A general method to determine sampling windows for nonlinear mixed effects models with an application to population pharmacokinetic studies

Optimal design methods have been proposed to determine the best sampling times when sparse blood sampling is required in clinical pharmacokinetic studies. However, the optimal blood sampling time points may not be feasible in clinical practice. Sampling windows, a time interval for blood sample collection, have been proposed to provide flexibility in blood sampling times while preserving efficient parameter estimation. Because of the complexity of the population pharmacokinetic models, which are generally nonlinear mixed effects models, there is no analytical solution available to determine sampling windows. We propose a method for determination of sampling windows based on MCMC sampling techniques. The proposed method attains a stationary distribution rapidly and provides time-sensitive windows around the optimal design points. The proposed method is applicable to determine sampling windows for any nonlinear mixed effects model although our work focuses on an application to population pharmacokinetic models.

Nonlinear H_infinity control of UAVs for collision avoidance in gusty environments

This paper proposes a nonlinear H_infinity controller for stabilization of velocities, attitudes and angular rates of a fixed-wing unmanned aerial vehicle (UAV) in a windy environment. The suggested controller aims to achieve a steady-state flight condition in the presence of wind gusts such that the host UAV can be maneuvered to avoid collision with other UAVs during cruise flight with safety guarantees. This paper begins with building a proper model capturing flight aerodynamics of UAVs. Then a nonlinear controller is developed with gust attenuation and rapid response properties. Simulations are conducted for the Shadow UAV to verify performance of the proposed con- troller. Comparative studies with the proportional-integral-derivative (PID) controllers demonstrate that the proposed controller exhibits great performance improvement in a gusty environment, making it suitable for integration into the design of flight control systems for cruise flight of UAVs.

Nonlinear pedagogy underpins intrinsic motivation in sports coaching

A key challenge for sports coaches is to provide performers with learning environments that result in sustainable motivation. In this paper, we will demonstrate that programmes based around the principles of Nonlinear Pedagogy can support the three basic psychological needs that underpin self-determined motivation. Coaches can therefore ensure that practice sessions provide for intrinsic motivation with its associated motivational and emotional benefits.

Effects of oxygen and culture system on in vitro propagation and redifferentiation of osteoarthritic human articular chondrocytes

Regenerative medicine-based approaches for the repair of damaged cartilage rely on the ability to propagate cells while promoting their chondrogenic potential. Thus, conditions for cell expansion should be optimized through careful environmental control. Appropriate oxygen tension and cell expansion substrates and controllable bioreactor systems are probably critical for expansion and subsequent tissue formation during chondrogenic differentiation. We therefore evaluated the effects of oxygen and microcarrier culture on the expansion and subsequent differentiation of human osteoarthritic chondrocytes. Freshly isolated chondrocytes were expanded on tissue culture plastic or CultiSpher-G microcarriers under hypoxic or normoxic conditions (5% or 20% oxygen partial pressure, respectively) followed by cell phenotype analysis with flow cytometry. Cells were redifferentiated in micromass pellet cultures over 4 weeks, under either hypoxia or normoxia. Chondrocytes cultured on tissue culture plastic proliferated faster, expressed higher levels of cell surface markers CD44 and CD105 and demonstrated stronger staining for proteoglycans and collagen type II in pellet cultures compared with microcarrier-cultivated cells. Pellet wet weight, glycosaminoglycan content and expression of chondrogenic genes were significantly increased in cells differentiated under hypoxia. Hypoxia-inducible factor-3alpha mRNA was up-regulated in these cultures in response to low oxygen tension. These data confirm the beneficial influence of reduced oxygen on ex vivo chondrogenesis. However, hypoxia during cell expansion and microcarrier bioreactor culture does not enhance intrinsic chondrogenic potential. Further improvements in cell culture conditions are therefore required before chondrocytes from osteoarthritic and aged patients can become a useful cell source for cartilage regeneration.

Towards Bayesian experimental design for nonlinear models that require a large number of sampling times

The use of Bayesian methodologies for solving optimal experimental design problems has increased. Many of these methods have been found to be computationally intensive for design problems that require a large number of design points. A simulation-based approach that can be used to solve optimal design problems in which one is interested in finding a large number of (near) optimal design points for a small number of design variables is presented. The approach involves the use of lower dimensional parameterisations that consist of a few design variables, which generate multiple design points. Using this approach, one simply has to search over a few design variables, rather than searching over a large number of optimal design points, thus providing substantial computational savings. The methodologies are demonstrated on four applications, including the selection of sampling times for pharmacokinetic and heat transfer studies, and involve nonlinear models. Several Bayesian design criteria are also compared and contrasted, as well as several different lower dimensional parameterisation schemes for generating the many design points.

Fiber Bragg grating strain modulation based on nonlinear string transverse force amplifier

The only effective method of Fiber Bragg Grating (FBG) strain modulation has been by changing the distance between its two fixed ends. We demonstrate an alternative being more sensitive to force based on the nonlinear amplification relationship between a transverse force applied to a stretched string and its induced axial force. It may improve the sensitivity and size of an FBG force sensor, reduce the number of FBGs needed for multi-axial force monitoring, and control the resonant frequency of an FBG accelerometer.

Efficient solution of two-sided nonlinear space-fractional diffusion equations using fast Poisson preconditioners

We develop a fast Poisson preconditioner for the efficient numerical solution of a class of two-sided nonlinear space fractional diffusion equations in one and two dimensions using the method of lines. Using the shifted Gr¨unwald finite difference formulas to approximate the two-sided(i.e. the left and right Riemann-Liouville) fractional derivatives, the resulting semi-discrete nonlinear systems have dense Jacobian matrices owing to the non-local property of fractional derivatives. We employ a modern initial value problem solver utilising backward differentiation formulas and Jacobian-free Newton-Krylov methods to solve these systems. For efficient performance of the Jacobianfree Newton-Krylov method it is essential to apply an effective preconditioner to accelerate the convergence of the linear iterative solver. The key contribution of our work is to generalise the fast Poisson preconditioner, widely used for integer-order diffusion equations, so that it applies to the two-sided space fractional diffusion equation. A number of numerical experiments are presented to demonstrate the effectiveness of the preconditioner and the overall solution strategy.

A banded preconditioner for the two-sided, nonlinear space-fractional diffusion equation

The method of lines is a standard method for advancing the solution of partial differential equations (PDEs) in time. In one sense, the method applies equally well to space-fractional PDEs as it does to integer-order PDEs. However, there is a significant challenge when solving space-fractional PDEs in this way, owing to the non-local nature of the fractional derivatives. Each equation in the resulting semi-discrete system involves contributions from every spatial node in the domain. This has important consequences for the efficiency of the numerical solver, especially when the system is large. First, the Jacobian matrix of the system is dense, and hence methods that avoid the need to form and factorise this matrix are preferred. Second, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. In this paper, we show how an effective preconditioner is essential for improving the efficiency of the method of lines for solving a quite general two-sided, nonlinear space-fractional diffusion equation. A key contribution is to show, how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

Computer simulation of underground blast response of pile in saturated soil

This paper treats the blast response of a pile foundation in saturated sand using explicit nonlinear finite element analysis, considering complex material behavior of soil and soil–pile interaction. Blast wave propagation in the soil is studied and the horizontal deformation of pile and effective stresses in the pile are presented. Results indicate that the upper part of the pile to be vulnerable and the pile response decays with distance from the explosive. The findings of this research provide valuable information on the effects of underground explosions on pile foundation and will guide future development, validation and application of computer models.

Numerical approximation for a variable-order nonlinear reaction–subdiffusion equation

Fractional reaction–subdiffusion equations are widely used in recent years to simulate physical phenomena. In this paper, we consider a variable-order nonlinear reaction–subdiffusion equation. A numerical approximation method is proposed to solve the equation. Its convergence and stability are analyzed by Fourier analysis. By means of the technique for improving temporal accuracy, we also propose an improved numerical approximation. Finally, the effectiveness of the theoretical results is demonstrated by numerical examples.

Blast induced ground shock effects on pile foundations

Due to increased number of terrorist attacks in recent years, loads induced by explosions need to be incorporated in building designs. For safer performance of a structure, its foundation should have sufficient strength and stability. Therefore, prior to any reconstruction or rehabilitation of a building subjected to blast, it is important to examine adverse effects on the foundation caused by blast induced ground shocks. This paper evaluates the effects of a buried explosion on a pile foundation. It treats the dynamic response of the pile in saturated sand, using explicit dynamic nonlinear finite element software LS-DYNA. The blast induced wave propagation in the soil and the horizontal deformation of pile are presented and the results are discussed. Further, a parametric study is carried out to evaluate the effect of varying the explosive shape on the pile response. This information can be used to evaluate the vulnerability of piled foundations to credible blast events as well as develop guidance for their design.

Nonlinear actuator fault detection for small-scale UAS

This paper presents a recursive strategy for online detection of actuator faults on a unmanned aerial system (UAS) subjected to accidental actuator faults. The proposed detection algorithm aims to provide a UAS with the capability of identifying and determining characteristics of actuator faults, offering necessary flight information for the design of fault-tolerant mechanism to compensate for the resultant side-effect when faults occur. The proposed fault detection strategy consists of a bank of unscented Kalman filters (UKFs) with each one detecting a specific type of actuator faults and estimating corresponding velocity and attitude information. Performance of the proposed method is evaluated using a typical nonlinear UAS model and it is demonstrated in simulations that our method is able to detect representative faults with a sufficient accuracy and acceptable time delay, and can be applied to the design of fault-tolerant flight control systems of UASs.

A nonlinear position controller for maritime operations of Rotary-wing UAVs

This paper presents a disturbance attenuation controller for horizontal position stabilization for hover and automatic landings of a Rotary-wing Unmanned Aerial Vehicle (RUAV) operating in rough seas. Based on a helicopter model representing aerodynamics during the landing phase, a nonlinear state feedback H-infinity controller is designed to achieve rapid horizontal position tracking in a gusty environment. The resultant control variables are further treated in consideration of practical constraints (flapping dynamics, servo dynamics and time lag effect) for implementation purpose. The high-fidelity closed-loop simulation using parameters of the Vario helicopter verifies performance of the proposed position controller. It not only increases the disturbance attenuation capability of the RUAV, but also enables rapid position response when gusts occur. Comparative studies show that the H-infinity controller exhibits great performance improvement and can be applied to ship/RUAV landing systems.

Bending properties of Ag nanowires with pre-existing surface defects

Materials used in the engineering always contain imperfections or defects which significantly affect their performances. Based on the large-scale molecular dynamics simulation and the Euler–Bernoulli beam theory, the influence from different pre-existing surface defects on the bending properties of Ag nanowires (NWs) is studied in this paper. It is found that the nonlinear-elastic deformation, as well as the flexural rigidity of the NW is insensitive to different surface defects for the studied defects in this paper. On the contrary, an evident decrease of the yield strength is observed due to the existence of defects. In-depth inspection of the deformation process reveals that, at the onset of plastic deformation, dislocation embryos initiate from the locations of surface defects, and the plastic deformation is dominated by the nucleation and propagation of partial dislocations under the considered temperature. Particularly, the generation of stair-rod partial dislocations and Lomer–Cottrell lock are normally observed for both perfect and defected NWs. The generation of these structures has thwarted attempts of the NW to an early yielding, which leads to the phenomenon that more defects does not necessarily mean a lower critical force.

Exploring new and emerging models for nonlinear performative works

This dissertation seeks to define and classify potential forms of Nonlinear structure and explore the possibilities they afford for the creation of new musical works. It provides the first comprehensive framework for the discussion of Nonlinear structure in musical works and provides a detailed overview of the rise of nonlinearity in music during the 20th century. Nonlinear events are shown to emerge through significant parametrical discontinuity at the boundaries between regions of relatively strong internal cohesion. The dissertation situates Nonlinear structures in relation to linear structures and unstructured sonic phenomena and provides a means of evaluating Nonlinearity in a musical structure through the consideration of the degree to which the structure is integrated, contingent, compressible and determinate as a whole. It is proposed that Nonlinearity can be classified as a three dimensional space described by three continuums: the temporal continuum, encompassing sequential and multilinear forms of organization, the narrative continuum encompassing processual, game structure and developmental narrative forms and the referential continuum encompassing stylistic allusion, adaptation and quotation. The use of spectrograms of recorded musical works is proposed as a means of evaluating Nonlinearity in a musical work through the visual representation of parametrical divergence in pitch, duration, timbre and dynamic over time. Spectral and structural analysis of repertoire works is undertaken as part of an exploration of musical nonlinearity and the compositional and performative features that characterize it. The contribution of cultural, ideological, scientific and technological shifts to the emergence of Nonlinearity in music is discussed and a range of compositional factors that contributed to the emergence of musical Nonlinearity is examined. The evolution of notational innovations from the mobile score to the screen score is plotted and a novel framework for the discussion of these forms of musical transmission is proposed. A computer coordinated performative model is discussed, in which a computer synchronises screening of notational information, provides temporal coordination of the performers through click-tracks or similar methods and synchronises the audio processing and synthesized elements of the work. It is proposed that such a model constitutes a highly effective means of realizing complex Nonlinear structures. A creative folio comprising 29 original works that explore nonlinearity is presented, discussed and categorised utilising the proposed classifications. Spectrograms of these works are employed where appropriate to illustrate the instantiation of parametrically divergent substructures and examples of structural openness through multiple versioning.