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.

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.

Evolution of multivariant microstructures with anisotropic misfit: A phase field study

We study, in two dimensions, the effect of misfit anisotropy on microstructural evolution during precipitation of an ordered beta phase from a disordered alpha matrix; these phases have, respectively, 2- and 6-fold rotation symmetries. Thus, precipitation produces three orientational variants of beta phase particles, and they have an anisotropic (and crystallographically equivalent) misfit strain with the matrix. The anisotropy in misfit is characterized using a parameter t = epsilon(yy)/epsilon(xx), where epsilon(xx) and epsilon(yy) are the principal components of the misfit strain tensor. Our phase field, simulations show that the morphology of beta phase particles is significantly influenced by 1, the level of misfit anisotropy. Particles are circular in systems with dilatational misfit (t = 1), elongated along the direction of lower principal misfit when 0 < t < 1 and elongated along the invariant direction when - 1 <= t <= 0. In the special case of a pure shear misfit strain (t = - 1), the microstructure exhibits star, wedge and checkerboard patterns; these microstructural features are in agreement with those in Ti-Al-Nb alloys.

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.

Enhanced sensitivity in detection of Kerr rotation by double modulation and time averaging based on Allan variance

Experiments in spintronics necessarily involve the detection of spin polarization. The sensitivity of this detection becomes an important factor to consider when extending the low temperature studies on semiconductor spintronic devices to room temperature, where the spin signal is weaker. In pump-probe experiments, which optically inject and detect spins, the sensitivity is often improved by using a photoelastic modulator (PEM) for lock-in detection. However, spurious signals can arise if diode lasers are used as optical sources in such experiments, along with a PEM. In this work, we eliminated the spurious electromagnetic coupling of the PEM onto the probe diode laser, by the double modulation technique. We also developed a test for spurious modulated interference in the pump-probe signal, due to the PEM. Besides, an order of magnitude enhancement in the sensitivity of detection of spin polarization by Kerr rotation, to 3x10(-8) rad was obtained by using the concept of Allan variance to optimally average the time series data over a period of 416 s. With these improvements, we are able to experimentally demonstrate at room temperature, photoinduced steady-state spin polarization in bulk GaAs. Thus, the advances reported here facilitate the use of diode lasers with a PEM for sensitive pump-probe experiments. They also constitute a step toward detection of spin-injection in Si at room temperature.

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.

A Global Constraint On Relative Rotation To Avoid Lumped Compliant Mechanisms In Topology Optimization

Some of the well known formulations for topology optimization of compliant mechanisms could lead to lumped compliant mechanisms. In lumped compliance, most of the elastic deformation in a mechanism occurs at few points, while rest of the mechanism remains more or less rigid. Such points are referred to as point-flexures. It has been noted in literature that high relative rotation is associated with point-flexures. In literature we also find a formulation of local constraint on relative rotations to avoid lumped compliance. However it is well known that a global constraint is easier to handle than a local constraint, by a numerical optimization algorithm. The current work presents a way of putting global constraint on relative rotations. This constraint is also simpler to implement since it uses linearized rotation at the center of finite-elements, to compute relative rotations. I show the results obtained by using this constraint oil the following benchmark problems - displacement inverter and gripper.

A Jacobian-Based Algorithm for Planning Attitude Maneuvers Using Forward and Reverse Rotations

Algorithms for planning quasistatic attitude maneuvers based on the Jacobian of the forward kinematic mapping of fully-reversed (FR) sequences of rotations are proposed in this paper. An FR sequence of rotations is a series of finite rotations that consists of initial rotations about the axes of a body-fixed coordinate frame and subsequent rotations that undo these initial rotations. Unlike the Jacobian of conventional systems such as a robot manipulator, the Jacobian of the system manipulated through FR rotations is a null matrix at the identity, which leads to a total breakdown of the traditional Jacobian formulation. Therefore, the Jacobian algorithm is reformulated and implemented so as to synthesize an FR sequence for a desired rotational displacement. The Jacobian-based algorithm presented in this paper identifies particular six-rotation FR sequences that synthesize desired orientations. We developed the single-step and the multiple-step Jacobian methods to accomplish a given task using six-rotation FR sequences. The single-step Jacobian method identifies a specific FR sequence for a given desired orientation and the multiple-step Jacobian algorithm synthesizes physically feasible FR rotations on an optimal path. A comparison with existing algorithms verifies the fast convergence ability of the Jacobian-based algorithm. Unlike closed-form solutions to the inverse kinematics problem, the Jacobian-based algorithm determines the most efficient FR sequence that yields a desired rotational displacement through a simple and inexpensive numerical calculation. The procedure presented here is useful for those motion planning problems wherein the Jacobian is singular or null.

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.