Matrix-vector multiplication and triangular linear solver using GPGPU for symmetric positive definite matrices derived from elliptic equations

The modern GPUs are well suited for intensive computational tasks and massive parallel computation. Sparse matrix multiplication and linear triangular solver are the most important and heavily used kernels in scientific computation, and several challenges in developing a high performance kernel with the two modules is investigated. The main interest it to solve linear systems derived from the elliptic equations with triangular elements. The resulting linear system has a symmetric positive definite matrix. The sparse matrix is stored in the compressed sparse row (CSR) format. It is proposed a CUDA algorithm to execute the matrix vector multiplication using directly the CSR format. A dependence tree algorithm is used to determine which variables the linear triangular solver can determine in parallel. To increase the number of the parallel threads, a coloring graph algorithm is implemented to reorder the mesh numbering in a pre-processing phase. The proposed method is compared with parallel and serial available libraries. The results show that the proposed method improves the computation cost of the matrix vector multiplication. The pre-processing associated with the triangular solver needs to be executed just once in the proposed method. The conjugate gradient method was implemented and showed similar convergence rate for all the compared methods. The proposed method showed significant smaller execution time.

Effect of microstructure and alloying elements on the resistance of fastener grade steels to hydrogen assisted cracking

Fastener grade steels with varying alloy contents and heat treatments were employed to measure changes in resistance to hydrogen assisted cracking. The testing procedure compared notched tension specimens fractured in air to threshold stress values obtained during hydrogen charging, utilizing a rising step load procedure. Bainitic structures improved resistance by 10-20% compared to tempered martensite structures. Dual phase steels with a tempered martensite matrix and 20% ferrite were more susceptible and notch sensitive. High strength, fully pearlitic structures showed an improvement in resistance. Carbon content, per se, had no effect on the resistance of steel to hydrogen assisted cracking. Chromium caused a deleterious effect but all other alloying elements studied did not cause much change in hydrogen assisted cracking susceptibility.

SPATIAL UNDERSTANDING OF MATRIX INVERSION FOR INVERSE FORCE ESTIMATION

A basic approach to study a NVH problem is to break down the system in three basic elements – source, path and receiver. While the receiver (response) and the transfer path can be measured, it is difficult to measure the source (forces) acting on the system. It becomes necessary to predict these forces to know how they influence the responses. This requires inverting the transfer path. Singular Value Decomposition (SVD) method is used to decompose the transfer path matrix into its principle components which is required for the inversion. The usual approach to force prediction requires rejecting the small singular values obtained during SVD by setting a threshold, as these small values dominate the inverse matrix. This assumption of the threshold may be subjected to rejecting important singular values severely affecting force prediction. The new approach discussed in this report looks at the column space of the transfer path matrix which is the basis for the predicted response. The response participation is an indication of how the small singular values influence the force participation. The ability to accurately reconstruct the response vector is important to establish a confidence in force vector prediction. The goal of this report is to suggest a solution that is mathematically feasible, physically meaningful, and numerically more efficient through examples. This understanding adds new insight to the effects of current code and how to apply algorithms and understanding to new codes.

Identification of two vitamin D response elements in the rat osteopontin gene

Studies to elucidate the function of vitamin D have demonstrated an important role in regulating bone-related cells, including osteoblasts and osteoclasts. A seemingly paradoxical observation is that 1,25(OH)$\sb2$D$\sb3$, the active metabolite of vitamin D, stimulates bone resorption, yet regulates transcription of genes expressed by osteoblasts. One mechanism that could explain these actions is the upregulation of transcription of osteoblast-specific genes. These gene products could then act as effectors to influence osteoclastic activity. We hypothesized that molecular signals could be deposited directly into the mineralized matrix in the form of noncollagenous proteins, such as osteopontin (OPN). The structure, biosynthesis and localization of OPN suggest that it could function to mediate the molecular "cross talk" between osteoblasts and osteoclasts in response to 1,25(OH)$\sb2$D$\sb3$. To begin to address this hypothesis, elucidation of the molecular mechanisms of action involved in the transactivation of OPN by 1,25(OH)$\sb2$D$\sb3$ is essential.^ In the present study, the rat opn gene was isolated and characterized. Functional analysis by transient transfection of the 5$\sp\prime$ flanking sequences of the rat opn gene fused to the luciferase gene demonstrated that OPN is transcriptionally upregulated by 1,25(OH)$\sb2$D$\sb3$, mediated through two vitamin D response elements (VDRE). Both proximal and distal VDREs are structurally similar (two imperfect direct repeats separated by a 3 nucleotide spacer) and bind protein complexes that include the VDR and retinoid-X receptor (RXR). Isolated VDRE expression constructs produce functional activity of equivalent magnitude of responsiveness to 1,25(OH)$\sb2$D$\sb3$. However, expression constructs containing either VDRE and at least 200 bp of 5$\sp\prime$ and 3$\sp\prime$ flanking sequence demonstrated that the distal VDRE produces an amplitude of response significantly higher than the proximal VDRE. We conclude that the transcriptional upregulation of the opn gene by 1,25(OH)$\sb2$D$\sb3$ involves the transactivation of two VDREs, while maximal responsiveness requires interaction of the VDREs with additional cis-elements contained in the 5$\sp\prime$ sequence. ^

Characterization of dermatan sulfate proteoglycan 3 (DSPG3) and cartilage oligomeric matrix protein (COMP)

This dissertation describes the identification and characterization of human dermatan sulfate proteoglycan 3 (DSPG3) and the characterization of the transcriptional regulation of human cartilage oligomeric matrix protein (COMP) in cartilage, ligament, and tendon cells. DSPG3 and COMP are two extracellular matrix proteins. The function of these ECM proteins is unknown.^ DSPG3 was cloned, sequenced, and shown to be expressed in cartilage, ligament, and placenta. DSPG3 was mapped to human chromosome 12q21, and the genomic structure was identified. 1.6 kb of the promoter region has been sequenced, and several putative SOX9 sites were identified as well as 3 TATA sites. Furthermore, an evolutionary tree of the SLRP gene family, which includes DSPG3, is presented.^ The promoter region of COMP was cloned and sequenced. Several putative transcription factor binding sites were identified including multiple AP2 and SP1 sites. Three transcription start sites were found to be located directly downstream of one of the SP1 sites. In addition, the expression of COMP was demonstrated to be higher in tendon than in cartilage and ligament by both Northern and Western blot analysis, and several regions of the COMP promoter were shown to contain cell-specific regulatory elements. Analysis of the proximal 370bp region of the COMP promoter has also identified distinct patterns of nuclear protein binding for the three tissues, and two SP1 sites may play a role in the tissue-specific expression of COMP. ^

LOCALIZATION OF DNA REPAIR FUNCTIONS TO THE NUCLEAR MATRIX

The nucleus of a eukaryotic cell contains both structural and functional elements that contribute to the controlled operation of the cell. In this context, functional components refers to those nuclear constituents that perform metabolic activities such as DNA replication and RNA transcription. Structural nuclear components, designated nuclear matrix, organize the DNA into loops or domains and appear to provide a framework for nuclear DNA organization. However, the boundary between structural and functional components is not clear cut as evinced by reports of associations between metabolic functions and the nuclear matrix. The studies reported here attempt to determine the relationship of another nuclear function, DNA repair, to the nuclear matrix.^ One objective of these studies was to study the initiation of DNA repair by directly measuring the UV-incision activities in human cells and determine the influence of various extractable nuclear components on these activities. The assay for incision activities required the development of a nuclear isolation protocol that produced nuclei with intact DNA; the conformation of the nuclear DNA and its physical characteristics in response to denaturing conditions were determined.^ The nuclei produced with this protocol were then used as substrates for endogenous UV-specific nuclease activities. The isolated nuclei were shown to contain activities that cause breaks in nuclear DNA in response to UV-irradiation. These UV-responsive activities were tightly associated with nuclear components, being unextractable with salt concentration of up to 0.6 M.^ The tight association of the incision activities with salt-extracted nuclei suggested that other repair function might also be associated with salt-stable components of the nucleus. The site of unscheduled DNA synthesis (UDS) was determined in salt-extracted nuclei (nucleoids) using autoradiography and fluorescent microscopy. UDS was found to occur in association with the nuclear matrix following low-doses (2.55 J/M('2)) of ultraviolet light, but the association became looser after higher doses of ultraviolet light (10-30 J/m('2)). ^

(Table 2) Trace element composition of seleceted clast and matrix materials from ODP Site 125-786

Shipboard examination of volcanic and sedimentary strata at Site 786 suggested that at least four types of breccias are present: flow-top breccias, associated with cooling and breakup on the upper surface of lava flows; autobreccias, formed by in-situ alteration at the base of flows; fault-gouge breccias; and true sedimentary breccias derived from weathering and erosion of underlying flows. It is virtually impossible to assess the origin of breccia matrix by textural and mineralogical analyses alone. However, it is fundamental for our understanding of breccia provenance to determine the source component of the matrix material. Whether the matrix is uniquely clastderived can be determined by geochemical fingerprinting. Trace elements that are immobile during weathering and alteration do not change their relative abundances. A contribution to the matrix from any source with an immobile trace element signature different from that of the clasts would appear as a perturbation of the trace element signature of the matrix. Trace element analysis of bulk samples from clasts and matrix material in individual breccia units was undertaken in a fashion similar to that used by Brimhall and Dietrich (1987, doi:10.1016/0016-7037(87)90070-6) in analyzing soil provenance: (1) to help distinguish between sedimentary and volcanic breccias, (2) to determine the degree of mixing and depth of erosion in sedimentary breccias, and (3) to analyze the local provenance of the individual breccia components (matrix and clasts). The following elements were analyzed by X-ray fluorescence (XRF): Rb, Sr, Ba, U, Zr, Cu, Zn, Ti, Cr, and V. Of these elements, Zr and Ti probably exhibit truly immobile behavior (Humphris and Thompson, 1978, doi:10.1016/0016-7037(78)90222-3 ). The remaining elements are useful as a reference for the extent of compositional change during the formation of matrix material (Brimhall and Dietrich, 1987, doi:10.1016/0016-7037(87)90070-6).

Composition of matrix glasses and melt inclusions of fallout tephra from ODP Hole 125-782A

We studied the systematics of Cl, F and H2O in Izu arc front volcanic rocks using basaltic through rhyolitic glass shards and melt inclusions (Izu glasses) from Oligocene to Quaternary distal fallout tephra. These glasses are low-K basalts to rhyolites that are equivalent to the Quaternary lavas of the Izu arc front (Izu VF). Most of the Izu glasses have Cl ~400-4000 ppm and F ~70-400 ppm (normal-group glasses). Rare andesitic melt inclusions (halogen-rich andesites; HRA) have very high abundances of Cl (~6600-8600 ppm) and F (~780-910 ppm), but their contents of incompatible large ion lithophile elements (LILE) are similar to the normal-group glasses. The preeruptive H2O of basalt to andesite melt inclusions in plagioclase is estimated to range from ~2 to ~10 wt% H2O. The Izu magmas should be undersaturated in H2O and the halogens at their preferred levels of crystallization in the middle to lower crust (~3 to ~11 kbar, ~820° to ~1200°C). A substantial portion of the original H2O is lost due to degassing during the final ascent to surface. By contrast, halogen loss is minor, except for loss of Cl from siliceous dacitic and rhyolitic compositions. The behavior of Cl, F and H2O in undegassed melts resembles the fluid mobile LILE (e.g.; K, Rb, Cs, Ba, U, Pb, Li). Most of the Cl (>99%), H2O (>95%) and F (>53%) in the Izu VF melts appear to originate from the subducting slab. At arc front depths, the slab fluid contains Cl = 0.94+/-0.25 wt%, F = 990+/-270 ppm and H2O = 25+/-7 wt%. If the subducting sediment and the altered basaltic crust were the only slab sources, then the subducted Cl appears to be almost entirely recycled at the Izu arc (~77-129%). Conversely, H2O (~13-22% recycled at arc) and F (~4-6% recycled) must be either lost during shallow subduction or retained in the slab to greater depths. If a seawater-impregnated serpentinite layer below the basaltic crust were an additional source of Cl and H2O, the calculated percentage of Cl and H2O recycled at arc would be lower. Extrapolating the Izu data to the total length of global arcs (~37000 km), the global arc outflux of fluid-recycled Cl and H2O at subduction zones amounts to Cl ~2.9-3.8 mln ton/yr and H2O ~70-100 mln ton/yr, respectively - comparable to previous estimates. Further, we obtain a first estimate of global arc outflux of fluid-recycled F of ~0.3-0.4 mln ton/yr. Despite the inherent uncertainties, our results support models suggesting that the slab becomes strongly depleted in Cl and H2O in subduction zones. In contrast, much of the subducted F appears to be returned to the deep mantle, implying efficient fractionation of Cl and H2O from F during the subduction process. However, if slab devolatilization produces slab fluids with high Cl/F (~9.5), slab melting will still produce components with low Cl/F ratios (~0.9), similar to those characteristic of the upper continental crust (Cl/F ~0.3-0.9).

Mineral composition, rare earth elements, and trace elements from samples of the northern Congo deep-sea fan

Authigenic carbonates were collected from methane seeps at Hydrate Hole at 3113 m water depth and Diapir Field at 2417 m water depth on the northern Congo deep-sea fan during RV Meteor cruise M56. The carbonate samples analyzed here are nodules, mainly composed of aragonite and high-Mg calcite. Abundant putative microbial carbonate rods and associated pyrite framboids were recognized within the carbonate matrix. The d13C values of the Hydrate Hole carbonates range from -62.5 permil to -46.3 permil PDB, while the d13C values of the Diapir Field carbonate are somewhat higher, ranging from -40.7 permil to -30.7 permil PDB, indicating that methane is the predominant carbon source at both locations. Relative enrichment of 18O (d18O values as high as 5.2 permil PDB) are probably related to localized destabilization of gas hydrate. The total content of rare earth elements (REE) of 5% HNO3-treated solutions derived from carbonate samples varies from 1.6 ppm to 42.5 ppm. The shale-normalized REE patterns all display positive Ce anomalies (Ce/Ce* > 1.3), revealing that the carbonates precipitated under anoxic conditions. A sample from Hydrate Hole shows a concentric lamination, corresponding to fluctuations in d13C values as well as trace elements contents. These fluctuations are presumed to reflect changes of seepage flux.

Tab. 1: Mineralogical composition and chemical analyses of major and trace elements of Ameghino Formation rocks

As a result of a petrographical, mineralogical and geochemical characterization of the Ameghino Formation mudstones (Upper Jurassic- Lower Cretaceous, Antarctic Peninsula), "epiclastic" radiolaria-rich and mixed (radiolaria-rich + tuff) mudstone types were recognized. Contents of clastic material in the mudstones generally increase with younger paleontological age, but local exceptions to this trend have been found. The anoxic environment of the lower part of the sequence changes to more oxidizing conditions towards the top, in transition to the Hauterivian - Barrêmian conglomerates. Element to element correlations show good agreement with the normal differentiation trends of volcanic (andesite-rhyolite) rocks, suggesting that the overall sequence is mainly volcanic in origin with various grade of reworking. For example, the radiolaria-rich mudstone matrix could have been originated from very fine touffaceous suspensions deposited very slowly after the main fall of the tuffs. However, in the upper part of the sequence, some epiclastic supply is revealed by petrographic evidence and illite crystallinity index. The clay mineral association (illite, chlorite and illite-smectite mixed layers) is mainly of diagenetic origin in the stratigraphically lower sections. Low percentages of expandable layers in the illite-smectite mixed layers, as well as the general mineralogical association, suggest a late mesodiagenetic stage, and together with geological evidence, a relatively deep burial (> 1000 m - probably > 2500 m) and temperatures exceeding 100°C.