Evolution PDEs and augmented eigenfunctions. half line.

The solution of an initial-boundary value problem for a linear evolution partial differential equation posed on the half-line can be represented in terms of an integral in the complex (spectral) plane. This representation is obtained by the unified transform introduced by Fokas in the 90's. On the other hand, it is known that many initial-boundary value problems can be solved via a classical transform pair, constructed via the spectral analysis of the associated spatial operator. For example, the Dirichlet problem for the heat equation can be solved by applying the Fourier sine transform pair. However, for many other initial-boundary value problems there is no suitable transform pair in the classical literature. Here we pose and answer two related questions: Given any well-posed initial-boundary value problem, does there exist a (non-classical) transform pair suitable for solving that problem? If so, can this transform pair be constructed via the spectral analysis of a differential operator? The answer to both of these questions is positive and given in terms of augmented eigenfunctions, a novel class of spectral functionals. These are eigenfunctions of a suitable differential operator in a certain generalised sense, they provide an effective spectral representation of the operator, and are associated with a transform pair suitable to solve the given initial-boundary value problem.

Communicating thematic data quality with web map services

Geospatial information of many kinds, from topographic maps to scientific data, is increasingly being made available through web mapping services. These allow georeferenced map images to be served from data stores and displayed in websites and geographic information systems, where they can be integrated with other geographic information. The Open Geospatial Consortium’s Web Map Service (WMS) standard has been widely adopted in diverse communities for sharing data in this way. However, current services typically provide little or no information about the quality or accuracy of the data they serve. In this paper we will describe the design and implementation of a new “quality-enabled” profile of WMS, which we call “WMS-Q”. This describes how information about data quality can be transmitted to the user through WMS. Such information can exist at many levels, from entire datasets to individual measurements, and includes the many different ways in which data uncertainty can be expressed. We also describe proposed extensions to the Symbology Encoding specification, which include provision for visualizing uncertainty in raster data in a number of different ways, including contours, shading and bivariate colour maps. We shall also describe new open-source implementations of the new specifications, which include both clients and servers.

Regulation of the ERK subgroup of MAP kinase cascades through G protein-coupled receptors.

The extracellularly-responsive kinase (ERK) subfamily of mitogen-activated protein kinases (MAPKs) has been implicated in the regulation of cell growth and differentiation. Activation of ERKs involves a two-step protein kinase cascade lying upstream from ERK, in which the Raf family are the MAPK kinase kinases and the MEK1/MEK2 isoforms are the MAPK kinases. The linear sequence of Raf --> MEK --> ERK constitutes the ERK cascade. Although the ERK cascade is activated through growth factor-regulated receptor protein tyrosine kinases, they are also modulated through G protein-coupled receptors (GPCRs). All four G protein subfamilies (Gq/11 Gi/o, Gs and G12/13) influence the activation state of ERKs. In this review, we describe the ERK cascade and characteristics of its activation through GPCRs. We also discuss the identity of the intervening steps that may couple agonist binding at GPCRs to activation of the ERK cascade.

Putting the Canal on the map: Panamanian agenda-setting and the 1973 Security Council meetings

In the early 1970s, Panama’s negotiations with the United States over the status of the Panama Canal ground to a standstill. General Omar Torrijos had rejected treaties left unratified by previous governments only to receive a less generous offer from the Nixon administration. Realizing that the talks were being ignored in Washington, the Panamanian government worked to internationalize the previously bilateral issue, creating and exploiting a high-profile forum: Extraordinary meetings of the UN Security Council in March 1973 held in Panama City. In those meetings, Panama isolated the United States in order to raise the issue’s profile and amplify the costs of leaving the matter unsettled. Using underutilized Panamanian sources, this article examines that meeting, the succeeding progress, and the effect of this early stage on the final negotiations several years later. The case also illustrates how, during the unsettled international environment of the 1970s, a small state utilized international organizations to obtain attention and support for its most important cause.

Moho map of South America from receiver functions and surface waves

We estimate crustal structure and thickness of South America north of roughly 40 degrees S. To this end, we analyzed receiver functions from 20 relatively new temporary broadband seismic stations deployed across eastern Brazil. In the analysis we include teleseismic and some regional events, particularly for stations that recorded few suitable earthquakes. We first estimate crustal thickness and average Poisson`s ratio using two different stacking methods. We then combine the new crustal constraints with results from previous receiver function studies. To interpolate the crustal thickness between the station locations, we jointly invert these Moho point constraints, Rayleigh wave group velocities, and regional S and Rayleigh waveforms for a continuous map of Moho depth. The new tomographic Moho map suggests that Moho depth and Moho relief vary slightly with age within the Precambrian crust. Whether or not a positive correlation between crustal thickness and geologic age is derived from the pre-interpolation point constraints depends strongly on the selected subset of receiver functions. This implies that using only pre-interpolation point constraints (receiver functions) inadequately samples the spatial variation in geologic age. The new Moho map also reveals an anomalously deep Moho beneath the oldest core of the Amazonian Craton.

O-GlcNAcylation Contributes to Augmented Vascular Reactivity Induced by Endothelin 1

O-GlcNAcylation augments vascular contractile responses, and O-GlcNAc-proteins are increased in the vasculature of deoxycorticosterone-acetate salt rats. Because endothelin 1 (ET-1) plays a major role in vascular dysfunction associated with salt-sensitive forms of hypertension, we hypothesized that ET-1-induced changes in vascular contractile responses are mediated by O-GlcNAc modification of proteins. Incubation of rat aortas with ET-1 (0.1 mu mol/L) produced a time-dependent increase in O-GlcNAc levels and decreased expression of O-GlcNAc transferase and beta-N-acetylglucosaminidase, key enzymes in the O-GlcNAcylation process. Overnight treatment of aortas with ET-1 increased phenylephrine vasoconstriction (maximal effect [in moles]: 19 +/- 5 versus 11 +/- 2 vehicle). ET-1 effects were not observed when vessels were previously instilled with anti-O-GlcNAc transferase antibody or after incubation with an O-GlcNAc transferase inhibitor (3-[2-adamantanylethyl]-2-[{4-chlorophenyl}azamethylene]-4-oxo-1,3-thiazaperhyd roine-6-carboxylic acid; 100 mu mol/L). Aortas from deoxycorticosterone-acetate salt rats, which exhibit increased prepro-ET-1, displayed increased contractions to phenylephrine and augmented levels of O-GlcNAc proteins. Treatment of deoxycorticosterone-acetate salt rats with an endothelin A antagonist abrogated augmented vascular levels of O-GlcNAc and prevented increased phenylephrine vasoconstriction. Aortas from rats chronically infused with low doses of ET-1 (2 pmol/kg per minute) exhibited increased O-GlcNAc proteins and enhanced phenylephrine responses (maximal effect [in moles]: 18 +/- 2 versus 10 +/- 3 control). These changes are similar to those induced by O-(2-acetamido-2-deoxy-D-glucopyranosylidene) amino-N-phenylcarbamate, an inhibitor of beta-N-acetylglucosaminidase. Systolic blood pressure (in millimeters of mercury) was similar between control and ET-1-infused rats (117 +/- 3 versus 123 +/- 4 mm Hg; respectively). We conclude that ET-1 indeed augments O-GlcNAc levels and that this modification contributes to the vascular changes induced by this peptide. Increased vascular O-GlcNAcylation by ET-1 may represent a mechanism for hypertension-associated vascular dysfunction or other pathological conditions associated with increased levels of ET-1. (Hypertension. 2010; 55: 180-188.)

p38 alpha MAP Kinase Controls IL-17 Synthesis in Vogt-Koyanagi-Harada Syndrome and Experimental Autoimmune Uveitis

PURPOSE. Interleukin (IL)-17, which is responsible for the initial influx of leukocytes into the target tissue, was recently described as the main cytokine involved in autoimmune diseases. Vogt-Koyanagi-Harada (VKH) syndrome is a significant cause of noninfectious blindness in the world. Herein the authors aimed at unraveling the involvement of IL-17 in VKH and in experimental autoimmune uveitis, focusing on the signaling pathways involved in IL-17 synthesis. METHODS. Mice were immunized with 161-180 peptide and pertussis toxin. Draining lymph node cells, harvested 21 days after immunization, were cultured in the presence or absence of p38 alpha mitogen-activated protein kinase (MAPK) inhibitor (SB203580) and assayed for cytokine production and quantification of CD4(+)IL-17(+) cells. Mice received intraocular injections of SB203580, and disease severity was evaluated by histologic examination of the enucleated eyes at day 21. CD4(+) lymphocytes from MSK-1/2-deficient mice, human CD4(+) cells silenced with MSK1 siRNA, or peripheral blood mononuclear cells (PBMCs) from VKH patients were cultured in the presence or absence of p38 alpha MAPK inhibitor and then assayed for IL-17, IFN-gamma, and IL-4 production. RESULTS. The inhibition of p38 alpha MAPK fully blocked the synthesis of IL-17 by PBMCs from VKH patients and lymphocytes from EAU mice. The absence of the msk1/2 gene resulted in failure to produce IL-17 by murine and human lymphocytes. Interestingly, intraocular injections of SB203580 in EAU mice did not suppress development of the disease. CONCLUSIONS. These data show that p38 alpha MAPK-MSK1/2 is involved in the control of IL-17 synthesis by CD4(+) T cells and that inhibition of p38 alpha MAPK in vitro suppresses IL-17 synthesis but that inhibition of this kinase in vivo did not protect from EAU. (Invest Ophthalmol Vis Sci. 2010;51:3567-3574) DOI: 10.1167/iovs.09-4393

Finite determinacy and Whitney equisingularity of map germs from C(n) to C(2n-1)

We show that a holomorphic map germ f : (C(n), 0) -> (C(2n-1), 0) is finitely determined if and only if the double point scheme D(f) is a reduced curve. If n >= 3, we have that mu(D(2)(f)) = 2 mu(D(2)(f)/S(2))+C(f)-1, where D(2)(f) is the lifting of the double point curve in (C(n) x C(n), 0), mu(X) denotes the Milnor number of X and C(f) is the number of cross-caps that appear in a stable deformation of f. Moreover, we consider an unfolding F(t, x) = (t, f(t)(x)) of f and show that if F is mu-constant, then it is excellent in the sense of Gaffney. Finally, we find a minimal set of invariants whose constancy in the family f(t) is equivalent to the Whitney equisingularity of F. We also give an example of an unfolding which is topologically trivial, but it is not Whitney equisingular.

Reduced gradient method combined with augmented Lagrangian and barrier for the optimal power flow problem

A new approach for solving the optimal power flow (OPF) problem is established by combining the reduced gradient method and the augmented Lagrangian method with barriers and exploring specific characteristics of the relations between the variables of the OPF problem. Computer simulations on IEEE 14-bus and IEEE 30-bus test systems illustrate the method. (c) 2007 Elsevier Inc. All rights reserved.

The doodle of a finitely determined map germ from R(2) to R(3)

Let f : U subset of R(2) -> R(3) be a representative of a finitely determined map germ f : (R(2), 0) -> (R(3), 0). Consider the curve obtained as the intersection of the image of the mapping f with a sufficiently small sphere s(epsilon)(2) centered at the origin in R(3), call this curve the associated doodle of the map germ f. For a large class of map germs the associated doodle has many transversal self-intersections. The topological classification of such map germs is considered from the point of view of the associated doodles. (C) 2009 Elsevier Inc. All rights reserved.

A note on finite determinacy for corank 2 map germs from surfaces to 3-space

We study properties of finitely determined corank 2 quasihomogeneous map germs f: (C(2), 0) -> (C(3), 0). Examples and counter examples of such map germs are presented.

Real map germs and higher open book structures

The paper focusses on the existence of higher open book structures defined by real map germs psi : (R(m), 0) -> (R(p), 0) such that Sing psi boolean AND psi(-1)(0) subset of {0}. A general existence criterion is proved, with view to weighted-homogeneous maps.

The non-twist standard map with robust tori

The non-twist standard map occurs frequently in many fields of science specially in modelling the dynamics of the magnetic field lines in tokamaks. Robust tori, dynamical barriers that impede the radial transport among different regions of the phase space, are introduced in the non-twist standard map in a conservative fashion. The resulting non-twist standard map with robust tori is an improved model to study transport barriers in plasmas confined in tokamaks.

Clustering and diffusion in a symplectic map lattice with non-local coupling

We study a symplectic chain with a non-local form of coupling by means of a standard map lattice where the interaction strength decreases with the lattice distance as a power-law, in Such a way that one can pass continuously from a local (nearest-neighbor) to a global (mean-field) type of coupling. We investigate the formation of map clusters, or spatially coherent structures generated by the system dynamics. Such clusters are found to be related to stickiness of chaotic phase-space trajectories near periodic island remnants, and also to the behavior of the diffusion coefficient. An approximate two-dimensional map is derived to explain some of the features of this connection. (C) 2008 Elsevier Ltd. All rights reserved.