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All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Deflation as a method of variance reduction for estimating the trace of a matrix inverse

Many fields require computing the trace of the inverse of a large, sparse matrix. The typical method used for such computations is the Hutchinson method which is a Monte Carlo (MC) averaging over matrix quadratures. To improve its convergence, several variance reductions techniques have been proposed. In this paper, we study the effects of deflating the near null singular value space. We make two main contributions. First, we analyze the variance of the Hutchinson method as a function of the deflated singular values and vectors. Although this provides good intuition in general, by assuming additionally that the singular vectors are random unitary matrices, we arrive at concise formulas for the deflated variance that include only the variance and mean of the singular values. We make the remarkable observation that deflation may increase variance for Hermitian matrices but not for non-Hermitian ones. This is a rare, if not unique, property where non-Hermitian matrices outperform Hermitian ones. The theory can be used as a model for predicting the benefits of deflation. Second, we use deflation in the context of a large scale application of "disconnected diagrams" in Lattice QCD. On lattices, Hierarchical Probing (HP) has previously provided an order of magnitude of variance reduction over MC by removing "error" from neighboring nodes of increasing distance in the lattice. Although deflation used directly on MC yields a limited improvement of 30% in our problem, when combined with HP they reduce variance by a factor of over 150 compared to MC. For this, we pre-computated 1000 smallest singular values of an ill-conditioned matrix of size 25 million. Furthermore, using PRIMME and a domain-specific Algebraic Multigrid preconditioner, we perform one of the largest eigenvalue computations in Lattice QCD at a fraction of the cost of our trace computation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Influence of Contrast Agent Dilution on Ballon Deflation Time and Visibility During Tracheal Balloon Dilation: A 3D Printed Phantom Study

PurposeTo determine the effect of contrast medium dilution during tracheal balloon dilation on balloon deflation time and visibility using a 3-dimensional (3D) printed airway phantom.Materials and MethodsA comparison study to investigate balloon deflation times and image quality was performed using two contrast agents with different viscosities, i.e., iohexol and ioxithalamate, and six contrast dilutions with a 3D printed airway phantom.ResultsCompared to 1:0 concentration, 3:1, 2:1, 1:1, 1:2, and 1:3, contrast/saline ratios resulted in a 46% (56.2 s), 59.8% (73.1 s), 74.9% (91.6 s), 81.7% (99.8 s), and 83.5% (102 s) reduction for iohexol, respectively, and a 51.8% (54.7 s), 63.8% (67.6 s), 74.7% (79.2 s), 80.5% (85.3 s), and 82.4% (87.4 s) reduction for ioxithalamate, respectively, in the mean balloon deflation time, although at the expense of decreased balloon opacity (3.5, 6.9, 11.1, 12.4, and 13.9%, for iohexol, respectively, and 3.2, 6, 9.6, 10.8, and 12.4%, for ioxithalamate, respectively).ConclusionsUse of a lower viscosity contrast agent and higher contrast dilution is considered to be able to reduce balloon deflation times and then simultaneously decrease visualization of balloons. The rapid balloon deflation time is likely to improve the safe performance of interventional procedures.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2020

Multigrid deflation for Lattice QCD

Computing the trace of the inverse of large matrices is typically addressed through statistical methods. Deflating out the lowest eigenvectors or singular vectors of the matrix reduces the variance of the trace estimator. This work summarizes our efforts to reduce the computational cost of computing the deflation space while achieving the desired variance reduction for Lattice QCD applications. Previous efforts computed the lower part of the singular spectrum of the Dirac operator by using an eigensolver preconditioned with a multigrid linear system solver. Despite the improvement in performance in those applications, as the problem size grows the runtime and storage demands of this approach will eventually dominate the stochastic estimation part of the computation. In this work, we propose to compute the deflation space in one of the following two ways. First, by using an inexact eigensolver on the Hermitian, but maximally indefinite, operator. Second, by exploiting the fact that the multigrid prolongator for this operator is rich in components toward the lower part of the singular spectrum. We show experimentally that the inexact eigensolver can approximate the lower part of the spectrum even for ill-conditioned operators. Also, the deflation based on the multigrid prolongator is more efficient to compute and apply, and, despite its limited ability to approximate the fine level spectrum, it obtains similar variance reduction on the trace estimator as deflating with approximate eigenvectors from the fine level operator.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1991

Critical behavior of two-dimensional vesicles in the deflated regime

The critical behavior of two-dimensional vesicles in the deflated regime is studied analytically using a mapping onto a gauge model, scaling arguments, and exact inequalities. In agreement with the results of earlier studies the critical behavior is governed by a branched-polymer fixed point. The shape of the critical line in the gauge model is deduced in the weak and in the infinitely deflated regime.

Banavar, Jayanth R.↗
NASA NTRS1989

Using deflation in the pole assignment problem with output feedback

A direct algorithm is suggested for the computation of a linear output feedback for a multi input, multi output system such that the resultant closed-loop matrix has eigenvalues that include a specified set of eigenvalues. The algorithm uses deflation based on unitary similarity transformations. Thus researchers hope the algorithm is numerically stable; however, this has not been proven as yet.

Miminis, George↗
NASA NTRS2000

Numerous Unpaired Meteorites Exposed on a Deflating Playa Lake at Lucerne Valley, California

Out of 16 well-characterized 1 to 37 g meteorite specimens recovered from Lucerne Dry Lake (an approximately 3 7 km playa in the southern Mojave Desert of California), there are 9 separate ordinary chondrite finds. The ratio of independent meteorites to total number of specimens (~0.6) is among the highest in the world. This is due to lack of initial deep burial of the small meteorites, significant deflation of the lake exposing falls of individual stones (or small numbers of paired meteorites), and the absence of a large meteorite shower in the region. Playas appear to be excellent candidates for high-yield meteorite-collecting areas.

Rubin, Alan E.↗
NASA NTRS2016

Statistical Analysis of Deflation in Covariance and Resultant Pc Values for AQUA, AURA and TERRA

This presentation will display statistical analysis performed for raw conjunction CDMs received for the EOS Aqua, Aura and Terra satellites within the period of February 2015 through July 2016. The analysis performed indicates a discernable deflation in covariance calculated at the JSpOC after the utilization of the dynamic drag consider parameter was implemented operationally in May 2015. As a result, the overall diminution in the conjunction plane intersection of the primary and secondary objects appears to be leading to reduced probability of collision (Pc) values for these conjunction events. This presentation also displays evidence for this theory with analysis of Pc trending plots using data calculated by the SpaceNav CRMS system.

raw conjunction↗
NASA NTRS1989

Polar cap deflation during magnetospheric substorms

The expanding/contracting polar cap model has been used to simulate DE-2 ion drift data during substorms as determined using the AL index. Of the 39 cases modeled, 57 percent required the opening of a nightside gap which maps to where reconnection occurs in the tail; 75 percent of the 16 recovery phase cases required a nightside gap, while only 29 percent of the 17 expansion phase cases required a nightside gap. On the basis of this result, it is concluded that if a nightside gap implies tail reconnection, then reconnection probably occurs after expansion phase onset and continues throughout most of the recovery phase of a substorm.

Moses, J. J.↗
DOE OSTI2025

Leveraging operator learning to accelerate convergence of the preconditioned conjugate gradient method

We propose a new deflation strategy to accelerate the convergence of the preconditioned conjugate gradient (PCG) method for solving parametric large-scale linear systems of equations. Unlike traditional deflation techniques that rely on eigenvector approximations or recycled Krylov subspaces, we generate the deflation subspaces using operator learning, specifically the Deep Operator Network (DeepONet). To this aim, we introduce two complementary approaches for assembling the deflation operators. The first approach approximates near-null space vectors of the discrete PDE operator using the basis functions learned by the DeepONet. The second approach directly leverages solutions predicted by the DeepONet. To further enhance convergence, we also propose several strategies for prescribing the sparsity pattern of the deflation operator. Here, a comprehensive set of numerical experiments encompassing steady-state, time-dependent, scalar, and vector-valued problems posed on both structured and unstructured geometries is presented and demonstrates the effectiveness of the proposed DeepONet-based deflated PCG method, as well as its generalization across a wide range of model parameters and problem resolutions.

Deflation↗
NASA NTRS1998

Potential Mars Surveyor 2001 Landing Sites: Low-Elevation Cratered "Highlands" in Central and Eastern Sinus Meridiani and Near Amenthes Fossae

The main scientific goal for the Mars Surveyor Program 2001 (MSP 01) landed mission is to collect and characterize 91 rock and 13 soil core samples using an integrated instrument suite onboard the Athena Rover. If possible, these samples will be retrieved and returned to Earth via a MSP 05 or MSP 07 mission. Preliminary engineering constraints for the MSP 01 landing site call for a location that lies between 15 S and 30 N, and below about 2 km elevation (based on Viking-era topography). Desirable landing sites for MSP 01 are to be located "in the ancient highlands where the environmental conditions may have been favorable to the preservation of evidence of possible prebiotic or biotic processes including the emergence (and, potentially, the persistence) of life". We interpret this to mean that the desirable sites include those that have evidence of aqueous sediments that might have been deposited during the Noachian and/or Hesperian Epochs of Mars' history. In addition to the search for subaqueous sedimentary deposits, we took into consideration the fact that the rover, Athena, will need to be able to access these materials. Thus, a site where aeolian deflation has occurred might be desirable because it might expose, in situ, layered sedimentary deposits. Deflated areas, of course, might include potential landing hazards in the form of meterscale buttes and mesas (e.g., Christmas Lake Valley, OR), thus careful study of such sites with high resolution images will be required before a decision is made to land. We have been examining three regions that have potential to be considered for MSP 01 landing sites. This work is based on Viking (VIS, IRTM) and Phobos 2 (Termoskan) observations and should be regarded as preliminary because we believe that the final site selection should also be based upon analysis of Mars Global Surveyor observations that help constrain mineralogy (TES) and local geomorphology (MOC, MOLA). (1) Eastern Sinus Meridiani Region (proposed by K. S. Edgett) Sinus Meridiani is a persistent low-albedo (< 0. 16) region on the martian equator that has been recognized for about 400 years. All of Sinus Meridiani is below the 2 km elevation constraint for MSP 01. The region includes cratered highlands, valley networks, aeolian dunes, and possible aqueous sedimentary deposits. The landing site study region is located in the eastern portion of Sinus Meridiani. It is bounded by latitudes 10 S to 2 N, longitudes 355 W to 345 W, and the elevations are mostly 1-2 km. The center of this area contains a medium-albedo (0.19-0.21), relatively smooth-surfaced deposit that was suggested by Rice to be a lacustrine deposit. Several potential landing areas can be suggested within this region. Based on Viking and Phobos 2 data, the favored sites so far are centered at 7.6 S, 346.9 W and 0.8 S, 349 W. Thermal inertias are 3.2-7.0 x 10(exp -3) cal /sq cm s(exp -0.5)/K; and rock abundances are around 2-6%. The site at 7.6 S, 346.9 W is at the southern end of the smooth, medium-albedo unit that might have a lacustrine origin. At this location, numerous channels appear to have drained toward the smooth unit. Viking images from orbit 747A show this area at about 15 m/pixel ground resolution. The images reveal that aeolian deflation has occurred along the deposit's margins. Bright (i.e., albedo >= 0.21) aeolian dunes are present on the channel floors and in some of the depressions on the smooth unit. The bright, apparently active dunes might consist of material (perhaps lakedeposited sands) that has been eroded from the smooth unit. The site at approximately 0.8 S, 349 W is selected because it offers an opportunity to solve a long-standing puzzle about Mars remote sensing. There are three main "color" units on Mars: "dark red, dark gray, and bright red". This landing site would allow the Athena rover an opportunity to investigate all three materials within close proximity (the best place on Mars to do so). There are no high resolution (better than 100 m/pixel) Viking or Mariner images of this site. (2) Central Sinus Meridiani Region (proposed by K. S. Edgett and T. J. Parker) Central Sinus Meridiani is characterized by two types of surfaces [4]. One is like typical martian cratered highlands elsewhere- there are old valley networks and old impact craters. The other is relatively smooth and flat. These two units are in contact around 3.1 S between 5 W and 4 E longitudes. Valley networks- including one at 6'S, 358 W that rivals the Grand Canyon of Arizona- once drained toward the smooth unit. Edgett and Parker [4] proposed that the smooth unit might consist of sediments laid down in a large Noachian-aged sea/ocean that would have covered much of the northern hemisphere. Schultz and Lutz [I I I suggested that it is a paleopolar layered deposit. Regardless, the smooth unit where it contacts the cratered terrain would make an excellent site for Athena rover to investigate. The site is best seen in Viking high resolution images from orbits 408B (about 30 m/pixel) and 746A (about 12 m/pixel). These images suggest that aeolian deflation has occurred along the margin of the smooth unit, and this deflation has exposed horizontal larrs of material. The elevation is about 0.5 km; thermal inertias are 6.5-8.0 x 10(exp -3) cal /sq cm s(exp -0.5) / K; rock abundances are 2-4%; and the surface is probably sandy with dark drifts and ripples but almost no actual dunes. We suggest a landing around 3.2 S, 3.0 W would test the aqueous sediment hypothesis and provide a potentially smooth surface on which to land. (3) Amenthes Fossae Region (proposed by S. N. Huntwork and K. S. Edgett) The Amenthes Fossae are a series of graben/fissures that are circumferential to the southeast side of Isidis Planitia. These fissures cross a variety of ancient, heavily cratered Noachian terrain and younger, Hesperian and Amazonian terrain. We focused our search on a region 0-15 N, 250 - 270 W. Elevations are -0.5 to 2 km. Depending upon whether Isidis Planitia was ever a water-rich environment, this region might have been influenced by aqueous sedimentation. Valley networks are common, and they drained toward the north and northwest. We focused our work on a set of Viking orbiter high-resolution images, 719A 1-48. These have resolutions 16-24 rri/pixel. We examined images 20-23, centered at 2 N, 258 W. This site, on the plains just southwest of a 42 km-diameter crater, includes a valley network channel, a relatively young crater ejecta deposit, a few buttes composed of presumably ancient, Noachian bedrock, and a "plains" unit. The plains might make an ideal landing surface, except for the presence of some fine-scale ridges (oriented approximately N-S). The ridges are probably yardangs, thus this site offers a place where aeolian deflation has probably exposed some of the layered rock units that comprise the "plains". Thermal inertias are 7.9-8.3 x 10(exp -3) cal/sq cm s(exp -0.5) /K and rock abundances are 10-15%. A rover traverse might include the opportunity to go down to the floor (and sample along the walls) of the valley network channel at 2 N 258.1 W.

Edgett, K. S.↗
DOE OSTI2017

Disconnected Diagrams in Lattice QCD

In this work, we present state-of-the-art numerical methods and their applications for computing a particular class of observables using lattice quantum chromodynamics (Lattice QCD), a discretized version of the fundamental theory of quarks and gluons. These observables require calculating so called \disconnected diagrams" and are important for understanding many aspects of hadron structure, such as the strange content of the proton. We begin by introducing the reader to the key concepts of Lattice QCD and rigorously define the meaning of disconnected diagrams through an example of the Wick contractions of the nucleon. Subsequently, the calculation of observables requiring disconnected diagrams is posed as the computationally challenging problem of finding the trace of the inverse of an incredibly large, sparse matrix. This is followed by a brief primer of numerical sparse matrix techniques that overviews broadly used methods in Lattice QCD and builds the background for the novel algorithm presented in this work. We then introduce singular value deflation as a method to improve convergence of trace estimation and analyze its effects on matrices from a variety of fields, including chemical transport modeling, magnetohydrodynamics, and QCD. Finally, we apply this method to compute observables such as the strange axial charge of the proton and strange sigma terms in light nuclei. The work in this thesis is innovative for four reasons. First, we analyze the effects of deflation with a model that makes qualitative predictions about its effectiveness, taking only the singular value spectrum as input, and compare deflated variance with different types of trace estimator noise. Second, the synergy between probing methods and deflation is investigated both experimentally and theoretically. Third, we use the synergistic combination of deflation and a graph coloring algorithm known as hierarchical probing to conduct a lattice calculation of light disconnected matrix elements of the nucleon at two different values of the lattice spacing. Finally, we employ these algorithms to do a high-precision study of strange sigma terms in light nuclei; to our knowledge this is the first calculation of its kind from Lattice QCD.

Gambhir, Arjun↗
NASA NTRS1992

The age of the meteorite recovery surfaces of Roosevelt County, New Mexico, USA

We have obtained minimum age estimates for the sand units underlying the two largest meteorite deflation surfaces in Roosevelt County, New Mexico, USA, using thermoluminescence dating techniques. The dates obtained ranged from 53.5 (+/- 5.4) to 95.2 (+/- 9.5) ka, and must be considered lower limits for the terrestrial ages of the meteorites found within these specific deflation surfaces. These ages greatly exceed previous measurements from adjacent meteorite-producing deflation basins. We find that Roosevelt County meteorites are probably terrestrial contemporaries of the meteorites found at most accumulation zones in Antarctica. The apparent high meteorite accumulation rate reported for Roosevelt County by Zolensky et al. (1990) is incorrect, as it used an age of 16 ka for all Roosevelt County recovery surfaces. We conclude that the extreme variability of terrestrial ages of the Roosevelt County deflation surfaces effectively precludes their use for calculations of the meteorite accumulation rate at the Earth's surface.

Zolensky, Michael E.↗
NASA NTRS1993

Ablative shielding for hypervelocity projectiles

A hypervelocity projectile shield which includes a hollow semi-flexible housing fabricated from a plastic like, or otherwise transparent membrane which is filled with a fluid (gas or liquid) is presented. The housing has a inlet valve, similar to that on a tire or basketball, to introduce an ablating fluid into the housing. The housing is attached by a Velcro mount or double-sided adhesive tape to the outside surface of a structure to be protected. The housings are arrayed in a side-by-side relationship for complete coverage of the surface to be protected. In use, when a hypervelocity projectile penetrates the outer wall of a housing it is broken up and then the projectile is ablated as it travels through the fluid, much like a meteorite 'burns up' as it enters the earth's atmosphere, and the housing is deflated. The deflated housing can be easily spotted for replacement, even from a distance. Replacement is then accomplished by simply pulling a deflated housing off the structure and installing a new housing.

Rucker, Michelle A.↗
NASA NTRS2003

A One Billion Year Martian Climate Model: The Importance of Seasonally Resolved Polar Caps and the Role of Wind

Wind deflation and deposition are powerful agents of surface change in the present Mars climate regime. Recent studies indicate that, while the distribution of regions of potential deflation (or erosion) and deposition is remarkably insensitive to changes in orbital parameters (obliquity, timing of perihelion passage, etc.), rates of aeolian surface modification may be highly sensitive to these parameters even if the atmospheric mass remains constant. But previous work suggested the atmospheric mass is likely to be sensitive to obliquity, especially if a significant mass of carbon dioxide can be stored in the regolith or deposited in the form of massive polar caps. Deflation and erosion are highly sensitive to surface pressure, so feedback between orbit variations and surface pressure can greatly enhance the sensitivity of aeolian modification rates to orbital parameters. We used statistics derived from a 1 Gyr orbital integration of the spin axis of Mars, coupled with 3D general circulation models (GCMs) at a variety of orbital conditions and pressures, to explore this feedback. We also employed a seasonally resolved 1D energy balance model to illuminate the gross characteristics of the longterm atmospheric evolution, wind erosion and deposition over one billion years. We find that seasonal polar cycles have a critical influence on the ability for the regolith to release CO2 at high obliquities, and find that the atmospheric CO2 actually decreases at high obliquities due to the cooling effect of polar deposits at latitudes where seasonal caps form. At low obliquity, the formation of massive, permanent polar caps depends critically on the values of the frost albedo, A(sub frost), and frost emissivity, E(sub frost). Using our 1D model with values of A(sub frost) = 0.67 and E(sub frost) = 0.55, matched to the NASA Ames GCM results, we find that permanent caps only form at low obliquities (< 10 degrees). Thus, contrary to expectations, the Martian atmospheric pressure is remarkable static over time, and decreases both at high and low obliquity. Also, from our one billion year orbital model, we present new results on the fraction of time Mars is expected to experience periods of high and low obliquity. Finally, using GCM runs at a variety of pressures, we examine the likely role of wind erosion under an early more massive Martian atmosphere.

J C Armstrong↗
NASA NTRS1998

Transfer function analysis of dynamic cerebral autoregulation in humans

To test the hypothesis that spontaneous changes in cerebral blood flow are primarily induced by changes in arterial pressure and that cerebral autoregulation is a frequency-dependent phenomenon, we measured mean arterial pressure in the finger and mean blood flow velocity in the middle cerebral artery (VMCA) during supine rest and acute hypotension induced by thigh cuff deflation in 10 healthy subjects. Transfer function gain, phase, and coherence function between changes in arterial pressure and VMCA were estimated using the Welch method. The impulse response function, calculated as the inverse Fourier transform of this transfer function, enabled the calculation of transient changes in VMCA during acute hypotension, which was compared with the directly measured change in VMCA during thigh cuff deflation. Beat-to-beat changes in VMCA occurred simultaneously with changes in arterial pressure, and the autospectrum of VMCA showed characteristics similar to arterial pressure. Transfer gain increased substantially with increasing frequency from 0.07 to 0.20 Hz in association with a gradual decrease in phase. The coherence function was > 0.5 in the frequency range of 0.07-0.30 Hz and < 0.5 at < 0.07 Hz. Furthermore, the predicted change in VMCA was similar to the measured VMCA during thigh cuff deflation. These data suggest that spontaneous changes in VMCA that occur at the frequency range of 0.07-0.30 Hz are related strongly to changes in arterial pressure and, furthermore, that short-term regulation of cerebral blood flow in response to changes in arterial pressure can be modeled by a transfer function with the quality of a high-pass filter in the frequency range of 0.07-0.30 Hz.

NASA Discipline Cardiopulmonary↗
NASA NTRS1985

Global map of eolian features on Mars

A variety of common eolian features on Mars have been identified from a survey of Mariner 9 and Viking orbiter images, and their regional and global distributions and orientations are discussed. Ten features have been mapped including: light and dark streaks, splotches, barchan and transverse dunes, crescentric and anomalous dunes, yardangs, wind grooves, and deflation pits. The north polar region shows a complex wind regime. Dunes and other ephemeral features reveal winds from the northwest and northeast. In the middle and low northern latitudes, northeasterly winds are the most effective winds. Southeast winds are the effective winds in most southern latitudes. Erosional features in bedrock indicate long-term and perhaps ancient wind trends, whereas depositional features may record relatively more recent winds. Deflation pits in the mantled terrain may contain the best record of both ancient and present-day winds.

Ward, A. W.↗