be found. We summarize expansions derived from a differential equation for large values of the $a-$parameter. We show how similar expansions can be derived by using integral representations, and we observe discrepancies with Slater's expansions.Comment: To appear in Advances in Dynamical Systems and Applications. Proceedings of the International Conference on Differential Equations, Difference Equations and Special Functions, Patras, Greece, September 3 - 9, 2012, dedicated to the memory of Panayiotis D. Siafarikas. 13 page

Simple bounds for queueing systems with breakdowns

Computationally attractive and intuitively obvious simple bounds are proposed for finite service systems which are subject to random breakdowns. The services are assumed to be exponential. The up and down periods are allowed to be generally distributed. The bounds are based on product-form modifications and depend only on means. A formal proof is presented. This proof is of interest in itself. Numerical support indicates a potential usefulness for quick engineering and performance evaluation purposes

Simple and insensitive bounds for a grading and an overflow model

Simple and intuitively obvious lower and upper bounds are suggested for a specific grading and an overflow model. The bounds are based on product-type modifications and are insensitive. Numerical support indicates a potential usefulness for quick engineering purposes

Biological taxonomy and ontology development: scope and limitations

The prospects of integrating full-blown biological taxonomies into an ontological reasoning framework are reviewed. We contrast the common usage of a static 'snapshot' hierarchy in ontological representations of taxonomy with a more realistic situation that involves dynamic, piece-meal revisions of particular taxonomic groups and requires alignment with relevant preceding perspectives. Taxonomic practice is characterized by a range of phenomena that are orthogonal to the logical semantic background from which ontological entities and relationships originate, and therefore pose special challenges to ontological representation and reasoning. Among these phenomena are: (1) the notion that there is a single phylogenetic hierarchy in nature which taxonomy can only gradually approximate; (2) the evolvability of taxa which means that taxon-defining features may be lost in subordinate members or independently gained across multiple sections of the tree of life; (3) the hybrid approach of defining taxa both in reference to properties (intensional) and members (ostensive) which undermines the individual/class dichotomy sustaining conventional ontologies; (4) the idiosyncratic yet inferentially valuable usage of Linnaean ranks; (5) the indelible and semantically complex 250-year legacy of nomenclatural and taxonomic changes that characterizes the current system; (6) the insufficient taxonomic exploration of large portions of the tree of life; and the need to use a sophisticated terminology for aligning taxonomic entities in order to integrate both (7) single and (8) multiple hierarchies. We briefly such how such integration may proceed based on an initial expert alignment of concept relationship and subsequent use of first-order logic algorithms to maximize consistency, reveal implied relationships, and ultimately merge taxonomies.
 In light of the aforementioned obstacles, we suggest that research along the taxonomy/ontology interface should focus on either strictly nomenclatural entities or specialize in ontology-driven methods for producing alignments between multiple taxonomies. We furthermore suggest that the prospects of developing successful ontologies for taxonomy will largely depend on the ability of the taxonomic expert community to present their phylogenies and classifications in a way that is more compatible with ontological reasoning than concurrent practice. Minimally, this means (1) adopting rigorous standards for linking new core taxonomies to relevant peripheral taxonomies through comprehensive alignments so that their ontological/taxonomic connections are transparent; (2) using lineage-specific ontological standards for phenotype-based accounts of taxa while taking into account the phylogenetic contextuality of phenotypic descriptors; (3) presenting all nomenclatural and taxonomic novelties in an explicit, ontology-compatible format, including intensional and ostensive definitions; and (4) offering comprehensive intensional/ostensive alignments to entities in relevant preceding taxonomies

Taxonomy for Humans or Computers? Cognitive Pragmatics for Big Data

Criticism of big data has focused on showing that more is not necessarily better, in the sense that data may lose their value when taken out of context and aggregated together. The next step is to incorporate an awareness of pitfalls for aggregation into the design of data infrastructure and institutions. A common strategy minimizes aggregation errors by increasing the precision of our conventions for identifying and classifying data. As a counterpoint, we argue that there are pragmatic trade-offs between precision and ambiguity that are key to designing effective solutions for generating big data about biodiversity. We focus on the importance of theory-dependence as a source of ambiguity in taxonomic nomenclature and hence a persistent challenge for implementing a single, long-term solution to storing and accessing meaningful sets of biological specimens. We argue that ambiguity does have a positive role to play in scientific progress as a tool for efficiently symbolizing multiple aspects of taxa and mediating between conflicting hypotheses about their nature. Pursuing a deeper understanding of the trade-offs and synthesis of precision and ambiguity as virtues of scientific language and communication systems then offers a productive next step for realizing sound, big biodiversity data services

The tail of the maximum of Brownian motion minus a parabola

We analyze the tail behavior of the maximum N of Brownian motion minus a parabola and give an asymptotic expansion for P(N>x) as x tends to infinity. This extends a first order result on the tail behavior, which can be deduced from Huesler and Piterbarg (1999). We also point out the relation between certain results in Groeneboom (2010) and Janson, Louchard and Martin-L\"of (2010).Comment: 12 pages, submitted to the Electronic Communications in Probabilit