A class of collinear scaling algorithms for bound-constrained optimization: Convergence theorems

A family of algorithms for approximate solution of the bound-constrained minimization problem was introduced in [K.A. Ariyawansa, W.L. Tabor, A class of collinear scaling algorithms for bound-constrained optimization: Derivation and computational results, Technical Report 2003-1, Department of Mathematics, Washington State University, Pullman, WA, 2003, submitted for publication. Available at http://www.math.wsu.edu/math/TRS/2003-1.pdf]. These algorithms employ the standard barrier method, with the inner iteration based on trust region methods. Local models are conic functions rather than the usual quadratic functions, and are required to match first and second derivatives of the barrier function at the current iterate. The various members of the family are distinguished by the choice of a vector-valued parameter, which is the zero vector in the degenerate case that quadratic local models are used. This paper presents a convergence analysis of the family of algorithms presented in [K.A. Ariyawansa, W.L. Tabor, A class of collinear scaling algorithms for bound-constrained optimization: Derivation and computational results, Technical Report 2003-1, Department of Mathematics, Washington State University, Pullman, WA, 2003, submitted for publication. Available at http://www.math.wsu.edu/math/TRS/2003-1.pdf]. Specifically, convergence properties similar to those of barrier methods using quadratic local models are established.     

Scan Statistics on Enron Graphs

We introduce a theory of scan statistics on graphs and apply the ideas to the problem of anomaly detection in a time series of Enron email graphs. Previous presentation: Workshop on Link Analysis, Counterterrorism and Security at the SIAM International Conference on Data Mining, Newport Beach, CA, April 23, 2005. Carey E. Priebe received the B.S. degree in mathematics from Purdue University in 1984, the M.S. degree in computer science from San Diego State University in 1988, and the Ph.D. degree in information technology (computational statistics) from George Mason University in 1993. From 1985 to 1994 he worked as a mathematician and scientist in the US Navy research and development laboratory system. Since 1994 he has been a professor in the Department of Applied Mathematics and Statistics, Whiting School of Engineering, Johns Hopkins University, Baltimore, Maryland. At Johns Hopkins, he holds joint appointments in the Department of Computer Science and the Center for Imaging Science. He is a past President of the Interface Foundation of North America—Computing Science & Statistics, a past Chair of the Section on Statistical Computing of the American Statistical Association, and on the editorial boards of Journal of Computational and Graphical Statistics, Computational Statistics and Data Analysis, and Computational Statistics. His research interests are in computational statistics, kernel and mixture estimates, statistical pattern recognition, statistical image analysis, and statistical inference for high-dimensional and graph data. He was elected Fellow of the American Statistical Association in 2002. John M. Conroy received a B.S. in Mathematics from Saint Joseph's University in 1980 and a Ph.D. in Applied Mathematics from the University of Maryland in 1986. Since then he has been a research staff member for the IDA Center for Computing Sciences in Bowie, MD. His research interest is applications of numerical linear algebra. He is a member of the Society for Industrial and Applied Mathematics, Institute of Electrical and Electronics Engineers (IEEE), and the Association for Computational Linguistics. David J. Marchette received a B.A. in 1980, and an M.A. in mathematics in 1982, from the University of California at San Diego. He received a Ph.D. in Computational Sciences and Informatics in 1996 from George Mason University under the direction of Ed Wegman. From 1985–1994 he worked at the Naval Ocean Systems Center in San Diego doing research on pattern recognition and computational statistics. In 1994 he moved to the Naval Surface Warfare Center in Dahlgren Virginia where he does research in computational statistics and pattern recognition, primarily applied to image processing, text processing, automatic target recognition and computer security. Dr. Marchette is a Fellow of the American Statistical Society. Youngser Park received the B.E. degree in electrical engineering from Inha University in Korea in 1985, the M.S. degree in computer science from The George Washington University in 1991, and had pursued a doctoral degree there. From 1998 to 2000 he worked at the Johns Hopkins Medical Institutes as a senior research engineer. Since 2003 he is working as a research analyst in the Center for Imaging Science at the Johns Hopkins University. His research interests are clustering algorithm, pattern classification, and data mining.     

Discussion of “Birnbaum‐Saunders distribution: A review of models,analysis and applications”

This paper provides the distribution of order statistics from a multivariate Birnbaum‐Saunders (GMBS) distribution which can be used in the reliability and lifetime analyses. Proposing a new generalization of Birnbaum‐Saunders distribution based on the unified skew‐elliptical model, some properties of the order statistics are also studied.     

An interview with Laurens de Haan

Laurens de Haan was born January 15, 1937 in Rotterdam, The Netherlands. He graduated 1966 in mathematics and received a doctoral degree in 1970 from the University of Amsterdam, while working at the Mathematical center CWI in Amsterdam. Since 1973 he was Professor for probability and mathematical statistics at the Econometric Institute of the Economic Faculty at the Erasmus University Rotterdam, where he retired 1998. Since 2008 he is part-time professor at the Department of Econometrics and Operations Research of Tilburg University. Laurens de Haan has been active in research throughout his career. He has published more than 110 scientific papers. Among other distinctions, he was elected IMS fellow for his seminal contributions to extreme value theory in 1977, and he was appointed Honorary Doctor of the University of Lisbon in 2000.     

Efficient algorithms for wavelength assignment on trees of rings

A fundamental problem in communication networks is wavelength assignment (WA): given a set of routing paths on a network, assign a wavelength to each path such that the paths with the same wavelength are edge-disjoint, using the minimum number of wavelengths. The WA problem is NP-hard for a tree of rings network which is well used in practice. In this paper, we give an efficient algorithm which solves the WA problem on a tree of rings with an arbitrary (node) degree using at most 3L wavelengths and achieves an approximation ratio of 2.75 asymptotically, where L is the maximum number of paths on any link in the network. The 3L upper bound is tight since there are instances of the WA problem that require 3L wavelengths even on a tree of rings with degree four. We also give a 3L and 2-approximation (resp. 2.5-approximation) algorithm for the WA problem on a tree of rings with degree at most six (resp. eight). Previous results include: 4L (resp. 3L) wavelengths for trees of rings with arbitrary degrees (resp. degree at most eight), and 2-approximation (resp. 2.5-approximation) algorithm for trees of rings with degree four (resp. six).     

Bivariate Birnbaum–Saunders distribution and associated inference

Univariate Birnbaum–Saunders distribution has been used quite effectively to model positively skewed data, especially lifetime data and crack growth data. In this paper, we introduce bivariate Birnbaum–Saunders distribution which is an absolutely continuous distribution whose marginals are univariate Birnbaum–Saunders distributions. Different properties of this bivariate Birnbaum–Saunders distribution are then discussed. This new family has five unknown parameters and it is shown that the maximum likelihood estimators can be obtained by solving two non-linear equations. We also propose simple modified moment estimators for the unknown parameters which are explicit and can therefore be used effectively as an initial guess for the computation of the maximum likelihood estimators. We then present the asymptotic distributions of the maximum likelihood estimators and use them to construct confidence intervals for the parameters. We also discuss likelihood ratio tests for some hypotheses of interest. Monte Carlo simulations are then carried out to examine the performance of the proposed estimators. Finally, a numerical data analysis is performed in order to illustrate all the methods of inference discussed here.     

Regular points for Lagrange interpolation on the unit disk

A set of points on the unit disk of the Euclidean plane is given, which admits unique Lagrange interpolation. The points have rotational symmetry and they form an example of natural lattices of Chung and Yao [2]. Properties of Lagrange interpolation with respect to these points are studied.Work done when visiting the University of Oregon at Eugene, Oregon.Supported by National Science Foundation under Grant No. 9302721.     

Pure Point Diffractive Substitution Delone Sets Have the Meyer Property

We prove that a primitive substitution Delone set, which is pure point diffractive, is a Meyer set. This answers a question of J.C. Lagarias. We also show that for primitive substitution Delone sets, being a Meyer set is equivalent to having a relatively dense set of Bragg peaks. The proof is based on tiling dynamical systems and the connection between the diffraction and dynamical spectra. The first author acknowledges support from the NSERC post-doctoral fellowship and thanks the University of Washington and the University of Victoria for being the host universities of the fellowship. The second author is grateful to the Weizmann Institute of Science where he was a Rosi and Max Varon Visiting Professor when this work was completed. He was also supported in part by NSF Grant DMS 0355187.     

Time series with Birnbaum‐Saunders marginal distributions

A stationary sequence of random variables with Birnbaum‐Saunders marginal distribution is constructed using a Gaussian autoregressive moving average sequence. The parameters of the model are then estimated by the maximum likelihood method, and the resulting estimators are shown to be consistent and asymptotically normal. A simulation study is carried out to assess the performance of the estimators. The proposed model is finally used to analyze 2 real data sets.     

Book Reviews

Book reviewed in this article: The Chemistry of the Non -Metals : by Jolly, William L., Professor of Chemistry, University of California, Berkeley. Ask Me a Question About the Weather , Ask Me a Question About the Earth , Ask Me a Question Alout the Heavens , Sam Rosenfeld.     

Graph Theoretic and Spectral Analysis of Enron Email Data

Analysis of social networks to identify communities and model their evolution has been an active area of recent research. This paper analyzes the Enron email data set to discover structures within the organization. The analysis is based on constructing an email graph and studying its properties with both graph theoretical and spectral analysis techniques. The graph theoretical analysis includes the computation of several graph metrics such as degree distribution, average distance ratio, clustering coefficient and compactness over the email graph. The spectral analysis shows that the email adjacency matrix has a rank-2 approximation. It is shown that preprocessing of data has significant impact on the results, thus a standard form is needed for establishing a benchmark data. Anurat Chapanond is currently a Ph.D. student in Computer Science, RPI. Anurat graduated B. Eng. degree in Computer Engineering from Chiangmai University (Thailand) in 1997, M. S. in Computer Science from Columbia University in 2002. His research interest is in web data mining analyses and algorithms. M.S. Krishnamoorthy received the B.E. degree (with honors) from Madras University in 1969, the M. Tech degree in Electrical Engineering from the Indian Institute of Technology, Kanpur, in 1971, and the Ph. D. degree in Computer Science, also from the Indian Institute of Technology, in 1976. From 1976 to 1979, he was an Assistant Professor of Computer Science at the Indian Institute of Technology, Kanpur. From 1979 to 1985, he was an Assistant Professor of Computer Science at Rensselaer Polytechnic Institute, Troy, NY, and since, 1985, he has been an Associate Professor of Computer Science at Rensselaer. Dr. Krishnamoorthy's research interests are in the design and analysis of combinatorial and algebraic algorithms, visualization algorithms and programming environments. Bulent Yener is an Associate Professor in the Department of Computer Science and Co-Director of Pervasive Computing and Networking Center at Rensselaer Polytechnic Institute in Troy, New York. He is also a member of Griffiss Institute of Information Assurance. Dr. Yener received MS. and Ph.D. degrees in Computer Science, both from Columbia University, in 1987 and 1994, respectively. Before joining to RPI, he was a Member of Technical Staff at the Bell Laboratories in Murray Hill, New Jersey. His current research interests include bioinformatics, medical informtatics, routing problems in wireless networks, security and information assurance, intelligence and security informatics. He has served on the Technical Program Committee of leading IEEE conferences and workshops. Currently He is an associate editor of ACM/Kluwer Winet journal and the IEEE Network Magazine. Dr. Yener is a Senior Member of the IEEE Computer Society.     

Kenneth O. May, 1915–1977 : His early life to 1946

Kenneth Ownsworth May graduated from the University of California at Berkeley in 1936 with highest honors in mathematics. The following year he received his Masters degree and became a fellow of the Institute of Current World Affairs, and during the next two years he traveled to England, Europe, and Russia. On his return to the United States he became active in the Communist Party, the consequences of which would plague him for years. He joined the United States Army in 1942, serving with distinction, and after the war returned to Berkeley, where he obtained his Ph.D. in 1946. He immediately accepted an assistant professorship at Carleton College in Northfield, Minnesota, later moving to the University of Toronto.This part of May's biography focuses on the events up to his accepting a position at Carleton College. In this early phase his openness, his emphasis on good communications in the process of education, and his interest in practical procedures emerge which later set the background for his successful career as a leading historian of mathematics and the founding editor of Historia Mathematica.     

Norm convergence of random walks on compact hypergroups

Research supported in part by the Office of Research and Sponsored Programs, University of Oregon     

A note on the fundamental theorem of algebra for the octonions

This paper is a revision of a portion of the author's doctoral dissertation submitted to the University of Oregon. Using elementary concepts of K$K$-theory, the Brouwer degree of the power map in the octonions is computed. Later, a proof of a weaker version of the fundamental theorem of algebra for polynomials with coefficients in the octonions is given. As a partial complement, a lower bound to the number of solutions of a homogeneous monomial equation over the octonions is obtained.     

Smoothly truncated stable distributions,GARCH-models,and option pricing

Although asset return distributions are known to be conditionally leptokurtic, this fact has rarely been addressed in the recent GARCH model literature. For this reason, we introduce the class of smoothly truncated stable distributions (STS distributions) and derive a generalized GARCH option pricing framework based on non-Gaussian innovations. Our empirical results show that (1) the model’s performance in the objective as well as the risk-neutral world is substantially improved by allowing for non-Gaussian innovations and (2) the model’s best option pricing performance is achieved with a new estimation approach where all model parameters are obtained from time-series information whereas the market price of risk and the spot variance are inverted from market prices of options. The paper subsumes a previous one under the title “A New Class of Probability Distributions and Its Application to Finance”. The authors gratefully acknowledge comments made by seminar participants at University of California, Santa Barbara, University of Washington, Seattle, Hochschule für Banken, Frankfurt, Cornell University, Princeton University, American University, Washington DC, and the Risk Management and Financial Engineering Conference held in Gainesville, FL in April 2005. All views and opinions expressed in this article are strictly those of the author and do not necessarily represent the views of Sal. Oppenheim.     

TIMBER MARKETS AND FUEL TREATMENTS IN THE WESTERN U.S.

ABSTRACT. We developed a model of interrelated timber markets in the U.S. West to assess the impacts of large‐scale fuel reduction programs on these markets, and concomitant effects ofthe market on the fuel reduction programs. The linear programming spatial equilibrium model allows interstate and international trade with western Canada and the rest of the world, while accounting for price effects of introducing softwood logs to the market. The model maximizes area treated, given fire regime‐condition class priorities, maximum increases in softwood processing capacity, maximum rates of annual treatments, prohibitions on exports of U.S. and Canadian softwood logs from public lands and a fixed annual treatment budget. Results show that the loss to U.S. private timber producers is less than the gains for timber consumers (mills). States receiving more treatments when spending is not constrained by state proportions include Idaho, Montana, New Mexico and Oregon. When only the wildland‐urban interface is treated, California, Oregon and Washington receive more treatments. Utah and Colorado receive more treatments when low risk stands are included.     

Minimal universal covers inE n

It is shown that any plane set of constant unit width contains a semi-circle of radius 1/2, and using this a minimal univeral plane cover is explicitly constructed. It is also shown that in an n-dimensional space with n>2 there are minimal universal covers of arbitrary large diameter. This paper was written while the author was a National Science Foundation Visiting Senior Fellow at the University of Washington, Seattle, Washington, U.S.A.     

Birnbaum‐Saunders autoregressive conditional range model applied to stock index data

This article proposes a new approach to the conditional autoregressive range (CARR) model using the Birnbaum‐Saunders (BS) distribution. The model aims to develop volatility clustering, which incorporates extreme fluctuations, using a time‐varying evolution of the range process called the BSCARR model. Furthermore, diagnosis analysis tools for diagnosis analysis were developed to evaluate the goodness of fit, such as residual analysis, global influence measures based on Cook's distance, and local influence analysis. For illustrative purposes, three real financial market indices are analyzed. A comparison with classical CARR models was also carried out in these examples. The results indicated that the proposed model outperformed some existing models in the literature, especially a recent CARR model based on the gamma distribution even under the presence of atypical cases (observed values).     

Book Vignettes

Darlington, C. D. and Bradshaw, A. D. (eds.), Teaching Genetics in School and University. Trelease, Sam F., How to Write Scientific and Technical Papers. Mellersh, H. E. L., Charles Darwin: Pioneer in the Theory of Evolution. Rosenfeld, Sam, Science Experiments With Air. Sciama, D. W., The Physical Foundations of General Relativity. Graham, L. A., The Surprise Attack in Mathematical Problems. Frey, Paul R., Chemistry Problems and How to Solve Them: Seventh Edition.