Generalization of a Conjecture in the Geometry of Polynomials

In this paper we survey work on and around the following conjecture, which was first stated about 45 years ago: If all the zeros of an algebraic polynomial p (of degree n ≥ 2) lie in a disk with radius r, then, for each zero z1 of p, the disk with center z1 and radius r contains at least one zero of the derivative p′ . Until now, this conjecture has been proved for n ≤ 8 only. We also put the conjecture in a more general framework involving higher order derivatives and sets defined by the zeros of the polynomials.

Generalization of Ehrlich-Kjurkchiev Method for Multiple Roots of Algebraic Equations

In this paper a new method which is a generalization of the Ehrlich-Kjurkchiev method is developed. The method allows to find simultaneously all roots of the algebraic equation in the case when the roots are supposed to be multiple with known multiplicities. The offered generalization does not demand calculation of derivatives of order higher than first simultaneously keeping quaternary rate of convergence which makes this method suitable for application from practical point of view.

The Development of the Generalization Algorithm Based on the Rough Set Theory

This paper considers the problem of concept generalization in decision-making systems where such features of real-world databases as large size, incompleteness and inconsistence of the stored information are taken into account. The methods of the rough set theory (like lower and upper approximations, positive regions and reducts) are used for the solving of this problem. The new discretization algorithm of the continuous attributes is proposed. It essentially increases an overall performance of generalization algorithms and can be applied to processing of real value attributes in large data tables. Also the search algorithm of the significant attributes combined with a stage of discretization is developed. It allows avoiding splitting of continuous domains of insignificant attributes into intervals.

Event trigger identification for biomedical events extraction using domain knowledge

Motivation: In molecular biology, molecular events describe observable alterations of biomolecules, such as binding of proteins or RNA production. These events might be responsible for drug reactions or development of certain diseases. As such, biomedical event extraction, the process of automatically detecting description of molecular interactions in research articles, attracted substantial research interest recently. Event trigger identification, detecting the words describing the event types, is a crucial and prerequisite step in the pipeline process of biomedical event extraction. Taking the event types as classes, event trigger identification can be viewed as a classification task. For each word in a sentence, a trained classifier predicts whether the word corresponds to an event type and which event type based on the context features. Therefore, a well-designed feature set with a good level of discrimination and generalization is crucial for the performance of event trigger identification. Results: In this article, we propose a novel framework for event trigger identification. In particular, we learn biomedical domain knowledge from a large text corpus built from Medline and embed it into word features using neural language modeling. The embedded features are then combined with the syntactic and semantic context features using the multiple kernel learning method. The combined feature set is used for training the event trigger classifier. Experimental results on the golden standard corpus show that >2.5% improvement on F-score is achieved by the proposed framework when compared with the state-of-the-art approach, demonstrating the effectiveness of the proposed framework. © 2014 The Author 2014. The source code for the proposed framework is freely available and can be downloaded at http://cse.seu.edu.cn/people/zhoudeyu/ETI_Sourcecode.zip.

Generalization of the Modified Bessel Function and Its Generating Function

2000 Mathematics Subject Classification: 33C10, 33-02, 60K25

Discrete Generalization of Gronwall-Bellman Inequality with Maxima and Application

Снежана Христова, Кремена Стефанова, Лиляна Ванкова - В работата са решени няколко нови видове линейни дискретни неравенства, които съдържат максимума на неизвестната функция в отминал интервал от време. Някои от тези неравенства са приложени за изучаване непрекъснатата зависимост от смущения при дискретни уравнения с максимуми.

Applying Associative Classifier PGN for Digitised Cultural Heritage Resource Discovery

Resource discovery is one of the key services in digitised cultural heritage collections. It requires intelligent mining in heterogeneous digital content as well as capabilities in large scale performance; this explains the recent advances in classification methods. Associative classifiers are convenient data mining tools used in the field of cultural heritage, by applying their possibilities to taking into account the specific combinations of the attribute values. Usually, the associative classifiers prioritize the support over the confidence. The proposed classifier PGN questions this common approach and focuses on confidence first by retaining only 100% confidence rules. The classification tasks in the field of cultural heritage usually deal with data sets with many class labels. This variety is caused by the richness of accumulated culture during the centuries. Comparisons of classifier PGN with other classifiers, such as OneR, JRip and J48, show the competitiveness of PGN in recognizing multi-class datasets on collections of masterpieces from different West and East European Fine Art authors and movements.

Establishing Correspondences between Attribute Spaces and Complex Concept Spaces Using Meta-PGN Classifier

In this paper, we present one approach for extending the learning set of a classification algorithm with additional metadata. It is used as a base for giving appropriate names to found regularities. The analysis of correspondence between connections established in the attribute space and existing links between concepts can be used as a test for creation of an adequate model of the observed world. Meta-PGN classifier is suggested as a possible tool for establishing these connections. Applying this approach in the field of content-based image retrieval of art paintings provides a tool for extracting specific feature combinations, which represent different sides of artists' styles, periods and movements.

Classifier PGN: Classification with High Confidence Rules

ACM Computing Classification System (1998): H.2.8, H.3.3.

Some generalization of Desargues and Veronese configurations

2000 Mathematics Subject Classification: 51E14, 51E30.

Another Generalization of Arhangel'skii's Theorem

MSC 2010: 54A25, 54A35.

On a Generalization of a Theorem due to Larcombe on the Sum of a 3F2 Series

MSC 2010: 33C20

Plus-Minus Property as a Generalization of the Daugavet Property

2000 Mathematics Subject Classification: Primary 46B20. Secondary 47A99, 46B42.

Uncovering the root cause of ethnic difference in ability testing:differential test functioning, test familiarity and trait optimism as explanations of ethnic group differences

The present research represents a coherent approach to understanding the root causes of ethnic group differences in ability test performance. Two studies were conducted, each of which was designed to address a key knowledge gap in the ethnic bias literature. In Study 1, both the LR Method of Differential Item Functioning (DIF) detection and Mixture Latent Variable Modelling were used to investigate the degree to which Differential Test Functioning (DTF) could explain ethnic group test performance differences in a large, previously unpublished dataset. Though mean test score differences were observed between a number of ethnic groups, neither technique was able to identify ethnic DTF. This calls into question the practical application of DTF to understanding these group differences. Study 2 investigated whether a number of non-cognitive factors might explain ethnic group test performance differences on a variety of ability tests. Two factors – test familiarity and trait optimism – were able to explain a large proportion of ethnic group test score differences. Furthermore, test familiarity was found to mediate the relationship between socio-economic factors – particularly participant educational level and familial social status – and test performance, suggesting that test familiarity develops over time through the mechanism of exposure to ability testing in other contexts. These findings represent a substantial contribution to the field’s understanding of two key issues surrounding ethnic test performance differences. The author calls for a new line of research into these performance facilitating and debilitating factors, before recommendations are offered for practitioners to ensure fairer deployment of ability testing in high-stakes selection processes.

PDNAsite:identification of DNA-binding site from protein sequence by incorporating spatial and sequence context

Protein-DNA interactions are involved in many fundamental biological processes essential for cellular function. Most of the existing computational approaches employed only the sequence context of the target residue for its prediction. In the present study, for each target residue, we applied both the spatial context and the sequence context to construct the feature space. Subsequently, Latent Semantic Analysis (LSA) was applied to remove the redundancies in the feature space. Finally, a predictor (PDNAsite) was developed through the integration of the support vector machines (SVM) classifier and ensemble learning. Results on the PDNA-62 and the PDNA-224 datasets demonstrate that features extracted from spatial context provide more information than those from sequence context and the combination of them gives more performance gain. An analysis of the number of binding sites in the spatial context of the target site indicates that the interactions between binding sites next to each other are important for protein-DNA recognition and their binding ability. The comparison between our proposed PDNAsite method and the existing methods indicate that PDNAsite outperforms most of the existing methods and is a useful tool for DNA-binding site identification. A web-server of our predictor (http://hlt.hitsz.edu.cn:8080/PDNAsite/) is made available for free public accessible to the biological research community.