Adaptive Randomized Sketching for Dynamic Nonsmooth Optimization
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Photographs and geologic maps of the area around Littrow rilles and eastern edge of Mare Serenitatis are presented, along with variations in the features and compositions of the region.
The author has identified the following significant results. The Earth Resources Technology Satellite Program has as an objective the development of tectonic maps for Bolivia. Maps were prepared using the images of ERTS-1 in a preliminary study of alignments observed and rapidly interpreted in images 1010-14033-3-4-5-6-7 on a scale of 1:1,000,000, and later verified on the ground with corresponding fault zones. This information was not shown on existing geologial maps. The ERTS-1 imagery was used in volcanology research for drawing the regional limits of volcanic formations as soon as the alignment and the extent of the volcanoes could be determined. The extensive coverage of ERTS-1 images provides an excellent opportunity for developing studies of regional structures.
On the basis of field and particle observations, it is suggested that a bright auroral display is a part of a magnetosphere-ionosphere current system which is fed by a charge-separation process in the outer magnetosphere (or the solar wind). The upward magnetic-field-aligned current is flowing out of the display, carried mainly by down-flowing electrons from the hot-particle populations in the outer magnetosphere (the ambient cold electrons being depleted at high altitudes). As a result of the magnetic mirroring of these downflowing current carriers, a large potential drop is set up along the magnetic field, increasing both the number flux and the kinetic energy of the precipitating electrons. It is found that this simple basic model, when combined with wave-particle interactions, may be able to explain a highly diversified selection of auroral particle observations. It may thus be possible to explain both inverted-V events and auroral rays in terms of a static parallel electric field, and the electric field may be compatible with a strongly variable pitch-angle distribution of the precipitating electrons, including distributions peaked at 90 deg as well as 0 deg. This model may also provide a simple explanation of the simultaneous precipitation of electrons and collimated positive ions.
Information is provided on how a potential user of remote sensing technology can gain access to all of the products and services he will need to get started. It was envisioned that these include data, training, hardware, and software. A very brief tutorial summary of the fundamentals of the technology is presented.
A chronological assessment is given of the broad spectra of technology associated with radar geology. Particular attention is given to the most recent developments made in the areas of microwave Earth resources applications and geologic remote sensing from aircraft and satellite. The significance of space derived radar in geologic investigations is discussed and the scientific basis for exploiting the sensitivity of radar signals to various aspects of geologic terrain is given.
A review of visual recognition studies is used to define two levels of information requirements. These two levels are related to two primary subdivisions of the spatial frequency domain of images and reflect two distinct different physical properties of arbitrary scenes. In particular, pathologies in recognition due to cerebral dysfunction point to a more complete split into two major types of processing: high spatial frequency edge based recognition vs. low spatial frequency lightness (and color) based recognition. The former is more central and general while the latter is more specific and is necessary for certain special tasks. The two modes of recognition can also be distinguished on the basis of physical scene properties: the highly localized edges associated with reflectance and sharp topographic transitions vs. smooth topographic undulation. The extreme case of heavily abstracted images is pursued to gain an understanding of the minimal information required to support both modes of recognition. Here the intention is to define the semantic core of transmission. This central core of processing can then be fleshed out with additional image information and coding and rendering techniques.
The years since the Workshop on the Chronology of Meteorites and the Early Solar System, are marked with ongoing progress in cosmochronology. Rapid improvements in techniques, discovery of new meteorites unlike any previously known, and findings that what was deemed well established constants are actually variables, will be reflected in an updated review of the solar system chronology we are currently preparing. Along with updating the database of meteorite ages, it will involve development of a set of criteria for evaluation of accuracy and consistency of isotopic dates across the entire range of meteorite classes and isotope chronometer systems. Here we present some ideas on what we think is important in meteorite chronology, and invite the cosmochemistry community to discuss them.
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Sketches of Comet Kohoutek drawn by the author during operations on Skylab are presented. The sketches are black and white, with darker color implying a higher observed brightness. Sketches were also made of what the isophotes would have looked like if they could have been measured. In addition, color sketches made after the flight and corresponding to each of the inflight sketches are presented. The sketches show the comet at perihelion minus 10 days and at perihelion plus 1-9 days. Sketches show the comet changing appreciably in form, color, texture, and length after perihelion. The sunward spike, visible at perihelion plus one day, is no longer visible at perihelion plus 4 days.
Least squares regression is a ubiquitous tool for building emulators (a.k.a. surrogate models) of problems across science and engineering for purposes such as design space exploration and uncertainty quantification. When the regression data are generated using an experimental design process (e.g., a quadrature grid) involving computationally expensive models, or when the data size is large, sketching techniques have shown promise at reducing the cost of the construction of the regression model while ensuring accuracy comparable to that of the full data. However, random sketching strategies, such as those based on leverage scores, lead to regression errors that are random and may exhibit large variability. To mitigate this issue, we present a novel boosting approach that leverages cheaper, lower-fidelity data of the problem at hand to identify the best sketch among a set of candidate sketches. This in turn specifies the sketch of the intended high-fidelity model and the associated data. We provide theoretical analyses of this bifidelity boosting (BFB) approach and discuss the conditions the low- and high-fidelity data must satisfy for a successful boosting. In doing so, we derive a bound on the residual norm of the BFB sketched solution relating it to its ideal, but computationally expensive, high-fidelity boosted counterpart. Finally, empirical results on both manufactured and PDE data corroborate the theoretical analyses and illustrate the efficacy of the BFB solution in reducing the regression error, as compared to the nonboosted solution.
Recently, randomized algorithms in numerical linear algebra, specifically those centered around random sketching, have gained traction in primarily theoretical research due to their potential to significantly reduce problem dimensionality at the cost of an O(1) multiplicative distortion factor. It has been assumed that this sketching can be done efficiently, but thorough investigation into how precisely to do it has been neglected. Moreover, the theory-based community has argued for sketching’s ability to reduce computational cost via complexity analysis, but has not researched how it affects the stability of the algorithms. At Sandia, efficient linear solvers that scale well on modern HPC architectures while maintaining stability are imperative for practical applications. In this LDRD, we developed a random sketching strategy that is substantially faster than existing ones, and demonstrate its superior performance in practice on a NVIDIA H100 GPU. Moreover, we show how this can be used to significantly outperform existing linear least squares solvers while improving the solver’s stability as well. Additionally, we demonstrate how this sketching strategy can be used to make a fast, stable QR factorization that can subsequently be used in s-step and block Krylov solvers. Finally, we incorporate a sketching-based block orthogonalization scheme into s-step GMRES, which is stable and faster than existing approaches on the Perlmutter supercomputer.
In many applications, an optical detector has to be located relative to mechanical reference points. One solution is to specify stringent requirements on (1) mounting the optical detector relative to the chip carrier, (2) soldering the chip carrier onto the printed circuit board (PCB), and (3) installing the PCB to the mechanical structure of the subsystem. Figure 1 shows a sketch of an optical detector mounted relative to mechanical reference with high positional accuracy. The optical detector is typically a fragile wafer that cannot be physically touched by any measurement tool. An optical coordinate measuring machine (CMM) can be used to position optical detectors relative to mechanical reference points. This approach will eliminate all requirements on positional tolerances. The only requirement is that the PCB is manufactured with oversized holes. An exaggerated sketch of this situation is shown in Figure 2. The sketch shows very loose tolerances on mounting the optical detector in the chip carrier, loose tolerance on soldering the chip carrier to the PCB, and finally large tolerance on where the mounting screws are located. The PCB is held with large screws and oversized holes. The PCB is mounted loosely so it can move freely around. The optical CMM measures the mechanical reference points. Based on these measurements, the required positions of the optical detector corners can be calculated. The optical CMM is commanded to go to the position where one detector corner is supposed to be. This is indicated with the cross-hairs in Figure 2(a). This figure is representative of the image of the optical CMM monitor. Using a suitable tapping tool, the PCB is manually tapped around until the corner of the optical detector is at the crosshairs of the optical CMM. The CMM is commanded to another corner, and the process is repeated a number of times until all corners of the optical detector are within a distance of 10 to 30 microns of the required position. The situation is sketched in Figure 2(b) (the figure also shows the tapping tool and where to tap). At this point the fasteners for the PCB are torqued slightly so the PCB can still move. The PCB location is adjusted again with the tapping tool. This process is repeated 3 to 4 times until the final torque is achieved. The oversized mounting holes are then filled with a liquid bonding agent to secure the board in position (not shown in the sketch). A 10- to 30-micron mounting accuracy has been achieved utilizing this method..
Here at Fermi National Accelerator Laboratory, particle accelerators are constantly running, giving off excess radioactive dust. This dust can be extremely harmful to people and the environment, posing numerous issues. The goal of this project is to conceptualize an automated cleaning solution. With this main goal in mind, the project started with a brainstorming session. The main concept relied on the use of a powder distributing system paired with a vacuum to easily attract and trap the dust. From this main concept, multiple sketches were produced, showing a robot with pieced-together systems. With the initial idea down, each subsystem could be brought further with the inner workings being sketched out. After sketches and proof of concept were polished, the next step was to begin 3D modeling, using NX, to bring life into the sketches. With every day came new ideas, modifying the previous sketches and models as necessary. Soon after the bigger structures were fleshed out, the focus could be shifted onto the less pressing subsystems. Adding a conveyor belt and spinning brush attachment to the powder hopper allowed for more even powder distribution. Along with that, the addition of spring-loaded brushes on the vacuum nozzle ensures constant dust agitation, improving overall functionality. A few other quality of life improvements, such as a removable dust reservoir with a ramp gave a push towards real life functionality. After considering the logistics of this robot functioning in real-life, pressure plates were provided to stop the robot from crashing into its surroundings. Having all of the individual models lead to an overall assembly. Making this robot programmable allowed for this project to meet the design requirements, providing a solution to the previous dilemma.