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2,623
A Unified Framework for Hybrid Control: Model and Optimal Control Theory
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 1998
"... Complex natural and engineered systems typically possess a hierarchical structure, characterized by continuousvariable dynamics at the lowest level and logical decisionmaking at the highest. Virtually all control systems todayfrom flight control to the factory floorperform computercoded chec ..."
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Cited by 183 (8 self)
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Complex natural and engineered systems typically possess a hierarchical structure, characterized by continuousvariable dynamics at the lowest level and logical decisionmaking at the highest. Virtually all control systems todayfrom flight control to the factory floorperform computercoded checks and issue logical as well as continuousvariable control commands. The interaction of these different types of dynamics and information leads to a challenging set of "hybrid" control problems. We propose a very general framework that systematizes the notion of a hybrid system, combining differential equations and automata, governed by a hybrid controller that issues continuousvariable commands and makes logical decisions. We first identify the phenomena that arise in realworld hybrid systems. Then, we introduce a mathematical model of hybrid systems as interacting collections of dynamical systems, evolving on continuousvariable state spaces and subject to continuous controls and discrete transitions. The model captures the identified phenomena, subsumes previous models, yet retains enough structure on which to pose and solve meaningful control problems. We develop a theory for synthesizing hybrid controllers for hybrid plants in an optimal control framework. In particular, we demonstrate the existence of optimal (relaxed) and nearoptimal (precise) controls and derive "generalized quasivariational inequalities" that the associated value function satisfies. We summarize algorithms for solving these inequalities based on a generalized Bellman equation, impulse control, and linear programming.
A Probabilistic Relational Algebra for the Integration of Information Retrieval and Database Systems
 ACM Transactions on Information Systems
, 1994
"... We present a probabilistic relational algebra (PRA) which is a generalization of standard relational algebra. Here tuples are assigned probabilistic weights giving the probability that a tuple belongs to a relation. Based on intensional semantics, the tuple weights of the result of a PRA expression ..."
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Cited by 173 (30 self)
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We present a probabilistic relational algebra (PRA) which is a generalization of standard relational algebra. Here tuples are assigned probabilistic weights giving the probability that a tuple belongs to a relation. Based on intensional semantics, the tuple weights of the result of a PRA expression always confirm to the underlying probabilistic model. We also show for which expressions extensional semantics yields the same results. Furthermore, we discuss complexity issues and indicate possibilities for optimization. With regard to databases, the approach allows for representing imprecise attribute values, whereas for information retrieval, probabilistic document indexing and probabilistic search term weighting can be modelled. As an important extension, we introduce the concept of vague predicates which yields a probabilistic weight instead of a Boolean value, thus allowing for queries with vague selection conditions. So PRA implements uncertainty and vagueness in combination with the...
A multifractal wavelet model with application to TCP network traffic
 IEEE TRANS. INFORM. THEORY
, 1999
"... In this paper, we develop a new multiscale modeling framework for characterizing positivevalued data with longrangedependent correlations (1=f noise). Using the Haar wavelet transform and a special multiplicative structure on the wavelet and scaling coefficients to ensure positive results, the mo ..."
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Cited by 171 (30 self)
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In this paper, we develop a new multiscale modeling framework for characterizing positivevalued data with longrangedependent correlations (1=f noise). Using the Haar wavelet transform and a special multiplicative structure on the wavelet and scaling coefficients to ensure positive results, the model provides a rapid O(N) cascade algorithm for synthesizing Npoint data sets. We study both the secondorder and multifractal properties of the model, the latter after a tutorial overview of multifractal analysis. We derive a scheme for matching the model to real data observations and, to demonstrate its effectiveness, apply the model to network traffic synthesis. The flexibility and accuracy of the model and fitting procedure result in a close fit to the real data statistics (variancetime plots and moment scaling) and queuing behavior. Although for illustrative purposes we focus on applications in network traffic modeling, the multifractal wavelet model could be useful in a number of other areas involving positive data, including image processing, finance, and geophysics.
Hidden Markov processes
 IEEE Trans. Inform. Theory
, 2002
"... Abstract—An overview of statistical and informationtheoretic aspects of hidden Markov processes (HMPs) is presented. An HMP is a discretetime finitestate homogeneous Markov chain observed through a discretetime memoryless invariant channel. In recent years, the work of Baum and Petrie on finite ..."
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Cited by 170 (3 self)
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Abstract—An overview of statistical and informationtheoretic aspects of hidden Markov processes (HMPs) is presented. An HMP is a discretetime finitestate homogeneous Markov chain observed through a discretetime memoryless invariant channel. In recent years, the work of Baum and Petrie on finitestate finitealphabet HMPs was expanded to HMPs with finite as well as continuous state spaces and a general alphabet. In particular, statistical properties and ergodic theorems for relative entropy densities of HMPs were developed. Consistency and asymptotic normality of the maximumlikelihood (ML) parameter estimator were proved under some mild conditions. Similar results were established for switching autoregressive processes. These processes generalize HMPs. New algorithms were developed for estimating the state, parameter, and order of an HMP, for universal coding and classification of HMPs, and for universal decoding of hidden Markov channels. These and other related topics are reviewed in this paper. Index Terms—Baum–Petrie algorithm, entropy ergodic theorems, finitestate channels, hidden Markov models, identifiability, Kalman filter, maximumlikelihood (ML) estimation, order estimation, recursive parameter estimation, switching autoregressive processes, Ziv inequality. I.
The positive false discovery rate: A Bayesian interpretation and the qvalue
 Annals of Statistics
, 2003
"... Multiple hypothesis testing is concerned with controlling the rate of false positives when testing several hypotheses simultaneously. One multiple hypothesis testing error measure is the false discovery rate (FDR), which is loosely defined to be the expected proportion of false positives among all s ..."
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Cited by 158 (3 self)
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Multiple hypothesis testing is concerned with controlling the rate of false positives when testing several hypotheses simultaneously. One multiple hypothesis testing error measure is the false discovery rate (FDR), which is loosely defined to be the expected proportion of false positives among all significant hypotheses. The FDR is especially appropriate for exploratory analyses in which one is interested in finding several significant results among many tests. In this work, we introduce a modified version of the FDR called the “positive false discovery rate ” (pFDR). We discuss the advantages and disadvantages of the pFDR and investigate its statistical properties. When assuming the test statistics follow a mixture distribution, we show that the pFDR can be written as a Bayesian posterior probability and can be connected to classification theory. These properties remain asymptotically true under fairly general conditions, even under certain forms of dependence. Also, a new quantity called the “qvalue ” is introduced and investigated, which is a natural “Bayesian posterior pvalue, ” or rather the pFDR analogue of the pvalue.
Inference in Linear Time Series Models with Some Unit Roots," Econometrica
, 1990
"... This paper considers estimation and hypothesis testing in linear time series models when some or all of the variables have unit roots. Our motivating example is a vector autoregression with some unit roots in the companion matrix, which might include polynomials in time as regressors. In the general ..."
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Cited by 158 (6 self)
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This paper considers estimation and hypothesis testing in linear time series models when some or all of the variables have unit roots. Our motivating example is a vector autoregression with some unit roots in the companion matrix, which might include polynomials in time as regressors. In the general formulation, the variable might be integrated or cointegrated of arbitrary orders, and might have drifts as well. We show that parameters that can be written as coefficients on mean zero, nonintegrated regressors have jointly normal asymptotic distributions, converging at the rate T'/2. In general, the other coefficients (including the coefficients on polynomials in time) will have nonnormal asymptotic distributions. The results provide a formal characterization of which t or F testssuch as Granger causality testswill be asymptotically valid, and which will have nonstandard limiting distributions.
Ripple Joins for Online Aggregation
"... We present a new family of join algorithms, called ripple joins, for online processing of multitable aggregation queries in a relational database management system (dbms). Such queries arise naturally in interactive exploratory decisionsupport applications. Traditional offline join algorithms are ..."
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Cited by 157 (11 self)
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We present a new family of join algorithms, called ripple joins, for online processing of multitable aggregation queries in a relational database management system (dbms). Such queries arise naturally in interactive exploratory decisionsupport applications. Traditional offline join algorithms are designed to minimize the time to completion of the query. In contrast, ripple joins are designed to minimize the time until an acceptably precise estimate of the query result is available, as measured by the length of a confidence interval. Ripple joins are adaptive, adjusting their behavior during processing in accordance with the statistical properties of the data. Ripple joins also permit the user to dynamically trade off the two key performance factors of online aggregation: the time between successive updates of the running aggregate, and the amount by which the confidenceinterval length decreases at each update. We show how ripple joins can be implemented in an existing dbms using iterators, and we give an overview of the methods used to compute confidence intervals and to adaptively optimize the ripple join "aspectratio" parameters. In experiments with an initial implementation of our algorithms in the postgres dbms, the time required to produce reasonably precise online estimates was up to two orders of magnitude smaller than the time required for the best offline join algorithms to produce exact answers.
Models of Random Regular Graphs
 In Surveys in combinatorics
, 1999
"... In a previous paper we showed that a random 4regular graph asymptotically almost surely (a.a.s.) has chromatic number 3. Here we extend the method to show that a random 6regular graph asymptotically almost surely (a.a.s.) has chromatic number 4 and that the chromatic number of a random dregular g ..."
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Cited by 157 (33 self)
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In a previous paper we showed that a random 4regular graph asymptotically almost surely (a.a.s.) has chromatic number 3. Here we extend the method to show that a random 6regular graph asymptotically almost surely (a.a.s.) has chromatic number 4 and that the chromatic number of a random dregular graph for other d between 5 and 10 inclusive is a.a.s. restricted to a range of two integer values: {3, 4} for d = 5, {4, 5} for d = 7, 8, 9, and {5, 6} for d = 10. The proof uses efficient algorithms which a.a.s. colour these random graphs using the number of colours specified by the upper bound. These algorithms are analysed using the differential equation method, including an analysis of certain systems of differential equations with discontinuous right hand sides. 1
Mixed MNL Models for Discrete Response
 JOURNAL OF APPLIED ECONOMETRICS
, 2000
"... This paper considers mixed, or random coefficients, multinomial logit (MMNL) models for discrete response, and establishes the following results: Under mild regularity conditions, any discrete choice model derived from random utility maximization has choice probabilities that can be approximated as ..."
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Cited by 157 (10 self)
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This paper considers mixed, or random coefficients, multinomial logit (MMNL) models for discrete response, and establishes the following results: Under mild regularity conditions, any discrete choice model derived from random utility maximization has choice probabilities that can be approximated as closely as one pleases by a MMNLmodel. Practical estimation of a parametric mixing family can be carried out by Maximum Simulated Likelihood Estimation or Method of Simulated Moments, and easily computed instruments are provided that make the latter procedure fairly efficient. The adequacy of a mixing specification can be tested simply as an omitted variable test with appropriately defined artificial variables. An application to a problem of demand for alternative vehicles shows that MMNL provides a flexible and computationally practical approach to discrete response analysis.