Voting Operators in the Space of Choice Functions

Assuming the individual and collective opinions are given as choice functions, a new formalization of the voting problem is considered. The notions of a local functional operator and the closedness of domains in choice-functional space relative to local operators are introduced. The problem of voting is reduced to an analysis of three kinds of operator classes and their mutual relations. The functional analogues well known in the theory of Arrow's paradox results are established

Lexicographic choice functions without archimedeanicity

We investigate the connection between choice functions and lexicographic probabilities, by means of the convexity axiom considered by Seidenfeld, Schervisch and Kadane (2010) but without imposing any Archimedean condition. We show that lexicographic probabilities are related to a particular type of sets of desirable gambles, and investigate the properties of the coherent choice function this induces via maximality. Finally, we show that the convexity axiom is necessary but not sufficient for a coherent choice function to be the infimum of a class of lexicographic ones

Voting Operators in the Space of Choice Functions

Assuming the individual and collective opinions are given as choice functions, a new formalization of the voting problem is considered. The notions of a local functional operator and the closedness of domains in choice-functional space relative to local operators are introduced. The problem of voting is reduced to an analysis of three kinds of operator classes and their mutual relations. The functional analogues well known in the theory of Arrow's paradox results are established

Theory, Politics... and History? Early post-war Soviet Control Engineering

A fascinating feature of post-war control engineering in the former Soviet Union was the rôle played by the study of the history of the discipline. Even before and during World War II some Soviet control scientists were actively researching the history of their subject; while after the war, historical studies played an important part both in technical developments and in legitimating a native Russian tradition. Two of the most important figures in this historical activity were A. A. Andronov and I. N. Voznesenskii, whose contributions are briefly considered

Notes About Theory of Pseudo-Criteria and Binary Pseudo-Relations and Their Application to the Theory of Choice and Voting

The pages of this working paper are copies of transparencies used in a lecture on the general theory of choice given at the California Institute of Technology June 1991

Notes About Theory of Pseudo-Criteria and Binary Pseudo-Relations and Their Application to the Theory of Choice and Voting

The pages of this working paper are copies of transparencies used in a lecture on the general theory of choice given at the California Institute of Technology June 1991

Data Mining and Machine Learning in Astronomy

We review the current state of data mining and machine learning in astronomy. 'Data Mining' can have a somewhat mixed connotation from the point of view of a researcher in this field. If used correctly, it can be a powerful approach, holding the potential to fully exploit the exponentially increasing amount of available data, promising great scientific advance. However, if misused, it can be little more than the black-box application of complex computing algorithms that may give little physical insight, and provide questionable results. Here, we give an overview of the entire data mining process, from data collection through to the interpretation of results. We cover common machine learning algorithms, such as artificial neural networks and support vector machines, applications from a broad range of astronomy, emphasizing those where data mining techniques directly resulted in improved science, and important current and future directions, including probability density functions, parallel algorithms, petascale computing, and the time domain. We conclude that, so long as one carefully selects an appropriate algorithm, and is guided by the astronomical problem at hand, data mining can be very much the powerful tool, and not the questionable black box.Comment: Published in IJMPD. 61 pages, uses ws-ijmpd.cls. Several extra figures, some minor additions to the tex

Profiles and Majority Voting-Based Ensemble Method for Protein Secondary Structure Prediction

Machine learning techniques have been widely applied to solve the problem of predicting protein secondary structure from the amino acid sequence. They have gained substantial success in this research area. Many methods have been used including k-Nearest Neighbors (k-NNs), Hidden Markov Models (HMMs), Artificial Neural Networks (ANNs) and Support Vector Machines (SVMs), which have attracted attention recently. Today, the main goal remains to improve the prediction quality of the secondary structure elements. The prediction accuracy has been continuously improved over the years, especially by using hybrid or ensemble methods and incorporating evolutionary information in the form of profiles extracted from alignments of multiple homologous sequences. In this paper, we investigate how best to combine k-NNs, ANNs and Multi-class SVMs (M-SVMs) to improve secondary structure prediction of globular proteins. An ensemble method which combines the outputs of two feed-forward ANNs, k-NN and three M-SVM classifiers has been applied. Ensemble members are combined using two variants of majority voting rule. An heuristic based filter has also been applied to refine the prediction. To investigate how much improvement the general ensemble method can give rather than the individual classifiers that make up the ensemble, we have experimented with the proposed system on the two widely used benchmark datasets RS126 and CB513 using cross-validation tests by including PSI-BLAST position-specific scoring matrix (PSSM) profiles as inputs. The experimental results reveal that the proposed system yields significant performance gains when compared with the best individual classifier

Classification of protein interaction sentences via gaussian processes

The increase in the availability of protein interaction studies in textual format coupled with the demand for easier access to the key results has lead to a need for text mining solutions. In the text processing pipeline, classification is a key step for extraction of small sections of relevant text. Consequently, for the task of locating protein-protein interaction sentences, we examine the use of a classifier which has rarely been applied to text, the Gaussian processes (GPs). GPs are a non-parametric probabilistic analogue to the more popular support vector machines (SVMs). We find that GPs outperform the SVM and na\"ive Bayes classifiers on binary sentence data, whilst showing equivalent performance on abstract and multiclass sentence corpora. In addition, the lack of the margin parameter, which requires costly tuning, along with the principled multiclass extensions enabled by the probabilistic framework make GPs an appealing alternative worth of further adoption