Synthesis and electrical properties of Li1+ x M x Ti2– x (PO4)3 (where M =Sc, Al, Fe, Y; x =0.3) superionic ceramics

Compounds of the system Li_{1+ x} M _x Ti_{2– x} (PO₄)₃ (where M=Sc, Al, Fe, Y; x=0.3) were synthesized by a solid-state reaction and studied by X-ray diffraction. The ceramic samples were sintered and investigated by complex impedance spectroscopy in the frequency range 10⁶–1.2×10⁹ Hz in the temperature range 300–600 K. Two relaxation dispersions related to the fast Li⁺ ion transport in bulk and grain boundaries were found. The activation energies of the bulk conductivity and relaxation frequency were obtained from the slops of Arrhenius plots. The values of the activation energies of the bulk ionic conductivity and relaxation frequency were found to be very similar in all the materials investigated. That can be attributed to the fact that the temperature dependences of the bulk conductivity are caused only by the mobility of the fast Li⁺ ions, while the number of charge carriers remains constant with temperature. Electronic Publication     

On zeta-functions associated to certain cusp forms. II

A formula for the mean value of multiplicative functions associated to certain cusp forms is obtained. The paper is a continuation of [4].     

Parallel branch and bound for multidimensional scaling with city-block distances

Multidimensional scaling is a technique for exploratory analysis of multidimensional data. The essential part of the technique is minimization of a multimodal function with unfavorable properties like invariants and non-differentiability. Recently a branch and bound algorithm for multidimensional scaling with city-block distances has been proposed for solution of medium-size problems exactly. The algorithm exploits piecewise quadratic structure of the objective function. In this paper a parallel version of the branch and bound algorithm for multidimensional scaling with city-block distances has been proposed and investigated. Parallel computing enabled solution of larger problems what was not feasible with the sequential version.     

On the Convergence of the P-Algorithm for One-Dimensional Global Optimization of Smooth Functions

The Wiener process is a widely used statistical model for stochastic global optimization. One of the first optimization algorithms based on a statistical model, the so-called P-algorithm, was based on the Wiener process. Despite many advantages, this process does not give a realistic model for many optimization problems, particularly from the point of view of local behavior. In the present paper, a version of the P-algorithm is constructed based on a stochastic process with smooth sampling functions. It is shown that, in such a case, the algorithm has a better convergence rate than in the case of the Wiener process. A similar convergence rate is proved for a combination of the Wiener model-based P-algorithm with quadratic fit-based local search.     

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.