Mathematical foundations for Informatics

The dissertation has four chapters: Chapter 1 - Background Materials; Chapter 2 - Analysis of an Algorithm in Indefinite Quadratic Programming; Chapter 3 - Qualitative Properties of the Minimum Sum-of-Squares Clustering Problem; Chapter 4 - Some Incremental Algorithms for the Clustering Problem.

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Objectives: The main objective of the dissertation is to research and develop fuzzy clustering techniques on remote sensing image data in order to improve accuracy and improve clustering quality of clustering algorithms.

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Research Aims: The thesis aims to develop deep neural networks for analyzing security data. These techniques improve the accuracy of machine learning-based models applied in NAD. Therefore, the thesis attempts to address the above challenging problems in NAD using models and techniques in deep neural networks. Specifically, the following problems are studied.

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The research objective: To study the methods used to modeling constraints and improve constraint solving capability. To apply symbolic execution technique in automatic test case generating. To implement proposed methods in automatic test case generating on string constraints and mixed constraints. To analyze and evaluate the obtained results.

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This thesis aims to research on overview of automatic test case generating, symbolic execution applied into automatic test case generating. The modeling techniques based on Automata and Bitvector are also studied in this thesis. Apart from that, the analysis and evaluation of available test case generating methods on different constraint are mentioned. The quality and effectiveness of test cases generated by using symbolic execution are assessed.

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Study methods of semantically expressing fuzzy concepts based the MF or other mathematical methods providing that they express the semantics of the most suitable concepts; studying methods of knowledge exploitation in general and fuzzy rules in particular; sesearch different data representations of information so that it can be exploited in ARs in a diverse and meaningful way.

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It is impossible to find an optimal algorithm that can reduce time and memory complexities with best detection performance. These aspects are always in conflict with each other. Thus, in each chapter, we will propose algorithms to solve each problem quite independently.

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Since data representation is one of the factors that affect the training and testing time, a compact and complete detector generation algorithm is investigated; the thesis investigates optimal algorithms to generate detector set in AIS; they help to reduce both training time and detecting time of AIS-based IDSs.

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