Kenneth Steiglitz

Bio: Kenneth Steiglitz is an academic researcher from Princeton University. The author has contributed to research in topics: Signal processing & Very-large-scale integration. The author has an hindex of 46, co-authored 202 publications receiving 14495 citations. Previous affiliations of Kenneth Steiglitz include Telcordia Technologies & Northwestern University.

Design of FIR digital phase networks

Abstract: The problem of the minimax design of FIR digital filters with prescribed phase characteristics and unit magnitude is a nonlinear optimization problem. In this paper it is approximated by a linear programming problem which is optimal to first order. That is, if δ 0 and e 0 are optimal deviations of magnitude and phase characteristics, then the actual deviations obtained from the linear program solution satisfy \delta \leq \delta_{0} + emin{0}\max{2} and eleq e_{0}(1+\delta_{0})/(1-\delta_{0}) . Design results are given for full-band M-term chirp filters, which (like linear phase filters) can be implemented with (M+1)/2 multiplications per point.

Sufficient Conditions on Pole and Zero Locations for Rational Positive-Real Functions

Abstract: The problem of finding sufficient conditions on the pole and zero locations to insure that a rational function W(s) is positive-real has been an outstanding one in network theory. Several solutions to this problem are presented in this paper. In particular, assuming that W(s) has n poles and n zeros, certain regions in the left-half s plane are constructed which have the following property: If these poles and zeros are placed in one of these regions in any arbitrary manner (with the restriction, of course, that complex elements appear in complex-conjugate pairs), the resulting W(s) will be positive-real. These results are then extended to the case where the number of poles and the number of zeros differ by one. In addition certain paths in these regions are derived which allow one to place any number of poles and zeros into any of these regions. That is, if the poles and zeros alternate in groups of n elements on any such path, W(s) will again be positive-real. The simple alternation of poles and zeros on the real negative axis and on a vertical line or circle in the closed left-half s plane, which is a known result, is a special case of these considerably more general conclusions.

A new derivation of Frisch's algorithm for calculating vertex-pair connectivity

Abstract: In this paper we give a new and conceptually simple version of Frisch's algorithm for calculating the vertex connectivity of a graph. We show how this algorithm is obtained immediately from the Ford and Fulkerson labelling algorithm by using a “2-ply” scanning step. Data structures are introduced which lead to efficiencies in execution, and the final algorithm is presented in a “go-to-less” notation.

Planarity Testing of Doubly Periodic Infinite Graphs

Abstract: This paper describes an efficient way to test the VAP-free (Vertex Accumulation Point free) planarity of one- and two-dimensional dynamic graphs. Dynamic graphs are infinite graphs consisting of an infinite number of basic cells connected regularly according to labels in a finite graph called a sraric graph. Dynamic graphs arize in the design of highly regular VLSI circuits, such as systolic arrays and digital signal processing chips. We show that VAP-free planarity testing of dynamic graphs can be done efficiently by making use of their regularity. First, we will establish necessary conditions for VAP-free planarity of dynamic graphs. Then we show the existence of a small finite graph which is planar if and only if the original dynamic graph is VAP-free planar. From this it follows that VAP-free planarity testing of one- and twodimensional dynamic graphs is asymptomically no more difficult than planarity testing of finite graphs, and thus can be done in linear time.

Numerical Optimization

Abstract: Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems. For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. The authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.

Machine Learning : A Probabilistic Perspective

Abstract: Today's Web-enabled deluge of electronic data calls for automated methods of data analysis. Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data. This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach. The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning. The book is written in an informal, accessible style, complete with pseudo-code for the most important algorithms. All topics are copiously illustrated with color images and worked examples drawn from such application domains as biology, text processing, computer vision, and robotics. Rather than providing a cookbook of different heuristic methods, the book stresses a principled model-based approach, often using the language of graphical models to specify models in a concise and intuitive way. Almost all the models described have been implemented in a MATLAB software package--PMTK (probabilistic modeling toolkit)--that is freely available online. The book is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.

Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

Abstract: A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and which have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical quantum computer. These algorithms take a number of steps polynomial in the input size, e.g., the number of digits of the integer to be factored.

Shape matching and object recognition using shape contexts

Abstract: We present a novel approach to measuring similarity between shapes and exploit it for object recognition. In our framework, the measurement of similarity is preceded by: (1) solving for correspondences between points on the two shapes; (2) using the correspondences to estimate an aligning transform. In order to solve the correspondence problem, we attach a descriptor, the shape context, to each point. The shape context at a reference point captures the distribution of the remaining points relative to it, thus offering a globally discriminative characterization. Corresponding points on two similar shapes will have similar shape contexts, enabling us to solve for correspondences as an optimal assignment problem. Given the point correspondences, we estimate the transformation that best aligns the two shapes; regularized thin-plate splines provide a flexible class of transformation maps for this purpose. The dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points, together with a term measuring the magnitude of the aligning transform. We treat recognition in a nearest-neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image. Results are presented for silhouettes, trademarks, handwritten digits, and the COIL data set.

Planning Algorithms: Introductory Material

Abstract: Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.