Jurisdictional Issues: The EEC Merger Control Regulation, Member State Laws, and Articles 85 and 86

This Article deals with two main issues. One is the division of powers between the European Economic Community and the Member States with regard to merger control after September 21, 1990. The other is the possible application, by the Commission of the European Communities or by national authorities, of Article 85 and 86 of the Treaty Establishing the European Economic Community to mergers covered by Regulation No. 4064/89. The Article casts a brief look at how the dividing line between merges and operations which do not qualify as mergers within the sense of article 3 of the Regulation will be treated in the future

An exact sequence for contact- and symplectic homology

A symplectic manifold $W$ with contact type boundary $M = \partial W$ induces a linearization of the contact homology of $M$ with corresponding linearized contact homology $HC(M)$. We establish a Gysin-type exact sequence in which the symplectic homology $SH(W)$ of $W$ maps to $HC(M)$, which in turn maps to $HC(M)$, by a map of degree -2, which then maps to $SH(W)$. Furthermore, we give a description of the degree -2 map in terms of rational holomorphic curves with constrained asymptotic markers, in the symplectization of $M$.Comment: Final version. Changes for v2: Proof of main theorem supplemented with detailed discussion of continuation maps. Description of degree -2 map rewritten with emphasis on asymptotic markers. Sec. 5.2 rewritten with emphasis on 0-dim. moduli spaces. Transversality discussion reorganized for clarity (now Remark 9). Various other minor modification

New obstructions to symplectic embeddings

In this paper we establish new restrictions on symplectic embeddings of certain convex domains into symplectic vector spaces. These restrictions are stronger than those implied by the Ekeland-Hofer capacities. By refining an embedding technique due to Guth, we also show that they are sharp.Comment: 80 pages, 3 figures, v2: improved exposition and minor corrections, v3: Final version, expanded and improved exposition and minor corrections. The final publication is available at link.springer.co

The introduction of Corded Ware Culture at a local level: an exploratory study of cultural change during the Late Neolithic of the Dutch West Coast through ceramic technology

The introduction of the Corded Ware Culture (3000–2500 BCE) is considered a formative event in Europe's past. Ancient DNA analyses demonstrate that migrations played a crucial role in this event. However, these analyses approach the issue at a supra-regional scale, leaving questions about the regional and local impact of this event unresolved. This study pilots an approach to ceramics that brings this small-scale impact into focus by using the transmission of ceramic technology as a proxy for social change. It draws on ethno-archaeological studies of the effects of social changes on the transmission of ceramic production techniques to hypothesise the impact of three idealised scenarios that archaeologists have proposed for the introduction of Corded Ware Culture: migration, diffusion, and network interactions. Subsequently, it verifies these hypotheses by integrating geochemical (WDXRF), mineralogical (petrography), and macromorphological analysis of ceramics with network analysis. This method is applied to 30 Late Neolithic ceramic vessels from three sites in the western coastal area of the Netherlands (Hazerswoude-Rijndijk N11, Zandwerven, and Voorschoten-De Donk). This study concludes that the introduction of Corded Ware material culture is a process that varies from site to site in the western coastal area of the Netherlands. Moreover, the introduction of the Corded Ware Culture is characterised by continuity in technological traditions throughout the study area, indicating a degree of social continuity despite typological changes in ceramics

Highly efficient synthesis of the tricyclic core of Taxol by cascade metathesis

An efficient enantioselective synthesis of the ABC tricyclic core of the anticancer drug Taxol is reported. The key step of this synthesis is a cascade metathesis reaction, which leads in one operation to the required tricycle if appropriate fine-tuning of the dienyne precursor is performed

Weak and strong fillability of higher dimensional contact manifolds

For contact manifolds in dimension three, the notions of weak and strong symplectic fillability and tightness are all known to be inequivalent. We extend these facts to higher dimensions: in particular, we define a natural generalization of weak fillings and prove that it is indeed weaker (at least in dimension five),while also being obstructed by all known manifestations of "overtwistedness". We also find the first examples of contact manifolds in all dimensions that are not symplectically fillable but also cannot be called overtwisted in any reasonable sense. These depend on a higher-dimensional analogue of Giroux torsion, which we define via the existence in all dimensions of exact symplectic manifolds with disconnected contact boundary.Comment: 68 pages, 5 figures. v2: Some attributions clarified, and other minor edits. v3: exposition improved using referee's comments. Published by Invent. Mat

Parameterized Algorithms for Graph Partitioning Problems

We study a broad class of graph partitioning problems, where each problem is specified by a graph $G=(V,E)$, and parameters $k$ and $p$. We seek a subset $U\subseteq V$ of size $k$, such that $\alpha_1m_1 + \alpha_2m_2$ is at most (or at least) $p$, where $\alpha_1,\alpha_2\in\mathbb{R}$ are constants defining the problem, and $m_1, m_2$ are the cardinalities of the edge sets having both endpoints, and exactly one endpoint, in $U$, respectively. This class of fixed cardinality graph partitioning problems (FGPP) encompasses Max $(k,n-k)$-Cut, Min $k$-Vertex Cover, $k$-Densest Subgraph, and $k$-Sparsest Subgraph. Our main result is an $O^*(4^{k+o(k)}\Delta^k)$ algorithm for any problem in this class, where $\Delta \geq 1$ is the maximum degree in the input graph. This resolves an open question posed by Bonnet et al. [IPEC 2013]. We obtain faster algorithms for certain subclasses of FGPPs, parameterized by $p$, or by $(k+p)$. In particular, we give an $O^*(4^{p+o(p)})$ time algorithm for Max $(k,n-k)$-Cut, thus improving significantly the best known $O^*(p^p)$ time algorithm