Regularity at infinity of real mappings and a Morse-Sard theorem

We prove a new Morse-Sard-type theorem for the asymptotic critical values of semi-algebraic mappings and a new fibration theorem at infinity for C-2 mappings. We show the equivalence of three different types of regularity conditions which have been used in the literature in order to control the asymptotic behaviour of mappings. The central role of our picture is played by the p-regularity and its bridge toward the rho-regularity which implies topological triviality at infinity.

Biogeographic and diversification patterns of Neotropical Troidini butterflies (Papilionidae) support a museum model of diversity dynamics for Amazonia

Background: The temporal and geographical diversification of Neotropical insects remains poorly understood because of the complex changes in geological and climatic conditions that occurred during the Cenozoic. To better understand extant patterns in Neotropical biodiversity, we investigated the evolutionary history of three Neotropical swallowtail Troidini genera (Papilionidae). First, DNA-based species delimitation analyses were conducted to assess species boundaries within Neotropical Troidini using an enlarged fragment of the standard barcode gene. Molecularly delineated species were then used to infer a time-calibrated species-level phylogeny based on a three-gene dataset and Bayesian dating analyses. The corresponding chronogram was used to explore their temporal and geographical diversification through distinct likelihood-based methods. Results: The phylogeny for Neotropical Troidini was well resolved and strongly supported. Molecular dating and biogeographic analyses indicate that the extant lineages of Neotropical Troidini have a late Eocene (33-42 Ma) origin in North America. Two independent lineages (Battus and Euryades + Parides) reached South America via the GAARlandia temporary connection, and later became extinct in North America. They only began substantive diversification during the early Miocene in Amazonia. Macroevolutionary analysis supports the "museum model" of diversification, rather than Pleistocene refugia, as the best explanation for the diversification of these lineages. Conclusions: This study demonstrates that: (i) current Neotropical biodiversity may have originated ex situ; (ii) the GAARlandia bridge was important in facilitating invasions of South America; (iii) colonization of Amazonia initiated the crown diversification of these swallowtails; and (iv) Amazonia is not only a species-rich region but also acted as a sanctuary for the dynamics of this diversity. In particular, Amazonia probably allowed the persistence of old lineages and contributed to the steady accumulation of diversity over time with constant net diversification rates, a result that contrasts with previous studies on other South American butterflies.

Phylogenetic relationships of rock-wallabies, Petrogale (Marsupialia: Macropodidae) and their biogeographic history within Australia

The rock-wallaby genus Petrogale comprises a group of habitat-specialist macropodids endemic to Australia. Their restriction to rocky outcrops, with infrequent interpopulation dispersal, has been suggested as the cause of their recent and rapid diversification. Molecular phylogenetic relationships within and among species of Petrogale were analysed using mitochondrial (cytochrome oxidase c subunit 1, cytochrome b. NADH dehydrogenase subunit 2) and nuclear (omega-globin intron, breast and ovarian cancer susceptibility gene) sequence data with representatives that encompassed the morphological and chromosomal variation within the genus, including for the first time both Petrogale concinna and Petrogale purpureicollis. Four distinct lineages were identified, (1) the brachyotis group, (2) Petrogale persephone, (3) Petrogale xanthopus and (4) the lateralis-penicillata group. Three of these lineages include taxa with the ancestral karyotype (2n = 22). Paraphyletic relationships within the brachyotis group indicate the need for a focused phylogeographic study. There was support for P. purpureicollis being reinstated as a full species and P. concinna being placed within Petrogale rather than in the monotypic genus Peradorcas. Bayesian analyses of divergence times suggest that episodes of diversification commenced in the late Miocene-Pliocene and continued throughout the Pleistocene. Ancestral state reconstructions suggest that Petrogale originated in a mesic environment and dispersed into more arid environments, events that correlate with the timing of radiations in other arid zone vertebrate taxa across Australia. Crown Copyright (C) 2011 Published by Elsevier Inc. All rights reserved.

MATHEMATICAL MODELS AND POLYHEDRAL STUDIES FOR INTEGRAL SHEET METAL DESIGN

We deal with the optimization of the production of branched sheet metal products. New forming techniques for sheet metal give rise to a wide variety of possible profiles and possible ways of production. In particular, we show how the problem of producing a given profile geometry can be modeled as a discrete optimization problem. We provide a theoretical analysis of the model in order to improve its solution time. In this context we give the complete convex hull description of some substructures of the underlying polyhedron. Moreover, we introduce a new class of facet-defining inequalities that represent connectivity constraints for the profile and show how these inequalities can be separated in polynomial time. Finally, we present numerical results for various test instances, both real-world and academic examples.

A control and automation system for wave basins

This paper presents the new active absorption wave basin, named Hydrodynamic Calibrator (HC), constructed at the University of São Paulo (USP), in the Laboratory facilities of the Numerical Offshore Tank (TPN). The square (14 m 14 m) tank is able to generate and absorb waves from 0.5 Hz to 2.0 Hz, by means of 148 active hinged flap wave makers. An independent mechanical system drives each flap by means of a 1HP servo-motor and a ball-screw based transmission system. A customized ultrasonic wave probe is installed in each flap, and is responsible for measuring wave elevation in the flap. A complex automation architecture was implemented, with three Programmable Logic Computers (PLCs), and a low-level software is responsible for all the interlocks and maintenance functions of the tank. Furthermore, all the control algorithms for the generation and absorption are implemented using higher level software (MATLAB /Simulink block diagrams). These algorithms calculate the motions of the wave makers both to generate and absorb the required wave field by taking into account the layout of the flaps and the limits of wave generation. The experimental transfer function that relates the flap amplitude to the wave elevation amplitude is used for the calculation of the motion of each flap. This paper describes the main features of the tank, followed by a detailed presentation of the whole automation system. It includes the measuring devices, signal conditioning, PLC and network architecture, real-time and synchronizing software and motor control loop. Finally, a validation of the whole automation system is presented, by means of the experimental analysis of the transfer function of the waves generated and the calculation of all the delays introduced by the automation system.