On effective linearly ordered sets of comparison functions

Both the existence and the non-existence of a linearly ordered (by certain natural order relations) effective set of comparison functions (=dense comparison classes) are compatible with the ZFC axioms of set theory.

Support vector machine classification for large data sets via minimum enclosing ball clustering

Support vector machine (SVM) is a powerful technique for data classification. Despite of its good theoretic foundations and high classification accuracy, normal SVM is not suitable for classification of large data sets, because the training complexity of SVM is highly dependent on the size of data set. This paper presents a novel SVM classification approach for large data sets by using minimum enclosing ball clustering. After the training data are partitioned by the proposed clustering method, the centers of the clusters are used for the first time SVM classification. Then we use the clusters whose centers are support vectors or those clusters which have different classes to perform the second time SVM classification. In this stage most data are removed. Several experimental results show that the approach proposed in this paper has good classification accuracy compared with classic SVM while the training is significantly faster than several other SVM classifiers.

Reduced-size polarized basis sets for calculations of molecular electric properties. III. Second-row atoms

Reduced-size polarized (ZmPolX) basis sets are developed for the second-row atoms X = Si, P, S, and Cl. The generation of these basis sets follows from a simple physical model of the polarization effect of the external electric field which leads to highly compact polarization functions to be added to the chosen initial basis set. The performance of the ZmPolX sets has been investigated in calculations of molecular dipole moments and polarizabilities. Only a small deterioration of the quality of the calculated molecular electric properties has been found. Simultaneously the size of the present reduced-size ZmPolX basis sets is about one-third smaller than that of the usual polarized (PolX) sets. This reduction considerably widens the range of applications of the ZmPolX sets in calculations of molecular dipole moments, dipole polarizabilities, and related properties.

Confounds in pictorial sets: The role of complexity and familiarity in basic-level picture processing

Complexity is conventionally defined as the level of detail or intricacy contained within a picture. The study of complexity has received relatively little attention-in part, because of the absence of an acceptable metric. Traditionally, normative ratings of complexity have been based on human judgments. However, this study demonstrates that published norms for visual complexity are biased. Familiarity and learning influence the subjective complexity scores for nonsense shapes, with a significant training x familiarity interaction [F(1,52) = 17.53, p <.05]. Several image-processing techniques were explored as alternative measures of picture and image complexity. A perimeter detection measure correlates strongly with human judgments of the complexity of line drawings of real-world objects and nonsense shapes and captures some of the processes important in judgments of subjective complexity, while removing the bias due to familiarity effects.

Unite and conquer: univariate and multivariate approaches for finding differentially expressed gene sets

Motivation: Recently, many univariate and several multivariate approaches have been suggested for testing differential expression of gene sets between different phenotypes. However, despite a wealth of literature studying their performance on simulated and real biological data, still there is a need to quantify their relative performance when they are testing different null hypotheses.

Results: In this article, we compare the performance of univariate and multivariate tests on both simulated and biological data. In the simulation study we demonstrate that high correlations equally affect the power of both, univariate as well as multivariate tests. In addition, for most of them the power is similarly affected by the dimensionality of the gene set and by the percentage of genes in the set, for which expression is changing between two phenotypes. The application of different test statistics to biological data reveals that three statistics (sum of squared t-tests, Hotelling's T2, N-statistic), testing different null hypotheses, find some common but also some complementing differentially expressed gene sets under specific settings. This demonstrates that due to complementing null hypotheses each test projects on different aspects of the data and for the analysis of biological data it is beneficial to use all three tests simultaneously instead of focusing exclusively on just one.

A general framework for measuring inconsistency through minimal inconsistent sets

Hunter and Konieczny explored the relationships between measures of inconsistency for a belief base and the minimal inconsistent subsets of that belief base in several of their papers. In particular, an inconsistency value termed MIVC, defined from minimal inconsistent subsets, can be considered as a Shapley Inconsistency Value. Moreover, it can be axiomatized completely in terms of five simple axioms. MinInc, one of the five axioms, states that each minimal inconsistent set has the same amount of conflict. However, it conflicts with the intuition illustrated by the lottery paradox, which states that as the size of a minimal inconsistent belief base increases, the degree of inconsistency of that belief base becomes smaller. To address this, we present two kinds of revised inconsistency measures for a belief base from its minimal inconsistent subsets. Each of these measures considers the size of each minimal inconsistent subset as well as the number of minimal inconsistent subsets of a belief base. More specifically, we first present a vectorial measure to capture the inconsistency for a belief base, which is more discriminative than MIVC. Then we present a family of weighted inconsistency measures based on the vectorial inconsistency measure, which allow us to capture the inconsistency for a belief base in terms of a single numerical value as usual. We also show that each of the two kinds of revised inconsistency measures can be considered as a particular Shapley Inconsistency Value, and can be axiomatically characterized by the corresponding revised axioms presented in this paper.

Feature Selection for Pose Invariant Lip Biometrics

For the first time in this paper the authors present results showing the effect of out of plane speaker head pose variation on a lip biometric based speaker verification system. Using appearance DCT based features, they adopt a Mutual Information analysis technique to highlight the class discriminant DCT components most robust to changes in out of plane pose. Experiments are conducted using the initial phase of a new multi view Audio-Visual database designed for research and development of pose-invariant speech and speaker recognition. They show that verification performance can be improved by substituting higher order horizontal DCT components for vertical, particularly in the case of a train/test pose angle mismatch.

The negatively charged nitrogen-vacancy centre in diamond: the electronic solution

The negatively charged nitrogen-vacancy centre in diamond is a unique defect centre in diamond that possesses properties highly suited to many applications, including quantum information processing, quantum metrology, and biolabelling. Although the unique properties of the centre have been extensively documented and utilised, a detailed understanding of the physics of the centre has not yet been achieved. Indeed there persists a number of points of contention regarding the electronic structure of the centre, such as the ordering of the dark intermediate singlet states. Without a sound model of the centre’s electronic structure, the understanding of the system’s unique dynamical properties can not effectively progress. In this work, the molecular model of the defect centre is fully developed to provide a self consistent model of the complete electronic structure of the centre. The application of the model to describe the effects of electric, magnetic and strain interactions, as well as the variation of the centre’s fine structure with temperature, provides an invaluable tool to those studying the centre and a means to design future experiments and ab initio studies of this important defect centre.

The level sets of the resolvent norm and convexity properties of Banach spaces

We construct a bounded linear operator on a separable, reflexive and strictly convex Banach space whose resolvent norm is constant in a neighbourhood of zero.