Degeneracy of velocity constraints in rigid body systems

The equations governing the dynamics of rigid body systems with velocity constraints are singular at degenerate configurations in the constraint distribution. In this report, we describe the causes of singularities in the constraint distribution of interconnected rigid body systems with smooth configuration manifolds. A convention of defining primary velocity constraints in terms of orthogonal complements of one-dimensional subspaces is introduced. Using this convention, linear maps are defined and used to describe the space of allowable velocities of a rigid body. Through the definition of these maps, we present a condition for non-degeneracy of velocity constraints in terms of the one dimensional subspaces defining the primary velocity constraints. A method for defining the constraint subspace and distribution in terms of linear maps is presented. Using these maps, the constraint distribution is shown to be singular at configuration where there is an increase in its dimension.

Raman spectroscopic study of vivianites of different origins

Raman spectroscopy has been used to study a selection of vivianites from different origins. A band is identified at around 3480 cm-1 whose intensity is sample dependent. The band is attributed to the stretching vibration of Fe3+ OH units which are formed through the autooxidation of the vivianite minerals either by self-oxidation or by photocatalytic oxidation according to the reaction: (Fe2+)3(PO4)2·8H2O + 1/2O2 (Fe2+)3– x(Fe3+)x(PO4)2(OH)x·(8–x)H2O in which some of the water of crystallization is converted to hydroxyl anions. Complexity of the OH stretching region through the overlap of broad bands is reflected in the water HOH deformation modes at 1660 cm–1. Using the infrared bands at 3281, 3105 and 3025 cm–1, hydrogen bond distances of 2.734(5), 2.675(2) and 2.655(2) Å are calculated. Vivianites are characterised by an intense band at 950 cm–1 assigned to the PO4 symmetric stretching vibration. Low Raman intensity bands are observed at ~1077, ~1050, 1015 and ~ 985 cm–1 assigned to the phosphate PO4 antisymmetric stretching vibrations. Multiple antisymmetric stretching vibrations are due to the reduced tetrahedral symmetry. This loss of degeneracy is also reflected in the bending modes. Two bands are observed at ~ 423 and ~ 456 cm–1 assigned to the2bending modes. For the vivianites four bands are observed at ~ 584, ~ 571, ~ 545 and ~ 525 cm–1 assigned to the 4modes of vivianite.

Dynamics of multi-articular coordination in neurobiological systems

Although previous work in nonlinear dynamics on neurobiological coordination and control has provided valuable insights from studies of single joint movements in humans, researchers have shown increasing interest in coordination of multi-articular actions. Multi-articular movement models have provided valuable insights on neurobiological systems conceptualised as degenerate, adaptive complex systems satisfying the constraints of dynamic environments. In this paper, we overview empirical evidence illustrating the dynamics of adaptive movement behavior in a range of multi-articular actions including kicking, throwing, hitting and balancing. We model the emergence of creativity and the diversity of neurobiological action in the meta-stable region of self organising criticality. We examine the influence on multi-articular actions of decaying and emerging constraints in the context of skill acquisition. We demonstrate how, in this context, transitions between preferred movement patterns exemplify the search for and adaptation of attractor states within the perceptual motor workspace as a function of practice. We conclude by showing how empirical analyses of neurobiological coordination and control have been used to establish a nonlinear pedagogical framework for enhancing acquisition of multi-articular actions.

On analysing and interpreting variability in motor output

A recent article in the Journal of Science and Medicine in Sport by Chapman et al.1 reported data from an empirical investigation comparing lower extremity joint motions, joint coordination and muscle recruitment in expert and novice cyclists. 3D kinematic and intramuscular electromyographic (EMG) analyses revealed no differences between expert and novice cyclists for normalised joint angles and velocities of the pelvis, hip, knee and ankle. However, significant differences in the strength of sagittal plane kinematics for hip–ankle and knee–ankle joint couplings were reported, with expert cyclists displaying tighter coupling relationships than novice cyclists. Furthermore, significant differences between expert and novice cyclists for all muscle recruitment parameters, except timing of peak EMG amplitude, were also reported.

The organisation of action in complex neurobiological systems

This chapter elucidates key ideas behind neurocomputational and ecological dynamics and perspectives of understanding the organisation of action in complex neurobiological systems. The need to study the close link between neurobiological systems and their environments (particularly their sensory and movement subsystems and the surrounding energy sources) is advocated. It is proposed how degeneracy in complex neurobiological systems provides the basis for functional variability in organisation of action. In such systems processes of cognition and action facilitate the specific interactions of each performer with particular task and environmental constraints.

Adaptive and phase transition behavior in performance of discrete multi-articular actions by degenerate neurobiological systems

The identification of attractors is one of the key tasks in studies of neurobiological coordination from a dynamical systems perspective, with a considerable body of literature resulting from this task. However, with regards to typical movement models investigated, the overwhelming majority of actions studied previously belong to the class of continuous, rhythmical movements. In contrast, very few studies have investigated coordination of discrete movements, particularly multi-articular discrete movements. In the present study, we investigated phase transition behavior in a basketball throwing task where participants were instructed to shoot at the basket from different distances. Adopting the ubiquitous scaling paradigm, throwing distance was manipulated as a candidate control parameter. Using a cluster analysis approach, clear phase transitions between different movement patterns were observed in performance of only two of eight participants. The remaining participants used a single movement pattern and varied it according to throwing distance, thereby exhibiting hysteresis effects. Results suggested that, in movement models involving many biomechanical degrees of freedom in degenerate systems, greater movement variation across individuals is available for exploitation. This observation stands in contrast to movement variation typically observed in studies using more constrained bi-manual movement models. This degenerate system behavior provides new insights and poses fresh challenges to the dynamical systems theoretical approach, requiring further research beyond conventional movement models.

The problem of measurement indeterminacy in complex neurobiological movement systems

In the study of complex neurobiological movement systems, measurement indeterminacy has typically been overcome by imposing artificial modelling constraints to reduce the number of unknowns (e.g., reducing all muscle, bone and ligament forces crossing a joint to a single vector). However, this approach prevents human movement scientists from investigating more fully the role, functionality and ubiquity of coordinative structures or functional motor synergies. Advancements in measurement methods and analysis techniques are required if the contribution of individual component parts or degrees of freedom of these task-specific structural units is to be established, thereby effectively solving the indeterminacy problem by reducing the number of unknowns. A further benefit of establishing more of the unknowns is that human movement scientists will be able to gain greater insight into ubiquitous processes of physical self-organising that underpin the formation of coordinative structures and the confluence of organismic, environmental and task constraints that determine the exact morphology of these special-purpose devices.

Deconstructing neurobiological coordination

Inherent indeterminacy of neurobiological systems has been revealed by research on coordination of multiarticular actions. We consider three important issues that these investigations raise for biomechanical measurement and performance modeling. These issues highlight the role of dynamic systems theory as a platform for integration of motor control and biomechanics in exercise and sports science.

Vision only pose estimation and scene reconstruction on airborne platforms

We aim to demonstrate unaided visual 3D pose estimation and map reconstruction using both monocular and stereo vision techniques. To date, our work has focused on collecting data from Unmanned Aerial Vehicles, which generates a number of significant issues specific to the application. Such issues include scene reconstruction degeneracy from planar data, poor structure initialisation for monocular schemes and difficult 3D reconstruction due to high feature covariance. Most modern Visual Odometry (VO) and related SLAM systems make use of a number of sensors to inform pose and map generation, including laser range-finders, radar, inertial units and vision [1]. By fusing sensor inputs, the advantages and deficiencies of each sensor type can be handled in an efficient manner. However, many of these sensors are costly and each adds to the complexity of such robotic systems. With continual advances in the abilities, small size, passivity and low cost of visual sensors along with the dense, information rich data that they provide our research focuses on the use of unaided vision to generate pose estimates and maps from robotic platforms. We propose that highly accurate (�5cm) dense 3D reconstructions of large scale environments can be obtained in addition to the localisation of the platform described in other work [2]. Using images taken from cameras, our algorithm simultaneously generates an initial visual odometry estimate and scene reconstruction from visible features, then passes this estimate to a bundle-adjustment routine to optimise the solution. From this optimised scene structure and the original images, we aim to create a detailed, textured reconstruction of the scene. By applying such techniques to a unique airborne scenario, we hope to expose new robotic applications of SLAM techniques. The ability to obtain highly accurate 3D measurements of an environment at a low cost is critical in a number of agricultural and urban monitoring situations. We focus on cameras as such sensors are small, cheap and light-weight and can therefore be deployed in smaller aerial vehicles. This, coupled with the ability of small aerial vehicles to fly near to the ground in a controlled fashion, will assist in increasing the effective resolution of the reconstructed maps.

Individual differences in the visual control of intercepting a penalty kick in association football

Recent perceptual-motor studies have revealed variations in learning trajectories of novices. Despite such observation, relatively little attention has been paid to studying individual differences in experienced performers’ perceptual-motor behaviors. The present study examined individual differences for a visual anticipation task. Experienced association football goalkeepers attempted to intercept penalty kicks taken with deceptive and non-deceptive kicking actions. Data revealed that differences in the action capabilities of goalkeepers affected the timing and accuracy of movement response behaviors. Faster goalkeepers tended to wait until later before initiating movement in comparison with slower goalkeepers. The study of affordances in sport environments offers a theoretical framework with which to overcome some of the reported methodological limitations in the visual anticipation literature.

Correlations between designability and various structural characteristics of protein lattice models

Using six kinds of lattice types (4×4 ,5×5 , and6×6 square lattices;3×3×3 cubic lattice; and2+3+4+3+2 and4+5+6+5+4 triangular lattices), three different size alphabets (HP ,HNUP , and 20 letters), and two energy functions, the designability of proteinstructures is calculated based on random samplings of structures and common biased sampling (CBS) of proteinsequence space. Then three quantities stability (average energy gap),foldability, and partnum of the structure, which are defined to elucidate the designability, are calculated. The authors find that whatever the type of lattice, alphabet size, and energy function used, there will be an emergence of highly designable (preferred) structure. For all cases considered, the local interactions reduce degeneracy and make the designability higher. The designability is sensitive to the lattice type, alphabet size, energy function, and sampling method of the sequence space. Compared with the random sampling method, both the CBS and the Metropolis Monte Carlo sampling methods make the designability higher. The correlation coefficients between the designability, stability, and foldability are mostly larger than 0.5, which demonstrate that they have strong correlation relationship. But the correlation relationship between the designability and the partnum is not so strong because the partnum is independent of the energy. The results are useful in practical use of the designability principle, such as to predict the proteintertiary structure.

Identifying constraints on children with movement difficulties : implications for pedagogues and clinicians

A constraints- based framework for understanding processes of movement coordination and control is predicated on a range of theoretical ideas including the work of Bernstein (1967), Gibson (1979), Newell (1986) and Kugler, Kelso & Turvey (1982). Contrary to a normative perspective that focuses on the production of idealized movement patterns to be acquired by children during development and learning (see Alain & Brisson, 1986), this approach formulates the emergence of movement co- ordination as a function of the constraints imposed upon each individual. In this framework, cognitive, perceptual and movement difficulties and disorders are considered to be constraints on the perceptual- motor system, and children’s movements are viewed as emergent functional adaptations to these constraints (Davids et al., 2008; Rosengren, Savelsbergh & van der Kamp, 2003). From this perspective, variability of movement behaviour is not viewed as noise or error to be eradicated during development, but rather, as essentially functional in facilitating the child to satisfy the unique constraints which impinge on his/her developing perceptual- motor and cognitive systems in everyday life (Davids et al., 2008). Recently, it has been reported that functional neurobiological variability is predicated on system degeneracy, an inherent feature of neurobiological systems which facilitates the achievement of task performance goals in a variety of different ways (Glazier & Davids, 2009). Degeneracy refers to the capacity of structurally different components of complex movement systems to achieve different performance outcomes in varying contexts (Tononi et al., 1999; Edelman & Gally, 2001). System degeneracy allows individuals with and without movement disorders to achieve their movement goals by harnessing movement variability during performance. Based on this idea, perceptual- motor disorders can be simply viewed as unique structural and functional system constraints which individuals have to satisfy in interactions with their environments. The aim of this chapter is to elucidate how the interaction of structural and functional organismic, and environmental constraints can be harnessed in a nonlinear pedagogy by individuals with movement disorders.

Exploring the parameter space of a rabbit ventricular action potential model to investigate the effect of variation on action potential and calcium transients

Computational models for cardiomyocyte action potentials (AP) often make use of a large parameter set. This parameter set can contain some elements that are fitted to experimental data independently of any other element, some elements that are derived concurrently with other elements to match experimental data, and some elements that are derived purely from phenomenological fitting to produce the desired AP output. Furthermore, models can make use of several different data sets, not always derived for the same conditions or even the same species. It is consequently uncertain whether the parameter set for a given model is physiologically accurate. Furthermore, it is only recently that the possibility of degeneracy in parameter values in producing a given simulation output has started to be addressed. In this study, we examine the effects of varying two parameters (the L-type calcium current (I(CaL)) and the delayed rectifier potassium current (I(Ks))) in a computational model of a rabbit ventricular cardiomyocyte AP on both the membrane potential (V(m)) and calcium (Ca(2+)) transient. It will subsequently be determined if there is degeneracy in this model to these parameter values, which will have important implications on the stability of these models to cell-to-cell parameter variation, and also whether the current methodology for generating parameter values is flawed. The accuracy of AP duration (APD) as an indicator of AP shape will also be assessed.

A multidisciplinary examination of fast bowling talent development in cricket

Research on expertise, talent identification and development has tended to be mono-disciplinary, typically adopting geno-centric or environmentalist positions, with an overriding focus on operational issues. In this thesis, the validity of dualist positions on sport expertise is evaluated. It is argued that, to advance understanding of expertise and talent development, a shift towards a multidisciplinary and integrative science focus is necessary, along with the development of a comprehensive multidisciplinary theoretical rationale. Dynamical systems theory is utilised as a multidisciplinary theoretical rationale for the succession of studies, capturing how multiple interacting constraints can shape the development of expert performers. Phase I of the research examines experiential knowledge of coaches and players on the development of fast bowling talent utilising qualitative research methodology. It provides insights into the developmental histories of expert fast bowlers, as well as coaching philosophies on the constraints of fast bowling expertise. Results suggest talent development programmes should eschew the notion of common optimal performance models and emphasize the individual nature of pathways to expertise. Coaching and talent development programmes should identify the range of interacting constraints that impinge on the performance potential of individual athletes, rather than evaluating current performance on physical tests referenced to group norms. Phase II of this research comprises three further studies that investigate several of the key components identified as important for fast bowling expertise, talent identification and development extrapolated from Phase I of this research. This multidisciplinary programme of work involves a comprehensive analysis of fast bowling performance in a cross-section of the Cricket Australia high performance pathways, from the junior, emerging and national elite fast bowling squads. Briefly, differences were found in trunk kinematics associated with the generation of ball speed across the three groups. These differences in release mechanics indicated the functional adaptations in movement patterns as bowlers’ physical and anatomical characteristics changed during maturation. Second to the generation of ball speed, the ability to produce a range of delivery types was highlighted as a key component of expertise in the qualitative phase. The ability of athletes to produce consistent results on different surfaces and in different environments has drawn attention to the challenge of measuring consistency and flexibility in skill assessments. Examination of fast bowlers in Phase II demonstrated that national bowlers can make adjustments to the accuracy of subsequent deliveries during performance of a cricket bowling skills test, and perform a range of delivery types with increased accuracy and consistency. Finally, variability in selected delivery stride ground reaction force components in fast bowling revealed the degenerate nature of this complex multi-articular skill where the same performance outcome can be achieved with unique movement strategies. Utilising qualitative and quantitative methodologies to examine fast bowling expertise, the importance of degeneracy and adaptability in fast bowling has been highlighted alongside learning design that promotes dynamic learning environments.

Attunement to haptic information helps skilled performers select implements for striking a ball in cricket

This study examined the perceptual attunement of relatively skilled individuals to physical properties of striking implements in the sport of cricket. We also sought to assess whether utilising bats of different physical properties influenced performance of a specific striking action: the front foot straight drive. Eleven, skilled male cricketers (mean age = 16.6 ± 0.3 years) from an elite school cricket development programme consented to participate in the study. Whist blindfolded, participants wielded six bats exhibiting different mass and moment of inertia (MOI) characteristics and were asked to identify their three most preferred bats for hitting a ball to a maximum distance by performing a front foot straight drive (a common shot in cricket). Next, participants actually attempted to hit balls projected from a ball machine using each of the six bat configurations to enable kinematic analysis of front foot straight drive performance with each implement. Results revealed that, on first choice, the two bats with the smallest mass and MOI values (1 and 2) were most preferred by almost two-thirds (63.7%) of the participants. Kinematic analysis of movement patterns revealed that bat velocity, step length and bat-ball contact position measures significantly differed between bats. Data revealed how skilled youth cricketers were attuned to the different bat characteristics and harnessed movement system degeneracy to perform this complex interceptive action.