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Bacterial communities may display metabolic complementation, in which different members of the association partially contribute to the same biosynthetic pathway. In this way, the end product of the pathway is synthesized by the community as a whole. However, the emergence and the benefits of such complementation are poorly understood. Herein, we present a simple model to analyze the metabolic interactions among bacteria, including the host in the case of endosymbiotic bacteria. The model considers two cell populations, with both cell types encoding for the same linear biosynthetic pathway. We have found that, for metabolic complementation to emerge as an optimal strategy, both product inhibition and large permeabilities are needed. In the light of these results, we then consider the patterns found in the case of tryptophan biosynthesis in the endosymbiont consortium hosted by the aphid Cinara cedri. Using in-silico computed physicochemical properties of metabolites of this and other biosynthetic pathways, we verified that the splitting point of the pathway corresponds to the most permeable intermediate. ; Financial support from Spanish Government (grant reference: BFU2012-39816-C02-01 co-financed by FEDER funds and Ministerio de Economía y Competitividad) and Generalitat Valenciana (grant reference: PROMETEOII/2014/065) is grateful acknowledged. ; Peer reviewed

The results of post-Communist reforms in the Central Europe Economies have been less than ideal; the republics of the former Soviet Union have fared even worse (Lee, 2006). Necessary and sufficient conditions for post-Communist reforms include those needed to design logical and viable policies, those required to protect viable policies from unreasonable attacks, and those necessary to ensure orderly implementation with the smallest risk to the countrys economic well being. At the least, reform policies must be theoretically rigorous and supported by comprehensive empirical evidence. Moreover, even policies proven to be effective in bring economic prosperity in other countries need to be tested in small scale, in-country proving grounds before they are expanded to the entire country. Finally, however viable the proposed policies, they cannot be implemented without the explicit approval and involvement of the country political leaders.

Theoretical "necessary but not sufficient" statements are common in the organizational sciences. Traditional data analyses approaches (e.g., correlation or multiple regression) are not appropriate for testing or inducing such statements. This article proposes necessary condition analysis (NCA) as a general and straightforward methodology for identifying necessary conditions in data sets. The article presents the logic and methodology of necessary but not sufficient contributions of organizational determinants (e.g., events, characteristics, resources, efforts) to a desired outcome (e.g., good performance). A necessary determinant must be present for achieving an outcome, but its presence is not sufficient to obtain that outcome. Without the necessary condition, there is guaranteed failure, which cannot be compensated by other determinants of the outcome. This logic and its related methodology are fundamentally different from the traditional sufficiency-based logic and methodology. Practical recommendations and free software are offered to support researchers to apply NCA.

AbstractThe aim of this paper is to study optimality conditions for differentiable linearly constrained pseudoconvex programs. The stated results are based on new transversality conditions which can be used instead of complementarity ones. Necessary and sufficient optimality conditions are stated under suitable generalized convexity properties. Moreover, two different pairs of dual problems are proposed and weak and strong duality results proved. Finally, it is shown how transversality conditions can be applied to characterize optimality of convex quadratic problems and to efficiently solve a particular class of Max-Min problems

ABSTRACTCharacterization of unacceptable solutions for linear programming (LP) discriminant models have been discussed in the literature and the results presented so far are not satisfactory. This paper establishes necessary and sufficient conditions of unacceptable solutions for a number of LP models, addresses the practical implications of these conditions, and discusses the relationship between unacceptable solutions and multiple solutions.