Hardness of Graph Pricing through Generalized Max-Dicut

The Graph Pricing problem is among the fundamental problems whose approximability is not well-understood. While there is a simple combinatorial 1/4-approximation algorithm, the best hardness result remains at 1/2 assuming the Unique Games Conjecture (UGC). We show that it is NP-hard to approximate within a factor better than 1/4 under the UGC, so that the simple combinatorial algorithm might be the best possible. We also prove that for any $\epsilon > 0$, there exists $\delta > 0$ such that the integrality gap of $n^{\delta}$-rounds of the Sherali-Adams hierarchy of linear programming for Graph Pricing is at most 1/2 + $\epsilon$. This work is based on the effort to view the Graph Pricing problem as a Constraint Satisfaction Problem (CSP) simpler than the standard and complicated formulation. We propose the problem called Generalized Max-Dicut($T$), which has a domain size $T + 1$ for every $T \geq 1$. Generalized Max-Dicut(1) is well-known Max-Dicut. There is an approximation-preserving reduction from Generalized Max-Dicut on directed acyclic graphs (DAGs) to Graph Pricing, and both our results are achieved through this reduction. Besides its connection to Graph Pricing, the hardness of Generalized Max-Dicut is interesting in its own right since in most arity two CSPs studied in the literature, SDP-based algorithms perform better than LP-based or combinatorial algorithms --- for this arity two CSP, a simple combinatorial algorithm does the best.Comment: 28 page

Identifying gaps between science and practitioners perspectives on land use: the case of managed realignment in the German Baltic coast

Through state-of-the art ecosystem modelling supported by ecological experimental data, the COMTESS Project (funding: German Federal Ministry of Education and Research) investigates potential synergies and trade offs in ecosystem service provision under different land-use scenarios in two German coastal areas till 2100. Overall goal is to explore alternative sustainable land-use strategies to best adapt to climate change. Two science-based land- use scenarios were developed for two study regions on the Baltic and North Sea coasts to contrast a business-as-usual scenario. We focus here on the Baltic Se case region. The underlying premise of these alternatives is managed realignment of current dikes inland for: 1) climate mitigation through wetland re-naturation or 2) multiple land use, including biomass harvesting for energetic purposes (Baltic Sea). Managed realignment is increasingly considered as a valid coastal defence strategy to lower long-term costs of hard coastal defence and restore critical coastal and experiments have been initiated since the 1990s in a number of northwest European countries. Though politically highly controversial and facing much public antagonism, managed realignment is effectively embedded in the current coastal management policy of the state of Mecklenburg Vorpommern on the German Baltic coast. Implementation, nevertheless, faces many obstacles. Project-based scenarios for the Baltic Sea were first evaluated by key regional and local policy, management and land use practitioners, each expert in their field of activity. Their evaluation and recommendations were subsequently used to develop a fourth land-use scenario. Using qualitative empirical social research methods we analyse divergences and convergences between expert views on the projects scenarios. We argue that managed realignment is currently being mainstreamed in science, policy and resource management arenas although representatives of local land users and inhabitants do not endorse this strategy and still foster a hard defence approach to coastal zone management. This is best illustrated in recurrent social mobilisation and resistance to managed realignment proposals. This points at important perception and preference gaps between science, policy and land users / inhabitants, which need to be resolved to formulate and implement sustainable and socially acceptable land use strategies

The antenna DSA 3 and its potential use for Radio Astronomy

The European Space Agency (ESA) will inaugurate its third Deep Space Antenna (DSA 3) by the end of 2012. DSA 3 will be located in Argentina near the city of Malarg"ue in the Mendoza province. While the instrument will be primarily dedicated to communications with interplanetary missions, the characteristics of its antenna and receivers will also enable standalone leading scientific contributions, with a high scientific-technological return. We outline here scientific proposals for a radio astronomical use of DSA 3.Comment: 4 pages, submitted as Proceedings for the BAA

The hyperspace of non-cut subcontinua of graphs and dendrites

Given a continuum $X$, let $C(X)$ denote the hyperspace of all subcontinua of $X$. In this paper we study the Vietoris hyperspace $NC^{*}(X)=\{ A \in C(X):X\setminus A\text{ is connected}\}$ when $X$ is a finite graph or a dendrite; in particular, we give conditions under which $NC^{*}(X)$ is compact, connected, locally connected or totally disconnected. Also, we prove that if $X$ is a dendrite and the set of endpoints of $X$ is dense, then $NC^{*}(X)$ is homeomorphic to the Baire space of irrational numbers

Ultrathin carbon nanotube with single, double, and triple bonds

A metastable carbon nanotube with single, double, and triple bonds has been predicted from abinitio simulation. It results from the relaxation of an ideal carbon nanotube with chirality (2,1), without any potential barrier between the ideal nanotube and the new structure. Ten-membered carbon rings are formed by breaking carbon bonds between adjacent hexagons; eight-membered rings, already present in the ideal structure, become the smallest rings. This structure is stable in molecular dynamics simulations at temperatures up to 1000K. Raman, infrared, and optical absorption spectra are simulated to allow its identification in the laboratory. The structure can be described as a double helical chain with alternating single, double, and triple bonds, where the chains are bridged by single bondsThis work was supported by Grants No. SB2010-0119 (MEC), No. CTQ2010-19232 (MICIN), and No. A1/035856/11 (AECID