DEA models for ratio data:convexity consideration

Data envelopment analysis (DEA) is defined based on observed units and by finding the distance of each unit to the border of estimated production possibility set (PPS). The convexity is one of the underlying assumptions of the PPS. This paper shows some difficulties of using standard DEA models in the presence of input-ratios and/or output-ratios. The paper defines a new convexity assumption when data includes a ratio variable. Then it proposes a series of modified DEA models which are capable to rectify this problem.

General and multiplicative non-parametric corporate performance models with interval ratio data

The increasing intensity of global competition has led organizations to utilize various types of performance measurement tools for improving the quality of their products and services. Data envelopment analysis (DEA) is a methodology for evaluating and measuring the relative efficiencies of a set of decision making units (DMUs) that use multiple inputs to produce multiple outputs. All the data in the conventional DEA with input and/or output ratios assumes the form of crisp numbers. However, the observed values of data in real-world problems are sometimes expressed as interval ratios. In this paper, we propose two new models: general and multiplicative non-parametric ratio models for DEA problems with interval data. The contributions of this paper are fourfold: (1) we consider input and output data expressed as interval ratios in DEA; (2) we address the gap in DEA literature for problems not suitable or difficult to model with crisp values; (3) we propose two new DEA models for evaluating the relative efficiencies of DMUs with interval ratios, and (4) we present a case study involving 20 banks with three interval ratios to demonstrate the applicability and efficacy of the proposed models where the traditional indicators are mostly financial ratios. © 2011 Elsevier Inc.

Measurement of the TeV atmospheric muon charge ratio with the complete OPERA data set

The OPERA detector, designed to search for νμ → ντ oscillations in the CNGS beam, is located in the underground Gran Sasso laboratory, a privileged location to study TeV-scale cosmic rays. For the analysis here presented, the detector was used to measure the atmospheric muon charge ratio in the TeV region. OPERA collected chargeseparated cosmic ray data between 2008 and 2012. More than 3 million atmospheric muon events were detected and reconstructed, among which about 110000 multiple muon bundles. The charge ratio Rμ ≡ Nμ+/Nμ− was measured separately for single and for multiple muon events. The analysis exploited the inversion of the magnet polarity which was performed on purpose during the 2012 Run. The combination of the two data sets with opposite magnet polarities allowedminimizing systematic uncertainties and reaching an accurate determination of the muon charge ratio. Data were fitted to obtain relevant parameters on the composition of primary cosmic rays and the associated kaon production in the forward fragmentation region. In the surface energy range 1–20 TeV investigated by OPERA, Rμ is well described by a parametric model including only pion and kaon contributions to themuon flux, showing no significant contribution of the prompt component. The energy independence supports the validity of Feynman scaling in the fragmentation region up to 200 TeV/nucleon primary energy.

Inbreeding and selection on sex ratio in the bark beetle Xylosandrus germanus.

ABSTRACT: BACKGROUND: Local Mate Competition (LMC) theory predicts a female should produce a more female-biased sex ratio if her sons compete with each other for mates. Because it provides quantitative predictions that can be experimentally tested, LMC is a textbook example of the predictive power of evolutionary theory. A limitation of many earlier studies in the field is that the population structure and mating system of the studied species are often estimated only indirectly. Here we use microsatellites to characterize the levels of inbreeding of the bark beetle Xylosandrus germanus, a species where the level of LMC is expected to be high. RESULTS: For three populations studied, genetic variation for our genetic markers was very low, indicative of an extremely high level of inbreeding (FIS = 0.88). There was also strong linkage disequilibrium between microsatellite loci and a very strong genetic differentiation between populations. The data suggest that matings among non-siblings are very rare (3%), although sex ratios from X. germanus in both the field and the laboratory have suggested more matings between non-sibs, and so less intense LMC. CONCLUSIONS: Our results confirm that caution is needed when inferring mating systems from sex ratio data, especially when a lack of biological detail means the use of overly simple forms of the model of interest.

Inbreeding and selection on sex ratio in the bark beetle Xylosandrus germanus

Background Local Mate Competition (LMC) theory predicts a female should produce a more female-biased sex ratio if her sons compete with each other for mates. Because it provides quantitative predictions that can be experimentally tested, LMC is a textbook example of the predictive power of evolutionary theory. A limitation of many earlier studies in the field is that the population structure and mating system of the studied species are often estimated only indirectly. Here we use microsatellites to characterize the levels of inbreeding of the bark beetle Xylosandrus germanus, a species where the level of LMC is expected to be high. Results For three populations studied, genetic variation for our genetic markers was very low, indicative of an extremely high level of inbreeding (FIS = 0.88). There was also strong linkage disequilibrium between microsatellite loci and a very strong genetic differentiation between populations. The data suggest that matings among non-siblings are very rare (3%), although sex ratios from X. germanus in both the field and the laboratory have suggested more matings between non-sibs, and so less intense LMC. Conclusions Our results confirm that caution is needed when inferring mating systems from sex ratio data, especially when a lack of biological detail means the use of overly simple forms of the model of interest.

Element ratio (Sr/Ca, Ba/Ca, B/Ca, and Mg/Ca) profiles throughout the larval life stage of Mytilus edulis, 2011

Rising anthropogenic CO2 in the surface ocean has raised serious concerns for the ability of calcifying organisms to secrete their shells and skeletons. Previous mollusc carbonate perturbation experiments report deleterious effects at lowered pH (7.8-7.4 pH units), including reduced shell length and thickness and deformed shell morphology. It is not clear whether the reduced shell growth results from a decrease in calcification rate due to lowered aragonite saturation or from an indirect effect on mollusc metabolism. We take a novel approach to discerning between these two processes by examining the impact of lowered pH on the 'vital-effect' associated with element ratios. Reported herein are the first element ratio (Sr/Ca, Ba/Ca, B/Ca, Mg/Ca and Mn/Ca) profiles throughout the larval life stage of Mytilus edulis. Element ratio data for individuals reared in ambient conditions provide new insights into biomineralization during larval development. Sr/Ca ratios are consistent with Sr incorporation in the mineral phase. Mg and Mn are likely hosted in an organic phase. The Ba partition coefficient of early larval shells is one of the highest reported in biogenic aragonite. The reason for the high Ba concentrations is unknown, but may reflect the assimilation of Ba from food and/or Ba concentration in an organic or amorphous carbonate phase. There is no observable difference in the way the studied elements are incorporated into the shells of individuals reared in ambient and lowered pH conditions. The reduced growth rate at lower pH may be a consequence of a disruption to the larval mollusc metabolism.

Prevention of Caval Collapse During Venous Drainage for CPB.

A new plastic self-expanding Smartcanula (Smartcanula LLC, Lausanne, Switzerland) is designed for central insertion and prevention of caval collapse. The objective of our work is to assess the influence of the new design on atrial chatter. Caval collapse over the entire caval axis, right atrial, hepatic, renal vein, and iliac vein is realized in drainage tubes with holes at 5 cm distance intervals. Smartcanulas with various lengths (26 cm [= right atrial], 34 cm [= hepatic], 43 cm [= renal], and 53 cm [= iliac]) versus two-stage cannulas are compared. Pressure drop (ΔP) is measured using Millar pressure-transducers. Flow rate (Q) is measured using an ultrasonic flow meter. Cannula resistance is defined as the ΔP/Q ratio. Data display and recording are controlled using LabView virtual instruments. At an 88 cm height differential, Q values are 8.69 and 6.8 l/min, and ΔP/Q ratios are 0.63 and 1.28 for the 26-cm Smartcanula and the reference cannula, respectively. The 34-cm Smartcanula showed 8.89 l/min and 0.6 ΔP/Q ratio vs. 7.59 l/min and 0.9 for the control cannula (P < 0.05). The 43-cm and 53-cm Smartcanulas showed Q values of 9.04 and 8.81 l/min, respectively, and ΔP/Q2 ratio of 0.6. The Smartcanula outperforms the two-stage cannula, and direct cannula insertion without guide wire is effective.