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.

Planning Algorithms: Introductory Material

Scoring rules assess the quality of probabilistic forecasts, by assigning a numerical score based on the predictive distribution and on the event or value that materializes. A scoring rule is proper if the forecaster maximizes the expected score for an observation drawn from the distributionF if he or she issues the probabilistic forecast F, rather than G ≠ F. It is strictly proper if the maximum is unique. In prediction problems, proper scoring rules encourage the forecaster to make careful assessments and to be honest. In estimation problems, strictly proper scoring rules provide attractive loss and utility functions that can be tailored to the problem at hand. This article reviews and develops the theory of proper scoring rules on general probability spaces, and proposes and discusses examples thereof. Proper scoring rules derive from convex functions and relate to information measures, entropy functions, and Bregman divergences. In the case of categorical variables, we prove a rigorous version of the ...

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Strictly Proper Scoring Rules, Prediction, and Estimation

Foundations of Confocal Scanned Imaging in Light Microscopy -- Fundamental Limits in Confocal Microscopy -- Special Optical Elements -- Points, Pixels, and Gray Levels: Digitizing Image Data -- Laser Sources for Confocal Microscopy -- Non-Laser Light Sources for Three-Dimensional Microscopy -- Objective Lenses for Confocal Microscopy -- The Contrast Formation in Optical Microscopy -- The Intermediate Optical System of Laser-Scanning Confocal Microscopes -- Disk-Scanning Confocal Microscopy -- Measuring the Real Point Spread Function of High Numerical Aperture Microscope Objective Lenses -- Photon Detectors for Confocal Microscopy -- Structured Illumination Methods -- Visualization Systems for Multi-Dimensional Microscopy Images -- Automated Three-Dimensional Image Analysis Methods for Confocal Microscopy -- Fluorophores for Confocal Microscopy: Photophysics and Photochemistry -- Practical Considerations in the Selection and Application of Fluorescent Probes -- Guiding Principles of Specimen Preservation for Confocal Fluorescence Microscopy -- Confocal Microscopy of Living Cells -- Aberrations in Confocal and Multi-Photon Fluorescence Microscopy Induced by Refractive Index Mismatch -- Interaction of Light with Botanical Specimens -- Signal-to-Noise Ratio in Confocal Microscopes -- Comparison of Widefield/Deconvolution and Confocal Microscopy for Three-Dimensional Imaging -- Blind Deconvolution -- Image Enhancement by Deconvolution -- Fiber-Optics in Scanning Optical Microscopy -- Fluorescence Lifetime Imaging in Scanning Microscopy -- Multi-Photon Molecular Excitation in Laser-Scanning Microscopy -- Multifocal Multi-Photon Microscopy -- 4Pi Microscopy -- Nanoscale Resolution with Focused Light: Stimulated Emission Depletion and Other Reversible Saturable Optical Fluorescence Transitions Microscopy Concepts -- Mass Storage, Display, and Hard Copy -- Coherent Anti-Stokes Raman Scattering Microscopy -- Related Methods for Three-Dimensional Imaging -- Tutorial on Practical Confocal Microscopy and Use of the Confocal Test Specimen -- Practical Confocal Microscopy -- Selective Plane Illumination Microscopy -- Cell Damage During Multi-Photon Microscopy -- Photobleaching -- Nonlinear (Harmonic Generation) Optical Microscopy -- Imaging Brain Slices -- Fluorescent Ion Measurement -- Confocal and Multi-Photon Imaging of Living Embryos -- Imaging Plant Cells -- Practical Fluorescence Resonance Energy Transfer or Molecular Nanobioscopy of Living Cells -- Automated Confocal Imaging and High-Content Screening for Cytomics -- Automated Interpretation of Subcellular Location Patterns from Three-Dimensional Confocal Microscopy -- Display and Presentation Software -- When Light Microscope Resolution Is Not Enough:Correlational Light Microscopy and Electron Microscopy -- Databases for Two- and Three-Dimensional Microscopical Images in Biology -- Confocal Microscopy of Biofilms — Spatiotemporal Approaches -- Bibliography of Confocal Microscopy.

Handbook of biological confocal microscopy

In the choice of an estimator for the spectrum of a stationary time series from a finite sample of the process, the problems of bias control and consistency, or "smoothing," are dominant. In this paper we present a new method based on a "local" eigenexpansion to estimate the spectrum in terms of the solution of an integral equation. Computationally this method is equivalent to using the weishted average of a series of direct-spectrum estimates based on orthogonal data windows (discrete prolate spheroidal sequences) to treat both the bias and smoothing problems. Some of the attractive features of this estimate are: there are no arbitrary windows; it is a small sample theory; it is consistent; it provides an analysis-of-variance test for line components; and it has high resolution. We also show relations of this estimate to maximum-likelihood estimates, show that the estimation capacity of the estimate is high, and show applications to coherence and polyspectrum estimates.

Spectrum estimation and harmonic analysis

This paper presents the first randomized approach to kinodynamic planning (also known as trajectory planning or trajectory design). The task is to determine control inputs to drive a robot from an ...

Randomized kinodynamic planning

The Nelder--Mead simplex algorithm, first published in 1965, is an enormously popular direct search method for multidimensional unconstrained minimization. Despite its widespread use, essentially no theoretical results have been proved explicitly for the Nelder--Mead algorithm. This paper presents convergence properties of the Nelder--Mead algorithm applied to strictly convex functions in dimensions 1 and 2. We prove convergence to a minimizer for dimension 1, and various limited convergence results for dimension 2. A counterexample of McKinnon gives a family of strictly convex functions in two dimensions and a set of initial conditions for which the Nelder--Mead algorithm converges to a nonminimizer. It is not yet known whether the Nelder--Mead method can be proved to converge to a minimizer for a more specialized class of convex functions in two dimensions.

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Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions

The path taken by a car with a given minimum turning radius has a lower bound on its radius of curvature at each point, but the path has cusps if the car shifts into or out of reverse gear. What is the shortest such path a car can travel between two points if its starting and ending directions are specified? One need consider only paths with at most 2 cusps or reversals

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Optimal paths for a car that goes both forwards and backwards.

A method is presented for estimating solutions of Fredholm integral equations of the first kind, given noisy data. Regularization is effected by a smoothing term which is the $L^2 $-norm of the estimate. We propose a scheme by which an approximately optimal amount of smoothing may be computed, based only on the data and the assumed known noise variances. Numerical examples are given for estimating inverse Laplace transforms.

https://www.jstor.org/stable/info/2156861

Estimating Solutions of First Kind Integral Equations with Nonnegative Constraints and Optimal Smoothing

A protocol for authenticating a cellular telephone to a service provider for the purpose of preventing the piracy of cellular services. A service provider assigns a unique "secret", along with other information such as a telephone number, to each cellular telephone when the telephone service is established with the service provider. Each base station of a service provider continuously broadcasts a periodically changing random number to all of the cellular telephones within the base station's jurisdiction. When a cellular telephone first enters the jurisdiction of a base station, it registers itself with the base station by concatenating a secret password and the most recently broadcast random number, along with other information, and passing the concatenated information to a hash function. The cellular telephone then sends the output of the hash function, along with other identifying information to the service provider. The service provider, upon learning of the cellular telephone's identity, feeds the secret assigned to that cellular telephone and the random number, along with other information, into the same hash function. When the result of the hashing performed by the service provider matches that provided by the cellular telephone, authentication for that cellular telephone is complete. Thereupon, the provider sends the cell a shared secret data field which is known to the mobile unit, and subsequent authentication processes are carried out between the mobile unit and the cell itself.

Service provision authentication protocol

A secure cellular telephony arrangement where the mobile unit maintains a secret that is assigned to it by the service provider, and which is known to the provider (home cellular geographic service are -- CGSA) but not to any other base station. A shared secret datum is generated by the home CGSA with the aid of the secret and some other data. That data is transmitted to the mobile unit to enable it to also generate the shared secret datum. A mobile unit wishing to communicate with a base station creates an authentication string with the aid of the shared secret datum and sends it and the unit's identity to the base station. A base station which does not have the shared secret datum is unable to immediately authenticate the mobile unit. It therefore contacts the home CGSA, receives the shared secret datum and the other data, and proceeds to authenticate the mobile unit's authentication string. With the information received from the home CGSA the base station can direct the mobile unit to regenerate the shared secret datum or even create a new one.

James A. Reeds

Papers

Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions

Optimal paths for a car that goes both forwards and backwards.

Estimating Solutions of First Kind Integral Equations with Nonnegative Constraints and Optimal Smoothing

Service provision authentication protocol

Cellular telephony authentication arrangement