Generalised Dirichelt-to-Neumann map in time dependent domains

We study the heat, linear Schrodinger and linear KdV equations in the domain l(t) < x < ∞, 0 < t < T, with prescribed initial and boundary conditions and with l(t) a given differentiable function. For the first two equations, we show that the unknown Neumann or Dirichlet boundary value can be computed as the solution of a linear Volterra integral equation with an explicit weakly singular kernel. This integral equation can be derived from the formal Fourier integral representation of the solution. For the linear KdV equation we show that the two unknown boundary values can be computed as the solution of a system of linear Volterra integral equations with explicit weakly singular kernels. The derivation in this case makes crucial use of analyticity and certain invariance properties in the complex spectral plane. The above Volterra equations are shown to admit a unique solution.

The Dirichlet-to-Neumann map for the elliptic sine Gordon

We analyse the Dirichlet problem for the elliptic sine Gordon equation in the upper half plane. We express the solution $q(x,y)$ in terms of a Riemann-Hilbert problem whose jump matrix is uniquely defined by a certain function $b(\la)$, $\la\in\R$, explicitly expressed in terms of the given Dirichlet data $g_0(x)=q(x,0)$ and the unknown Neumann boundary value $g_1(x)=q_y(x,0)$, where $g_0(x)$ and $g_1(x)$ are related via the global relation $\{b(\la)=0$, $\la\geq 0\}$. Furthermore, we show that the latter relation can be used to characterise the Dirichlet to Neumann map, i.e. to express $g_1(x)$ in terms of $g_0(x)$. It appears that this provides the first case that such a map is explicitly characterised for a nonlinear integrable {\em elliptic} PDE, as opposed to an {\em evolution} PDE.

Franz Neumann, the rule of law and the unfulfilled promise of classical liberal thought

This thesis draws on the work of Franz Neumann, a critical theorist associated with the early Frankfurt School, to evaluate liberal arguments about political legitimacy and to develop an original account of the justification for the liberal state.

Lagrangian analysis of low level anthropogenic plume processing across the North Atlantic

The photochemical evolution of an anthropogenic plume from the New-York/Boston region during its transport at low altitudes over the North Atlantic to the European west coast has been studied using a Lagrangian framework. This plume, originally strongly polluted, was sampled by research aircraft just off the North American east coast on 3 successive days, and 3 days downwind off the west coast of Ireland where another aircraft re-sampled a weakly polluted plume. Changes in trace gas concentrations during transport were reproduced using a photochemical trajectory model including deposition and mixing effects. Chemical and wet deposition processing dominated the evolution of all pollutants in the plume. The mean net O3 production was evaluated to be -5 ppbv/day leading to low values of O3 by the time the plume reached Europe. Wet deposition of nitric acid was responsible for an 80% reduction in this O3 production. If the plume had not encountered precipitation, it would have reached the Europe with O3 levels up to 80-90 ppbv, and CO levels between 120 and 140 ppbv. Photochemical destruction also played a more important role than mixing in the evolution of plume CO due to high levels of both O3 and water vapour showing that CO cannot always be used as a tracer for polluted air masses, especially for plumes transported at low altitudes. The results also show that, in this case, an important increase in the O3/CO slope can be attributed to chemical destruction of CO and not to photochemical O3 production as is often assumed.

ken

From the beginning, the world of game-playing by machine has been fortunate in attracting contributions from the leading names of computer science. Charles Babbage, Konrad Zuse, Claude Shannon, Alan Turing, John von Neumann, John McCarthy, Alan Newell, Herb Simon and Ken Thompson all come to mind, and each reader will wish to add to this list. Recently, the Journal has saluted both Claude Shannon and Herb Simon. Ken’s retirement from Lucent Technologies’ Bell Labs to the start-up Entrisphere is also a good moment for reflection.

A Nyström method for a boundary value problem arising in unsteady water wave problems

This paper is concerned with solving numerically the Dirichlet boundary value problem for Laplace’s equation in a nonlocally perturbed half-plane. This problem arises in the simulation of classical unsteady water wave problems. The starting point for the numerical scheme is the boundary integral equation reformulation of this problem as an integral equation of the second kind on the real line in Preston et al. (2008, J. Int. Equ. Appl., 20, 121–152). We present a Nystr¨om method for numerical solution of this integral equation and show stability and convergence, and we present and analyse a numerical scheme for computing the Dirichlet-to-Neumann map, i.e., for deducing the instantaneous fluid surface velocity from the velocity potential on the surface, a key computational step in unsteady water wave simulations. In particular, we show that our numerical schemes are superalgebraically convergent if the fluid surface is infinitely smooth. The theoretical results are illustrated by numerical experiments.

An RNA molecule that specifically inhibits G-protein-coupled receptor kinase 2 in vitro

G-protein-coupled receptors are desensitized by a two-step process. In a first step, G-protein-coupled receptor kinases (GRKs) phosphorylate agonist-activated receptors that subsequently bind to a second class of proteins, the arrestins. GRKs can be classified into three subfamilies, which have been implicated in various diseases. The physiological role(s) of GRKs have been difficult to study as selective inhibitors are not available. We have used SELEX (systematic evolution of ligands by exponential enrichment) to develop RNA aptamers that potently and selectively inhibit GRK2. This process has yielded an aptamer, C13, which bound to GRK2 with a high affinity and inhibited GRK2-catalyzed rhodopsin phosphorylation with an IC50 of 4.1 nM. Phosphorylation of rhodopsin catalyzed by GRK5 was also inhibited, albeit with 20-fold lower potency (IC50 of 79 nM). Furthermore, C13 reveals significant specificity, since almost no inhibitory activity was detectable testing it against a panel of 14 other kinases. The aptamer is two orders of magnitude more potent than the best GRK2 inhibitors described previously and shows high selectivity for the GRK family of protein kinases.

Economic models and algorithms for distributed systems

Distributed computing paradigms for sharing resources such as Clouds, Grids, Peer-to-Peer systems, or voluntary computing are becoming increasingly popular. While there are some success stories such as PlanetLab, OneLab, BOINC, BitTorrent, and SETI@home, a widespread use of these technologies for business applications has not yet been achieved. In a business environment, mechanisms are needed to provide incentives to potential users for participating in such networks. These mechanisms may range from simple non-monetary access rights, monetary payments to specific policies for sharing. Although a few models for a framework have been discussed (in the general area of a "Grid Economy"), none of these models has yet been realised in practice. This book attempts to fill this gap by discussing the reasons for such limited take-up and exploring incentive mechanisms for resource sharing in distributed systems. The purpose of this book is to identify research challenges in successfully using and deploying resource sharing strategies in open-source and commercial distributed systems.

Parallel Monte Carlo approach for integration of the rendering equation

This paper is addressed to the numerical solving of the rendering equation in realistic image creation. The rendering equation is integral equation describing the light propagation in a scene accordingly to a given illumination model. The used illumination model determines the kernel of the equation under consideration. Nowadays, widely used are the Monte Carlo methods for solving the rendering equation in order to create photorealistic images. In this work we consider the Monte Carlo solving of the rendering equation in the context of the parallel sampling scheme for hemisphere. Our aim is to apply this sampling scheme to stratified Monte Carlo integration method for parallel solving of the rendering equation. The domain for integration of the rendering equation is a hemisphere. We divide the hemispherical domain into a number of equal sub-domains of orthogonal spherical triangles. This domain partitioning allows to solve the rendering equation in parallel. It is known that the Neumann series represent the solution of the integral equation as a infinity sum of integrals. We approximate this sum with a desired truncation error (systematic error) receiving the fixed number of iteration. Then the rendering equation is solved iteratively using Monte Carlo approach. At each iteration we solve multi-dimensional integrals using uniform hemisphere partitioning scheme. An estimate of the rate of convergence is obtained using the stratified Monte Carlo method. This domain partitioning allows easy parallel realization and leads to convergence improvement of the Monte Carlo method. The high performance and Grid computing of the corresponding Monte Carlo scheme are discussed.

SORMA - business cases for an open grid market: concept and implementation

Economic mechanisms enhance technological solutions by setting the right incentives to reveal information about demand and supply accurately. Market or pricing mechanisms are ones that foster information exchange and can therefore attain efficient allocation. By assigning a value (also called utility) to their service requests, users can reveal their relative urgency or costs to the service. The implementation of theoretical sound models induce further complex challenges. The EU-funded project SORMA analyzes these challenges and provides a prototype as a proof-of-concept. In this paper the approach within the SORMA-project is described on both conceptual and technical level.

Complexity of Monte Carlo algorithms for a class of integral equations

In this work we study the computational complexity of a class of grid Monte Carlo algorithms for integral equations. The idea of the algorithms consists in an approximation of the integral equation by a system of algebraic equations. Then the Markov chain iterative Monte Carlo is used to solve the system. The assumption here is that the corresponding Neumann series for the iterative matrix does not necessarily converge or converges slowly. We use a special technique to accelerate the convergence. An estimate of the computational complexity of Monte Carlo algorithm using the considered approach is obtained. The estimate of the complexity is compared with the corresponding quantity for the complexity of the grid-free Monte Carlo algorithm. The conditions under which the class of grid Monte Carlo algorithms is more efficient are given.