The algebraic dichotomy conjecture for infinite domain Constraint Satisfaction Problems

We prove that an $\omega$-categorical core structure primitively positively interprets all finite structures with parameters if and only if some stabilizer of its polymorphism clone has a homomorphism to the clone of projections, and that this happens if and only if its polymorphism clone does not contain operations $\alpha$, $\beta$, $s$ satisfying the identity $\alpha s(x,y,x,z,y,z) \approx \beta s(y,x,z,x,z,y)$. This establishes an algebraic criterion equivalent to the conjectured borderline between P and NP-complete CSPs over reducts of finitely bounded homogenous structures, and accomplishes one of the steps of a proposed strategy for reducing the infinite domain CSP dichotomy conjecture to the finite case. Our theorem is also of independent mathematical interest, characterizing a topological property of any $\omega$-categorical core structure (the existence of a continuous homomorphism of a stabilizer of its polymorphism clone to the projections) in purely algebraic terms (the failure of an identity as above).Comment: 15 page

Constraint satisfaction problems for reducts of homogeneous graphs

For n >= 3, let (Hn, E) denote the n-th Henson graph, i.e., the unique countable homogeneous graph with exactly those finite graphs as induced subgraphs that do not embed the complete graph on n vertices. We show that for all structures Gamma with domain Hn whose relations are first-order definable in (Hn, E) the constraint satisfaction problem for Gamma is either in P or is NP-complete. We moreover show a similar complexity dichotomy for all structures whose relations are first-order definable in a homogeneous graph whose reflexive closure is an equivalence relation. Together with earlier results, in particular for the random graph, this completes the complexity classification of constraint satisfaction problems of structures first-order definable in countably infinite homogeneous graphs: all such problems are either in P or NP-complete

The STAR MAPS-based PiXeL detector

The PiXeL detector (PXL) for the Heavy Flavor Tracker (HFT) of the STAR experiment at RHIC is the first application of the state-of-the-art thin Monolithic Active Pixel Sensors (MAPS) technology in a collider environment. Custom built pixel sensors, their readout electronics and the detector mechanical structure are described in detail. Selected detector design aspects and production steps are presented. The detector operations during the three years of data taking (2014-2016) and the overall performance exceeding the design specifications are discussed in the conclusive sections of this paper

The Hardness of Embedding Grids and Walls

The dichotomy conjecture for the parameterized embedding problem states that the problem of deciding whether a given graph $G$ from some class $K$ of "pattern graphs" can be embedded into a given graph $H$ (that is, is isomorphic to a subgraph of $H$) is fixed-parameter tractable if $K$ is a class of graphs of bounded tree width and $W[1]$-complete otherwise. Towards this conjecture, we prove that the embedding problem is $W[1]$-complete if $K$ is the class of all grids or the class of all walls

Constraint satisfaction problems for reducts of homogeneous graphs

For n >= 3, let (H-n, E) denote the nth Henson graph, i.e., the unique countable homogeneous graph with exactly those finite graphs as induced subgraphs that do not embed the complete graph on n vertices. We show that for all structures Gamma with domain H-n whose relations are first-order definable in (H-n, E) the constraint satisfaction problem for F either is in P or is NP-complete. We moreover show a similar complexity dichotomy for all structures whose relations are first-order definable in a homogeneous graph whose reflexive closure is an equivalence relation. Together with earlier results, in particular for the random graph, this completes the complexity classification of constraint satisfaction problems of structures first-order definable in countably infinite homogeneous graphs: all such problems are either in P or NP-complete

Constraint Satisfaction Problems over the Integers with Successor

A distance constraint satisfaction problem is a constraint satisfaction problem (CSP) whose constraint language consists of relations that are first-order definable over (Z;succ)(Z;succ), i.e., over the integers with the successor function. Our main result says that every distance CSP is in P or NP-complete, unless it can be formulated as a finite domain CSP in which case the computational complexity is not known in general

Tropically convex constraint satisfaction

A semilinear relation S is max-closed if it is preserved by taking the componentwise maximum. The constraint satisfaction problem for max-closed semilinear constraints is at least as hard as determining the winner in Mean Payoff Games, a notorious problem of open computational complexity. Mean Payoff Games are known to be in the intersection of NP and co-NP, which is not known for max-closed semilinear constraints. Semilinear relations that are max-closed and additionally closed under translations have been called tropically convex in the literature. One of our main results is a new duality for open tropically convex relations, which puts the CSP for tropically convex semilinaer constraints in general into NP intersected co-NP. This extends the corresponding complexity result for scheduling under and-or precedence constraints, or equivalently the max-atoms problem. To this end, we present a characterization of max-closed semilinear relations in terms of syntactically restricted first-order logic, and another characterization in terms of a finite set of relations L that allow primitive positive definitions of all other relations in the class. We also present a subclass of max-closed constraints where the CSP is in P; this class generalizes the class of max-closed constraints over finite domains, and the feasibility problem for max-closed linear inequalities. Finally, we show that the class of max-closed semilinear constraints is maximal in the sense that as soon as a single relation that is not max-closed is added to L, the CSP becomes NP-hard.Comment: 29 pages, 2 figure

Focus on reactive nitrogen and the UN sustainable development goals

The scientific evidence assembled in this Focus Collection on 'Reactive nitrogen and the UN sustainable development goals' emphasizes the relevance of agriculture as a key sector for nitrogen application as well as its release to the environment and the observed impacts. Published work proves the multiple connections and their causality, and presents pathways to mitigate negative effects while maintaining the benefits, foremost the production of food to sustain humanity. Providing intersections from field to laboratory studies and to modelling approaches, across multiple scales and for all continents, the Collection displays an overview of the state of nitrogen science in the early 21st century. Extending science to allow for policy-relevant messages renders the evidence provided a valuable basis for a global assessment of reactive nitrogen

Global consequences of afforestation and bioenergy cultivation on ecosystem service indicators

Land management for carbon storage is discussed as being indispensable for climate change mitigation because of its large potential to remove carbon dioxide from the atmosphere, and to avoid further emissions from deforestation. However, the acceptance and feasibility of land-based mitigation projects depends on potential side effects on other important ecosystem functions and their services. Here, we use projections of future land use and land cover for different land-based mitigation options from two land-use models (IMAGE and MAgPIE) and evaluate their effects with a global dynamic vegetation model (LPJ-GUESS). In the land-use models, carbon removal was achieved either via growth of bioenergy crops combined with carbon capture and storage, via avoided deforestation and afforestation, or via a combination of both. We compare these scenarios to a reference scenario without land-based mitigation and analyse the LPJ-GUESS simulations with the aim of assessing synergies and trade-offs across a range of ecosystem service indicators: carbon storage, surface albedo, evapotranspiration, water runoff, crop production, nitrogen loss, and emissions of biogenic volatile organic compounds. In our mitigation simulations cumulative carbon storage by year 2099 ranged between 55 and 89 GtC. Other ecosystem service indicators were influenced heterogeneously both positively and negatively, with large variability across regions and land-use scenarios. Avoided deforestation and afforestation led to an increase in evapotranspiration and enhanced emissions of biogenic volatile organic compounds, and to a decrease in albedo, runoff, and nitrogen loss. Crop production could also decrease in the afforestation scenarios as a result of reduced crop area, especially for MAgPIE land-use patterns, if assumed increases in crop yields cannot be realized. Bioenergy-based climate change mitigation was projected to affect less area globally than in the forest expansion scenarios, and resulted in less pronounced changes in most ecosystem service indicators than forest-based mitigation, but included a possible decrease in nitrogen loss, crop production, and biogenic volatile organic compounds emissions