On the Value Distribution of Shifts of Universal Dirichlet Series

Shifts of universal Dirichlet series are jointly universal, that means, roughly speaking, they approximate simultaneously any given family of non-vanishing analytic functions. In this note we study consequences of this remarkable property on the value-distribution. Partially supported by the Foundation for Polish Science (FNP) and KBN grant 1 PO3A 00826. Partially supported by Lithuanian Foundation for Studies and Science.     

Two level minimization in multidimensional scaling

Multidimensional scaling with city block norm in embedding space is considered. Construction of the corresponding algorithm is reduced to minimization of a piecewise quadratic function. The two level algorithm is developed combining combinatorial minimization at upper level with local minimization at lower level. Results of experimental investigation of the efficiency of the proposed algorithm are presented as well as examples of its application to visualization of multidimensional data.     

On global optimization in two-dimensional scaling

We consider multidimensional scaling for embedding dimension two, which allows the detection of structures in dissimilarity data by simply drawing two-dimensional figures. The corresponding objective function, called STRESS, is generally nondifferentiable and has many local minima. In this paper we investigate several features of this function, and discuss the application of different global optimization procedures. A method based on combining a local search algorithm with an evolutionary strategy of generating new initial points is proposed, and its efficiency is investigated by numerical examples.This paper was written while the second author was visiting Professor at Aachen University of Technology, funded by the Deutsche Forschungsgemeinschaft.     

Categorizing Normal and Pathological Voices: Automated and Perceptual Categorization

Objectives

The aims of the present study were to evaluate the accuracy of an elaborated automated voice categorization system that classified voice signal samples into healthy and pathological classes and to compare it with classification accuracy that was attained by human experts.

Material and Methods

We investigated the effectiveness of 10 different feature sets in the classification of voice recordings of the sustained phonation of the vowel sound /a/ into the healthy and two pathological voice classes, and proposed a new approach to building a sequential committee of support vector machines (SVMs) for the classification. By applying “genetic search” (a search technique used to find solutions to optimization problems), we determined the optimal values of hyper-parameters of the committee and the feature sets that provided the best performance. Four experienced clinical voice specialists who evaluated the same voice recordings served as experts. The “gold standard” for classification was clinically and histologically proven diagnosis.

Results

A considerable improvement in the classification accuracy was obtained from the committee when compared with the single feature type-based classifiers. In the experimental investigations that were performed using 444 voice recordings coming from 148 subjects, three recordings from each subject, we obtained the correct classification rate (CCR) of over 92% when classifying into the healthy-pathological voice classes, and over 90% when classifying into three classes (healthy voice and two nodular or diffuse lesion voice classes). The CCR obtained from human experts was about 74% and 60%, respectively.

Conclusion

When operating under the same experimental conditions, the automated voice discrimination technique based on sequential committee of SVM was considerably more effective than the human experts.     

Effective Universality Theorem: A Survey

In 1975, S.M. Voronin proved the universality theorem for the Riemann zeta-function. This famous theorem is ineffective. Here we survey results related to the effectivization of Voronin’s theorem.

     

Nucleophilic substitution of the acetoxy group in 3-methylbenzoylaminomethyl acetate

Replacement of the acetoxy group in 3-methylbenzoylaminomethyl acetate with N- and S-nucleophiles generated from amines and thio compounds using sodium hydride gives the corresponding N-aminomethyl- and N-thiomethylbenzamides.     

An Adaptive Univariate Global Optimization Algorithm and Its Convergence Rate for Twice Continuously Differentiable Functions

We describe an adaptive algorithm for approximating the global minimum of a continuous univariate function. The convergence rate of the error is studied for the case of a twice continuously differentiable function.     

Branch and bound algorithm for multidimensional scaling with city-block metric

A two level global optimization algorithm for multidimensional scaling (MDS) with city-block metric is proposed. The piecewise quadratic structure of the objective function is employed. At the upper level a combinatorial global optimization problem is solved by means of branch and bound method, where an objective function is defined as the minimum of a quadratic programming problem. The later is solved at the lower level by a standard quadratic programming algorithm. The proposed algorithm has been applied for auxiliary and practical problems whose global optimization counterpart was of dimensionality up to 24.     

An algorithm of simplicial Lipschitz optimization with the bi-criteria selection of simplices for the bi-section

An algorithm of simplicial optimization is proposed where a bi-criteria selection of a simplex for the bi-section is applied. The first criterion is the minimum of estimated Lipschitz lower bound over the considered simplex. The second criterion is the diameter of the simplex. The results of experimental testing are included.