Sustainability assessment and complementarity

Sustainability assessments bring together different perspectives that pertain to sustainability in order to produce overall assessments and a wealth of approaches and tools have been developed in the past decades. But two major problematics remain. The problem of integration concerns the surplus of possibilities for integration; different tools produce different assessments. The problem of implementation concerns the barrier between assessment and transformation; assessments do not lead to the expected changes in practice. This paper aims to analyze issues of complementarity in sustainability assessment and transformation as a key to better handling the problems of integration and implementation. Based on a generalization of Niels Bohr’s complementarity from quantum mechanics, we have identified two forms of complementarity in sustainability assessment, observer stance complementarity and value complementarity. Unlike many other problems of sustainability assessment, complementarity is of a fundamental character connected to the very conditions for observation. Therefore complementarity cannot be overcome methodologically; only handled better or worse. Science is essential to the societal goal of sustainability, but these issues of complementarity impede the constructive role of science in the transition to more sustainable structures and practices in food systems. The agencies of sustainability assessment and transformation need to be acutely aware of the importance of different perspectives and values and the complementarities that may be connected to these differences. An improved understanding of complementarity can help to better recognize and handle issues of complementarity. These deliberations have relevance not only for sustainability assessment, but more generally for transdisciplinary research on wicked problems

Reformulations of mathematical programming problems as linear complementarity problems

A family of complementarity problems are defined as extensions of the well known Linear Complementarity Problem (LCP). These are (i.) Second Linear Complementarity Problem (SLCP) which is an LCP extended by introducing further equality restrictions and unrestricted variables, (ii.) Minimum Linear Complementarity Problem (MLCP) which is an LCP with additional variables not required to be complementary and with a linear objective function which is to be minimized, (iii.) Second Minimum Linear Complementarity Problem (SMLCP) which is an MLCP but the nonnegative restriction on one of each pair of complementary variables is relaxed so that it is allowed to be unrestricted in value. A number of well known mathematical programming problems, namely quadratic programming (convex, nonconvex, pseudoconvex nonconvex), bilinear programming, game theory, zero-one integer programming, the fixed charge problem, absolute value programming, variable separable programming are reformulated as members of this family of four complementarity problems

Local/Non-Local Complementarity in Topological Effects

In certain topological effects the accumulation of a quantum phase shift is accompanied by a local observable effect. We show that such effects manifest a complementarity between non-local and local attributes of the topology, which is reminiscent but yet different from the usual wave-particle complementarity. This complementarity is not a consequence of non-commutativity, rather it is due to the non-canonical nature of the observables. We suggest that a local/non-local complementarity is a general feature of topological effects that are ``dual'' to the AB effect.Comment: 4 page

Quantification of complementarity in multi-qubit systems

Complementarity was originally introduced as a qualitative concept for the discussion of properties of quantum mechanical objects that are classically incompatible. More recently, complementarity has become a \emph{quantitative} relation between classically incompatible properties, such as visibility of interference fringes and "which-way" information, but also between purely quantum mechanical properties, such as measures of entanglement. We discuss different complementarity relations for systems of 2-, 3-, or \textit{n} qubits. Using nuclear magnetic resonance techniques, we have experimentally verified some of these complementarity relations in a two-qubit system.Comment: 12 pages, 10 figures (A display error about the figures in the previous version

When are signals complements or substitutes?

The paper introduces a notion of complementarity (substitutability) of two signals which requires that in all decision problems each signal becomes more (less) valuable when the other signal becomes available. We provide a general characterization which relates complementarity and substitutability to a Blackwell-comparison of two auxiliary signals. In a special setting with a binary state space and binary, symmetric signals, we find an explicit characterization that permits an intuitive interpretation of complementarity and substitutability. We demonstrate how these conditions extend to the general case. Finally, we study implications of complementarity and substitutability for information acquisition and in a second price auction

Quark-lepton complementarity and self-complementarity in different schemes

With the progress of increasingly precise measurements on the neutrino mixing angles, phenomenological relations such as quark-lepton complementarity (QLC) among mixing angles of quarks and leptons and self-complementarity (SC) among lepton mixing angles have been observed. Using the latest global fit results of the quark and lepton mixing angles in the standard Chau-Keung scheme, we calculate the mixing angles and CP-violating phases in the other eight different schemes. We check the dependence of these mixing angles on the CP-violating phases in different phase schemes. The dependence of QLC and SC relations on the CP phase in the other eight schemes is recognized and then analyzed, suggesting that measurements on CP-violating phases of the lepton sector are crucial to the explicit forms of QLC and SC in different schemes.Comment: 11 pages, 3 figures, version accepted for publication in PR