Accounting for management costs in sensitivity analyses of matrix population models

Traditional sensitivity and elasticity analyses of matrix population models have been used to inform management decisions, but they ignore the economic costs of manipulating vital rates. For example, the growth rate of a population is often most sensitive to changes in adult survival rate, but this does not mean that increasing that rate is the best option for managing the population because it may be much more expensive than other options. To explore how managers should optimize their manipulation of vital rates, we incorporated the cost of changing those rates into matrix population models. We derived analytic expressions for locations in parameter space where managers should shift between management of fecundity and survival, for the balance between fecundity and survival management at those boundaries, and for the allocation of management resources to sustain that optimal balance. For simple matrices, the optimal budget allocation can often be expressed as simple functions of vital rates and the relative costs of changing them. We applied our method to management of the Helmeted Honeyeater (Lichenostomus melanops cassidix; an endangered Australian bird) and the koala (Phascolarctos cinereus) as examples. Our method showed that cost-efficient management of the Helmeted Honeyeater should focus on increasing fecundity via nest protection, whereas optimal koala management should focus on manipulating both fecundity and survival simultaneously. These findings are contrary to the cost-negligent recommendations of elasticity analysis, which would suggest focusing on managing survival in both cases. A further investigation of Helmeted Honeyeater management options, based on an individual-based model incorporating density dependence, spatial structure, and environmental stochasticity, confirmed that fecundity management was the most cost-effective strategy. Our results demonstrate that decisions that ignore economic factors will reduce management efficiency. ©2006 Society for Conservation Biology.

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.

Best individual template selection from deformation tensor minimization

We study the influence of the choice of template in tensor-based morphometry. Using 3D brain MR images from 10 monozygotic twin pairs, we defined a tensor-based distance in the log-Euclidean framework [1] between each image pair in the study. Relative to this metric, twin pairs were found to be closer to each other on average than random pairings, consistent with evidence that brain structure is under strong genetic control. We also computed the intraclass correlation and associated permutation p-value at each voxel for the determinant of the Jacobian matrix of the transformation. The cumulative distribution function (cdf) of the p-values was found at each voxel for each of the templates and compared to the null distribution. Surprisingly, there was very little difference between CDFs of statistics computed from analyses using different templates. As the brain with least log-Euclidean deformation cost, the mean template defined here avoids the blurring caused by creating a synthetic image from a population, and when selected from a large population, avoids bias by being geometrically centered, in a metric that is sensitive enough to anatomical similarity that it can even detect genetic affinity among anatomies.

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.

Improved linear cryptanalysis of reduced-round SIMON-32 and SIMON-48

In this paper we analyse two variants of SIMON family of light-weight block ciphers against variants of linear cryptanalysis and present the best linear cryptanalytic results on these variants of reduced-round SIMON to date. We propose a time-memory trade-off method that finds differential/linear trails for any permutation allowing low Hamming weight differential/linear trails. Our method combines low Hamming weight trails found by the correlation matrix representing the target permutation with heavy Hamming weight trails found using a Mixed Integer Programming model representing the target differential/linear trail. Our method enables us to find a 17-round linear approximation for SIMON-48 which is the best current linear approximation for SIMON-48. Using only the correlation matrix method, we are able to find a 14-round linear approximation for SIMON-32 which is also the current best linear approximation for SIMON-32. The presented linear approximations allow us to mount a 23-round key recovery attack on SIMON-32 and a 24-round Key recovery attack on SIMON-48/96 which are the current best results on SIMON-32 and SIMON-48. In addition we have an attack on 24 rounds of SIMON-32 with marginal complexity.

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.

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.