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Rigidity of inflnite disk patterns By ZhengXu He*
"... Let P be a locally flnite disk pattern on the complex plane C whose combinatorics are described by the oneskeleton G of a triangulation of the open topological disk and whose dihedral angles are equal to a function £: E! [0; …=2] on the set of edges. Let P ⁄ be a combinatorially equivalent disk pat ..."
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Let P be a locally flnite disk pattern on the complex plane C whose combinatorics are described by the oneskeleton G of a triangulation of the open topological disk and whose dihedral angles are equal to a function £: E! [0; …=2] on the set of edges. Let P ⁄ be a combinatorially equivalent disk pattern on the plane with the same dihedral angle function. We show that P and P ⁄ difier only by a euclidean similarity. In particular, when the dihedral angle function £ is identically zero, this yields the rigidity theorems of B. Rodin and D. Sullivan, and of O. Schramm, whose arguments rely essentially on the pairwise disjointness of the interiors of the disks. The approach here is analytical, and uses the maximum principle, the concept of vertex extremal length, and the recurrency of a family of electrical networks obtained by placing resistors on the edges in the contact graph of the pattern. A similar rigidity property holds for locally flnite disk patterns in the hyperbolic plane, where the proof follows by a simple use of the maximum principle. Also, we have a uniformization result for disk patterns. In a future paper, the techniques of this paper will be extended to the case when 0 • £ < …. In particular, we will show a rigidity property for a class of inflnite convex polyhedra in the 3dimensional hyperbolic space. 1.
Constrained model predictive control: Stability and optimality
 AUTOMATICA
, 2000
"... Model predictive control is a form of control in which the current control action is obtained by solving, at each sampling instant, a finite horizon openloop optimal control problem, using the current state of the plant as the initial state; the optimization yields an optimal control sequence and t ..."
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Cited by 696 (15 self)
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Model predictive control is a form of control in which the current control action is obtained by solving, at each sampling instant, a finite horizon openloop optimal control problem, using the current state of the plant as the initial state; the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant. An important advantage of this type of control is its ability to cope with hard constraints on controls and states. It has, therefore, been widely applied in petrochemical and related industries where satisfaction of constraints is particularly important because efficiency demands operating points on or close to the boundary of the set of admissible states and controls. In this review, we focus on model predictive control of constrained systems, both linear and nonlinear and discuss only briefly model predictive control of unconstrained nonlinear and/or timevarying systems. We concentrate our attention on research dealing with stability and optimality; in these areas the subject has developed, in our opinion, to a stage where it has achieved sufficient maturity to warrant the active interest of researchers in nonlinear control. We distill from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature. In some cases the finite horizon optimal control problem solved online is exactly equivalent to the same problem with an infinite horizon; in other cases it is equivalent to a modified infinite horizon optimal control problem. In both situations, known advantages of infinite horizon optimal control accrue.
Gapped Blast and PsiBlast: a new generation of protein database search programs
 NUCLEIC ACIDS RESEARCH
, 1997
"... The BLAST programs are widely used tools for searching protein and DNA databases for sequence similarities. For protein comparisons, a variety of definitional, algorithmic and statistical refinements described here permits the execution time of the BLAST programs to be decreased substantially while ..."
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Cited by 8393 (85 self)
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The BLAST programs are widely used tools for searching protein and DNA databases for sequence similarities. For protein comparisons, a variety of definitional, algorithmic and statistical refinements described here permits the execution time of the BLAST programs to be decreased substantially while enhancing their sensitivity to weak similarities. A new criterion for triggering the extension of word hits, combined with a new heuristic for generating gapped alignments, yields a gapped BLAST program that runs at approximately three times the speed of the original. In addition, a method is introduced for automatically combining statistically significant alignments produced by BLAST into a positionspecific score matrix, and searching the database using this matrix. The resulting PositionSpecific Iterated BLAST (PSIBLAST) program runs at approximately the same speed per iteration as gapped BLAST, but in many cases is much more sensitive to weak but biologically relevant sequence similarities. PSIBLAST is used to uncover several new and interesting members of the BRCT superfamily.
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5350 (67 self)
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In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a long time, ‘variational ’ problems have been identified mostly with the ‘calculus of variations’. In that venerable subject, built around the minimization of integral functionals, constraints were relatively simple and much of the focus was on infinitedimensional function spaces. A major theme was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory progressed also to the study of socalled stationary points, critical points, and other indications of singularity that a point might have relative to its neighbors, especially in association with existence theorems for differential equations.
Wireless Communications
, 2005
"... Copyright c ○ 2005 by Cambridge University Press. This material is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University ..."
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Cited by 1129 (32 self)
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Copyright c ○ 2005 by Cambridge University Press. This material is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning under uncertainty, sensorbased planning, visibility, decisiontheoretic planning, game theory, information spaces, reinforcement learning, nonlinear systems, trajectory planning, nonholonomic planning, and kinodynamic planning.
Enterprise restructuring in transition: A quantitative survey, Washington: The World Bank (mimeographed
, 2000
"... NOTE: We will make final revisions to this paper in July 2000, at which time we will make reference to all pertinent papers that have come to our attention by June 30, 2000. If anyone reading this survey knows of a pertinent paper not presently included in the list of references, please send a copy ..."
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Cited by 359 (10 self)
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NOTE: We will make final revisions to this paper in July 2000, at which time we will make reference to all pertinent papers that have come to our attention by June 30, 2000. If anyone reading this survey knows of a pertinent paper not presently included in the list of references, please send a copy or a reference to one of us. *Djankov is Financial Economist at the World Bank. Murrell is Professor of Economics and Chair of the Academic Council of the IRIS Center, University of Maryland. We would like to thank Judy Hellerstein, John McMillan, John Nellis, and Jan Svejnar for helpful advice and Wooyoung Kim and Tatiana Nenova for research assistance. This research was made possible through support provided by the World Bank and by the U.S. Agency for International Development under Cooperative Agreement No. DHR0015A00003100 to the Center for Institutional Reform and the Informal Sector (IRIS). The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the IRIS Center, US AID, the World Bank, its Executive Directors, or the countries they represent. Enterprise Restructuring in Transition: A Quantitative Survey Abstract. There are now over 125 empirical papers that analyze the process of enterprise restructuring in transition
Active learning literature survey
, 2010
"... The key idea behind active learning is that a machine learning algorithm can achieve greater accuracy with fewer labeled training instances if it is allowed to choose the data from which is learns. An active learner may ask queries in the form of unlabeled instances to be labeled by an oracle (e.g., ..."
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Cited by 311 (1 self)
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The key idea behind active learning is that a machine learning algorithm can achieve greater accuracy with fewer labeled training instances if it is allowed to choose the data from which is learns. An active learner may ask queries in the form of unlabeled instances to be labeled by an oracle (e.g., a human annotator). Active learning is wellmotivated in many modern machine learning problems, where unlabeled data may be abundant but labels are difficult, timeconsuming, or expensive to obtain. This report provides a general introduction to active learning and a survey of the literature. This includes a discussion of the scenarios in which queries can be formulated, and an overview of the query strategy frameworks proposed in the literature to date. An analysis of the empirical and theoretical evidence for active learning, a summary of several problem setting variants, and a discussion
Vigilante: EndtoEnd Containment of Internet Worm Epidemics
, 2008
"... Worm containment must be automatic because worms can spread too fast for humans to respond. Recent work proposed networklevel techniques to automate worm containment; these techniques have limitations because there is no information about the vulnerabilities exploited by worms at the network level. ..."
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Cited by 299 (6 self)
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Worm containment must be automatic because worms can spread too fast for humans to respond. Recent work proposed networklevel techniques to automate worm containment; these techniques have limitations because there is no information about the vulnerabilities exploited by worms at the network level. We propose Vigilante, a new endtoend architecture to contain worms automatically that addresses these limitations. In Vigilante, hosts detect worms by instrumenting vulnerable programs to analyze infection attempts. We introduce dynamic dataflow analysis: a broadcoverage hostbased algorithm that can detect unknown worms by tracking the flow of data from network messages and disallowing unsafe uses of this data. We also show how to integrate other hostbased detection mechanisms into the Vigilante architecture. Upon detection, hosts generate selfcertifying alerts (SCAs), a new type of security alert that can be inexpensively verified by any vulnerable host. Using SCAs, hosts can cooperate to contain an outbreak, without having to trust each other. Vigilante broadcasts SCAs over an overlay network that propagates alerts rapidly and resiliently. Hosts receiving an SCA protect themselves by generating filters with vulnerability condition slicing: an algorithm that performs dynamic analysis of the vulnerable program to identify controlflow conditions that lead
Results 1  10
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