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A Toolkit for Analyzing Nonlinear Dynamic Stochastic Models Easily
"... Often, researchers wish to analyze nonlinear dynamic discretetime stochastic models. This chapter provides a toolkit for solving such models easily, building on loglinearizing the necessary equations characterizing the equilibrium and solving for the recursive equilibrium law of motion with the me ..."
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Cited by 96 (1 self)
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Often, researchers wish to analyze nonlinear dynamic discretetime stochastic models. This chapter provides a toolkit for solving such models easily, building on loglinearizing the necessary equations characterizing the equilibrium and solving for the recursive equilibrium law of motion with the method of undetermined coefficients. This chapter contains nothing substantially new. Instead, the chapter simplifies and unifies existing approaches to make them accessible for a wide audience, showing how to loglinearizing the nonlinear equations without the need for explicit di erentiation, how to use the method of undetermined coefficients for models with a vector of endogenous state variables, to provide a general solution by characterizing the solution with a matrix quadratic equation and solving it, and to provide frequencydomain techniques to calculate the second order properties of the model in its HPfiltered version without resorting to simulations. Since the method is an Eulerequation based approach rather than an approach based on solving a social planners problem, models with externalities or distortionary taxation do not pose additional problems. MATLAB programs to carry out the calculations in this chapter are made available. This chapter should be useful for researchers and Ph.D. students alike.
Automatic Software Clustering via Latent Semantic Analysis
 in Proceedings 14th IEEE International Conference on Automated Software Engineering (ASE'99), Cocoa Beach Florida
, 1999
"... The paper describes the initial results of applying Latent Semantic Analysis (LSA) to program source code and associated documentation. Latent Semantic Analysis is a corpusbased statistical method for inducing and representing aspects of the meanings of words and passages (of natural language) refl ..."
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Cited by 23 (8 self)
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The paper describes the initial results of applying Latent Semantic Analysis (LSA) to program source code and associated documentation. Latent Semantic Analysis is a corpusbased statistical method for inducing and representing aspects of the meanings of words and passages (of natural language) reflective in their usage. This methodology is assessed for application to the domain of software components (i.e., source code and its accompanying documentation). The intent of applying Latent Semantic Analysis to software components is to automatically induce a specific semantic meaning of a given component. Here LSA is used as the basis to cluster software components. Results of applying this method to the LEDA library and MINIX operating system are given. Applying Latent Semantic Analysis to the domain of source code and internal documentation for the support of software reuse is a new application of this method and a departure from the normal application domain of natural language. 1.
A singularly valuable decomposition: The SVD of a matrix
 College Math Journal
, 1996
"... Every teacher of linear algebra should be familiar with the matrix singular value decomposition (or SVD). It has interesting and attractive algebraic properties, and conveys important geometrical and theoretical insights about linear transformations. The close connection between the SVD and the well ..."
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Cited by 14 (0 self)
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Every teacher of linear algebra should be familiar with the matrix singular value decomposition (or SVD). It has interesting and attractive algebraic properties, and conveys important geometrical and theoretical insights about linear transformations. The close connection between the SVD and the well known theory of diagonalization for symmetric matrices makes the topic immediately accessible to linear algebra teachers, and indeed, a natural extension of what these teachers already know. At the same time, the SVD has fundamental importance in several different applications of linear algebra. Strang was aware of these facts when he introduced the SVD in his now classical text [22, page 142], observing...it is not nearly as famous as it should be. Golub and Van Loan ascribe a central significance to the SVD in their definitive explication of numerical matrix methods [8, page xiv] stating...perhaps the most recurring theme in the book is the practical and theoretical value of [the SVD]. Additional evidence of the significance of the SVD is its central role in a number of papers in recent years in Mathematics Magazine and The American Mathematical Monthly (for example [2, 3, 17, 23]). Although it is probably not feasible to include the SVD in the first linear algebra course, it definitely deserves a place in more advanced undergraduate courses, particularly those with a numerical or applied emphasis. My primary goals in this article are to bring the topic to the attention of a broad audience,
Privacy Preserving Link Analysis on Dynamic Weighted Graph
 Computational & Mathematical Organization Theory
, 2005
"... Abstract. Link analysis algorithms have been used successfully on hyperlinked data to identify authoritative documents and retrieve other information. They also showed great potential in many new areas such as counterterrorism and surveillance. Emergence of new applications and changes in existing o ..."
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Cited by 4 (0 self)
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Abstract. Link analysis algorithms have been used successfully on hyperlinked data to identify authoritative documents and retrieve other information. They also showed great potential in many new areas such as counterterrorism and surveillance. Emergence of new applications and changes in existing ones created new opportunities, as well as difficulties, for them: (1) In many situations where link analysis is applicable, there may not be an explicit hyperlinked structure. (2) The system can be highly dynamic, resulting in constant update to the graph. It is often too expensive to rerun the algorithm for each update. (3) The application often relies heavily on client side logging and the information encoded in the graph can be very personal and sensitive. In this case privacy becomes a major concern. Existing link analysis algorithms, and their traditional implementations, are not adequate in face of these new challenges. In this paper we propose the use of weighted graph to define and/or augment a link structure. We present a generalized HITS algorithm that is suitable for running in a dynamic environment. The algorithm uses the idea of “lazy update ” to amortize cost across multiple updates while still providing accurate ranking to users in the mean time. We prove the convergence of the new algorithm and evaluate its benefit using the Enron email dataset. Finally we devise a distributed implementation of the algorithm that preserves user privacy thus making it socially acceptable in realworld applications. 1
Grounding Collaborative Knowledge Building in SemanticsBased Critiquing
 In Proceedings of the Advances in WebBased Learning (Hong Kong
, 2005
"... Abstract. In this paper we investigate the use of Latent Semantic Analysis (LSA), Critiquing Systems, and Knowledge Building to support computerbased teaching of English composition. We have built and tested an English Composition Critiquing System that make use of LSA to analyze student essays and ..."
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Abstract. In this paper we investigate the use of Latent Semantic Analysis (LSA), Critiquing Systems, and Knowledge Building to support computerbased teaching of English composition. We have built and tested an English Composition Critiquing System that make use of LSA to analyze student essays and compute feedback by comparing their essays with teacher’s model essays. LSA values are input to a critiquing component to provide a user interface for the students. A software agent can also use the critic feedback to coordinate a collaborative knowledge building session with multiple users (students and teachers). Shared feedback provides seed questions that can trigger discussion and extended reflection about the next phase of writing. We present the first version of a prototype we have built, and report the results from an informal experiment. We end the paper by describing our plans for future work. 1
Differential Privacy for Sum Queries without External Noise
"... We consider privacy issues in statistical database and data mining where queries are executed on data collected from a large number of individuals. It is generally established that a strong notion of privacy is guaranteed if the results are perturbed by random noise with sufficient variance (e.g., [ ..."
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Cited by 1 (0 self)
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We consider privacy issues in statistical database and data mining where queries are executed on data collected from a large number of individuals. It is generally established that a strong notion of privacy is guaranteed if the results are perturbed by random noise with sufficient variance (e.g., [5, 27, 44]). In this paper, we point out a vulnerability in such an approach and show that for some types of queries, when the dataset is sufficiently large, the inherent uncertainty associated with unknown quantities is enough to provide similar perturbation and the same privacy can be obtained without external noise. One type of such queries is sum queries which aggregate across all records. This is a surprisingly general primitive supporting various data mining algorithms, including many nonlinear ones such as SVD, PCA, kmeans, ID3, SVM, EM, and all the algorithms in the statistical query model. We derive privacy conditions for sum queries and, for the first time, provide mathematical proof for the intuition that aggregates across a large number of individuals is private using a widely accepted notion of privacy. Our results are also relevant in query auditing and we show how they can be used to construct simulatable query auditing algorithms that handle online and offline auditing in a uniform way with stronger privacy than ever achieved before.
ii
, 2001
"... declare that the work submitted in this thesis is my own, except as acknowledged in the text and footnotes, and has not been previously submitted for a degree at the University of Queensland or any other institution. Yours faithfully ..."
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declare that the work submitted in this thesis is my own, except as acknowledged in the text and footnotes, and has not been previously submitted for a degree at the University of Queensland or any other institution. Yours faithfully
Impulse Response Sequences and Construction of Number Sequence Identities
"... In this paper, we investigate impulse response sequences over the integers by presenting their generating functions and expressions. We also establish some of the corresponding identities. In addition, we give the relationship between an impulse response sequence and all linear recurring sequences s ..."
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In this paper, we investigate impulse response sequences over the integers by presenting their generating functions and expressions. We also establish some of the corresponding identities. In addition, we give the relationship between an impulse response sequence and all linear recurring sequences satisfying the same linear recurrence relation, which can be used to transfer the identities among different sequences. Finally, we discuss some applications of impulse response sequences to the structure of Stirling numbers of the second kind, the Wythoff array, and the Boustrophedon transform. 1