Spatial conservation planning under uncertainty: adapting to climate change risks using modern portfolio theory.

Climate change and urban growth impact habitats, species, and ecosystem services. To buffer against global change, an established adaptation strategy is designing protected areas to increase representation and complementarity of biodiversity features. Uncertainty regarding the scale and magnitude of landscape change complicates reserve planning and exposes decision makers to the risk of failing to meet conservation goals. Conservation planning tends to treat risk as an absolute measure, ignoring the context of the management problem and risk preferences of stakeholders. Application of risk management theory to conservation emphasizes the diversification of a portfolio of assets, with the goal of reducing the impact of system volatility on investment return. We use principles of Modern Portfolio Theory (MPT), which quantifies risk as the variance and correlation among assets, to formalize diversification as an explicit strategy for managing risk in climate-driven reserve design. We extend MPT to specify a framework that evaluates multiple conservation objectives, allows decision makers to balance management benefits and risk when preferences are contested or unknown, and includes additional decision options such as parcel divestment when evaluating candidate reserve designs. We apply an efficient search algorithm that optimizes portfolio design for large conservation problems and a game theoretic approach to evaluate portfolio trade-offs that satisfy decision makers with divergent benefit and risk tolerances, or when a single decision maker cannot resolve their own preferences. Evaluating several risk profiles for a case study in South Carolina, our results suggest that a reserve design may be somewhat robust to differences in risk attitude but that budgets will likely be important determinants of conservation planning strategies, particularly when divestment is considered a viable alternative. We identify a possible fiscal threshold where adequate resources allow protecting a sufficiently diverse portfolio of habitats such that the risk of failing to achieve conservation objectives is considerably lower. For a range of sea-level rise projections, conversion of habitat to open water (14-180%) and wetland loss (1-7%) are unable to be compensated under the current protected network. In contrast, optimal reserve design outcomes are predicted to ameliorate expected losses relative to current and future habitat protected under the existing conservation estate.

Multi-Query Optimization Revisited: A Full-Query Algebraic Method.

Sharing data and computation among concurrent queries has been an active research topic in database systems. While work in this area developed algorithms and systems that are shown to be effective, there is a lack of logical foundation for query processing and optimization. In this paper, we present PsiDB, a system model for processing a large number of database queries in a batch. The key idea is to generate a single query expression that returns a global relation containing all the data needed for individual queries. For that, we propose the use of a type of relational operators called ψ-operators in combining the individual queries into the global expression. We tackle the algebraic optimization problem in PsiDB by developing equivalence rules to transform concurrent queries with the purpose of revealing query optimization opportunities. Centering around the ψ-operator, our rules not only cover many optimization techniques adopted in existing batch processing systems, but also revealed new optimization opportunities. Experiments conducted on an early prototype of PsiDB show a performance improvement of up to 36X over a mainstream commercial DBMS.

A cooperative game solution approach for intensity modulated radiation therapy design: Nash Social Welfare optimization.

We study the fluency map optimization problem in Intensity Modulated Radiation Therapy from a cooperative game theory point of view. We consider the cancerous and healthy organs in a patient's body as players of a game, where cancerous organs seek to eliminate the cancerous cells and healthy organs seek to receive no harm. The goal is to balance the trade-offs between the utility of players by forming a grand coalition between them. We do so by proposing a methodology that solves a few convex optimization problems in order to transform the fluency map optimization problem into a bargaining game. To solve the bargaining game, we employ the concept of Nash Social Welfare (NSW) optimization due to the desirable efficiency and fairness properties of its outcomes. The proposed NSW optimization is convex and can be solved by powerful commercial solvers such as CPLEX. An additional advantage of the proposed approach is that it has a new control lever for the fluency map optimization, the so-called negotiation powers, which enables practitioners to put more emphasis on an organ by changing its negotiation power. To show the efficacy of our proposed methodology, we apply it to the TG-119 case and a liver case. We compare our proposed approach with a state-of-the-art approach through creating Dose Volume Histograms.