Linear Inequality Concepts and Social Welfare

The paper presents an abstract definition of linear inequality concepts leading to linearly invariant inequality measures and characterizes the class of linear concepts completely. Two general methods of deriving ethical measures are proposed. They imply an Atkinson-Kolm-Sen index and a new dual index reflecting the inequality of living standard. Then all separable social welfare orderings which generate linearly invariant measures are characterized. The measures are presented and their general properties discussed. Dual measures prove to be additively decomposable. Linear welfare orderings defined on rank-ordered income vectors are examined. They are consistent with all linear inequality and yield an inequality ordering for every concept.inequality concept, ethical inequality measures, decomposability, social welfare

Quantifying quantum discord and entanglement of formation via unified purifications

We propose a scheme to evaluate the amount of quantum discord and entanglement of formation for mixed states, and reveal their ordering relation via an intrinsic relationship between the two quantities distributed in different partners of the associated purification. This approach enables us to achieve analytical expressions of the two measures for a sort of quantum states, such as an arbitrary two-qubit density matrix reduced from pure three-qubit states and a class of rank-2 mixed states of 4\times 2 systems. Moreover, we apply the scheme to characterize fully the dynamical behavior of quantum correlations for the specified physical systems under decoherence.Comment: 4 pages, 2 figures, accepted for publication in Phys. Rev.

Methodology of measuring performance in alternative investment

The development of alternative investment has highlighted the limitations of standard performance measures like the Sharpe ratio, primarily because alternative strategies yield returns distributions which can be far from gaussian. In this paper, we propose a new framework in which trades, portfolios or strategies of various types can be analysed regardless of assumptions on payoff. The proposed class of measures is derived from natural and simple properties of the asset allocation. We establish representation results which allow us to describe our set of measures and involve the log-Laplace transform of the asset distribution. These measures include as particular cases the squared Sharpe ratio, Stutzer's rank ordering index and Hodges' Generalised Sharpe Ratio. Any measure is shown to be proportional to the squared Sharpe ratio for gaussian distributions. For non gaussian distributions, asymmetry and fat tails are taken into account. More precisely, the risk preferences are separated into gaussian and non-gaussian risk aversions.Alternative investment, performance measure, additive independence condition, generalised Sharpe ratio, portfolio optimization.

Application of social networking algorithms in program analysis: understanding execution frequencies

2011 Summer.Includes bibliographical references.There may be some parts of a program that are more commonly used at runtime, whereas there may be other parts that are less commonly used or not used at all. In this exploratory study, we propose an approach to predict how frequently or rarely different parts of a program will get used at runtime without actually running the program. Knowledge of the most frequently executed parts can help identify the most critical and the most testable parts of a program. The portions predicted to be the less commonly executed tend to be hard to test parts of a program. Knowing the hard to test parts of a program can aid the early development of test cases. In our approach we statically analyse code or static models of code (like UML class diagrams), using quantified social networking measures and web structure mining measures. These measures assign ranks to different portions of code for use in predictions of the relative frequency that a section of code will be used. We validated these rank ordering of predictions by running the program with a common set of use cases and identifying the actual rank ordering. We compared the predictions with other measures that use direct coupling or lines of code. We found that our predictions fared better as they were statistically more correlated to the actual rank ordering than the other measures. We present a prototype tool written as an eclipse plugin, that implements and validates our approach. Given the source code of a Java program, our tool computes the values of the metrics required by our approach to present ranks of all classes in order of how frequently they are expected to get used. Our tool can also instrument the source code to log all the necessary information at runtime that is required to validate our predictions

Comparison of hearing aids and assistive listening devices with omni-directional and directional microphones at personal communication distances

This study was conducted to compare performance between binaural hearing aids and an ALD used in two modes (companion mode and interview mode). Performance was evaluated on the basis of word recognition at two distances and SMI at four distances. Additionally, this study was conducted to determine if directional microphones can be used to significantly improve performance with both hearing aids and an ALD using measures of word recognition and SNR. Word recognition performance measures indicated a rank ordering of the amplification devices with the poorest performance with the HA, improving with the ALDI and best when using the ALDC. The use of directional microphones improved word recognition for each device but the improvement was not sufficient to change the rank ordering of devices. As communication distance increased, the SMR decreased for three amplification devices. The measures of SNR found the least favorable SNR to be with the HA improving with the ALDI and best with the ALDC. The use of directional microphones increased the SNR for the amplification devices over use of omni-directional microphones, however, the rank ordering did not change. Additionally, a critical SNR was established for the listeners in this study. Improving the SNR above the level of the SNR did not significantly improve word recognition performance regardless of amplification device or communication distance. These results provide clear evidence that the ALD can improve both word recognition performance and SNR more than HAs. While the use of directional microphones can be beneficial, the benefit of directional microphones in HA does not out-perform the benefit of directional microphones in ALD. Additionally, the results indicate that the ALD can be used effectively in the interview mode at personal communication distances

The simultaneous valuation of states from multiple instruments using ranking and VAS data: methods and preliminary results

Background: Previous methods of empirical mapping involve using regressions on patient or general population self-report data from datasets involving 2 or more instruments. This approach relies on overlap in the descriptive systems of the measures, but key dimensions may not be present in both measures. Furthermore, this assumes it is appropriate to use different instruments on the same population, which may not be the case for all patient groups. The aim of the study described here is to develop a new method of mapping using general population preferences for hypothetical health states defined by the descriptive systems of different measures. This paper presents a description of the methods used in the study and reports on the results of the valuation study including details about the respondents, feasibility and quality (e.g. response rate, completion and consistency) and descriptive results on VAS and ranking data. The use of these results to estimate mapping functions between instruments will be presented in a companion paper. Methods: The study used interviewer administered versions of ranking and VAS techniques to value 13 health states defined by each of 6 instruments: EQ-5D (generic), SF-6D (generic), HUI2 (generic for children), AQL-5D (asthma specific), OPUS (social care specific), ICECAP (capabilities). Each interview involved 3 ranking and visual analogue scale (VAS) tasks with states from 3 different instruments where each task involves the simultaneous valuation of multiple instruments. The study includes 13 health and well-being states for each instrument (16 for EQ-5D) that reflect a range of health state values according to the published health state values for each instrument and each health state is valued approximately 75-100 times. Results: The sample consists of 499 members of the UK general population with a reasonable spread of background characteristics (response rate=55%). The study achieved a completion rate of 99% for all states included in the rank and rating tasks and 94.8% of respondents have complete VAS responses and 97.2% have complete rank responses. Interviewers reported that it is doubtful for 4.1% of respondents that they understood the tasks, and 29.3% of respondents stated that they found the tasks difficult. The results suggest important differences in the range of mean VAS and mean rank values per state across instruments; for example, mean VAS values for the worst state vary across instruments from 0.075 to 0.324. Respondents are able to change the ordering of states between the rank and VAS tasks and 12.0% of respondents have one or more differences in their rank and VAS orderings for every task. Conclusions: This study has demonstrated the feasibility of simultaneously valuing health states from different preference-based instruments. The preliminary analysis of the results presented here provides the basis for a new method of mapping between measures based on general population preferences

The simultaneous valuation of states from multiple instruments using ranking and VAS data: methods and preliminary results

Background: Previous methods of empirical mapping involve using regressions on patient or general population self-report data from datasets involving two or more instruments. This approach relies on overlap in the descriptive systems of the measures, but key dimensions may not be present in both measures. Furthermore this assumes it is appropriate to use different instruments on the same population, which may not be the case for all patient groups. The aim of the study described here is to develop a new method of mapping using general population preferences for hypothetical health states defined by the descriptive systems of different measures. This paper presents a description of the methods used in the study and reports on the results of the valuation study including details about the respondents, feasibility and quality (e.g. response rate, completion and consistency) and descriptive results on VAS and ranking data. The use of these results to estimate mapping functions between instruments will be presented in a companion paper. Methods: The study used interviewer administered versions of ranking and VAS techniques to value 13 health states defined by each of 6 instruments: EQ-5D (generic), SF-6D (generic), HUI2 (generic for children), AQL-5D (asthma specific), OPUS (social care specific), ICECAP (capabilities). Each interview involved 3 ranking and visual analogue scale (VAS) tasks with states from 3 different instruments where each task involves the simultaneous valuation of multiple instruments. The study includes 13 health and well-being states for each instrument (16 for EQ-5D) that reflect a range of health state values according to the published health state values for each instrument and each health state is valued approximately 75-100 times. Results: The sample consists of 499 members of the UK general population with a reasonable spread of background characteristics (response rate=55%). The study achieved a completion rate of 99% for all states included in the rank and rating tasks and 94.8% of respondents have complete VAS responses and 97.2% have complete rank responses. Interviewers reported that it is doubtful for 4.1% of respondents that they understood the tasks, and 29.3% of respondents stated that they found the tasks difficult. The results suggest important differences in the range of mean VAS and mean rank values per state across instruments, for example mean VAS values for the worst state vary across instruments from 0.075 to 0.324. Respondents are able to change the ordering of states between the rank and VAS tasks and 12.0% of respondents have one or more differences in their rank and VAS orderings for every task. Conclusions: This study has demonstrated the feasibility of simultaneously valuing health states from different preference-based instruments. The preliminary analysis of the results presented here provides the basis for a new method of mapping between measures based on general population preferences.preference-based measures of health; quality of life; mapping; visual analogue scale; ranking