Author
Arthur E. Frazho
Other affiliations: Georgia Institute of Technology, Tel Aviv University, Indiana University
Bio: Arthur E. Frazho is an academic researcher from Purdue University. The author has contributed to research in topics: Commutant lifting theorem & Interpolation. The author has an hindex of 16, co-authored 101 publications receiving 1964 citations. Previous affiliations of Arthur E. Frazho include Georgia Institute of Technology & Tel Aviv University.
Papers published on a yearly basis
Papers
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01 Jan 1990
TL;DR: Inverse Scattering Algorithms for the Commutant Lifting Theorem as discussed by the authors have been proposed to solve the Caratheodory Interpolation Problem for Positive-Real Functions.
Abstract: I. Analysis of the Caratheodory Interpolation Problem.- II. Analysis of the Caratheodory Interpolation Problem for Positive-Real Functions.- III. Schur Numbers, Geophysics and Inverse Scattering Problems.- IV. Contractive Expansions on Euclidian and Hilbert Space.- V. Contractive One Step Intertwining Liftings.- VI. Isometric and Unitary Dilations.- VII. The Commutant Lifting Theorem.- VIII. Geometric Applications of the Commutant lifting Theorem.- IX. H? Optimization and Functional Models.- X. Some Classical Interpolation Problems.- XI. Interpolation as a Momentum Problem.- XII. Numerical Algorithms for H? Optimization in Control Theory.- XIII. Inverse Scattering Algorithms for the Commutant Lifting Theorem.- XIV. The Schur Representation.- XV. A Geometric Approach to Positive Definite Sequences.- XVI. Positive Definite Block Matrices.- XVII. A Physical Basis for the Layered Medium Model.- References.- Notation.
581 citations
TL;DR: It is found that in the author co-citation network, citation rank is highly correlated with PageRank with different damping factors and also with different weighted PageRank algorithms; citation rank and PageRank are not significantly correlated with centrality measures; and h-index rank does not significantly correlate with centraly measures but does significantly correlates with other measures.
Abstract: This paper studies how varied damping factors in the PageRank algorithm influence the ranking of authors and proposes weighted PageRank algorithms. We selected the 108 most highly cited authors in the information retrieval (IR) area from the 1970s to 2008 to form the author co-citation network. We calculated the ranks of these 108 authors based on PageRank with the damping factor ranging from 0.05 to 0.95. In order to test the relationship between different measures, we compared PageRank and weighted PageRank results with the citation ranking, h-index, and centrality measures. We found that in our author co-citation network, citation rank is highly correlated with PageRank with different damping factors and also with different weighted PageRank algorithms; citation rank and PageRank are not significantly correlated with centrality measures; and h-index rank does not significantly correlate with centrality measures but does significantly correlate with other measures. The key factors that have impact on the PageRank of authors in the author co-citation network are being co-cited with important authors. © 2009 Wiley Periodicals, Inc.
301 citations
Posted Content•
TL;DR: It is found that in the author co-citation network, citation rank is highly correlated with PageRank's with different damping factors and also with different PageRank algorithms; citation rank and PageRank are not significantly correlation with centrality measures; and h-index is not significantly correlated withcentrality measures.
Abstract: Google's PageRank has created a new synergy to information retrieval for a better ranking of Web pages. It ranks documents depending on the topology of the graphs and the weights of the nodes. PageRank has significantly advanced the field of information retrieval and keeps Google ahead of competitors in the search engine market. It has been deployed in bibliometrics to evaluate research impact, yet few of these studies focus on the important impact of the damping factor (d) for ranking purposes. This paper studies how varied damping factors in the PageRank algorithm can provide additional insight into the ranking of authors in an author co-citation network. Furthermore, we propose weighted PageRank algorithms. We select 108 most highly cited authors in the information retrieval (IR) area from the 1970s to 2008 to form the author co-citation network. We calculate the ranks of these 108 authors based on PageRank with damping factor ranging from 0.05 to 0.95. In order to test the relationship between these different measures, we compare PageRank and weighted PageRank results with the citation ranking, h-index, and centrality measures. We found that in our author co-citation network, citation rank is highly correlated with PageRank's with different damping factors and also with different PageRank algorithms; citation rank and PageRank are not significantly correlated with centrality measures; and h-index is not significantly correlated with centrality measures.
255 citations
Book•
18 Feb 1998
TL;DR: In this paper, a general completion theorem is applied to interpolation parameterization of all solutions of the three-chains completion problem, and a nonstationary interpolation and time-varying system is presented.
Abstract: Part 1 Interpolation and time-invariant system: interpolation problems for time-valued functions proofs using the commutant lifting theorem time invariant systems central commutant lifting central state space solutions parametization of intertwinning and its applications applications to control systems. Part 2 Nonstationary interpolation and time-varying systems nonstationary interpolation theorems nonstationary systems and point evaluation reduction techniques - from nonstationary to stationary and vice versa proofs of the nonstationary interpolation theorems by reduction to the stationary case a general completion theorem applications of the three chains completion theorem to interpolation parameterization of all solutions of the three chains completion problem.
147 citations
TL;DR: In this article, a model theory for a pair of noncommuting operators using backward shift operators on a Fock space Rota's Theorem is generalized, i.e., it is shown that any two bounded operators on the Hilbert space are simultaneously similar to part of a backward shift operator on a fock space.
134 citations
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05 Oct 1997TL;DR: In this article, the authors introduce linear algebraic Riccati Equations and linear systems with Ha spaces and balance model reduction, and Ha Loop Shaping, and Controller Reduction.
Abstract: 1. Introduction. 2. Linear Algebra. 3. Linear Systems. 4. H2 and Ha Spaces. 5. Internal Stability. 6. Performance Specifications and Limitations. 7. Balanced Model Reduction. 8. Uncertainty and Robustness. 9. Linear Fractional Transformation. 10. m and m- Synthesis. 11. Controller Parameterization. 12. Algebraic Riccati Equations. 13. H2 Optimal Control. 14. Ha Control. 15. Controller Reduction. 16. Ha Loop Shaping. 17. Gap Metric and ...u- Gap Metric. 18. Miscellaneous Topics. Bibliography. Index.
3,471 citations
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TL;DR: In this paper, the authors studied the effect of local derivatives on the detection of intensity edges in images, where the local difference of intensities is computed for each pixel in the image.
Abstract: Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:
1,829 citations
TL;DR: This paper endeavor to present an overview of the bibliometric methodology, with a particular focus on its different techniques, while offering step-by-step guidelines that can be relied upon to rigorously perform bibliomet analysis with confidence.
1,756 citations
TL;DR: A thorough bibliometric and network analysis of the emergent field of green supply chain management provides insights not previously fully grasped or evaluated by other reviews on this topic.
1,166 citations
TL;DR: In this paper, the state-of-the-art algorithms for vital node identification in real networks are reviewed and compared, and extensive empirical analyses are provided to compare well-known methods on disparate real networks.
919 citations