Jumping plant-lice of the Paurocephalinae (Insecta, Hemiptera, Psylloidea): systematics and phylogeny

Much confusion exists with respect to the content and definition of the psyUid subfamily Paurocephalinae. Based on a cladistic analysis of 22 morphological characters (16 adult and 6 larval), the subfamily is redefined to comprise the following five valid genera: Aphorma (3 species), Camarotoscena (12 valid species, with 1 new synonymy), DiC/idophlebia (= Aconopsylla, Haplaphalara, Paraphalaroida, Sinuonemopsylla and Woldaia; 24 species), Paurocephala (52 species) and Syntomoza (= Anomoterga and Homalocephata; 7 species). The tribe Diclidophlebiini is synonymised with the subfamily Paurocephalinae. The seven new generic synonymies produce 25 new species combinations. A key to genera for adults and fifth instar larvae is presented. In their revised definitions the genera exhibit relatively restricted distributions and host ranges: Aphorma: Palaearctic, Oriental - Ranunculaceae; Camarotoscena: Palaearctic - Salicaceae; Diclidophtebia: pantropical - Tiliaceae, Malvaceae, Sterculiaceae, Melastomataceae, Rhamnaceae, Ulmaceae and Euphorbiaceae; Paurocephala: Old World tropics - Moraceae, Urticaceae. Ulmaceae (all Urticales), Malvaceae. Sterculiaceae (all Malvales) and Clusiaceae (rheales); Syntomoza: Oriental, Afrotropical, Palaearctic - Flacourtiaceae, Salicaceae. The following taxa which have been referred to the Paurocephalinae are transferred to other taxa: Atmetocranium to the Calophyidae and Primascena to the Aphalaroidinae; Pseudaphorma is symonymised with Aphatara, and P. astigma with A. polygoni; the position of Strophingia is confirmed in the Strophingiinae.peer-reviewe

On the reproducing kernel Hilbert spaces associated with the fractional and bi-fractional Brownian motions

We present decompositions of various positive kernels as integrals or sums of positive kernels. Within this framework we study the reproducing kernel Hilbert spaces associated with the fractional and bi-fractional Brownian motions. As a tool, we define a new function of two complex variables, which is a natural generalization of the classical Gamma function for the setting we conside

CLT for an iterated integral with respect to fBm with H > 1/2

We construct an iterated stochastic integral with fractional Brownian motion with H > 1/2. The first integrand is a deterministic function, and each successive integral is with respect to an independent fBm. We show that this symmetric stochastic integral is equal to the Malliavin divergence integral. By a version of the Fourth Moment theorem of Nualart and Peccati, we show that a family of such integrals converges in distribution to a scaled Brownian motion. An application is an approximation to the windings for a planar fBm, previously studied by Baudoin and Nualart

Graph-RAT: Combining data sources in music recommendation systems

The complexity of music recommendation systems has increased rapidly in recent years, drawing upon different sources of information: content analysis, web-mining, social tagging, etc. Unfortunately, the tools to scientifically evaluate such integrated systems are not readily available; nor are the base algorithms available. This article describes Graph-RAT (Graph-based Relational Analysis Toolkit), an open source toolkit that provides a framework for developing and evaluating novel hybrid systems. While this toolkit is designed for music recommendation, it has applications outside its discipline as well. An experiment—indicative of the sort of procedure that can be configured using the toolkit—is provided to illustrate its usefulness

Polynomial integration on regions defined by a triangle and a conic

We present an efficient solution to the following problem, of relevance in a numerical optimization scheme: calculation of integrals of the type $$\iint_{T \cap \{f\ge0\}} \phi_1\phi_2 \, dx\,dy$$ for quadratic polynomials $f,\phi_1,\phi_2$ on a plane triangle $T$. The naive approach would involve consideration of the many possible shapes of $T\cap\{f\geq0\}$ (possibly after a convenient transformation) and parameterizing its border, in order to integrate the variables separately. Our solution involves partitioning the triangle into smaller triangles on which integration is much simpler.Comment: 8 pages, accepted by ISSAC 201