Associations between step duration variability and inertial measurement unit derived gait characteristics

Inertial measurement units (IMU) provide a convenient tool for gait stability assessment. However, it is unclear how various gait characteristics relate to each other and whether gait characteristics can be obtained from resultant acceleration. Therefore, step duration variability was measured in treadmill walking from 39 young ambulant volunteers (age 24.2 [± 2.5] y; height 1.79 [± 0.09] m; mass 71.6 [± 12.0] kg) using motion capture. Accelerations and gyrations were simultaneously recorded with an IMU. Harmonic ratio, maximum Lyapunov exponents, and multiscale sample entropy (MSE) were calculated. Step duration variability was positively associated with MSE with coarseness levels = 3-6 (r = -.33 to -.42, P ≤ .045). Harmonic ratio and MSE with all coarseness levels were negatively associated (r = -.45 to -.57, P ≤ .004). The MSE with coarseness level = 2 was negatively associated with short-term maximum Lyapunov exponents (r = -.32, P = .047). The agreement between resultant and vertical acceleration derived gait characteristics was excellent (ICC = 0.97-0.99). In conclusion, MSE with varying coarseness levels was associated with the other gait characteristics evaluated in the study. Resultant and vertical acceleration derived results had excellent agreement, which suggests that resultant acceleration is a viable alternative to considering the acceleration dimensions independently.

Multifractality and long-range dependence of asset returns: the scaling behavior of the Markov-switching multifractal model with lognormal volatility components

In this paper, we consider daily financial data from various sources (stock market indices, foreign exchange rates and bonds) and analyze their multiscaling properties by estimating the parameters of a Markov-switching multifractal (MSM) model with Lognormal volatility components. In order to see how well estimated models capture the temporal dependency of the empirical data, we estimate and compare (generalized) Hurst exponents for both empirical data and simulated MSM models. In general, the Lognormal MSM models generate "apparent" long memory in good agreement with empirical scaling provided that one uses sufficiently many volatility components. In comparison with a Binomial MSM specification [11], results are almost identical. This suggests that a parsimonious discrete specification is flexible enough and the gain from adopting the continuous Lognormal distribution is very limited.

Multi-scaling modelling in financial markets

In the recent years, a new wave of interest spurred the involvement of complexity in finance which might provide a guideline to understand the mechanism of financial markets, and researchers with different backgrounds have made increasing contributions introducing new techniques and methodologies. In this paper, Markov-switching multifractal models (MSM) are briefly reviewed and the multi-scaling properties of different financial data are analyzed by computing the scaling exponents by means of the generalized Hurst exponent H(q). In particular we have considered H(q) for price data, absolute returns and squared returns of different empirical financial time series. We have computed H(q) for the simulated data based on the MSM models with Binomial and Lognormal distributions of the volatility components. The results demonstrate the capacity of the multifractal (MF) models to capture the stylized facts in finance, and the ability of the generalized Hurst exponents approach to detect the scaling feature of financial time series.

True and apparent scaling : the proximity of the Markov-switching multifractal model to long-range dependence

In this paper, we consider daily financial data of a collection of different stock market indices, exchange rates, and interest rates, and we analyze their multi-scaling properties by estimating a simple specification of the Markov-switching multifractal (MSM) model. In order to see how well the estimated model captures the temporal dependence of the data, we estimate and compare the scaling exponents H(q) (for q=1,2) for both empirical data and simulated data of the MSM model. In most cases the multifractal model appears to generate ‘apparent’ long memory in agreement with the empirical scaling laws.

Finite-time consensus algorithm of multi-agent networks

This paper is concerned with leader-follower finite-time consensus control of multi-agent networks with input disturbances. Terminal sliding mode control scheme is used to design the distributed control law. A new terminal sliding mode surface is proposed to guarantee finite-time consensus under fixed topology, with the common assumption that the position and the velocity of the active leader is known to its neighbors only. By using the finite-time Lyapunov stability theorem, it is shown that if the directed graph of the network has a directed spanning tree, then the terminal sliding mode control law can guarantee finite-time consensus even under the assumption that the time-varying control input of the active leader is unknown to any follower.

Adaptive fast finite time control of a class of uncertain nonlinear systems

This paper concerns the adaptive fast finite time control of a class of nonlinear uncertain systems of which the upper bounds of the system uncertainties are unknown. By using the fast non-smooth control Lyapunov function and the method of so-called adding a power integrator merging with adaptive technique, a recursive design procedure is provided, which guarantees the fast finite time stability of the closed-loop system. It is proved that the control input is bounded, and a simulation example is given to illustrate the effectiveness of the theoretical results.

Stability theory and numerical analysis of non-autonomous dynamical systems

The development and use of cocycles for analysis of non-autonomous behaviour is a technique that has been known for several years. Initially developed as an extension to semi-group theory for studying rion-autonornous behaviour, it was extensively used in analysing random dynamical systems [2, 9, 10, 12]. Many of the results regarding asymptotic behaviour developed for random dynamical systems, including the concept of cocycle attractors were successfully transferred and reinterpreted for deterministic non-autonomous systems primarily by P. Kloeden and B. Schmalfuss [20, 21, 28, 29]. The theory concerning cocycle attractors was later developed in various contexts specific to particular classes of dynamical systems [6, 7, 13], although a comprehensive understanding of cocycle attractors (redefined as pullback attractors within this thesis) and their role in the stability of non-autonomous dynamical systems was still at this stage incomplete. It was this purpose that motivated Chapters 1-3 to define and formalise the concept of stability within non-autonomous dynamical systems. The approach taken incorporates the elements of classical asymptotic theory, and refines the notion of pullback attraction with further development towards a study of pull-back stability arid pullback asymptotic stability. In a comprehensive manner, it clearly establishes both pullback and forward (classical) stability theory as fundamentally unique and essential components of non-autonomous stability. Many of the introductory theorems and examples highlight the key properties arid differences between pullback and forward stability. The theory also cohesively retains all the properties of classical asymptotic stability theory in an autonomous environment. These chapters are intended as a fundamental framework from which further research in the various fields of non-autonomous dynamical systems may be extended. A preliminary version of a Lyapunov-like theory that characterises pullback attraction is created as a tool for examining non-autonomous behaviour in Chapter 5. The nature of its usefulness however is at this stage restricted to the converse theorem of asymptotic stability. Chapter 7 introduces the theory of Loci Dynamics. A transformation is made to an alternative dynamical system where forward asymptotic (classical asymptotic) behaviour characterises pullback attraction to a particular point in the original dynamical system. This has the advantage in that certain conventional techniques for a forward analysis may be applied. The remainder of the thesis, Chapters 4, 6 and Section 7.3, investigates the effects of perturbations and discretisations on non-autonomous dynamical systems known to possess structures that exhibit some form of stability or attraction. Chapter 4 investigates autonomous systems with semi-group attractors, that have been non-autonomously perturbed, whilst Chapter 6 observes the effects of discretisation on non-autonomous dynamical systems that exhibit properties of forward asymptotic stability. Chapter 7 explores the same problem of discretisation, but for pullback asymptotically stable systems. The theory of Loci Dynamics is used to analyse the nature of the discretisation, but establishment of results directly analogous to those discovered in Chapter 6 is shown to be unachievable. Instead a case by case analysis is provided for specific classes of dynamical systems, for which the results generate a numerical approximation of the pullback attraction in the original continuous dynamical system. The nature of the results regarding discretisation provide a non-autonomous extension to the work initiated by A. Stuart and J. Humphries [34, 35] for the numerical approximation of semi-group attractors within autonomous systems. . Of particular importance is the effect on the system's asymptotic behaviour over non-finite intervals of discretisation.

Visual narratives in the children's picture story book : an investigation of the extent to which the formal structuring of a visual narrative retrieves a pastiche of past experiences and images which in turn shapes and redirects the story

Throughout this research, the notion that illustrators of children's books embark on two types of activity has been reinforced at every turn. On one hand the artist acknowledges the external world by organising images of actions and events in the contexts of place and time. This process involves bringing ideas into a physical form and demands the structuring of characters, settings, and story development. Planning and decisions are informed by imperatives that recognise the need for conventions of articulation and communication to a particular target audience. These then become a mayor priority of bookmaking and are constantly impacted on by publishers1 demands and ethical constraints. The other perspective sees the illustrator as expresser where the core of visual narratives for children celebrates the potency of imagination. Here dreams, fantasies, memories and the unconscious become the conduits to shaping sequential images. The artist is engaged not simply in visually telling a story, but rather telling facets of his or her own story. This exegesis traces the evolution of my own picture story book Eddie's Fantastic Fortnight published by Five Mile Press Publishers in tandem with the insights and reflections of five of Australia's most prominent illustrators. It examines whether the structure invested in a visual narrative liberates expressive response, ascribing to the premise that bookmaking plays an informing role to imagination. Equally it adopts the alternative position which asserts that the essence of children's books is indeed fantasy, memory and dreams. This proposition views imagination and inspiration as the primary catalyst around which illustrators build their narrative. In the often lengthy processes of bookmaking, these considerations constantly shift. I have attempted to explore and reveal these mobile and ever changing priorities, not only in my own work, but also through leading exponents in the field.

Improvement on delay dependent absolute stability of Lurie control systems with multiple time delays

Absolute stability of Lurie control systems with multiple time-delays is studied in this paper. By using extended Lyapunov functionals, we avoid the use of the stability assumption on the main operator and derive improved stability criteria, which are strictly less conservative than the criteria in [2,3].

Exponential stabilization of neural networks with various activation functions and mixed time-varying delays

This paper presents some results on the global exponential stabilization for neural networks with various activation functions and time-varying continuously distributed delays. Based on augmented time-varying Lyapunov-Krasovskii functionals, new delay-dependent conditions for the global exponential stabilization are obtained in terms of linear matrix inequalities. A numerical example is given to illustrate the feasibility of our results.

Parameter-dependent H∞ control for time varying delay polytopic systems

This paper addresses the robust stabilization and H_∞ control problem for a class of linear polytopic systems with continuously distributed delays. The control objective is to design a robust H_∞ controller that satisfies some exponential stability constraints on the closed-loop poles. Using improved parameter-dependent Lyapunov Krasovskii functionals, new delay-dependent conditions for the robust H_∞ control are established in terms of linear matrix inequalities.

Fast finite-time consensus of a class of high-order uncertain nonlinear systems

This paper poses and solves a new problem of consensus control where the task is to make the fixed-topology multi-agent network, with each agent described by an uncertain nonlinear system in chained form, to reach consensus in a fast finite time. Our development starts with a set of new sliding mode surfaces. It is proven that, on these sliding mode surfaces, consensus can be achieved if the communication graph has the proposed directed spanning tree. Next, we introduce the multi-surface sliding mode control to drive the sliding variables to the sliding mode surfaces in a fast finite time. The control Lyapunov function for fast finite time stability, motivated by the fast terminal sliding mode control, is used to prove the reachability of the sliding mode surface. A recursive design procedure is provided, which guarantees the boundedness of the control input.

Comments on "finite-time stability theorem of stochastic nonlinear systems" [Automatica 46 (2010) 2105-2108]

In this comment, we will point out some errors existing in Chen and Jiao (2010) from definitions to the proof of the main result, where the authors discussed the finite-time stability of stochastic nonlinear systems and proved a Lyapunov theorem on the finitetime stability.