GPU accelerated algorithms for computing matrix function vector products with applications to exponential integrators and fractional diffusion

The efficient computation of matrix function vector products has become an important area of research in recent times, driven in particular by two important applications: the numerical solution of fractional partial differential equations and the integration of large systems of ordinary differential equations. In this work we consider a problem that combines these two applications, in the form of a numerical solution algorithm for fractional reaction diffusion equations that after spatial discretisation, is advanced in time using the exponential Euler method. We focus on the efficient implementation of the algorithm on Graphics Processing Units (GPU), as we wish to make use of the increased computational power available with this hardware. We compute the matrix function vector products using the contour integration method in [N. Hale, N. Higham, and L. Trefethen. Computing Aα, log(A), and related matrix functions by contour integrals. SIAM J. Numer. Anal., 46(5):2505–2523, 2008]. Multiple levels of preconditioning are applied to reduce the GPU memory footprint and to further accelerate convergence. We also derive an error bound for the convergence of the contour integral method that allows us to pre-determine the appropriate number of quadrature points. Results are presented that demonstrate the effectiveness of the method for large two-dimensional problems, showing a speedup of more than an order of magnitude compared to a CPU-only implementation.

Characteristics and alteration origins of matrix minerals in volcaniclastic kimberlite of the Muskox pipe (Nunavut, Canada)

The matrix of volcaniclastic kimberlite (VK) from the Muskox pipe (Northern Slave Province, Nunavut, Canada) is interpreted to represent an overprint of an original clastic matrix. Muskox VK is subdivided into three different matrix mineral assemblages that reflect differences in the proportions of original primary matrix constituents, temperature of formation and nature of the altering fluids. Using whole rock X-ray fluorescence (XRF), whole rock X-ray diffraction (XRD), microprobe analyses, back-scatter electron (BSE) imaging, petrography and core logging, we find that most matrix minerals (serpentine, phlogopite, chlorite, saponite, monticellite, Fe-Ti oxides and calcite) lack either primary igneous or primary clastic textures. The mineralogy and textures are most consistent with formation through alteration overprinting of an original clastic matrix that form by retrograde reactions as the deposit cools, or, in the case of calcite, by precipitation from Ca-bearing fluids into a secondary porosity. The first mineral assemblage consists largely of serpentine, phlogopite, calcite, Fe-Ti oxides and monticellite and occurs in VK with relatively fresh framework clasts. Alteration reactions, driven by deuteric fluids derived from the juvenile constituents, promote the crystallisation of minerals that indicate relatively high temperatures of formation (> 400 °C). Lower-temperature minerals are not present because permeability was occluded before the deposit cooled to low temperatures, thus shielding the facies from further interaction with fluids. The other two matrix mineral assemblages consist largely of serpentine, phlogopite, calcite, +/- diopside, and +/- chlorite. They form in VK that contains more country rock, which may have caused the deposit to be cooler upon emplacement. Most framework components are completely altered, suggesting that larger volumes of fluids drove the alteration reactions. These fluids were likely of meteoric provenance and became heated by the volcaniclastic debris when they percolated into the VK infill. Most alteration reactions ceased at temperatures > 200 °C, as indicated by the absence or paucity of lower-temperature phases in most samples, such as saponite. Recognition that Muskox VK contains an original clastic matrix is a necessary first step for evaluating the textural configuration, which is important for reconstructing the physical processes responsible for the formation of the deposit.

Hierarchical clustering of the genetic connectivity matrix reveals the network topology of gene action on brain microstructure: An N=531 twin study

Genetic correlation (rg) analysis determines how much of the correlation between two measures is due to common genetic influences. In an analysis of 4 Tesla diffusion tensor images (DTI) from 531 healthy young adult twins and their siblings, we generalized the concept of genetic correlation to determine common genetic influences on white matter integrity, measured by fractional anisotropy (FA), at all points of the brain, yielding an NxN genetic correlation matrix rg(x,y) between FA values at all pairs of voxels in the brain. With hierarchical clustering, we identified brain regions with relatively homogeneous genetic determinants, to boost the power to identify causal single nucleotide polymorphisms (SNP). We applied genome-wide association (GWA) to assess associations between 529,497 SNPs and FA in clusters defined by hubs of the clustered genetic correlation matrix. We identified a network of genes, with a scale-free topology, that influences white matter integrity over multiple brain regions.

Scoring rules and abnormally low bids criteria in construction tenders: A taxonomic review

In the global construction context, the Best Value or Most Economically Advantageous Tender is becoming a widespread approach for contractor selection, as an alternative to other traditional awarding criteria such as the Lowest Price. In these multi-attribute tenders, the owner or auctioneer solicits proposals containing both a price bid and additional technical features. Once the proposals are received, each bidder's price bid is given an economic score according to a scoring rule, generally called an Economic Scoring Formula (ESF) and a technical score according to pre-specified criteria. Eventually, the contract is awarded to the bidder with the highest weighted overall score (economic + technical). However, Economic Scoring Formula selection by auctioneers is invariably and paradoxically a highly intuitive process in practice, involving few theoretical or empirical considerations, despite having being considered traditionally and mistakenly as objective, due to its mathematical nature. This paper provides a taxonomic classification of a wide variety of ESF and Abnormally Low Bid Criteria (ALBC) gathered in several countries with different tendering approaches. Practical implications concern the optimal design of price scoring rules in construction contract tenders, as well as future analyses of the effects of ESF and ALBC on competitive bidding behaviour.

Multiple alignment and sorting of peptides derived from phage-displayed random peptide libraries with polyclonal sera allows discrimination of relevant phagotopes

Biopanning of phage-displayed random peptide libraries is a powerful technique for identifying peptides that mimic epitopes (mimotopes) for monoclonal antibodies (mAbs). However, peptides derived using polyclonal antisera may represent epitopes for a diverse range of antibodies. Hence following screening of phage libraries with polyclonal antisera, including autoimmune disease sera, a procedure is required to distinguish relevant from irrelevant phagotopes. We therefore applied the multiple sequence alignment algorithm PILEUP together with a matrix for scoring amino acid substitutions based on physicochemical properties to generate guide trees depicting relatedness of selected peptides. A random heptapeptide library was biopanned nine times using no selecting antibodies, immunoglobulin G (IgG) from sera of subjects with autoimmune diseases (primary biliary cirrhosis (PBC) and type 1 diabetes) and three murine ascites fluids that contained mAbs to overlapping epitope(s) on the Ross River Virus envelope protein 2. Peptides randomly sampled from the library were distributed throughout the guide tree of the total set of peptides whilst many of the peptides derived in the absence of selecting antibody aligned to a single cluster. Moreover peptides selected by different sources of IgG aligned to separate clusters, each with a different amino acid motif. These alignments were validated by testing all of the 53 phagotopes derived using IgG from PBC sera for reactivity by capture ELISA with antibodies affinity purified on the E2 subunit of the pyruvate dehydrogenase complex (PDC-E2), the major autoantigen in PBC: only those phagotopes that aligned to PBC-associated clusters were reactive. Hence the multiple sequence alignment procedure discriminates relevant from irrelevant phagotopes and thus a major difficulty with biopanning phage-displayed random peptide libraries with polyclonal antibodies is surmounted.

High threshold of β1 integrin inhibition required to block collagen I-induced membrane type-1 matrix metalloproteinase (MT1-MMP) activation of matrix metalloproteinase 2 (MMP-2)

Background Matrix metalloproteinase-2 (MMP-2) is an endopeptidase that facilitates extracellular matrix remodeling and molecular regulation, and is implicated in tumor metastasis. Type I collagen (Col I) regulates the activation of MMP-2 through both transcriptional and post-transcriptional means; however gaps remain in our understanding of the involvement of collagen-binding ?1 integrins in collagen-stimulated MMP-2 activation. Methods Three ?1 integrin siRNAs were used to elucidate the involvement of ?1 integrins in the Col I-induced MMP-2 activation mechanism. ?1 integrin knockdown was analyzed by quantitative RT-PCR, Western Blot and FACS analysis. Adhesion assay and collagen gel contraction were used to test the biological effects of ?1 integrin abrogation. MMP-2 activation levels were monitored by gelatin zymography. Results All three ?1 integrin siRNAs were efficient at ?1 integrin knockdown and FACS analysis revealed commensurate reductions of integrins ?2 and ?3, which are heterodimeric partners of ?1, but not ?V, which is not. All three ?1 integrin siRNAs inhibited adhesion and collagen gel contraction, however only the siRNA showing the greatest magnitude of ?1 knockdown inhibited Col I-induced MMP-2 activation and reduced the accompanying upregulation of MT1-MMP, suggesting a dose response threshold effect. Re-transfection with codon-swapped ?1 integrin overcame the reduction in MMP-2 activation induced by Col-1, confirming the ?1 integrin target specificity. MMP-2 activation induced by TPA or Concanavalin A (Con A) was not inhibited by ?1 integrin siRNA knockdown. Conclusion Together, the data reveals that strong abrogation of ?1 integrin is required to block MMP-2 activation induced by Col I, which may have implications for the therapeutic targeting of ?1 integrin.

Interpersonal coordination tendencies supporting the creation/prevention of goal scoring opportunities in futsal

Research on 1vs1 sub-phases in team sports has shown how one player coordinates his/her actions with his/her opponent and the location of a target/goal to attain performance objectives. In this study, we extended this approach to analysis of 5vs5 competitive performance in the team sport of futsal to provide a performance analysis framework that explains how players coordinate their actions to create/prevent opportunities to score goals. For this purpose, we recorded all 10 futsal matches of the 2009 Lusophony Games held in Lisbon. We analysed the displacement trajectories of a shooting attacker and marking defender in plays ending in a goal, a goalkeeper's save, and a defender's interception, at four specific moments during performance: (1) assisting attacker's ball reception; (2) moment of passing; (3) shooter's ball reception, and; (4) shot on goal. Statistical analysis showed that when a goal was scored, the defender's angle to the goal and to the attacker tended to decrease, the attacker was able to move to the same distance to the goal alongside the defender, and the attacker was closer to the defender and moving at the same velocity (at least) as the defender. This study identified emergent patterns of coordination between attackers and defenders under key competitive task constraints, such as the location of the goal, which supported successful performance in futsal.

Effect of decellularization on the load-bearing characteristics of articular cartilage matrix

The application of decellularized extracellular matrices to aid tissue regeneration in reconstructive surgery and regenerative medicine has been promising. Several decellularization protocols for removing cellular materials from natural tissues such as heart valves are currently in use. This paper evaluates the feasibility of potential extension of this methodology relative to the desirable properties of load bearing joint tissues such as stiffness, porosity and ability to recover adequately after deformation to facilitate physiological function. Two decellularization protocols, namely: Trypsin and Triton X-100 were evaluated against their effects on bovine articular cartilage, using biomechanical, biochemical and microstructural techniques. These analyses revealed that decellularization with trypsin resulted in severe loss of mechanical stiffness including deleterious collapse of the collagen architecture which in turn significantly compromised the porosity of the construct. In contrast, triton X-100 detergent treatment yielded samples that retain mechanical stiffness relative to that of the normal intact cartilage sample, but the resulting construct contained ruminant cellular constituents. We conclude that both of these common decellularization protocols are inadequate for producing constructs that can serve as effective replacement and scaffolds to regenerate articular joint tissue.

Nano-indentation studies on polymer matrix composites reinforced by few-layer graphene

The mechanical properties of polyvinyl alcohol (PVA) and poly(methyl methacrylate) (PMMA)-matrix composites reinforced by functionalized few-layer graphene (FG) have been evaluated using the nano-indentation technique. A significant increase in both the elastic modulus and hardness is observed with the addition of 0.6 wt% of graphene. The crystallinity of PVA also increases with the addition of FG. This and the good mechanical interaction between the polymer and the FG, which provides better load transfer between the matrix and the fiber, are suggested to be responsible for the observed improvement in mechanical properties of the polymers.

Inverse Sensitivity Analysis of Singular Solutions of FRF matrix in Structural System Identification

The problem of structural damage detection based on measured frequency response functions of the structure in its damaged and undamaged states is considered. A novel procedure that is based on inverse sensitivity of the singular solutions of the system FRF matrix is proposed. The treatment of possibly ill-conditioned set of equations via regularization scheme and questions on spatial incompleteness of measurements are considered. The application of the method in dealing with systems with repeated natural frequencies and (or) packets of closely spaced modes is demonstrated. The relationship between the proposed method and the methods based on inverse sensitivity of eigensolutions and frequency response functions is noted. The numerical examples on a 5-degree of freedom system, a one span free-free beam and a spatially periodic multi-span beam demonstrate the efficacy of the proposed method and its superior performance vis-a-vis methods based on inverse eigensensitivity.

Feasibility of autologous bone marrow mesenchymal stem cell-derived extracellular matrix scaffold for cartilage tissue engineering

Extracellular matrix (ECM) materials are widely used in cartilage tissue engineering. However, the current ECM materials are unsatisfactory for clinical practice as most of them are derived from allogenous or xenogenous tissue. This study was designed to develop a novel autologous ECM scaffold for cartilage tissue engineering. The autologous bone marrow mesenchymal stem cell-derived ECM (aBMSC-dECM) membrane was collected and fabricated into a three-dimensional porous scaffold via cross-linking and freeze-drying techniques. Articular chondrocytes were seeded into the aBMSC-dECM scaffold and atelocollagen scaffold, respectively. An in vitro culture and an in vivo implantation in nude mice model were performed to evaluate the influence on engineered cartilage. The current results showed that the aBMSC-dECM scaffold had a good microstructure and biocompatibility. After 4 weeks in vitro culture, the engineered cartilage in the aBMSC-dECM scaffold group formed thicker cartilage tissue with more homogeneous structure and higher expressions of cartilaginous gene and protein compared with the atelocollagen scaffold group. Furthermore, the engineered cartilage based on the aBMSC-dECM scaffold showed better cartilage formation in terms of volume and homogeneity, cartilage matrix content, and compressive modulus after 3 weeks in vivo implantation. These results indicated that the aBMSC-dECM scaffold could be a successful novel candidate scaffold for cartilage tissue engineering.

Coronary calcium scoring: Calcium location needs to be integrated!

Coronary calcium scoring (CCS) has been a topic of great interest lately. In a large population-based study comprising 6,722 patients, Detrano et al. (1) have effectively shown that CCS can be a strong predictor of incident coronary heart disease among different racial groups. Henneman et al. (2) have, however, reported that CCS does not reliably exclude the presence of (significant) atherosclerosis. This topic is quite controversial as there is significant evidence from Detrano's work that higher CCS is associated with an increased risk of acute coronary events. We think that the location of calcium within the coronary arteries should also be considered. Li et al. (3,4) have shown that the position of the calcium in the plaque is a better determinant of plaque vulnerability than the total calcium load. Using a biomechanical model, predicted maximum stress was found to increase by 47.5% when calcium deposits were located in the thin fibrous cap. The presence of calcium deposits in the lipid core or remote from the fibrous cap resulted in no increase in maximum stress. It was also noted that the presence of calcification within the lipid core may even stabilize the plaque. Integration of calcium location in CCS will, therefore, enable better assessment of severity of atherosclerosis and prediction of future cardiovascular events.

Discussion of “Generalized estimating equations: Notes on the choice of the working correlation matrix”

Objective To discuss generalized estimating equations as an extension of generalized linear models by commenting on the paper of Ziegler and Vens "Generalized Estimating Equations. Notes on the Choice of the Working Correlation Matrix". Methods Inviting an international group of experts to comment on this paper. Results Several perspectives have been taken by the discussants. Econometricians have established parallels to the generalized method of moments (GMM). Statisticians discussed model assumptions and the aspect of missing data Applied statisticians; commented on practical aspects in data analysis. Conclusions In general, careful modeling correlation is encouraged when considering estimation efficiency and other implications, and a comparison of choosing instruments in GMM and generalized estimating equations, (GEE) would be worthwhile. Some theoretical drawbacks of GEE need to be further addressed and require careful analysis of data This particularly applies to the situation when data are missing at random.

On the probability that the determinant of an nxn matrix over a finite field vanishe

An expression is derived for the probability that the determinant of an n x n matrix over a finite field vanishes; from this it is deduced that for a fixed field this probability tends to 1 as n tends to.

Fast matrix transposition computer implementation

Eklundh's (1972) algorithm to transpose a large matrix stored on an external device such as a disc has been programmed and tested. A simple description of computer implementation is given in this note.