Bad semidefinite programs: they all look the same

Conic linear programs, among them semidefinite programs, often behave pathologically: the optimal values of the primal and dual programs may differ, and may not be attained. We present a novel analysis of these pathological behaviors. We call a conic linear system $Ax <= b$ {\em badly behaved} if the value of $\sup { | A x <= b }$ is finite but the dual program has no solution with the same value for {\em some} $c.$ We describe simple and intuitive geometric characterizations of badly behaved conic linear systems. Our main motivation is the striking similarity of badly behaved semidefinite systems in the literature; we characterize such systems by certain {\em excluded matrices}, which are easy to spot in all published examples. We show how to transform semidefinite systems into a canonical form, which allows us to easily verify whether they are badly behaved. We prove several other structural results about badly behaved semidefinite systems; for example, we show that they are in $NP \cap co-NP$ in the real number model of computing. As a byproduct, we prove that all linear maps that act on symmetric matrices can be brought into a canonical form; this canonical form allows us to easily check whether the image of the semidefinite cone under the given linear map is closed.Comment: For some reason, the intended changes between versions 4 and 5 did not take effect, so versions 4 and 5 are the same. So version 6 is the final version. The only difference between version 4 and version 6 is that 2 typos were fixed: in the last displayed formula on page 6, "7" was replaced by "1"; and in the 4th displayed formula on page 12 "A_1 - A_2 - A_3" was replaced by "A_3 - A_2 - A_1

Ecohydrology in a Colorado River riparian forest: implications for the decline of Populus fremontii

Journal ArticlePopulus fremontii (Fremont cottonwood) was once a dominant species in desert riparian forests but has been increasingly replaced by the exotic invasive Tamarix ramosissima (saltcedar). Interspecific competition, reduced flooding frequency, and increased salinity have been implicated in the widespread decline of P. fremontii. To elucidate some of the multiple and interacting mechanisms of this decline, we examined ecological processes in a control stand of P. fremontii along the Colorado River in Utah, USA, as well as a disturbed stand characterized by high groundwater salinity and invasion of T. ramosissima. Sap flux data showed that P. fremontii at the saline site experienced large reductions in afternoon canopy stomatal conductance relative to the control. Thus, average daily stand transpiration was 4.8 6 0.1 mm/d at the saline site in comparison to 9.3 6 0.2 mm/d at the control site over a two-month period. Light-saturated photosynthesis and apparent quantum yield were also reduced in saline P. fremontii. Stable isotope analysis indicated that trees at the saline site utilized evaporatively enriched groundwater that was likely derived from a nearby pond of irrigation runoff; this was also the probable source of high salinity. Interspecific competition for water at the saline site is unlikely, as T. ramosissima is still a minor species that is present only in the understory. However, reduced tissue N content in P. fremontii at the saline site suggested that physiological stress during salinity and halophyte invasion may be exacerbated by altered N relations

Characterizing the universal rigidity of generic frameworks

A framework is a graph and a map from its vertices to E^d (for some d). A framework is universally rigid if any framework in any dimension with the same graph and edge lengths is a Euclidean image of it. We show that a generic universally rigid framework has a positive semi-definite stress matrix of maximal rank. Connelly showed that the existence of such a positive semi-definite stress matrix is sufficient for universal rigidity, so this provides a characterization of universal rigidity for generic frameworks. We also extend our argument to give a new result on the genericity of strict complementarity in semidefinite programming.Comment: 18 pages, v2: updates throughout; v3: published versio

Changes in isotopic signatures of soil carbon and CO2 respiration immediately and one year after Miscanthus removal

The removal of perennial bioenergy crops, such as Miscanthus, has rarely been studied although it is an important form of land use change. Miscanthus is a C4 plant, and the carbon (C) it deposits during its growth has a different isotopic signature (12/13C) compared to a C3 plant. Identifying the proportion of C stored and released to the atmosphere is important information for ecosystem models and life cycle analyses. During a removal experiment in June 2011 of a 20-year old Miscanthus field (Grignon, France), vegetation was removed mechanically and chemically. Two replicate plots were converted into a rotation of annual crops, two plots had Miscanthus removed with no soil disturbance, followed by bare soil (set-aside), one control plot was left with continued Miscanthus cultivation, and an adjacent field was used as annual arable crops control. There was a significant difference in the isotopic composition of the total soil C under Miscanthus compared with adjacent annual arable crops in all three measured soil layers (0–5, 5–10 and 10–20 cm). Before Miscanthus removal, total C in the soil under Miscanthus ranged from 4.9% in the top layer to 3.9% in the lower layers with δ13C values of −16.3 to −17.8 while soil C under the adjacent arable crop was significantly lower and ranged from 1.6 to 2% with δ13C values of −23.2. This did not change much in 2012, suggesting the accumulation of soil C under Miscanthus persists for at least the first year. In contrast, the isotopic signals of soil respiration 1 year after Miscanthus removal from recultivated and set-aside plots were similar to that of the annual arable control, while just after removal the signals were similar to that of the Miscanthus control. This suggests a rapid change in the form of soil C pools that are respired

Selecting appropriate methods of knowledge synthesis to inform biodiversity policy

Responding to different questions generated by biodiversity and ecosystem services policy or management requires different forms of knowledge (e.g. scientific, experiential) and knowledge synthesis. Additionally, synthesis methods need to be appropriate to policy context (e.g. question types, budget, timeframe, output type, required scientific rigour). In this paper we present a range of different methods that could potentially be used to conduct a knowledge synthesis in response to questions arising from knowledge needs of decision makers on biodiversity and ecosystem services policy and management. Through a series of workshops attended by natural and social scientists and decision makers we compiled a range of question types, different policy contexts and potential methodological approaches to knowledge synthesis. Methods are derived from both natural and social sciences fields and reflect the range of question and study types that may be relevant for syntheses. Knowledge can be available either in qualitative or quantitative form and in some cases also mixed. All methods have their strengths and weaknesses and we discuss a sample of these to illustrate the need for diversity and importance of appropriate selection. To summarize this collection, we present a table that identifies potential methods matched to different combinations of question types and policy contexts, aimed at assisting teams undertaking knowledge syntheses to select appropriate methods

Convergent Surface Water Distributions in U.S. Cities

Earth's surface is rapidly urbanizing, resulting in dramatic changes in the abundance, distribution and character of surface water features in urban landscapes. However, the scope and consequences of surface water redistribution at broad spatial scales are not well understood. We hypothesized that urbanization would lead to convergent surface water abundance and distribution: in other words, cities will gain or lose water such that they become more similar to each other than are their surrounding natural landscapes. Using a database of more than 1 million water bodies and 1 million km of streams, we compared the surface water of 100 US cities with their surrounding undeveloped land. We evaluated differences in areal (A WB) and numeric densities (N WB) of water bodies (lakes, wetlands, and so on), the morphological characteristics of water bodies (size), and the density (D C) of surface flow channels (that is, streams and rivers). The variance of urban A WB, N WB, and D C across the 100 MSAs decreased, by 89, 25, and 71%, respectively, compared to undeveloped land. These data show that many cities are surface water poor relative to undeveloped land; however, in drier landscapes urbanization increases the occurrence of surface water. This convergence pattern strengthened with development intensity, such that high intensity urban development had an areal water body density 98% less than undeveloped lands. Urbanization appears to drive the convergence of hydrological features across the US, such that surface water distributions of cities are more similar to each other than to their surrounding landscapes. © 2014 The Author(s)

Networks at the science-policy-interface : Challenges, opportunities and the viability of the ‘network-of-networks’ approach

An approach that has been suggested as potentially addressing the challenges of science-policy-interfaces (SPIs) is the mobilization of existing networks through a ‘network-of-networks’ (NoN) approach. This paper shares empirical findings from a mixed-method study, combining qualitative and quantitative data, that critically evaluates the ‘network-of-networks’ approach for SPIs. To establish whether and how a NoN can help existing networks act more effectively at the boundary of science and policy, we use the Eklipse Mechanism as a key example. We analyse the major characteristics of networks active in biodiversity-focused science-policy interactions, the potential roles and types of engagement of participants, and the major challenges faced by networks and individuals when acting at the boundaries of science and policy. Results suggest that the more diverse the actors involved, the more effective the SPI. While a formalized EU-level SPI for biodiversity is welcomed by most respondents, willingness and actual potential to contribute to such an entity differed amongst networks, highlighting that contributions to SPIs are highly dependent on individual and organizational capacities. The challenges faced by individuals and networks range from limited resources to effective communication and achieving meaningful impact even if the institutional context is unrewarding. To make a ‘network-of-networks’ model fully operational requires meeting the capacity building needs of networks, providing institutional support, and creating room for wider engagement

Evaluating methane inventories by isotopic analysis in the London region

A thorough understanding of methane sources is necessary to accomplish methane reduction targets. Urban environments, where a large variety of methane sources coexist, are one of the most complex areas to investigate. Methane sources are characterised by specific δ13C-CH4 signatures, so high precision stable isotope analysis of atmospheric methane can be used to give a better understanding of urban sources and their partition in a source mix. Diurnal measurements of methane and carbon dioxide mole fraction, and isotopic values at King’s College London, enabled assessment of the isotopic signal of the source mix in central London. Surveys with a mobile measurement system in the London region were also carried out for detection of methane plumes at near ground level, in order to evaluate the spatial allocation of sources suggested by the inventories. The measured isotopic signal in central London (−45.7 ±0.5‰) was more than 2‰ higher than the isotopic value calculated using emission inventories and updated δ13C-CH4 signatures. Besides, during the mobile surveys, many gas leaks were identified that are not included in the inventories. This suggests that a revision of the source distribution given by the emission inventories is needed

Integrating solutions to adapt cities for climate change

Record climate extremes are reducing urban liveability, compounding inequality, and threatening infrastructure. Adaptation measures that integrate technological, nature-based, and social solutions can provide multiple co-benefits to address complex socioecological issues in cities while increasing resilience to potential impacts. However, there remain many challenges to developing and implementing integrated solutions. In this Viewpoint, we consider the value of integrating across the three solution sets, the challenges and potential enablers for integrating solution sets, and present examples of challenges and adopted solutions in three cities with different urban contexts and climates (Freiburg, Germany; Durban, South Africa; and Singapore). We conclude with a discussion of research directions and provide a road map to identify the actions that enable successful implementation of integrated climate solutions. We highlight the need for more systematic research that targets enabling environments for integration; achieving integrated solutions in different contexts to avoid maladaptation; simultaneously improving liveability, sustainability, and equality; and replicating via transfer and scale-up of local solutions. Cities in systematically disadvantaged countries (sometimes referred to as the Global South) are central to future urban development and must be prioritised. Helping decision makers and communities understand the potential opportunities associated with integrated solutions for climate change will encourage urgent and deliberate strides towards adapting cities to the dynamic climate reality.Peer reviewe