This is a review of Collected Works of John Tate. Parts I, II, edited by Barry Mazur and Jean-Pierre Serre. American Mathematical Society, Providence, Rhode Island, 2016. For several decades it has been clear to the friends and colleagues of John Tate that a “Collected Works” was merited. The award of the Abel Prize to Tate in 2010 added impetus, and finally, in Tate’s ninety-second year we have these two magnificent volumes, edited by Barry Mazur and Jean-Pierre Serre. Beyond Tate’s published articles, they include five unpublished articles and a selection of his letters, most accompanied by Tate’s comments, and a collection of photographs of Tate. For an overview of Tate’s work, the editors refer the reader to [4]. Before discussing the volumes, I describe some of Tate’s work. 1. Hecke L-series and Tate’s thesis Like many budding number theorists, Tate’s favorite theorem when young was Gauss’s law of quadratic reciprocity. When he arrived at Princeton as a graduate student in 1946, he was fortunate to find there the person, Emil Artin, who had discovered the most general reciprocity law, so solving Hilbert’s ninth problem. By 1920, the German school of algebraic number theorists (Hilbert, Weber, . . .) together with its brilliant student Takagi had succeeded in classifying the abelian extensions of a number field K: to each group I of ideal classes in K, there is attached an extension L of K (the class field of I); the group I determines the arithmetic of the extension L/K, and the Galois group of L/K is isomorphic to I. Artin’s contribution was to prove (in 1927) that there is a natural isomorphism from I to the Galois group of L/K. When the base field contains an appropriate root of 1, Artin’s isomorphism gives a reciprocity law, and all possible reciprocity laws arise this way. In the 1930s, Chevalley reworked abelian class field theory. In particular, he replaced “ideals” with his “idèles” which greatly clarified the relation between the local and global aspects of the theory. For his thesis, Artin suggested that Tate do the same for Hecke L-series. When Hecke proved that the abelian L-functions of number fields (generalizations of Dirichlet’s L-functions) have an analytic continuation throughout the plane with a functional equation of the expected type, he saw that his methods applied even to a new kind of L-function, now named after him. Once Tate had developed his harmonic analysis of local fields and of the idèle group, he was able prove analytic continuation and functional equations for all the relevant L-series without Hecke’s complicated theta-formulas. Received by the editors September 5, 2016. 2010 Mathematics Subject Classification. Primary 01A75, 11-06, 14-06. c ©2017 American Mathematical Society

The collected works

Laboratory-based courses play a critical role in scientific education. Automation is changing the nature of these laboratories, and there is a long-running debate about the value of hands-on versus simulated laboratories. In addition, the introduction of remote laboratories adds a third category to the debate. Through a review of the literature related to these labs in education, the authors draw several conclusions about the state of current research. The debate over different technologies is confounded by the use of different educational objectives as criteria for judging the laboratories: Hands-on advocates emphasize design skills, while remote lab advocates focus on conceptual understanding. We observe that the boundaries among the three labs are blurred in the sense that most laboratories are mediated by computers, and that the psychology of presence may be as important as technology. We also discuss areas for future research.

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Hands-on, simulated, and remote laboratories: A comparative literature review

Typical video footage captured using an off-the-shelf camcorder suffers from limited dynamic range. This paper describes our approach to generate high dynamic range (HDR) video from an image sequence of a dynamic scene captured while rapidly varying the exposure of each frame. Our approach consists of three parts: automatic exposure control during capture, HDR stitching across neighboring frames, and tonemapping for viewing. HDR stitching requires accurately registering neighboring frames and choosing appropriate pixels for computing the radiance map. We show examples for a variety of dynamic scenes. We also show how we can compensate for scene and camera movement when creating an HDR still from a series of bracketed still photographs.

High dynamic range video

We have recently observed a convergence of technologies to foster the emergence of lifelogging as a mainstream activity. Computer storage has become significantly cheaper, and advancements in sensing technology allows for the efficient sensing of personal activities, locations and the environment. This is best seen in the growing popularity of the quantified self movement, in which life activities are tracked using wearable sensors in the hope of better understanding human performance in a variety of tasks. This review aims to provide a comprehensive summary of lifelogging, to cover its research history, current technologies, and applications. Thus far, most of the lifelogging research has focused predominantly on visual lifelogging, hence we maintain this focus in this review. However, we also reflect on the challenges lifelogging poses for information access and retrieval in general. This review is a suitable reference for those seeking an information retrieval scientist's perspective on lifelogging and the quantified self.

/pdf/lifelogging-personal-big-data-3lrkb80bdr.pdf

Lifelogging: Personal Big Data

This paper describes novel implementations of the KLT feature track- ing and SIFT feature extraction algorithms that run on the graphics processing unit (GPU) and is suitable for video analysis in real-time vision systems. While significant acceleration over standard CPU implementations is obtained by ex- ploiting parallelism provided by modern programmable graphics hardware, the CPU is freed up to run other computations in parallel. Our GPU-based KLT im- plementation tracks about a thousand features in real-time at 30 Hz on 1024 £ 768 resolution video which is a 20 times improvement over the CPU. It works on both ATI and NVIDIA graphics cards. The GPU-based SIFT implementation works on NVIDIA cards and extracts about 800 features from 640 £ 480 video at 10Hz which is approximately 10 times faster than an optimized CPU implementation.

/pdf/gpu-based-video-feature-tracking-and-matching-o3by4wugzu.pdf

GPU-based Video Feature Tracking And Matching

Graphics and vision are approximate inverses of each other: ordinarily Graphics Processing Units (GPUs) are used to convert "numbers into pictures" (i.e. computer graphics). In this paper, we propose using GPUs in approximately the reverse way: to assist in "converting pictures into numbers" (i.e. computer vision). The OpenVIDIA project uses single or multiple graphics cards to accelerate image analysis and computer vision. It is a library and API aimed at providing a graphics hardware accelerated processing framework for image processing and computer vision. OpenVIDIA explores the creation of a parallel computer architecture consisting of multiple Graphics Processing Units (GPUs) built entirely from commodity hardware. OpenVIDIA uses multiple Graphic.Processing Units in parallel to operate as a general-purpose parallel computer architecture. It provides a simple API which implements some common computer vision algorithms. Many components can be used immediately and because the project is Open Source, the code is intended to serve as templates and examples for how similar algorithms are mapped onto graphics hardware. Implemented are image processing techniques (Canny edge detection, filtering), image feature handling (identifying and matching features) and image registration, to name a few.

/pdf/openvidia-parallel-gpu-computer-vision-zb1h60ws57.pdf

OpenVIDIA: parallel GPU computer vision

In the classical Economic Manufacturing Quantity (EMQ) model, it is assumed that all items produced are of perfect quality and the production facility never breaks down However, in real production, the product quality is usually a function of the state of the production process which may deteriorate over time and the production facility may fail randomly In this paper, we study the effect of machine failures on the optimal lot size and on the optimal number of inspections in a production cycle The formula for the long-run expected average cost per unit time is obtained for a generally distributed time to failure An optimal production/inspection policy is found by minimising the expected average cost

An EMQ model with inspections and random machine failures

Humans increasingly engage themselves in their computational world as much as the physical world. Following this need for constant connectivity, computing devices such as Personal Digital Assistants (PDAs) and camera phones have become more wearable. We introduce the EyeTap personal experience capturing system EyeTap digital eyeglasses cause the eye to, in effect, function as if it were both a camera and display, by mapping an effective camera and display inside the eye. Eyetap therefore captures images exactly as they were originally seen by the user. Since sight is a primary sense this interface becomes intuitive and easy to use for continuous capture and sharing of personal experiences. This paper will discuss the EyeTap’s evolution over the last 30 years; some encountered design principles, the various EyeTap applications and future social aspects that may arise from EyeTap technology. ACM Classification

Designing EyeTap Digital Eyeglasses for Continuous Lifelong Capture and Sharing of Personal Experiences

When we ask the fundamental question "What does a camera measure?", we arrive at the concept of quantimetric imaging, which uses a new quantimetric unit, q, characteristic of a particular camera (e.g. each kind of camera defines its own quantimetric unit q based on its spectral response, etc.). Fluctuations in interframe exposures, along a sequence of images, give rise to a comparametric relationship between successive pairs of images. This allows us to estimate the response function of the camera (to derive the quantimetric unit q) as well as the relative differences in exposure. A new method of video image processing that exploits multiple differently exposed pictures (frames of the video sequence) of overlapping subject matter is thus possible. The method may be used whenever a video camera having automatic exposure captures multiple frames of video with the same subject matter appearing in regions of overlap between at least some of the successive video frames. Since almost all cameras have an automatic exposure feature, typically center weighted, when a light object falls in the center of the frame the exposure is automatically decreased, whereas the exposure is automatically increased when the camera swings around to point at a darker object. Such fluctuations in gain may be used to estimate the camera's response function, to estimate exposure differences, to do quantimetric processing, as well as to obtain images having both extended dynamic range and extended dynamic domain.

/pdf/painting-with-looks-photographic-images-from-video-using-5aqp3nh1y9.pdf

Painting with looks: photographic images from video using quantimetric processing

Diminished reality is as important as augmented reality, and both are possible with a device called the Reality Mediator. Over the past two decades, we have designed, built, worn, and tested many different embodiments of this device in the context of wearable computing, Incorporated into the Reality Mediator is an "EyeTap" system, which is a device that quantifies and resynthesizes light that would otherwise pass through one or both lenses of the eye(s) of a wearer. The functional principles of EyeTap devices are discussed, in detail. The EyeTap diverts into a spatial measurement system at least a portion of light that would otherwise pass through the center of projection of at least one lens of an eye of a wearer. The Reality Mediator has at least one mode of operation in which it reconstructs these rays of light, under the control of a wearable computer system. The computer system then uses new results in algebraic projective geometry and comparametric equations to perform head tracking, as well as to track motion of rigid planar patches present in the scene. We describe how our tracking algorithm allows an EyeTap to alter the light from a particular portion of the scene to give rise to a computer-controlled, selectively mediated reality. An important difference between mediated reality and augmented reality includes the ability to not just augment but also deliberately diminish or otherwise alter the visual perception of reality. For example, diminished reality allows additional information to be inserted without causing the user to experience information overload. Our tracking algorithm also takes into account the effects of automatic gain control, by performing motion estimation in both spatial as well as tonal motion coordinates.

http://eyetap.org/papers/docs/presence.pdf

James Fung

Papers

OpenVIDIA: parallel GPU computer vision

An EMQ model with inspections and random machine failures

Designing EyeTap Digital Eyeglasses for Continuous Lifelong Capture and Sharing of Personal Experiences

Painting with looks: photographic images from video using quantimetric processing

EyeTap devices for augmented, deliberately diminished, or otherwise altered visual perception of rigid planar patches of real-world scenes