This book, written by two major figures in adaptive control, provides a wealth of material for researchers, practitioners, and students. While some researchers in adaptive control may note the absence of a particular topic, the book‘s scope represents a high-gain instrument. It can be used by designers of control systems to enhance their work through the information on many new theoretical developments, and can be used by mathematical control theory specialists to adapt their research to practical needs. The book is strongly recommended to anyone interested in adaptive control.

Adaptive Control

PART I: FOUNDATIONS 1. Introduction to Fixed-Parameter Algorithms 2. Preliminaries and Agreements 3. Parameterized Complexity Theory - A Primer 4. Vertex Cover - An Illustrative Example 5. The Art of Problem Parameterization 6. Summary and Concluding Remarks PART II: ALGORITHMIC METHODS 7. Data Reduction and Problem Kernels 8. Depth-Bounded Search Trees 9. Dynamic Programming 10. Tree Decompositions of Graphs 11. Further Advanced Techniques 12. Summary and Concluding Remarks PART III: SOME THEORY, SOME CASE STUDIES 13. Parameterized Complexity Theory 14. Connections to Approximation Algorithms 15. Selected Case Studies 16. Zukunftsmusik References Index

Invitation to fixed-parameter algorithms

This paper studies various algorithmic issues in reconstructing a species tree from gene trees under the duplication and the mutation cost model. This is a fundamental problem in computational molecular biology. Our main results are as follows. 
A linear time algorithm is presented for computing all the losses in duplications associated with the least common ancestor mapping from a gene tree to a species tree. This answers a problem raised recently by Eulenstein, Mirkin, and Vingron [J. Comput. Bio., 5 (1998), pp. 135--148]. The complexity of finding an optimal species tree from gene trees is studied. The problem is proved to be NP-hard for the duplication cost and for the mutation cost. Further, the concept of reconciled trees was introduced by Goodman et al. and formalized by Page for visualizing the relationship between gene and species trees. We show that constructing an optimal reconciled tree for gene trees is also NP-hard. Finally, we consider a general reconstruction problem and show it to be NP-hard even for the well-known nearest neighbor interchange distance. A new and efficiently computable metric is defined based on the duplication cost. We show that the problem of finding an optimal species tree from gene trees is NP-hard under this new metric but it can be approximated within factor 2 in polynomial time. Using this approximation result, we propose a heuristic method for finding a species tree from gene trees with uniquely labeled leaves under the duplication cost. Our experimental tests demonstrate that when the number of species is larger than 15 and gene trees are close to each other, our heuristic method is significantly better than the existing program in Page's GeneTree 1.0 that starts the search from a random tree.

From Gene Trees to Species Trees

Creating functional electrical circuits using individual or ensemble molecules, often termed as “molecular-scale electronics”, not only meets the increasing technical demands of the miniaturization of traditional Si-based electronic devices, but also provides an ideal window of exploring the intrinsic properties of materials at the molecular level. This Review covers the major advances with the most general applicability and emphasizes new insights into the development of efficient platform methodologies for building reliable molecular electronic devices with desired functionalities through the combination of programmed bottom-up self-assembly and sophisticated top-down device fabrication. First, we summarize a number of different approaches of forming molecular-scale junctions and discuss various experimental techniques for examining these nanoscale circuits in details. We then give a full introduction of characterization techniques and theoretical simulations for molecular electronics. Third, we highlig...

Molecular-Scale Electronics: From Concept to Function

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The Growth of Logical Thinking from Childhood to Adolescence

In this paper we give a programmatic overview of parame-terized computational complexity in the broad context of the problem of coping with computational intractability. We give some examples of how xed-parameter tractability techniques can deliver practical algorithms in two diierent ways: (1) by providing useful exact algorithms for small parameter ranges, and (2) by providing guidance in the design of heuristic algorithms. In particular, we describe an improved FPT ker-nelization algorithm for Vertex Cover, a practical FPT algorithm for the Maximum Agreement Subtree (MAST) problem parameterized by the number of species to be deleted, and new general heuristics for these problems based on FPT techniques. In the course of making this overview, we also investigate some structural and hardness issues. We prove that an important naturally parameterized problem in artiicial intelligence, STRIPS Planning (where the parameter is the size of the plan) is complete for W1]. As a corollary, this implies that k-Step Reachability for Petri Nets is complete for W1]. We describe how the concept of treewidth can be applied to STRIPS Planning and other problems of logic to obtain FPT results. We describe a surprising structural result concerning the top end of the parameterized complexity hierarchy: the naturally parameterized Graph k-Coloring problem cannot be resolved with respect to XP either by showing membership in XP, or by showing hardness for XP without settling the P = NP question one way or the other.

Parameterized complexity: A framework for systematically confronting computational intractability.

https://web.cs.dal.ca/~arc/publications/1-22/paper.pdf

Solving large FPT problems on coarse-grained parallel machines

We establish refined search tree techniques for the parameterized dominating set problem on planar graphs. We derive a fixed parameter algorithm with running time O(8kn), where k is the size of the dominating set and n is the number of vertices in the graph. For our search tree, we firstly provide a set of reduction rules. Secondly, we prove an intricate branching theorem based on the Euler formula. In addition, we give an example graph showing that the bound of the branching theorem is optimal with respect to our reduction rules. Our final algorithm is very easy (to implement); its analysis, however, is involved.

http://www.mrfellows.net/papers/AFFFNRS05_PlanarDS.pdf

Refined Search Tree Technique for DOMINATING SET on Planar Graphs

We obtain faster algorithms for problems such as r-dimensional matching and r-set packing when the size k of the solution is considered a parameter. We first establish a general framework for finding and exploiting small problem kernels (of size polynomial in k). This technique lets us combine Alon, Yuster and Zwick’s color-coding technique with dynamic programming to obtain faster fixed-parameter algorithms for these problems. Our algorithms run in time O(n+2 O(k)), an improvement over previous algorithms for some of these problems running in time O(n+k O(k)). The flexibility of our approach allows tuning of algorithms to obtain smaller constants in the exponent.

https://www.cs.mcgill.ca/~sue/papers/fpt-puzzles.pdf

Faster Fixed-Parameter Tractable Algorithms for Matching and Packing Problems

We describe some new, simple and apparently general methods for designing FPT algorithms, and illustrate how these can be used to obtain a significantly improved FPT algorithm for the MAXIMUM LEAF SPANNING TREE problem. Furthermore, we sketch how the methods can be applied to a number of other well-known problems, including the parametric dual of DOMINATING SET (also known as NONBLOCKER), MATRIX DOMINATION, EDGE DOMINATING SET, and FEEDBACK VERTEX SET FOR UNDIRECTED GRAPHS. The main payoffs of these new methods are in improved functions f(k) in the FPT running times, and in general systematic approaches that seem to apply to a wide variety of problems.

http://www.mrfellows.net/papers/C40-KernelsCatalytic-2000.pdf

Ulrike Stege

Papers

Parameterized complexity: A framework for systematically confronting computational intractability.

Solving large FPT problems on coarse-grained parallel machines

Refined Search Tree Technique for DOMINATING SET on Planar Graphs

Faster Fixed-Parameter Tractable Algorithms for Matching and Packing Problems

Coordinatized Kernels and Catalytic Reductions: An Improved FPT Algorithm for Max Leaf Spanning Tree and Other Problems