Stochastic optimization for the calculation of the time dependency of the physiological demand during exercise and recovery

The stochastic optimization method ALOPEX IV is successfully applied to the problem of estimating the time dependency of the physiological demand in response to exercise. This is a fundamental and unsolved problem in the area of exercise physiology, where the lack of appropriate tools and techniques forces the assumption and the use of a constant demand during exercise. By the use of an appropriate partition of the physiological time series and by means of stochastic optimization, the time dependency of the physiological demand during heavy intensity exercise and its subsequent recovery is, for the first time, revealed.     

Stochastic optimization for modeling physiological time series: application to the heart rate response to exercise

Stochastic optimization is applied to the problem of optimizing the fit of a model to the time series of raw physiological (heart rate) data. The physiological response to exercise has been recently modeled as a dynamical system. Fitting the model to a set of raw physiological time series data is, however, not a trivial task. For this reason and in order to calculate the optimal values of the parameters of the model, the present study implements the powerful stochastic optimization method ALOPEX IV, an algorithm that has been proven to be fast, effective and easy to implement. The optimal parameters of the model, calculated by the optimization method for the particular athlete, are very important as they characterize the athlete's current condition. The present study applies the ALOPEX IV stochastic optimization to the modeling of a set of heart rate time series data corresponding to different exercises of constant intensity. An analysis of the optimization algorithm, together with an analytic proof of its convergence (in the absence of noise), is also presented.     

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 problem of 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.     

PANMIN: sequential and parallel global optimization procedures with a variety of options for the local search strategy

We present two sequential and one parallel global optimization codes, that belong to the stochastic class, and an interface routine that enables the use of the Merlin/MCL environment as a non-interactive local optimizer. This interface proved extremely important, since it provides flexibility, effectiveness and robustness to the local search task that is in turn employed by the global procedures. We demonstrate the use of the parallel code to a molecular conformation problem.

Program summary

Title of program: PANMINCatalogue identifier: ADSUProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSUProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandComputer for which the program is designed and others on which it has been tested: PANMIN is designed for UNIX machines. The parallel code runs on either shared memory architectures or on a distributed system. The code has been tested on a SUN Microsystems ENTERPRISE 450 with four CPUs, and on a 48-node cluster under Linux, with both the GNU g77 and the Portland group compilers. The parallel implementation is based on MPI and has been tested with LAM MPI and MPICHInstallation: University of Ioannina, GreeceProgramming language used: Fortran-77Memory required to execute with typical data: Approximately O(n²) words, where n is the number of variablesNo. of bits in a word: 64No. of processors used: 1 or manyHas the code been vectorised or parallelized?: Parallelized using MPINo. of bytes in distributed program, including test data, etc.: 147163No. of lines in distributed program, including the test data, etc.: 14366Distribution format: gzipped tar fileNature of physical problem: A multitude of problems in science and engineering are often reduced to minimizing a function of many variables. There are instances that a local optimum does not correspond to the desired physical solution and hence the search for a better solution is required. Local optimization techniques can be trapped in any local minimum. Global Optimization is then the appropriate tool. For example, solving a non-linear system of equations via optimization, one may encounter many local minima that do not correspond to solutions, i.e. they are far from zeroMethod of solution: PANMIN is a suite of programs for Global Optimization that take advantage of the Merlin/MCL optimization environment [1,2]. We offer implementations of two algorithms that belong to the stochastic class and use local searches either as intermediate steps or as solution refinementRestrictions on the complexity of the problem: The only restriction is set by the available memory of the hardware configuration. The software can handle bound constrained problems. The Merlin Optimization environment must be installed. Availability of an MPI installation is necessary for executing the parallel codeTypical running time: Depending on the objective functionReferences: [1] D.G. Papageorgiou, I.N. Demetropoulos, I.E. Lagaris, Merlin-3.0. A multidimensional optimization environment, Comput. Phys. Commun. 109 (1998) 227-249. [2] D.G. Papageorgiou, I.N. Demetropoulos, I.E. Lagaris, The Merlin Control Language for strategic optimization, Comput. Phys. Commun. 109 (1998) 250-275.     

A new algorithm for fast simulation of optical spectra generated in a nonlinear media

A new and highly efficient algorithm developed under MATLAB for calculating the optical spectra generated by non-resonant optical parametric fluorescence is presented. This algorithm, which allows quick simulation of the spectra, is shown to be much more rapid than standard ones. The ways to modify the algorithm for other environments are discussed.

Program summary

Title of the program:OPFSpectraFinderCatalogue number: ADTKProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTKProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions: Persons requesting the program must sign the standard CPC non-profit use licenseComputers on which the program has been tested: Intel Pentium, SUN HPC3500Operating system under which the program, has been tested: Microsoft Windows 2000, Unix Solaris 7.0Programming language used: MATLAB 6.0Memory required to execute with typical data: 256 M (the total computer memory)No. of processors used: 1No. of bytes in distributed program, including test data, etc.: 935 376No. of lines in distributed program, including test data, etc.: 6667Distribution format: tar gzip fileNature of physical problem: Obtaining the form of optical spectra of light generated in the process of optical parametric fluorescence in a periodically poled quadratically nonlinear mediumMethod of solution: Linearization of the set of nonlinear equations, obtaining the set of equations with constant coefficients, finding the solution as the matrix exponentialRestrictions on the complexity of the problem: not knownTypical running time: 80 seconds for obtaining the data for data set by default in the files submitted on a PC mentioned aboveReferences: The physical discussion is given in V. Beskrovnyy, P. Baldi, Optical parametric fluorescence spectra in periodically poled media, Optics Express 10 (2002) 990     

A pitfall in the use of extended likelihood for fitting fractions of pure samples in a mixed sample

The paper elucidates, with an analytic example, a subtle mistake in the application of the extended likelihood method to the problem of determining the fractions of pure samples in a mixed sample from the shape of the distribution of a random variable. This mistake, which affects two widely used software packages, leads to a misestimate of the errors.     

A numerical procedure for inferring from experimental data the optimization cost functions using a multibody model of the neuro-musculoskeletal system

We propose a computational procedure for inferring the cost functions that, according to the Principle of Optimality, underlie experimentally observed motor strategies. In the current use of optimization-based mathematical models of neuro-musculoskeletal systems, the cost functions are not known a-priori, since they can not be directly observed or measured on the real bio-system. Consequently, cost functions need to be hypothesized for any given motor task of interest, based on insight into the physical processes that govern the problem.This work tries to overcome the need to hypothesize the cost functions, extracting this non-directly observable information from experimental data. Optimality criteria of observed motor tasks are here indirectly derived using: (a) a mathematical model of the bio-system; and (b) a parametric mathematical model of the possible cost functions, i.e. a search space constructed in such a way as to presumably contain the unknown function that was used by the bio-system in the given motor task of interest. The cost function that best matches the experimental data is identified within the search space by solving a nested optimization problem. This problem can be recast as a non-linear programming problem and therefore solved using standard techniques.The methodology is here formulated for both static and dynamic problems, and then tested on representative examples.     

Development of a model for the estimation of photosynthetically active radiation from geostationary satellite data in a tropical environment

This paper presents a model for the estimation of photosynthetically active radiation (PAR) from geostationary satellite data. The model is aimed to estimate the monthly average hourly PAR in a tropical environment. This model represents a physical relation of PAR incident on the earth's surface and satellite-derived earth-atmospheric albedo together with the absorption and scattering coefficients of various atmospheric constituents. The earth-atmospheric albedo was obtained from the Multifunctional Transport Satellite-1R (MTSAT-1R). The absorption of PAR by water vapor, an important process for the tropics, was computed from the ambient temperature and relative humidity. The absorption of PAR by aerosols was estimated by using the visibility data and aerosol optical properties obtained from the Aerosol Robotic Network (AERONET) of NASA in this region. The total column ozone from the Ozone Monitoring Instrument onboard of AURA satellite (OMI/AURA) was used for the estimation of the absorption of PAR by ozone. The model was validated against the monthly average hourly PAR from measurements at four solar radiation measuring stations situated in the tropical environment of Thailand. The values of the monthly average hourly PAR estimated from the model and those obtained from the measurement were in good agreement, with the root mean square error (RMSE) and mean bias error (MBE) of 9.8% and 0.6%, respectively. After the validation, the model was employed to estimate the monthly average hourly PAR over Thailand using a 4-year period of data from MTSAT-1R and other ancillary surface data. Values of the monthly average hourly PAR were presented as maps showing the geographical distribution of PAR. These maps reveal the diurnal and seasonal variation of PAR over the country.