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.

State transformations of colliding optical solitons and possible application to computation in bulk media

Abstract: Using explicit, bright-soliton solutions for the coupled Manakov system recently described by Radhakrishnan, Lakshmanan, and Hietarinta, we show that collisions of these solitons can be completely described by explicit linear fractional transformations of a complex-valued polarization state. We design sequences of solitons operating on other sequences of solitons that effect logic operations, including controlled NOT gates. Both data and logic operators have the self-restoring and reusability features of digital logic circuits. This suggests a method for implementing computation in a bulk nonlinear medium without interconnecting discrete components.

Optimal Design of Offshore Natural-Gas Pipeline Systems

Abstract: The exploitation of offshore natural gas reserves involves several phases, including production from reservoirs, separation of byproducts, and transportation to markets. The gas, which may originate as far as 100 miles from land, must be transported through pipelines to onshore delivery points. This paper develops techniques for solving the following problems: (1) selection of pipe diameters in a specified pipeline network to minimize the sum of investment and operation costs; (2) selection of minimum-cost network structures, given gas-field location and flow requirements; (3) optimal expansion of existing pipeline networks to include newly discovered gas fields. The techniques incorporate procedures for globally optimizing pipeline diameters for fixed tree structures and heuristic procedures for generating low-cost structures.

Characterization and Theoretical Comparison of Branch-and-Bound Algorithms for Permutation Problems

Abstract: Branch-and-bound implicit enumeration algorithms for permutation problems (discrete optimization problems where the set of feasible solutions is the permutation group Sn) are characterized in terms of a sextuple (Bp S,E,D,L,U), where (1) Bp is the branching rule for permutation problems, (2) S is the next node selection rule, (3) E is the set of node elimination rules, (4) D is the node dominance function, (5) L is the node lower-bound cost function, and (6) U is an upper-bound solution cost. A general algorithm based on this characterization is presented and the dependence of the computational requirements on the choice of algorithm parameters, S, E, D, L, and U is investigated theoretically. The results verify some intuitive notions but disprove others.

Time-gated Manakov spatial solitons are computationally universal.

Abstract: We prove that time-gated Manakov (1+1)-dimensional spatial solitons can perform arbitrary computation in a homogeneous medium with beams entering only at one boundary.

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.