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International Trade Network
Hanousek, Milan ; Krištoufek, Ladislav (advisor) ; Parrák, Radovan (referee)
This paper studies the topological properties of the International Trade Network (ITN) among world countries using a network analysis. We explore the distribu- tions of the most important network statistics measuring connectivity, assortativ- ity and clustering. We show that the topological properties of the weighted rep- resentation of the ITN are very different from those obtained by a binary network approach. In particular, we find that: (i) the majority of countries are character- ized by weak trade relationships, (ii) well connected countries tend to trade with poorly connected partners and (iii) countries holding more intense trade relation- ships are more clustered. Finally, we display that all structural properties of the ITN have remained remarkably stable over time.
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The optimal solution set of interval linear programming problems
Garajová, Elif ; Hladík, Milan (advisor) ; Zimmermann, Karel (referee)
Determining the set of all optimal solutions of a linear program with interval data is one of the main problems discussed in interval optimization. We review two methods based on duality in linear programming, which are used to approximate the optimal set. Additionally, another decomposition method based on complementary slackness is proposed. This method provides the exact description of the optimal set for problems with a fixed coefficient matrix. The second part of the thesis is focused on studying the topological and geometric properties of the optimal set. We examine sufficient conditions for closedness, boundedness, connectedness and convexity. We also prove that testing boundedness is co- NP-hard for inequality-constrained problems with free variables. Stronger results are derived for some special classes of interval linear programs, such as problems with a fixed coefficient matrix. Furthermore, we study the effect of transformations commonly used in linear programming on interval problems, which allows for a direct generalization of some results to different types of interval linear programs. Powered by TCPDF (www.tcpdf.org)
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International Trade Network
Hanousek, Milan ; Krištoufek, Ladislav (advisor) ; Parrák, Radovan (referee)
This paper studies the topological properties of the International Trade Network (ITN) among world countries using a network analysis. We explore the distribu- tions of the most important network statistics measuring connectivity, assortativ- ity and clustering. We show that the topological properties of the weighted rep- resentation of the ITN are very different from those obtained by a binary network approach. In particular, we find that: (i) the majority of countries are character- ized by weak trade relationships, (ii) well connected countries tend to trade with poorly connected partners and (iii) countries holding more intense trade relation- ships are more clustered. Finally, we display that all structural properties of the ITN have remained remarkably stable over time.
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