Scalable iterative methods for sampling from massive Gaussian random vectors

Sampling from Gaussian Markov random fields (GMRFs), that is multivariate Gaussian ran- dom vectors that are parameterised by the inverse of their covariance matrix, is a fundamental problem in computational statistics. In this paper, we show how we can exploit arbitrarily accu- rate approximations to a GMRF to speed up Krylov subspace sampling methods. We also show that these methods can be used when computing the normalising constant of a large multivariate Gaussian distribution, which is needed for both any likelihood-based inference method. The method we derive is also applicable to other structured Gaussian random vectors and, in particu- lar, we show that when the precision matrix is a perturbation of a (block) circulant matrix, it is still possible to derive O(n log n) sampling schemes.Comment: 17 Pages, 4 Figure

Three-dimensional low Reynolds number flows near biological filtering and protective layers

Mesoscale filtering and protective layers are replete throughout the natural world. Within the body, arrays of extracellular proteins, microvilli, and cilia can act as both protective layers and mechanosensors. For example, blood flow profiles through the endothelial surface layer determine the amount of shear stress felt by the endothelial cells and may alter the rates at which molecules enter and exit the cells. Characterizing the flow profiles through such layers is therefore critical towards understanding the function of such arrays in cell signaling and molecular filtering. External filtering layers are also important to many animals and plants. Trichomes (the hairs or fine outgrowths on plants) can drastically alter both the average wind speed and profile near the leaf's surface, affecting the rates of nutrient and heat exchange. In this paper, dynamically scaled physical models are used to study the flow profiles outside of arrays of cylinders that represent such filtering and protective layers. In addition, numerical simulations using the Immersed Boundary Method are used to resolve the 3D flows within the layers. The experimental and computational results are compared to analytical results obtained by modeling the layer as a homogeneous porous medium with free flow above the layer. The experimental results show that the bulk flow is well described by simple analytical models. The numerical results show that the spatially averaged flow within the layer is well described by the Brinkman model. The numerical results also demonstrate that the flow can be highly 3D with fluid moving into and out of the layer. These effects are not described by the Brinkman model and may be significant for biologically relevant volume fractions. The results of this paper can be used to understand how variations in density and height of such structures can alter shear stresses and bulk flows.Comment: 28 pages, 10 figure

IB2d : a Python and MATLAB implementation of the immersed boundary method

The development of fluid-structure interaction (FSI) software involves trade-offs between ease of use, generality, performance, and cost. Typically there are large learning curves when using low-level software to model the interaction of an elastic structure immersed in a uniform density fluid. Many existing codes are not publicly available, and the commercial software that exists usually requires expensive licenses and may not be as robust or allow the necessary flexibility that in house codes can provide. We present an open source immersed boundary software package, IB2d, with full implementations in both MATLAB and Python, that is capable of running a vast range of biomechanics models and is accessible to scientists who have experience in high-level programming environments. IB2d contains multiple options for constructing material properties of the fiber structure, as well as the advection-diffusion of a chemical gradient, muscle mechanics models, and artificial forcing to drive boundaries with a preferred motion

Agent-based and continuous models of hopper bands for the Australian plague locust: How resource consumption mediates pulse formation and geometry

Locusts are significant agricultural pests. Under favorable environmental conditions flightless juveniles may aggregate into coherent, aligned swarms referred to as hopper bands. These bands are often observed as a propagating wave having a dense front with rapidly decreasing density in the wake. A tantalizing and common observation is that these fronts slow and steepen in the presence of green vegetation. This suggests the collective motion of the band is mediated by resource consumption. Our goal is to model and quantify this effect. We focus on the Australian plague locust, for which excellent field and experimental data is available. Exploiting the alignment of locusts in hopper bands, we concentrate solely on the density variation perpendicular to the front. We develop two models in tandem; an agent-based model that tracks the position of individuals and a partial differential equation model that describes locust density. In both these models, locust are either stationary (and feeding) or moving. Resources decrease with feeding. The rate at which locusts transition between moving and stationary (and vice versa) is enhanced (diminished) by resource abundance. This effect proves essential to the formation, shape, and speed of locust hopper bands in our models. From the biological literature we estimate ranges for the ten input parameters of our models. Sobol sensitivity analysis yields insight into how the band's collective characteristics vary with changes in the input parameters. By examining 4.4 million parameter combinations, we identify biologically consistent parameters that reproduce field observations. We thus demonstrate that resource-dependent behavior can explain the density distribution observed in locust hopper bands. This work suggests that feeding behaviors should be an intrinsic part of future modeling efforts.Comment: 26 pages, 11 figures, 3 tables, 3 appendices with 1 figure; revised Introduction, Sec 1.1, and Discussion; cosmetic changes to figures; fixed typos and made clarifications throughout; results unchange

Extreme oxygen isotope zoning in garnet and zircon from a metachert block in melange reveals metasomatism at the peak of subduction metamorphism

A tectonic block of garnet quartzite in the amphibolite-facies melange of the Catalina Schist (Santa Catalina Island, California, USA) records the metasomatic pre-treatment of high-delta O-18 sediments as they enter the subduction zone. The block is primarily quartz, but contains two generations of garnet that record extreme oxygen isotope disequilibrium and inverse fractionations between garnet cores and matrix quartz. Rare millimeter-scale garnet crystals record prograde cation zoning patterns, whereas more abundant similar to 200-mu m-diameter crystals have the same composition as rims on the larger garnets. Garnets of both generations have high-delta O-18 cores (20.8 parts per thousand-26.3 parts per thousand, Vienna standard mean ocean water) that require an unusually high-delta O-18 protolith and lower-delta O-18, less variable rims (10.0 parts per thousand-11.2 parts per thousand). Matrix quartz values are homogeneous (13.6 parts per thousand). Zircon crystals contain detrital cores (delta O-18 = 4.7 parts per thousand-8.5 parts per thousand, 124.6 + 1.4/-2.9 Ma) with a characteristic igneous trace element composition likely sourced from arc volcanics, surrounded by zircon with metamorphic age (115.1 +/- 2.5 Ma) and trace element compositions that suggest growth in the presence of garnet. Metamorphic zircon decreases in delta O-18 from near-core (24.1 parts per thousand) to rim (12.4 parts per thousand), in equilibrium with zoned garnets. Collectively, the data document the subduction of a mixed high-delta O-18 siliceous ooze and/or volcanic ash protolith reaching temperatures of 550-625 degrees C prior to the nucleation of small garnets without influence from external fluids. Metasomatism was recorded in rims of both garnet and zircon populations as large volumes of broadly homogeneous subduction fluids stripped matrix quartz of its extremely high oxygen isotope signature. Thus, zoned garnet and zircon in high-delta O-18 subducted sediments offer a detailed window into subduction fluids

Consequences of Intraspecific Variation in Seed Dispersal for Plant Demography, Communities, Evolution and Global Change

As the single opportunity for plants to move, seed dispersal has an important impact on plant fitness, species distributions and patterns of biodiversity. However, models that predict dynamics such as risk of extinction, range shifts and biodiversity loss tend to rely on the mean value of parameters and rarely incorporate realistic dispersal mechanisms. By focusing on the mean population value, variation among individuals or variability caused by complex spatial and temporal dynamics is ignored. This calls for increased efforts to understand individual variation in dispersal and integrate it more explicitly into population and community models involving dispersal. However, the sources, magnitude and outcomes of intraspecific variation in dispersal are poorly characterized, limiting our understanding of the role of dispersal in mediating the dynamics of communities and their response to global change. In this manuscript, we synthesize recent research that examines the sources of individual variation in dispersal and emphasize its implications for plant fitness, populations and communities. We argue that this intraspecific variation in seed dispersal does not simply add noise to systems, but, in fact, alters dispersal processes and patterns with consequences for demography, communities, evolution and response to anthropogenic changes. We conclude with recommendations for moving this field of research forward

Consequences of Intraspecific Variation in Seed Dispersal for Plant Demography, Communities, Evolution and Global Change

As the single opportunity for plants to move, seed dispersal has an important impact on plant fitness, species distributions and patterns of biodiversity. However, models that predict dynamics such as risk of extinction, range shifts and biodiversity loss tend to rely on the mean value of parameters and rarely incorporate realistic dispersal mechanisms. By focusing on the mean population value, variation among individuals or variability caused by complex spatial and temporal dynamics is ignored. This calls for increased efforts to understand individual variation in dispersal and integrate it more explicitly into population and community models involving dispersal. However, the sources, magnitude and outcomes of intraspecific variation in dispersal are poorly characterized, limiting our understanding of the role of dispersal in mediating the dynamics of communities and their response to global change. In this manuscript, we synthesize recent research that examines the sources of individual variation in dispersal and emphasize its implications for plant fitness, populations and communities. We argue that this intraspecific variation in seed dispersal does not simply add noise to systems, but, in fact, alters dispersal processes and patterns with consequences for demography, communities, evolution and response to anthropogenic changes. We conclude with recommendations for moving this field of research forward