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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.
Uniform proofs as a foundation for logic programming
 ANNALS OF PURE AND APPLIED LOGIC
, 1991
"... A prooftheoretic characterization of logical languages that form suitable bases for Prologlike programming languages is provided. This characterization is based on the principle that the declarative meaning of a logic program, provided by provability in a logical system, should coincide with its ..."
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Cited by 425 (124 self)
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A prooftheoretic characterization of logical languages that form suitable bases for Prologlike programming languages is provided. This characterization is based on the principle that the declarative meaning of a logic program, provided by provability in a logical system, should coincide with its operational meaning, provided by interpreting logical connectives as simple and fixed search instructions. The operational semantics is formalized by the identification of a class of cutfree sequent proofs called uniform proofs. A uniform proof is one that can be found by a goaldirected search that respects the interpretation of the logical connectives as search instructions. The concept of a uniform proof is used to define the notion of an abstract logic programming language, and it is shown that firstorder and higherorder Horn clauses with classical provability are examples of such a language. Horn clauses are then generalized to hereditary Harrop formulas and it is shown that firstorder and higherorder versions of this new class of formulas are also abstract logic programming languages if the inference rules are those of either intuitionistic or minimal logic. The programming language significance of the various generalizations to firstorder Horn clauses is briefly discussed.
ON PÓSA’S CONJECTURE FOR RANDOM GRAPHS
, 2012
"... The famous Pósa conjecture states that every graph of minimum degree at least 2n/3 contains the square of a Hamilton cycle. This has been proved for large n by Komlós, Sarközy and Szemerédi. Here we prove that if p ≥ n −1/2+ε, then asymptotically almost surely, the binomial random graph Gn,p conta ..."
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Cited by 5 (2 self)
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The famous Pósa conjecture states that every graph of minimum degree at least 2n/3 contains the square of a Hamilton cycle. This has been proved for large n by Komlós, Sarközy and Szemerédi. Here we prove that if p ≥ n −1/2+ε, then asymptotically almost surely, the binomial random graph Gn
POSA: a userdriven, interactive multiple protein structure alignment server
 Nucleic Acids Res
, 2014
"... POSA (Partial Order Structure Alignment), available at ..."
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Cited by 1 (1 self)
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POSA (Partial Order Structure Alignment), available at
Filling the gap between Turán’s theorem and Pósa’s conjecture
, 2009
"... Much of extremal graph theory has concentrated either on finding very small subgraphs of a large graph (such as Turán’s theorem) or on finding spanning subgraphs (such as Dirac’s theorem or more recently the Pósa conjecture). Only a few results give conditions to obtain some intermediatesized subgr ..."
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Much of extremal graph theory has concentrated either on finding very small subgraphs of a large graph (such as Turán’s theorem) or on finding spanning subgraphs (such as Dirac’s theorem or more recently the Pósa conjecture). Only a few results give conditions to obtain some intermediate
A MODEST PRoPosa ‘ro DEREGUL~&n INFANT ADOPTIONS
"... In his famous satire, JonathanSwift “modestly”proposed slaughtering babIes and feedIng them to hungry Irish folk, flanks to Swift’s masterful lampoon, any proposal for modestly changing public policy affecting children risks being brandeda satire. So I proclaim up front my sincerItyIn proposIngthat ..."
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In his famous satire, JonathanSwift “modestly”proposed slaughtering babIes and feedIng them to hungry Irish folk, flanks to Swift’s masterful lampoon, any proposal for modestly changing public policy affecting children risks being brandeda satire. So I proclaim up front my sincerItyIn proposIngthat pregnantwomen, and women who have just gIven bIrth, be allowed to contract freelywIth adoptive parents at mutually agreeableprIces forthesaleofparental rights In their infants. The proposal Is not original. RIchard Posner has long championed the cause of a liberalized adoption market. ’ But most replies to his proposal have been crItIcal, too often falling to rise above InvectIve.’ Such negative reactIon belles both the modesty and the worthiness ofPosner’s proposal. The proposal Is modest becauseItmerely extends to birth mothers a liberty now enjoyed by many adoptIon agencies: the liberty to sell parental rights to adoptIve parents at mutually agreeable prices. The proposal Is worthwhile becauseIt promIsesgains to all relevant parties to adoptIons—birth mothers, couples wi~hing OpposItion to birth mothers ’ voluntary sales of parental rights Is founded on faulty reasoning. I use basIc economics to l’ilpjillght the benefits of liberalized adoption and to address some of the most common objections raised by those who Insist that children or society would be harmed by the free exchange of parental rights in infants.
Solving Systems of Polynomial Equations
 AMERICAN MATHEMATICAL SOCIETY, CBMS REGIONAL CONFERENCES SERIES, NO 97
, 2002
"... One of the most classical problems of mathematics is to solve systems of polynomial equations in several unknowns. Today, polynomial models are ubiquitous and widely applied across the sciences. They arise in robotics, coding theory, optimization, mathematical biology, computer vision, game theory, ..."
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Cited by 221 (14 self)
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One of the most classical problems of mathematics is to solve systems of polynomial equations in several unknowns. Today, polynomial models are ubiquitous and widely applied across the sciences. They arise in robotics, coding theory, optimization, mathematical biology, computer vision, game theory, statistics, machine learning, control theory, and numerous other areas. The set of solutions to a system of polynomial equations is an algebraic variety, the basic object of algebraic geometry. The algorithmic study of algebraic varieties is the central theme of computational algebraic geometry. Exciting recent developments in symbolic algebra and numerical software for geometric calculations have revolutionized the field, making formerly inaccessible problems tractable, and providing fertile ground for experimentation and conjecture. The first half of this book furnishes an introduction and represents a snapshot of the state of the art regarding systems of polynomial equations. Afficionados of the wellknown text books by Cox, Little, and O’Shea will find familiar themes in the first five chapters: polynomials in one variable, Gröbner
Geographical routing using partial information for wireless ad hoc networks
 IEEE Personal Communications
, 2001
"... In this paper we present an algorithm for routing in wireless ad hoc networks using information about geographical location of the nodes. We assume each node knows its geographical position and the position of the node to which it wants to send a packet. Initially, the nodes know only their neighbor ..."
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Cited by 179 (1 self)
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their neighbors, but over time they discover other nodes in the network. The routing table at a node S is a list h(pi�Si)i, where pi is a geographical position and Si is a neighbor of node S. When node S receives a packet for a node D at position pos(D), it finds the pi in its routing table which is closest
Results 1  10
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