Choquet integrals, entropy, the Gini index, and applications

State estimation in a discrete-time linear dynamical system is considered in the presence of random process noise, in addition to a malicious adversary able to manipulate some measurements of the system. The adversary has access to only a subset of the measurements, but the particular subset is unknown, and it may adjust these measurements in an arbitrary fashion. A specific attack is proposed that gives a lower bound on the mean squared error for any estimator. Two estimators are proposed; one based on a non-convex optimization problem using sparsity constraints, the second a convex relaxation using a mixed ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> /ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm. The performance of both estimators are studied using simulations.

The favourable growth performance of SSA over the last 20 years (figure 15.1) has been accompanied by a modest decline in poverty, from 59 to 48 per cent over 1993-2010, i.e., much less than that recorded in South Asia (Ferreira, 2014). This aggregate trend, however, conceals substantial cross-country variations. The key question, then, is: How can such differences in poverty reduction rates be explained? The standard approach (Bourguignon, 2003) shows that a percentage change in poverty incidence can be decomposed into the percentage changes in the growth rate of GDP per capita and in the Gini coefficient, plus a small residual. In this regard, it must be noted that in SSA, the average GDP growth per capita oscillated in a narrow range, i.e., between 1.7 per cent in non-resource-rich countries and 2.6 per cent in resource-rich ones. The reason that poverty declined at different rates is, therefore, to be found in the divergence of inequality trends experienced by the SSA countries. Indeed, this chapter and Chapter 2 argue that over 1991-2011, income inequality rose in several countries but declined in a similar number.

Density Peaks Clustering (DPC) is a density-based clustering algorithm that has the advantage of not requiring clustering parameters and detecting non-spherical clusters. The density peaks algorithm obtains the actual cluster center by inputting the cutoff distance and manually selecting the cluster center. Thus, the clustering center point is not selected on the basis of considering the whole data set. This paper proposes a method called G-KNN-DPC to calculate the cutoff distance based on the Gini coefficient and K-nearest neighbor. G-KNN-DPC first finds the optimal cutoff distance with Gini coefficient, and then the center point with the K-nearest neighbor. The automatic clustering center method can not only avoid the error that a cluster detects two center points but also effectively solve the traditional DPC algorithm defect that cannot handle complex data sets. Compared with DPC, Fuzzy C-Means, K-means, KDPC and DBSCAN, the proposed algorithm creates better clusters on different data sets.

There are different nonlinear integrals that could be used as an aggregation tool in information fusion and data mining. The Choquet integral with respect to fuzzy measures is one of them. We present some methods to identify fuzzy measures based on the Choquet integral in this paper. An iterative method introduced by Grabisch is discussed with some counterexamples. Furthermore, after removing some restrictions which are used in Grabisch's model, we introduce an algebraic method and a genetic algorithm to identify fuzzy measures and present some experimental results on both artificial and real-world data sets to show their effectiveness.

Choquet integral is a powerful aggregation tool in information fusion and classification. It is established with respect to signed fuzzy measure. The nonadditivity of the signed fuzzy measure provides an effective representation to describe the interaction among contributions from the predictive attributes to the objective attributes. Currently, the values of the signed fuzzy measure in most classifiers based on Choquet integral are either preset subjectively by experience, or retrieved by global optimization methods which are time-consuming. In this paper, a new discriminant analysis algorithm to retrieve the values of signed fuzzy measure in classification models based on Choquet integral is proposed via Fisher's linear discriminant. It is the first time to derive the values of the signed fuzzy measure directly in an analytic form. Performance validation on synthetics and benchmark data sets are conducted to reveal the feasibility and effectiveness of the proposed method.

Algorithm for Vascular Access in our Imaging Department

Relationships between grandparents and grandchildren are a vital aspect of family life, yet little is known about how grandchild contact affects grandparents' emotions in daily life. This study aims to examine the short-term impact of grandchild contact on grandparents' positive and negative emotions. Analyzing a sample of 125 grandparents from the "Daily Experiences and Wellbeing study" followed for a period of 5 days (6 assessments per day) with multilevel structural equation modeling, we compared grandparents' positive and negative emotions when being with their grandchildren to contact with close others and to time with their spouse or alone. Additionally, using snippets of ambient sound recordings, we investigated whether grandparents used more positive and fewer negative emotion-related words when they had contact with grandchildren compared to time spent with others. Interactions with grandchildren were associated with increased positive emotions, especially more love and pride, and a higher use of positive words compared to interactions with other close social members and time spent alone or with a spouse. We found limited evidence that grandparents also reported feeling sadder and more worried when with their grandchildren, although these effects were less robust. Our findings, based on multiple assessment methods (self-report and language use), indicate that grandchild contact is associated with increases in specific self-reported emotions, which are also mirrored in the language used in daily life. These particular emotions (love and pride) may highlight the unique relationship between grandchildren and grandparents, marked by affection and opportunities to express generativity.

Alternans, a beat-to-beat alternation in cardiac signals, may serve as a precursor to lethal cardiac arrhythmias, including ventricular tachycardia and ventricular fibrillation. Therefore, alternans is a desirable target of early arrhythmia prediction/detection. For long-term records and in the presence of noise, the definition of alternans is qualitative and ambiguous. This makes their automatic detection in large spatiotemporal data sets almost impossible. We present here a quantitative combinatorics-derived definition of alternans in the presence of random noise and a novel algorithm for automatic alternans detection using criteria like temporal persistence (TP), representative phase (RP) and alternans ratio (AR). This technique is validated by comparison to theoretically-derived probabilities and by test data sets with white noise. Finally, the algorithm is applied to ultra-high resolution optical mapping data from cultured cell monolayers, exhibiting calcium alternans. Early fine-scale alternans, close to the noise level, were revealed and linked to the later formation of larger regions and evolution of spatially discordant alternans (SDA). This robust new technique can be useful in quantification and better understanding of the onset of arrhythmias and in general analysis of space-time alternating signals.

Many of the recent company collapses, such as Enron, WorldCom, Tyco and Global Crossing, are believed to have been predictable by the detailed reading of several years of a company’s annual report and accounts. A company’s published annual report and accounts are important primary documents for anyone with an interest in the organization and electronic databases are therefore frequently seen as one convenient method of providing access to annual report information. Typical databases providing this service include: Perfect Information; Juniper; UK Company Factfinder; Global Access; Business Browser; and CAROL (Company Annual Reports Online). A closer look, however, reveals that these services, in addition to being expensive, have a number of inherent limitations. A project was undertaken by the libraries of London Business School, Manchester Business School, the University of Strathclyde, and the University of Warwick to find a solution to this problem. The project, “Company annual reports: assuring the distributed national print archive”, funded by the Research Support Libraries Programme (RSLP) and running from October 2000 to July 2002, aimed: to provide a comprehensive national resource for researchers interested in using annual report literature; to identify and catalogue major collections of historic company annual reports (substantive collections of pre-1995 material); to address collection development issues, in particular retention policies; and to investigate the potential for the development of a national collection strategy for company annual reports. The project outcome was the development of the SCoRe Database (Search Company Reports) (http://www.score.ac.uk), a Web based, national union catalogue of company annual report holdings in major collections held by academic and national libraries.

The Gini index is a measure of the inequality of a distribution that can be derived from Lorenz curves. While commonly used in, e.g., economic research, it suffers from ambiguity via lack of Lorenz dominance preservation. Here, investigation of large sets of empirical distributions of incomes of the World’s countries over several years indicated firstly, that the Gini indices are centered on a value of 33.33% corresponding to the Gini index of the uniform distribution and secondly, that the Lorenz curves of these distributions are consistent with Lorenz curves of log-normal distributions. This can be employed to provide a Lorenz dominance preserving equivalent of the Gini index. Therefore, a modified measure based on log-normal approximation and standardization of Lorenz curves is proposed. The so-called UGini index provides a meaningful and intuitive standardization on the uniform distribution as this characterizes societies that provide equal chances. The novel UGini index preserves Lorenz dominance. Analysis of the probability density distributions of the UGini index of the World’s counties income data indicated multimodality in two independent data sets. Applying Bayesian statistics provided a data-based classification of the World’s countries’ income distributions. The UGini index can be re-transferred into the classical index to preserve comparability with previous research.

ABSTRACTPolitical science takes pride in objective and methodologically rigorous research. This should be reflected in a clear and concise writing style that convinces readers by the content of the research, not by the language used to report about it. This article demonstrates that this is true but only to a limited extent. It shows that—similar to recent findings from natural-sciences research—the frequency of positive words that political scientists use to describe their research has increased markedly in recent decades. At the same time, however, the magnitude of this increase is much less pronounced. The article discusses and analyzes potential explanations for this trend. We suspect that it can be attributed at least partly to changing norms in the discipline, in which research framed in a positive way is more likely to be published.

A New Heuristic for generating height balanced compact decision trees with reduced path length has been proposed in this paper. The proposed node split measure (MGI) modifies attribute selection process of gini index by giving importance to almost equal sized sub partitions and at same time counts frequently occurring target classes in those sub partitions. This results in less skewed decision trees, while maintaining similar accuracy as provided by gini index. As a part of data pre processing step, MGI gives a new approach to handle missing values and also provides initial data set size reduction. The performance evaluation is done on few sample data sets taken from UCI Machine learning repository. The experimental evaluation of MGI node split measure is done with gini index which shows that the proposed split measure produces height balanced decision tree of reduced height, which in turn reduces antecedents in the rule generated.

"This paper aims to examine the extent of corporate social reporting practices in the annual reports of companies in India and to ascertain the differences if any, between public sector and private sector companies and to investigate what were the determinants of corporate social reporting . The study intends to answer the research questions which include: a) what variables could represent a Conceptual Model of Corporate Social Reporting consists of dependent variables and Independent variables? b) What are the factors of Corporate Social Reporting (COSOR) and how valid and reliable are these factors? c) What is the degree of COSOR by factors in public and private sector companies? d) What are the determinants of COSOR? What is the level of their influence on COSOR? A sample of 120 listed companies of National Stock Exchange of India was chosen and they were stratified in to public and private sector companies. A Corporate social reporting Index was constructed for data collection through content analysis from the annual reports. The results of the study revealed that social accounting information were disclosed in company’s annual reports, chairman’s speech, directors’ reports, notes to accounts, schedule to accounts and auditor’s report. The degree of corporate social reporting varies between public sector and private sector companies. The public sector companies have disclosed more corporate social reporting information than the private sector companies. The study found that higher the level of capital employed, earnings before depreciation and taxes, total assets and total sales higher was the level of corporate social reporting. However, the degree of influence of determinants on corporate social reporting was different among public and private sector companies. Most of the companies have disclosed corporate social information on voluntary basis. To improve the understandably, uniformity, and comparability of corporate social information, this study suggests making it mandatory. A standard format for disclosure of corporate social information shall be prescribed by the Ministry of Corporate Affairs by amending the Indian Companies Act. The concept of social accounting is relatively new in India. This study suggests to include it in the commerce curriculum and also in the curriculum of CA/CWA/CS. Corporate Social Reporting is such a vast area of research that no single study can cover different dimensions related to it. Though some studies including the present study have been conducted on Corporate Social Reporting Practices in India, but still there is much potential of research in this area. Future research in this area will hopefully bring more brightening result measuring and analysing social costs and benefits data by manager as well as by other concerned. Since the subject is in the primary stage, an in-depth research is needed to be done in different sectors such as banking information technology, manufacturing etc. The results are specifically applicable to sample companies and generalisations can be made with caution. The results of the study are based on the data collected from published annual reports of sample companies using content analysis method. Corporate social reporting in company websites, brochures etc are not covered. Social cost and benefit analysis is not covered in this study.

This paper addresses the robot selection problem by using a multi-criteria decision making approach based on the Choquet integral. The key feature of the Choquet integral is that it can incorporate interaction among attributes into the decision analysis, an issue that has been generally overlooked in earlier robot selection studies. The proposed decision framework makes use of the information previously elicited from experts analyzing a reference set of robot alternatives with the same selection criteria as in the current evaluation, and applies the Choquet integral to determine the most suitable robot. A comprehensive illustrative example is presented using a previously published data set, and the results obtained using the proposed approach are compared with those of another multi-criteria decision aid, which has been also employed in earlier studies addressing robot selection.KeywordsMulticriteria DecisionFuzzy MeasureAggregation ToolChoquet IntegralFuzzy IntegralThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The presence of random noise, interference, echoes, and imperfect frequency response in terrestrial broadcasting channels, and of pervasive low-level reflections in cable systems, degrades the quality of most television reception. These effects tend to reduce the difference between the quality of NTSC and that of various advanced television systems, as actually delivered to the home via such channels. In this article, several methods are presented to deal with these effects, and thus to preserve the improved quality made possible by currently proposed EDTV and HDTV systems. Automatic channel equalization is used for first-order correction of echoes and frequency distortion. A scrambling method is described that transforms all remaining degradations to additive random noise, which, for a given noise power, is of minimum visibility. Random noise, whether additive or produced by scrambling of other defects, is suppressed by adaptive modulation of the various signal components. If the channel carrier-to-noise ratio (CNR) is high enough, some digital data can be transmitted in addition to the analog signal by a method called “data under.” These methods are applied to a receiver-compatible system that utilizes a very low power 3-MHz augmentation channel as well as to a bandwidth-efficient 6-MHz system that is not receiver compatible. One version of the latter system can be operated at such low CNR that it may be possible to utilize the taboo channels.