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Querying Proofs

We motivate and introduce a query language PrQL designed for inspecting machine representations of proofs. PrQL natively supports hiproofs which express proof structure using hierarchical nested labelled trees. The core language presented in this paper is locally structured (first-order), with queries built using recursion and patterns over proof structure and rule names. We define the syntax and semantics of locally structured queries, demonstrate their power, and sketch some implementation experiments.

Aspinall, David

A sorghum pangenome reference improves global crop trait discovery

Although the green revolution adapted a handful of crops to homogeneous and high-input industrialized agriculture, much of the global population still relies on the local production of variable crop cultivars by low-input smallholder farms. This diversity of unhomogenized crops, like that of the grain and bioenergy crop sorghum, offers raw materials for genetic gain and cultivar improvement. However, breeding efforts can be constrained by highly specialized traits and breeding targets Here, to bridge this diversity, we constructed a 33-member pangenome reference and a diversity panel across 1,984 cultivars and landraces. We leveraged these resources to explore the complex interplay among historical contingency, ongoing adaptation and previously uncharacterized structural diversity. Specifically, our analyses conclusively demonstrated multiple nested and deeply diverged structural variants in the domestication gene SHATTERING1, which distinguish the previously established multicentric origin of sorghum. We then applied landscape genomics to reveal how gene flow and secondary contact created the complex genetic mosaic in contemporary breeding networks. As proof of concept for pangenome-accelerated trait discovery, we connected biosynthetic gene cluster structural variation to phenotypic leaf concentration of the cyanogenic glucoside dhurrin. Combined, these approaches will accelerate breeding and trait discovery and provide a framework for similar applications in other crops.

agricultural genetics

A Semantic Basis for Proof Queries and Transformations

We extend the query language PrQL, designed for inspecting machine representations of proofs, to also allow transformation of proofs. PrQL natively supports hiproofs which express proof structure using hierarchically nested labelled trees, which we claim is a natural way of taming the complexity of huge proofs. Query-driven transformations enable manipulation of this structure, in particular, to transform proofs produced by interactive theorem provers into forms that assist their understanding, or that could be consumed by other tools. In this paper we motivate and define basic transformation operations, using an abstract denotational semantics of hiproofs and queries. This extends our previous semantics for queries based on syntactic tree representations.We define update operations that add and remove sub-proofs, and manipulate the hierarchy to group and ungroup nodes. We show that

Proof Queries

Freely Suspended Smectic Filaments and the Structure of the B7 Phase of MHOBOW

Our recent discovery of the spontaneous formation of chiral domains in fluid smectic phases of achiral bow-shaped molecules opens up a wide variety of possibilities for new liquid crystal phases and phenomena. The basic, spontaneously chiral layer structure of the highest temperature fluid smectic phases, the B2 and B7, are shown. One of the most intriguing aspects of this structure is the plethora of possible phases coming from different stacking sequences of the polar ordering and tilt directions. The four possibilities of next-nearest neighbor alternation are shown. In the original material studied, NOBOW, the ground states found are antiferroelectric, either the racemic SmC(sub S)P(sub A) or the chiral SmC(sub A)P(sub A). We are currently studying MHOBOW, synthesized by D. Walba which, by virtue of its methyl hexyloxy tail has a tendency to form anticlinic layer interfaces, in the hope of finding a phase with a ferroelectric ground state, either SmC(sub A)P(sub S) or SmC(sub S)P(sub A), which can be obtained in NOBOW only by applying a field. Preliminary observations of MHO-BOW have made its study, from the point of view of understanding novel LC structures, extremely high priority. The following truly remarkable characteristics have been revealed: (i) The smectic phase grows out of the isotropic in the form of helical ribbons. The resulting planar aligned textures of focal conics with layers normal to glass plates exhibit bizarre modulations, including stripes and checker-boards. These have also been seen in other materials suggesting that this is a new phase (tentatively called B7), which is a fluid smectic with some kind of in-layer structure. (ii) It is virtually impossible to make freely suspended films of MHOBOW. Rather it makes the freely suspended filaments which preliminary x-ray scattering experiments reveal to have the nested cylinder layer structure indicated; (iii) The powder x-ray diffraction exhibits four resolution-limited smectic layering peaks, very close in layer spacing, which vary continuously with T. This is further evidence for a more complex three dimensional structure than NOBOW, which has a typical single layering reflection. (iv) The x-ray structure factor of the layering peak of the filaments is extraordinarily complex and rich. Varying in qL (the scattering vector component along the filament axis) from a double slit-like pattern to modulated layer-like patterns, as qH (the scattering vector component normal to the filament axis) is varied over the range where the four powder peaks are located. These results suggest some kind of mosaic structure, perhaps with different layer spacings corresponding to the different stacking sequences. Recent x-ray diffraction experiments show that the peaks are modulated in intensity upon translation along a filament, in domains of several hundred microns dimension. These preliminary experiments suggest that the B7 is a fluid smectic with extremely unusual and fascinating structures. Of all of the many hundreds of fluid smectic materials we have attempted to study in the freely suspended film geometry over the years, only a few have failed to form films, and none showed any great tendency to form filaments, although this clearly should be a possible freely suspended smectic LC morphology. On several occasions in the past we have intentionally tried to make filaments from a variety of smectics without success. Thus the smectic filament formation property makes the B7 phase unique. It seems quite likely that the stability of filaments is related to the in-plane structure. The filaments exhibit other interesting structural and optical features. They are birefringent with a local optic axis which is oblique and which can vary continuously along filament and which can be manipulated with an electric field applied normal to the fiber, as if the field were causing a rotation of the optic axis about the fiber axis. Rapid displacement of the ends of the fiber toward one another causes a macroscopic helixing at low T and causes thick regions to transiently appear at high T, a 1D analog of island formation on a rapidly compressed film.

Clark, N.

An Efficient Scheme for Updating Sparse Cholesky Factors

Raghavan had earlier developed the software package DCSPACK which can be used for solving sparse linear systems where the coefficient matrix is symmetric and positive definite (this project was not funded by NASA but by agencies such as NSF). DSCPACK-S is the serial code and DSCPACK-P is a parallel implementation suitable for multiprocessors or networks-of-workstations with message passing using MCI. The main algorithm used is the Cholesky factorization of a sparse symmetric positive positive definite matrix A = LL(T). The code can also compute the factorization A = LDL(T). The complexity of the software arises from several factors relating to the sparsity of the matrix A. A sparse N x N matrix A has typically less that cN nonzeroes where c is a small constant. If the matrix were dense, it would have O(N2) nonzeroes. The most complicated part of such sparse Cholesky factorization relates to fill-in, i.e., zeroes in the original matrix that become nonzeroes in the factor L. An efficient implementation depends to a large extent on complex data structures and on techniques from graph theory to reduce, identify, and manage fill. DSCPACK is based on an efficient multifrontal implementation with fill-managing algorithms and implementation arising from earlier research by Raghavan and others. Sparse Cholesky factorization is typically a four step process: (1) ordering to compute a fill-reducing numbering, (2) symbolic factorization to determine the nonzero structure of L, (3) numeric factorization to compute L, and, (4) triangular solution to solve L(T)x = y and Ly = b. The first two steps are symbolic and are performed using the graph of the matrix. The numeric factorization step is of dominant cost and there are several schemes for improving performance by exploiting the nested and dense structure of groups of columns in the factor. The latter are aimed at better utilization of the cache-memory hierarchy on modem processors to prevent cache-misses and provide execution rates (operations/second) that are close to the peak rates for dense matrix computations. Currently, EPISCOPACY is being used in an application at NASA directed by J. Newman and M. James. We propose the implementation of efficient schemes for updating the LL(T) or LDL(T) factors computed in DSCPACK-S to meet the computational requirements of their project. A brief description is provided in the next section.

Raghavan, Padma

Covariance and the hierarchy of frame bundles

This is an essay on the general concept of covariance, and its connection with the structure of the nested set of higher frame bundles over a differentiable manifold. Examples of covariant geometric objects include not only linear tensor fields, densities and forms, but affinity fields, sectors and sector forms, higher order frame fields, etc., often having nonlinear transformation rules and Lie derivatives. The intrinsic, or invariant, sets of forms that arise on frame bundles satisfy the graded Cartan-Maurer structure equations of an infinite Lie algebra. Reduction of these gives invariant structure equations for Lie pseudogroups, and for G-structures of various orders. Some new results are introduced for prolongation of structure equations, and for treatment of Riemannian geometry with higher-order moving frames. The use of invariant form equations for nonlinear field physics is implicitly advocated.

Estabrook, Frank B.

Scattering by ensembles of small particles experiment, theory and application

A hypothetical self consistent picture of evolution of prestellar intertellar dust through a comet phase leads to predictions about the composition of the circum-solar dust cloud. Scattering properties of thus resulting conglomerates with a bird's-nest type of structure are investigated using a micro-wave analogue technique. Approximate theoretical methods of general interest are developed which compared favorably with the experimental results. The principal features of scattering of visible radiation by zodiacal light particles are reasonably reproduced. A component which is suggestive of (ALPHA)-meteoroids is also predicted.

Gustafson, B. A. S.

A Table-Driven Control Method to Meet Continuous, Near-Real-Time Observation Requirements for the Solar X-Ray Imager

The design of the Solar X-Ray Imager (SXI) for the Geostationary Operational Environmental Satellite (GOES) presents an unusual scenario for controlling the observing sequences. The SXI is an operational instrument, designed not primarily for scientific research, but for providing "operational" data used by the National Oceanic and Atmospheric Administration (NOAA) to forecast the near-term space weather. To this end, a sequence of images selected to cover the full dynamic range of the sun will be executed routinely. As the dynamics of the sun have differing temporal cadences, the frequency of various images will differ. These images must be routinely received at the forecast center in near real-time, 24-hours a day, with a minimum of interruptions. While these requirements clearly lead to a 'routine patrol' of images, the parameters for each do not form a static set. The dynamics of the sun will change with the I 1-year solar cycle. The performance of the imaging will vary with on-orbit conditions and time. And while the SXI is not intended as a research instrument, forecasting techniques may change with time, which in turn will further alter the imaging sequences. An additional complication is the highly restricted commanding window, and a very slow commanding rate. To fulfill these requirements, the SXI was designed to utilize a table-driven approach. Sequences are defined using structured loops, with nested repetitions and delays. These sequences reference combinations of imaging parameters which in turn reference tables of parameters than can be loaded by ground commands. Multiple sequences can be built and stored in preparation for execution when determined appropriate by the NOAA forecasters. The result is an approach that can be used to provide a flexible, yet autonomous SXI capable of meeting both arbitrary forecasting requirements, and operating within the commanding constraints.

Wallace, Shawn

NASA Tech Briefs, February 2010

Topics covered include: Insulation-Testing Cryostat With Lifting Mechanism; Optical Testing of Retroreflectors for Cryogenic Applications; Measuring Cyclic Error in Laser Heterodyne Interferometers; Self-Referencing Hartmann Test for Large-Aperture Telescopes; Measuring a Fiber-Optic Delay Line Using a Mode-Locked Laser; Reconfigurable Hardware for Compressing Hyperspectral Image Data; Spatio-Temporal Equalizer for a Receiving-Antenna Feed Array; High-Speed Ring Bus; Nanoionics-Based Switches for Radio-Frequency Applications; Lunar Dust-Tolerant Electrical Connector; Compact, Reliable EEPROM Controller; Quad-Chip Double-Balanced Frequency Tripler; Ka-Band Waveguide Two-Way Hybrid Combiner for MMIC Amplifiers; Radiation-Hardened Solid-State Drive; Use of Nanofibers to Strengthen Hydrogels of Silica, Other Oxides, and Aerogels; Two Concepts for Deployable Trusses; Concentric Nested Toroidal Inflatable Structures; Investigating Dynamics of Eccentricity in Turbomachines; Improved Low-Temperature Performance of Li-Ion Cells Using New Electrolytes; Integrity Monitoring of Mercury Discharge Lamps; White-Light Phase-Conjugate Mirrors as Distortion Correctors; Biasable, Balanced, Fundamental Submillimeter Monolithic Membrane Mixer; ICER-3D Hyperspectral Image Compression Software; and Context Modeler for Wavelet Compression of Spectral Hyperspectral Images.

Source record

Recognition and characterization of hierarchical interstellar structure. II - Structure tree statistics

A new method of image analysis is described, in which images partitioned into 'clouds' are represented by simplified skeleton images, called structure trees, that preserve the spatial relations of the component clouds while disregarding information concerning their sizes and shapes. The method can be used to discriminate between images of projected hierarchical (multiply nested) and random three-dimensional simulated collections of clouds constructed on the basis of observed interstellar properties, and even intermediate systems formed by combining random and hierarchical simulations. For a given structure type, the method can distinguish between different subclasses of models with different parameters and reliably estimate their hierarchical parameters: average number of children per parent, scale reduction factor per level of hierarchy, density contrast, and number of resolved levels. An application to a column density image of the Taurus complex constructed from IRAS data is given. Moderately strong evidence for a hierarchical structural component is found, and parameters of the hierarchy, as well as the average volume filling factor and mass efficiency of fragmentation per level of hierarchy, are estimated. The existence of nested structure contradicts models in which large molecular clouds are supposed to fragment, in a single stage, into roughly stellar-mass cores.

Houlahan, Padraig

Arc structure in Saturn's radio dynamic spectra

It is pointed out that one of the most spectacular findings of the Voyager 1 planetary radio astronomy experiment (PRA) was the discovery of nested arc-like structures in the dynamic spectra of Jupiter's decametric emission. These arcs have curvature in either a direction towards increasing or decreasing time. Similar arc structures are also evident in Saturn kilometric radiation. These structures appear superimposed on the strong intensity modulation which is controlled by the rotation of the planet and on fast and narrow band fluctuations which give a very large variability to the PRA observations on a 6-s, 20-kHz scale. The characteristics of the arcs are examined and compared with the arc structure in Jupiter. The similarities between Saturn's and Jupiter's arc structures are found to imply that they are probably due to the same physical mechanism.

Boischot, A.

Symmetry breaking forms split-off flat bands in quantum oxides controlling metal versus insulator phases

The crystal structure used as input to electronic structure calculation of conventionally bonded solids consists primarily of the standard crystallographic degrees of freedom. Quantum solids sometimes have additional microscopic degrees of freedom (m-DOF) nested within the crystallographic structure. These might include local motifs including positional (Peierls dimers, deformed octahedra, Jahn-Teller distortions), magnetic (local moment configurations) and dipolar (local ferroelectric configurations). Such motifs can be observed experimentally via local probes that avoid averaging, and theoretically as distinct total energy lowering features relative to more simplified “average crystallographic structures”. Here we examine the ability of electronic structure methods independent of strong correlation physics to explain the broad phenomenology of metal-insulator selectivity in quantum oxides by energy-lowering symmetry breaking. We do this by avoiding the restriction of considering only (i) electron-electron interactions in a fixed unresponsive lattice—as done in Mott strong correlation explanations—allowing, however, (ii) local positional and magnetic motifs that coexist within a crystallographic landscape. We find in a broad range of quantum oxides with different symmetry breaking modes the formation of split-off flat bands that can also control metallic versus insulating characteristics. The split-off band effect is common to magnetic and non-magnetic materials, including both binary and ternary oxides. One finds that when such local symmetry breaking motifs are considered in mean-field-like (e.g. density functional theory) electronic structure calculations of quantum oxides, they explain many of the observed trends in metal vs insulator phases discussed otherwise in prior literature via strong correlation in symmetry unbroken view.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

Thin Films and Inflatable Applications in Exploration Habitat Structures

NASA's vision to return to the Moon and then extend human exploration to Mars will benefit from human habitat technology development using new and creative applications of polymer materials and concepts. Thin Film and Inflatable (TFVI) materials are particularly interesting for exploration applications due to their light weight and low volume. Whereas TF/I materials can be launched and carried from Earth to multiple and distant exploration sites without the constraints of upmass limitations, eventually, with recycling and reclamation efforts, these materials may be developed using in-situ resources. These materials can be useful for fabricating, patching and repairing vehicles, replacement parts and even habitat structures, as well as for developing stand-alone habitat structure technologies and for nested and integrated applications. TF/Is can also be ideal environmental containment vessels within lunar or Martian regolith walls or as liners inside caves or raw regolith exterior structures for the provisions of atmosphere containment, debris protection and cleanliness. Further, TFOs can be specialized and matured for various and diverse applications. The desired range of applications will require materials specification for such properties as transparency, elasticity, thermal conductivity, mechanical strength, heat capacity, chemical resistance, and permeability. This paper will discuss Marshall Space Flight Center's plans to analyze and prioritize TF/I materials properties and classifications and to develop applications for these highly desirable materials in human habitat construction projects on the Moon and Mars.

Frazier, Donald O.

An Overview of the XRT Observations for the September 10 2017 X Flare

The September 10 2017 X8 flare was one of the biggest of the current solar cycle, and it was also incredibly well observed. This presentation will review the available XRT data for this flare. XRT observed the initial flux rope eruption, which was also well observed by AIA and SUVI. XRT data is missing for some of the impulsive phase of the flare, but the late phase shows some very interesting features. There is some nice XRT imaging of a plasma sheet above cusp-shaped loops between 16:47 and 18:39 UT. After 18:40 UT, a double loop structure becomes apparent, with a more rounded loop nested within a larger, cusp-shaped structure. The flare loops continue to grow, and at around 1 UT on September 11, supra-arcade down flows and shrinking loops become visible. There is also interesting data in the late phase of this flare from RHESSI and the Expanded Owens Valley Solar Array (EOVSA).

Reeves, Kathy

An embedded grid formulation applied to delta wings

An embedded grid algorithm for the Euler and/or Navier-Stokes equations is developed and applied to delta wings at high angles of attack in low speed flow. The Navier-Stokes code is an implicit, finite volume algorithm, using flux difference splitting for the convective and pressure terms and central differencing for the viscous and heat transfer terms. Calculations are compared with detailed experimental results over an angle of attack range up to and beyond the maximum lift coefficient, corresponding to vortex breakdown at the trailing edge, for a delta wing nominally of unit aspect ratio. The results indicate that the overall flowfield, including surface pressures, surface streamlines, and vortex trajectories, can be simulated accurately with the global grid version of the present algorithm. However, comparison of computed velocities and vorticity with experimentally measured off-body values at an angle of attack of 20.5 deg indicates the core region is substantially more diffuse in the computations than that measured with either a five-hole probe or a laser velocimeter. Embedded grids, used to improve the numerical discretization in the core region, are formulated within the framework of the implicit, upwind-biased multi-grid algorithm. Structured levels of local nested refinements are made. Three-dimensional results for both Euler and Navier-Stokes calculations are shown, with up to 3 levels of embedded refinement. The embedding procedure was effective in eliminating a crossflow secondary separation produced in the Euler solutions on coarse grids.

Thomas, James L.

Cellerator: extending a computer algebra system to include biochemical arrows for signal transduction simulations

Cellerator describes single and multi-cellular signal transduction networks (STN) with a compact, optionally palette-driven, arrow-based notation to represent biochemical reactions and transcriptional activation. Multi-compartment systems are represented as graphs with STNs embedded in each node. Interactions include mass-action, enzymatic, allosteric and connectionist models. Reactions are translated into differential equations and can be solved numerically to generate predictive time courses or output as systems of equations that can be read by other programs. Cellerator simulations are fully extensible and portable to any operating system that supports Mathematica, and can be indefinitely nested within larger data structures to produce highly scaleable models.

Non-NASA Center

Free Space Optical Link Utilizing a Modulated Retro-Reflector Intended for Planetary Duplex Communication Links Between an Orbiter and Surface Unit

Presented are simulation and experimental results that provide duplex optical-free space communication links with minimal power and pointing requirements by using a modulated retro-reflector (MRR) for planetary communications. The design is the MRR resides on the surface of a planet or moon, where energy is scarce, while the source of the communication laser resides on an orbiter to achieve satellite-to-ground communications. Also, a simulated scenario using the Mars Reconnaissance Orbiter (MRO) is provided for real world potential results. The information sent through this communication path can range from raw scientific data to multimedia files such as videos and pictures. Bidirectional communications is established with the MRR by using a nested pulse position modulation (PPM) structure. This modulation scheme is then evaluated for its validity in a proof-of-concept experiment. Initial results indicate a promising return-link performance of at least 300 kbps in the nested arrangement.

Booth, Stephanie