A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws

In this article we consider one-dimensional random systems of hyperbolic conservation laws. We first establish existence and uniqueness of random entropy admissible solutions for initial value problems of conservation laws which involve random initial data and random flux functions. Based on these results we present an a posteriori error analysis for a numerical approximation of the random entropy admissible solution. For the stochastic discretization, we consider a non-intrusive approach, the Stochastic Collocation method. The spatio-temporal discretization relies on the Runge--Kutta Discontinuous Galerkin method. We derive the a posteriori estimator using continuous reconstructions of the discrete solution. Combined with the relative entropy stability framework this yields computable error bounds for the entire space-stochastic discretization error. The estimator admits a splitting into a stochastic and a deterministic (space-time) part, allowing for a novel residual-based space-stochastic adaptive mesh refinement algorithm. We conclude with various numerical examples investigating the scaling properties of the residuals and illustrating the efficiency of the proposed adaptive algorithm

Collaborative Gaze Channelling for Improved Cooperation During Robotic Assisted Surgery

The use of multiple robots for performing complex tasks is becoming a common practice for many robot applications. When different operators are involved, effective cooperation with anticipated manoeuvres is important for seamless, synergistic control of all the end-effectors. In this paper, the concept of Collaborative Gaze Channelling (CGC) is presented for improved control of surgical robots for a shared task. Through eye tracking, the fixations of each operator are monitored and presented in a shared surgical workspace. CGC permits remote or physically separated collaborators to share their intention by visualising the eye gaze of their counterparts, and thus recovers, to a certain extent, the information of mutual intent that we rely upon in a vis-à-vis working setting. In this study, the efficiency of surgical manipulation with and without CGC for controlling a pair of bimanual surgical robots is evaluated by analysing the level of coordination of two independent operators. Fitts' law is used to compare the quality of movement with or without CGC. A total of 40 subjects have been recruited for this study and the results show that the proposed CGC framework exhibits significant improvement (p<0.05) on all the motion indices used for quality assessment. This study demonstrates that visual guidance is an implicit yet effective way of communication during collaborative tasks for robotic surgery. Detailed experimental validation results demonstrate the potential clinical value of the proposed CGC framework. © 2012 Biomedical Engineering Society.link_to_subscribed_fulltex

Accretions of Various Types of Dark Energies onto Morris-Thorne Wormhole

In this work, we have studied accretion of the dark energies onto Morris-Thorne wormhole. For quintessence like dark energy, the mass of the wormhole decreases and phantom like dark energy, the mass of wormhole increases. We have assumed two types of dark energy like variable modified Chaplygin gas (VMCG) and generalized cosmic Chaplygin gas (GCCG). We have found the expression of wormhole mass in both cases. We have found the mass of the wormhole at late universe and this is finite. For our choices the parameters and the function $B(a)$, these models generate only quintessence dark energy (not phantom) and so wormhole mass decreases during evolution of the universe. Next we have assumed 5 kinds of parametrizations of well known dark energy models. These models generate both quintessence and phantom scenarios. So if these dark energies accrete onto the wormhole, then for quintessence stage, wormhole mass decreases upto a certain value (finite value) and then again increases to infinite value for phantom stage during whole evolution of the universe. We also shown these results graphically.Comment: 9 pages, 7 figures. arXiv admin note: text overlap with arXiv:1112.615

Contribution of anadromous fish to the diet of European catfish in a large river system

Many anadromous fish species, when migrating from the sea to spawn in fresh waters, can potentially be a valuable prey for larger predatory fish, thereby efficiently linking these two ecosystems. Here, we assess the contribution of anadromous fish to the diet of European catfish (Silurus glanis) in a large river system (Garonne, southwestern France) using stable isotope analysis and allis shad (Alosa alosa) as an example of anadromous fish. Allis shad caught in the Garonne had a very distinct marine delta(13)C value, over 8 per thousand higher after lipid extraction compared to the mean delta(13)C value of all other potential freshwater prey fish. The delta(13)C values of European catfish varied considerably between these two extremes and some individuals were clearly specializing on freshwater prey, whereas others specialized on anadromous fish. The mean contribution of anadromous fish to the entire European catfish population was estimated to be between 53% and 65%, depending on the fractionation factor used for delta(13)C

Recognizing recurrent neural networks (rRNN): Bayesian inference for recurrent neural networks

Recurrent neural networks (RNNs) are widely used in computational neuroscience and machine learning applications. In an RNN, each neuron computes its output as a nonlinear function of its integrated input. While the importance of RNNs, especially as models of brain processing, is undisputed, it is also widely acknowledged that the computations in standard RNN models may be an over-simplification of what real neuronal networks compute. Here, we suggest that the RNN approach may be made both neurobiologically more plausible and computationally more powerful by its fusion with Bayesian inference techniques for nonlinear dynamical systems. In this scheme, we use an RNN as a generative model of dynamic input caused by the environment, e.g. of speech or kinematics. Given this generative RNN model, we derive Bayesian update equations that can decode its output. Critically, these updates define a 'recognizing RNN' (rRNN), in which neurons compute and exchange prediction and prediction error messages. The rRNN has several desirable features that a conventional RNN does not have, for example, fast decoding of dynamic stimuli and robustness to initial conditions and noise. Furthermore, it implements a predictive coding scheme for dynamic inputs. We suggest that the Bayesian inversion of recurrent neural networks may be useful both as a model of brain function and as a machine learning tool. We illustrate the use of the rRNN by an application to the online decoding (i.e. recognition) of human kinematics

Virtual Partner Interaction (VPI): Exploring Novel Behaviors via Coordination Dynamics

Inspired by the dynamic clamp of cellular neuroscience, this paper introduces VPI—Virtual Partner Interaction—a coupled dynamical system for studying real time interaction between a human and a machine. In this proof of concept study, human subjects coordinate hand movements with a virtual partner, an avatar of a hand whose movements are driven by a computerized version of the Haken-Kelso-Bunz (HKB) equations that have been shown to govern basic forms of human coordination. As a surrogate system for human social coordination, VPI allows one to examine regions of the parameter space not typically explored during live interactions. A number of novel behaviors never previously observed are uncovered and accounted for. Having its basis in an empirically derived theory of human coordination, VPI offers a principled approach to human-machine interaction and opens up new ways to understand how humans interact with human-like machines including identification of underlying neural mechanisms

Neurobiological degeneracy and affordance perception support functional intra-individual variability of inter-limb coordination during ice climbing

This study investigated the functional intra-individual movement variability of ice climbers differing in skill level to understand how icefall properties were used by participants as affordances to adapt inter-limb coordination patterns during performance. Seven expert climbers and seven beginners were observed as they climbed a 30 m icefall. Movement and positioning of the left and right hand ice tools, crampons and the climber's pelvis over the first 20 m of the climb were recorded and digitized using video footage from a camera (25 Hz) located perpendicular to the plane of the icefall. Inter-limb coordination, frequency and types of action and vertical axis pelvis displacement exhibited by each climber were analysed for the first five minutes of ascent. Participant perception of climbing affordances was assessed through: (i) calculating the ratio between exploratory movements and performed actions, and (ii), identifying, by self-confrontation interviews, the perceptual variables of environmental properties, which were significant to climbers for their actions. Data revealed that experts used a wider range of upper and lower limb coordination patterns, resulting in the emergence of different types of action and fewer exploratory movements, suggesting that effective holes in the icefall provided affordances to regulate performance. In contrast, beginners displayed lower levels of functional intra-individual variability of motor organization, due to repetitive swinging of ice tools and kicking of crampons to achieve and maintain a deep anchorage, suggesting lack of perceptual attunement and calibration to environmental properties to support climbing performanc

A parsimonious oscillatory model of handwriting

International audienceWe propose an oscillatory model that is theoretically parsimonious, empirically efficient and biologically plausible. Building on Hollerbach’s (Biol Cybern 39:139–156, 1981) model, our Parsimonious Oscillatory Model of Handwriting (POMH) overcomes the latter’s main shortcomings by making it possible to extract its parameters from the trace itself and by reinstating symmetry between the x and y coordinates. The benefit is a capacity to autonomously generate a smooth continuous trace that reproduces the dynamics of the handwriting movements through an extremely sparse model, whose efficiency matches that of other, more computationally expensive optimizing methods. Moreover, the model applies to 2D trajectories, irrespective of their shape, size, orientation and length. It is also independent of the endeffectors mobilized and of the writing direction