Book•
Numerical Analysis
01 Jan 1978-
TL;DR: This report contains a description of the typical topics covered in a two-semester sequence in Numerical Analysis, and describes the accuracy, efficiency and robustness of these algorithms.
Abstract: Introduction. Mathematical approximations have been used since ancient times to estimate solutions, but with the rise of digital computing the field of numerical analysis has become a discipline in its own right. Numerical analysts develop and study algorithms that provide approximate solutions to various types of numerical problems, and they analyze the accuracy, efficiency and robustness of these algorithms. As technology becomes ever more essential for the study of mathematics, learning algorithms that provide approximate solutions to mathematical problems and understanding the accuracy of such approximations becomes increasingly important. This report contains a description of the typical topics covered in a two-semester sequence in Numerical Analysis.
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TL;DR: Bayesian model averaging (BMA) provides a coherent mechanism for ac- counting for this model uncertainty and provides improved out-of- sample predictive performance.
Abstract: Standard statistical practice ignores model uncertainty. Data analysts typically select a model from some class of models and then proceed as if the selected model had generated the data. This approach ignores the uncertainty in model selection, leading to over-confident inferences and decisions that are more risky than one thinks they are. Bayesian model averaging (BMA)provides a coherent mechanism for accounting for this model uncertainty. Several methods for implementing BMA have recently emerged. We discuss these methods and present a number of examples.In these examples, BMA provides improved out-of-sample predictive performance. We also provide a catalogue of currently available BMA software.
3,942 citations
TL;DR: A review of the literature reveals a significant number of early studies on biochar-type materials as soil amendments either for managing pathogens, as inoculant carriers or for manipulative experiments to sorb signaling compounds or toxins as mentioned in this paper.
Abstract: Soil amendment with biochar is evaluated globally as a means to improve soil fertility and to mitigate climate change. However, the effects of biochar on soil biota have received much less attention than its effects on soil chemical properties. A review of the literature reveals a significant number of early studies on biochar-type materials as soil amendments either for managing pathogens, as inoculant carriers or for manipulative experiments to sorb signaling compounds or toxins. However, no studies exist in the soil biologyliterature that recognize the observed largevariations ofbiochar physico-chemical properties. This shortcoming has hampered insight into mechanisms by which biochar influences soil microorganisms, fauna and plant roots. Additional factors limiting meaningful interpretation of many datasets are the clearly demonstrated sorption properties that interfere with standard extraction procedures for soil microbial biomass or enzyme assays, and the confounding effects of varying amounts of minerals. In most studies, microbial biomass has been found to increase as a result of biochar additions, with significant changes in microbial community composition and enzyme activities that may explain biogeochemical effects of biochar on element cycles, plant pathogens, and crop growth. Yet, very little is known about the mechanisms through which biochar affects microbial abundance and community composition. The effects of biochar on soil fauna are even less understood than its effects on microorganisms, apart from several notable studies on earthworms. It is clear, however, that sorption phenomena, pH and physical properties of biochars such as pore structure, surface area and mineral matter play important roles in determining how different biochars affect soil biota. Observations on microbial dynamics lead to the conclusion of a possible improved resource use due to co-location of various resources in and around biochars. Sorption and therebyinactivation of growth-inhibiting substances likelyplaysa rolefor increased abundance of soil biota. No evidence exists so far for direct negative effects of biochars on plant roots. Occasionally observed decreases in abundance of mycorrhizal fungi are likely caused by concomitant increases in nutrient availability,reducing theneedfor symbionts.Inthe shortterm,therelease ofavarietyoforganic molecules from fresh biochar may in some cases be responsible for increases or decreases in abundance and activity of soil biota. A road map for future biochar research must include a systematic appreciation of different biochar-types and basic manipulative experiments that unambiguously identify the interactions between biochar and soil biota.
3,612 citations
Book•
01 Jan 1998
TL;DR: In this article, the authors present techniques from the numerical analysis and applied mathematics literatures and show how to use them in economic analyses, including linear equations, iterative methods, optimization, nonlinear equations, approximation methods, numerical integration and differentiation, and Monte Carlo methods.
Abstract: To harness the full power of computer technology, economists need to use a broad range of mathematical techniques. In this book, Kenneth Judd presents techniques from the numerical analysis and applied mathematics literatures and shows how to use them in economic analyses. The book is divided into five parts. Part I provides a general introduction. Part II presents basics from numerical analysis on R^n, including linear equations, iterative methods, optimization, nonlinear equations, approximation methods, numerical integration and differentiation, and Monte Carlo methods. Part III covers methods for dynamic problems, including finite difference methods, projection methods, and numerical dynamic programming. Part IV covers perturbation and asymptotic solution methods. Finally, Part V covers applications to dynamic equilibrium analysis, including solution methods for perfect foresight models and rational expectation models. A web site contains supplementary material including programs and answers to exercises.
2,880 citations
TL;DR: The paper summarizes the capabilities of the modeling system with respect to evaluating how fisheries and the environment impact ecosystems and presents an overview of the computational aspects of the Ecopath, Ecosim and Ecospace modules as they are implemented in the most recent software version.
1,648 citations
Dissertation•
01 Jan 2002
TL;DR: This thesis presents a theoretical model that can be used to describe the long-term behaviour of the Particle Swarm Optimiser and results are presented to support the theoretical properties predicted by the various models, using synthetic benchmark functions to investigate specific properties.
Abstract: Many scientific, engineering and economic problems involve the optimisation of a set of parameters. These problems include examples like minimising the losses in a power grid by finding the optimal configuration of the components, or training a neural network to recognise images of people's faces. Numerous optimisation algorithms have been proposed to solve these problems, with varying degrees of success. The Particle Swarm Optimiser (PSO) is a relatively new technique that has been empirically shown to perform well on many of these optimisation problems. This thesis presents a theoretical model that can be used to describe the long-term behaviour of the algorithm. An enhanced version of the Particle Swarm Optimiser is constructed and shown to have guaranteed convergence on local minima. This algorithm is extended further, resulting in an algorithm with guaranteed convergence on global minima. A model for constructing cooperative PSO algorithms is developed, resulting in the introduction of two new PSO-based algorithms. Empirical results are presented to support the theoretical properties predicted by the various models, using synthetic benchmark functions to investigate specific properties. The various PSO-based algorithms are then applied to the task of training neural networks, corroborating the results obtained on the synthetic benchmark functions.
1,498 citations
Cites background from "Numerical Analysis"
...In this form it is immediately clear that the trajectory of a particle is analogous to the dampened vibrations observed in a spring-dashpot system [14]....
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