Stochastic ordinary differential equations

Diplomová práce se zabývá problematikou obyčejných stochastických diferenciálních rovnic. Po souhrnu teorie stochastických procesů, zejména tzv. Brownova pohybu je zaveden stochastický Itôův integrál, diferenciál a tzv. Itôova formule. Poté je definováno řešení počáteční úlohy stochastické diferenciální rovnice a uvedena věta o existenci a jednoznačnosti řešení. Pro případ lineární rovnice je odvozen tvar řešení a rovnice pro jeho střední hodnotu a rozptzyl. Závěr tvoří rozbor vybraných rovnic.This thesis deals with the issue of stochastic ordinary differential equations. After the summary of the theory of stochastic processes, namely the Brownian motion, the stochastic Itô's integral, differential and so called Itô's formula are introduced. Thereafter the solution of the initial value problem for the stochastic equation is defined and the theorem of its existence and uniqueness is stated. For the case of the linear equation the explicit formula for the solution is derived as well as the equations for its expected value and variance. The last part is the analysis of selected equations.

Basics of space motion

Tato bakalářská práce je přehledovým textem, který se zabývá problematikou pohybu vesmírných těles. Je rozebírán problém jednoho, dvou a tří těles. U prvních dvou úloh odvodíme analytický tvar trajektorie pohybu. Z čehož odvodíme Keplerovy zákony, které jsou základem pro pochopení pohybu vesmírných těles. Dále budeme diskutovat vztah trajektorie k pojmu kosmické rychlosti. Pro problém tří těles v obecném případě analytické řešení v uzavřeném tvaru neexistuje. Existují speciální případy, tzv. stabilní orbity, pro které je analytické řešení známo. Navrhneme tedy numerické řešení explicitní Runge-Kutta-Bogacki-Shampine metodou a metodou zpětného derivování a jejich výsledky otestujeme na příkladu stabilní orbit.This Bachelor thesis is a summarising text which deals with the issue of space motion. We analyse one-body, two-body and three-body problems. We derive analytical solution for the first two problems, from which we derive Kepler's laws, which are important for understanding of the space motion. We also discuss the relation of analytical solution to escape velocities. The closed form of analytical solution for general case of three-body problem does not exist. There are special cases, so-called stable orbits, for which the analytical solution is known. We design the numerical solution by explicit Runge-Kutta-Bogacki-Shampine method and back diferentiation method and we will test the results on the stable orbits.

Semantic Surface Segmentation for RC car model

Tato práce se zabývá návrhem systému pro sémantickou segmentaci povrchu pro autonomní řízení. K sémantické segmentaci povrchu byla natrénována plně konvoluční neuronová síť U-net architectury. Učení a validace proběhlo na ručně anotovaném datasetu, který vznikl v rámci této práce. Za účelem zlepšení přesnosti a robustnosti klasifikace byla použita modifikovaná fokální ztrátová funkce. Modifikace spočívá ve váhování jednotlivých obrazových bodů podle jejich pozice v obrazu. Výsledný model pak vykazuje vyšší přesnost a robustnost segmentace, než model natrénovaný s křížovou entropií, běžně používanou ztrátovou funkcí. Systém sémantické segmentace byl zapracován do již existující platformy založené na modelu RC auta. K ověření funkcionality byly provedeny experimenty v reálném prostředí. Experimenty spočívaly v autonomní jízdě vozidla po předem daném povrchu. Toho bylo docíleno zpracováním segmentační mapy jednoduchým algoritmem, jehož výstupem je směrová reference. K řízení rychlosti a zatáčení jsou použity P regulátory. Provedené experimenty ukázaly schopnost navrženého řešení zajistit segmentační mapu s dostatečnou přesností pro autonomní jízdu vozidla.This work proposes a system for semantic surface segmentation for autonomous driving control. A fully convolutional neuron network of U-net architecture was trained for semantic surface segmentation. Learning and validation took place on a manually annotated data set, which was collected within this work. A modified focal loss function was used to improve the accuracy and robustness of the classification. The modification includes weighting of individual pixels according to their position in the image. The resulting model then shows higher accuracy and robustness of segmentation than the model trained cross-entropy, a common loss function. The semantic segmentation system was implemented into an existing subscale mobile platform based on the RC model. To verify the functionality of the proposed solution, experiments were performed in a real environment. The experiments consisted of autonomous drive of the platform on a selected surface. This was done by processing the segmentation map by an simple algorithm resulting in heading reference. Having the reference computed, P controller is used to control the velocity and steering of the vehicle. The performed experiments showed the ability of the proposed solution to provide a segmentation map with sufficient accuracy for autonomous driving of the subscale vehicle

Deviations from Low-energy Theorem for VLVLV_L V_L Scattering due to Pseudo-Goldstone Bosons

Possible deviations from a low-energy theorem for the scattering of strongly interacting longitudinally polarized $W$ and $Z$ bosons are discussed within a particular scheme of electroweak symmetry breaking. The scheme (suggested earlier by other authors in a slightly different context) is based on spontaneous breakdown of a SU(4) symmetry to custodial SU(2) subgroup. The physical spectrum of such a model contains a set of relatively light pseudo-Goldstone bosons whose interactions with vector bosons modify the low-energy theorem proven for a ``minimal'' symmetry-breaking sector. The Goldstone-boson manifold $SU(4)/SU(2)$ is not a symmetric space. In this context it is observed that, on the other hand, there is a large class of models of electroweak symmetry breaking, involving groups $G$ and $H$ such that the $G/H$ is a symmetric space and the corresponding rich multiplets of pseudo-Goldstone bosons do not influence the canonical low-energy theorem. For the scheme considered here, the relevant interactions are described in terms of an effective chiral Lagrangian and tree-level contributions of the pseudo-Goldstone boson exchanges to the vector boson scattering are computed explicitly. A comparison with the Standard Model is made.Comment: LaTeX, 16 pages, 4 eps figures, new title, new introduction and other revisions of the text, To appear in Mod.Phys.Lett.

Predictors of Bribe-Taking: The Role of Bribe Size and Personality

Laboratory studies allow studying the predictors of bribe-taking in a controlled setting. However, presently used laboratory tasks often lack any connection to norm violation or invite participants to role-play. A new experimental task for studying the decision to take a bribe was designed in this study to overcome these problems by embedding the opportunity for bribe-taking in an unrelated task that participants perform. Using this new experimental task, we found that refraining from harming a third party by taking a bribe was associated with lower offered bribes and higher scores of the participants on the honesty-humility scale from the HEXACO personality inventory. A trial-level analysis showed that response times were longer for trials with bribes and even longer for trials in which bribes were accepted. These results suggest that taking a bribe may require overcoming automatic honest response and support the validity of the honesty-humility scale in predicting moral behavior

Taking Algorithmic (Vs. Human) Advice Reveals Different Goals to Others

People are increasingly likely to obtain advice from algorithms. But what does taking advice from an algorithm (as opposed to a human) reveal to others about the advice seekers’ goals? In five studies (total N = 1927), we find that observers attribute the primary goal that an algorithm is designed to pursue in a situation to advice seekers. As a result, when explaining advice seekers’ subsequent behaviors and decisions, primarily this goal is taken into account, leaving less room for other possible motives that could account for people’s actions. Such secondary goals are, however, more readily taken into account when (the same) advice comes from human advisors, leading to different judgments about advice seekers’ motives. Specifically, advice seekers’ goals were perceived differently in terms of fairness, profit-seeking, and prosociality depending on whether the obtained advice came from an algorithm or another human. We find that these differences are in part guided by the different expectations people have of the type of information that algorithmic- vs. human advisors take into account when making their recommendations. The presented work has implications for (algorithmic) fairness perceptions and human-computer interaction.</p

Domain formation in thin ferroelectric films: The role of depolarization energy

Formulae for equlibrium stripe domain width Weq in a nonductive ferroelectric plate of thickness d are deduced, taking into account electrostatic interaction of surfaces. It is shown that the classical formula giving W eq ∞ d 1/2 is not applicable when the sample thickness decreases below the value dcrit which is a function of dielectric properties and domain wall energy density. For many ferroelectrics the value of dcrit lies in a range which can be easily reached far below the transition point by contemporary thin film techniques; it further increases as the transition point is approached. In the region d < dcrit the width Weq increases with decreasing d. For samples with thickness d << dcrit the domain structure becomes insensitive to electrical boundary conditions and will be primarily determined by other factors