A dynamical systems framework for intermittent data assimilation

We consider the problem of discrete time filtering (intermittent data assimilation) for differential equation models and discuss methods for its numerical approximation. The focus is on methods based on ensemble/particle techniques and on the ensemble Kalman filter technique in particular. We summarize as well as extend recent work on continuous ensemble Kalman filter formulations, which provide a concise dynamical systems formulation of the combined dynamics-assimilation problem. Possible extensions to fully nonlinear ensemble/particle based filters are also outlined using the framework of optimal transportation theory.

Participatory research approaches in the development of improved management practices in indigenous chickens production systems with smallholder farmers in Kenya

This thesis is concerned with development of improved management practices in indigenous chicken production systems in a research process that includes participatory approaches with smallholder farmers and other stakeholders in Kenya. The research process involved a wide range of activities that included on-station experiments, field surveys, stakeholder consultations in workshops, seminars and visits, and on-farm farmer participatory research to evaluate the effect of some improved management interventions on production performance of indigenous chickens. The participatory research was greatly informed from collective experiences and lessons of the previous activities. The on-station studies focused on hatching, growth and nutritional characteristics of the indigenous chickens. Four research publications from these studies are included in this thesis. Quantitative statistical analyses were applied and they involved use of growth models estimated with non-linear regressions for the growth characteristics, chi-square determinations to investigate differences among different reciprocal crosses of indigenous chickens and general linear models and covariance determination for the nutrition study. The on-station studies brought greater understanding of performance and production characteristics of indigenous chickens and the influence of management practices on these characteristics. The field surveys and stakeholder consultations helped in understanding the overarching issues affecting the productivity of the indigenous chickens systems and their place in the livelihoods of smallholder farmers. These activities created strong networking opportunities with stakeholders from a wide spectrum. The on-farm farmer participatory research involved selection of 200 farmers in five regions followed by training and introduction of interventions on improved management practices which included housing, vaccination, deworming and feed supplementation. Implementation and monitoring was mainly done by individual farmers continuously for close to one and half years. Six quarterly visits to the farms were made by the research team to monitor and provide support for on-going project activities. The data collected has been analysed for 5 consecutive 3-monthly periods. Descriptive and inferential statistics were applied to analyse the data collected involving treatment applications, production characteristics and flock demography characteristics. Out of the 200 farmers initially selected, 173 had records on treatment applications and flock demography characteristics while 127 farmers had records on production characteristics. The demographic analysis with a dissimilarity index of flock size produced 7 distinct farm groups from among the 173 farms. Two of these farm groups were represented in similar numbers in each of the five regions. The research process also involved a number of dissemination and communication strategies that have brought the process and project outcomes into the domain of accessibility by wider readership locally and globally. These include workshops, seminars, field visits and consultations, local and international conferences, electronic conferencing, publications and personal communication via emailing and conventional posting. A number of research and development proposals were also developed based on the knowledge and experiences gained from the research process. The thesis captures the research process activities and outcomes in 8 chapters which include in ascending order – introduction, theoretical concepts underpinning FPR, research methodology and process, on-station research output, FPR descriptive statistical analysis, FPR inferential statistical analysis on production characteristics, FPR demographic analysis and conclusions. Various research approaches both quantitative and qualitative have been applied in the research process indicating the possibilities and importance of combining both systems for greater understanding of issues being studied. In our case, participatory studies of the improved management of indigenous chickens indicates their potential importance as livelihood assets for poor people.

Complex-valued B-spline neural networks for modeling and inverting Hammerstein systems

Many communication signal processing applications involve modelling and inverting complex-valued (CV) Hammerstein systems. We develops a new CV B-spline neural network approach for efficient identification of the CV Hammerstein system and effective inversion of the estimated CV Hammerstein model. Specifically, the CV nonlinear static function in the Hammerstein system is represented using the tensor product from two univariate B-spline neural networks. An efficient alternating least squares estimation method is adopted for identifying the CV linear dynamic model’s coefficients and the CV B-spline neural network’s weights, which yields the closed-form solutions for both the linear dynamic model’s coefficients and the B-spline neural network’s weights, and this estimation process is guaranteed to converge very fast to a unique minimum solution. Furthermore, an accurate inversion of the CV Hammerstein system can readily be obtained using the estimated model. In particular, the inversion of the CV nonlinear static function in the Hammerstein system can be calculated effectively using a Gaussian-Newton algorithm, which naturally incorporates the efficient De Boor algorithm with both the B-spline curve and first order derivative recursions. The effectiveness of our approach is demonstrated using the application to equalisation of Hammerstein channels.

Single-carrier frequency domain equalisation for hammerstein communication systems using complex-valued neural networks

Single-carrier (SC) block transmission with frequency-domain equalisation (FDE) offers a viable transmission technology for combating the adverse effects of long dispersive channels encountered in high-rate broadband wireless communication systems. However, for high bandwidthefficiency and high power-efficiency systems, the channel can generally be modelled by the Hammerstein system that includes the nonlinear distortion effects of the high power amplifier (HPA) at transmitter. For such nonlinear Hammerstein channels, the standard SC-FDE scheme no longer works. This paper advocates a complex-valued (CV) B-spline neural network based nonlinear SC-FDE scheme for Hammerstein channels. Specifically, We model the nonlinear HPA, which represents the CV static nonlinearity of the Hammerstein channel, by a CV B-spline neural network, and we develop two efficient alternating least squares schemes for estimating the parameters of the Hammerstein channel, including both the channel impulse response coefficients and the parameters of the CV B-spline model. We also use another CV B-spline neural network to model the inversion of the nonlinear HPA, and the parameters of this inverting B-spline model can easily be estimated using the standard least squares algorithm based on the pseudo training data obtained as a natural byproduct of the Hammerstein channel identification. Equalisation of the SC Hammerstein channel can then be accomplished by the usual one-tap linear equalisation in frequency domain as well as the inverse B-spline neural network model obtained in time domain. Extensive simulation results are included to demonstrate the effectiveness of our nonlinear SC-FDE scheme for Hammerstein channels.

A study of anticipatory non-autonomous systems

Rhythms are manifested ubiquitously in dynamical biological processes. These fundamental processes which are necessary for the survival of living organisms include metabolism, breathing, heart beat, and, above all, the circadian rhythm coupled to the diurnal cycle. Thus, in mathematical biology, biological processes are often represented as linear or nonlinear oscillators. In the framework of nonlinear and dissipative systems (ie. the flow of energy, substances, or sensory information), they generate stable internal oscillations as a response to environmental input and, in turn, utilise such output as a means of coupling with the environment.

Fractional order and non-linear system identification algorithms for biomedical applications

We discuss the modelling of dielectric responses of amorphous biological samples. Such samples are commonly encountered in impedance spectroscopy studies as well as in UV, IR, optical and THz transient spectroscopy experiments and in pump-probe studies. In many occasions, the samples may display quenched absorption bands. A systems identification framework may be developed to provide parsimonious representations of such responses. To achieve this, it is appropriate to augment the standard models found in the identification literature to incorporate fractional order dynamics. Extensions of models using the forward shift operator, state space models as well as their non-linear Hammerstein-Wiener counterpart models are highlighted. We also discuss the need to extend the theory of electromagnetically excited networks which can account for fractional order behaviour in the non-linear regime by incorporating nonlinear elements to account for the observed non-linearities. The proposed approach leads to the development of a range of new chemometrics tools for biomedical data analysis and classification.

Towards a general theory of extremes for observables of chaotic dynamical systems

In this paper we provide a connection between the geometrical properties of the attractor of a chaotic dynamical system and the distribution of extreme values. We show that the extremes of so-called physical observables are distributed according to the classical generalised Pareto distribution and derive explicit expressions for the scaling and the shape parameter. In particular, we derive that the shape parameter does not depend on the cho- sen observables, but only on the partial dimensions of the invariant measure on the stable, unstable, and neutral manifolds. The shape parameter is negative and is close to zero when high-dimensional systems are considered. This result agrees with what was derived recently using the generalized extreme value approach. Combining the results obtained using such physical observables and the properties of the extremes of distance observables, it is possible to derive estimates of the partial dimensions of the attractor along the stable and the unstable directions of the flow. Moreover, by writing the shape parameter in terms of moments of the extremes of the considered observable and by using linear response theory, we relate the sensitivity to perturbations of the shape parameter to the sensitivity of the moments, of the partial dimensions, and of the Kaplan–Yorke dimension of the attractor. Preliminary numer- ical investigations provide encouraging results on the applicability of the theory presented here. The results presented here do not apply for all combinations of Axiom A systems and observables, but the breakdown seems to be related to very special geometrical configurations.

Nonlinear equalization of Hammerstein OFDM systems

A practical orthogonal frequency-division multiplexing (OFDM) system can generally be modelled by the Hammerstein system that includes the nonlinear distortion effects of the high power amplifier (HPA) at transmitter. In this contribution, we advocate a novel nonlinear equalization scheme for OFDM Hammerstein systems. We model the nonlinear HPA, which represents the static nonlinearity of the OFDM Hammerstein channel, by a B-spline neural network, and we develop a highly effective alternating least squares algorithm for estimating the parameters of the OFDM Hammerstein channel, including channel impulse response coefficients and the parameters of the B-spline model. Moreover, we also use another B-spline neural network to model the inversion of the HPA’s nonlinearity, and the parameters of this inverting B-spline model can easily be estimated using the standard least squares algorithm based on the pseudo training data obtained as a byproduct of the Hammerstein channel identification. Equalization of the OFDM Hammerstein channel can then be accomplished by the usual one-tap linear equalization as well as the inverse B-spline neural network model obtained. The effectiveness of our nonlinear equalization scheme for OFDM Hammerstein channels is demonstrated by simulation results.

Adaptive B-spline neural network based nonlinear equalization for high-order QAM systems with nonlinear transmit high power amplifier

High bandwidth-efficiency quadrature amplitude modulation (QAM) signaling widely adopted in high-rate communication systems suffers from a drawback of high peak-toaverage power ratio, which may cause the nonlinear saturation of the high power amplifier (HPA) at transmitter. Thus, practical high-throughput QAM communication systems exhibit nonlinear and dispersive channel characteristics that must be modeled as a Hammerstein channel. Standard linear equalization becomes inadequate for such Hammerstein communication systems. In this paper, we advocate an adaptive B-Spline neural network based nonlinear equalizer. Specifically, during the training phase, an efficient alternating least squares (LS) scheme is employed to estimate the parameters of the Hammerstein channel, including both the channel impulse response (CIR) coefficients and the parameters of the B-spline neural network that models the HPA’s nonlinearity. In addition, another B-spline neural network is used to model the inversion of the nonlinear HPA, and the parameters of this inverting B-spline model can easily be estimated using the standard LS algorithm based on the pseudo training data obtained as a natural byproduct of the Hammerstein channel identification. Nonlinear equalisation of the Hammerstein channel is then accomplished by the linear equalization based on the estimated CIR as well as the inverse B-spline neural network model. Furthermore, during the data communication phase, the decision-directed LS channel estimation is adopted to track the time-varying CIR. Extensive simulation results demonstrate the effectiveness of our proposed B-Spline neural network based nonlinear equalization scheme.

Anticipatory engineering: anticipation in sensory-motor systems of human

In visual tracking experiments, distributions of the relative phase be-tween target and tracer showed positive relative phase indicating that the tracer precedes the target position. We found a mode transition from the reactive to anticipatory mode. The proposed integrated model provides a framework to understand the antici-patory behaviour of human, focusing on the integration of visual and soma-tosensory information. The time delays in visual processing and somatosensory feedback are explicitly treated in the simultaneous differential equations. The anticipatory behaviour observed in the visual tracking experiments can be ex-plained by the feedforward term of target velocity, internal dynamics, and time delay in somatosensory feedback.

Cardiac protein kinases: the cardiomyocyte kinome and differential kinase expression in human failing hearts

Aims. Protein kinases are potential therapeutic targets for heart failure, but most studies of cardiac protein kinases derive from other systems, an approach that fails to account for specific kinases expressed in the heart and the contractile cardiomyocytes. We aimed to define the cardiomyocyte kinome (i.e. the protein kinases expressed in cardiomyocytes) and identify kinases with altered expression in human failing hearts. Methods and Results. Expression profiling (Affymetrix microarrays) detected >400 protein kinase mRNAs in rat neonatal ventricular myocytes (NVMs) and/or adult ventricular myocytes (AVMs), 32 and 93 of which were significantly upregulated or downregulated (>2-fold), respectively, in AVMs. Data for AGC family members were validated by qPCR. Proteomics analysis identified >180 cardiomyocyte protein kinases, with high relative expression of mitogen-activated protein kinase cascades and other known cardiomyocyte kinases (e.g. CAMKs, cAMP-dependent protein kinase). Other kinases are poorly-investigated (e.g. Slk, Stk24, Oxsr1). Expression of Akt1/2/3, BRaf, ERK1/2, Map2k1, Map3k8, Map4k4, MST1/3, p38-MAPK, PKCδ, Pkn2, Ripk1/2, Tnni3k and Zak was confirmed by immunoblotting. Relative to total protein, Map3k8 and Tnni3k were upregulated in AVMs vs NVMs. Microarray data for human hearts demonstrated variation in kinome expression that may influence responses to kinase inhibitor therapies. Furthermore, some kinases were upregulated (e.g. NRK, JAK2, STK38L) or downregulated (e.g. MAP2K1, IRAK1, STK40) in human failing hearts. Conclusions. This characterization of the spectrum of kinases expressed in cardiomyocytes and the heart (cardiomyocyte and cardiac kinomes) identified novel kinases, some of which are differentially expressed in failing human hearts and could serve as potential therapeutic targets.

Physiological and morphological adaptations of herbaceous perennial legumes allow differential access to sources of varyingly soluble phosphate

The aim of this study was to investigate the capacity of three perennial legume species to access sources of varyingly soluble phosphorus (P) and their associated morphological and physiological adaptations. Two Australian native legumes with pasture potential (Cullen australasicum and Kennedia prostrata) and Medicago sativa cv. SARDI 10 were grown in sand under two P levels (6 and 40 µg P g−1) supplied as Ca(H2PO4)2·H2O (Ca-P, highly soluble, used in many fertilizers) or as one of three sparingly soluble forms: Ca10(OH)2(PO4)6 (apatite-P, found in relatively young soils; major constituent of rock phosphate), C6H6O24P6Na12 (inositol-P, the most common form of organic P in soil) and FePO4 (Fe-P, a poorly-available inorganic source of P). All species grew well with soluble P. When 6 µg P g−1 was supplied as sparingly soluble P, plant dry weight (DW) and P uptake were very low for C. australasicum and M. sativa (0.1–0.4 g DW) with the exception of M. sativa supplied with apatite-P (1.5 g). In contrast, K. prostrata grew well with inositol-P (1.0 g) and Fe-P (0.7 g), and even better with apatite-P (1.7 g), similar to that with Ca-P (1.9 g). Phosphorus uptake at 6 µg P g−1 was highly correlated with total root length, total rhizosphere carboxylate content and total rhizosphere acid phosphatase (EC 3.1.3.2) activity. These findings provide strong indications that there are opportunities to utilize local Australian legumes in low P pasture systems to access sparingly soluble soil P and increase perennial legume productivity, diversity and sustainability.

Differential uptake, partitioning and transfer of Cd and Zn in the soil-pea plant-aphid system

The biomagnification of trace metals during transfer from contaminated soil to higher trophic levels may potentially result in the exposure of predatory arthropods to toxic concentrations of these elements. This study examined the transfer of Cd and Zn in a soil−plant−arthropod system grown in series of field plots that had received two annual applications of municipal biosolids with elevated levels of Cd and Zn. Results showed that biosolids amendment significantly increased the concentration of Cd in the soil and the shoots of pea plants and the concentration of Zn in the soil, pea roots, shoots, and pods. In addition, the ratio of Cd to Zn concentration showed that Zn was preferentially transferred compared to Cd through all parts of the system. As a consequence, Zn was biomagnified by the system whereas Cd was biominimized. Cd and Zn are considered to exhibit similar behaviors in biological systems. However, the Cd/Zn ratios demonstrated that in this system, Cd is much less labile in the root−shoot−pod and shoot−aphid pathways than Zn.

Evaluation of positioning error-induced pixel shifts on satellite linear push-broom imagery

Georeferencing is one of the major tasks of satellite-borne remote sensing. Compared to traditional indirect methods, direct georeferencing through a Global Positioning System/inertial navigation system requires fewer and simpler steps to obtain exterior orientation parameters of remotely sensed images. However, the pixel shift caused by geographic positioning error, which is generally derived from boresight angle as well as terrain topography variation, can have a great impact on the precision of georeferencing. The distribution of pixel shifts introduced by the positioning error on a satellite linear push-broom image is quantitatively analyzed. We use the variation of the object space coordinate to simulate different kinds of positioning errors and terrain topography. Then a total differential method was applied to establish a rigorous sensor model in order to mathematically obtain the relationship between pixel shift and positioning error. Finally, two simulation experiments are conducted using the imaging parameters of Chang’ E-1 satellite to evaluate two different kinds of positioning errors. The experimental results have shown that with the experimental parameters, the maximum pixel shift could reach 1.74 pixels. The proposed approach can be extended to a generic application for imaging error modeling in remote sensing with terrain variation.

In situ gelling systems based on Pluronic F127/Pluronic F68 formulations for ocular drug delivery

This study evaluated the use of Pluronic F127 and Pluronic F68 as excipients for formulating in situ gelling systems for ocular drug delivery. Thermal transitions have been studied in aqueous solutions of Pluronic F127, Pluronic F68 as well as their binary mixtures using differential scanning calorimetry, rheological measurements, and dynamic light scattering. It was established that the formation of transparent gels at physiologically relevant temperatures is observed only in the case of 20 wt % of Pluronic F127. The addition of Pluronic F68 to Pluronic F127 solutions increases the gelation temperature of binary formulation to above physiological range of temperatures. The biocompatibility evaluation of these formulations using slug mucosa irritation assay and bovine corneal erosion studies revealed that these polymers and their combinations do not cause significant irritation. In vitro drug retention study on glass surfaces and freshly excised bovine cornea showed superior performance of 20 wt % Pluronic F127 compared to other formulations. In addition, in vivo studies in rabbits demonstrated better retention performance of 20 wt % Pluronic F127 compared to Pluronic F68. These results confirmed that 20 wt % Pluronic F127 offers an attractive ocular formulation that can form a transparent gel in situ under physiological conditions with minimal irritation.