Direct multiple shooting and direct collocation perform similarly in biomechanical predictive simulations

Direct multiple shooting (DMS) and direct collocation (DC) are two common transcription methods for solving optimal control problems (OCP) in biomechanics and robotics. They have rarely been compared in terms of solution and speed. Through five examples of predictive simulations solved using five transcription methods and 100 initial guesses in the Bioptim software, we showed that not a single method outperformed systematically better. All methods converged to almost the same solution (cost, states, and controls) in all but one OCP, with several local minima being found in the latter. Nevertheless, DC based on fourth-order Legendre polynomials provided overall better results, especially in terms of dynamic consistency compared to DMS based on a fourth-order Runge-Kutta method. Furthermore, expressing the rigid-body constraints using inverse dynamics was usually faster than forward dynamics. DC with dynamics constraints based on inverse dynamics converged to better and less variable solutions. Consequently, we recommend starting with this transcription to solve OCPs but keep testing other methods.Comment: 19 pages, 4 figure

Transcriptome-wide analysis reveals different categories of response to a standardised immune challenge in a wild rodent

Individuals vary in their immune response and, as a result, some are more susceptible to infectious disease than others. Little is known about the nature of this individual variation in natural populations, or which components of immune pathways are most responsible, but defining this underlying landscape of variation is an essential first step to understanding the drivers of this variation and, ultimately, predicting the outcome of infection. We describe transcriptome-wide variation in response to a standardised immune challenge in wild field voles. We find that markers can be categorised into a limited number of types. For the majority of markers, the response of an individual is dependent on its baseline expression level, with significant enrichment in this category for conventional immune pathways. Another, moderately sized, category contains markers for which the responses of different individuals are also variable but independent of their baseline expression levels. This category lacks any enrichment for conventional immune pathways. We further identify markers which display particularly high individual variability in response, and could be used as markers of immune response in larger studies. Our work shows how a standardised challenge performed on a natural population can reveal the patterns of natural variation in immune response

AN ALGORITHM TO COMPUTE ABSOLUTE 3D KINEMATICS FROM A MOVING MOTION ANALYSIS SYSTEM

INTRODUCTION: Recently, Colloud et al. showed the feasibility of using a moving motion analysis system to acquire three dimensional (3d) kinematics over a large volume. They placed a motion analysis system on a rigid rolling frame that followed the displacement of a known object. In this pilot study, Colloud et al. obtained accuracy similar to those report for motion analysis systems (Richards, 1999). As a result, the rolling system is accurate enough for capturing the local 3d kinematics. However, the expression of the kinematics in a global frame – i.e. the absolute kinematics – has not been assessed. Thus it is impossible to calculate spatial-temporal parameters (e.g. step length, step width, walking speed in gait analysis). The purpose of this study is to propose an algorithm for calculating the 3d global kinematic of a subject walking on a 40 m-long pathway. METHODS: One male participant (age: 21 yr, height: 170 cm, mass: 62 kg) equipped with 22 reflective markers performed five trials on 40 meters. He was followed by a rolling frame (4.4 × 4.0 × 2.5 m) with a 8-camera motion analysis system (T40 series, Vicon, Oxford, UK) sampled at 100 Hz. Forty-one reflective markers were placed every meter on the ground on an horizontal line using a tape measurer and a self levelling laser. The algorithm consists in three steps: (i) estimation of the kinematics from the camera frame (AL) to a local frame (Ai) using two markers (gi and gj) seen on the ground, (ii) expressed this local kinematics in a global frame (AG) and (iii) calculation of the roto-translation (iRj) from this current local frame (Ai) to the next local frame (Aj) before gi disappears. This last step requires three visible ground markers (gi, gj and gk). An elimination procedure that minimizes the norm of Frobenius is used until 50% of the image remained. The accuracy and precision of the reconstruction were evaluated as the deviation of reconstructed marker position relative to its reference and as the radius of the spheres of 95% confidence for the ground markers express in the global frame, respectively. RESULTS and DISCUSSION: The accuracy was up to 16 mm in antero-posterior direction but could reach 138 and 163 mm in lateral and vertical directions over the 40 m translation. The deviations differed in direction and magnitude between the trials. The precision was lower than the precision estimated with a rigid object (1.3 mm). Although their position was fixed in the global frame, the markers were shaking, in the worst case, in a sphere of 20 mm. The errors in marker position could be reduced with a reconstruction using at least three cameras. CONCLUSION: This algorithm is efficient for the analysis of human movement on horizontal ground. It allows the calculation of spatio-temporal parameters related to the performance in ecological environments over many cycles for walking and many sports (e.g. running) REFERENCES: Colloud, F., Chèze, L., Andrè, N., Bahuaud, P. (2008). An innovative solution for 3D kinematics measurement for large volume. Journal of Biomechanics, 41(S1), S57. Richards, J., 1999. The measurement of human motion: A comparison of commercially available systems. Human Movement Science, 18, 589–602. Acknowledgement: The financial support of Région Rhône-Alpes (Projet Emergence) and Région Poitou-Charentes--European Union (CPER 2007-2013) is gratefully acknowledged

AN ORIGINAL INVERSE KINEMATICS ALGORITHM FOR KAYAKING

For some sports, e.g. kayaking and rowing, ecological conditions represent a challenge for collecting three-dimensional kinematics. The lower-limbs are partially hidden by the boat and motion analysis systems used in laboratory are not suitable for outdoor and on-water measurements. An inverse kinematics (IK) approach has been proposed where a few tasks would be measured by inertial sensors or inclinometers (Begon & Sardain, 2007). However, due to the lack of actual kinematics, the authors could not assess its reliability. The purpose of this study is to assess the accuracy of this IK algorithm by comparison with a standard algorithm of global optimization

Turing patterns and apparent competition in predator-prey food webs on networks

Reaction-diffusion systems may lead to the formation of steady state heterogeneous spatial patterns, known as Turing patterns. Their mathematical formulation is important for the study of pattern formation in general and play central roles in many fields of biology, such as ecology and morphogenesis. In the present study we focus on the role of Turing patterns in describing the abundance distribution of predator and prey species distributed in patches in a scale free network structure. We extend the original model proposed by Nakao and Mikhailov by considering food chains with several interacting pairs of preys and predators. We identify patterns of species distribution displaying high degrees of apparent competition driven by Turing instabilities. Our results provide further indication that differences in abundance distribution among patches may be, at least in part, due to self organized Turing patterns, and not necessarily to intrinsic environmental heterogeneity

Coexistence and critical behaviour in a lattice model of competing species

In the present paper we study a lattice model of two species competing for the same resources. Monte Carlo simulations for d=1, 2, and 3 show that when resources are easily available both species coexist. However, when the supply of resources is on an intermediate level, the species with slower metabolism becomes extinct. On the other hand, when resources are scarce it is the species with faster metabolism that becomes extinct. The range of coexistence of the two species increases with dimension. We suggest that our model might describe some aspects of the competition between normal and tumor cells. With such an interpretation, examples of tumor remission, recurrence and of different morphologies are presented. In the d=1 and d=2 models, we analyse the nature of phase transitions: they are either discontinuous or belong to the directed-percolation universality class, and in some cases they have an active subcritical phase. In the d=2 case, one of the transitions seems to be characterized by critical exponents different than directed-percolation ones, but this transition could be also weakly discontinuous. In the d=3 version, Monte Carlo simulations are in a good agreement with the solution of the mean-field approximation. This approximation predicts that oscillatory behaviour occurs in the present model, but only for d>2. For d>=2, a steady state depends on the initial configuration in some cases.Comment: 11 pages, 14 figure

Mathematical Model of Easter Island Society Collapse

In this paper we consider a mathematical model for the evolution and collapse of the Easter Island society, starting from the fifth century until the last period of the society collapse (fifteen century). Based on historical reports, the available primary sources consisted almost exclusively on the trees. We describe the inhabitants and the resources as an isolated system and both considered as dynamic variables. A mathematical analysis about why the structure of the Easter Island community collapse is performed. In particular, we analyze the critical values of the fundamental parameters driving the interaction humans-environment and consequently leading to the collapse. The technological parameter, quantifying the exploitation of the resources, is calculated and applied to the case of other extinguished civilization (Cop\'an Maya) confirming, with a sufficiently precise estimation, the consistency of the adopted model.Comment: 9 pages, 1 figure, final version published on EuroPhysics Letter

Host-parasite biology in the real world: the field voles of Kielder

Peer reviewedPublisher PD

Statistical mechanics and stability of a model eco-system

We study a model ecosystem by means of dynamical techniques from disordered systems theory. The model describes a set of species subject to competitive interactions through a background of resources, which they feed upon. Additionally direct competitive or co-operative interaction between species may occur through a random coupling matrix. We compute the order parameters of the system in a fixed point regime, and identify the onset of instability and compute the phase diagram. We focus on the effects of variability of resources, direct interaction between species, co-operation pressure and dilution on the stability and the diversity of the ecosystem. It is shown that resources can be exploited optimally only in absence of co-operation pressure or direct interaction between species.Comment: 23 pages, 13 figures; text of paper modified, discussion extended, references adde