An affine combination of two LMS adaptive filters - Transient mean-square analysis

This paper studies the statistical behavior of an affine combination of the outputs of two LMS adaptive filters that simultaneously adapt using the same white Gaussian inputs. The purpose of the combination is to obtain an LMS adaptive filter with fast convergence and small steady-state mean-square deviation (MSD). The linear combination studied is a generalization of the convex combination, in which the combination factor $\lambda(n)$ is restricted to the interval $(0,1)$. The viewpoint is taken that each of the two filters produces dependent estimates of the unknown channel. Thus, there exists a sequence of optimal affine combining coefficients which minimizes the MSE. First, the optimal unrealizable affine combiner is studied and provides the best possible performance for this class. Then two new schemes are proposed for practical applications. The mean-square performances are analyzed and validated by Monte Carlo simulations. With proper design, the two practical schemes yield an overall MSD that is usually less than the MSD's of either filter

New Insights into History Matching via Sequential Monte Carlo

The aim of the history matching method is to locate non-implausible regions of the parameter space of complex deterministic or stochastic models by matching model outputs with data. It does this via a series of waves where at each wave an emulator is fitted to a small number of training samples. An implausibility measure is defined which takes into account the closeness of simulated and observed outputs as well as emulator uncertainty. As the waves progress, the emulator becomes more accurate so that training samples are more concentrated on promising regions of the space and poorer parts of the space are rejected with more confidence. Whilst history matching has proved to be useful, existing implementations are not fully automated and some ad-hoc choices are made during the process, which involves user intervention and is time consuming. This occurs especially when the non-implausible region becomes small and it is difficult to sample this space uniformly to generate new training points. In this article we develop a sequential Monte Carlo (SMC) algorithm for implementation which is semi-automated. Our novel SMC approach reveals that the history matching method yields a non-implausible distribution that can be multi-modal, highly irregular and very difficult to sample uniformly. Our SMC approach offers a much more reliable sampling of the non-implausible space, which requires additional computation compared to other approaches used in the literature

Stochastic oscillations of adaptive networks: application to epidemic modelling

Adaptive-network models are typically studied using deterministic differential equations which approximately describe their dynamics. In simulations, however, the discrete nature of the network gives rise to intrinsic noise which can radically alter the system's behaviour. In this article we develop a method to predict the effects of stochasticity in adaptive networks by making use of a pair-based proxy model. The technique is developed in the context of an epidemiological model of a disease spreading over an adaptive network of infectious contact. Our analysis reveals that in this model the structure of the network exhibits stochastic oscillations in response to fluctuations in the disease dynamic.Comment: 11 pages, 4 figure

Solving the G-problems in less than 500 iterations: Improved efficient constrained optimization by surrogate modeling and adaptive parameter control

Constrained optimization of high-dimensional numerical problems plays an important role in many scientific and industrial applications. Function evaluations in many industrial applications are severely limited and no analytical information about objective function and constraint functions is available. For such expensive black-box optimization tasks, the constraint optimization algorithm COBRA was proposed, making use of RBF surrogate modeling for both the objective and the constraint functions. COBRA has shown remarkable success in solving reliably complex benchmark problems in less than 500 function evaluations. Unfortunately, COBRA requires careful adjustment of parameters in order to do so. In this work we present a new self-adjusting algorithm SACOBRA, which is based on COBRA and capable to achieve high-quality results with very few function evaluations and no parameter tuning. It is shown with the help of performance profiles on a set of benchmark problems (G-problems, MOPTA08) that SACOBRA consistently outperforms any COBRA algorithm with fixed parameter setting. We analyze the importance of the several new elements in SACOBRA and find that each element of SACOBRA plays a role to boost up the overall optimization performance. We discuss the reasons behind and get in this way a better understanding of high-quality RBF surrogate modeling

Real options for adaptive decisions in primary industries

Abstract The long term sustainability of Australian crop and livestock farms is threatened with climate change and climate variability. In response, farmers may decide to (1) adjust practices and technologies, (2) change production systems, or (3) transform their industries, for example, by relocating to new geographical areas. Adjustments to existing practices are easy to make relative to changes to production systems or transformations of an industry. Switching between production regimes requires new investments and infrastructure and can leave assets stranded. These changes can be partially or wholly irreversible but hysteresis effects can make switching difficult and mistakes costly to reverse. ‘Real options’ is a framework to structure thinking and analysis of these difficult choices. Previous work has demonstrated how real options can be applied to adaptation, and extends traditional economic analyses of agricultural investment decisions based on net present values to better represent the uncertainty and risks of climate change. This project uses transects across space as analogues for future climate scenarios. We simulate yields from climate data and draw on data from actual farms to estimate a real options model referred to as ‘Real Options for Adaptive Decisions’ (ROADs). We present results for the transformation of wheat dominant cropping systems in South Australia, New South Wales, and Western Australia. We find that farmers’ decisions, as much as a changing climate, determine how agriculture will be transformed. Please cite this report as: Hertzler, G, Sanderson, T, Capon, T, Hayman, P, Kingwell, R, McClintock, A, Crean, J, Randall, A 2013 Will primary producers continue to adjust practices and technologies, change production systems or transform their industry – an application of real options,  National Climate Change Adaptation Research Facility, Gold Coast, pp. 93. The long term sustainability of Australian crop and livestock farms is threatened with climate change and climate variability. In response, farmers may decide to (1) adjust practices and technologies, (2) change production systems, or (3) transform their industries, for example, by relocating to new geographical areas. Adjustments to existing practices are easy to make relative to changes to production systems or transformations of an industry. Switching between production regimes requires new investments and infrastructure and can leave assets stranded. These changes can be partially or wholly irreversible but hysteresis effects can make switching difficult and mistakes costly to reverse. ‘Real options’ is a framework to structure thinking and analysis of these difficult choices. Previous work has demonstrated how real options can be applied to adaptation, and extends traditional economic analyses of agricultural investment decisions based on net present values to better represent the uncertainty and risks of climate change. This project uses transects across space as analogues for future climate scenarios. We simulate yields from climate data and draw on data from actual farms to estimate a real options model referred to as ‘Real Options for Adaptive Decisions’ (ROADs). We present results for the transformation of wheat dominant cropping systems in South Australia, New South Wales, and Western Australia. We find that farmers’ decisions, as much as a changing climate, determine how agriculture will be transformed

Local ensemble transform Kalman filter, a fast non-stationary control law for adaptive optics on ELTs: theoretical aspects and first simulation results

We propose a new algorithm for an adaptive optics system control law, based on the Linear Quadratic Gaussian approach and a Kalman Filter adaptation with localizations. It allows to handle non-stationary behaviors, to obtain performance close to the optimality defined with the residual phase variance minimization criterion, and to reduce the computational burden with an intrinsically parallel implementation on the Extremely Large Telescopes (ELTs).Comment: This paper was published in Optics Express and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/oe/ . Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under la