Marko Janev

Fully fractional anisotropic diffusion for image denoising

This paper introduces a novel Fully Fractional Anisotropic Diffusion Equation for noise removal which contains spatial as well as time fractional derivatives. It is a generalization of a method proposed by Cuesta which interpolates between the heat and the wave equation by the use of time fractional derivatives, and the method proposed by Bai and Feng, which interpolates between the second and the fourth order anisotropic diffusion equation by the use of spatial fractional derivatives. This equation has the benefits of both of these methods. For the construction of a numerical scheme, the proposed partial differential equation (PDE) has been treated as a spatially discretized Fractional Ordinary Differential Equation (FODE) model, and then the Fractional Linear Multistep Method (FLMM) combined with the discrete Fourier transform (DFT) is used. We prove that the analytical solution to the proposed FODE has certain regularity properties which are sufficient to apply a convergent and stable fractional numerical procedure. Experimental results confirm that our model manages to preserve edges, especially highly oscillatory regions, more efficiently than the baseline parabolic diffusion models.

Eigenvalues Driven Gaussian Selection in continuous speech recognition using HMMs with full covariance matrices

In this paper a novel algorithm for Gaussian Selection (GS) of mixtures used in a continuous speech recognition system is presented. The system is based on hidden Markov models (HMM), using Gaussian mixtures with full covariance matrices as output distributions. The purpose of Gaussian selection is to increase the speed of a speech recognition system, without degrading the recognition accuracy. The basic idea is to form hyper-mixtures by clustering close mixtures into a single group by means of Vector Quantization (VQ) and assigning it unique Gaussian parameters for estimation. In the decoding process only those hyper-mixtures which are above a designated threshold are selected, and only mixtures belonging to them are evaluated, improving computational efficiency. There is no problem with the clustering and evaluation if overlaps between the mixtures are small, and their variances are of the same range. However, in real case, there are numerous models which do not fit this profile. A Gaussian selection scheme proposed in this paper addresses this problem. For that purpose, beside the clustering algorithm, it also incorporates an algorithm for mixture grouping. The particular mixture is assigned to a group from the predefined set of groups, based on a value aggregated from eigenvalues of the covariance matrix of that mixture using Ordered Weighted Averaging operators (OWA). After the grouping of mixtures is carried out, Gaussian mixture clustering is performed on each group separately.

Speech Technologies for Serbian and Kindred South Slavic Languages

This chapter will present the results of the research and development of speech technologies for Serbian and other kindred South Slavic languages used in five countries of the Western Balkans, carried out by the University of Novi Sad, Serbia in cooperation with the company AlfaNum. The first section will describe particularities of highly inflected languages (such as Serbian and other languages dealt with in this chapter) from the point of view of speech technologies. The following sections will describe the existing speech and language resources for these languages, the automatic speech recognition (ASR) and text-to-speech synthesis (TTS) systems developed on the basis of these resources as well as auxiliary software components designed in order to aid this development. It will be explained how the resources originally built for the Serbian language facilitated the development of speech technologies in Croatian, Bosnian, and Macedonian as well. The paper is concluded by the directions of further research aimed at development of multimodal dialogue systems in South Slavic languages.

An expansion formula for fractional derivatives of variable order

In this work we extend our previous results and derive an expansion formula for fractional derivatives of variable order. The formula is used to determine fractional derivatives of variable order of two elementary functions. Also we propose a constitutive equation describing a solidifying material and determine the corresponding stress relaxation function.

A novel split-and-merge algorithm for hierarchical clustering of Gaussian mixture models

The paper presents a novel split-and-merge algorithm for hierarchical clustering of Gaussian mixture models, which tends to improve on the local optimal solution determined by the initial constellation. It is initialized by local optimal parameters obtained by using a baseline approach similar to k-means, and it tends to approach more closely to the global optimum of the target clustering function, by iteratively splitting and merging the clusters of Gaussian components obtained as the output of the baseline algorithm. The algorithm is further improved by introducing model selection in order to obtain the best possible trade-off between recognition accuracy and computational load in a Gaussian selection task applied within an actual recognition system. The proposed method is tested both on artificial data and in the framework of Gaussian selection performed within a real continuous speech recognition system, and in both cases an improvement over the baseline method has been observed.

Space–time fractional Zener wave equation

The space–time fractional Zener wave equation, describing viscoelastic materials obeying the time-fractional Zener model and the space-fractional strain measure, is derived and analysed. This model includes waves with finite speed, as well as non-propagating disturbances. The existence and the uniqueness of the solution to the generalized Cauchy problem are proved. Special cases are investigated and numerical examples are presented.

Energy Normalization in Automatic Speech Recognition

In this paper a novel method for energy normalization is presented. The objective of this method is to remove unwanted energy variations caused by different microphone gains, various loudness levels across speakers, as well as changes of single speaker loudness level over time. The solution presented here is based on principles used in automatic gain control. The use of this method results in relative improvement of the performances of an automatic speech recognition system by 26 %.

Wave equation for generalized Zener model containing complex order fractional derivatives

We study waves in a viscoelastic rod whose constitutive equation is of generalized Zener type that contains fractional derivatives of complex order. The restrictions following from the Second Law of Thermodynamics are derived. The initial boundary value problem for such materials is formulated and solution is presented in the form of convolution. Two specific examples are analyzed.

Viscoelastic properties of uncured resin composites: Dynamic oscillatory shear test and fractional derivative model

OBJECTIVE In this study we analyze viscoelastic properties of three flowable (Wave, Wave MV, Wave HV) and one universal hybrid resin (Ice) composites, prior to setting. We developed a mathematical model containing fractional derivatives in order to describe their properties. METHODS Isothermal experimental study was conducted on a rheometer with parallel plates. In dynamic oscillatory shear test, storage and loss modulus, as well as the complex viscosity where determined. We assumed four different fractional viscoelastic models, each belonging to one particular class, derivable from distributed-order fractional constitutive equation. The restrictions following from the Second law of thermodynamics are imposed on each model. The optimal parameters corresponding to each model are obtained by minimizing the error function that takes into account storage and loss modulus, thus obtaining the best fit to the experimental data. RESULTS In the frequency range considered, we obtained that for Wave HV and Wave MV there exist a critical frequency for which loss and storage modulus curves intersect, defining a boundary between two different types of behavior: one in which storage modulus is larger than loss modulus and the other in which the situation is opposite. Loss and storage modulus curves for Ice and Wave do not show this type of behavior, having either elastic, or viscous effects dominating in entire frequency range considered. SIGNIFICANCE The developed models may be used to predict behavior of four tested composites in different flow conditions (different deformation speed), thus helping to estimate optimal handling characteristics for specific clinical applications.

Convergence analysis of a numerical scheme for two classes of non-linear fractional differential equations

We use the expansion formula for the fractional derivatives to reduce the problem of solving non-linear fractional order differential equations arising in mechanics to the problem of solving a system of integer order differential equations. We prove the convergence of the solutions to the reduced integer order systems to the solutions of the original problem. The procedure is illustrated by two specific examples.