Strong duality in conic linear programming: facial reduction and extended duals

The facial reduction algorithm of Borwein and Wolkowicz and the extended dual of Ramana provide a strong dual for the conic linear program $$(P) \sup {<c, x> | Ax \leq_K b}$$ in the absence of any constraint qualification. The facial reduction algorithm solves a sequence of auxiliary optimization problems to obtain such a dual. Ramana's dual is applicable when (P) is a semidefinite program (SDP) and is an explicit SDP itself. Ramana, Tuncel, and Wolkowicz showed that these approaches are closely related; in particular, they proved the correctness of Ramana's dual using certificates from a facial reduction algorithm. Here we give a clear and self-contained exposition of facial reduction, of extended duals, and generalize Ramana's dual: -- we state a simple facial reduction algorithm and prove its correctness; and -- building on this algorithm we construct a family of extended duals when $K$ is a {\em nice} cone. This class of cones includes the semidefinite cone and other important cones.Comment: A previous version of this paper appeared as "A simple derivation of a facial reduction algorithm and extended dual systems", technical report, Columbia University, 2000, available from http://www.unc.edu/~pataki/papers/fr.pdf Jonfest, a conference in honor of Jonathan Borwein's 60th birthday, 201

Genetic Variability of Yield and Its Components in Winter Forage Pea Cultivars

The genus Pisum (peas) is rich in variability of morphological traits. It provides an excellent basis for breeding, but is also one of the reasons for the still undefined status of Pisum taxons (Mihailović et al., 2004a). The majority of forage pea cultivars used belongs to subspecies sativum and variety arvense (Maxted & Ambrose, 2000). The objective of our study was to determine genetic variability of yield and its components in six winter forage pea cultivars of different origin and to evaluate their breeding potential

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

Effect of Cutting Date on Quality of Red Clover Forage

Development stage or plant age is an important factor determining the chemical composition and quality of red clover forage (Ignjatovic et al., 2001). In early spring, young red clover plants have large leaf mass, high contents of moisture, protein and minerals and a low fibre content. In the course of the growing season, under the effects of long days and high temperatures, the plant undergoes morphological changes: leaves grow more slowly, the stem elongates, dry matter yield increases and quality drops, especially digestibility and the contents of protein and minerals

Nanofibrous solid dosage form of living bacteria prepared by electrospinning

The aim of this work was to investigate the suitability of electrospinning for biodrug delivery and to develop an electrospinning-based method to produce vaginal drug delivery systems. Lactobacillus acidophilus bacteria were encapsulated into nanofibers of three different polymers (polyvinyl alcohol and polyvinylpyrrolidone with two different molar masses). Shelf life of the bacteria could be enhanced by the exclusion of water and by preparing a solid dosage form, which is an advantageous and patient-friendly way of administration. The formulations were stored at –20, 7 and 25°C, respectively. Viability testing showed that the nanofibers can provide long term stability for huge amounts of living bacteria if they are kept at (or below) 7°C. Furthermore, all kinds of nanowebs prepared in this work dissolved instantly when they got in contact with water, thus the developed biohybrid nanowebs can provide new potential ways for curing bacterial vaginosis

Assessing connectivity between an overlying aquifer and a coal seam gas resource using methane isotopes, dissolved organic carbon and tritium

Coal seam gas (CSG) production can have an impact on groundwater quality and quantity in adjacent or overlying aquifers. To assess this impact we need to determine the background groundwater chemistry and to map geological pathways of hydraulic connectivity between aquifers. In south-east Queensland (Qld), Australia, a globally important CSG exploration and production province, we mapped hydraulic connectivity between the Walloon Coal Measures (WCM, the target formation for gas production) and the overlying Condamine River Alluvial Aquifer (CRAA), using groundwater methane (CH4) concentration and isotopic composition (δ13C-CH4), groundwater tritium (3H) and dissolved organic carbon (DOC) concentration. A continuous mobile CH4 survey adjacent to CSG developments was used to determine the source signature of CH4 derived from the WCM. Trends in groundwater δ13C-CH4 versus CH4 concentration, in association with DOC concentration and 3H analysis, identify locations where CH4 in the groundwater of the CRAA most likely originates from the WCM. The methodology is widely applicable in unconventional gas development regions worldwide for providing an early indicator of geological pathways of hydraulic connectivity

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