The Diploma thesis deals with the topic of conditionally suspended sentence of imprisonment as a separate type of punishment which is not considered merely as a variation of an unconditional imprisonment sentence. It analyses the individual elements of this institute, its history and development, the conditions of imposing and methods of termination. It also includes a comparison with foreign legislation that should bring suggestions for a better and more efficient execution of conditionally suspended sentence of imprisonment. The thesis is divided into eight chapters. The first chapter deals with general knowledge of conditionally suspended sentence of imprisonment as an alternative punishment and its legal nature. In the second chapter is outlined the historical development of the institute both in the world and in the territory of Czechoslovakia, respectively the Czech Republic. The third chapter is a major part of the thesis and describes the conditions under which conditionally suspended sentence of imprisonment may be imposed, as well as examining the probation period, adequate restraints and adequate duties or compensation for the damage or detriment caused by the offense, or the unjust enrichment gained by the crime. Following chapter relates to the decision on conditionally suspended...

Markov processes have been widely studied and used for modeling problems. A Markov process has two main components (i.e., an evolution law and an initial distribution). Markov processes are not suitable for modeling some problems, for example, the problem of predicting a trajectory with a known destination. Such a problem has three main components: an origin, an evolution law, and a destination. The conditionally Markov (CM) process is a powerful mathematical tool for generalizing the Markov process. One class of CM processes, called $CM_L$, fits the above components of trajectories with a destination. The CM process combines the Markov property and conditioning. The CM process has various classes that are more general and powerful than the Markov process, are useful for modeling various problems, and possess many Markov-like attractive properties. Reciprocal processes were introduced in connection to a problem in quantum mechanics and have been studied for years. But the existing viewpoint for studying reciprocal processes is not revealing and may lead to complicated results which are not necessarily easy to apply. We define and study various classes of Gaussian CM sequences, obtain their models and characterizations, study their relationships, demonstrate their applications, and provide general guidelines for applying Gaussian CM sequences. We develop various results about Gaussian CM sequences to provide a foundation and tools for general application of Gaussian CM sequences including trajectory modeling and prediction. We initiate the CM viewpoint to study reciprocal processes, demonstrate its significance, obtain simple and easy to apply results for Gaussian reciprocal sequences, and recommend studying reciprocal processes from the CM viewpoint. For example, we present a relationship between CM and reciprocal processes that provides a foundation for studying reciprocal processes from the CM viewpoint. Then, we obtain a model for nonsingular Gaussian reciprocal sequences with white dynamic noise, which is easy to apply. Also, this model is extended to the case of singular sequences and its application is demonstrated. A model for singular sequences has not been possible for years based on the existing viewpoint for studying reciprocal processes. This demonstrates the significance of studying reciprocal processes from the CM viewpoint.

The aim of this thesis is to experimentally evaluate the performance of several distinct representations of transition functions for cellular automata. Cellular automata have many potential applications for simulating various phenomena (e.g. natural processes, physical systems, etc.). Parallel computation of cellular automata is based on local cell interactions. Such computation, however, may prove difficult to program the CA, which is the reason for applying evolutionary techniques for the design of cellular automata in many cases. Evolutionary algorithms, based on Darwin's theory of evolution, have been used to find human-competitive solutions to many problems. In order to perform the evolutionary design of cellular automata, special encodings of the candidate solutions are often necessary. For this purpose the performance testing of various representations of the transition functions will be investigated. In particular, table representation, conditionally matching rules, and genetic programming will be treated. The problem of square calculations in cellular automata will be considered as a case study.

Classical partial transport barriers govern both classical and quantum dynamics of generic Hamiltonian systems. Chaotic eigenstates of quantum systems are known to localize on either side of a partial barrier if the flux connecting the two sides is not resolved by means of Heisenberg's uncertainty. Surprisingly, in open systems, in which orbits can escape, chaotic resonance states exhibit such a localization even if the flux across the partial barrier is quantum mechanically resolved. We explain this using the concept of conditionally invariant measures by introducing a new quantum mechanically relevant class of such fractal measures. We numerically find quantum-to-classical correspondence for localization transitions depending on the openness of the system and on the decay rate of resonance states. Moreover, we show that the number of long-lived chaotic resonance states that localize on one particular side of the partial barrier is described by an individual fractal Weyl law. For a generic phase space, this implies a hierarchy of fractal Weyl laws, one for each region of the hierarchical decomposition of phase space.

In this work, we generalize three famous results obtained by Schoenberg: I) the characterization of the continuous positive definite isotropic kernels defined on a real sphere; II) the characterization of the continuous positive definite radial kernels defined on an Euclidean space; III) the characterization of the continuous conditionally negative radial kernels defined on an Euclidean space. From this new approach, we reobtain several results in the literature and obtain some new ones as well. With the exception of S1 and R , we obtain necessary and sufficient conditions in order that these kernels be strictly positive definite and strictly conditionally negative definite. / Neste trabalho, nós generalizamos três resultados famosos obtidos por Schoenberg: I) a caracterização dos núcleos contínuos isotrópicos positivos definidos em esferas reais; II) a caracterização dos núcleos contínuos radiais positivos definidos em espaços Euclidianos; III) a caracterização dos núcleos contínuos radiais condicionalmente negativos definidos em espaços Euclidianos. A partir destas novas abordagens, reobtemos vários resultados da literatura assim como obtemos novos. Com a exceção de S1 e R, obtemos condições necessárias e suficientes para que estes núcleos sejam estritamente positivos definidos e estritamente condicionalmente negativos definidos.

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<p>Prostate cancer is one leading cause of cancer-related death among men in Western countries. The standard therapies for localized prostate cancer include radical prostatectomy and radiation therapy. Such measures are relatively effective in the short term, but many patients ultimately relapse. These patients may benefit from a combination of standard therapy and oncolytic virus therapy. My work aimed to develop viruses for this purpose.</p><p>TARP is a protein that in males is specifically expressed in prostate epithelial and cancer cells. In my thesis, I characterized the TARP promoter and showed that TARP expression is regulated at the transcriptional level by testosterone through binding of the androgen receptor in the proximal TARP promoter. I further developed TARP promoter-based regulatory sequences for prostate-specific gene expression. A sequence comprising a PSA enhancer, a PSMA enhancer and the TARP promoter was constructed and designated PPT. An adenoviral vector containing the PPT sequence shielded from transcriptional interference by an H19 insulator showed high prostate-specific transcriptional activity in human cells both in the presence and absence of testosterone. However, in experimental murine prostate cancer the PPT sequence is not active. Therefore, a two-step transcriptional amplification (TSTA) system was used together with the PPT sequence to develop an adenovirus that confers prostate-specific transgene expression also in murine cells.</p><p>I constructed a conditionally replicating adenovirus where the E1A gene expression is controlled by an H19 insulator-shielded PPT regulatory sequence, Ad[I/PPT-E1A]. This virus exhibited absolute prostate specificity in terms of E1A expression, viral replication and cytolysis <i>in vitro</i> and <i>in vivo</i>. Importantly, our virus is active both in the presence and absence of testosterone, which may prove beneficial for patients treated by hormonal withdrawal. </p><p>Hopefully, my work will improve existing gene therapy strategies for prostate cancer and in the long term improve the prognosis for patients with prostate cancer.</p>

Prostate cancer is one leading cause of cancer-related death among men in Western countries. The standard therapies for localized prostate cancer include radical prostatectomy and radiation therapy. Such measures are relatively effective in the short term, but many patients ultimately relapse. These patients may benefit from a combination of standard therapy and oncolytic virus therapy. My work aimed to develop viruses for this purpose. TARP is a protein that in males is specifically expressed in prostate epithelial and cancer cells. In my thesis, I characterized the TARP promoter and showed that TARP expression is regulated at the transcriptional level by testosterone through binding of the androgen receptor in the proximal TARP promoter. I further developed TARP promoter-based regulatory sequences for prostate-specific gene expression. A sequence comprising a PSA enhancer, a PSMA enhancer and the TARP promoter was constructed and designated PPT. An adenoviral vector containing the PPT sequence shielded from transcriptional interference by an H19 insulator showed high prostate-specific transcriptional activity in human cells both in the presence and absence of testosterone. However, in experimental murine prostate cancer the PPT sequence is not active. Therefore, a two-step transcriptional amplification (TSTA) system was used together with the PPT sequence to develop an adenovirus that confers prostate-specific transgene expression also in murine cells. I constructed a conditionally replicating adenovirus where the E1A gene expression is controlled by an H19 insulator-shielded PPT regulatory sequence, Ad[I/PPT-E1A]. This virus exhibited absolute prostate specificity in terms of E1A expression, viral replication and cytolysis in vitro and in vivo. Importantly, our virus is active both in the presence and absence of testosterone, which may prove beneficial for patients treated by hormonal withdrawal. Hopefully, my work will improve existing gene therapy strategies for prostate cancer and in the long term improve the prognosis for patients with prostate cancer.

Classical partial transport barriers govern both classical and quantum dynamics of generic Hamiltonian systems. Chaotic eigenstates of quantum systems are known to localize on either side of a partial barrier if the flux connecting the two sides is not resolved by means of Heisenberg's uncertainty. Surprisingly, in open systems, in which orbits can escape, chaotic resonance states exhibit such a localization even if the flux across the partial barrier is quantum mechanically resolved. We explain this using the concept of conditionally invariant measures by introducing a new quantum mechanically relevant class of such fractal measures. We numerically find quantum-to-classical correspondence for localization transitions depending on the openness of the system and on the decay rate of resonance states. Moreover, we show that the number of long-lived chaotic resonance states that localize on one particular side of the partial barrier is described by an individual fractal Weyl law. For a generic phase space, this implies a hierarchy of fractal Weyl laws, one for each region of the hierarchical decomposition of phase space.

Nous proposons une approche spectrale permettant d'aborder des problèmes d'interpolation à noyaux dont la résolution numérique n'est pas directement envisageable. Un tel cas de figure se produit en particulier lorsque le nombre de données est infini. Nous considérons dans un premier temps le cadre de l'interpolation optimale dans les sous-espaces hilbertiens. Pour un problème donné, un opérateur intégral est défini à partir du noyau sous-jacent et d'une paramétrisation de l'ensemble des données basée sur un espace mesuré. La décomposition spectrale de l'opérateur est utilisée afin d'obtenir une formule de représentation pour l'interpolateur optimal et son approximation est alors rendu possible par troncature du spectre. Le choix de la mesure induit une fonction d'importance sur l'ensemble des données qui se traduit, en cas d'approximation, par une plus ou moins grande précision dans le rendu des données. Nous montrons à titre d'exemple comment cette approche peut être utilisée afin de rendre compte de contraintes de type "conditions aux limites" dans les modèles d'interpolation à noyaux. Le problème du conditionnement des processus gaussiens est également étudié dans ce contexte. Nous abordons enfin dans la dernière partie de notre manuscrit la notion de noyaux conditionnellement positifs. Nous proposons la définition générale de noyaux symétriques conditionnellement positifs relatifs à une espace de référence donné et développons la théorie des sous-espaces semi-hilbertiens leur étant associés. Nous étudions finalement la théorie de l'interpolation optimale dans cette classe d'espaces. / We propose a spectral approach for the resolution of kernel-based interpolation problems of which numerical solution can not be directly computed. Such a situation occurs in particular when the number of data is infinite. We first consider optimal interpolation in Hilbert subspaces. For a given problem, an integral operator is defined from the underlying kernel and a parameterization of the data set based on a measurable space. The spectral decomposition of the operator is used in order to obtain a representation formula for the optimal interpolator and spectral truncation allows its approximation. The choice of the measure on the parameters space introduces a hierarchy onto the data set which allows a tunable precision of the approximation. As an example, we show how this methodology can be used in order to enforce boundary conditions in kernel-based interpolation models. The Gaussian processes conditioning problem is also studied in this context. The last part of this thesis is devoted to the notion of conditionally positive kernels. We propose a general definition of symmetric conditionally positive kernels relative to a given space and exposed the associated theory of semi-Hilbert subspaces. We finally study the optimal interpolation problem in such spaces.