Modelling and control of nonlinear systems using Gaussian processes with partial model information

Gaussian processes are gaining increasing popularity among the control community, in particular for the modelling of discrete time state space systems. However, it has not been clear how to incorporate model information, in the form of known state relationships, when using a Gaussian process as a predictive model. An obvious example of known prior information is position and velocity related states. Incorporation of such information would be beneficial both computationally and for faster dynamics learning. This paper introduces a method of achieving this, yielding faster dynamics learning and a reduction in computational effort from O(Dn2) to O((D - F)n2) in the prediction stage for a system with D states, F known state relationships and n observations. The effectiveness of the method is demonstrated through its inclusion in the PILCO learning algorithm with application to the swing-up and balance of a torque-limited pendulum and the balancing of a robotic unicycle in simulation. © 2012 IEEE.

Reconstruction of arbitrary biochemical reaction networks: A compressive sensing approach

Reconstruction of biochemical reaction networks (BRN) and genetic regulatory networks (GRN) in particular is a central topic in systems biology which raises crucial theoretical challenges in system identification. Nonlinear Ordinary Differential Equations (ODEs) that involve polynomial and rational functions are typically used to model biochemical reaction networks. Such nonlinear models make the problem of determining the connectivity of biochemical networks from time-series experimental data quite difficult. In this paper, we present a network reconstruction algorithm that can deal with ODE model descriptions containing polynomial and rational functions. Rather than identifying the parameters of linear or nonlinear ODEs characterised by pre-defined equation structures, our methodology allows us to determine the nonlinear ODEs structure together with their associated parameters. To solve the network reconstruction problem, we cast it as a compressive sensing (CS) problem and use sparse Bayesian learning (SBL) algorithms as a computationally efficient and robust way to obtain its solution. © 2012 IEEE.

Global analysis of dynamical decision-making models through local computation around the hidden saddle

Bistable dynamical switches are frequently encountered in mathematical modeling of biological systems because binary decisions are at the core of many cellular processes. Bistable switches present two stable steady-states, each of them corresponding to a distinct decision. In response to a transient signal, the system can flip back and forth between these two stable steady-states, switching between both decisions. Understanding which parameters and states affect this switch between stable states may shed light on the mechanisms underlying the decision-making process. Yet, answering such a question involves analyzing the global dynamical (i.e., transient) behavior of a nonlinear, possibly high dimensional model. In this paper, we show how a local analysis at a particular equilibrium point of bistable systems is highly relevant to understand the global properties of the switching system. The local analysis is performed at the saddle point, an often disregarded equilibrium point of bistable models but which is shown to be a key ruler of the decision-making process. Results are illustrated on three previously published models of biological switches: two models of apoptosis, the programmed cell death and one model of long-term potentiation, a phenomenon underlying synaptic plasticity. © 2012 Trotta et al.

Lyapunov functions for stable cascades and applications to global stabilization

This paper generalizes recent Lyapunov constructions for a cascade of two nonlinear systems, one of which is stable rather than asymptotically stable. A new cross-term construction in the Lyapunov function allows us to replace earlier growth conditions by a necessary boundedness condition. This method is instrumental in the global stabilization of feedforward systems, and new stabilization results are derived from the generalized construction.

Degenerate four-wave mixing based all-optical wavelength conversion in a semiconductor optical amplifier and highly-nonlinear photonic crystal fiber parametric loop mirror

The idler is separated from the co-propagating pump in a degenerate four-wave mixing (DFWM) with a symmetrical parametric loop mirror (PALM), which is composed of two identical SOAs and a 70 m highly-nonlinear photonic crystal fiber (HN-PCF). The signal and pump are coupled into the symmetrical PALM from different ports, respectively. After the DFWM based wavelength conversion (WC) in the clockwise and anticlockwise, the idler exits from the signal port, while the pump outputs from its input port. Therefore, the pump is effectively suppressed in the idler channel without a high-speed tunable filter. Contrast to a traditional PALM, the DFWM based conversion efficiency is increased greatly, and the functions of the amplification and the WC are integrated in the smart SOA and HN-PCF PALM. (C) 2008 Elsevier B.V. All rights reserved.

Decision tree classification of land cover from remotely sensed data

Decision tree classification algorithms have significant potential for land cover mapping problems and have not been tested in detail by the remote sensing community relative to more conventional pattern recognition techniques such as maximum likelihood classification. In this paper, we present several types of decision tree classification algorithms arid evaluate them on three different remote sensing data sets. The decision tree classification algorithms tested include an univariate decision tree, a multivariate decision tree, and a hybrid decision tree capable of including several different types of classification algorithms within a single decision tree structure. Classification accuracies produced by each of these decision tree algorithms are compared with both maximum likelihood and linear discriminant function classifiers. Results from this analysis show that the decision tree algorithms consistently outperform the maximum likelihood and linear discriminant function classifiers in regard to classf — cation accuracy. In particular, the hybrid tree consistently produced the highest classification accuracies for the data sets tested. More generally, the results from this work show that decision trees have several advantages for remote sensing applications by virtue of their relatively simple, explicit, and intuitive classification structure. Further, decision tree algorithms are strictly nonparametric and, therefore, make no assumptions regarding the distribution of input data, and are flexible and robust with respect to nonlinear and noisy relations among input features and class labels.

Comparison of nonlinear and linear PCA on surface wind, surface height, and SST in the South China Sea

We compared nonlinear principal component analysis (NLPCA) with linear principal component analysis (LPCA) with the data of sea surface wind anomalies (SWA), surface height anomalies (SSHA), and sea surface temperature anomalies (SSTA), taken in the South China Sea (SCS) between 1993 and 2003. The SCS monthly data for SWA, SSHA and SSTA (i.e., the anomalies with climatological seasonal cycle removed) were pre-filtered by LPCA, with only three leading modes retained. The first three modes of SWA, SSHA, and SSTA of LPCA explained 86%, 71%, and 94% of the total variance in the original data, respectively. Thus, the three associated time coefficient functions (TCFs) were used as the input data for NLPCA network. The NLPCA was made based on feed-forward neural network models. Compared with classical linear PCA, the first NLPCA mode could explain more variance than linear PCA for the above data. The nonlinearity of SWA and SSHA were stronger in most areas of the SCS. The first mode of the NLPCA on the SWA and SSHA accounted for 67.26% of the variance versus 54.7%, and 60.24% versus 50.43%, respectively for the first LPCA mode. Conversely, the nonlinear SSTA, localized in the northern SCS and southern continental shelf region, resulted in little improvement in the explanation of the variance for the first NLPCA.

Large-Amplitude nonlinear stability results for atmospheric circulations

Douglas, Robert; Cullen, M.J.P., (2002) 'Large-Amplitude nonlinear stability results for atmospheric circulations', The Quarterly Journal of the Royal Meteorological Society 129 pp.1969-1988 RAE2008

Hybrid simulation of ion cyclotron resonance in the solar wind: evolution of velocity distribution functions

Li, Xing; Habbal, S.R., (2005) 'Hybrid simulation of ion cyclotron resonance in the solar wind: evolution of velocity distribution functions', Journal of Geophysical Research 110(A10) pp.A10109 RAE2008

Utility-Based Decision-Making in Wireless Sensor Networks

We consider challenges associated with application domains in which a large number of distributed, networked sensors must perform a sensing task repeatedly over time. For the tasks we consider, there are three significant challenges to address. First, nodes have resource constraints imposed by their finite power supply, which motivates computations that are energy-conserving. Second, for the applications we describe, the utility derived from a sensing task may vary depending on the placement and size of the set of nodes who participate, which often involves complex objective functions for nodes to target. Finally, nodes must attempt to realize these global objectives with only local information. We present a model for such applications, in which we define appropriate global objectives based on utility functions and specify a cost model for energy consumption. Then, for an important class of utility functions, we present distributed algorithms which attempt to maximize the utility derived from the sensor network over its lifetime. The algorithms and experimental results we present enable nodes to adaptively change their roles over time and use dynamic reconfiguration of routes to load balance energy consumption in the network.

Reasoning with imprecise trade-offs in decision making under certainty and uncertainty

In many real world situations, we make decisions in the presence of multiple, often conflicting and non-commensurate objectives. The process of optimizing systematically and simultaneously over a set of objective functions is known as multi-objective optimization. In multi-objective optimization, we have a (possibly exponentially large) set of decisions and each decision has a set of alternatives. Each alternative depends on the state of the world, and is evaluated with respect to a number of criteria. In this thesis, we consider the decision making problems in two scenarios. In the first scenario, the current state of the world, under which the decisions are to be made, is known in advance. In the second scenario, the current state of the world is unknown at the time of making decisions. For decision making under certainty, we consider the framework of multiobjective constraint optimization and focus on extending the algorithms to solve these models to the case where there are additional trade-offs. We focus especially on branch-and-bound algorithms that use a mini-buckets algorithm for generating the upper bound at each node of the search tree (in the context of maximizing values of objectives). Since the size of the guiding upper bound sets can become very large during the search, we introduce efficient methods for reducing these sets, yet still maintaining the upper bound property. We define a formalism for imprecise trade-offs, which allows the decision maker during the elicitation stage, to specify a preference for one multi-objective utility vector over another, and use such preferences to infer other preferences. The induced preference relation then is used to eliminate the dominated utility vectors during the computation. For testing the dominance between multi-objective utility vectors, we present three different approaches. The first is based on a linear programming approach, the second is by use of distance-based algorithm (which uses a measure of the distance between a point and a convex cone); the third approach makes use of a matrix multiplication, which results in much faster dominance checks with respect to the preference relation induced by the trade-offs. Furthermore, we show that our trade-offs approach, which is based on a preference inference technique, can also be given an alternative semantics based on the well known Multi-Attribute Utility Theory. Our comprehensive experimental results on common multi-objective constraint optimization benchmarks demonstrate that the proposed enhancements allow the algorithms to scale up to much larger problems than before. For decision making problems under uncertainty, we describe multi-objective influence diagrams, based on a set of p objectives, where utility values are vectors in Rp, and are typically only partially ordered. These can be solved by a variable elimination algorithm, leading to a set of maximal values of expected utility. If the Pareto ordering is used this set can often be prohibitively large. We consider approximate representations of the Pareto set based on ϵ-coverings, allowing much larger problems to be solved. In addition, we define a method for incorporating user trade-offs, which also greatly improves the efficiency.

Biased group decision-making and the effect of computer-mediated communication: separating the effects of anonymity, voting and blind picking

The influence of communication technology on group decision-making has been examined in many studies. But the findings are inconsistent. Some studies showed a positive effect on decision quality, other studies have shown that communication technology makes the decision even worse. One possible explanation for these different findings could be the use of different Group Decision Support Systems (GDSS) in these studies, with some GDSS better fitting to the given task than others and with different sets of functions. This paper outlines an approach with an information system solely designed to examine the effect of (1) anonymity, (2) voting and (3) blind picking on decision quality, discussion quality and perceived quality of information.

Decision support systems for eco-friendly electronic products

This paper discusses an optimisation based decision support system and methodology for electronic packaging and product design and development which is capable of addressing in efficient manner specified environmental, reliability and cost requirements. A study which focuses on the design of a flip-chip package is presented. Different alternatives for the design of the flip-chip package are considered based on existing options for the applied underfill and volume of solder material used to form the interconnects. Variations in these design input parameters have simultaneous effect on package aspects such as cost, environmental impact and reliability. A decision system for the design of the flip-chip that uses numerical optimisation approach is used to identify the package optimal specification which satisfies the imposed requirements. The reliability aspect of interest is the fatigue of solder joints under thermal cycling. Transient nonlinear finite element analysis (FEA) is used to simulate the thermal fatigue damage in solder joints subject to thermal cycling. Simulation results are manipulated within design of experiments and response surface modelling framework to provide numerical model for reliability which can be used to quantify the package reliability. Assessment of the environmental impact of the package materials is performed by using so called Toxic Index (TI). In this paper we demonstrate the evaluation of the environmental impact only for underfill and lead-free solder materials. This evaluation is based on the amount of material per flip-chip package. Cost is the dominant factor in contemporary flip-chip packaging industry. In the optimisation based decision support system for the design of the flip-chip package, cost of materials which varies as a result of variations in the design parameters is considered.

Numerical solutions of certain nonlinear models in European options on a distributed computing environment

Financial modelling in the area of option pricing involves the understanding of the correlations between asset and movements of buy/sell in order to reduce risk in investment. Such activities depend on financial analysis tools being available to the trader with which he can make rapid and systematic evaluation of buy/sell contracts. In turn, analysis tools rely on fast numerical algorithms for the solution of financial mathematical models. There are many different financial activities apart from shares buy/sell activities. The main aim of this chapter is to discuss a distributed algorithm for the numerical solution of a European option. Both linear and non-linear cases are considered. The algorithm is based on the concept of the Laplace transform and its numerical inverse. The scalability of the algorithm is examined. Numerical tests are used to demonstrate the effectiveness of the algorithm for financial analysis. Time dependent functions for volatility and interest rates are also discussed. Applications of the algorithm to non-linear Black-Scholes equation where the volatility and the interest rate are functions of the option value are included. Some qualitative results of the convergence behaviour of the algorithm is examined. This chapter also examines the various computational issues of the Laplace transformation method in terms of distributed computing. The idea of using a two-level temporal mesh in order to achieve distributed computation along the temporal axis is introduced. Finally, the chapter ends with some conclusions.