3,628 research outputs found
The effect of soil fertility levels on the dry weight and nutrient composition of corn plant parts during the seed-filling period
Corn plants were sampled from two field experiments in 1984 and 1985 to study the effects of N, P, and K fertility levels on the dry weight and nutrient composition of corn plant parts during the seed-filling period. P and K fertility variables represented previously established levels in the soil; N fertility was achieved by applications of urea prior to planting. Selected plant samples at different stages of development were chemically analyzed for several elements;Grain yields ranged from 3350 to 8640 kg/ha in 1984 and from 5640 to 11100 kg/ha in 1985, with the depressed yields in 1984 resulting from late-season moisture stress. Fertilizer N produced much larger increases in the dry weights of all plant parts during the seed-filling period and in final grain yields than did increased levels of P and K. Differences in fertility did not influence the relative proportion of different plant parts or the pattern of dry matter accumulation in the ears;Changes in nutrient concentrations varied for different elements, plant parts and positions on the plants, and with fertility levels. Of the vegetative plant parts, leaves best reflected the nutritional status of the plants. Leaf concentrations of N, P, K, and S at 75% silking in 1985 were below the lower limits of established sufficiency ranges;Fertilizer N increased the concentrations of N, P, S, Mn, Cu, and Zn in the leaves and of N, S, and Fe in the grain, but decreased the concentration of Ca in the grain. Increased soil test P levels increased leaf P, N, and Ca concentrations and grain P concentration, but decreased Zn concentrations in the leaves and grain and Cu concentration in the grain. Higher soil K levels increased K concentration and decreased P, S, Ca, Mg, Mn, and Fe concentrations in the leaves, but did not influence nutrient concentrations in the grain. Differences in nutrient concentrations due to different fertility levels generally persisted in the leaves throughout the seed-filling period and increased in the grain as it developed;Increases in the dry weights of leaves and grain in response to increased fertility were reflected in increased nutrient contents in these parts. Differences in fertility did not markedly influence the amounts of nutrients in the grain during early stages, but increased fertility progressively increased the quantity of nutrients in the grain as it developed
Model Reduction on the Wnt Pathway Leads to Biological Adaptation
Complex systems are an unavoidable problem in the field of biology. One of the ways that scientists have tried to overcome this problem is by building mathematical models—manageable representations designed to look at specific physical phenomena. The Wnt Signaling Pathway is a complex system known to regulate cell-to-cell interactions, play a crucial role in Embryonic Development, and has been implicated in the study of cancer. Typically, the Wnt signal is observed through the behavior of a protein called beta-Catenin (β-Catenin). In 2003, Lee et al. built a model of the Wnt pathway which caused β-Catenin to increase over time. However, in 2010, Jensen et al. built a different model of the Wnt pathway which caused β-Catenin to oscillate over time. This project called for model reduction on the Jensen et al. model to identify the phenomenological parameter combinations that determined features of the Wnt oscillations. The method used to reduce the model is called the Manifold Boundary Approximation Method, which is a geometric, parameter-independent method of reducing the model one parameter at a time. Reduction of the model showed that there were 5 variables and 8 parameters which drove the oscillating behavior of the system. After comparing our results to the Lee et al. reduced model of the Wnt pathway done by student Dane Bjork, a minimal model was constructed which predicted a novel class behavior of the Wnt system: biological adaptation
A Krylov subspace algorithm for evaluating the phi-functions appearing in exponential integrators
We develop an algorithm for computing the solution of a large system of
linear ordinary differential equations (ODEs) with polynomial inhomogeneity.
This is equivalent to computing the action of a certain matrix function on the
vector representing the initial condition. The matrix function is a linear
combination of the matrix exponential and other functions related to the
exponential (the so-called phi-functions). Such computations are the major
computational burden in the implementation of exponential integrators, which
can solve general ODEs. Our approach is to compute the action of the matrix
function by constructing a Krylov subspace using Arnoldi or Lanczos iteration
and projecting the function on this subspace. This is combined with
time-stepping to prevent the Krylov subspace from growing too large. The
algorithm is fully adaptive: it varies both the size of the time steps and the
dimension of the Krylov subspace to reach the required accuracy. We implement
this algorithm in the Matlab function phipm and we give instructions on how to
obtain and use this function. Various numerical experiments show that the phipm
function is often significantly more efficient than the state-of-the-art.Comment: 20 pages, 3 colour figures, code available from
http://www.maths.leeds.ac.uk/~jitse/software.html . v2: Various changes to
improve presentation as suggested by the refere
Batch solution of small PDEs with the OPS DSL
In this paper we discuss the challenges and optimisations opportunities when solving a large number of small, equally sized discretised PDEs on regular grids. We present an extension of the OPS (Oxford Parallel library for Structured meshes) embedded Domain Specific Language, and show how support can be added for solving multiple systems, and how OPS makes it easy to deploy a variety of transformations and optimisations. The new capabilities in OPS allow to automatically apply data structure transformations, as well as execution schedule transformations to deliver high performance on a variety of hardware platforms. We evaluate our work on an industrially representative finance simulation on Intel CPUs, as well as NVIDIA GPUs
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