This thesis is focused around Edgeworths expansion for aproximation of distribution for parameter estimation. Aim of the thesis is to introduce term Edgeworths expansion, its assumptions and terminology associeted with it. Afterwords demonstrate process of deducting first term of Edgeworths expansion. In the end demonstrate this deduction on examples and compare it with different approximations (mainly central limit theorem), and show strong and weak points of Edgeworths expansion.

This thesis is focused around Edgeworth's expansion for approximation of distribution for parameter estimation. Aim of the thesis is to introduce term Edgeworth's expansion, its assumptions and terminology associated with it. Afterwards demonstrate process of deducting first term of Edgeworth's expansion. In the end demonstrate this deduction on examples and compare it with different approximations (mainly central limit theorem), and show strong and weak points of Edgeworth's expansion.

Title: Complexity Theory in Feasible Mathematics Author: Ján Pich Department: Department of Algebra Supervisor: Prof. RNDr. Jan Krajíček, DrSc., MAE Abstract: We study the provability of statements and conjectures from Complex- ity Theory in Bounded Arithmetic. First, modulo a hardness assumption, we show that theories weaker in terms of provably total functions than Buss's theory S1 2 cannot prove nk -size circuit lower bounds for SAT formalized as a Σb 2-formula LB(SAT, nk ). In particular, the true universal first-order theory in the language containing names for all uniform NC1 algorithms denoted TNC1 does not prove LB(SAT, n4kc ) where k ≥ 1, c ≥ 2 unless each function f ∈ SIZE(nk ) can be approximated by formulas Fn of subexponential size 2O(n1/c) with subexponential advantage: Px∈{0,1}n [Fn(x) = f(x)] ≥ 1/2 + 1/2O(n1/c) . Unconditionally, V 0 does not prove quasipolynomial nlog n -size circuit lower bounds for SAT. Considering upper bounds, we prove the PCP theorem in Cook's theory PV1. This includes a formalization of the (n, d, λ)-graphs in PV1. A consequence of the result is that Extended Frege proof system admits p-size proofs of tautologies encoding the PCP theorem. Keywords: Circuit Lower Bounds, Bounded Arithmetic, The PCP theorem

This thesis focuses on the correlation of the UNSC voting behaviour of the People's Republic of China and its foreign policy. China's importance as a global power at the platform of the UN has been rising ever since 1971, the year of China's admittance as a new member of the UN and more importantly also the permanent member of the Security Council with the power of veto. Given that the veto power strongly influences the actions of the UNSC, its use has served as a major indicator of what issues are considered as most unfavourable and threatening to China's national interests and foreign policy goals. This thesis elaborates on the development of the foreign policy of China, which has changed significantly since the year of its acquired UN membership but has also kept many principles, present even before the establishment of the People's Republic of China in 1949. By specifically concentrating on the individual cast vetoes, also considering the use of a so-called hidden veto and the reasons behind them being cast, this thesis tries to find out, how China has been using its veto power with regards to its declared foreign policy objectives within the UN Security Council.

In present thesis we study and describe a stochastic loss reserve model for individual insurers. Specifically, it is the model based on the three following features. Modelling of expected claims depends on unknown parameters which estimates need to be the most accurate. Aggregated occurred and paid losses for particular years are modelled by a collective risk model. The final reserve is estimated by Bayesian methodology that uses a prior information from a significant number of insurers. Part of the thesis is also an implementation of the program that calculates reserves by using our model and its testing on simulated data.

e Abstract (in English): The aim of the present thesis is to investigate the differences in cohesive devices use in selected Japanese texts of different genes. The English conception of cohesion (based on Halliday and Hasan's "Cohesion in English") is applied to Japanese with several slight modifications and the following devices and their sub-types are examined: reference, substitution, ellipsis, conjunction and lexical cohesion. Using three texts of different genres- book review, newspaper article and a fictional narrative- the assumption of genre-conditioned variation of cohesive devices employment is scrutinized and the distinctions and similitudes are described. The first, general theory part of the thesis presents the basic concepts related to cohesion. In the second part, both English and Japanese perspectives on cohesion are presented. Subsequently, the English (Halliday and Hasan's) concept is evaluated as a more pertinent one and applied in the Japanese textual environment. Subsequent parts of the paper present research questions as well as supporting arguments to the examined underlying assumption and provide an overview of methodology applied in analysis of the selected texts. In the final part, the results concerning cohesion articulation in various genres in Japanese obtained from the analysed...

Fluid inclusion and mineralogical features indicative of boiling have been characterized in 855 samples from epithermal precious metals deposits along the Veta Madre at Guanajuato, Mexico. Features associated with boiling that have been identified at Guanajuato include colloform texture silica, plumose texture silica, moss texture silica, ghost-sphere texture silica, lattice-bladed calcite, lattice-bladed calcite replaced by quartz and pseudo-acicular quartz after calcite and coexisting liquid-rich and vapor-rich fluid inclusions. Most samples were assayed for Au, Ag, Cu, Pb, Zn, As and Sb, and were divided into high-grade and low-grade samples based on the gold and silver concentrations. For silver, the cutoff for high grade was 100 ppm Ag, and for gold the cutoff was 1 ppm Au. The feature that is most closely associated with high grades of both gold and silver is colloform texture silica, and this feature also shows the largest difference in grade between the presence or absence of that feature (178.8 ppm Ag versus 17.2 ppm Ag, and 1.1 ppm Au versus 0.2 ppm Au). For both Ag and Au, there is no significant difference in average grade as a function of whether or not coexisting liquid-rich and vapor-rich fluid inclusions are present. The textural and fluid inclusion data obtained in this study were analyzed using the binary classifier within SPSS Clementine. The models that correctly predicted high versus low grade samples most consistently (~70-75% of the tests) for both Ag and Au were the neural network, the C5 decision tree and Quest decision tree models. For both Au and Ag, the presence of colloform silica texture was the variable with the greatest importance, i.e., the variable that has the greatest predictive power. Boiling features are absent or rare in samples collected along a traverse perpendicular to the Veta Madre. This suggests that if an explorationist observes these features in samples collected during exploration that an environment favorable to precious metal mineralization is nearby. Similarly, good evidence for boiling is observed in the deepest levels of the Veta Madre that have been sampled in the mines and drill cores, suggesting that additional precious metal reserves are likely beneath the deepest levels sampled. / Master of Science

The modern swedish atheism is led by Christer Sturmark, chairman of Humanisterna, the swedish humanists. In this essay I study the epistemology of Christer Sturmark to find out on what basis he makes his assumptions about knowledge, faith, belief and his view that scientism is the only way to reach real knowledge. I present a closer historical look at the research about and philosophy of epistemology in general and then I analyze Christer Sturmarks book "Tro och Vetande 3.0 - Upplysning i det 21:a århundradet" and compare the views presented in that book to historical and contemporary philopsohers and religous scholars to extract the epistemology of Christer Sturmark, as it is presented in his book. To gain a more thorough understanding of his epistemolgy, I then compare his view to the swedish churchs´view of God as omnipotent. Finally I present a conclusion about the nature of Christer Sturmarks epistemology, if it is logically consistent and how it relates to the way humans can organize their understanding of the world.

Reform of the UN Security Council and a stumbling block associated with it - abstract This thesis deals with matter of the Security Council reform, the most crucial body of the United Nations. It examines approaches of eleven specific countries which are divided into two groups. The first group is comprised by permanent members of the Security Council, the second one by states which, in case of their creation, could claim new permanent seats in this body. This thesis examines not only their real policies, but also their policies from theoretical - specifically neorealistic - point of view. Two different hypotheses were deduced from neorealism which were tested and subsequently evaluated as (in)valid. Hypothesis emerging from a standard neorealism put emphasis on policy whose goal is to maintain, alternatively to increase a state's autonomy (autonomy-seeking policy). International organizations are viewed as entity which limits, to some extent, this autonomy. On the other hand, hypothesis emerging from a modified neorealism put emphasis on policy whose goal is to gain, alternatively to increase influence on other actors (influence-seeking policy). On the contrary, within this policy international organizations are an useful entity because it is possible to achieve such an influence by means of them. In the...