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38
Mixing times of lozenge tiling and card shuffling Markov chains
, 1997
"... Abstract. We show how to combine Fourier analysis with coupling arguments to bound the mixing times of a variety of Markov chains. The mixing time is the number of steps a Markov chain takes to approach its equilibrium distribution. One application is to a class of Markov chains introduced by Luby, ..."
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Cited by 69 (1 self)
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Abstract. We show how to combine Fourier analysis with coupling arguments to bound the mixing times of a variety of Markov chains. The mixing time is the number of steps a Markov chain takes to approach its equilibrium distribution. One application is to a class of Markov chains introduced by Luby, Randall, and Sinclair to generate random tilings of regions by lozenges. For an ℓ×ℓ region we bound the mixing time by O(ℓ 4 log ℓ), which improves on the previous bound of O(ℓ 7), and we show the new bound to be essentially tight. In another application we resolve a few questions raised by Diaconis and SaloffCoste by lower bounding the mixing time of various cardshuffling Markov chains. Our lower bounds are within a constant factor of their upper bounds. When we use our methods to modify a pathcoupling analysis of Bubley and Dyer, we obtain an O(n 3 log n) upper bound on the mixing time of the KarzanovKhachiyan Markov chain for linear extensions. 1.
Toward CaseBased Preference Elicitation: Similarity Measures on Preference Structures
 In Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence
, 1998
"... While decision theory provides an appealing normative framework for representing rich preference structures, eliciting utility or value functions typically incurs a large cost. For many applications involving interactive systems this overhead precludes the use of formal decisiontheoretic models of ..."
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Cited by 49 (6 self)
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While decision theory provides an appealing normative framework for representing rich preference structures, eliciting utility or value functions typically incurs a large cost. For many applications involving interactive systems this overhead precludes the use of formal decisiontheoretic models of preference. Instead of performing elicitation in a vacuum, it would be useful if we could augment directly elicited preferences with some appropriate default information. In this paper we propose a casebased approach to alleviating the preference elicitation bottleneck. Assuming the existence of a population of users from whom we have elicited complete or incomplete preference structures, we propose eliciting the preferences of a new user interactively and incrementally, using the closest existing preference structures as potential defaults. Since a notion of closeness demands a measure of distance among preference structures, this paper takes the first step of studying various distance mea...
On The Complexity Of Computing Mixed Volumes
 SIAM J. Comput
, 1998
"... . This paper gives various (positive and negative) results on the complexity of the problem of computing and approximating mixed volumes of polytopes and more general convex bodies in arbitrary dimension. On the negative side, we present several #Phardness results that focus on the di#erence of com ..."
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Cited by 30 (1 self)
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. This paper gives various (positive and negative) results on the complexity of the problem of computing and approximating mixed volumes of polytopes and more general convex bodies in arbitrary dimension. On the negative side, we present several #Phardness results that focus on the di#erence of computing mixed volumes versus computing the volume of polytopes. We show that computing the volume of zonotopes is #Phard (while each corresponding mixed volume can be computed easily) but also give examples showing that computing mixed volumes is hard even when computing the volume is easy. On the positive side, we derive a randomized algorithm for computing the mixed volumes V ( m 1 z } { K 1 , . . . , K 1 , m 2 z } { K 2 , . . . , K 2 , . . . , ms z } { Ks , . . . , Ks ) of wellpresented convex bodies K 1 , . . . , Ks , where m 1 , . . . , ms # N 0 and m 1 # n  #(n) with #(n) = o( log n log log n ). The algorithm is an interpolation method based on polynomialtime ra...
Multiple Indicators, partially ordered sets, and linear extensions: Multicriterion ranking and prioritization
, 2004
"... ..."
Similarity of Personal Preferences: Theoretical Foundations and Empirical Analysis
, 2003
"... We study the problem of defining similarity measures on preferences from a decisiontheoretic point of view. We propose a similarity measure, called probabilistic distance, that originates from the Kendall's tau function, a wellknown concept in the statistical literature. We compare this measure to ..."
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Cited by 20 (0 self)
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We study the problem of defining similarity measures on preferences from a decisiontheoretic point of view. We propose a similarity measure, called probabilistic distance, that originates from the Kendall's tau function, a wellknown concept in the statistical literature. We compare this measure to other existing similarity measures on preferences. The key advantage of this measure is its extensibility to accommodate partial preferences and uncertainty. We develop e#cient methods to compute this measure, exactly or approximately, under all circumstances. These methods make use of recent advances in the area of Markov chain Monte Carlo simulation. We discuss two applications of the probabilistic distance: in the construction of the DecisionTheoretic Video Advisor (diva), and in robustness analysis of a theory refinement technique for preference elicitation.
The Posterior Probability of Bayes Nets with Strong Dependences
 Soft Computing
, 1999
"... Stochastic independence is an idealized relationship located at one end of a continuum of values measuring degrees of dependence. Modeling real world systems, we are often not interested in the distinction between exact independence and any degree of dependence, but between weak ignorable and strong ..."
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Cited by 14 (1 self)
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Stochastic independence is an idealized relationship located at one end of a continuum of values measuring degrees of dependence. Modeling real world systems, we are often not interested in the distinction between exact independence and any degree of dependence, but between weak ignorable and strong substantial dependence. Good models map significant deviance from independence and neglect approximate independence or dependence weaker than a noise threshold. This intuition is applied to learning the structure of Bayes nets from data. We determine the conditional posterior probabilities of structures given that the degree of dependence at each of their nodes exceeds a critical noise level. Deviance from independence is measured by mutual information. Arc probabilities are determined by the amount of mutual information the neighbors contribute to a node, is greater than a critical minimum deviance from independence. A Ø 2 approximation for the probability density function of mutual info...
Statistical problems involving permutations with restricted positions
 IMS Lecture Notes Monogr. Ser
, 1999
"... The rich world of permutation tests can be supplemented by a variety of applications where only some permutations are permitted. We consider two examples: testing independence with truncated data and testing extrasensory perception with feedback. We review relevant literature on permanents, rook po ..."
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Cited by 14 (2 self)
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The rich world of permutation tests can be supplemented by a variety of applications where only some permutations are permitted. We consider two examples: testing independence with truncated data and testing extrasensory perception with feedback. We review relevant literature on permanents, rook polynomials and complexity. The statistical applications call for new limit theorems. We prove a few of these and o er an approach to the rest via Stein's method. Tools from the proof of van der Waerden's permanent conjecture are applied to prove a natural monotonicity conjecture. 1
On the Properties of Sequences of Reversals that Sort a Signed Permutation
 JOBIM
, 2002
"... The sorting by reversals problem is classical in the field of whole genome comparison. In this paper, we provide experimental and theoretical evidence showing that, typically, there is a huge number of optimal sequences of reversals that sort a given signed permutation. We study these sets of optima ..."
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Cited by 12 (3 self)
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The sorting by reversals problem is classical in the field of whole genome comparison. In this paper, we provide experimental and theoretical evidence showing that, typically, there is a huge number of optimal sequences of reversals that sort a given signed permutation. We study these sets of optimal sequences using secondary sorting constraints, and using theoretical tools developed in the context of trace monoids. We show that most sorting strategies work well with random permutations, and identify combinatorial parameters, such as stack height, that can be used to classify sequences of reversals, and permutations.
Evolution on distributive lattices
 J Theor Biol
"... Abstract. We consider the directed evolution of a population after an intervention that has significantly altered the underlying fitness landscape. We model the space of genotypes as a distributive lattice; the fitness landscape is a realvalued function on that lattice. The risk of escape from inte ..."
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Cited by 10 (5 self)
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Abstract. We consider the directed evolution of a population after an intervention that has significantly altered the underlying fitness landscape. We model the space of genotypes as a distributive lattice; the fitness landscape is a realvalued function on that lattice. The risk of escape from intervention, i.e., the probability that the population develops an escape mutant before extinction, is encoded in the risk polynomial. Tools from algebraic combinatorics are applied to compute the risk polynomial in terms of the fitness landscape. In an application to the development of drug resistance in HIV, we study the risk of viral escape from treatment with the protease inhibitors ritonavir and indinavir.
An Efficient Proactive Reactive Scheduling Approach to Hedge against Shop Floor Disturbances
 In Proceedings of the 1 st Multidisciplinary International Conference on Scheduling: Theory and Applications, MISTA 2003
"... We consider the single machine scheduling problem with dynamic job arrival and total weighted tardiness and makespan as objective functions. The machine is subject to disruptions related to late raw material arrival and machine breakdowns. We propose a proactivereactive approach to deal with possib ..."
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Cited by 10 (0 self)
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We consider the single machine scheduling problem with dynamic job arrival and total weighted tardiness and makespan as objective functions. The machine is subject to disruptions related to late raw material arrival and machine breakdowns. We propose a proactivereactive approach to deal with possible perturbations. In the proactive phase, instead of providing only one schedule to the decision maker, we present a set of predictive schedules. This set is characterized by a partial order of jobs and a type of associated schedules, here semiactive schedules. This allows to dispose of some flexibility in job sequencing and flexibility in time that can be used online by the reactive algorithm to hedge against unforeseen disruptions. We conduct computational experiments which prove that our approach outperforms a predictive reactive approach particularly for disruptions with low to medium amplitude.