László Szeidl

Diversity partitioning of Rao's quadratic entropy.

Many applications of diversity indices are only valid if they are first transformed into their equivalent number of species. These equivalent numbers of species can be multiplicatively partitioned into independent alpha, beta and gamma components, and can be formed into mathematically consistent similarity measures. The utility of beta diversity and similarity measures that incorporate information about the degree of ecological dissimilarity between species is becoming increasingly recognized. The concept of equivalent number of species is here extended to Raos quadratic entropy, opening the way to methods of diversity partitioning that take into account taxonomic or ecological differences between species.

On tensor-product model based representation of neural networks

The approximation methods of mathematics are widely used in theory and practice for several problems. In the framework of the paper a novel tensor-product based approach for representation of neural networks (NNs) is proposed. The NNs in this case stand for local models based on which a more complex parameter varying model can numerically be reconstructed and reduced using the higher order singular value decomposition (HOSVD). The HOSVD as well as the tensor-product based representation of NNs will be discussed in detail.

HOSVD Based Method for Surface Data Approximation and Compression

The main aim of this paper is to introduce a method for approximating surfaces given by a set of discrete points with possible additional parameters. The method uses the higher order singular value decomposition based on canonical form of two-variable TP (tensor product) functions. Except of approximation abilities of this principle, the paper focuses on the compression properties of the method, as well. The method is able to achieve high compression rate in the input data by keeping the error at remarkable lower level.

The HOSVD Based Canonical Form of Functions and Its Applications

The paper deals with the theoretical background of the higher order singular value decomposition (HOSVD) based canonical form of functions. Furthermore in special case it describes the relation between the canonical form and the Hilbert-Schmidt type integral operators. The described techniques have a variety of applications, e.g. image processing, system identification, data compression, filtering, etc. As an example of application from the field of intelligent systems, a tensor-product based concept is introduced useful for approximating the behavior of a strongly non-linear system by locally tuned neural network models. The proposed approach may be a useful tool for solving many kind of black-box like identification problems. The weights in the corresponding layers of the input local models are jointly expressed in tensor-product form such a way ensuring the efficient approximation. Similar concept has been used by the authors for approximating the system matrix of linear parameter varying systems in state space representation. We hope that the proposed concept could be an efficient compromised modeling view using both the analytical and heuristic approaches.

Polytopic Decomposition of the Linear Parameter-varying Model of the Parallel-type Double inverted Pendulum

Most of the formal controller synthesis approaches require conditions like controllability, observability of the systems, however it is still difficult to verify these properties in general. In case of polytopic models these conditions and the feasibility of the linear matrix inequalities (LMI) based design strongly depends on the weighting of the LTI vertex components of the polytopic model. With tensor product (TP) model transformation it is possible to decompose linear parameter-varying (LPV) models into polytopic forms in various ways and also provides the appropriate weighting functions. The objective of this paper is to use this decomposition on the the parallel-type double inverted pendulum control problem.

Numerical Reconstruction and Compression of Thermal Image Sequences

Data compression and enhancement represent an important consideration in many application areas. The transmission bandwidth and storage capacity are often crucial factors. The efficiency of the processing of data in numerous cases strongly depends on the form of data representation. In the present paper a method, based on the so called higher order singular value decomposition and tensor-product transformation, is introduced for multidimensional scaling and compression of thermal images sequences. The proposed approach operates with smooth functions forming an orthonormal basis. Because of the smoothness property of these orthonormal components, the method can advantageously be utilized for the efficient compression of thermal image sequences.

A partial ordering approach for functional diversity

Functional diversity is generally regarded as the constituent of biological diversity that considers how the species functional traits affect ecosystem processes. Due to its ecological relevance, a number of indices of functional diversity have been proposed to date based on distinct objectives and motivations. Such proliferation of indices can be at least partially overcome by a more fundamental mathematical approach. In this paper we propose an intrinsic ordering approach for abundance-weighted measures of functional diversity that is similar to the Lorenz curves used by ecologists for ordering evenness measures. We then discuss the relevance of a number of functional diversity indices that have a behavior compatible with the proposed partial ordering.

Stochastic modelling of stress processes in power plant boiler walls

A stochastic model of the integrated firing and supply system was set up, using the theory of semi-Markov processes and assuming a stochastically identified firing system model. On the basis of the results of the paper a proposed basic statistics, mainly the expected intersection number, of the repeating mechanical stress level of the combustion chambers structure can be determined. According to the introduced method, the characteristic mechanical stress level can be limited, which prevents early fatigue and rupture of the important structural elements of the combustion chamber.

Image processing using polylinear functions on HOSVD basis

The main aim of the paper is to introduce a new representation domain advantageously usable also in the field of image processing. In this case the image is represented by polylinear functions on HOSVD basis. The paper gives an overview, how these functions can be reconstructed and how they can be applied in case of image processing. Comparing to other domains, using the proposed domain the image can be expressed by a reduced number of components (polylinear functions) by maintaining its quality. The efficiency of this representation form is demonstrated by performing an image resolution enhancement trough this new domain by maintaining its quality significantly.