The similarity metric

A new class of distances appropriate for measuring similarity relations between sequences, say one type of similarity per distance, is studied. We propose a new ``normalized information distance'', based on the noncomputable notion of Kolmogorov complexity, and show that it is in this class and it minorizes every computable distance in the class (that is, it is universal in that it discovers all computable similarities). We demonstrate that it is a metric and call it the {\em similarity metric}. This theory forms the foundation for a new practical tool. To evidence generality and robustness we give two distinctive applications in widely divergent areas using standard compression programs like gzip and GenCompress. First, we compare whole mitochondrial genomes and infer their evolutionary history. This results in a first completely automatic computed whole mitochondrial phylogeny tree. Secondly, we fully automatically compute the language tree of 52 different languages.Comment: 13 pages, LaTex, 5 figures, Part of this work appeared in Proc. 14th ACM-SIAM Symp. Discrete Algorithms, 2003. This is the final, corrected, version to appear in IEEE Trans Inform. T

Adaptive Extremum Control and Wind Turbine Control

Modelling (IMM), the Technical University of Denmark (DTU). This thesis consists of two parts, i.e., adaptive extremum control and modelling and control of a wind turbine. The rst part of the thesis discusses design of adaptive extremum controllers for some processes which havethe behaviour that the process should have as high e ciency as possible. The main contribution is the development of an adaptive extremum control algorithm based on the parameter estimation for the processes with output nonlinearity. The second part of the thesis is concerned with modelling and control of a wind turbine. The investigation of control design is divided into below rated operation and above rated operation. The behaviour of wind turbines in below rated operation belongs to the process discussed in the rst part of the thesis, which can be considered as a connection between two parts. i ii Acknowledgements It is pleasure for me take the opportunity to express my gratefulness to everybody who enabled me to perform the work presented in this thesis. First, I wish to express my thanks to my supervisor Niels Kj stad Poulsen (IMM) and Henrik Bindner (Ris National Laboratory) for their willing to be my supervisors and their interests in the project. Further, I thank them for reading the rst version of the thesis and for giving helpful comments. Iwould also like to thank the sta at the IMM, my friends Anca Daniella Hansen for enjoyable daily company, and Lars Henrik Hansen who has always time and patience with my questions. Especially I wish to thank the librarian Finn Kuno Christensen for his help to nd literature sources. I greatly appreciate the support by my parents and my parents-in-law, who have helped me to take careofmy son during my study. I would also like to thank my son Johan Ziruo Ye for his understanding. iii iv Finally, A special acknowledge is to my husband Tao Ye, whom I can never thank enough for his support and encouragement

Resolving subcategories and dimensions in recollements of extriangulated categories

Recently, Wang, Wei and Zhang introduced the notion of recollements of extriangulated categories. In this paper, let $(\mathcal{A},\mathcal{B},\mathcal{C})$ be a recollement of extriangulated categories. We provide some methods to construct resolving subcategories in $(\mathcal{A},\mathcal{B},\mathcal{C})$. As applications of the Auslander-Reiten correspondence, we get the gluing of cotilting modules in a recollement of module categories for artin algebras. We also give some bounds of resolution dimensions of the categories involved in $(\mathcal{A},\mathcal{B},\mathcal{C})$ with respect to resolving subcategories, which generalize some known results.Comment: 21 page