In this work, a method to choose the best run order for a given experimental design is proposed, for the simple linear regression model with MA errors. More specifically we investigate the best run order of an uniform design when errors follow a MA(1) or a subset MA(k) process where k is a positive integer. The correlation matrix P resulting from the errors is usually difficult to obtain a good estimate. Using the change of variance function(CVF) to see the relation of the uncorrelated and the serially correlated errors. Criterion proposed by Zhou (2001), we find the best run order of the uniform design on [-1,1] to minimize the robust criterion, |CVF|. We will display the permutation of a run order after rearrangement by our method and show how the structure is decomposed into three categories to solve the problem.

This thesis is based on top of the previous thesis "Security of modern encryption protocols" where we introduced a new paradigm for constructing quantum circuits. We have built circuits for modular arithmetic (addition, multiplication and exponentiation) in order to break El-Gamal asymmetric cryptosystem. Current thesis reviews all proposed circuits and discusses possibilities of their further optimization in goal of lowering the number of used qbits at least by an order of magnitude. It also shows that this is not possible due to existence of COPY gates which make the design inherently unoptimizable. Getting rid of COPY gates is, however, not possible without substantial rewrite of the whole paradigm. The overall estimate of number of qbits used in circuits thus remains O(log(m)log^2(N)) where m is a processed number and N is a modulus. The thesis also proposes optimization of the modular multiplication circuit that, if issues with COPY gates are resolved, allows us to lower the number of used qbits by about O(log(m)) at the price of a longer execution time.

電腦實驗(computer experiment)是探索複雜系統輸出反應值和輸入參數之間關係的重要工具，其重要特性是每一次的實驗非常耗費時間及運算的成本。一般在電腦實驗中，研究者較常關心的多是反應曲面的配適和輸出反應值的最佳化等問題(如極大或極小值)。借由一真實平行分散處理系統的啟發，本文所關心的是如何找出系統反應值的局部目標區域。此目標區域有一個非常重要的特性，即區域內外的輸出值所呈現的反應曲面並不連續，因此一般傳統的反應曲面法(response surface methodology)無法適用。本文提出一個新的、可估計不同類型電腦實驗目標區域的有效方法，其中包含了逐步均勻設計和建立分類模型的概 念，電腦模擬的結果也證明了所提方法準確又有效率。 / Computer experiment has been an important tool for exploring the relationships between the input factors and the output responses. It’s important feature is that conducting an experiment is usually time consuming and computationally expensive. In general, researchers are more interested in finding an adequate model for the response surface and the related output optimization problems over the entire input space. Motivated by a real-life parallel and distributed system, here we focus on finding a localized “target region” for the computer experiment. The experiment here has an important characteristic - the response surface is not continuous over the target region of interest. Thus, the traditional response surface methodology (RSM) cannot be directly applied. In this thesis, a novel and efficient methodology for estimating this type of target regions of computer experiment is proposed. The method incorporates the concept of sequential uniform design (UD) and the development of classification techniques based on support vector machines (SVM). Computer simulation shows that the proposed method can efficiently and precisely estimate the target region of computer experiment with different shapes.

The diploma thesis is focused on create an optimization methodology for CFD issues or any other computationally demanding software. Optimization method is applied on simplified model of car, where improves its aerodynamic properties

In this study, the effect of a passive trapped-vortex cell on lift to drag (L/D) ratio of an FFA-W3-301 airfoil is studied. The upper surface of the airfoil was modified to incorporate a cavity defined by seven parameters. The L/D ratio of the airfoil is modeled using a radial basis function metamodel. This model is used to find the optimal design parameter values that give the highest L/D. The numerical results indicate that the L/D ratio is most sensitive to the position on an airfoil’s upper surface at which the cavity starts, the position of the end point of the cavity, and the vertical distance of the cavity end point relative to the airfoil surface. The L/D ratio can be improved by locating the cavity start point at the point of separation for a particular angle of attack. The optimal cavity shape (o19_aXX) is also tested for a NACA0024 airfoil.