ecorative lighting strips could be used to the backlight of furniture, to creating a modern interior design. From an architectural point of view, this design is very difficult and requires a strong sense of aesthetics. More easier is to use the LED strips to the advertising trailers or to backlighting car parts. RGB strip will be powered by switching power supply with galvanic isolation. Colour will be changed by the combination of basic colours RGB, by using 3-channel PWM of Atmel microcontroller, controlled via a wireless module, providing two-way communication..

Práce uvádí základní informace o průmyslové sběrnici AS-Interface a popisuje její funkce. Dále se zabývá rozšířením stávajícího FTZ AS-Interface Slave Simulátoru o dotykový display, který značně usnadní ovládání tohoto simulačního nástroje. Je zde nastíněn návrh a řešení uživatelského dotykového rozhraní k tomuto simulátoru s použitím Amulet LCD modulu STK 480272C. Vývoj tohoto rozhraní je proveden pomocí GEMstudia, softwaru firmy Amulet Technologies a grafických programů. Dále tato studie pojednává o softwarové úpravě FTZ AS-i Slave Smilulátoru. Jedná se o úpravu řídícího FPGA v jazyce VHDL zajišťující komunikaci s dotykovým displejem. Poslední kapitola se týká problematiky spojené s návrhem uživatelsky přívětivé aplikace.

The state-variable analog filter topologies are described. Using the transfer function theory and operational configurations suitable for integration and derivation, a new universal filter topology are proposed. The circuit has been implemented in CMOS technology by using six operational amplifiers, eight analog switches and five programming resistor array. Tunable corner frequencies, quality factors and gain are realized. Using the serial peripheral interface or digital memory can be realized this real-time digitally programmable first- and second-order analog filter with the tunable parameters.

Práce je zaměřena na vzájemnou interakci několika odvětví matematiky. Hlavní myšlenkou práce bylo najít závislosti, vztahy a analogie mezi nimi. První část práce se týká vztahu mezi formální pojmovou analýzou, topologií a parciálními metrikami. Formální kontext je velice obecná matematická struktura, která může reprezentovat ostatní matematické struktury v jednotné a sjednocené formě. Přirozeným způsobem bychom mohli reprezentovat informaci podobně jako v tabulce, reprezentující formální kontext (s respektem ke všem množinově-teoretickým omezením) a generovat určité topologie na množinách atributů a objektů. V druhé části studujeme především pretopologické systémy jako speciální případ formálních kontextů. Od topologických systémů se pretopologické systémy liší především obecnější uspořádanou strukturou na množině atributů, reprezentujících zobecněné otevřené množiny. Vlastnosti tohoto uspořádání podstatně ovlivňují chování celé struktury a proto mu věnujeme zvláštní pozornost v závěru kapitoly, kde se mj. zabýváme konstrukcí analogie de Grootova duálu, včetně jeho iterovaných vlastností. Třetí část práce je zasvěcena struktuře framework, která má přirozenou strukturu formálního kontextu. Framework se skládá ze dvojice množin, z nichž první je množina míst a druhá obsahuje jistý systém podmnožin první množiny, aniž by bylo vyžadováno splnění nějakých axiómů. Struktura je opatřena jednoduchou konstrukcí duality, umožňující přepínání mezi klasickým, bodově-množinovým přístupem, podobně jako v topologii a bezbodovou reprezentací topologických vztahů. V závěru navrhujeme a studujeme, jak aproximovat libovolný framework pomocí usměrněného souboru konečných frameworků z hlediska generované topologie. V poslední části práce používáme metody obecné topologie ke korekci a zlepšení jednoho ze základních teorémů teorie her. Dokázali jsme mimo jiné, že pro hru v normální formě, v níž má i-tý hráč spojitou výherní funkci a množina jeho strategií je skoro-kompaktní, má tento hráč nedominovanou strategii. Kromě tohoto výsledku v poslední a předposlední kapitole ukazujeme, že teorie her přirozeným způsobem generuje velmi obecné, například nehausdorffovské topologické a kontextové struktury, čímž posouvá tradiční chápání reality neobvyklým směrem.

Gossip is a generic protocol which was designed for spreading information between nodes in large distributed decentralised systems. This protocol can be also used for many different applications including data aggregation, topology construction, etc. This work presents and describes a framework designed for facilitating modelling and simulation of Gossip-based systems.

This master‘s thesis describes research, design and development of system for topology recognition from crossroad plan. It explains the methods used for image processing, image segmentation, object recognition. It describes approaches in processing of maps represented by raster images and target software, in which the final product of practical part of project will be integrated. Thesis is focused mainly on comparison of different approaches in feature extraction from raster maps and determination their semantic meaning. Practical part of project is implemented in C# language with OpenCV library.

Dans la première partie de cette thèse on étudiera la conjecture de généricité: dans le graphe de Cayley du groupe modulaire d'une surface fermée on regarde une boule centrée à l'identité et on s'intéresse à la proportion de sommets pseudo-Anosov dans cette boule. La conjecture de généricité affirme que cette proportion doit tendre vers 1 quand le rayon de la boule tend vers l'infini. On montre qu'elle est bornée inférieurement par un nombre strictement positif et on montre des résultats similaires pour une grande classe de sous-groupes du groupe modulaire. On présente aussi des résultats analogues pour des groupes d'Artin-Tits de type sphérique, en sachant que dans ce cas, être pseudo-Anosov est analogue à agir loxodromiquement sur un complexe delta-hyperbolique convenable. Dans la deuxième partie on donne des résultats sur les sous-groupes paraboliques des groupes d'Artin-Tits de type sphérique: le standardisateur minimal d'une courbe dans le disque troué est la tresse minimale positive qui la fait devenir ronde. On construit un algorithme pour le calculer d'une façon géométrique. Ensuite, on généralise le problème pour les groupes d'Artin-Tits de type sphérique. On montre aussi que l'intersection de deux sous-groupes paraboliques est un sous-groupe parabolique et que l'ensemble de sous-groupes paraboliques est un treillis par rapport à l'inclusion. Finalement, on définit le complexe simplicial des sous-groupes paraboliques irréductibles, et on le propose comme l'analogue du complexe de courbes. / In the first part of this thesis we study the genericity conjecture: In the Cayley graph of the mapping class group of a closed surface we look at a ball of large radius centered on the identity vertex, and at the proportion of pseudo-Anosov vertices among the vertices in this ball. The genericity conjecture states that this proportion should tend to one as the radius tends to infinity. We prove that it stays bounded away from zero and prove similar results for a large class of subgroups of the mapping class group. We also present analogous results for Artin--Tits groups of spherical type, knowing that in this case being pseudo-Anosov is analogous to being a loxodromically acting element. In the second part we provide results about parabolic subgroups of Artin-Tits groups of spherical type: The minimal standardizer of a curve on a punctured disk is the minimal positive braid that transforms it into a round curve. We give an algorithm to compute it in a geometrical way. Then, we generalize this problem algebraically to parabolic subgroups of Artin--Tits groups of spherical type. We also show that the intersection of two parabolic subgroups is a parabolic subgroup and that the set of parabolic subgroups forms a lattice with respect to inclusion. Finally, we define the simplicial complex of irreducible parabolic subgroups, and we propose it as the analogue of the curve complex for mapping class groups.

Dans cette thèse, l'emphase est mise sur la réconciliation de l'analyse de structure et de séquence pour les protéines. L'analyse de séquence brille lorsqu'il s'agit de comparer des protéines présentant une forte identité de séquence (≤ 30\%) mais laisse à désirer pour identifier des homologues lointains. L'analyse de structure est une alternative intéressante. Cependant, les méthodes de résolution de structures sont coûteuses et complexes - lorsque toutefois elles produisent des résultats. Ces observations rendent évident la nécessité de développer des méthodes hybrides, exploitant l'information extraite des structures disponibles pour l'injecter dans des modèles de séquence. Cette thèse produit quatre contributions principales dans ce domaine. Premièrement, nous présentons une nouvelle distance structurale, le RMSDcomb, basée sur des patterns de conservation structurale locale, les motifs structuraux. Deuxièmement, nous avons développé une méthode pour identifier des motifs structuraux entre deux structures exploitant un bootstrap dépendant de filtrations. Notre approche n'est pas un compétiteur direct des aligneurs flexibles mais permet plutôt de produire des analyses multi-échelles de similarités structurales. Troisièmement, nous exploitons les méthodes suscitées pour construire des modèles de Markov cachés hybrides biaisés vers des régions mieux conservées structurellement. Nous utilisons un tel modèle pour caractériser les protéines de fusion virales de classe II, une tâche particulièrement ardue du fait de leur faible identité de séquence et leur conservation structurale moyenne. Ce faisant, nous parvenons à trouver un certain nombre d'homologues distants connues des protéines virales, notamment chez la Drosophile. Enfin, en formalisant un sous-problème rencontré lors de la comparaison de filtrations, nous présentons un nouveau problème théorique - le D-family matching - sur lequel nous démontrons des résultats algorithmiques variés. Nous montrons - d'une façon analogue à la comparaison de régions de deux conformations d'une protéine - comment exploiter ce modèle théorique pour comparer deux clusterings d'un même jeu de données. / In this thesis, the focus is set on reconciling the realms of structure and sequence for protein analysis. Sequence analysis tools shine when faced with proteins presenting high sequence identity (≤ 30\%), but are lack - luster when it comes to remote homolog detection. Structural analysis tools present an interesting alternative, but solving structures - when at all possible- is a tedious and expensive process. These observations make the need for hybrid methods - which inject information obtained from available structures in a sequence model - quite clear. This thesis makes four main contributions toward this goal. First we present a novel structural measure, the RMSDcomb, based on local structural conservation patterns - the so called structural motifs. Second, we developed a method to identify structural motifs between two structures using a bootstrap method which relies on filtrations. Our approach is not a direct competitor to flexible aligners but can provide useful to perform a multiscale analysis of structural similarities. Third, we build upon the previous methods to design hybrid Hidden Markov Models which are biased towards regions of increased structural conservation between sets of proteins. We test this tool on the class II fusion viral proteins - particularly challenging because of their low sequence identity and mild structural homology. We find that we are able to recover known remote homologs of the viral proteins in the Drosophila and other organisms. Finally, formalizing a sub - problem encountered when comparing filtrations, we present a new theoretical problem - the D-family matching - on which we present various algorithmic results. We show - in a manner that is analogous to comparing parts of two protein conformations - how it is possible to compare two clusterings of the same data set using such a theoretical model.

This thesis is about visualizing a kind of data that is trivial to process by computers but difficult to imagine by humans because nature does not allow for intuition with this type of information: high-dimensional data. Such data often result from representing observations of objects under various aspects or with different properties. In many applications, a typical, laborious task is to find related objects or to group those that are similar to each other. One classic solution for this task is to imagine the data as vectors in a Euclidean space with object variables as dimensions. Utilizing Euclidean distance as a measure of similarity, objects with similar properties and values accumulate to groups, so-called clusters, that are exposed by cluster analysis on the high-dimensional point cloud. Because similar vectors can be thought of as objects that are alike in terms of their attributes, the point cloud\''s structure and individual cluster properties, like their size or compactness, summarize data categories and their relative importance. The contribution of this thesis is a novel analysis approach for visual exploration of high-dimensional point clouds without suffering from structural occlusion. The work is based on implementing two key concepts: The first idea is to discard those geometric properties that cannot be preserved and, thus, lead to the typical artifacts. Topological concepts are used instead to shift away the focus from a point-centered view on the data to a more structure-centered perspective. The advantage is that topology-driven clustering information can be extracted in the data\''s original domain and be preserved without loss in low dimensions. The second idea is to split the analysis into a topology-based global overview and a subsequent geometric local refinement. The occlusion-free overview enables the analyst to identify features and to link them to other visualizations that permit analysis of those properties not captured by the topological abstraction, e.g. cluster shape or value distributions in particular dimensions or subspaces. The advantage of separating structure from data point analysis is that restricting local analysis only to data subsets significantly reduces artifacts and the visual complexity of standard techniques. That is, the additional topological layer enables the analyst to identify structure that was hidden before and to focus on particular features by suppressing irrelevant points during local feature analysis. This thesis addresses the topology-based visual analysis of high-dimensional point clouds for both the time-invariant and the time-varying case. Time-invariant means that the points do not change in their number or positions. That is, the analyst explores the clustering of a fixed and constant set of points. The extension to the time-varying case implies the analysis of a varying clustering, where clusters appear as new, merge or split, or vanish. Especially for high-dimensional data, both tracking---which means to relate features over time---but also visualizing changing structure are difficult problems to solve.

Bulk metallic glasses represent a newly developed class of materials. Some metallic glasses possess combinations of very good or even excellent mechanical, chemical and/or magnetic properties uncovering a broad range of both industrial and vital applications. Besides all advantages metallic glasses have also significant drawbacks, which have to be overcome for commercial application. Apart from low critical thicknesses, brittleness and chemical inhomogeneity one important problem of metallic glasses is the lack of an appropriate theory describing their structure. Therefore, the search for new glass forming compositions as well as the improving of existing ones occurs at present by means of trial-and-error methods and a number of empirical rules. Empirical rules for good glass-forming ability of bulk metallic glasses have been established in recent years by Inoue and Egami. Two of these rules, (i) Preference of more than 3 elements and (ii) Need of more than 12 % radii difference of base elements, seem to be closely related to topological (geometrical) criteria. From this point of view topological parameters contribute essentially to the glass-forming ability. The third rule (iii) demands a negative mixing enthalpy of base elements and refers to the chemical interaction of the atoms. The generalized Bernal’s model (hard-sphere approximation) was used for the simulation of monatomic, binary and multi-component structures. Excluding chemical interaction, this method allows the investigation of topological criteria of the glass-forming ability. Bernal’s hard-sphere model was shown to be a good approximation for bulk metallic glasses and metallic liquids and yields good coincidence of experimental and theoretical results. • The Laguerre (weighted Voronoi) tessellation technique was used as the main tool for the structural analysis. Due to very complex structures it is impossible to determine the structure of bulk metallic glasses by means of standard crystallographic methods. • Density, radial distribution function, coordination number and Laguerre polyhedra analysis confirm amorphism of the simulated structures and are in a good agreement with available experimental results. • The ratio of the fractions of non-crystalline to crystalline Laguerre polyhedra faces was introduced as a new parameter . This parameter reflects the total non-crystallinity of a structure and the amount of atomic rearrangements necessary for crystallization. Thus, the parameter is related to the glass-forming ability. It depends strongly on composition and atomic size ratio and indicates a region of enhanced glass-forming ability in binary mixtures at 80 % of small atoms and atomic size ratio of 1.3. All found maxima of parameter for ternary mixtures have compositions and size ratios which are nearly the same as for the binary mixture with the maximum value of . • A new method of multiple-compression was introduces in order to test the tendency towards densification and/or crystallization of the simulated mixtures. The results of the multiple-compression of monatomic mixtures indicate a limiting value of about 0.6464 for the density of the amorphous state. Further densification is necessarily connected to formation and growth of nano-crystalline regions. • The results of the multiple-compression for binary mixtures shows a new maximum of the density at the size ratio of 1.3 and 30 % to 90 % of small atoms. This maximum indicates a local island of stability of the amorphous state. The maximal receivable density without crystallization in this region is enhanced compared to neighbouring regions. • The comparison of the parameter and the density to the distribution of known binary bulk metallic (metal-metal) glasses clearly shows that both parameters play a significant role in the glass-forming ability. • The polyhedra analysis shows regions with enhanced fraction of the icosahedral short-range order (polyhedron (0, 0, 12)) in the binary systems with the maximum at 80 % of small atoms and size ratio of 1.3. Comparison of the distribution of the (0, 0, 12) polyhedra to the distribution of known binary metallic (metal-metal) glasses and to the parameter shows that icosahedral short-range order is not related to the glass-forming ability and is a consequence of the high non-crystallinity (high values of ) of the mixtures and non vice versa. Results for the ternary mixtures confirm this observation. • A new approach for the calculation of the mixing enthalpy is proposed. The new method is based on the combination of Miedema’s semi-empirical model and Laguerre tessellation technique. The new method as well as 6 other methods including the original Miedema’s model were tested for more than 1400 ternary and quaternary alloys. The results show a better agreement with experimental values of the mixing enthalpy for the new model compared to all other methods. The new model takes into account the local structure at atom site and can be applied to all metallic alloys without additional extrapolations if the atomic structure of the considered alloy is known from a suitable atomistic structure model.