Michael Fuchs Ph.D. in Mathematics, Vienna University of Technology
Mailing Address:	Department of Mathematical Sciences, National Chengchi University, Taipei, 116, Taiwan.
Tel:	(+886)-2-29393091/67390
Fax:	(+886)-2-29387905
E-mail:	mfuchs@nccu.edu.tw

Short Curriculum Vitae

• 1999-2002: Teaching assistant, Institute of Applied and Numerical Mathematics, Vienna University of Technology, Vienna, Austria.
• 2000: Master degree (Dipl.-Ing.), Vienna University of Technology, Vienna, Austria.
• 05/2000-07/2002: Research assistant in the FWF Project Statistical Properties of Number Systems, Vienna, Austria.
• 2002: Ph.D. (Dr. techn.), Vienna University of Technology, Vienna, Austria.
• 08/2002-06/2004: Postdoctoral position at Academia Sinica, Taipei, Taiwan.
• 08/2004-07/2008: Assistant Professor at National Chiao Tung University, Hsinchu, Taiwan.
• 08/2008-07/2013: Associate Professor at National Chiao Tung University, Hsinchu, Taiwan.
• 08/2013-07/2019: Professor at National Chiao Tung University, Hsinchu, Taiwan.
• Since 08/2019: Professor at National Chengchi University, Taipei, Taiwan.

Teaching

• Fall Semester, 2024
  • Sabbatical
• Spring Semester, 2024
  • Combinatorics (II)
  • Mathematical Foundations of Cryptography

Students

• Graduated
• Master students:
• Kuan-Cheng Li (2006);
• Yi-Shen Lin (2009);
• Che-Hao Chen (2009);
• Po-Han Tseng (2009);
• Shu-Yi Chen (2012);
• Yen-Ting Kuo (2012);
• Yi-Wen Lee (2012);
• Chi-Wei Chiang (2012);
• Li-Ting Lin (2013);
• Chia-Ying Lin (2014);
• Guan-Ru Yu (2014);
• Ming-Shi Gao (2014);
• Feng-Shan Chang (2015);
• Li-An Chen (2015);
• Yu-Sheng Chang (2016);
• Hung-Yi Chiu (2017);
• Yu-Xiang Gao (2017);
• Chih-Hong Lee (2019);
• Wan-Zhen Wu (2019);
• Chun-Yen Huang (2019);
• En-Yu Huang (2022);
• Hexuan Liu (2022);
• Hao-Jun Li (2024).
• Ph.D. students:
• Chung-Kuei Lee: Probabilistic Analysis of Additive Shape Paramters in Random Digital Trees, 2014.
• Ariel R. Paningbatan: Three Combinatorial Topics Arising from Phylogenetics, 2020.
• Current
• Master student(s): Wei-Chi Chang.
• Ph.D. student(s): Yu-Sheng Chang, Chung-Hsuan Hsieh.
• Postdoc(s): Currently none; if you are interested in my research work, please contact me.

Research Interests

• Analytic Combinatorics
• Discrete Probability Theory
• Combinatorial Phylogenetics
• (Probabilistic) Analysis of Algorithms
• Metric Number Theory

Publications

• Papers
  • On Metric Diophantine Approximation in the Field of Formal Laurent Series, Finite Fields Appl., 8:3, 343-368 (2002).
  • Digital Expansion of Exponential Sequences, J. Theor. Nombres Bordeaux, 14:2, 477-487 (2002).
  • Functional Limit Theorems for Digital Expansions, (with M. Drmota and E. Manstavicius), Acta Math. Hungar., 98:3, 175-201 (2003).
  • On a Problem of W. J. LeVeque concerning Metric Diophantine Approximation, Trans. Amer. Math. Soc., 355:5, 1787-1801 (2003).
  • Invariance Principles in Metric Diophantine Approximation, Monatsh. Math., 139:3, 177-203 (2003).
  • An Analogue of a Theorem of Szusz for Formal Laurent Series over Finite Fields, J. Number Theory, 101:1, 105-130 (2003).
  • On a Problem of W. J. LeVeque concerning Metric Diophantine Approximation II, Math. Proc. Cambridge Philos. Soc., 137:1, 17-41 (2004).
  • Profiles of Random Trees: Limit Theorems for Random Recursive Trees and Binary Search Trees, (with H.-K. Hwang and R. Neininger), Algorithmica, 46:3-4, 367-407 (2006).
  • Invariance Principles for Diophantine Approximation of Formal Laurent Series over a Finite Base Field, (with E. Deligero and H. Nakada), Finite Fields Appl., 13:3, 535-545 (2007).
  • Phase Changes in Random Point Quadtrees, (with H.-H. Chern and H.-K. Hwang), ACM Trans. Algorithms, 3:3, 51 pages (2007).
  • Subtree Sizes in Recursive Trees and Binary Search Trees: Berry-Esseen Bounds and Poisson Approximations, Combin. Probab. Comput., 17:5, 661-680 (2008).
  • Limit Theorems for Patterns in Phylogenetic Trees, (with H. Chang), J. Math. Biol., 60:4, 481-512 (2010).
  • Metrical Theorems for Inhomogeneous Diophantine Approximation in Positive Characteristic, Acta Arith., 141:2, 191-208 (2010).
  • Asymptotic Variance of Random Symmetric Digital Search Trees, (with H.-K. Hwang and V. Zacharovas), Discrete Math. Theor. Comput. Sci. (special issue in honor of Philippe Flajolet), 12:2, 103-166 (2010).
  • The Variance for Partial Match Retrievals in k-dimensional Bucket Digital Trees, Discrete Math. Theor. Comput. Sci. Proc., Proceedings of the 21st International Meeting on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, 261-276 (2010).
  • The Subtree Size Profile of Plane-oriented Recursive Trees, Proceedings of the Eighth Workshop on Analytic Algorithmics and Combinatorics (ANALCO11), 85-92 (2011).
  • A Note on Simultaneous Diophantine Approximation in Positive Characteristic, Acta Arith., 147:2, 161-171 (2011).
  • On the Moment-Transfer Approach for Random Variables satisfying a One-Sided Distributional Recurrence, (with C.-H. Chen), Electron. J. Probab., 16, 903-928 (2011).
  • Limit Theorems for Subtree Size Profiles of Increasing Trees, Combin. Probab. Comput., 21:3, 412-441 (2012).
  • Approximate Counting via the Poisson-Laplace-Mellin Method, (with C.-K. Lee and H. Prodinger), Discrete Math. Theor. Comput. Sci. Proc., Proceedings of the 23rd International Meeting on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, 13-28 (2012).
  • A Higher-dimensional Kurzweil Theorem for Formal Laurent Series over Finite Fields, (with S.-Y. Chen), Finite Fields Appl., 18:6, 1195-1206 (2012).
  • Words with a Generalized Restricted Growth Property, (with H. Prodinger), Indag. Math. (special issue in memory of N. G. de Bruijn), 24:4, 1024-1033 (2013).
  • An Analytic Approach to the Asymptotic Variance of Trie Statistics and Related Structures, (with H.-K. Hwang and V. Zacharovas), Theor. Comput. Sci., 527, 1-36 (2014).
  • A General Central Limit Theorem for Shape Parameters of m-ary Tries and PATRICIA Tries, (with C.-K. Lee), Electron. J. Combin., 21:1, 26 pages (2014).
  • Limit Laws for the Number of Groups formed by Social Animals under the Extra Clustering Model, (with M. Drmota and Y.-W. Lee), Discrete Math. Theor. Comput. Sci. Proc., Proceedings of the 25th International Meeting on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, 73-84 (2014).
  • A Binomial Splitting Process in Connection with Corner Parking Problems, (with H.-K. Hwang, Y. Itoh, and H. M. Mahmoud), J. Appl. Probab., 51:4, 971-989 (2014).
  • Rumor Source Detection for Rumor Spreading on Random Increasing Trees, (with P.-D. Yu), Electron. Commun. Probab., 20, 12 pages (2015).
  • The Wiener Index of Random Digital Trees, (with C.-K. Lee), SIAM J. Discrete Math., 29:1, 586-614 (2015).
  • A Note on the Quicksort Asymptotics, Random Struct. Algor., 46:4, 677-687 (2015).
  • Equality of Shapley Value and Fair Proportion Index in Phylogenetic Trees, (with E. Y. Jin), J. Math. Biol., 71:5, 1133-1147 (2015).
  • Limit Behavior of Maxima in Geometric Words representing Set Partitions, (with M. Javanian), Appl. Anal. Discrete Math., 9:2, 313-331 (2015).
  • On 2-Protected Nodes in Random Digital Trees, (with C.-K. Lee and G.-R. Yu), Theor. Comput. Sci., 622, 111-122 (2016).
  • On Kurzweil's 0-1 Law in Inhomogeneous Diophantine Approximation, (with D. H. Kim), Acta Arith., 173:1, 41-57 (2016).
  • Stochastic Analysis of the Extra Clustering Model for Animal Grouping, (with M. Drmota and Y.-W. Lee), J. Math. Biol., 73:1, 123-159 (2016).
  • Dependence between External Path-Length and Size in Random Tries, (with H.-K. Hwang), Proceedings of the 27th International Meeting on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, Paper 10 (2016).
  • External Profile of Symmetric Digital Search Trees, (with M. Drmota, H.-K. Hwang, and R. Neininger), Proceedings of the Fourteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO17), 124-130 (2017).
  • From Coin-Tossing to Rock-Paper-Scissors and Beyond: A Log-Exp Gap Theorem for Selecting a Leader, (with H.-K. Hwang and Y. Itoh), J. Appl. Probab., 54:1, 213-235 (2017).
  • Dependence and Phase Changes in Random m-ary Search Trees, (with H.-H. Chern, H.-K. Hwang, and R. Neininger), Random Struct. Algor. (the version here is the unabridged version of the journal version), 50:3, 353-379 (2017).
  • Dependence between Path-Length and Size in Random Digital Trees, (with H.-K. Hwang), J. Appl. Probab., 54:4, 1125-1143 (2017).
  • Refined Asymptotics for the Number of Leaves of Random Point Quadtrees, (with N. S. Mueller and H. Sulzbach), LIPICS, Proceedings of the 29th International Meeting on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, 110, Paper 23 (2018).
  • Counting Phylogenetic Networks with Few Reticulation Vertices: Tree-Child and Normal Networks, (with B. Gittenberger and M. Mansouri), Australas. J. Combin., 73:2, 385-423 (2019).
  • Distributional Analysis of the Extra-Clustering Model with Uniformly Generated Phylogenetic Trees, (with C.-H. Lee and A. R. Paningbatan), Electron. Commun. Probab., 25, 13 pages (2020).
  • Correlation between Shapley Values of Rooted Phylogenetic Trees under the Beta-Splitting Model, (with A. R. Paningbatan), J. Math. Biol., 80:3, 627-653 (2020).
  • On Binomial and Poisson Sums Arising from the Displacement of Randomly Placed Sensors, (with L. Kao and W.-Z. Wu), Taiwanese J. Math., 24:6, 1353-1382 (2020).
  • On the Asymptotic Growth of the Number of Tree-Child Networks, (with G.-R. Yu and L. Zhang), European J. Combin., 93, 103278 (2021). (A maple worksheet verifying Propositions 4 and 5 can be found here.)
  • A Note on the Independence Number, Domination Number and Related Parameters of Random Binary Search Trees and Random Recursive Trees, (with C. Holmgren, D. Mitsche, and R. Neininger), Discrete Appl. Math., 292, 64-71 (2021).
  • Node Profiles of Symmetric Digital Search Trees: Concentration Properties, (with M. Drmota, H.-K. Hwang, and R. Neininger), Random Struc. Algor., 58:3, 430-467 (2021).
  • Counting Phylogenetic Networks with Few Reticulation Vertices: Exact Enumeration and Corrections, (with B. Gittenberger and M. Mansouri), Australas. J. Combin., 81:2, 257-282 (2021).
  • A Short Note on the Exact Counting of Tree-Child Networks, (with H. Liu and G.-R. Yu), 6 pages, arXiv:2110.03842 (2021).
  • Asymptotic Enumeration and Distributional Properties of Galled Networks, (with G.-R. Yu and L. Zhang), J. Comb. Theory Ser. A., 189, 105599 (2022).
  • Bijections for Ranked Tree-Child Networks, (with A. Caraceni and G.-R. Yu), Discrete Math., 345:9, 112944 (2022).
  • Enumeration of d-combining Tree-Child Networks, (with Y.-S. Chang, H. Liu, M. Wallner, and G.-R. Yu), LIPICS, Proceedings of the 33rd International Meeting on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, 225, Paper 5 (2022).
  • Counting Phylogenetic Networks with Few Reticulation Vertices: A Second Approach, (with E.-Y. Huang and G.-R. Yu), Discrete Appl. Math., 320, 140-149 (2022).
  • Two Results about the Sackin and Colless Indices for Phylogenetic Trees and Their Shapes, (with G. Goh and L. Zhang), J. Math. Biol., 85:6-7, Paper 69 (2022).
  • The Distributions under Two Species-Tree Models of the Number of Root Ancestral Configurations for Matching Gene Trees and Species Trees, (with F. Disanto, A. R. Paningbatan, and N. A. Rosenberg), Ann. Appl. Probab., 32:6, 4426-4458 (2022).
  • Asymptotic Normality for the Size of Graph Tries built from M-ary Tree Labelings, (with T.-C. Yu), Theor. Comput. Sci., 968, 114011 (2023).
  • Distribution of External Branch Lengths in Yule Histories, (with F. Disanto), Electron. J. Combin., 30:3, 22 pages (2023).
  • The Distributions under Two Species-Tree Models of the Total Number of Ancestral Configurations for Matching Gene Trees and Species Trees, (with F. Disanto, C.-Y. Huang, A. R. Paningbatan, and N. A. Rosenberg), Adv. in Appl. Math., 152, 102594 (2024).
  • Limit Theorems for Patterns in Ranked Tree-Child Networks, (with H. Liu and T.-C. Yu), Random Struc. Algor., 64:1, 15-37 (2024).
  • Enumerative and Distributional Results for d-combining Tree-Child Networks, (with Y.-S. Chang, H. Liu, M. Wallner, and G.-R. Yu), Adv. in Appl. Math., 157, 102704 (2024).
  • Counting Phylogenetic Networks with Few Reticulation Vertices: Galled and Reticulation-Visible Networks, (with Y.-S. Chang), Bull. Math. Biol., 86:7, Paper 76 (2024).
  • Galled Tree-Child Networks, (with Y.-S. Chang and G.-R. Yu), LIPICS, Proceedings of the 35th International Meeting on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, 302, Paper 8 (2024).
  • Asymptotic Enumeration of Rooted Binary Unlabeled Galled Trees with a Fixed Number of Galls, (with L. Agranat-Tamir, B. Gittenberger, and N. A. Rosenberg), LIPICS, Proceedings of the 35th International Meeting on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, 302, Paper 27 (2024).
  • Shape Paramters of Evolutionary Trees in Theoretical Computer Science, Philos. Trans. R. Soc. B, in press.
  • Sackin Indices for Labeled and Unlabed Classes of Galled Trees, (with B. Gittenberger), 25 pages, submitted.
  • The B2 Index of Galled Trees, (with F. Bienvenu, J.-J. Duchamps, and T.-C. Yu), 46 pages, submitted.