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At least 217 records · Page 12

Quantum Adiabatic Optimization and Combinatorial Landscapes

In this paper we analyze the performance of the Quantum Adiabatic Evolution (QAE) algorithm on a variant of Satisfiability problem for an ensemble of random graphs parametrized by the ratio of clauses to variables, gamma = M / N. We introduce a set of macroscopic parameters (landscapes) and put forward an ansatz of universality for random bit flips. We then formulate the problem of finding the smallest eigenvalue and the excitation gap as a statistical mechanics problem. We use the so-called annealing approximation with a refinement that a finite set of macroscopic variables (verses only energy) is used, and are able to show the existence of a dynamic threshold gamma = gammad, beyond which QAE should take an exponentially long time to find a solution. We compare the results for extended and simplified sets of landscapes and provide numerical evidence in support of our universality ansatz.

Smelyanskiy, V. N.↗

Diffusion Codes: Self-Correction from Small(er)-Set Expansion with Tunable Non-locality

Optimal constructions of classical LDPC codes can be obtained by choosing the Tanner graph uniformly at random among biregular graphs. We introduce a class of codes that we call ``diffusion codes'', defined by placing each edge connecting bits and checks on some graph, and acting on that graph with a random SWAP network. By tuning the depth of the SWAP network, we can tune a tradeoff between the amount of randomness -- and hence the optimality of code parameters -- and locality with respect to the underlying graph. For diffusion codes defined on the cycle graph, if the SWAP network has depth $\sim Tn$ with $T> n^{2β}$ for arbitrary $β>0$, then we prove that almost surely the Tanner graph is a lossless ``smaller set'' vertex expander for small sets up size $δ\sim \sqrt T \sim n^β$, with bounded bit and check degree. At the same time, the geometric size of the largest stabilizer is bounded by $\sqrt T$ in graph distance. We argue, based on physical intuition, that this result should hold more generally on arbitrary graphs. By taking hypergraph products of these classical codes we obtain quantum LDPC codes defined on the torus with smaller-set boundary and co-boundary expansion and the same expansion/locality tradeoffs as for the classical codes. These codes are self-correcting and admit single-shot decoding, while having the geometric size of the stabilizer growing as an arbitrarily small power law. Our proof technique establishes mixing of a random SWAP network on small subsystems at times scaling with only the subsystem size, which may be of independent interest.

Combinatorics (math.CO)↗

Application of multivariable search techniques to the optimization of airfoils in a low speed nonlinear inviscid flow field

Multivariable search techniques are applied to a particular class of airfoil optimization problems. These are the maximization of lift and the minimization of disturbance pressure magnitude in an inviscid nonlinear flow field. A variety of multivariable search techniques contained in an existing nonlinear optimization code, AESOP, are applied to this design problem. These techniques include elementary single parameter perturbation methods, organized search such as steepest-descent, quadratic, and Davidon methods, randomized procedures, and a generalized search acceleration technique. Airfoil design variables are seven in number and define perturbations to the profile of an existing NACA airfoil. The relative efficiency of the techniques are compared. It is shown that elementary one parameter at a time and random techniques compare favorably with organized searches in the class of problems considered. It is also shown that significant reductions in disturbance pressure magnitude can be made while retaining reasonable lift coefficient values at low free stream Mach numbers.

Hague, D. S.↗

A Probabilistic Design Method Applied to Smart Composite Structures

A probabilistic design method is described and demonstrated using a smart composite wing. Probabilistic structural design incorporates naturally occurring uncertainties including those in constituent (fiber/matrix) material properties, fabrication variables, structure geometry and control-related parameters. Probabilistic sensitivity factors are computed to identify those parameters that have a great influence on a specific structural reliability. Two performance criteria are used to demonstrate this design methodology. The first criterion requires that the actuated angle at the wing tip be bounded by upper and lower limits at a specified reliability. The second criterion requires that the probability of ply damage due to random impact load be smaller than an assigned value. When the relationship between reliability improvement and the sensitivity factors is assessed, the results show that a reduction in the scatter of the random variable with the largest sensitivity factor (absolute value) provides the lowest failure probability. An increase in the mean of the random variable with a negative sensitivity factor will reduce the failure probability. Therefore, the design can be improved by controlling or selecting distribution parameters associated with random variables. This can be implemented during the manufacturing process to obtain maximum benefit with minimum alterations.

Shiao, Michael C.↗

On the existence, uniqueness, and asymptotic normality of a consistent solution of the likelihood equations for nonidentically distributed observations: Applications to missing data problems

A general theorem is given which establishes the existence and uniqueness of a consistent solution of the likelihood equations given a sequence of independent random vectors whose distributions are not identical but have the same parameter set. In addition, it is shown that the consistent solution is a MLE and that it is asymptotically normal and efficient. Two applications are discussed: one in which independent observations of a normal random vector have missing components, and the other in which the parameters in a mixture from an exponential family are estimated using independent homogeneous sample blocks of different sizes.

Peters, C.↗

ytopt: Autotuning Scientific Applications for Energy Efficiency at Large Scales

As we enter the exascale computing era, efficiently utilizing power and optimizing the performance of scientific applications under power and energy constraints has become critical and challenging. We propose a low-overhead autotuning framework to autotune performance and energy for various hybrid MPI/OpenMP scientific applications at large scales and to explore the tradeoffs between application runtime and power/energy for energy efficient application execution, then use this framework to autotune four ECP proxy applications—XSBench, AMG, SWFFT, and SW4lite. Our approach uses Bayesian optimization with a Random Forest surrogate model to effectively search parameter spaces with up to 6 million different configurations on two large-scale HPC production systems, Theta at Argonne National Laboratory and Summit at Oak Ridge National Laboratory. The experimental results show that our autotuning framework at large scales has low overhead and achieves good scalability. Using the proposed autotuning framework to identify the best configurations, we achieve up to 91.59% performance improvement, up to 21.2% energy savings, and up to 37.84% EDP (energy delay product) improvement on up to 4096 nodes.

Autotuning↗

Development and optimization of a nonlinear multiparameter model for the human operator

A systematic method is proposed for the development, optimization, and comparison of controller-models for the human operator. This is suitable for any designed model, even multiparameter systems. A random search technique is chosen for the parameter optimization. As valuation criteria for the quality of the model development the criterion function - the comparison between the input and output functions of the human operator and those of the model - and the most important characteristic values and functions of the statistical signal theory are used. A nonlinear multiparameter model for the human operator is being designed which considers the complex input information rate per time in a single display. The nonlinear features of the model are effected by a modified threshold element and a decision algorithm. Different display-configurations as well as various transfer functions of the controlled element are explained by different optimized parameter-combinations.

Johannsen, G.↗

A discussion of dynamic stability measurement techniques

Techniques for the measurement of the dynamic stability of linear systems are discussed. Particular attention is given to an analysis of the errors in the procedures, and to methods for calculating the system damping from the data. The techniques discussed include: transient decay, moving block analysis, spectral analysis, random decrement signatures, transfer function analysis, and parameter identification methods. The special problems of rotorcraft dynamic stability testing are discussed.

Johnson, W.↗

System identification of large space structures

The paper deals with the problem of system identifiability for a linear dynamical system. Two theorems are given relating the sufficient condition of system identifiability for certain linear structures to the total number of inputs and outputs. The principle of least squares, that seeks the minimization of a cost function is employed to carry out the system identification process. To illustrate the concept of the paper, a structural model of a beam with point masses is examined. Parameter identification methods are studied and a random search technique is introduced.

Juang, J. N.↗

Non-Gaussian statistical models of surface wave fields for remote sensing applications

Based on the complete Stokes wave model with the bias term and using a simple mapping approach and an iteration solution method, we established a formula for the joint probability density function of the surface slope elevation of a nonlinear random wave field. The formula requires three parameters to define the whole density function: the rms surface elevation and slope values and the significant slope. This model represents the dynamics of the wave in a more direct way than the Gram-Charlier approximation. Based on this new statistical model and laboratory experiments, formula and numerical values of EM bias and dynamics bias are derived. The results indicate that various biases should be considered seriously if accuracy of the altimeter measurement is required in centimeter range.

Huang, N. E.↗

Maximum likelihood algorithm using an efficient scheme for computing sensitivities and parameter confidence intervals

Improved techniques for estimating airplane stability and control derivatives and their standard errors are presented. A maximum likelihood estimation algorithm is developed which relies on an optimization scheme referred to as a modified Newton-Raphson scheme with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort compared to integrating the analytically-determined sensitivity equations or using a finite difference scheme. An aircraft estimation problem is solved using real flight data to compare MNRES with the commonly used modified Newton-Raphson technique; MNRES is found to be faster and more generally applicable. Parameter standard errors are determined using a random search technique. The confidence intervals obtained are compared with Cramer-Rao lower bounds at the same confidence level. It is observed that the nonlinearity of the cost function is an important factor in the relationship between Cramer-Rao bounds and the error bounds determined by the search technique.

Murphy, P. C.↗

Fuzzy sets predict flexural strength and density of silicon nitride ceramics

In this work, we utilize fuzzy sets theory to evaluate and make predictions of flexural strength and density of NASA 6Y silicon nitride ceramic. Processing variables of milling time, sintering time, and sintering nitrogen pressure are used as an input to the fuzzy system. Flexural strength and density are the output parameters of the system. Data from 273 Si3N4 modulus of rupture bars tested at room temperature and 135 bars tested at 1370 C are used in this study. Generalized mean operator and Hamming distance are utilized to build the fuzzy predictive model. The maximum test error for density does not exceed 3.3 percent, and for flexural strength 7.1 percent, as compared with the errors of 1.72 percent and 11.34 percent obtained by using neural networks, respectively. These results demonstrate that fuzzy sets theory can be incorporated into the process of designing materials, such as ceramics, especially for assessing more complex relationships between the processing variables and parameters, like strength, which are governed by randomness of manufacturing processes.

Cios, Krzysztof J.↗

A comparative study of clock rate and drift estimation

Five different methods of drift determination and four different methods of rate determination were compared using months of hourly phase and frequency data from a sample of cesium clocks and active hydrogen masers. Linear least squares on frequency is selected as the optimal method of determining both drift and rate, more on the basis of parameter parsimony and confidence measures than on random and systematic errors.

Breakiron, Lee A.↗

The Prospect for Remote Sensing of Cirrus Clouds with a Submillimeter-Wave Spectrometer

Given the substantial radiative effects of cirrus clouds and the need to validate cirrus cloud mass in climate models, it is important to measure the global distribution of cirrus properties with satellite remote sensing. Existing cirrus remote sensing techniques, such as solar reflectance methods, measure cirrus ice water path (IWP) rather indirectly and with limited accuracy. Submillimeter/wave radiometry is an independent method of cirrus remote sensing based on ice particles scattering the upwelling radiance emitted by the lower atmosphere. A new aircraft instrument, the Far Infrared Sensor for Cirrus (FIRSC), is described. The FIRSC employs a Fourier Transform Spectrometer (FTS). which measures the upwelling radiance across the whole submillimeter region (0.1 1.0-mm wavelength). This wide spectral coverage gives high sensitivity to most cirrus particle sizes and allows accurate determination of the characteristic particle size. Radiative transfer modeling is performed to analyze the capabilities of the submillimeter FTS technique. A linear inversion analysis is done to show that cirrus IWP, particle size, and upper-tropospheric temperature and water vapor may be accurately measured, A nonlinear statistical algorithm is developed using a database of 20000 spectra simulated by randomly varying most relevant cirrus and atmospheric parameters. An empirical orthogonal function analysis reduces the 500-point spectrum (20 - 70/cm) to 15 "pseudo-channels" that are then input to a neural network to retrieve cirrus IWP and median particle diameter. A Monte Carlo accuracy study is performed with simulated spectra having realistic noise. The retrieval errors are low for IWP (rms less than a factor of 1.5) and for particle sizes (rins less than 30%) for IWP greater than 5 g/sq m and a wide range of median particle sizes. This detailed modeling indicates that there is good potential to accurately measure cirrus properties with a submillimeter FTS.

Evans, K. Franklin↗

Novel Image Processing Interface to Relate DSB Spatial Distribution from Immunofluorescence Foci Experiments to the State-of-the-Art Models of DNA Breakage

A recently developed software (NASARadiationTrackImage) allows a quick and automatic segmentation of foci that indicate spatial localization of specific proteins that are visualized by immunofluorescence. Of interest are the spatial and temporal distribution of foci such as gammaH2AX, a signal of the phosphorylation of a variant of the histone H2A that has been shown to correspond to DSBs, or proteins involved in DSB processing, such as ATM, Rad51, and p53, following exposures of human cells to high charge and energy (HZE) ion irradiation. Experimental data are recorded as sets of two-dimensional images in color with cells and foci of gammaH2AX, ATM, Rad51 or others shown. Different cells, levels of radiation and timing after radiation were recorded. The software allows us to calculate the number of foci per cell, overall intensity of light in foci and their spatial organization. A simple statistical model allows for testing of foci overlap (eclipse). A more complex statistical model previously known as DNAbreak simulates track structure and random chromosome geometry. It has one adjustable parameter corresponding to an average intensity of DSB creation in cubic micrometers of DNA volume per particle track or unit dose. Its limitation is the low-resolution limit both in physical space and DSB's along DNA. It works adequately on the scale of a cell and provides further insights on how the geometry of tracks and DNA affects genomic damage of the cell and subsequent repair. Future developments of the model for the description of the time evolution of DNA damage response proteins, and more robust track structure models will be discussed.

Ponomarev, A. L.↗

Space-Time Data Fusion

Space-time Data Fusion (STDF) is a methodology for combing heterogeneous remote sensing data to optimally estimate the true values of a geophysical field of interest, and obtain uncertainties for those estimates. The input data sets may have different observing characteristics including different footprints, spatial resolutions and fields of view, orbit cycles, biases, and noise characteristics. Despite these differences all observed data can be linked to the underlying field, and therefore the each other, by a statistical model. Differences in footprints and other geometric characteristics are accounted for by parameterizing pixel-level remote sensing observations as spatial integrals of true field values lying within pixel boundaries, plus measurement error. Both spatial and temporal correlations in the true field and in the observations are estimated and incorporated through the use of a space-time random effects (STRE) model. Once the models parameters are estimated, we use it to derive expressions for optimal (minimum mean squared error and unbiased) estimates of the true field at any arbitrary location of interest, computed from the observations. Standard errors of these estimates are also produced, allowing confidence intervals to be constructed. The procedure is carried out on a fine spatial grid to approximate a continuous field. We demonstrate STDF by applying it to the problem of estimating CO2 concentration in the lower-atmosphere using data from the Atmospheric Infrared Sounder (AIRS) and the Japanese Greenhouse Gasses Observing Satellite (GOSAT) over one year for the continental US.

Greenhouse Gases Observing Satellite (GOSAT)↗

On-line methods for rotorcraft aeroelastic mode identification

The requirements for the on-line identification of rotorcraft aeroelastic blade modes from random response test data are presented. A recursive maximum likelihood (RML) technique is used in conjunction with a bandpass filter to identify isolated blade mode damping and frequency. The RML technique is demonstrated to have excellent convergence characteristics in random measurement noise and random process noise excitation. The RML identification technique uses an ARMA representation for the aeroelastic stochastic system and requires virtually no user interaction while providing accurate confidence bands on the parameter estimates. Comparisons are made with an off-line Newton type maximum likelihood algorithm which uses a state variable model representation. Results are presented from simulation random response data which quantify the identifed parameter convergence behavior for various levels of random excitation which is typical of wind tunnel turbulence levels. The RML technique is applied to hingless rotor test data from the NASA Langley Research Center Helicopter Hover Facility.

Molusis, J. A.↗