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When applying homogenization techniques to problems involving lattice structures, it is necessary to extend certain functions defined on a perforated domain to a simply connected domain. This paper provides general extension operators which preserve bounds on derivatives of order l. Only the special case of honeycomb structures is considered.
We introduce a new class of automated proof methods for the termination of rewriting systems on strings. The basis of all these methods is to show that rewriting preserves regular languages. To this end, letters are annotated with natural numbers, called match heights. If the minimal height of all positions in a redex is h+1 then every position in the reduct will get height h+1. In a match-bounded system, match heights are globally bounded. Using recent results on deleting systems, we prove that rewriting by a match-bounded system preserves regular languages. Hence it is decidable whether a given rewriting system has a given match bound. We also provide a sufficient criterion for the abence of a match-bound. The problem of existence of a match-bound is still open. Match-boundedness for all strings can be used as an automated criterion for termination, for match-bounded systems are terminating. This criterion can be strengthened by requiring match-boundedness only for a restricted set of strings, for instance the set of right hand sides of forward closures.
Annotating a letter by a number, one can record information about its history during a reduction. A string rewriting system is called match-bounded if there is a global upper bound to these numbers. In earlier papers we established match-boundedness as a strong sufficient criterion for both termination and preservation of regular languages. We show now that the string rewriting system whose inverse (left and right hand sides exchanged) is match-bounded, also have exceptional properties, but slightly different ones. Inverse match-bounded systems effectively preserve context-free languages; their sets of normalized strings and their sets of immortal strings are effectively regular. These sets of strings can be used to decide the normalization, the termination and the uniform termination problems of inverse match-bounded systems. We also show that the termination problem is decidable in linear time, and that a certain strong reachability problem is deciable, thus solving two open problems of McNaughton's.
This report considers the problem of intersecting aircraft flows under decentralized conflict avoidance rules. Using an Eulerian standpoint (aircraft flow through a fixed control volume), new air traffic control models and scenarios are defined that enable the study of long-term airspace stability problems. Considering a class of two intersecting aircraft flows, it is shown that airspace stability, defined both in terms of safety and performance, is preserved under decentralized conflict resolution algorithms. Performance bounds are derived for the aircraft flow problem under different maneuver models. Besides analytical approaches, numerical examples are presented to test the theoretical results, as well as to generate some insight about the structure of the traffic flow after resolution. Considering more than two intersecting aircraft flows, simulations indicate that flow stability may not be guaranteed under simple conflict avoidance rules. Finally, a comparison is made with centralized strategies to conflict resolution.
Independent checkpointing allows maximum process autonomy but suffers from potential domino effects. Coordinated checkpointing eliminates the domino effect by sacrificing a certain degree of process autonomy. In this paper, we propose the technique of lazy checkpoint coordination which preserves process autonomy while employing communication-induced checkpoint coordination for bounding rollback propagation. The introduction of the notion of laziness allows a flexible trade-off between the cost for checkpoint coordination and the average rollback distance. Worst-case overhead analysis provides a means for estimating the extra checkpoint overhead. Communication trace-driven simulation for several parallel programs is used to evaluate the benefits of the proposed scheme for real applications.
Independent checkpointing allows maximum process autonomy but suffers from potential domino effects. Coordinated checkpointing eliminates the domino effect by sacrificing a certain degree of process autonomy. In this paper, we propose the technique of lazy checkpoint coordination which preserves process autonomy while employing communication-induced checkpoint coordination for bounding rollback propagation. The introduction of the notion of laziness allows a flexible trade-off between the cost for checkpoint coordination and the average rollback distance. Worst-case overhead analysis provides a means for estimating the extra checkpoint overhead. Communication trace-driven simulation for several parallel programs is used to evaluate the benefits of the proposed scheme for real applications.
The problem of robust stability in linear systems with parametric uncertainties is considered. A method is developed to determine bounds on uncertain parameters in the state-space model of the system, so that stability is preserved. Both continuous- and discrete-time systems are considered. Unlike previous results, the stability bounds are derived in terms of actual parameters instead of their absolute values, and consequently the stable region in the parameter space is not necessarily symmetric with respect to the origin. Furthermore, the uncertain parameters do not have to be linearly independent to each other.
The role of reconstruction in avoiding oscillations in upwind schemes is reexamined, with the aim of providing simple, concise proofs. In one dimension, it is shown that if the reconstruction is any arbitrary function bounded by neighboring cell averages and increasing within a cell for increasing data, the resulting scheme is monotonicity preserving, even though the reconstructed function may have overshoots and undershoots at the cell edges and is in general not a monotone function. In the special case of linear reconstruction, it is shown that merely bounding the reconstruction between neighboring cell averages is sufficient to obtain a monotonicity preservinc,y scheme. In two dimensions, it is shown that some ID TVD limiters applied in each direction result in schemes that are not positivity preserving, i.e. do not give positive updates when the data are positive. A simple proof is given to show that if the reconstruction inside the cell is bounded by the neighboring cell averages (including corner neighbors), then the scheme is positivity preserving. A new limiter that enforces this condition but is not as dissipative as the Minmod limiter is also presented.
To construct Venus' gravity disturbance field (or gravity anomaly) with the spacecraft-observer line of site (LOS) acceleration perturbation data, both a global and a local approach can be used. The global approach, e.g., spherical harmonic coefficients, and the local approach, e.g., the integral operator method, based on geodetic techniques are generally not the same, so that they must be used separately for mapping long wavelength features and short wavelength features. Harmonic spline, as an interpolation and extrapolation technique, is intrinsically flexible to both global and local mapping of a potential field. Theoretically, it preserves the information of the potential field up to the bound by sampling theorem regardless of whether it is global or local mapping, and is never bothered with truncation errors. The improvement of harmonic spline methodology for global mapping is reported. New basis functions, a singular value decomposition (SVD) based modification to Parker & Shure's numerical procedure, and preliminary results are presented.
Various remote sensing agencies of the world have created a data rich environment for research and applications over the last three decades. Especially over the last decade, the volume and variety of data useful for Earth system science have increased quite rapidly. One of the key purposes of collecting these data and generating useful digital products containing derived geophysical parameters is to study the long-term trends in the Earth s behavior. Long-term observational data and derived products are essential for validating results from models that predict the future behavior of the Earth system. Given the significant resources expended in gathering the observational data and developing the derived products, it is important to preserve them for the benefit of future generations of users. Preservation involves maintaining the bits with no loss (or loss within scientifically acceptable bounds) as they move across systems as well as over time, ensuring readability over time, and providing for long-term understandability and repeatability of previously obtained results. In order to ensure long-term understandability and repeatability, it is necessary to identify all items of content that must be preserved and plan for such preservation. This paper discusses the need for a standard enumerating and describing such content items and reports on the progress made by NASA and the Federation of Earth Science Information Partners (ESIP Federation) in the U.S. towards such a standard.
Kerogen is the residue that remains after the minerals and organic compounds have been extracted from a rock using acid and organic solvents, respectively [1]. It is not only the largest organic carbon sink in the geological record but the best-preserved fraction due to its recalcitrance and ability to retain syngenetic source information during deposition [2]. Due to the complex, macromolecular, cross-linked polymeric structure of kerogen, it is difficult to analyse intact, often requiring breakdown into smaller subunits through thermal (pyrolysis) or chemical treatment (chemolysis) [3]. Saline and hypersaline environments host diverse microbial communities, which can trap and bind organic matrices such as cellular components (e.g., extracellular polymeric substances, cell wall, peptidoglycan, sheath material, etc.) with sediments, forming layered, laminated structures called microbial mats. Here we present depth profiles of two hypersaline cores through a microbial mat with differing total salinities. We looked at the composition of organic compounds released from kerogen during high temperature, hydrogen-assisted, pyrolysis to understand the effect of salinity on the composition and timing of their incorporation [4]. Field Site: The Exportadora del Sal S. A. (ESSA) saltern of Guerrero Negro (Baja California Sur, Mexico) lies within a typical sabhka environment adjacent to Laguna Ojo de Liebre. Note the spatial extent of the 13 major ponds of the ESSA system. The GN ponds thrive under well-monitored and stable conditions with steady state accretion and degradation of mat layers (around 0.5–1.4 cm per year). Organic mats typically attain up to 10 cm in thickness, depending on the location, which represents about 60 years of growth since these ponds were established. Sedimentation rate is rapid in these non-lithifying and non-mineralising mats, 1–1.5 cm per year. This environment is ideal for investigating in situ lipid preservation and diagenesis without the influence of constantly changing physical parameters. Methods: P4n5 and P5AB cores were collected as ~9 cm and 6.5 cm fresh cores, respectively, in June 2001 and September 2010, respectively from the ESSA saltern. The P4n5 core (9-9.1% salinity) was taken from Pond 4 near 5 and sub-divided into 10 layers. The P5AB core (11.2% salinity) was taken from Pond 5A near 5B and sub-divided into 8 layers. Lyophilised microbial mat powders were solvent-extracted using a modified Bligh-Dyer method and analysed by gas chromatography-mass spectrometry (GC-MS). Additionally, a subset of layers—layer 4 and layer 7—which represented active biomass and sediment-processed, respectively, were subjected to mild-acid methanolysis. The respective residues from conventional solvent extraction and acid methanolysis were loaded with a molybdenum sulfide catalyst and placed into a stainless-steel reactor. Samples were run on the hydropyrolysis set up (heated to 500 °C with 13-15 MPa of H2 pressure), extracted, and analysed by GC-MS. Results: Molecular profiles from the two ponds were significantly different and reflect the contributions of different photosynthetic and respiratory microbial communities to preserved organic matter. For example, the higher salinity P5AB core showed evidence of greater archaeal inputs (similarly observed in lab culture experiments [5]) as well as potential kerogen-bound carotenoids/carotenoid rearranged products or fragments. A hydrophobic emulsion formed during the acid methanolysis processing of layer 4 from both P4n5 and P5AB and layer 7 of P5AB. Hydropyrolysis of this hydrophobic residues released a greater abundance of polycyclic lipids relative to the pre-extracted control. Implications and Future Work: Catalytic hydropyrolysis of kerogen can rapidly generate abundant saturated pyrolysate products from the bound biomarker pool without altering the structures or stereochemistries of the products [6]. Chemical processing of solvent-extractable residues indicated that cellular matrices such as extracellular polymeric substances (EPS) may play a role in the sequestration of polycyclic lipid biomarkers such as steranes and hopanes. Their higher relative abundance compared to the pre-extracted control in the higher salinity layers and cores preliminarily aligns with this hypothesis, although further experiments are required to confirm this. It has been well-documented that EPS plays an important role in mineralisation, specifically carbonate formation, in microbial ecosystems. EPS can enhance calcium carbonate precipitation by providing diffusion-limited sites that create alkalinity gradients in response to microbial processes [7]. It has been experimentally demonstrated that salinity influences the total amount of EPS (both loosely- and tightly-bound) which increases with increasing salinity [8]. The higher salinity at Guerrero Negro switches the microbial population from filamentous Microcoleus to being dominated by Phormidium, Oscillatoria, and unicellular cyanobacteria. We demonstrated that lipid binding into kerogen via strong covalent linkages occurs at the very earliest stages of sedimentary diagenesis. We are currently investigating the influence of salinity on organic preservation through experimental and modelling approaches. Understanding how key biomarkers transform into preserved organic matter (i.e., from precursor biolipids to bound geolipids) in brine ecosystems will aid the search for organic biosignatures on other planetary bodies, especially Icy Moons and modern Mars.
We give a pattern search adaptation of an augmented Lagrangian method due to Conn, Gould, and Toint. The algorithm proceeds by successive bound constrained minimization of an augmented Lagrangian. In the pattern search adaptation we solve this subproblem approximately using a bound constrained pattern search method. The stopping criterion proposed by Conn, Gould, and Toint for the solution of this subproblem requires explicit knowledge of derivatives. Such information is presumed absent in pattern search methods; however, we show how we can replace this with a stopping criterion based on the pattern size in a way that preserves the convergence properties of the original algorithm. In this way we proceed by successive, inexact, bound constrained minimization without knowing exactly how inexact the minimization is. So far as we know, this is the first provably convergent direct search method for general nonlinear programming.
Analyses of sediments from the vicinity of active methane seeps have uncovered a particular suite of lipid biomarker patterns that characterize methane consuming archaea and their syntrophic, sulfate reducing partners. These isoprenoid biomarkers, largely identified by their anomalously light carbon isotopic signatures, have been a topic of intense research activity and are recorded in numerous methane-rich environments from Holocene to Cenozoic. This phenomenon has implications for depleted kerogens at 2.7 Ga on early Earth (Hinrichs 2002). In contrast, the lipid biosignatures of methane producing archaea are not readily identified through distinct isotopic labels and have received comparably little attention in analyses of archaea in environmental samples. Indeed, environmental analyses generally detect only free archaeal lipids, not the intact, polar molecules found in the membrane of living organisms. As part of the Ames NAI, the 'Early Microbial Ecosystem Research Group' (EMERG) is working to understand microbial processes in the hypersaline cyanobacterial mats growing in the salt evaporation ponds of the Exportadora de Sal at Guerrero Negro, Baja California Sur, Mexico. The aim of this study was to develop methods by which we could identify the organisms responsible for methane generation in this environment. While the ester-bound fatty acids, hopanoids and wax esters provide a means to identify most of the bacterial components of these mats, the archaea which Ere evidently present through genomic assays and the fact of intense methane production (Hoehler et al. 200l), have not been identified through their corresponding lipid signatures. Archaeal core lipids present a number of analytical challenges. The core lipids of methanogens comprise C20, C40 and sometimes C25 isoprenoid chains, linked through ether bonds to glycerol. As well as archaeal (C20), sn-2- and sn-3-hydroxyarchaeol are associated particularly with methylotrophic methanogens. Recently, we have also identified a dihydroxyarchaeol in a hyperthermophilic methanogen (Summons et al. 2002). Additional structural diversity is encoded into the polar head groups that are attached to the glycerol ether cores. The C20 core lipids are readily analyzed by GC-MS as their volatile trimethylsilyl derivatives while compounds with intact polar head groups can only be detected using LC-MS approaches. Our approach was to utilize the alternative of an ether cleavage reagent (BBr3 vs. HI) and a hydride reducing agent to convert all ether lipids to hydrocarbon in order to provide a vertical profile of quantitative information that might be matched to methane fluxes. We have found that while conventional acid hydrolysis and HI treatment will destroy hydroxyarchaeols, molecular information remains intact through use of BBr3 for ether cleavage. This method revealed the presence of traces of biphytane and various ether alkyls associated with some sulfate reducing bacteria within the mat structure. An interesting, and potentially valuable, byproduct of the method utilizing HI was the identification of abundant homohopanoids after superhydride reduction. Evidently present as sulfur-bound diagenetic products these hopanoids are likely cyanobacterial biomarkers in the early stages of diagenetic preservation.
Dark halo craters on grooved terrain on Ganymede represent potential probes of the subsurface geology. These craters are surrounded by a broad, diffuse low albedo annulus, or halo and have apparently lost the bright rim and ray deposits associated with very young craters. The recognition of dark halo craters, almost all greater than 12 km in diameter, indicates that material darker and redder than grooved terrain material forms a stratigraphy horizon at about 1 km depth the present surface of grooved terrain in Uruk Sulcus. This material is most likely downdropped cratered terrain material, which only larger craters have excavated into. This is most consistent with extensional tectonic models for grooved terrain formation whereby the lithosphere is stretched and blocks of ancient cratered terrain are downdropped along bounding faults, and subsequently resurfaced by a shallow layer of relatively clean icy material. Evidence for the preservation of cratered terrain material at shallow depth beneath grooved terrain material poses great difficulties for alternative grooved and smoothed terrain formation mechanisms.
Shape preserving approximations are constructed by interpolating the data with polynomial splines of arbitrary degree. A regularity condition is formulated on the data which insures the existence of such a shape preserving spline, an algorithm is presented for its construction, and the uniform norm of the error is bound which results when the algorithm is used to produce an approximation to a given f epsilon Ca,b.
Molecular biomarkers are the most direct biosignatures of life on early Earth and a key target in the search for life on Mars. Lipid biomarkers are of particular interest given their ability to survive oxidative degradation and record microbial presence and activity of microorganisms that occurred billions of years ago (Eigenbrode, 2008). Environmental conditions that suspend biotic and abiotic degradative processes prior to lithification can lead to enhanced biomolecular preservation over geological time-scales. The hyperarid core of the Atacama Desert in northern Chile offers a unique environment to investigate lipid biomarker taphonomy under extreme and prolonged dryness. We investigated the accumulation and degree of preservation of lipid biomarkers in million-year-old hyperarid soils where primarily abiotic conditions influence their taphonomy. Soils were extracted and free and membrane bound lipids were analyzed across a vertical profile of 2.5 meters in the Yungay hyper-arid core of the Atacama Desert. Due to the extremely low inventory of biomass in Atacama soils, samples were collected by scientists wearing cleanroom suits to minimize anthropogenic contamination during sampling. Fatty acids were found to be well preserved in Yungay soils, and were most abundant in the clay-rich soils at approx.2 m depth (approx.750 ng of fatty acid methyl ester/g of soil). These buried clays layers were fluvially deposited approximately 2 million years ago, and have been excluded from exposure to rainwater and modern surficial processes since their emplacement (Ewing et al., 2008). Monocarboxylic fatty acid, monohydroxy fatty acid, glycerol tetraether, and n-alkane hydrocarbon content was found to change with depth. Lipid biomarker content in deeper soil layers is suggestive of soils having been formed at a time when environmental conditions were capable of supporting active microbial communities and plants. In short, total lipid extracts reveal a remarkable degree of lipid biomarker preservation even in the oldest soils analyzed (ca. 2 Myr) indicating that typical diagenetic processes of lipid destruction are arrested under extreme dryness. This result has implications for the search for molecular biomarkers on Mars, which could have experienced millions to billions of years of extreme hyperaridity.
Conjugate gradient type methods are considered for the solution of large linear systems Ax = b with complex coefficient matrices of the type A = T + i(sigma)I where T is Hermitian and sigma, a real scalar. Three different conjugate gradient type approaches with iterates defined by a minimal residual property, a Galerkin type condition, and an Euclidian error minimization, respectively, are investigated. In particular, numerically stable implementations based on the ideas behind Paige and Saunder's SYMMLQ and MINRES for real symmetric matrices are proposed. Error bounds for all three methods are derived. It is shown how the special shift structure of A can be preserved by using polynomial preconditioning. Results on the optimal choice of the polynomial preconditioner are given. Also, some numerical experiments for matrices arising from finite difference approximations to the complex Helmholtz equation are reported.
An adaptive method in which cruise and nonlinear orbit determination problems can be solved using a single program is presented. It involves singular value decomposition augmented with an extended partial step algorithm. The extended partial step algorithm constrains the size of the correction to the spacecraft state and other solve-for parameters. The correction is controlled by an a priori covariance and a user-supplied bounds parameter. The extended partial step method is an extension of the update portion of the singular value decomposition algorithm. It thus preserves the numerical stability of the singular value decomposition method, while extending the region over which it converges. In linear cases, this method reduces to the singular value decomposition algorithm with the full rank solution. Two examples are presented to illustrate the method's utility.