Simple examples of distinct Liouville-type symplectic structures

We discuss some examples of open manifolds which admit non-isomorphic symplectic structures of Liouville type.Comment: v2: one remark added, minor change

Numerical Evolution of Dynamic 3D Black Holes: Extracting Waves

We consider the numerical evolution of dynamic black hole initial data sets with a full 3D, nonlinear evolution code. These data sets consist of single black holes distorted by strong gravitational waves, and mimic the late stages of coalescing black holes. Through comparison with results from well established axisymmetric codes, we show that these dynamic black holes can be accurately evolved. In particular, we show that with present computational resources and techniques, the process of excitation and ringdown of the black hole can be evolved, and one can now extract accurately the gravitational waves emitted from the 3D Cartesian metric functions, even though they may be buried in the metric at levels on the order of $10^{-3}$ and below. Waveforms for both the $\ell=2$ and the much more difficult $\ell=4$ modes are computed and compared with axisymmetric calculations. In addition to exploring the physics of distorted black hole data sets, and showing the extent to which the waves can be accurately extracted, these results also provide important testbeds for all fully nonlinear numerical codes designed to evolve black hole spacetimes in 3D, whether they use singularity avoiding slicings, apparent horizon boundary conditions, or other evolution methods.Comment: 9 pages, 3 figures, LaTe

The Challenges of Enlargement and GATT Trade Negotiations: Explaining the Resilience of the European Community’s Common Agricultural Policy in the 1970s

Both a flagship policy and a costly and wasteful liability – since its inception in the 1960s, the common agricultural policy (CAP) of the European Community (EC) has been controversial. This article investigates why the CAP survived largely unchanged through the 1970s, a decade of economic and political crisis and transformation, and maintained its centrality in the Community. The article focuses first on the entrenched institutional interests in the Council of Ministers and the Commission before analyzing two key events that could have led to a shift of interests in the EC and a reform of the policy: the accession of the United Kingdom to the EC in 1973 and the Tokyo Round of the General Agreement on Tariffs and Trade (GATT) (1973-9). The decision of the Community to protect the CAP against these challenges is revealing with regard to the state and outlook of the Community in the 1970s. The article argues that in a period of uncertainty and transformation, the CAP maintained a reluctant centrality in the EC, underscoring European unity and commitment to European integration. Internal challenges such as enlargement with the UK and external ones such as the GATT trade negotiations were thus met with the determination to keep the CAP intact

Setting the agenda on Britain’s policy towards the European Community: Miriam Camps at Chatham House

Historical analysis of the United Kingdom government’s policy towards European integration is mostly confined to the ‘official’ sphere, that is government, civil service and professional diplomacy. Non-governmental actors within the wider field of para-diplomacy such as policy entrepreneurs or elite foreign policy think tanks have not yet been systematically incorporated in this history. This article explores when and under what circumstances such diplomatic actors can influence government foreign policy formulation. The case explored here is that of Miriam Camps (1916-1994), a scholar, former US diplomat and senior researcher at Chatham House. Camps utilised her Chatham House contacts, including key Foreign Office officials as well as her wider transnational network, to influence the Foreign Office’s stance on the so-called ‘empty chair’ crisis of the European Economic Community in 1965/66. The article argues that during the crisis Camps acted as a policy entrepreneur with the aim of advancing her own ideas and changing the government of the United Kingdom’s position towards the European Economic Community. Besides demonstrating the influence of unofficial diplomats on policy formulation, the article also contributes to the growing literature on the varied roles of women in international relations and diplomacy

Britain, the common agricultural policy and the challenges of membership in the European Community: a political balancing act

When the United Kingdom joined the European Community (EC) in January 1973 it did not simply join a ‘common market’ for industrial goods, it joined a Community with a fully developed protectionist common agricultural policy (CAP). The policy encompassed up to ninety percent of the EC budget to which Britain was due to become a net contributor at the end of the transition period in 1979. This article will analyse Britain’s tempestuous relationship with the CAP from the country’s accession to the end of the Labour government in 1979. Following accession, the country’s relationship with the EC became increasingly awkward as Labour leaders Harold Wilson and James Callaghan prioritised policies and favoured behaviour they deemed conducive to maintaining the unity of the Labour party. The perceived disadvantages of the CAP for Britain gave politicians additional justification for adopting a confrontational attitude towards the EC. The CAP, the article argues, can serve as a lens to shed light on the wider question of how Britain’s leading politicians adapted to Community membership politically, tactically and psychologically

Suspending Lefschetz fibrations, with an application to Local Mirror Symmetry

We consider the suspension operation on Lefschetz fibrations, which takes p(x) to p(x)-y^2. This leaves the Fukaya category of the fibration invariant, and changes the category of the fibre (or more precisely, the subcategory consisting of a basis of vanishing cycles) in a specific way. As an application, we prove part of Homological Mirror Symmetry for the total spaces of canonical bundles over toric del Pezzo surfaces.Comment: v2: slightly expanded expositio

Three Dimensional Distorted Black Holes: Initial Data and Evolution

We present a new class of 3D black hole initial data sets for numerical relativity. These data sets go beyond the axisymmetric, ``gravity wave plus rotating black hole'' single black hole data sets by creating a dynamic, distorted hole with adjustable distortion parameters in 3D. These data sets extend our existing test beds for 3D numerical relativity, representing the late stages of binary black hole collisions resulting from on-axis collision or 3D spiralling coalescence, and should provide insight into the physics of such systems. We describe the construction of these sets, the properties for a number of example cases, and report on progress evolving them.Comment: 3 pages, 2 postscript figures, LaTeX, uses mprocl.sty (available at http://shemesh.fiz.huji.ac.il/MG8/submission.html) To appear in the proceedings of the Marcel Grossmann 8 (Jerusalem, 1997

Neural View-Interpolation for Sparse Light Field Video

We suggest representing light field (LF) videos as "one-off" neural networks (NN), i.e., a learned mapping from view-plus-time coordinates to high-resolution color values, trained on sparse views. Initially, this sounds like a bad idea for three main reasons: First, a NN LF will likely have less quality than a same-sized pixel basis representation. Second, only few training data, e.g., 9 exemplars per frame are available for sparse LF videos. Third, there is no generalization across LFs, but across view and time instead. Consequently, a network needs to be trained for each LF video. Surprisingly, these problems can turn into substantial advantages: Other than the linear pixel basis, a NN has to come up with a compact, non-linear i.e., more intelligent, explanation of color, conditioned on the sparse view and time coordinates. As observed for many NN however, this representation now is interpolatable: if the image output for sparse view coordinates is plausible, it is for all intermediate, continuous coordinates as well. Our specific network architecture involves a differentiable occlusion-aware warping step, which leads to a compact set of trainable parameters and consequently fast learning and fast execution

Semi-dynamic connectivity in the plane

Motivated by a path planning problem we consider the following procedure. Assume that we have two points $s$ and $t$ in the plane and take $\mathcal{K}=\emptyset$. At each step we add to $\mathcal{K}$ a compact convex set that does not contain $s$ nor $t$. The procedure terminates when the sets in $\mathcal{K}$ separate $s$ and $t$. We show how to add one set to $\mathcal{K}$ in $O(1+k\alpha(n))$ amortized time plus the time needed to find all sets of $\mathcal{K}$ intersecting the newly added set, where $n$ is the cardinality of $\mathcal{K}$, $k$ is the number of sets in $\mathcal{K}$ intersecting the newly added set, and $\alpha(\cdot)$ is the inverse of the Ackermann function

Exact Lagrangian submanifolds in simply-connected cotangent bundles

We consider exact Lagrangian submanifolds in cotangent bundles. Under certain additional restrictions (triviality of the fundamental group of the cotangent bundle, and of the Maslov class and second Stiefel-Whitney class of the Lagrangian submanifold) we prove such submanifolds are Floer-cohomologically indistinguishable from the zero-section. This implies strong restrictions on their topology. An essentially equivalent result was recently proved independently by Nadler, using a different approach.Comment: 28 pages, 3 figures. Version 2 -- derivation and discussion of the spectral sequence considerably expanded. Other minor change