Krishnendu Chakrabarty

Bio: Krishnendu Chakrabarty is an academic researcher from Duke University. The author has contributed to research in topics: Biochip & Automatic test pattern generation. The author has an hindex of 79, co-authored 996 publications receiving 27583 citations. Previous affiliations of Krishnendu Chakrabarty include Huawei & Wake Forest University.

Sensor deployment and target localization based on virtual forces

Abstract: The effectiveness of cluster-based distributed sensor networks depends to a large extent on the coverage provided by the sensor deployment. We propose a virtual force algorithm (VFA) as a sensor deployment strategy to enhance the coverage after an initial random placement of sensors. For a given number of sensors, the VFA algorithm attempts to maximize the sensor field coverage. A judicious combination of attractive and repulsive forces is used to determine virtual motion paths and the rate of movement for the randomly-placed sensors. Once the effective sensor positions are identified, a one-time movement with energy consideration incorporated is carried out, i.e., the sensors are redeployed to these positions. We also propose a novel probabilistic target localization algorithm that is executed by the cluster head. The localization results are used by the cluster head to query only a few sensors (out of those that report the presence of a target) for more detailed information. Simulation results are presented to demonstrate the effectiveness of the proposed approach.

Grid coverage for surveillance and target location in distributed sensor networks

Abstract: We present novel grid coverage strategies for effective surveillance and target location in distributed sensor networks. We represent the sensor field as a grid (two or three-dimensional) of points (coordinates) and use the term target location to refer to the problem of locating a target at a grid point at any instant in time. We first present an integer linear programming (ILP) solution for minimizing the cost of sensors for complete coverage of the sensor field. We solve the ILP model using a representative public-domain solver and present a divide-and-conquer approach for solving large problem instances. We then use the framework of identifying codes to determine sensor placement for unique target location, We provide coding-theoretic bounds on the number of sensors and present methods for determining their placement in the sensor field. We also show that grid-based sensor placement for single targets provides asymptotically complete (unambiguous) location of multiple targets in the grid.

Sensor placement for effective coverage and surveillance in distributed sensor networks

Abstract: We present two algorithms for the efficient placement of sensors in a sensor field. The proposed approach is aimed at optimizing the number of sensors and determining their placement to support distributed sensor networks. The optimization framework is inherently probabilistic due to the uncertainty associated with sensor detections. The proposed algorithms address coverage optimization under the constraints of imprecise detections and terrain properties. These algorithms are targeted at average coverage as well as at maximizing the coverage of the most vulnerable grid points. The issue of preferential coverage of grid points (based on relative measures of security and tactical importance) is also modeled. Experimental results for an example sensor field with obstacles demonstrate the application of our approach.

Sensor deployment and target localization in distributed sensor networks

Abstract: The effectiveness of cluster-based distributed sensor networks depends to a large extent on the coverage provided by the sensor deployment. We propose a virtual force algorithm (VFA) as a sensor deployment strategy to enhance the coverage after an initial random placement of sensors. For a given number of sensors, the VFA algorithm attempts to maximize the sensor field coverage. A judicious combination of attractive and repulsive forces is used to determine the new sensor locations that improve the coverage. Once the effective sensor positions are identified, a one-time movement with energy consideration incorporated is carried out, that is, the sensors are redeployed, to these positions. We also propose a novel probabilistic target localization algorithm that is executed by the cluster head. The localization results are used by the cluster head to query only a few sensors (out of those that report the presence of a target) for more detailed information. Simulation results are presented to demonstrate the effectiveness of the proposed approach.

On a new class of codes for identifying vertices in graphs

Abstract: We investigate a new class of codes for the optimal covering of vertices in an undirected graph G such that any vertex in G can be uniquely identified by examining the vertices that cover it. We define a ball of radius t centered on a vertex /spl upsi/ to be the set of vertices in G that are at distance at most t from /spl upsi/. The vertex /spl upsi/ is then said to cover itself and every other vertex in the ball with center /spl upsi/. Our formal problem statement is as follows: given an undirected graph G and an integer t/spl ges/1, find a (minimal) set C of vertices such that every vertex in G belongs to a unique set of balls of radius t centered at the vertices in C. The set of vertices thus obtained constitutes a code for vertex identification. We first develop topology-independent bounds on the size of C. We then develop methods for constructing C for several specific topologies such as binary cubes, nonbinary cubes, and trees. We also describe the identification of sets of vertices using covering codes that uniquely identify single vertices. We develop methods for constructing optimal topologies that yield identifying codes with a minimum number of codewords. Finally, we describe an application of the theory developed in this paper to fault diagnosis of multiprocessor systems.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

The Design and Analysis of Experiments

Abstract: THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

Pattern Recognition and Machine Learning

Abstract: Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.