Stochastic optimization for a tip-tilt adaptive correcting system

We present computer simulations of a tip-tilt adaptive optics system, where stochastic optimization is applied to the problemof dynamic compensation of atmospheric turbulence. The system uses a simple measure of the light intensity that passes through a mask and is recorded on the image plane, to generate signals for the tip-tilt mirror. A feedback system rotates the mirror adaptively and in phase with the rapidly changing atmospheric conditions. Computer simulations and a series of numerical experiments investigate the implementation of the method in the presence of drifting atmosphere. In particular, the study examines the system’s sensitivity to the rate of change of the atmospheric conditions and investigates the optimal size of the mirror’s masking area and the algorithm’s optimal degree of stochasticity.Peer Reviewe

Stochastic optimization for adaptive real -time wavefront correction

We have investigated the performance of an adaptive optics system subjected to changing atmospheric conditions, under the guidance of the ALOPEX stochastic optimization. Atmospheric distortions are smoothed out by means of a deformable mirror, the shape of which can be altered in order to follow the rapidly changing atmospheric phase fluctuations. In a simulation model, the total intensity of the light measured on a central area of the image (masking area) is used as the cost function for our stochastic optimization algorithm, while the surface of the deformable mirror is approximated by a Zernike polynomial expansion. Atmospheric turbulence is simulated by a number of Kolmogorov filters. The method's effectiveness, that is its ability to follow the motion of the turbulent wavefronts, is studied in detail and as it pertains to the size of the mirror's masking area, to the number of Zernike polynomials used and to the degree of the algorithm's stochasticity in relation to the mean rate of change of atmospheric distortions. Computer simulations and a series of numerical experiments are reported to show the successful implementation of the method

The point of maximum curvature as a marker for physiological time series

We present a geometric analysis of the model of Stirling. In particular we analyze the curvature of a heart rate time series in response to a step like increment in the exercise intensity. We present solutions for the point of maximum curvature which can be used as a marker of physiological interest. This marker defines the point after which the heart rate no longer continues to rapidly rise and instead follows either a steady state or slow rise. These methods are then applied to find analytic solutions for a mono exponential model which is commonly used in the literature to model the response to a moderate exercise intensity. Numerical solutions are then found for the full model and parameter values presented in Stirling

Obtaining the basic response pattern of physiological time series data : a comparison of methods

An understanding of the kinetics of physiological variables such as the heart rate or the rate of change of volume of oxygen uptake is fundamental not only to training methodology and competitive success in sport and exercise, but also to our knowledge of cardiovascular health. A correct and efficient means of interpreting and analyzing the data obtained is of vast importance, as exercise testing is routinely used in both of these areas

Geometry and transport in a model of two coupled quadratic nonlinear waveguides

This paper applies geometric methods developed to understand chaos and transport in Hamiltonian systems to the study of power distribution in nonlinear waveguide arrays. The specific case of two linearly coupled X(2) waveguides is modeled and analyzed in terms of transport and geometry in the phase space. This gives us a transport problem in the phase space resulting from the coupling of the two Hamiltonian systems for each waveguide. In particular, the effect of the presence of partial and complete barriers in the phase space on the transfer of intensity between the waveguides is studied, given a specific input and range of material properties. We show how these barriers break down as the coupling between the waveguides is increased and what the role of resonances in the phase space has in this. We also show how an increase in the coupling can lead to chaos and global transport and what effect this has on the intensity

Rotated balance in humans due to repetitive rotational movement

We show how asymmetries in the movement patterns during the process of regaining balance after perturbation from quiet stance can be modeled by a set of coupled vector fields for the derivative with respect to time of the angles between the resultant ground reaction forces and the vertical in the anteroposterior and mediolateral directions. In our model, which is an adaption of the model of Stirling and Zakynthinaki (2004), the critical curve, defining the set of maximum angles one can lean to and still correct to regain balance, can be rotated and skewed so as to model the effects of a repetitive training of a rotational movement pattern. For the purposes of our study a rotation and a skew matrix is applied to the critical curve of the model. We present here a linear stability analysis of the modified model, as well as a fit of the model to experimental data of two characteristic “asymmetric” elite athletes and to a “symmetric” elite athlete for comparison. The new adapted model has many uses not just in sport but also in rehabilitation, as many work place injuries are caused by excessive repetition of unaligned and rotational movement patterns

Stochastic optimization for a tip-tilt adaptive correcting system

We present computer simulations of a tip-tilt adaptive optics system, where stochastic optimization is applied to the problemof dynamic compensation of atmospheric turbulence. The system uses a simple measure of the light intensity that passes through a mask and is recorded on the image plane, to generate signals for the tip-tilt mirror. A feedback system rotates the mirror adaptively and in phase with the rapidly changing atmospheric conditions. Computer simulations and a series of numerical experiments investigate the implementation of the method in the presence of drifting atmosphere. In particular, the study examines the system’s sensitivity to the rate of change of the atmospheric conditions and investigates the optimal size of the mirror’s masking area and the algorithm’s optimal degree of stochasticity.Peer Reviewe

Stochastic optimization for adaptive real -time wavefront correction

We have investigated the performance of an adaptive optics system subjected to changing atmospheric conditions, under the guidance of the ALOPEX stochastic optimization. Atmospheric distortions are smoothed out by means of a deformable mirror, the shape of which can be altered in order to follow the rapidly changing atmospheric phase fluctuations. In a simulation model, the total intensity of the light measured on a central area of the image (masking area) is used as the cost function for our stochastic optimization algorithm, while the surface of the deformable mirror is approximated by a Zernike polynomial expansion. Atmospheric turbulence is simulated by a number of Kolmogorov filters. The method's effectiveness, that is its ability to follow the motion of the turbulent wavefronts, is studied in detail and as it pertains to the size of the mirror's masking area, to the number of Zernike polynomials used and to the degree of the algorithm's stochasticity in relation to the mean rate of change of atmospheric distortions. Computer simulations and a series of numerical experiments are reported to show the successful implementation of the method

Stochastic optimization for adaptive real -time wavefront correction

We have investigated the performance of an adaptive optics system subjected to changing atmospheric conditions, under the guidance of the ALOPEX stochastic optimization. Atmospheric distortions are smoothed out by means of a deformable mirror, the shape of which can be altered in order to follow the rapidly changing atmospheric phase fluctuations. In a simulation model, the total intensity of the light measured on a central area of the image (masking area) is used as the cost function for our stochastic optimization algorithm, while the surface of the deformable mirror is approximated by a Zernike polynomial expansion. Atmospheric turbulence is simulated by a number of Kolmogorov filters. The method's effectiveness, that is its ability to follow the motion of the turbulent wavefronts, is studied in detail and as it pertains to the size of the mirror's masking area, to the number of Zernike polynomials used and to the degree of the algorithm's stochasticity in relation to the mean rate of change of atmospheric distortions. Computer simulations and a series of numerical experiments are reported to show the successful implementation of the method

Obtaining the basic response pattern of physiological time series data : a comparison of methods

An understanding of the kinetics of physiological variables such as the heart rate or the rate of change of volume of oxygen uptake is fundamental not only to training methodology and competitive success in sport and exercise, but also to our knowledge of cardiovascular health. A correct and efficient means of interpreting and analyzing the data obtained is of vast importance, as exercise testing is routinely used in both of these areas