Holistic projection of initial conditions onto a finite difference approximation

Modern dynamical systems theory has previously had little to say about finite difference and finite element approximations of partial differential equations (Archilla, 1998). However, recently I have shown one way that centre manifold theory may be used to create and support the spatial discretisation of \pde{}s such as Burgers' equation (Roberts, 1998a) and the Kuramoto-Sivashinsky equation (MacKenzie, 2000). In this paper the geometric view of a centre manifold is used to provide correct initial conditions for numerical discretisations (Roberts, 1997). The derived projection of initial conditions follows from the physical processes expressed in the PDEs and so is appropriately conservative. This rational approach increases the accuracy of forecasts made with finite difference models.Comment: 8 pages, LaTe

Huge automatically extracted training sets for multilingual Word Sense Disambiguation

We release to the community six large-scale sense-annotated datasets in multiple language to pave the way for supervised multilingual Word Sense Disambiguation. Our datasets cover all the nouns in the English WordNet and their translations in other languages for a total of millions of sense-tagged sentences. Experiments prove that these corpora can be effectively used as training sets for supervised WSD systems, surpassing the state of the art for low- resourced languages and providing competitive results for English, where manually annotated training sets are accessible. The data is available at trainomatic. org

Semi-active tuned mass damper building systems: Design

Passive and semi-active tuned mass damper (PTMD and SATMD) building systems are proposed to mitigate structural response due to seismic loads. The structure's upper portion self plays a role either as a tuned mass passive damper or a semi-active resetable device is adopted as a control feature for the PTMD, creating a SATMD system. Two-degree-of-freedom analytical studies are employed to design the prototype structural system, specify its element characteristics and effectiveness for seismic responses, including defining the resetable device dynamics. The optimal parameters are derived for the large mass ratio by numerical analysis. For the SATMD building system the stiffness of the resetable device design is combined with rubber bearing stiffness. From parametric studies, effective practical control schemes can be derived for the SATMD system. To verify the principal efficacy of the conceptual system, the controlled system response is compared with the response spectrum of the earthquake suites used. The control ability of the SATMD scheme is compared with that of an uncontrolled (No TMD) and an ideal PTMD building systems for multi-level seismic intensity. Copyright © 2009 John Wiley & Sons, Lt

A SUSY A4 model for fermion masses and mixings

We study a supersymmetric extension of the Standard Model based on discrete A4xZ3xZ4 flavor symmetry. We obtain quark mixing angles as well as a realistic fermion mass spectrum and we predict tribimaximal leptonic mixing by a spontaneous breaking of A4. The top quark Yukawa interaction is present at the renormalizable level in the superpotential while all the other Yukawa interactions arise only at higher orders. We study the Higgs potential and show that it can potentially solve the so called vacuum alignment problem. The leading order predictions are not spoiled by subleading corrections.Comment: version accepted in JHEP, Z3xZ2 changed in Z3xZ4, typos in table corrected, references adde

The inertial dynamics of thin film flow of non-Newtonian fluids

Consider the flow of a thin layer of non-Newtonian fluid over a solid surface. I model the case of a viscosity that depends nonlinearly on the shear-rate; power law fluids are an important example, but the analysis here is for general nonlinear dependence. The modelling allows for large changes in film thickness provided the changes occur over a large enough lateral length scale. Modifying the surface boundary condition for tangential stress forms an accessible base for the analysis where flow with constant shear is a neutral critical mode, in addition to a mode representing conservation of fluid. Perturbatively removing the modification then constructs a model for the coupled dynamics of the fluid depth and the lateral momentum. For example, the results model the dynamics of gravity currents of non-Newtonian fluids even when the flow is not very slow

Initial Conditions for Models of Dynamical Systems

The long-time behaviour of many dynamical systems may be effectively predicted by a low-dimensional model that describes the evolution of a reduced set of variables. We consider the question of how to equip such a low-dimensional model with appropriate initial conditions, so that it faithfully reproduces the long-term behaviour of the original high-dimensional dynamical system. Our method involves putting the dynamical system into normal form, which not only generates the low-dimensional model, but also provides the correct initial conditions for the model. We illustrate the method with several examples. Keywords: normal form, isochrons, initialisation, centre manifoldComment: 24 pages in standard LaTeX, 66K, no figure

Effectively attractive Bose-Einstein condensates in a rotating toroidal trap

We examine an effectively attractive quasi-one-dimensional Bose-Einstein condensate of atoms confined in a rotating toroidal trap, as the magnitude of the coupling constant and the rotational frequency are varied. Using both a variational mean-field approach, as well as a diagonalization technique, we identify the phase diagram between a uniform and a localized state and we describe the system in the two phases.Comment: 4 pages, 4 ps figures, RevTe

Vav Proteins in Development of the Brain: A Potential Relationship to the Pathogenesis of Congenital Zika Syndrome?

Zika virus (ZIKV) infection during pregnancy can result in a significant impact on the brain and eye of the developing fetus, termed congenital zika syndrome (CZS). At a morphological level, the main serious presentations of CZS are microcephaly and retinal scarring. At a cellular level, many cell types of the brain may be involved, but primarily neuronal progenitor cells (NPC) and developing neurons. Vav proteins have guanine exchange activity in converting GDP to GTP on proteins such as Rac1, Cdc42 and RhoA to stimulate intracellular signaling pathways. These signaling pathways are known to play important roles in maintaining the polarity and self-renewal of NPC pools by coordinating the formation of adherens junctions with cytoskeletal rearrangements. In developing neurons, these same pathways are adopted to control the formation and growth of neurites and mediate axonal guidance and targeting in the brain and retina. This review describes the role of Vavs in these processes and highlights the points of potential ZIKV interaction, such as (i) the binding and entry of ZIKV in cells via TAM receptors, which may activate Vav/Rac/RhoA signaling; (ii) the functional convergence of ZIKV NS2A with Vav in modulating adherens junctions; (iii) ZIKV NS4A/4B protein effects on PI3K/AKT in a regulatory loop via PPI3 to influence Vav/Rac1 signaling in neurite outgrowth; and (iv) the induction of SOCS1 and USP9X following ZIKV infection to regulate Vav protein degradation or activation, respectively, and impact Vav/Rac/RhoA signaling in NPC and neurons. Experiments to define these interactions will further our understanding of the molecular basis of CZS and potentially other developmental disorders stemming from in utero infections. Additionally, Vav/Rac/RhoA signaling pathways may present tractable targets for therapeutic intervention or molecular rationale for disease severity in CZS.Aidan J. Norbury, Lachlan A. Jolly, Luke P. Kris, and Jillian M. Car

Cauliflower mosaic virus protein P6 inhibits signaling responses to salicylic acid and regulates innate immunity

Cauliflower mosaic virus (CaMV) encodes a multifunctional protein P6 that is required for translation of the 35S RNA and also acts as a suppressor of RNA silencing. Here we demonstrate that P6 additionally acts as a pathogenicity effector of an unique and novel type, modifying NPR1 (a key regulator of salicylic acid (SA)- and jasmonic acid (JA)-dependent signaling) and inhibiting SA-dependent defence responses We find that that transgene-mediated expression of P6 in Arabidopsis and transient expression in Nicotiana benthamiana has profound effects on defence signaling, suppressing expression of representative SA-responsive genes and increasing expression of representative JA-responsive genes. Relative to wild-type Arabidopsis P6-expressing transgenics had greatly reduced expression of PR-1 following SA-treatment, infection by CaMV or inoculation with an avirulent bacterial pathogen Pseudomonas syringae pv tomato (Pst). Similarly transient expression in Nicotiana benthamiana of P6 (including a mutant form defective in translational transactivation activity) suppressed PR-1a transcript accumulation in response to Agrobacterium infiltration and following SA-treatment. As well as suppressing the expression of representative SA-regulated genes, P6-transgenic Arabidopsis showed greatly enhanced susceptibility to both virulent and avirulent Pst (titres elevated 10 to 30-fold compared to non-transgenic controls) but reduced susceptibility to the necrotrophic fungus Botrytis cinerea. Necrosis following SA-treatment or inoculation with avirulent Pst was reduced and delayed in P6-transgenics. NPR1 an important regulator of SA/JA crosstalk, was more highly expressed in the presence of P6 and introduction of the P6 transgene into a transgenic line expressing an NPR1:GFP fusion resulted in greatly increased fluorescence in nuclei even in the absence of SA. Thus in the presence of P6 an inactive form of NPR1 is mislocalized in the nucleus even in uninduced plants. These results demonstrate that P6 is a new type of pathogenicity effector protein that enhances susceptibility to biotrophic pathogens by suppressing SA- but enhancing JA-signaling responses