The aim of the thesis is to present the process connected with the identification of industrial clusters and to point out possible methods and instruments that are useable by such identification. The target is not only focussed on description of these methods but also on consideration that the methods are likewise useful in regions of Czech Republic, especially taken into account the existing offer of regional data. The diplom thesis consists of three parts. The first part represents theoretical introduction to clusters' problem. The second part, also the theoretical one, deals widely with quantitative and qualitative methods and with procedures and clasification that belong to these methods. The third part applies the theoretical knowledge into practices. The comparison methods are used in the theoretical part and the methods of analysis, synthesis, comparison and induction are used in the practical part. The diplom thesis brings a quantitative extension of methods that have been used so far when identifying the industrial clusters in Czech Republic. Due to the present trend of prefering the qualitative methods, the extension of quantitative methods could be seen as a retrograde act. But the conditions of Czech Republic tourned out that, in fact, it is a suitable extension of statistical instruments.

The Polar Decomposition (PD) of a dense matrix is an important operation in linear algebra, while being a building block for solving the Symmetric Eigenvalue Problem (SEP) and computing the Singular Value Decomposition (SVD). It can be directly calculated through the SVD itself, or iteratively using the QR Dynamically-Weighted Halley (QDWH) algorithm. The former is difficult to parallelize due to the preponderant number of memory-bound operations during the bidiagonal reduction. The latter is an iterative method, which performs more floating-point operations than the SVD approach, but exposes at the same time more parallelism. Looking at the roadmap of the hardware technology scaling, algorithms perform- ing floating-point operations on locally cached data should be favored over those requiring expensive horizontal data movement. In this context, this thesis investigates new high-performance algorithmic designs of QDWH algorithm to compute the PD. Originally introduced by Nakatsukasa et al. [1, 2], our algorithmic contributions include mixed precision techniques, task-based formulations, and parallel asynchronous executions. Moreover, by making the PD competitive, its application to the SEP and the SVD becomes practical. In particular, we introduce for the first time new algorithms for partial SVD decomposition using QDWH. By the same token, we extend the QDWH to support partial eigen decomposition for SEP. We present new high-performance implementations of the QDWH-based algorithms relying on fine-grained computations, which allows exploiting the sparsity of the underlying data structure. To demonstrate performance efficiency, portability and scalability, we conduct benchmarking campaigns on some of the latest shared/distributed-memory systems. Our QDWH-based algorithm implementations outperform the state-of-the-art numerical libraries by up to 2.8x and 12x on shared and distributed-memory, respectively. The task-based QDWH has been integrated into the Chameleon library (https://gitlab.inria.fr/solverstack/chameleon) for support on shared-memory systems with hardware accelerators. It is also currently being used by astronomers from the Subaru telescope located at the summit of Mauna Kea, Hawaii, USA. The distributed-memory software library of QDWH and its SVD extension are freely available under modified-BSD license at https: //github.com/ecrc/qdwh.git and https://github.com/ecrc/ksvd.git, respectively. Both software libraries have been integrated into the Cray Scientific numerical library LibSci v17.11.1 and v19.02.1.

[pt] Neste trabalho é feito um estudo sobre compressão de imagens para canal ruidoso.Inicialmente, esquemas de complexidade moderada sem a utilização do princípio da separação de Shannon são investigados e simulados. Com isso, mostra-se que esquemas eficientes de codificação conjunta fonte/canal existem e podem eventualmente apresentar melhor performance do que esquemas separados de codificação e canal e fonte. São também investigados, algoritmos de codificação de imagens visando a transmissão num capital ruidoso. Nesse contexto, é proposto um esquema utilizando transformadas com superposição com boa performance, como mostram as simulações realizadas. O esquema posteriormente estendido para imagens multi- espectrais mostrando-se igualmente eficiente. / [en] In the present dissertation we investigate image compression techniques for transmission over binary symmetric channels poluted with noise. Frist we simulate some known techniques for joint source/channel coding that dispenses with the use of error correcting codes. These techiniques may exhibit better performance when complexity and delay constraits are at stake. We further propose an image compression algorithm for noisy channels based on lapped/block transforms and block source/channel coding. We simulate the proposed scheme for various channel situations. The algorithm is further extented to handle compression and transmission of multiepectral remote sensing satellite imagery. Results for natural and multiespectral images are presented showing the good performance attained by the proposed schemes.

In this thesis there is description of cryptographic algorithms. Their properties are being compared, weak and strong points and right usage of particular algorithms. The main topics are safeness of algorithms, their bugs and improvements and difficulty of breaching. As a complement to ciphers there are also hash functions taken in consideration. There are also showed the most common methods of cryptanalysis. As a practical application of described algorithms I analyze systems for secure data transfer SSH and SSL/TLS and demonstrate an attack on SSL connection. In conclusion there is recommendation of safe algorithms for further usage and safe parameters of SSH and SSL/TLS connections.

La modélisation des problèmes d'interactions sol-structure et fluide-structure couvre plusieurs domaines de recherche très actifs qui traitent une multitude d'aspects tels que la géométrie non bornée du sol et dans certains cas du fluide stocké, les effets dissipatifs visqueux et radiatifs, l'application du chargement sismique, le choix des variables de base, les propriétés algébriques des systèmes d'équations résultant du couplage,... etc. Dans le présent travail, différents modèles numériques de couplage sol-structure et fluide-structure ont été examinés. Les limites de troncature géométrique du sol et du fluide on été traitées avec des éléments infinis dont les performances ont été comparées à celles des conditions de radiations. Le problème de vibrations libres couplées des systèmes fluide-structure a été résolu en introduisant de nouvelles techniques de symétrisation efficaces. De plus, une nouvelle formulation symétrique en éléments de frontière a été proposée. Cette formulation permet de produire une matrice symétrique définie positive et aboutit ainsi à un système algébrique similaire à celui qui découle de la discrétisation en éléments finis. La matrice bâtie dite "raideur équivalente" peut facilement être assemblée ou couplée avec les matrices de la formulation en éléments finis. Toutes les applications qui ont servi soit à comparer des modèles soit à valider les programmes développés, ont été effectué es dans le cas des barrages poids en béton. Ce cas constitue un problème de couplage fluide-sol-structure typique / Modeling fluid-structure and soil-structure interaction problems covers several research fields dealing with multiple aspects such as : unbounded geometry of soil media and in some cases of retained fluid, viscous and radiation dissipative effects, application of seismic loading, choice of the basic variables, algebraic properties of the resulting coupled system, ... etc. In this work, different numerical models of soil-structure and fluid-structure coupling have been studied. The truncation boundaries of the soil and of the fluid domains have been considered by using infinite elements whose performances were compared to those of radiation conditions. The problem of the free coupled vibrations of the fluid-structure systems has been solved by introducing efficient symmetrization techniques. In addition, a new symmetric boundary element formulation is proposed. It allows to produce a positive definite and symmetric matrix and therefore to conduct to an algebraic system similar to the one obtained from finite element discretization. The produced matrix called "equivalent stiffness matrix" can easily be assembled or coupled to finite element matrices. All of the applications which have been done in order to compare models or to validate the developed programs were built in the case of concrete gravity dams, which constitute typical coupled fluid- soil-structure problems

The subject of my thesis dscribes function and principles of the public key infrastructure as well as certificate authority. Under the operation system Linux was created self signed certificate authority. Web interface was devoloped in PHP for the purpose of the generation, distribution and rejection certificates. Configuration files for OpenVPN are included in the thesis and wireless security is achived by OpenVPN.

Ce manuscrit est consacré à l'étude de la combinatoire de deux algèbres de Hopf d'extraction-contraction. La première est l'algèbre de Hopf de mots tassés WMat introduite par Duchamp, Hoang-Nghia et Tanasa dont l'objectif était la construction d'un modèle de coproduit d'extraction-contraction pour les mots tassés. Nous expliquons certains sous-objets ou objets quotients ainsi que des applications vers d'autres algèbres de Hopf. Ainsi, nous considérons une algèbre de permutations dont le dual gradué possède un coproduit de déconcaténation par blocs et un produit de double battage décalé. Le double battage engendre la commutativité de l'algèbre qui est donc distincte de celle de Malvenuto et Reutenauer. Nous introduisons également une algèbre de Hopf engendrée par les mots tassés de la forme x₁...x₁. Elle est isomorphe à l'algèbre de Hopf des fonctions symétriques non commutatives. Son dual gradé est donc isomorphe à l'algèbre de Hopf des fonctions quasi-symétriques. Nous considérons également une algèbre de Hopf de compositions et donnons son interprétation en termes de coproduit semi-direct d'algèbres de Hopf. Le deuxième objet d'étude est l'algèbre de Hopf de diagrammes de dissection HD introduite par Dupont en théorie des nombres. Nous cherchons des éléments de réponse concernant la nature de sa cogèbre sous-jacente. Est-elle colibre ? La dimension des éléments primitifs de degré 3 ne permet pas de conclure. Le cas du degré 5 permet d'établir la non-coliberté dans le cas où le paramètre de HD vaut - 1. Nous étudions également la structure pré-Lie du dual gradué HD. Nous réduisons le champ de recherche à la sous-algèbre pré-Lie non triviale engendrée par le diagramme de dissection de degré 1. Cette algèbre pré-Lie n'est pas libre. / This thesis deals with the study of combinatorics of two Hopf algebras. The first one is the packed words Hopf algebra WMAT introduced by Duchamp, Hoang-Nghia, and Tanasa who wanted to build a coalgebra model for packed words by using a selection-quotient process. We describe certain sub-objects or quotient objects as well as maps to other Hopf algebras. We consider first a Hopf algebra of permutations. Its graded dual has a block deconcatenation coproduct and double shuffle product. The double shuffle product is commutative so the Hopf algebra is different from the Malvenuto and Reutenauer one. We analyze then the Hopf algebra generated by packed words looking like x₁...x₁. This Hopf algebra and non commutative symmetric functions are isomorphic. So its graded dual and quasi-symmetric functions are isomorphic too. Finally we consider a Hopf algebra of compositions an give its interpretation in terms of a semi-direct coproduct structure. The second objet we study is the Hopf algebra of dissection diagrams HD introduced by Dupont in number theory. We study the cofreedom problem. We can't conclude with homogeneous primitive elements of degree 3. With the degree 5 case, we can say that is not cofree with the parameter -1. We study the pre-Lie algebra structure of HD's graded dual too. We consider in particular the sup-pre-Lie algebra generated by the dissection diagram of degree 1. It is not a free pre-Lie algebra.

This diploma’s thesis discourses the cryptographic systems and ciphers, whose function, usage and practical implementation are analysed. In the first chapter basic cryptographic terms, symmetric and asymetric cryptographic algorithms and are mentioned. Also usage and reliability are analysed. Following chapters mention substitution, transposition, block and stream ciphers, which are elementary for most cryptographic algorithms. There are also mentioned the modes, which the ciphers work in. In the fourth chapter are described the principles of some chosen cryptographic algorithms. The objective is to make clear the essence of the algorithms’ behavior. When describing some more difficult algorithms the block scheme is added. At the end of each algorithm’s description the example of practical usage is written. The chapter no. five discusses the hardware implementation. Hardware and software implementation is compared from the practical point of view. Several design instruments are described and different hardware design programming languages with their progress, advantages and disadvantages are mentioned. Chapter six discourses the hardware implementation design of chosen ciphers. Concretely the design of stream cipher with pseudo-random sequence generator is designed in VHDL and also in Matlab. As the second design was chosen the block cipher GOST, which was designed in VHDL too. Both designs were tested and verified and then the results were summarized.