Computations of Aerodynamic Performance Databases Using Output-Based Refinement

NASA Technical Reports Server (NTRS)

Nemec, Marian; Aftosmis, Michael J.

2009-01-01

Objectives: Handle complex geometry problems; Control discretization errors via solution-adaptive mesh refinement; Focus on aerodynamic databases of parametric and optimization studies: 1. Accuracy: satisfy prescribed error bounds 2. Robustness and speed: may require over 105 mesh generations 3. Automation: avoid user supervision Obtain "expert meshes" independent of user skill; and Run every case adaptively in production settings.

Parameter estimation of qubit states with unknown phase parameter

NASA Astrophysics Data System (ADS)

Suzuki, Jun

2015-02-01

We discuss a problem of parameter estimation for quantum two-level system, qubit system, in presence of unknown phase parameter. We analyze trade-off relations for mean square errors (MSEs) when estimating relevant parameters with separable measurements based on known precision bounds; the symmetric logarithmic derivative (SLD) Cramér-Rao (CR) bound and Hayashi-Gill-Massar (HGM) bound. We investigate the optimal measurement which attains the HGM bound and discuss its properties. We show that the HGM bound for relevant parameters can be attained asymptotically by using some fraction of given n quantum states to estimate the phase parameter. We also discuss the Holevo bound which can be attained asymptotically by a collective measurement.

Model reduction by trimming for a class of semi-Markov reliability models and the corresponding error bound

NASA Technical Reports Server (NTRS)

White, Allan L.; Palumbo, Daniel L.

1991-01-01

Semi-Markov processes have proved to be an effective and convenient tool to construct models of systems that achieve reliability by redundancy and reconfiguration. These models are able to depict complex system architectures and to capture the dynamics of fault arrival and system recovery. A disadvantage of this approach is that the models can be extremely large, which poses both a model and a computational problem. Techniques are needed to reduce the model size. Because these systems are used in critical applications where failure can be expensive, there must be an analytically derived bound for the error produced by the model reduction technique. A model reduction technique called trimming is presented that can be applied to a popular class of systems. Automatic model generation programs were written to help the reliability analyst produce models of complex systems. This method, trimming, is easy to implement and the error bound easy to compute. Hence, the method lends itself to inclusion in an automatic model generator.

Adaptive Fuzzy Bounded Control for Consensus of Multiple Strict-Feedback Nonlinear Systems.

PubMed

Wang, Wei; Tong, Shaocheng

2018-02-01

This paper studies the adaptive fuzzy bounded control problem for leader-follower multiagent systems, where each follower is modeled by the uncertain nonlinear strict-feedback system. Combining the fuzzy approximation with the dynamic surface control, an adaptive fuzzy control scheme is developed to guarantee the output consensus of all agents under directed communication topologies. Different from the existing results, the bounds of the control inputs are known as a priori, and they can be determined by the feedback control gains. To realize smooth and fast learning, a predictor is introduced to estimate each error surface, and the corresponding predictor error is employed to learn the optimal fuzzy parameter vector. It is proved that the developed adaptive fuzzy control scheme guarantees the uniformly ultimate boundedness of the closed-loop systems, and the tracking error converges to a small neighborhood of the origin. The simulation results and comparisons are provided to show the validity of the control strategy presented in this paper.

IBM system/360 assembly language interval arithmetic software

NASA Technical Reports Server (NTRS)

Phillips, E. J.

1972-01-01

Computer software designed to perform interval arithmetic is described. An interval is defined as the set of all real numbers between two given numbers including or excluding one or both endpoints. Interval arithmetic consists of the various elementary arithmetic operations defined on the set of all intervals, such as interval addition, subtraction, union, etc. One of the main applications of interval arithmetic is in the area of error analysis of computer calculations. For example, it has been used sucessfully to compute bounds on sounding errors in the solution of linear algebraic systems, error bounds in numerical solutions of ordinary differential equations, as well as integral equations and boundary value problems. The described software enables users to implement algorithms of the type described in references efficiently on the IBM 360 system.

Qualitative fusion technique based on information poor system and its application to factor analysis for vibration of rolling bearings

NASA Astrophysics Data System (ADS)

Xia, Xintao; Wang, Zhongyu

2008-10-01

For some methods of stability analysis of a system using statistics, it is difficult to resolve the problems of unknown probability distribution and small sample. Therefore, a novel method is proposed in this paper to resolve these problems. This method is independent of probability distribution, and is useful for small sample systems. After rearrangement of the original data series, the order difference and two polynomial membership functions are introduced to estimate the true value, the lower bound and the supper bound of the system using fuzzy-set theory. Then empirical distribution function is investigated to ensure confidence level above 95%, and the degree of similarity is presented to evaluate stability of the system. Cases of computer simulation investigate stable systems with various probability distribution, unstable systems with linear systematic errors and periodic systematic errors and some mixed systems. The method of analysis for systematic stability is approved.

Optimization of Error-Bounded Lossy Compression for Hard-to-Compress HPC Data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Di, Sheng; Cappello, Franck

Since today’s scientific applications are producing vast amounts of data, compressing them before storage/transmission is critical. Results of existing compressors show two types of HPC data sets: highly compressible and hard to compress. In this work, we carefully design and optimize the error-bounded lossy compression for hard-tocompress scientific data. We propose an optimized algorithm that can adaptively partition the HPC data into best-fit consecutive segments each having mutually close data values, such that the compression condition can be optimized. Another significant contribution is the optimization of shifting offset such that the XOR-leading-zero length between two consecutive unpredictable data points canmore » be maximized. We finally devise an adaptive method to select the best-fit compressor at runtime for maximizing the compression factor. We evaluate our solution using 13 benchmarks based on real-world scientific problems, and we compare it with 9 other state-of-the-art compressors. Experiments show that our compressor can always guarantee the compression errors within the user-specified error bounds. Most importantly, our optimization can improve the compression factor effectively, by up to 49% for hard-tocompress data sets with similar compression/decompression time cost.« less

The calculation of average error probability in a digital fibre optical communication system

NASA Astrophysics Data System (ADS)

Rugemalira, R. A. M.

1980-03-01

This paper deals with the problem of determining the average error probability in a digital fibre optical communication system, in the presence of message dependent inhomogeneous non-stationary shot noise, additive Gaussian noise and intersymbol interference. A zero-forcing equalization receiver filter is considered. Three techniques for error rate evaluation are compared. The Chernoff bound and the Gram-Charlier series expansion methods are compared to the characteristic function technique. The latter predicts a higher receiver sensitivity

A note on the bounds of the error of Gauss-Turan-type quadratures

NASA Astrophysics Data System (ADS)

Milovanovic, Gradimir V.; Spalevic, Miodrag M.

2007-03-01

This note is concerned with estimates for the remainder term of the Gauss-Turan quadrature formula,where is the Gori-Michelli weight function, with Un-1(t) denoting the (n-1)th degree Chebyshev polynomial of the second kind, and f is a function analytic in the interior of and continuous on the boundary of an ellipse with foci at the points +/-1 and sum of semiaxes [varrho]>1. The present paper generalizes the results in [G.V. Milovanovic, M.M. Spalevic, Bounds of the error of Gauss-Turan-type quadratures, J. Comput. Appl. Math. 178 (2005) 333-346], which is concerned with the same problem when s=1.

SHARP ENTRYWISE PERTURBATION BOUNDS FOR MARKOV CHAINS.

PubMed

Thiede, Erik; VAN Koten, Brian; Weare, Jonathan

For many Markov chains of practical interest, the invariant distribution is extremely sensitive to perturbations of some entries of the transition matrix, but insensitive to others; we give an example of such a chain, motivated by a problem in computational statistical physics. We have derived perturbation bounds on the relative error of the invariant distribution that reveal these variations in sensitivity. Our bounds are sharp, we do not impose any structural assumptions on the transition matrix or on the perturbation, and computing the bounds has the same complexity as computing the invariant distribution or computing other bounds in the literature. Moreover, our bounds have a simple interpretation in terms of hitting times, which can be used to draw intuitive but rigorous conclusions about the sensitivity of a chain to various types of perturbations.

Adaptive dynamic programming for finite-horizon optimal control of discrete-time nonlinear systems with ε-error bound.

PubMed

Wang, Fei-Yue; Jin, Ning; Liu, Derong; Wei, Qinglai

2011-01-01

In this paper, we study the finite-horizon optimal control problem for discrete-time nonlinear systems using the adaptive dynamic programming (ADP) approach. The idea is to use an iterative ADP algorithm to obtain the optimal control law which makes the performance index function close to the greatest lower bound of all performance indices within an ε-error bound. The optimal number of control steps can also be obtained by the proposed ADP algorithms. A convergence analysis of the proposed ADP algorithms in terms of performance index function and control policy is made. In order to facilitate the implementation of the iterative ADP algorithms, neural networks are used for approximating the performance index function, computing the optimal control policy, and modeling the nonlinear system. Finally, two simulation examples are employed to illustrate the applicability of the proposed method.

ALGORITHM TO REDUCE APPROXIMATION ERROR FROM THE COMPLEX-VARIABLE BOUNDARY-ELEMENT METHOD APPLIED TO SOIL FREEZING.

USGS Publications Warehouse

Hromadka, T.V.; Guymon, G.L.

1985-01-01

An algorithm is presented for the numerical solution of the Laplace equation boundary-value problem, which is assumed to apply to soil freezing or thawing. The Laplace equation is numerically approximated by the complex-variable boundary-element method. The algorithm aids in reducing integrated relative error by providing a true measure of modeling error along the solution domain boundary. This measure of error can be used to select locations for adding, removing, or relocating nodal points on the boundary or to provide bounds for the integrated relative error of unknown nodal variable values along the boundary.

Bounds on stochastic chemical kinetic systems at steady state

NASA Astrophysics Data System (ADS)

Dowdy, Garrett R.; Barton, Paul I.

2018-02-01

The method of moments has been proposed as a potential means to reduce the dimensionality of the chemical master equation (CME) appearing in stochastic chemical kinetics. However, attempts to apply the method of moments to the CME usually result in the so-called closure problem. Several authors have proposed moment closure schemes, which allow them to obtain approximations of quantities of interest, such as the mean molecular count for each species. However, these approximations have the dissatisfying feature that they come with no error bounds. This paper presents a fundamentally different approach to the closure problem in stochastic chemical kinetics. Instead of making an approximation to compute a single number for the quantity of interest, we calculate mathematically rigorous bounds on this quantity by solving semidefinite programs. These bounds provide a check on the validity of the moment closure approximations and are in some cases so tight that they effectively provide the desired quantity. In this paper, the bounded quantities of interest are the mean molecular count for each species, the variance in this count, and the probability that the count lies in an arbitrary interval. At present, we consider only steady-state probability distributions, intending to discuss the dynamic problem in a future publication.

Geometry of Quantum Computation with Qudits

PubMed Central

Luo, Ming-Xing; Chen, Xiu-Bo; Yang, Yi-Xian; Wang, Xiaojun

2014-01-01

The circuit complexity of quantum qubit system evolution as a primitive problem in quantum computation has been discussed widely. We investigate this problem in terms of qudit system. Using the Riemannian geometry the optimal quantum circuits are equivalent to the geodetic evolutions in specially curved parametrization of SU(dn). And the quantum circuit complexity is explicitly dependent of controllable approximation error bound. PMID:24509710

Combined Uncertainty and A-Posteriori Error Bound Estimates for General CFD Calculations: Theory and Software Implementation

NASA Technical Reports Server (NTRS)

Barth, Timothy J.

2014-01-01

This workshop presentation discusses the design and implementation of numerical methods for the quantification of statistical uncertainty, including a-posteriori error bounds, for output quantities computed using CFD methods. Hydrodynamic realizations often contain numerical error arising from finite-dimensional approximation (e.g. numerical methods using grids, basis functions, particles) and statistical uncertainty arising from incomplete information and/or statistical characterization of model parameters and random fields. The first task at hand is to derive formal error bounds for statistics given realizations containing finite-dimensional numerical error [1]. The error in computed output statistics contains contributions from both realization error and the error resulting from the calculation of statistics integrals using a numerical method. A second task is to devise computable a-posteriori error bounds by numerically approximating all terms arising in the error bound estimates. For the same reason that CFD calculations including error bounds but omitting uncertainty modeling are only of limited value, CFD calculations including uncertainty modeling but omitting error bounds are only of limited value. To gain maximum value from CFD calculations, a general software package for uncertainty quantification with quantified error bounds has been developed at NASA. The package provides implementations for a suite of numerical methods used in uncertainty quantification: Dense tensorization basis methods [3] and a subscale recovery variant [1] for non-smooth data, Sparse tensorization methods[2] utilizing node-nested hierarchies, Sampling methods[4] for high-dimensional random variable spaces.

Synchronization error estimation and controller design for delayed Lur'e systems with parameter mismatches.

PubMed

He, Wangli; Qian, Feng; Han, Qing-Long; Cao, Jinde

2012-10-01

This paper investigates the problem of master-slave synchronization of two delayed Lur'e systems in the presence of parameter mismatches. First, by analyzing the corresponding synchronization error system, synchronization with an error level, which is referred to as quasi-synchronization, is established. Some delay-dependent quasi-synchronization criteria are derived. An estimation of the synchronization error bound is given, and an explicit expression of error levels is obtained. Second, sufficient conditions on the existence of feedback controllers under a predetermined error level are provided. The controller gains are obtained by solving a set of linear matrix inequalities. Finally, a delayed Chua's circuit is chosen to illustrate the effectiveness of the derived results.

Selecting a restoration technique to minimize OCR error.

PubMed

Cannon, M; Fugate, M; Hush, D R; Scovel, C

2003-01-01

This paper introduces a learning problem related to the task of converting printed documents to ASCII text files. The goal of the learning procedure is to produce a function that maps documents to restoration techniques in such a way that on average the restored documents have minimum optical character recognition error. We derive a general form for the optimal function and use it to motivate the development of a nonparametric method based on nearest neighbors. We also develop a direct method of solution based on empirical error minimization for which we prove a finite sample bound on estimation error that is independent of distribution. We show that this empirical error minimization problem is an extension of the empirical optimization problem for traditional M-class classification with general loss function and prove computational hardness for this problem. We then derive a simple iterative algorithm called generalized multiclass ratchet (GMR) and prove that it produces an optimal function asymptotically (with probability 1). To obtain the GMR algorithm we introduce a new data map that extends Kesler's construction for the multiclass problem and then apply an algorithm called Ratchet to this mapped data, where Ratchet is a modification of the Pocket algorithm . Finally, we apply these methods to a collection of documents and report on the experimental results.

Distributed Synchronization Control of Multiagent Systems With Unknown Nonlinearities.

PubMed

Su, Shize; Lin, Zongli; Garcia, Alfredo

2016-01-01

This paper revisits the distributed adaptive control problem for synchronization of multiagent systems where the dynamics of the agents are nonlinear, nonidentical, unknown, and subject to external disturbances. Two communication topologies, represented, respectively, by a fixed strongly-connected directed graph and by a switching connected undirected graph, are considered. Under both of these communication topologies, we use distributed neural networks to approximate the uncertain dynamics. Decentralized adaptive control protocols are then constructed to solve the cooperative tracker problem, the problem of synchronization of all follower agents to a leader agent. In particular, we show that, under the proposed decentralized control protocols, the synchronization errors are ultimately bounded, and their ultimate bounds can be reduced arbitrarily by choosing the control parameter appropriately. Simulation study verifies the effectiveness of our proposed protocols.

Goal-oriented explicit residual-type error estimates in XFEM

NASA Astrophysics Data System (ADS)

Rüter, Marcus; Gerasimov, Tymofiy; Stein, Erwin

2013-08-01

A goal-oriented a posteriori error estimator is derived to control the error obtained while approximately evaluating a quantity of engineering interest, represented in terms of a given linear or nonlinear functional, using extended finite elements of Q1 type. The same approximation method is used to solve the dual problem as required for the a posteriori error analysis. It is shown that for both problems to be solved numerically the same singular enrichment functions can be used. The goal-oriented error estimator presented can be classified as explicit residual type, i.e. the residuals of the approximations are used directly to compute upper bounds on the error of the quantity of interest. This approach therefore extends the explicit residual-type error estimator for classical energy norm error control as recently presented in Gerasimov et al. (Int J Numer Meth Eng 90:1118-1155, 2012a). Without loss of generality, the a posteriori error estimator is applied to the model problem of linear elastic fracture mechanics. Thus, emphasis is placed on the fracture criterion, here the J-integral, as the chosen quantity of interest. Finally, various illustrative numerical examples are presented where, on the one hand, the error estimator is compared to its finite element counterpart and, on the other hand, improved enrichment functions, as introduced in Gerasimov et al. (2012b), are discussed.

A bounding-based solution approach for the continuous arc covering problem

NASA Astrophysics Data System (ADS)

Wei, Ran; Murray, Alan T.; Batta, Rajan

2014-04-01

Road segments, telecommunication wiring, water and sewer pipelines, canals and the like are important features of the urban environment. They are often conceived of and represented as network-based arcs. As a result of the usefulness and significance of arc-based features, there is a need to site facilities along arcs to serve demand. Examples of such facilities include surveillance equipment, cellular towers, refueling centers and emergency response stations, with the intent of being economically efficient as well as providing good service along the arcs. While this amounts to a continuous location problem by nature, various discretizations are generally relied upon to solve such problems. The result is potential for representation errors that negatively impact analysis and decision making. This paper develops a solution approach for the continuous arc covering problem that theoretically eliminates representation errors. The developed approach is applied to optimally place acoustic sensors and cellular base stations along a road network. The results demonstrate the effectiveness of this approach for ameliorating any error and uncertainty in the modeling process.

Genetic Algorithm for Optimization: Preprocessing with n Dimensional Bisection and Error Estimation

NASA Technical Reports Server (NTRS)

Sen, S. K.; Shaykhian, Gholam Ali

2006-01-01

A knowledge of the appropriate values of the parameters of a genetic algorithm (GA) such as the population size, the shrunk search space containing the solution, crossover and mutation probabilities is not available a priori for a general optimization problem. Recommended here is a polynomial-time preprocessing scheme that includes an n-dimensional bisection and that determines the foregoing parameters before deciding upon an appropriate GA for all problems of similar nature and type. Such a preprocessing is not only fast but also enables us to get the global optimal solution and its reasonably narrow error bounds with a high degree of confidence.

Consensus of satellite cluster flight using an energy-matching optimal control method

NASA Astrophysics Data System (ADS)

Luo, Jianjun; Zhou, Liang; Zhang, Bo

2017-11-01

This paper presents an optimal control method for consensus of satellite cluster flight under a kind of energy matching condition. Firstly, the relation between energy matching and satellite periodically bounded relative motion is analyzed, and the satellite energy matching principle is applied to configure the initial conditions. Then, period-delayed errors are adopted as state variables to establish the period-delayed errors dynamics models of a single satellite and the cluster. Next a novel satellite cluster feedback control protocol with coupling gain is designed, so that the satellite cluster periodically bounded relative motion consensus problem (period-delayed errors state consensus problem) is transformed to the stability of a set of matrices with the same low dimension. Based on the consensus region theory in the research of multi-agent system consensus issues, the coupling gain can be obtained to satisfy the requirement of consensus region and decouple the satellite cluster information topology and the feedback control gain matrix, which can be determined by Linear quadratic regulator (LQR) optimal method. This method can realize the consensus of satellite cluster period-delayed errors, leading to the consistency of semi-major axes (SMA) and the energy-matching of satellite cluster. Then satellites can emerge the global coordinative cluster behavior. Finally the feasibility and effectiveness of the present energy-matching optimal consensus for satellite cluster flight is verified through numerical simulations.

Estimation variance bounds of importance sampling simulations in digital communication systems

NASA Technical Reports Server (NTRS)

Lu, D.; Yao, K.

1991-01-01

In practical applications of importance sampling (IS) simulation, two basic problems are encountered, that of determining the estimation variance and that of evaluating the proper IS parameters needed in the simulations. The authors derive new upper and lower bounds on the estimation variance which are applicable to IS techniques. The upper bound is simple to evaluate and may be minimized by the proper selection of the IS parameter. Thus, lower and upper bounds on the improvement ratio of various IS techniques relative to the direct Monte Carlo simulation are also available. These bounds are shown to be useful and computationally simple to obtain. Based on the proposed technique, one can readily find practical suboptimum IS parameters. Numerical results indicate that these bounding techniques are useful for IS simulations of linear and nonlinear communication systems with intersymbol interference in which bit error rate and IS estimation variances cannot be obtained readily using prior techniques.

Resilient filtering for time-varying stochastic coupling networks under the event-triggering scheduling

NASA Astrophysics Data System (ADS)

Wang, Fan; Liang, Jinling; Dobaie, Abdullah M.

2018-07-01

The resilient filtering problem is considered for a class of time-varying networks with stochastic coupling strengths. An event-triggered strategy is adopted to save the network resources by scheduling the signal transmission from the sensors to the filters based on certain prescribed rules. Moreover, the filter parameters to be designed are subject to gain perturbations. The primary aim of the addressed problem is to determine a resilient filter that ensures an acceptable filtering performance for the considered network with event-triggering scheduling. To handle such an issue, an upper bound on the estimation error variance is established for each node according to the stochastic analysis. Subsequently, the resilient filter is designed by locally minimizing the derived upper bound at each iteration. Moreover, rigorous analysis shows the monotonicity of the minimal upper bound regarding the triggering threshold. Finally, a simulation example is presented to show effectiveness of the established filter scheme.

An Algorithm for Efficient Maximum Likelihood Estimation and Confidence Interval Determination in Nonlinear Estimation Problems

NASA Technical Reports Server (NTRS)

Murphy, Patrick Charles

1985-01-01

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The algorithm was developed for airplane parameter estimation problems but is well suited for most nonlinear, multivariable, dynamic systems. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson 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. MNRES determines the sensitivities with less computational effort than using either a finite-difference method or integrating the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, thus eliminating algorithm reformulation with each new model and providing flexibility to use model equations in any format that is convenient. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. It is observed that the degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. The CR bounds were found to be close to the bounds determined by the search when the degree of nonlinearity was small. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels for the parameter confidence limits. The primary utility of the measure, however, was found to be in predicting the degree of agreement between Cramer-Rao bounds and search estimates.

Efficiently characterizing the total error in quantum circuits

NASA Astrophysics Data System (ADS)

Carignan-Dugas, Arnaud; Wallman, Joel J.; Emerson, Joseph

A promising technological advancement meant to enlarge our computational means is the quantum computer. Such a device would harvest the quantum complexity of the physical world in order to unfold concrete mathematical problems more efficiently. However, the errors emerging from the implementation of quantum operations are likewise quantum, and hence share a similar level of intricacy. Fortunately, randomized benchmarking protocols provide an efficient way to characterize the operational noise within quantum devices. The resulting figures of merit, like the fidelity and the unitarity, are typically attached to a set of circuit components. While important, this doesn't fulfill the main goal: determining if the error rate of the total circuit is small enough in order to trust its outcome. In this work, we fill the gap by providing an optimal bound on the total fidelity of a circuit in terms of component-wise figures of merit. Our bound smoothly interpolates between the classical regime, in which the error rate grows linearly in the circuit's length, and the quantum regime, which can naturally allow quadratic growth. Conversely, our analysis substantially improves the bounds on single circuit element fidelities obtained through techniques such as interleaved randomized benchmarking. This research was supported by the U.S. Army Research Office through Grant W911NF- 14-1-0103, CIFAR, the Government of Ontario, and the Government of Canada through NSERC and Industry Canada.

An Algebraic Approach to Guarantee Harmonic Balance Method Using Gröbner Base

NASA Astrophysics Data System (ADS)

Yagi, Masakazu; Hisakado, Takashi; Okumura, Kohshi

Harmonic balance (HB) method is well known principle for analyzing periodic oscillations on nonlinear networks and systems. Because the HB method has a truncation error, approximated solutions have been guaranteed by error bounds. However, its numerical computation is very time-consuming compared with solving the HB equation. This paper proposes an algebraic representation of the error bound using Gröbner base. The algebraic representation enables to decrease the computational cost of the error bound considerably. Moreover, using singular points of the algebraic representation, we can obtain accurate break points of the error bound by collisions.

An Upper Bound on Orbital Debris Collision Probability When Only One Object has Position Uncertainty Information

NASA Technical Reports Server (NTRS)

Frisbee, Joseph H., Jr.

2015-01-01

Upper bounds on high speed satellite collision probability, P (sub c), have been investigated. Previous methods assume an individual position error covariance matrix is available for each object. The two matrices being combined into a single, relative position error covariance matrix. Components of the combined error covariance are then varied to obtain a maximum P (sub c). If error covariance information for only one of the two objects was available, either some default shape has been used or nothing could be done. An alternative is presented that uses the known covariance information along with a critical value of the missing covariance to obtain an approximate but useful P (sub c) upper bound. There are various avenues along which an upper bound on the high speed satellite collision probability has been pursued. Typically, for the collision plane representation of the high speed collision probability problem, the predicted miss position in the collision plane is assumed fixed. Then the shape (aspect ratio of ellipse), the size (scaling of standard deviations) or the orientation (rotation of ellipse principal axes) of the combined position error ellipse is varied to obtain a maximum P (sub c). Regardless as to the exact details of the approach, previously presented methods all assume that an individual position error covariance matrix is available for each object and the two are combined into a single, relative position error covariance matrix. This combined position error covariance matrix is then modified according to the chosen scheme to arrive at a maximum P (sub c). But what if error covariance information for one of the two objects is not available? When error covariance information for one of the objects is not available the analyst has commonly defaulted to the situation in which only the relative miss position and velocity are known without any corresponding state error covariance information. The various usual methods of finding a maximum P (sub c) do no good because the analyst defaults to no knowledge of the combined, relative position error covariance matrix. It is reasonable to think, given an assumption of no covariance information, an analyst might still attempt to determine the error covariance matrix that results in an upper bound on the P (sub c). Without some guidance on limits to the shape, size and orientation of the unknown covariance matrix, the limiting case is a degenerate ellipse lying along the relative miss vector in the collision plane. Unless the miss position is exceptionally large or the at-risk object is exceptionally small, this method results in a maximum P (sub c) too large to be of practical use. For example, assuming that the miss distance is equal to the current ISS alert volume along-track (+ or -) distance of 25 kilometers and that the at-risk area has a 70 meter radius. The maximum (degenerate ellipse) P (sub c) is about 0.00136. At 40 kilometers, the maximum P (sub c) would be 0.00085 which is still almost an order of magnitude larger than the ISS maneuver threshold of 0.0001. In fact, a miss distance of almost 340 kilometers is necessary to reduce the maximum P (sub c) associated with this degenerate ellipse to the ISS maneuver threshold value. Such a result is frequently of no practical value to the analyst. Some improvement may be made with respect to this problem by realizing that while the position error covariance matrix of one of the objects (usually the debris object) may not be known the position error covariance matrix of the other object (usually the asset) is almost always available. Making use of the position error covariance information for the one object provides an improvement in finding a maximum P (sub c) which, in some cases, may offer real utility. The equations to be used are presented and their use discussed.

Determining relative error bounds for the CVBEM

USGS Publications Warehouse

Hromadka, T.V.

1985-01-01

The Complex Variable Boundary Element Methods provides a measure of relative error which can be utilized to subsequently reduce the error or provide information for further modeling analysis. By maximizing the relative error norm on each boundary element, a bound on the total relative error for each boundary element can be evaluated. This bound can be utilized to test CVBEM convergence, to analyze the effects of additional boundary nodal points in reducing the modeling error, and to evaluate the sensitivity of resulting modeling error within a boundary element from the error produced in another boundary element as a function of geometric distance. ?? 1985.

Dynamic State Estimation of Power Systems With Quantization Effects: A Recursive Filter Approach.

PubMed

Hu, Liang; Wang, Zidong; Liu, Xiaohui

2016-08-01

In this paper, a recursive filter algorithm is developed to deal with the state estimation problem for power systems with quantized nonlinear measurements. The measurements from both the remote terminal units and the phasor measurement unit are subject to quantizations described by a logarithmic quantizer. Attention is focused on the design of a recursive filter such that, in the simultaneous presence of nonlinear measurements and quantization effects, an upper bound for the estimation error covariance is guaranteed and subsequently minimized. Instead of using the traditional approximation methods in nonlinear estimation that simply ignore the linearization errors, we treat both the linearization and quantization errors as norm-bounded uncertainties in the algorithm development so as to improve the performance of the estimator. For the power system with such kind of introduced uncertainties, a filter is designed in the framework of robust recursive estimation, and the developed filter algorithm is tested on the IEEE benchmark power system to demonstrate its effectiveness.

A Class of Prediction-Correction Methods for Time-Varying Convex Optimization

NASA Astrophysics Data System (ADS)

Simonetto, Andrea; Mokhtari, Aryan; Koppel, Alec; Leus, Geert; Ribeiro, Alejandro

2016-09-01

This paper considers unconstrained convex optimization problems with time-varying objective functions. We propose algorithms with a discrete time-sampling scheme to find and track the solution trajectory based on prediction and correction steps, while sampling the problem data at a constant rate of $1/h$, where $h$ is the length of the sampling interval. The prediction step is derived by analyzing the iso-residual dynamics of the optimality conditions. The correction step adjusts for the distance between the current prediction and the optimizer at each time step, and consists either of one or multiple gradient steps or Newton steps, which respectively correspond to the gradient trajectory tracking (GTT) or Newton trajectory tracking (NTT) algorithms. Under suitable conditions, we establish that the asymptotic error incurred by both proposed methods behaves as $O(h^2)$, and in some cases as $O(h^4)$, which outperforms the state-of-the-art error bound of $O(h)$ for correction-only methods in the gradient-correction step. Moreover, when the characteristics of the objective function variation are not available, we propose approximate gradient and Newton tracking algorithms (AGT and ANT, respectively) that still attain these asymptotical error bounds. Numerical simulations demonstrate the practical utility of the proposed methods and that they improve upon existing techniques by several orders of magnitude.

Explicit error bounds for the α-quasi-periodic Helmholtz problem.

PubMed

Lord, Natacha H; Mulholland, Anthony J

2013-10-01

This paper considers a finite element approach to modeling electromagnetic waves in a periodic diffraction grating. In particular, an a priori error estimate associated with the α-quasi-periodic transformation is derived. This involves the solution of the associated Helmholtz problem being written as a product of e(iαx) and an unknown function called the α-quasi-periodic solution. To begin with, the well-posedness of the continuous problem is examined using a variational formulation. The problem is then discretized, and a rigorous a priori error estimate, which guarantees the uniqueness of this approximate solution, is derived. In previous studies, the continuity of the Dirichlet-to-Neumann map has simply been assumed and the dependency of the regularity constant on the system parameters, such as the wavenumber, has not been shown. To address this deficiency, in this paper an explicit dependence on the wavenumber and the degree of the polynomial basis in the a priori error estimate is obtained. Since the finite element method is well known for dealing with any geometries, comparison of numerical results obtained using the α-quasi-periodic transformation with a lattice sum technique is then presented.

Helmholtz and parabolic equation solutions to a benchmark problem in ocean acoustics.

PubMed

Larsson, Elisabeth; Abrahamsson, Leif

2003-05-01

The Helmholtz equation (HE) describes wave propagation in applications such as acoustics and electromagnetics. For realistic problems, solving the HE is often too expensive. Instead, approximations like the parabolic wave equation (PE) are used. For low-frequency shallow-water environments, one persistent problem is to assess the accuracy of the PE model. In this work, a recently developed HE solver that can handle a smoothly varying bathymetry, variable material properties, and layered materials, is used for an investigation of the errors in PE solutions. In the HE solver, a preconditioned Krylov subspace method is applied to the discretized equations. The preconditioner combines domain decomposition and fast transform techniques. A benchmark problem with upslope-downslope propagation over a penetrable lossy seamount is solved. The numerical experiments show that, for the same bathymetry, a soft and slow bottom gives very similar HE and PE solutions, whereas the PE model is far from accurate for a hard and fast bottom. A first attempt to estimate the error is made by computing the relative deviation from the energy balance for the PE solution. This measure gives an indication of the magnitude of the error, but cannot be used as a strict error bound.

Convergence analysis of surrogate-based methods for Bayesian inverse problems

NASA Astrophysics Data System (ADS)

Yan, Liang; Zhang, Yuan-Xiang

2017-12-01

The major challenges in the Bayesian inverse problems arise from the need for repeated evaluations of the forward model, as required by Markov chain Monte Carlo (MCMC) methods for posterior sampling. Many attempts at accelerating Bayesian inference have relied on surrogates for the forward model, typically constructed through repeated forward simulations that are performed in an offline phase. Although such approaches can be quite effective at reducing computation cost, there has been little analysis of the approximation on posterior inference. In this work, we prove error bounds on the Kullback-Leibler (KL) distance between the true posterior distribution and the approximation based on surrogate models. Our rigorous error analysis show that if the forward model approximation converges at certain rate in the prior-weighted L 2 norm, then the posterior distribution generated by the approximation converges to the true posterior at least two times faster in the KL sense. The error bound on the Hellinger distance is also provided. To provide concrete examples focusing on the use of the surrogate model based methods, we present an efficient technique for constructing stochastic surrogate models to accelerate the Bayesian inference approach. The Christoffel least squares algorithms, based on generalized polynomial chaos, are used to construct a polynomial approximation of the forward solution over the support of the prior distribution. The numerical strategy and the predicted convergence rates are then demonstrated on the nonlinear inverse problems, involving the inference of parameters appearing in partial differential equations.

Error analysis of analytic solutions for self-excited near-symmetric rigid bodies - A numerical study

NASA Technical Reports Server (NTRS)

Kia, T.; Longuski, J. M.

1984-01-01

Analytic error bounds are presented for the solutions of approximate models for self-excited near-symmetric rigid bodies. The error bounds are developed for analytic solutions to Euler's equations of motion. The results are applied to obtain a simplified analytic solution for Eulerian rates and angles. The results of a sample application of the range and error bound expressions for the case of the Galileo spacecraft experiencing transverse torques demonstrate the use of the bounds in analyses of rigid body spin change maneuvers.

Axioms of adaptivity

PubMed Central

Carstensen, C.; Feischl, M.; Page, M.; Praetorius, D.

2014-01-01

This paper aims first at a simultaneous axiomatic presentation of the proof of optimal convergence rates for adaptive finite element methods and second at some refinements of particular questions like the avoidance of (discrete) lower bounds, inexact solvers, inhomogeneous boundary data, or the use of equivalent error estimators. Solely four axioms guarantee the optimality in terms of the error estimators. Compared to the state of the art in the temporary literature, the improvements of this article can be summarized as follows: First, a general framework is presented which covers the existing literature on optimality of adaptive schemes. The abstract analysis covers linear as well as nonlinear problems and is independent of the underlying finite element or boundary element method. Second, efficiency of the error estimator is neither needed to prove convergence nor quasi-optimal convergence behavior of the error estimator. In this paper, efficiency exclusively characterizes the approximation classes involved in terms of the best-approximation error and data resolution and so the upper bound on the optimal marking parameters does not depend on the efficiency constant. Third, some general quasi-Galerkin orthogonality is not only sufficient, but also necessary for the R-linear convergence of the error estimator, which is a fundamental ingredient in the current quasi-optimality analysis due to Stevenson 2007. Finally, the general analysis allows for equivalent error estimators and inexact solvers as well as different non-homogeneous and mixed boundary conditions. PMID:25983390

Confidence set inference with a prior quadratic bound

NASA Technical Reports Server (NTRS)

Backus, George E.

1989-01-01

In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z=(z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y (sup 0) = (y (sub 1) (sup 0), ..., y (sub D (sup 0)), using full or partial knowledge of the statistical distribution of the random errors in y (sup 0). The data space Y containing y(sup 0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x, Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. Confidence set inference is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface.

The Limits of Coding with Joint Constraints on Detected and Undetected Error Rates

NASA Technical Reports Server (NTRS)

Dolinar, Sam; Andrews, Kenneth; Pollara, Fabrizio; Divsalar, Dariush

2008-01-01

We develop a remarkably tight upper bound on the performance of a parameterized family of bounded angle maximum-likelihood (BA-ML) incomplete decoders. The new bound for this class of incomplete decoders is calculated from the code's weight enumerator, and is an extension of Poltyrev-type bounds developed for complete ML decoders. This bound can also be applied to bound the average performance of random code ensembles in terms of an ensemble average weight enumerator. We also formulate conditions defining a parameterized family of optimal incomplete decoders, defined to minimize both the total codeword error probability and the undetected error probability for any fixed capability of the decoder to detect errors. We illustrate the gap between optimal and BA-ML incomplete decoding via simulation of a small code.

Adaptive robust fault tolerant control design for a class of nonlinear uncertain MIMO systems with quantization.

PubMed

Ao, Wei; Song, Yongdong; Wen, Changyun

2017-05-01

In this paper, we investigate the adaptive control problem for a class of nonlinear uncertain MIMO systems with actuator faults and quantization effects. Under some mild conditions, an adaptive robust fault-tolerant control is developed to compensate the affects of uncertainties, actuator failures and errors caused by quantization, and a range of the parameters for these quantizers is established. Furthermore, a Lyapunov-like approach is adopted to demonstrate that the ultimately uniformly bounded output tracking error is guaranteed by the controller, and the signals of the closed-loop system are ensured to be bounded, even in the presence of at most m-q actuators stuck or outage. Finally, numerical simulations are provided to verify and illustrate the effectiveness of the proposed adaptive schemes. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

The random coding bound is tight for the average code.

NASA Technical Reports Server (NTRS)

Gallager, R. G.

1973-01-01

The random coding bound of information theory provides a well-known upper bound to the probability of decoding error for the best code of a given rate and block length. The bound is constructed by upperbounding the average error probability over an ensemble of codes. The bound is known to give the correct exponential dependence of error probability on block length for transmission rates above the critical rate, but it gives an incorrect exponential dependence at rates below a second lower critical rate. Here we derive an asymptotic expression for the average error probability over the ensemble of codes used in the random coding bound. The result shows that the weakness of the random coding bound at rates below the second critical rate is due not to upperbounding the ensemble average, but rather to the fact that the best codes are much better than the average at low rates.

A methodology for airplane parameter estimation and confidence interval determination in nonlinear estimation problems. Ph.D. Thesis - George Washington Univ., Apr. 1985

NASA Technical Reports Server (NTRS)

Murphy, P. C.

1986-01-01

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. With the fitted surface, sensitivity information can be updated at each iteration with less computational effort than that required by either a finite-difference method or integration of the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, and thus provides flexibility to use model equations in any convenient format. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. The degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels and to predict the degree of agreement between CR bounds and search estimates.

ON COMPUTING UPPER LIMITS TO SOURCE INTENSITIES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kashyap, Vinay L.; Siemiginowska, Aneta; Van Dyk, David A.

2010-08-10

A common problem in astrophysics is determining how bright a source could be and still not be detected in an observation. Despite the simplicity with which the problem can be stated, the solution involves complicated statistical issues that require careful analysis. In contrast to the more familiar confidence bound, this concept has never been formally analyzed, leading to a great variety of often ad hoc solutions. Here we formulate and describe the problem in a self-consistent manner. Detection significance is usually defined by the acceptable proportion of false positives (background fluctuations that are claimed as detections, or Type I error),more » and we invoke the complementary concept of false negatives (real sources that go undetected, or Type II error), based on the statistical power of a test, to compute an upper limit to the detectable source intensity. To determine the minimum intensity that a source must have for it to be detected, we first define a detection threshold and then compute the probabilities of detecting sources of various intensities at the given threshold. The intensity that corresponds to the specified Type II error probability defines that minimum intensity and is identified as the upper limit. Thus, an upper limit is a characteristic of the detection procedure rather than the strength of any particular source. It should not be confused with confidence intervals or other estimates of source intensity. This is particularly important given the large number of catalogs that are being generated from increasingly sensitive surveys. We discuss, with examples, the differences between these upper limits and confidence bounds. Both measures are useful quantities that should be reported in order to extract the most science from catalogs, though they answer different statistical questions: an upper bound describes an inference range on the source intensity, while an upper limit calibrates the detection process. We provide a recipe for computing upper limits that applies to all detection algorithms.« less

Localization from near-source quasi-static electromagnetic fields

NASA Astrophysics Data System (ADS)

Mosher, J. C.

1993-09-01

A wide range of research has been published on the problem of estimating the parameters of electromagnetic and acoustical sources from measurements of signals measured at an array of sensors. In the quasi-static electromagnetic cases examined here, the signal variation from a point source is relatively slow with respect to the signal propagation and the spacing of the array of sensors. As such, the location of the point sources can only be determined from the spatial diversity of the received signal across the array. The inverse source localization problem is complicated by unknown model order and strong local minima. The nonlinear optimization problem is posed for solving for the parameters of the quasi-static source model. The transient nature of the sources can be exploited to allow subspace approaches to separate out the signal portion of the spatial correlation matrix. Decomposition techniques are examined for improved processing, and an adaptation of MUltiple SIgnal Characterization (MUSIC) is presented for solving the source localization problem. Recent results on calculating the Cramer-Rao error lower bounds are extended to the multidimensional problem here. This thesis focuses on the problem of source localization in magnetoencephalography (MEG), with a secondary application to thunderstorm source localization. Comparisons are also made between MEG and its electrical equivalent, electroencephalography (EEG). The error lower bounds are examined in detail for several MEG and EEG configurations, as well as localizing thunderstorm cells over Cape Canaveral and Kennedy Space Center. Time-eigenspectrum is introduced as a parsing technique for improving the performance of the optimization problem.

Localization from near-source quasi-static electromagnetic fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mosher, John Compton

1993-09-01

A wide range of research has been published on the problem of estimating the parameters of electromagnetic and acoustical sources from measurements of signals measured at an array of sensors. In the quasi-static electromagnetic cases examined here, the signal variation from a point source is relatively slow with respect to the signal propagation and the spacing of the array of sensors. As such, the location of the point sources can only be determined from the spatial diversity of the received signal across the array. The inverse source localization problem is complicated by unknown model order and strong local minima. Themore » nonlinear optimization problem is posed for solving for the parameters of the quasi-static source model. The transient nature of the sources can be exploited to allow subspace approaches to separate out the signal portion of the spatial correlation matrix. Decomposition techniques are examined for improved processing, and an adaptation of MUtiple SIgnal Characterization (MUSIC) is presented for solving the source localization problem. Recent results on calculating the Cramer-Rao error lower bounds are extended to the multidimensional problem here. This thesis focuses on the problem of source localization in magnetoencephalography (MEG), with a secondary application to thunderstorm source localization. Comparisons are also made between MEG and its electrical equivalent, electroencephalography (EEG). The error lower bounds are examined in detail for several MEG and EEG configurations, as well as localizing thunderstorm cells over Cape Canaveral and Kennedy Space Center. Time-eigenspectrum is introduced as a parsing technique for improving the performance of the optimization problem.« less

Minimum-error quantum distinguishability bounds from matrix monotone functions: A comment on 'Two-sided estimates of minimum-error distinguishability of mixed quantum states via generalized Holevo-Curlander bounds' [J. Math. Phys. 50, 032106 (2009)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tyson, Jon

2009-06-15

Matrix monotonicity is used to obtain upper bounds on minimum-error distinguishability of arbitrary ensembles of mixed quantum states. This generalizes one direction of a two-sided bound recently obtained by the author [J. Tyson, J. Math. Phys. 50, 032106 (2009)]. It is shown that the previously obtained special case has unique properties.

Estimation of distributed Fermat-point location for wireless sensor networking.

PubMed

Huang, Po-Hsian; Chen, Jiann-Liang; Larosa, Yanuarius Teofilus; Chiang, Tsui-Lien

2011-01-01

This work presents a localization scheme for use in wireless sensor networks (WSNs) that is based on a proposed connectivity-based RF localization strategy called the distributed Fermat-point location estimation algorithm (DFPLE). DFPLE applies triangle area of location estimation formed by intersections of three neighboring beacon nodes. The Fermat point is determined as the shortest path from three vertices of the triangle. The area of estimated location then refined using Fermat point to achieve minimum error in estimating sensor nodes location. DFPLE solves problems of large errors and poor performance encountered by localization schemes that are based on a bounding box algorithm. Performance analysis of a 200-node development environment reveals that, when the number of sensor nodes is below 150, the mean error decreases rapidly as the node density increases, and when the number of sensor nodes exceeds 170, the mean error remains below 1% as the node density increases. Second, when the number of beacon nodes is less than 60, normal nodes lack sufficient beacon nodes to enable their locations to be estimated. However, the mean error changes slightly as the number of beacon nodes increases above 60. Simulation results revealed that the proposed algorithm for estimating sensor positions is more accurate than existing algorithms, and improves upon conventional bounding box strategies.

Reduction of the two dimensional stationary Navier-Stokes problem to a sequence of Fredholm integral equations of the second kind

NASA Technical Reports Server (NTRS)

Gabrielsen, R. E.

1981-01-01

Present approaches to solving the stationary Navier-Stokes equations are of limited value; however, there does exist an equivalent representation of the problem that has significant potential in solving such problems. This is due to the fact that the equivalent representation consists of a sequence of Fredholm integral equations of the second kind, and the solving of this type of problem is very well developed. For the problem in this form, there is an excellent chance to also determine explicit error estimates, since bounded, rather than unbounded, linear operators are dealt with.

Error control techniques for satellite and space communications

NASA Technical Reports Server (NTRS)

Costello, Daniel J., Jr.

1990-01-01

An expurgated upper bound on the event error probability of trellis coded modulation is presented. This bound is used to derive a lower bound on the minimum achievable free Euclidean distance d sub (free) of trellis codes. It is shown that the dominant parameters for both bounds, the expurgated error exponent and the asymptotic d sub (free) growth rate, respectively, can be obtained from the cutoff-rate R sub O of the transmission channel by a simple geometric construction, making R sub O the central parameter for finding good trellis codes. Several constellations are optimized with respect to the bounds.

Minimax confidence intervals in geomagnetism

NASA Technical Reports Server (NTRS)

Stark, Philip B.

1992-01-01

The present paper uses theory of Donoho (1989) to find lower bounds on the lengths of optimally short fixed-length confidence intervals (minimax confidence intervals) for Gauss coefficients of the field of degree 1-12 using the heat flow constraint. The bounds on optimal minimax intervals are about 40 percent shorter than Backus' intervals: no procedure for producing fixed-length confidence intervals, linear or nonlinear, can give intervals shorter than about 60 percent the length of Backus' in this problem. While both methods rigorously account for the fact that core field models are infinite-dimensional, the application of the techniques to the geomagnetic problem involves approximations and counterfactual assumptions about the data errors, and so these results are likely to be extremely optimistic estimates of the actual uncertainty in Gauss coefficients.

Computational efficiency of parallel combinatorial OR-tree searches

NASA Technical Reports Server (NTRS)

Li, Guo-Jie; Wah, Benjamin W.

1990-01-01

The performance of parallel combinatorial OR-tree searches is analytically evaluated. This performance depends on the complexity of the problem to be solved, the error allowance function, the dominance relation, and the search strategies. The exact performance may be difficult to predict due to the nondeterminism and anomalies of parallelism. The authors derive the performance bounds of parallel OR-tree searches with respect to the best-first, depth-first, and breadth-first strategies, and verify these bounds by simulation. They show that a near-linear speedup can be achieved with respect to a large number of processors for parallel OR-tree searches. Using the bounds developed, the authors derive sufficient conditions for assuring that parallelism will not degrade performance and necessary conditions for allowing parallelism to have a speedup greater than the ratio of the numbers of processors. These bounds and conditions provide the theoretical foundation for determining the number of processors required to assure a near-linear speedup.

An error bound for a discrete reduced order model of a linear multivariable system

NASA Technical Reports Server (NTRS)

Al-Saggaf, Ubaid M.; Franklin, Gene F.

1987-01-01

The design of feasible controllers for high dimension multivariable systems can be greatly aided by a method of model reduction. In order for the design based on the order reduction to include a guarantee of stability, it is sufficient to have a bound on the model error. Previous work has provided such a bound for continuous-time systems for algorithms based on balancing. In this note an L-infinity bound is derived for model error for a method of order reduction of discrete linear multivariable systems based on balancing.

A discontinuous Galerkin method with a bound preserving limiter for the advection of non-diffusive fields in solid Earth geodynamics

NASA Astrophysics Data System (ADS)

He, Ying; Puckett, Elbridge Gerry; Billen, Magali I.

2017-02-01

Mineral composition has a strong effect on the properties of rocks and is an essentially non-diffusive property in the context of large-scale mantle convection. Due to the non-diffusive nature and the origin of compositionally distinct regions in the Earth the boundaries between distinct regions can be nearly discontinuous. While there are different methods for tracking rock composition in numerical simulations of mantle convection, one must consider trade-offs between computational cost, accuracy or ease of implementation when choosing an appropriate method. Existing methods can be computationally expensive, cause over-/undershoots, smear sharp boundaries, or are not easily adapted to tracking multiple compositional fields. Here we present a Discontinuous Galerkin method with a bound preserving limiter (abbreviated as DG-BP) using a second order Runge-Kutta, strong stability-preserving time discretization method for the advection of non-diffusive fields. First, we show that the method is bound-preserving for a point-wise divergence free flow (e.g., a prescribed circular flow in a box). However, using standard adaptive mesh refinement (AMR) there is an over-shoot error (2%) because the cell average is not preserved during mesh coarsening. The effectiveness of the algorithm for convection-dominated flows is demonstrated using the falling box problem. We find that the DG-BP method maintains sharper compositional boundaries (3-5 elements) as compared to an artificial entropy-viscosity method (6-15 elements), although the over-/undershoot errors are similar. When used with AMR the DG-BP method results in fewer degrees of freedom due to smaller regions of mesh refinement in the neighborhood of the discontinuity. However, using Taylor-Hood elements and a uniform mesh there is an over-/undershoot error on the order of 0.0001%, but this error increases to 0.01-0.10% when using AMR. Therefore, for research problems in which a continuous field method is desired the DG-BP method can provide improved tracking of sharp compositional boundaries. For applications in which strict bound-preserving behavior is desired, use of an element that provides a divergence-free condition on the weak formulation (e.g., Raviart-Thomas) and an improved mesh coarsening scheme for the AMR are required.

Low-dimensional Representation of Error Covariance

NASA Technical Reports Server (NTRS)

Tippett, Michael K.; Cohn, Stephen E.; Todling, Ricardo; Marchesin, Dan

2000-01-01

Ensemble and reduced-rank approaches to prediction and assimilation rely on low-dimensional approximations of the estimation error covariances. Here stability properties of the forecast/analysis cycle for linear, time-independent systems are used to identify factors that cause the steady-state analysis error covariance to admit a low-dimensional representation. A useful measure of forecast/analysis cycle stability is the bound matrix, a function of the dynamics, observation operator and assimilation method. Upper and lower estimates for the steady-state analysis error covariance matrix eigenvalues are derived from the bound matrix. The estimates generalize to time-dependent systems. If much of the steady-state analysis error variance is due to a few dominant modes, the leading eigenvectors of the bound matrix approximate those of the steady-state analysis error covariance matrix. The analytical results are illustrated in two numerical examples where the Kalman filter is carried to steady state. The first example uses the dynamics of a generalized advection equation exhibiting nonmodal transient growth. Failure to observe growing modes leads to increased steady-state analysis error variances. Leading eigenvectors of the steady-state analysis error covariance matrix are well approximated by leading eigenvectors of the bound matrix. The second example uses the dynamics of a damped baroclinic wave model. The leading eigenvectors of a lowest-order approximation of the bound matrix are shown to approximate well the leading eigenvectors of the steady-state analysis error covariance matrix.

An iterative truncation method for unbounded electromagnetic problems using varying order finite elements

NASA Astrophysics Data System (ADS)

Paul, Prakash

2009-12-01

The finite element method (FEM) is used to solve three-dimensional electromagnetic scattering and radiation problems. Finite element (FE) solutions of this kind contain two main types of error: discretization error and boundary error. Discretization error depends on the number of free parameters used to model the problem, and on how effectively these parameters are distributed throughout the problem space. To reduce the discretization error, the polynomial order of the finite elements is increased, either uniformly over the problem domain or selectively in those areas with the poorest solution quality. Boundary error arises from the condition applied to the boundary that is used to truncate the computational domain. To reduce the boundary error, an iterative absorbing boundary condition (IABC) is implemented. The IABC starts with an inexpensive boundary condition and gradually improves the quality of the boundary condition as the iteration continues. An automatic error control (AEC) is implemented to balance the two types of error. With the AEC, the boundary condition is improved when the discretization error has fallen to a low enough level to make this worth doing. The AEC has these characteristics: (i) it uses a very inexpensive truncation method initially; (ii) it allows the truncation boundary to be very close to the scatterer/radiator; (iii) it puts more computational effort on the parts of the problem domain where it is most needed; and (iv) it can provide as accurate a solution as needed depending on the computational price one is willing to pay. To further reduce the computational cost, disjoint scatterers and radiators that are relatively far from each other are bounded separately and solved using a multi-region method (MRM), which leads to savings in computational cost. A simple analytical way to decide whether the MRM or the single region method will be computationally cheaper is also described. To validate the accuracy and savings in computation time, different shaped metallic and dielectric obstacles (spheres, ogives, cube, flat plate, multi-layer slab etc.) are used for the scattering problems. For the radiation problems, waveguide excited antennas (horn antenna, waveguide with flange, microstrip patch antenna) are used. Using the AEC the peak reduction in computation time during the iteration is typically a factor of 2, compared to the IABC using the same element orders throughout. In some cases, it can be as high as a factor of 4.

Fast alternating projection methods for constrained tomographic reconstruction

PubMed Central

Liu, Li; Han, Yongxin

2017-01-01

The alternating projection algorithms are easy to implement and effective for large-scale complex optimization problems, such as constrained reconstruction of X-ray computed tomography (CT). A typical method is to use projection onto convex sets (POCS) for data fidelity, nonnegative constraints combined with total variation (TV) minimization (so called TV-POCS) for sparse-view CT reconstruction. However, this type of method relies on empirically selected parameters for satisfactory reconstruction and is generally slow and lack of convergence analysis. In this work, we use a convex feasibility set approach to address the problems associated with TV-POCS and propose a framework using full sequential alternating projections or POCS (FS-POCS) to find the solution in the intersection of convex constraints of bounded TV function, bounded data fidelity error and non-negativity. The rationale behind FS-POCS is that the mathematically optimal solution of the constrained objective function may not be the physically optimal solution. The breakdown of constrained reconstruction into an intersection of several feasible sets can lead to faster convergence and better quantification of reconstruction parameters in a physical meaningful way than that in an empirical way of trial-and-error. In addition, for large-scale optimization problems, first order methods are usually used. Not only is the condition for convergence of gradient-based methods derived, but also a primal-dual hybrid gradient (PDHG) method is used for fast convergence of bounded TV. The newly proposed FS-POCS is evaluated and compared with TV-POCS and another convex feasibility projection method (CPTV) using both digital phantom and pseudo-real CT data to show its superior performance on reconstruction speed, image quality and quantification. PMID:28253298

Finite-horizon differential games for missile-target interception system using adaptive dynamic programming with input constraints

NASA Astrophysics Data System (ADS)

Sun, Jingliang; Liu, Chunsheng

2018-01-01

In this paper, the problem of intercepting a manoeuvring target within a fixed final time is posed in a non-linear constrained zero-sum differential game framework. The Nash equilibrium solution is found by solving the finite-horizon constrained differential game problem via adaptive dynamic programming technique. Besides, a suitable non-quadratic functional is utilised to encode the control constraints into a differential game problem. The single critic network with constant weights and time-varying activation functions is constructed to approximate the solution of associated time-varying Hamilton-Jacobi-Isaacs equation online. To properly satisfy the terminal constraint, an additional error term is incorporated in a novel weight-updating law such that the terminal constraint error is also minimised over time. By utilising Lyapunov's direct method, the closed-loop differential game system and the estimation weight error of the critic network are proved to be uniformly ultimately bounded. Finally, the effectiveness of the proposed method is demonstrated by using a simple non-linear system and a non-linear missile-target interception system, assuming first-order dynamics for the interceptor and target.

Achieving unequal error protection with convolutional codes

NASA Technical Reports Server (NTRS)

Mills, D. G.; Costello, D. J., Jr.; Palazzo, R., Jr.

1994-01-01

This paper examines the unequal error protection capabilities of convolutional codes. Both time-invariant and periodically time-varying convolutional encoders are examined. The effective free distance vector is defined and is shown to be useful in determining the unequal error protection (UEP) capabilities of convolutional codes. A modified transfer function is used to determine an upper bound on the bit error probabilities for individual input bit positions in a convolutional encoder. The bound is heavily dependent on the individual effective free distance of the input bit position. A bound relating two individual effective free distances is presented. The bound is a useful tool in determining the maximum possible disparity in individual effective free distances of encoders of specified rate and memory distribution. The unequal error protection capabilities of convolutional encoders of several rates and memory distributions are determined and discussed.

Signal processing of white-light interferometric low-finesse fiber-optic Fabry-Perot sensors.

PubMed

Ma, Cheng; Wang, Anbo

2013-01-10

Signal processing for low-finesse fiber-optic Fabry-Perot sensors based on white-light interferometry is investigated. The problem is demonstrated as analogous to the parameter estimation of a noisy, real, discrete harmonic of finite length. The Cramer-Rao bounds for the estimators are given, and three algorithms are evaluated and proven to approach the bounds. A long-standing problem with these types of sensors is the unpredictable jumps in the phase estimation. Emphasis is made on the property and mechanism of the "total phase" estimator in reducing the estimation error, and a varying phase term in the total phase is identified to be responsible for the unwanted demodulation jumps. The theories are verified by simulation and experiment. A solution to reducing the probability of jump is demonstrated. © 2013 Optical Society of America

On the accurate long-time solution of the wave equation in exterior domains: Asymptotic expansions and corrected boundary conditions

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas; Hariharan, S. I.; Maccamy, R. C.

1993-01-01

We consider the solution of scattering problems for the wave equation using approximate boundary conditions at artificial boundaries. These conditions are explicitly viewed as approximations to an exact boundary condition satisfied by the solution on the unbounded domain. We study the short and long term behavior of the error. It is provided that, in two space dimensions, no local in time, constant coefficient boundary operator can lead to accurate results uniformly in time for the class of problems we consider. A variable coefficient operator is developed which attains better accuracy (uniformly in time) than is possible with constant coefficient approximations. The theory is illustrated by numerical examples. We also analyze the proposed boundary conditions using energy methods, leading to asymptotically correct error bounds.

Bounding the errors for convex dynamics on one or more polytopes.

PubMed

Tresser, Charles

2007-09-01

We discuss the greedy algorithm for approximating a sequence of inputs in a family of polytopes lying in affine spaces by an output sequence made of vertices of the respective polytopes. More precisely, we consider here the case when the greed of the algorithm is dictated by the Euclidean norms of the successive cumulative errors. This algorithm can be interpreted as a time-dependent dynamical system in the vector space, where the errors live, or as a time-dependent dynamical system in an affine space containing copies of all the original polytopes. This affine space contains the inputs, as well as the inputs modified by adding the respective former errors; it is the evolution of these modified inputs that the dynamical system in affine space describes. Scheduling problems with many polytopes arise naturally, for instance, when the inputs are from a single polytope P, but one imposes the constraint that whenever the input belongs to a codimension n face, the output has to be in the same codimension n face (as when scheduling drivers among participants of a carpool). It has been previously shown that the error is bounded in the case of a single polytope by proving the existence of an arbitrary large convex invariant region for the dynamics in affine space: A region that is simultaneously invariant for several polytopes, each considered separately, was also constructed. It was then shown that there cannot be an invariant region in affine space in the general case of a family of polytopes. Here we prove the existence of an arbitrary large convex invariant set for the dynamics in the vector space in the case when the sizes of the polytopes in the family are bounded and the set of all the outgoing normals to all the faces of all the polytopes is finite. It was also previously known that starting from zero as the initial error set, the error set could not be saturated in finitely many steps in some cases with several polytopes: Contradicting a former conjecture, we show that the same happens for some single quadrilaterals and for a single pentagon with an axial symmetry. The disproof of that conjecture is the new piece of information that leads us to expect, and then to verify, as we recount here, that the proof that the errors are bounded in the general case could be a small step beyond the proof of the same statement for the single polytope case.

Bounding the errors for convex dynamics on one or more polytopes

NASA Astrophysics Data System (ADS)

Tresser, Charles

2007-09-01

We discuss the greedy algorithm for approximating a sequence of inputs in a family of polytopes lying in affine spaces by an output sequence made of vertices of the respective polytopes. More precisely, we consider here the case when the greed of the algorithm is dictated by the Euclidean norms of the successive cumulative errors. This algorithm can be interpreted as a time-dependent dynamical system in the vector space, where the errors live, or as a time-dependent dynamical system in an affine space containing copies of all the original polytopes. This affine space contains the inputs, as well as the inputs modified by adding the respective former errors; it is the evolution of these modified inputs that the dynamical system in affine space describes. Scheduling problems with many polytopes arise naturally, for instance, when the inputs are from a single polytope P, but one imposes the constraint that whenever the input belongs to a codimension n face, the output has to be in the same codimension n face (as when scheduling drivers among participants of a carpool). It has been previously shown that the error is bounded in the case of a single polytope by proving the existence of an arbitrary large convex invariant region for the dynamics in affine space: A region that is simultaneously invariant for several polytopes, each considered separately, was also constructed. It was then shown that there cannot be an invariant region in affine space in the general case of a family of polytopes. Here we prove the existence of an arbitrary large convex invariant set for the dynamics in the vector space in the case when the sizes of the polytopes in the family are bounded and the set of all the outgoing normals to all the faces of all the polytopes is finite. It was also previously known that starting from zero as the initial error set, the error set could not be saturated in finitely many steps in some cases with several polytopes: Contradicting a former conjecture, we show that the same happens for some single quadrilaterals and for a single pentagon with an axial symmetry. The disproof of that conjecture is the new piece of information that leads us to expect, and then to verify, as we recount here, that the proof that the errors are bounded in the general case could be a small step beyond the proof of the same statement for the single polytope case.

Efficient Measurement of Quantum Gate Error by Interleaved Randomized Benchmarking

NASA Astrophysics Data System (ADS)

Magesan, Easwar; Gambetta, Jay M.; Johnson, B. R.; Ryan, Colm A.; Chow, Jerry M.; Merkel, Seth T.; da Silva, Marcus P.; Keefe, George A.; Rothwell, Mary B.; Ohki, Thomas A.; Ketchen, Mark B.; Steffen, M.

2012-08-01

We describe a scalable experimental protocol for estimating the average error of individual quantum computational gates. This protocol consists of interleaving random Clifford gates between the gate of interest and provides an estimate as well as theoretical bounds for the average error of the gate under test, so long as the average noise variation over all Clifford gates is small. This technique takes into account both state preparation and measurement errors and is scalable in the number of qubits. We apply this protocol to a superconducting qubit system and find a bounded average error of 0.003 [0,0.016] for the single-qubit gates Xπ/2 and Yπ/2. These bounded values provide better estimates of the average error than those extracted via quantum process tomography.

iGen: An automated generator of simplified models with provable error bounds.

NASA Astrophysics Data System (ADS)

Tang, D.; Dobbie, S.

2009-04-01

Climate models employ various simplifying assumptions and parameterisations in order to increase execution speed. However, in order to draw conclusions about the Earths climate from the results of a climate simulation it is necessary to have information about the error that these assumptions and parameterisations introduce. A novel computer program, called iGen, is being developed which automatically generates fast, simplified models by analysing the source code of a slower, high resolution model. The resulting simplified models have provable bounds on error compared to the high resolution model and execute at speeds that are typically orders of magnitude faster. iGen's input is a definition of the prognostic variables of the simplified model, a set of bounds on acceptable error and the source code of a model that captures the behaviour of interest. In the case of an atmospheric model, for example, this would be a global cloud resolving model with very high resolution. Although such a model would execute far too slowly to be used directly in a climate model, iGen never executes it. Instead, it converts the code of the resolving model into a mathematical expression which is then symbolically manipulated and approximated to form a simplified expression. This expression is then converted back into a computer program and output as a simplified model. iGen also derives and reports formal bounds on the error of the simplified model compared to the resolving model. These error bounds are always maintained below the user-specified acceptable error. Results will be presented illustrating the success of iGen's analysis of a number of example models. These extremely encouraging results have lead on to work which is currently underway to analyse a cloud resolving model and so produce an efficient parameterisation of moist convection with formally bounded error.

Class-specific Error Bounds for Ensemble Classifiers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Prenger, R; Lemmond, T; Varshney, K

2009-10-06

The generalization error, or probability of misclassification, of ensemble classifiers has been shown to be bounded above by a function of the mean correlation between the constituent (i.e., base) classifiers and their average strength. This bound suggests that increasing the strength and/or decreasing the correlation of an ensemble's base classifiers may yield improved performance under the assumption of equal error costs. However, this and other existing bounds do not directly address application spaces in which error costs are inherently unequal. For applications involving binary classification, Receiver Operating Characteristic (ROC) curves, performance curves that explicitly trade off false alarms and missedmore » detections, are often utilized to support decision making. To address performance optimization in this context, we have developed a lower bound for the entire ROC curve that can be expressed in terms of the class-specific strength and correlation of the base classifiers. We present empirical analyses demonstrating the efficacy of these bounds in predicting relative classifier performance. In addition, we specify performance regions of the ROC curve that are naturally delineated by the class-specific strengths of the base classifiers and show that each of these regions can be associated with a unique set of guidelines for performance optimization of binary classifiers within unequal error cost regimes.« less

Graph traversals, genes, and matroids: An efficient case of the travelling salesman problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gusfield, D.; Stelling, P.; Wang, Lusheng

1996-12-31

In this paper the authors consider graph traversal problems that arise from a particular technology for DNA sequencing - sequencing by hybridization (SBH). They first explain the connection of the graph problems to SBH and then focus on the traversal problems. They describe a practical polynomial time solution to the Travelling Salesman Problem in a rich class of directed graphs (including edge weighted binary de Bruijn graphs), and provide a bounded-error approximation algorithm for the maximum weight TSP in a superset of those directed graphs. The authors also establish the existence of a matroid structure defined on the set ofmore » Euler and Hamilton paths in the restricted class of graphs. 8 refs., 5 figs.« less

Distributed adaptive neural network control for a class of heterogeneous nonlinear multi-agent systems subject to actuation failures

NASA Astrophysics Data System (ADS)

Cui, Bing; Zhao, Chunhui; Ma, Tiedong; Feng, Chi

2017-02-01

In this paper, the cooperative adaptive consensus tracking problem for heterogeneous nonlinear multi-agent systems on directed graph is addressed. Each follower is modelled as a general nonlinear system with the unknown and nonidentical nonlinear dynamics, disturbances and actuator failures. Cooperative fault tolerant neural network tracking controllers with online adaptive learning features are proposed to guarantee that all agents synchronise to the trajectory of one leader with bounded adjustable synchronisation errors. With the help of linear quadratic regulator-based optimal design, a graph-dependent Lyapunov proof provides error bounds that depend on the graph topology, one virtual matrix and some design parameters. Of particular interest is that if the control gain is selected appropriately, the proposed control scheme can be implemented in a unified framework no matter whether there are faults or not. Furthermore, the fault detection and isolation are not needed to implement. Finally, a simulation is given to verify the effectiveness of the proposed method.

Beamforming Based Full-Duplex for Millimeter-Wave Communication

PubMed Central

Liu, Xiao; Xiao, Zhenyu; Bai, Lin; Choi, Jinho; Xia, Pengfei; Xia, Xiang-Gen

2016-01-01

In this paper, we study beamforming based full-duplex (FD) systems in millimeter-wave (mmWave) communications. A joint transmission and reception (Tx/Rx) beamforming problem is formulated to maximize the achievable rate by mitigating self-interference (SI). Since the optimal solution is difficult to find due to the non-convexity of the objective function, suboptimal schemes are proposed in this paper. A low-complexity algorithm, which iteratively maximizes signal power while suppressing SI, is proposed and its convergence is proven. Moreover, two closed-form solutions, which do not require iterations, are also derived under minimum-mean-square-error (MMSE), zero-forcing (ZF), and maximum-ratio transmission (MRT) criteria. Performance evaluations show that the proposed iterative scheme converges fast (within only two iterations on average) and approaches an upper-bound performance, while the two closed-form solutions also achieve appealing performances, although there are noticeable differences from the upper bound depending on channel conditions. Interestingly, these three schemes show different robustness against the geometry of Tx/Rx antenna arrays and channel estimation errors. PMID:27455256

Random measurement error: Why worry? An example of cardiovascular risk factors.

PubMed

Brakenhoff, Timo B; van Smeden, Maarten; Visseren, Frank L J; Groenwold, Rolf H H

2018-01-01

With the increased use of data not originally recorded for research, such as routine care data (or 'big data'), measurement error is bound to become an increasingly relevant problem in medical research. A common view among medical researchers on the influence of random measurement error (i.e. classical measurement error) is that its presence leads to some degree of systematic underestimation of studied exposure-outcome relations (i.e. attenuation of the effect estimate). For the common situation where the analysis involves at least one exposure and one confounder, we demonstrate that the direction of effect of random measurement error on the estimated exposure-outcome relations can be difficult to anticipate. Using three example studies on cardiovascular risk factors, we illustrate that random measurement error in the exposure and/or confounder can lead to underestimation as well as overestimation of exposure-outcome relations. We therefore advise medical researchers to refrain from making claims about the direction of effect of measurement error in their manuscripts, unless the appropriate inferential tools are used to study or alleviate the impact of measurement error from the analysis.

Regularity Aspects in Inverse Musculoskeletal Biomechanics

NASA Astrophysics Data System (ADS)

Lund, Marie; Stâhl, Fredrik; Gulliksson, Mârten

2008-09-01

Inverse simulations of musculoskeletal models computes the internal forces such as muscle and joint reaction forces, which are hard to measure, using the more easily measured motion and external forces as input data. Because of the difficulties of measuring muscle forces and joint reactions, simulations are hard to validate. One way of reducing errors for the simulations is to ensure that the mathematical problem is well-posed. This paper presents a study of regularity aspects for an inverse simulation method, often called forward dynamics or dynamical optimization, that takes into account both measurement errors and muscle dynamics. Regularity is examined for a test problem around the optimum using the approximated quadratic problem. The results shows improved rank by including a regularization term in the objective that handles the mechanical over-determinancy. Using the 3-element Hill muscle model the chosen regularization term is the norm of the activation. To make the problem full-rank only the excitation bounds should be included in the constraints. However, this results in small negative values of the activation which indicates that muscles are pushing and not pulling, which is unrealistic but the error maybe small enough to be accepted for specific applications. These results are a start to ensure better results of inverse musculoskeletal simulations from a numerical point of view.

A comparison of error bounds for a nonlinear tracking system with detection probability Pd < 1.

PubMed

Tong, Huisi; Zhang, Hao; Meng, Huadong; Wang, Xiqin

2012-12-14

Error bounds for nonlinear filtering are very important for performance evaluation and sensor management. This paper presents a comparative study of three error bounds for tracking filtering, when the detection probability is less than unity. One of these bounds is the random finite set (RFS) bound, which is deduced within the framework of finite set statistics. The others, which are the information reduction factor (IRF) posterior Cramer-Rao lower bound (PCRLB) and enumeration method (ENUM) PCRLB are introduced within the framework of finite vector statistics. In this paper, we deduce two propositions and prove that the RFS bound is equal to the ENUM PCRLB, while it is tighter than the IRF PCRLB, when the target exists from the beginning to the end. Considering the disappearance of existing targets and the appearance of new targets, the RFS bound is tighter than both IRF PCRLB and ENUM PCRLB with time, by introducing the uncertainty of target existence. The theory is illustrated by two nonlinear tracking applications: ballistic object tracking and bearings-only tracking. The simulation studies confirm the theory and reveal the relationship among the three bounds.

A Comparison of Error Bounds for a Nonlinear Tracking System with Detection Probability Pd < 1

PubMed Central

Tong, Huisi; Zhang, Hao; Meng, Huadong; Wang, Xiqin

2012-01-01

Error bounds for nonlinear filtering are very important for performance evaluation and sensor management. This paper presents a comparative study of three error bounds for tracking filtering, when the detection probability is less than unity. One of these bounds is the random finite set (RFS) bound, which is deduced within the framework of finite set statistics. The others, which are the information reduction factor (IRF) posterior Cramer-Rao lower bound (PCRLB) and enumeration method (ENUM) PCRLB are introduced within the framework of finite vector statistics. In this paper, we deduce two propositions and prove that the RFS bound is equal to the ENUM PCRLB, while it is tighter than the IRF PCRLB, when the target exists from the beginning to the end. Considering the disappearance of existing targets and the appearance of new targets, the RFS bound is tighter than both IRF PCRLB and ENUM PCRLB with time, by introducing the uncertainty of target existence. The theory is illustrated by two nonlinear tracking applications: ballistic object tracking and bearings-only tracking. The simulation studies confirm the theory and reveal the relationship among the three bounds. PMID:23242274

Multilevel Sequential Monte Carlo Samplers for Normalizing Constants

DOE PAGES

Moral, Pierre Del; Jasra, Ajay; Law, Kody J. H.; ...

2017-08-24

This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the discrete approximation error must be balanced. A multilevel strategy is utilized to substantially reduce the cost to obtain a given error level in the approximation as compared to standard estimators. Two estimators are considered and relative variance bounds are given. The theoretical results are numerically illustrated for two Bayesian inverse problems arising from elliptic partial differential equations (PDEs). The examples involve the inversion of observations of themore » solution of (i) a 1-dimensional Poisson equation to infer the diffusion coefficient, and (ii) a 2-dimensional Poisson equation to infer the external forcing.« less

Model reduction of dynamical systems by proper orthogonal decomposition: Error bounds and comparison of methods using snapshots from the solution and the time derivatives [Proper orthogonal decomposition model reduction of dynamical systems: error bounds and comparison of methods using snapshots from the solution and the time derivatives

DOE PAGES

Kostova-Vassilevska, Tanya; Oxberry, Geoffrey M.

2017-09-17

In this study, we consider two proper orthogonal decomposition (POD) methods for dimension reduction of dynamical systems. The first method (M1) uses only time snapshots of the solution, while the second method (M2) augments the snapshot set with time-derivative snapshots. The goal of the paper is to analyze and compare the approximation errors resulting from the two methods by using error bounds. We derive several new bounds of the error from POD model reduction by each of the two methods. The new error bounds involve a multiplicative factor depending on the time steps between the snapshots. For method M1 themore » factor depends on the second power of the time step, while for method 2 the dependence is on the fourth power of the time step, suggesting that method M2 can be more accurate for small between-snapshot intervals. However, three other factors also affect the size of the error bounds. These include (i) the norm of the second (for M1) and fourth derivatives (M2); (ii) the first neglected singular value and (iii) the spectral properties of the projection of the system’s Jacobian in the reduced space. Because of the interplay of these factors neither method is more accurate than the other in all cases. Finally, we present numerical examples demonstrating that when the number of collected snapshots is small and the first neglected singular value has a value of zero, method M2 results in a better approximation.« less

Model reduction of dynamical systems by proper orthogonal decomposition: Error bounds and comparison of methods using snapshots from the solution and the time derivatives [Proper orthogonal decomposition model reduction of dynamical systems: error bounds and comparison of methods using snapshots from the solution and the time derivatives

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kostova-Vassilevska, Tanya; Oxberry, Geoffrey M.

In this study, we consider two proper orthogonal decomposition (POD) methods for dimension reduction of dynamical systems. The first method (M1) uses only time snapshots of the solution, while the second method (M2) augments the snapshot set with time-derivative snapshots. The goal of the paper is to analyze and compare the approximation errors resulting from the two methods by using error bounds. We derive several new bounds of the error from POD model reduction by each of the two methods. The new error bounds involve a multiplicative factor depending on the time steps between the snapshots. For method M1 themore » factor depends on the second power of the time step, while for method 2 the dependence is on the fourth power of the time step, suggesting that method M2 can be more accurate for small between-snapshot intervals. However, three other factors also affect the size of the error bounds. These include (i) the norm of the second (for M1) and fourth derivatives (M2); (ii) the first neglected singular value and (iii) the spectral properties of the projection of the system’s Jacobian in the reduced space. Because of the interplay of these factors neither method is more accurate than the other in all cases. Finally, we present numerical examples demonstrating that when the number of collected snapshots is small and the first neglected singular value has a value of zero, method M2 results in a better approximation.« less

Power of one nonclean qubit

NASA Astrophysics Data System (ADS)

Morimae, Tomoyuki; Fujii, Keisuke; Nishimura, Harumichi

2017-04-01

The one-clean qubit model (or the DQC1 model) is a restricted model of quantum computing where only a single qubit of the initial state is pure and others are maximally mixed. Although the model is not universal, it can efficiently solve several problems whose classical efficient solutions are not known. Furthermore, it was recently shown that if the one-clean qubit model is classically efficiently simulated, the polynomial hierarchy collapses to the second level. A disadvantage of the one-clean qubit model is, however, that the clean qubit is too clean: for example, in realistic NMR experiments, polarizations are not high enough to have the perfectly pure qubit. In this paper, we consider a more realistic one-clean qubit model, where the clean qubit is not clean, but depolarized. We first show that, for any polarization, a multiplicative-error calculation of the output probability distribution of the model is possible in a classical polynomial time if we take an appropriately large multiplicative error. The result is in strong contrast with that of the ideal one-clean qubit model where the classical efficient multiplicative-error calculation (or even the sampling) with the same amount of error causes the collapse of the polynomial hierarchy. We next show that, for any polarization lower-bounded by an inverse polynomial, a classical efficient sampling (in terms of a sufficiently small multiplicative error or an exponentially small additive error) of the output probability distribution of the model is impossible unless BQP (bounded error quantum polynomial time) is contained in the second level of the polynomial hierarchy, which suggests the hardness of the classical efficient simulation of the one nonclean qubit model.

Validating Clusters with the Lower Bound for Sum-of-Squares Error

ERIC Educational Resources Information Center

Steinley, Douglas

2007-01-01

Given that a minor condition holds (e.g., the number of variables is greater than the number of clusters), a nontrivial lower bound for the sum-of-squares error criterion in K-means clustering is derived. By calculating the lower bound for several different situations, a method is developed to determine the adequacy of cluster solution based on…

Full-Duplex Bidirectional Secure Communications Under Perfect and Distributionally Ambiguous Eavesdropper's CSI

NASA Astrophysics Data System (ADS)

Li, Qiang; Zhang, Ying; Lin, Jingran; Wu, Sissi Xiaoxiao

2017-09-01

Consider a full-duplex (FD) bidirectional secure communication system, where two communication nodes, named Alice and Bob, simultaneously transmit and receive confidential information from each other, and an eavesdropper, named Eve, overhears the transmissions. Our goal is to maximize the sum secrecy rate (SSR) of the bidirectional transmissions by optimizing the transmit covariance matrices at Alice and Bob. To tackle this SSR maximization (SSRM) problem, we develop an alternating difference-of-concave (ADC) programming approach to alternately optimize the transmit covariance matrices at Alice and Bob. We show that the ADC iteration has a semi-closed-form beamforming solution, and is guaranteed to converge to a stationary solution of the SSRM problem. Besides the SSRM design, this paper also deals with a robust SSRM transmit design under a moment-based random channel state information (CSI) model, where only some roughly estimated first and second-order statistics of Eve's CSI are available, but the exact distribution or other high-order statistics is not known. This moment-based error model is new and different from the widely used bounded-sphere error model and the Gaussian random error model. Under the consider CSI error model, the robust SSRM is formulated as an outage probability-constrained SSRM problem. By leveraging the Lagrangian duality theory and DC programming, a tractable safe solution to the robust SSRM problem is derived. The effectiveness and the robustness of the proposed designs are demonstrated through simulations.

An Upper Bound on High Speed Satellite Collision Probability When Only One Object has Position Uncertainty Information

NASA Technical Reports Server (NTRS)

Frisbee, Joseph H., Jr.

2015-01-01

Upper bounds on high speed satellite collision probability, PC †, have been investigated. Previous methods assume an individual position error covariance matrix is available for each object. The two matrices being combined into a single, relative position error covariance matrix. Components of the combined error covariance are then varied to obtain a maximum PC. If error covariance information for only one of the two objects was available, either some default shape has been used or nothing could be done. An alternative is presented that uses the known covariance information along with a critical value of the missing covariance to obtain an approximate but potentially useful Pc upper bound.

Dynamical error bounds for continuum discretisation via Gauss quadrature rules—A Lieb-Robinson bound approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Woods, M. P.; Centre for Quantum Technologies, National University of Singapore; QuTech, Delft University of Technology, Lorentzweg 1, 2611 CJ Delft

2016-02-15

Instances of discrete quantum systems coupled to a continuum of oscillators are ubiquitous in physics. Often the continua are approximated by a discrete set of modes. We derive error bounds on expectation values of system observables that have been time evolved under such discretised Hamiltonians. These bounds take on the form of a function of time and the number of discrete modes, where the discrete modes are chosen according to Gauss quadrature rules. The derivation makes use of tools from the field of Lieb-Robinson bounds and the theory of orthonormal polynomials.

Disturbance observer-based adaptive sliding mode hybrid projective synchronisation of identical fractional-order financial systems

NASA Astrophysics Data System (ADS)

Khan, Ayub; Tyagi, Arti

2018-05-01

In this paper, we have studied the hybrid projective synchronisation for incommensurate, integer and commensurate fractional-order financial systems with unknown disturbance. To tackle the problem of unknown bounded disturbance, fractional-order disturbance observer is designed to approximate the unknown disturbance. Further, we have introduced simple sliding mode surface and designed adaptive sliding mode controllers incorporating with the designed fractional-order disturbance observer to achieve a bounded hybrid projective synchronisation between two identical fractional-order financial model with different initial conditions. It is shown that the slave system with disturbance can be synchronised with the projection of the master system generated through state transformation. Simulation results are presented to ensure the validity and effectiveness of the proposed sliding mode control scheme in the presence of external bounded unknown disturbance. Also, synchronisation error for commensurate, integer and incommensurate fractional-order financial systems is studied in numerical simulation.

Pre-Test Assessment of the Upper Bound of the Drag Coefficient Repeatability of a Wind Tunnel Model

NASA Technical Reports Server (NTRS)

Ulbrich, N.; L'Esperance, A.

2017-01-01

A new method is presented that computes a pre{test estimate of the upper bound of the drag coefficient repeatability of a wind tunnel model. This upper bound is a conservative estimate of the precision error of the drag coefficient. For clarity, precision error contributions associated with the measurement of the dynamic pressure are analyzed separately from those that are associated with the measurement of the aerodynamic loads. The upper bound is computed by using information about the model, the tunnel conditions, and the balance in combination with an estimate of the expected output variations as input. The model information consists of the reference area and an assumed angle of attack. The tunnel conditions are described by the Mach number and the total pressure or unit Reynolds number. The balance inputs are the partial derivatives of the axial and normal force with respect to all balance outputs. Finally, an empirical output variation of 1.0 microV/V is used to relate both random instrumentation and angle measurement errors to the precision error of the drag coefficient. Results of the analysis are reported by plotting the upper bound of the precision error versus the tunnel conditions. The analysis shows that the influence of the dynamic pressure measurement error on the precision error of the drag coefficient is often small when compared with the influence of errors that are associated with the load measurements. Consequently, the sensitivities of the axial and normal force gages of the balance have a significant influence on the overall magnitude of the drag coefficient's precision error. Therefore, results of the error analysis can be used for balance selection purposes as the drag prediction characteristics of balances of similar size and capacities can objectively be compared. Data from two wind tunnel models and three balances are used to illustrate the assessment of the precision error of the drag coefficient.

Self-Configuration and Localization in Ad Hoc Wireless Sensor Networks

DTIC Science & Technology

2010-08-31

Goddard I. SUMMARY OF CONTRIBUTIONS We explored the error mechanisms of iterative decoding of low-density parity-check ( LDPC ) codes . This work has resulted...important problems in the area of channel coding , as their unpredictable behavior has impeded the deployment of LDPC codes in many real-world applications. We...tree-based decoders of LDPC codes , including the extrinsic tree decoder, and an investigation into their performance and bounding capabilities [5], [6

Parameter Identification

DTIC Science & Technology

1979-11-01

Science Aeronautique, Vol. 6, pp. 38-49, 1950. 9. Anon.: "Methods of testing at constant attitude", ICAO Circular 16-AN/13, 1951. 10. H.L. Jonkers...spectral density analysis, it was determined that a notch filter at 17.7 hertz and a third-order Butterworth low-pass filter with a break frequency of 20...of the effects of specific errors, they are circular in nature and do not address the basic theoretical problem. Therefore, the Cramer-Rao bound

Sensor selection cost optimisation for tracking structurally cyclic systems: a P-order solution

NASA Astrophysics Data System (ADS)

Doostmohammadian, M.; Zarrabi, H.; Rabiee, H. R.

2017-08-01

Measurements and sensing implementations impose certain cost in sensor networks. The sensor selection cost optimisation is the problem of minimising the sensing cost of monitoring a physical (or cyber-physical) system. Consider a given set of sensors tracking states of a dynamical system for estimation purposes. For each sensor assume different costs to measure different (realisable) states. The idea is to assign sensors to measure states such that the global cost is minimised. The number and selection of sensor measurements need to ensure the observability to track the dynamic state of the system with bounded estimation error. The main question we address is how to select the state measurements to minimise the cost while satisfying the observability conditions. Relaxing the observability condition for structurally cyclic systems, the main contribution is to propose a graph theoretic approach to solve the problem in polynomial time. Note that polynomial time algorithms are suitable for large-scale systems as their running time is upper-bounded by a polynomial expression in the size of input for the algorithm. We frame the problem as a linear sum assignment with solution complexity of ?.

Joint Chance-Constrained Dynamic Programming

NASA Technical Reports Server (NTRS)

Ono, Masahiro; Kuwata, Yoshiaki; Balaram, J. Bob

2012-01-01

This paper presents a novel dynamic programming algorithm with a joint chance constraint, which explicitly bounds the risk of failure in order to maintain the state within a specified feasible region. A joint chance constraint cannot be handled by existing constrained dynamic programming approaches since their application is limited to constraints in the same form as the cost function, that is, an expectation over a sum of one-stage costs. We overcome this challenge by reformulating the joint chance constraint into a constraint on an expectation over a sum of indicator functions, which can be incorporated into the cost function by dualizing the optimization problem. As a result, the primal variables can be optimized by a standard dynamic programming, while the dual variable is optimized by a root-finding algorithm that converges exponentially. Error bounds on the primal and dual objective values are rigorously derived. We demonstrate the algorithm on a path planning problem, as well as an optimal control problem for Mars entry, descent and landing. The simulations are conducted using a real terrain data of Mars, with four million discrete states at each time step.

Quantum State Tomography via Linear Regression Estimation

PubMed Central

Qi, Bo; Hou, Zhibo; Li, Li; Dong, Daoyi; Xiang, Guoyong; Guo, Guangcan

2013-01-01

A simple yet efficient state reconstruction algorithm of linear regression estimation (LRE) is presented for quantum state tomography. In this method, quantum state reconstruction is converted into a parameter estimation problem of a linear regression model and the least-squares method is employed to estimate the unknown parameters. An asymptotic mean squared error (MSE) upper bound for all possible states to be estimated is given analytically, which depends explicitly upon the involved measurement bases. This analytical MSE upper bound can guide one to choose optimal measurement sets. The computational complexity of LRE is O(d4) where d is the dimension of the quantum state. Numerical examples show that LRE is much faster than maximum-likelihood estimation for quantum state tomography. PMID:24336519

Event-based recursive filtering for a class of nonlinear stochastic parameter systems over fading channels

NASA Astrophysics Data System (ADS)

Shen, Yuxuan; Wang, Zidong; Shen, Bo; Alsaadi, Fuad E.

2018-07-01

In this paper, the recursive filtering problem is studied for a class of time-varying nonlinear systems with stochastic parameter matrices. The measurement transmission between the sensor and the filter is conducted through a fading channel characterized by the Rice fading model. An event-based transmission mechanism is adopted to decide whether the sensor measurement should be transmitted to the filter. A recursive filter is designed such that, in the simultaneous presence of the stochastic parameter matrices and fading channels, the filtering error covariance is guaranteed to have an upper bound and such an upper bound is then minimized by appropriately choosing filter gain matrix. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed filtering scheme.

A simple method to derive bounds on the size and to train multilayer neural networks

NASA Technical Reports Server (NTRS)

Sartori, Michael A.; Antsaklis, Panos J.

1991-01-01

A new derivation is presented for the bounds on the size of a multilayer neural network to exactly implement an arbitrary training set; namely, the training set can be implemented with zero error with two layers and with the number of the hidden-layer neurons equal to no.1 is greater than p - 1. The derivation does not require the separation of the input space by particular hyperplanes, as in previous derivations. The weights for the hidden layer can be chosen almost arbitrarily, and the weights for the output layer can be found by solving no.1 + 1 linear equations. The method presented exactly solves (M), the multilayer neural network training problem, for any arbitrary training set.

Adaptive Neural Networks Decentralized FTC Design for Nonstrict-Feedback Nonlinear Interconnected Large-Scale Systems Against Actuator Faults.

PubMed

Li, Yongming; Tong, Shaocheng

The problem of active fault-tolerant control (FTC) is investigated for the large-scale nonlinear systems in nonstrict-feedback form. The nonstrict-feedback nonlinear systems considered in this paper consist of unstructured uncertainties, unmeasured states, unknown interconnected terms, and actuator faults (e.g., bias fault and gain fault). A state observer is designed to solve the unmeasurable state problem. Neural networks (NNs) are used to identify the unknown lumped nonlinear functions so that the problems of unstructured uncertainties and unknown interconnected terms can be solved. By combining the adaptive backstepping design principle with the combination Nussbaum gain function property, a novel NN adaptive output-feedback FTC approach is developed. The proposed FTC controller can guarantee that all signals in all subsystems are bounded, and the tracking errors for each subsystem converge to a small neighborhood of zero. Finally, numerical results of practical examples are presented to further demonstrate the effectiveness of the proposed control strategy.The problem of active fault-tolerant control (FTC) is investigated for the large-scale nonlinear systems in nonstrict-feedback form. The nonstrict-feedback nonlinear systems considered in this paper consist of unstructured uncertainties, unmeasured states, unknown interconnected terms, and actuator faults (e.g., bias fault and gain fault). A state observer is designed to solve the unmeasurable state problem. Neural networks (NNs) are used to identify the unknown lumped nonlinear functions so that the problems of unstructured uncertainties and unknown interconnected terms can be solved. By combining the adaptive backstepping design principle with the combination Nussbaum gain function property, a novel NN adaptive output-feedback FTC approach is developed. The proposed FTC controller can guarantee that all signals in all subsystems are bounded, and the tracking errors for each subsystem converge to a small neighborhood of zero. Finally, numerical results of practical examples are presented to further demonstrate the effectiveness of the proposed control strategy.

Robust THP Transceiver Designs for Multiuser MIMO Downlink with Imperfect CSIT

NASA Astrophysics Data System (ADS)

Ubaidulla, P.; Chockalingam, A.

2009-12-01

We present robust joint nonlinear transceiver designs for multiuser multiple-input multiple-output (MIMO) downlink in the presence of imperfections in the channel state information at the transmitter (CSIT). The base station (BS) is equipped with multiple transmit antennas, and each user terminal is equipped with one or more receive antennas. The BS employs Tomlinson-Harashima precoding (THP) for interuser interference precancellation at the transmitter. We consider robust transceiver designs that jointly optimize the transmit THP filters and receive filter for two models of CSIT errors. The first model is a stochastic error (SE) model, where the CSIT error is Gaussian-distributed. This model is applicable when the CSIT error is dominated by channel estimation error. In this case, the proposed robust transceiver design seeks to minimize a stochastic function of the sum mean square error (SMSE) under a constraint on the total BS transmit power. We propose an iterative algorithm to solve this problem. The other model we consider is a norm-bounded error (NBE) model, where the CSIT error can be specified by an uncertainty set. This model is applicable when the CSIT error is dominated by quantization errors. In this case, we consider a worst-case design. For this model, we consider robust (i) minimum SMSE, (ii) MSE-constrained, and (iii) MSE-balancing transceiver designs. We propose iterative algorithms to solve these problems, wherein each iteration involves a pair of semidefinite programs (SDPs). Further, we consider an extension of the proposed algorithm to the case with per-antenna power constraints. We evaluate the robustness of the proposed algorithms to imperfections in CSIT through simulation, and show that the proposed robust designs outperform nonrobust designs as well as robust linear transceiver designs reported in the recent literature.

Performance analysis of a cascaded coding scheme with interleaved outer code

NASA Technical Reports Server (NTRS)

Lin, S.

1986-01-01

A cascaded coding scheme for a random error channel with a bit-error rate is analyzed. In this scheme, the inner code C sub 1 is an (n sub 1, m sub 1l) binary linear block code which is designed for simultaneous error correction and detection. The outer code C sub 2 is a linear block code with symbols from the Galois field GF (2 sup l) which is designed for correcting both symbol errors and erasures, and is interleaved with a degree m sub 1. A procedure for computing the probability of a correct decoding is presented and an upper bound on the probability of a decoding error is derived. The bound provides much better results than the previous bound for a cascaded coding scheme with an interleaved outer code. Example schemes with inner codes ranging from high rates to very low rates are evaluated. Several schemes provide extremely high reliability even for very high bit-error rates say 10 to the -1 to 10 to the -2 power.

Breaking Lander-Waterman’s Coverage Bound

PubMed Central

Nashta-ali, Damoun; Motahari, Seyed Abolfazl; Hosseinkhalaj, Babak

2016-01-01

Lander-Waterman’s coverage bound establishes the total number of reads required to cover the whole genome of size G bases. In fact, their bound is a direct consequence of the well-known solution to the coupon collector’s problem which proves that for such genome, the total number of bases to be sequenced should be O(G ln G). Although the result leads to a tight bound, it is based on a tacit assumption that the set of reads are first collected through a sequencing process and then are processed through a computation process, i.e., there are two different machines: one for sequencing and one for processing. In this paper, we present a significant improvement compared to Lander-Waterman’s result and prove that by combining the sequencing and computing processes, one can re-sequence the whole genome with as low as O(G) sequenced bases in total. Our approach also dramatically reduces the required computational power for the combined process. Simulation results are performed on real genomes with different sequencing error rates. The results support our theory predicting the log G improvement on coverage bound and corresponding reduction in the total number of bases required to be sequenced. PMID:27806058

Modeling error analysis of stationary linear discrete-time filters

NASA Technical Reports Server (NTRS)

Patel, R.; Toda, M.

1977-01-01

The performance of Kalman-type, linear, discrete-time filters in the presence of modeling errors is considered. The discussion is limited to stationary performance, and bounds are obtained for the performance index, the mean-squared error of estimates for suboptimal and optimal (Kalman) filters. The computation of these bounds requires information on only the model matrices and the range of errors for these matrices. Consequently, a design can easily compare the performance of a suboptimal filter with that of the optimal filter, when only the range of errors in the elements of the model matrices is available.

Uniformly stable backpropagation algorithm to train a feedforward neural network.

PubMed

Rubio, José de Jesús; Angelov, Plamen; Pacheco, Jaime

2011-03-01

Neural networks (NNs) have numerous applications to online processes, but the problem of stability is rarely discussed. This is an extremely important issue because, if the stability of a solution is not guaranteed, the equipment that is being used can be damaged, which can also cause serious accidents. It is true that in some research papers this problem has been considered, but this concerns continuous-time NN only. At the same time, there are many systems that are better described in the discrete time domain such as population of animals, the annual expenses in an industry, the interest earned by a bank, or the prediction of the distribution of loads stored every hour in a warehouse. Therefore, it is of paramount importance to consider the stability of the discrete-time NN. This paper makes several important contributions. 1) A theorem is stated and proven which guarantees uniform stability of a general discrete-time system. 2) It is proven that the backpropagation (BP) algorithm with a new time-varying rate is uniformly stable for online identification and the identification error converges to a small zone bounded by the uncertainty. 3) It is proven that the weights' error is bounded by the initial weights' error, i.e., overfitting is eliminated in the proposed algorithm. 4) The BP algorithm is applied to predict the distribution of loads that a transelevator receives from a trailer and places in the deposits in a warehouse every hour, so that the deposits in the warehouse are reserved in advance using the prediction results. 5) The BP algorithm is compared with the recursive least square (RLS) algorithm and with the Takagi-Sugeno type fuzzy inference system in the problem of predicting the distribution of loads in a warehouse, giving that the first and the second are stable and the third is unstable. 6) The BP algorithm is compared with the RLS algorithm and with the Kalman filter algorithm in a synthetic example.

Fast and reliable symplectic integration for planetary system N-body problems

NASA Astrophysics Data System (ADS)

Hernandez, David M.

2016-06-01

We apply one of the exactly symplectic integrators, which we call HB15, of Hernandez & Bertschinger, along with the Kepler problem solver of Wisdom & Hernandez, to solve planetary system N-body problems. We compare the method to Wisdom-Holman (WH) methods in the MERCURY software package, the MERCURY switching integrator, and others and find HB15 to be the most efficient method or tied for the most efficient method in many cases. Unlike WH, HB15 solved N-body problems exhibiting close encounters with small, acceptable error, although frequent encounters slowed the code. Switching maps like MERCURY change between two methods and are not exactly symplectic. We carry out careful tests on their properties and suggest that they must be used with caution. We then use different integrators to solve a three-body problem consisting of a binary planet orbiting a star. For all tested tolerances and time steps, MERCURY unbinds the binary after 0 to 25 years. However, in the solutions of HB15, a time-symmetric HERMITE code, and a symplectic Yoshida method, the binary remains bound for >1000 years. The methods' solutions are qualitatively different, despite small errors in the first integrals in most cases. Several checks suggest that the qualitative binary behaviour of HB15's solution is correct. The Bulirsch-Stoer and Radau methods in the MERCURY package also unbind the binary before a time of 50 years, suggesting that this dynamical error is due to a MERCURY bug.

Controller certification: The generalized stability margin inference for a large number of MIMO controllers

NASA Astrophysics Data System (ADS)

Park, Jisang

In this dissertation, we investigate MIMO stability margin inference of a large number of controllers using pre-established stability margins of a small number of nu-gap-wise adjacent controllers. The generalized stability margin and the nu-gap metric are inherently able to handle MIMO system analysis without the necessity of repeating multiple channel-by-channel SISO analyses. This research consists of three parts: (i) development of a decision support tool for inference of the stability margin, (ii) computational considerations for yielding the maximal stability margin with the minimal nu-gap metric in a less conservative manner, and (iii) experiment design for estimating the generalized stability margin with an assured error bound. A modern problem from aerospace control involves the certification of a large set of potential controllers with either a single plant or a fleet of potential plant systems, with both plants and controllers being MIMO and, for the moment, linear. Experiments on a limited number of controller/plant pairs should establish the stability and a certain level of margin of the complete set. We consider this certification problem for a set of controllers and provide algorithms for selecting an efficient subset for testing. This is done for a finite set of candidate controllers and, at least for SISO plants, for an infinite set. In doing this, the nu-gap metric will be the main tool. We provide a theorem restricting a radius of a ball in the parameter space so that the controller can guarantee a prescribed level of stability and performance if parameters of the controllers are contained in the ball. Computational examples are given, including one of certification of an aircraft engine controller. The overarching aim is to introduce truly MIMO margin calculations and to understand their efficacy in certifying stability over a set of controllers and in replacing legacy single-loop gain and phase margin calculations. We consider methods for the computation of; maximal MIMO stability margins bP̂,C, minimal nu-gap metrics deltanu , and the maximal difference between these two values, through the use of scaling and weighting functions. We propose simultaneous scaling selections that attempt to maximize the generalized stability margin and minimize the nu-gap. The minimization of the nu-gap by scaling involves a non-convex optimization. We modify the XY-centering algorithm to handle this non-convexity. This is done for applications in controller certification. Estimating the generalized stability margin with an accurate error bound has significant impact on controller certification. We analyze an error bound of the generalized stability margin as the infinity norm of the MIMO empirical transfer function estimate (ETFE). Input signal design to reduce the error on the estimate is also studied. We suggest running the system for a certain amount of time prior to recording of each output data set. The assured upper bound of estimation error can be tuned by the amount of the pre-experiment.

Adaptive Neural Networks Prescribed Performance Control Design for Switched Interconnected Uncertain Nonlinear Systems.

PubMed

Li, Yongming; Tong, Shaocheng

2017-06-28

In this paper, an adaptive neural networks (NNs)-based decentralized control scheme with the prescribed performance is proposed for uncertain switched nonstrict-feedback interconnected nonlinear systems. It is assumed that nonlinear interconnected terms and nonlinear functions of the concerned systems are unknown, and also the switching signals are unknown and arbitrary. A linear state estimator is constructed to solve the problem of unmeasured states. The NNs are employed to approximate unknown interconnected terms and nonlinear functions. A new output feedback decentralized control scheme is developed by using the adaptive backstepping design technique. The control design problem of nonlinear interconnected switched systems with unknown switching signals can be solved by the proposed scheme, and only a tuning parameter is needed for each subsystem. The proposed scheme can ensure that all variables of the control systems are semi-globally uniformly ultimately bounded and the tracking errors converge to a small residual set with the prescribed performance bound. The effectiveness of the proposed control approach is verified by some simulation results.

On position/force tracking control problem of cooperative robot manipulators using adaptive fuzzy backstepping approach.

PubMed

Baigzadehnoe, Barmak; Rahmani, Zahra; Khosravi, Alireza; Rezaie, Behrooz

2017-09-01

In this paper, the position and force tracking control problem of cooperative robot manipulator system handling a common rigid object with unknown dynamical models and unknown external disturbances is investigated. The universal approximation properties of fuzzy logic systems are employed to estimate the unknown system dynamics. On the other hand, by defining new state variables based on the integral and differential of position and orientation errors of the grasped object, the error system of coordinated robot manipulators is constructed. Subsequently by defining the appropriate change of coordinates and using the backstepping design strategy, an adaptive fuzzy backstepping position tracking control scheme is proposed for multi-robot manipulator systems. By utilizing the properties of internal forces, extra terms are also added to the control signals to consider the force tracking problem. Moreover, it is shown that the proposed adaptive fuzzy backstepping position/force control approach ensures all the signals of the closed loop system uniformly ultimately bounded and tracking errors of both positions and forces can converge to small desired values by proper selection of the design parameters. Finally, the theoretic achievements are tested on the two three-link planar robot manipulators cooperatively handling a common object to illustrate the effectiveness of the proposed approach. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

ADRC for spacecraft attitude and position synchronization in libration point orbits

NASA Astrophysics Data System (ADS)

Gao, Chen; Yuan, Jianping; Zhao, Yakun

2018-04-01

This paper addresses the problem of spacecraft attitude and position synchronization in libration point orbits between a leader and a follower. Using dual quaternion, the dimensionless relative coupled dynamical model is derived considering computation efficiency and accuracy. Then a model-independent dimensionless cascade pose-feedback active disturbance rejection controller is designed to spacecraft attitude and position tracking control problems considering parameter uncertainties and external disturbances. Numerical simulations for the final approach phase in spacecraft rendezvous and docking and formation flying are done, and the results show high-precision tracking errors and satisfactory convergent rates under bounded control torque and force which validate the proposed approach.

Finite-error metrological bounds on multiparameter Hamiltonian estimation

NASA Astrophysics Data System (ADS)

Kura, Naoto; Ueda, Masahito

2018-01-01

Estimation of multiple parameters in an unknown Hamiltonian is investigated. We present upper and lower bounds on the time required to complete the estimation within a prescribed error tolerance δ . The lower bound is given on the basis of the Cramér-Rao inequality, where the quantum Fisher information is bounded by the squared evolution time. The upper bound is obtained by an explicit construction of estimation procedures. By comparing the cases with different numbers of Hamiltonian channels, we also find that the few-channel procedure with adaptive feedback and the many-channel procedure with entanglement are equivalent in the sense that they require the same amount of time resource up to a constant factor.

Powered Descent Guidance with General Thrust-Pointing Constraints

NASA Technical Reports Server (NTRS)

Carson, John M., III; Acikmese, Behcet; Blackmore, Lars

2013-01-01

The Powered Descent Guidance (PDG) algorithm and software for generating Mars pinpoint or precision landing guidance profiles has been enhanced to incorporate thrust-pointing constraints. Pointing constraints would typically be needed for onboard sensor and navigation systems that have specific field-of-view requirements to generate valid ground proximity and terrain-relative state measurements. The original PDG algorithm was designed to enforce both control and state constraints, including maximum and minimum thrust bounds, avoidance of the ground or descent within a glide slope cone, and maximum speed limits. The thrust-bound and thrust-pointing constraints within PDG are non-convex, which in general requires nonlinear optimization methods to generate solutions. The short duration of Mars powered descent requires guaranteed PDG convergence to a solution within a finite time; however, nonlinear optimization methods have no guarantees of convergence to the global optimal or convergence within finite computation time. A lossless convexification developed for the original PDG algorithm relaxed the non-convex thrust bound constraints. This relaxation was theoretically proven to provide valid and optimal solutions for the original, non-convex problem within a convex framework. As with the thrust bound constraint, a relaxation of the thrust-pointing constraint also provides a lossless convexification that ensures the enhanced relaxed PDG algorithm remains convex and retains validity for the original nonconvex problem. The enhanced PDG algorithm provides guidance profiles for pinpoint and precision landing that minimize fuel usage, minimize landing error to the target, and ensure satisfaction of all position and control constraints, including thrust bounds and now thrust-pointing constraints.

Contagious error sources would need time travel to prevent quantum computation

NASA Astrophysics Data System (ADS)

Kalai, Gil; Kuperberg, Greg

2015-08-01

We consider an error model for quantum computing that consists of "contagious quantum germs" that can infect every output qubit when at least one input qubit is infected. Once a germ actively causes error, it continues to cause error indefinitely for every qubit it infects, with arbitrary quantum entanglement and correlation. Although this error model looks much worse than quasi-independent error, we show that it reduces to quasi-independent error with the technique of quantum teleportation. The construction, which was previously described by Knill, is that every quantum circuit can be converted to a mixed circuit with bounded quantum depth. We also consider the restriction of bounded quantum depth from the point of view of quantum complexity classes.

Computer search for binary cyclic UEP codes of odd length up to 65

NASA Technical Reports Server (NTRS)

Lin, Mao-Chao; Lin, Chi-Chang; Lin, Shu

1990-01-01

Using an exhaustive computation, the unequal error protection capabilities of all binary cyclic codes of odd length up to 65 that have minimum distances at least 3 are found. For those codes that can only have upper bounds on their unequal error protection capabilities computed, an analytic method developed by Dynkin and Togonidze (1976) is used to show that the upper bounds meet the exact unequal error protection capabilities.

On the error probability of general tree and trellis codes with applications to sequential decoding

NASA Technical Reports Server (NTRS)

Johannesson, R.

1973-01-01

An upper bound on the average error probability for maximum-likelihood decoding of the ensemble of random binary tree codes is derived and shown to be independent of the length of the tree. An upper bound on the average error probability for maximum-likelihood decoding of the ensemble of random L-branch binary trellis codes of rate R = 1/n is derived which separates the effects of the tail length T and the memory length M of the code. It is shown that the bound is independent of the length L of the information sequence. This implication is investigated by computer simulations of sequential decoding utilizing the stack algorithm. These simulations confirm the implication and further suggest an empirical formula for the true undetected decoding error probability with sequential decoding.

Automatic Estimation of Verified Floating-Point Round-Off Errors via Static Analysis

NASA Technical Reports Server (NTRS)

Moscato, Mariano; Titolo, Laura; Dutle, Aaron; Munoz, Cesar A.

2017-01-01

This paper introduces a static analysis technique for computing formally verified round-off error bounds of floating-point functional expressions. The technique is based on a denotational semantics that computes a symbolic estimation of floating-point round-o errors along with a proof certificate that ensures its correctness. The symbolic estimation can be evaluated on concrete inputs using rigorous enclosure methods to produce formally verified numerical error bounds. The proposed technique is implemented in the prototype research tool PRECiSA (Program Round-o Error Certifier via Static Analysis) and used in the verification of floating-point programs of interest to NASA.

Multi-fidelity stochastic collocation method for computation of statistical moments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhu, Xueyu, E-mail: xueyu-zhu@uiowa.edu; Linebarger, Erin M., E-mail: aerinline@sci.utah.edu; Xiu, Dongbin, E-mail: xiu.16@osu.edu

We present an efficient numerical algorithm to approximate the statistical moments of stochastic problems, in the presence of models with different fidelities. The method extends the multi-fidelity approximation method developed in . By combining the efficiency of low-fidelity models and the accuracy of high-fidelity models, our method exhibits fast convergence with a limited number of high-fidelity simulations. We establish an error bound of the method and present several numerical examples to demonstrate the efficiency and applicability of the multi-fidelity algorithm.

Time domain convergence properties of Lyapunov stable penalty methods

NASA Technical Reports Server (NTRS)

Kurdila, A. J.; Sunkel, John

1991-01-01

Linear hyperbolic partial differential equations are analyzed using standard techniques to show that a sequence of solutions generated by the Liapunov stable penalty equations approaches the solution of the differential-algebraic equations governing the dynamics of multibody problems arising in linear vibrations. The analysis does not require that the system be conservative and does not impose any specific integration scheme. Variational statements are derived which bound the error in approximation by the norm of the constraint violation obtained in the approximate solutions.

Adaptive output feedback control of uncertain nonlinear systems using single-hidden-layer neural networks.

PubMed

Hovakimyan, N; Nardi, F; Calise, A; Kim, Nakwan

2002-01-01

We consider adaptive output feedback control of uncertain nonlinear systems, in which both the dynamics and the dimension of the regulated system may be unknown. However, the relative degree of the regulated output is assumed to be known. Given a smooth reference trajectory, the problem is to design a controller that forces the system measurement to track it with bounded errors. The classical approach requires a state observer. Finding a good observer for an uncertain nonlinear system is not an obvious task. We argue that it is sufficient to build an observer for the output tracking error. Ultimate boundedness of the error signals is shown through Lyapunov's direct method. The theoretical results are illustrated in the design of a controller for a fourth-order nonlinear system of relative degree two and a high-bandwidth attitude command system for a model R-50 helicopter.

Prescribed performance distributed consensus control for nonlinear multi-agent systems with unknown dead-zone input

NASA Astrophysics Data System (ADS)

Cui, Guozeng; Xu, Shengyuan; Ma, Qian; Li, Yongmin; Zhang, Zhengqiang

2018-05-01

In this paper, the problem of prescribed performance distributed output consensus for higher-order non-affine nonlinear multi-agent systems with unknown dead-zone input is investigated. Fuzzy logical systems are utilised to identify the unknown nonlinearities. By introducing prescribed performance, the transient and steady performance of synchronisation errors are guaranteed. Based on Lyapunov stability theory and the dynamic surface control technique, a new distributed consensus algorithm for non-affine nonlinear multi-agent systems is proposed, which ensures cooperatively uniformly ultimately boundedness of all signals in the closed-loop systems and enables the output of each follower to synchronise with the leader within predefined bounded error. Finally, simulation examples are provided to demonstrate the effectiveness of the proposed control scheme.

Adaptive Neural Tracking Control for Switched High-Order Stochastic Nonlinear Systems.

PubMed

Zhao, Xudong; Wang, Xinyong; Zong, Guangdeng; Zheng, Xiaolong

2017-10-01

This paper deals with adaptive neural tracking control design for a class of switched high-order stochastic nonlinear systems with unknown uncertainties and arbitrary deterministic switching. The considered issues are: 1) completely unknown uncertainties; 2) stochastic disturbances; and 3) high-order nonstrict-feedback system structure. The considered mathematical models can represent many practical systems in the actual engineering. By adopting the approximation ability of neural networks, common stochastic Lyapunov function method together with adding an improved power integrator technique, an adaptive state feedback controller with multiple adaptive laws is systematically designed for the systems. Subsequently, a controller with only two adaptive laws is proposed to solve the problem of over parameterization. Under the designed controllers, all the signals in the closed-loop system are bounded-input bounded-output stable in probability, and the system output can almost surely track the target trajectory within a specified bounded error. Finally, simulation results are presented to show the effectiveness of the proposed approaches.

Ensembles vs. information theory: supporting science under uncertainty

NASA Astrophysics Data System (ADS)

Nearing, Grey S.; Gupta, Hoshin V.

2018-05-01

Multi-model ensembles are one of the most common ways to deal with epistemic uncertainty in hydrology. This is a problem because there is no known way to sample models such that the resulting ensemble admits a measure that has any systematic (i.e., asymptotic, bounded, or consistent) relationship with uncertainty. Multi-model ensembles are effectively sensitivity analyses and cannot - even partially - quantify uncertainty. One consequence of this is that multi-model approaches cannot support a consistent scientific method - in particular, multi-model approaches yield unbounded errors in inference. In contrast, information theory supports a coherent hypothesis test that is robust to (i.e., bounded under) arbitrary epistemic uncertainty. This paper may be understood as advocating a procedure for hypothesis testing that does not require quantifying uncertainty, but is coherent and reliable (i.e., bounded) in the presence of arbitrary (unknown and unknowable) uncertainty. We conclude by offering some suggestions about how this proposed philosophy of science suggests new ways to conceptualize and construct simulation models of complex, dynamical systems.

More on the decoder error probability for Reed-Solomon codes

NASA Technical Reports Server (NTRS)

Cheung, K.-M.

1987-01-01

The decoder error probability for Reed-Solomon codes (more generally, linear maximum distance separable codes) is examined. McEliece and Swanson offered an upper bound on P sub E (u), the decoder error probability given that u symbol errors occurs. This upper bound is slightly greater than Q, the probability that a completely random error pattern will cause decoder error. By using a combinatoric technique, the principle of inclusion and exclusion, an exact formula for P sub E (u) is derived. The P sub e (u) for the (255, 223) Reed-Solomon Code used by NASA, and for the (31,15) Reed-Solomon code (JTIDS code), are calculated using the exact formula, and the P sub E (u)'s are observed to approach the Q's of the codes rapidly as u gets larger. An upper bound for the expression is derived, and is shown to decrease nearly exponentially as u increases. This proves analytically that P sub E (u) indeed approaches Q as u becomes large, and some laws of large numbers come into play.

Theoretical Bounds of Direct Binary Search Halftoning.

PubMed

Liao, Jan-Ray

2015-11-01

Direct binary search (DBS) produces the images of the best quality among half-toning algorithms. The reason is that it minimizes the total squared perceived error instead of using heuristic approaches. The search for the optimal solution involves two operations: (1) toggle and (2) swap. Both operations try to find the binary states for each pixel to minimize the total squared perceived error. This error energy minimization leads to a conjecture that the absolute value of the filtered error after DBS converges is bounded by half of the peak value of the autocorrelation filter. However, a proof of the bound's existence has not yet been found. In this paper, we present a proof that shows the bound existed as conjectured under the condition that at least one swap occurs after toggle converges. The theoretical analysis also indicates that a swap with a pixel further away from the center of the autocorrelation filter results in a tighter bound. Therefore, we propose a new DBS algorithm which considers toggle and swap separately, and the swap operations are considered in the order from the edge to the center of the filter. Experimental results show that the new algorithm is more efficient than the previous algorithm and can produce half-toned images of the same quality as the previous algorithm.

Upper bounds on sequential decoding performance parameters

NASA Technical Reports Server (NTRS)

Jelinek, F.

1974-01-01

This paper presents the best obtainable random coding and expurgated upper bounds on the probabilities of undetectable error, of t-order failure (advance to depth t into an incorrect subset), and of likelihood rise in the incorrect subset, applicable to sequential decoding when the metric bias G is arbitrary. Upper bounds on the Pareto exponent are also presented. The G-values optimizing each of the parameters of interest are determined, and are shown to lie in intervals that in general have nonzero widths. The G-optimal expurgated bound on undetectable error is shown to agree with that for maximum likelihood decoding of convolutional codes, and that on failure agrees with the block code expurgated bound. Included are curves evaluating the bounds for interesting choices of G and SNR for a binary-input quantized-output Gaussian additive noise channel.

Local synchronization of chaotic neural networks with sampled-data and saturating actuators.

PubMed

Wu, Zheng-Guang; Shi, Peng; Su, Hongye; Chu, Jian

2014-12-01

This paper investigates the problem of local synchronization of chaotic neural networks with sampled-data and actuator saturation. A new time-dependent Lyapunov functional is proposed for the synchronization error systems. The advantage of the constructed Lyapunov functional lies in the fact that it is positive definite at sampling times but not necessarily between sampling times, and makes full use of the available information about the actual sampling pattern. A local stability condition of the synchronization error systems is derived, based on which a sampled-data controller with respect to the actuator saturation is designed to ensure that the master neural networks and slave neural networks are locally asymptotically synchronous. Two optimization problems are provided to compute the desired sampled-data controller with the aim of enlarging the set of admissible initial conditions or the admissible sampling upper bound ensuring the local synchronization of the considered chaotic neural networks. A numerical example is used to demonstrate the effectiveness of the proposed design technique.

Formation tracker design of multiple mobile robots with wheel perturbations: adaptive output-feedback approach

NASA Astrophysics Data System (ADS)

Yoo, Sung Jin

2016-11-01

This paper presents a theoretical design approach for output-feedback formation tracking of multiple mobile robots under wheel perturbations. It is assumed that these perturbations are unknown and the linear and angular velocities of the robots are unmeasurable. First, adaptive state observers for estimating unmeasurable velocities of the robots are developed under the robots' kinematics and dynamics including wheel perturbation effects. Then, we derive a virtual-structure-based formation tracker scheme according to the observer dynamic surface design procedure. The main difficulty of the output-feedback control design is to manage the coupling problems between unmeasurable velocities and unknown wheel perturbation effects. These problems are avoided by using the adaptive technique and the function approximation property based on fuzzy logic systems. From the Lyapunov stability analysis, it is shown that point tracking errors of each robot and synchronisation errors for the desired formation converge to an adjustable neighbourhood of the origin, while all signals in the controlled closed-loop system are semiglobally uniformly ultimately bounded.

Error and Complexity Analysis for a Collocation-Grid-Projection Plus Precorrected-FFT Algorithm for Solving Potential Integral Equations with LaPlace or Helmholtz Kernels

NASA Technical Reports Server (NTRS)

Phillips, J. R.

1996-01-01

In this paper we derive error bounds for a collocation-grid-projection scheme tuned for use in multilevel methods for solving boundary-element discretizations of potential integral equations. The grid-projection scheme is then combined with a precorrected FFT style multilevel method for solving potential integral equations with 1/r and e(sup ikr)/r kernels. A complexity analysis of this combined method is given to show that for homogeneous problems, the method is order n natural log n nearly independent of the kernel. In addition, it is shown analytically and experimentally that for an inhomogeneity generated by a very finely discretized surface, the combined method slows to order n(sup 4/3). Finally, examples are given to show that the collocation-based grid-projection plus precorrected-FFT scheme is competitive with fast-multipole algorithms when considering realistic problems and 1/r kernels, but can be used over a range of spatial frequencies with only a small performance penalty.

Semiclassical Dynamicswith Exponentially Small Error Estimates

NASA Astrophysics Data System (ADS)

Hagedorn, George A.; Joye, Alain

We construct approximate solutions to the time-dependent Schrödingerequation for small values of ħ. If V satisfies appropriate analyticity and growth hypotheses and , these solutions agree with exact solutions up to errors whose norms are bounded by for some C and γ>0. Under more restrictive hypotheses, we prove that for sufficiently small T', implies the norms of the errors are bounded by for some C', γ'>0, and σ > 0.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Preston, Leiph

Although using standard Taylor series coefficients for finite-difference operators is optimal in the sense that in the limit of infinitesimal space and time discretization, the solution approaches the correct analytic solution to the acousto-dynamic system of differential equations, other finite-difference operators may provide optimal computational run time given certain error bounds or source bandwidth constraints. This report describes the results of investigation of alternative optimal finite-difference coefficients based on several optimization/accuracy scenarios and provides recommendations for minimizing run time while retaining error within given error bounds.

Magnitude error bounds for sampled-data frequency response obtained from the truncation of an infinite series, and compensator improvement program

NASA Technical Reports Server (NTRS)

Mitchell, J. R.

1972-01-01

The frequency response method of analyzing control system performance is discussed, and the difficulty of obtaining the sampled frequency response of the continuous system is considered. An upper bound magnitude error equation is obtained which yields reasonable estimates of the actual error. Finalization of the compensator improvement program is also reported, and the program was used to design compensators for Saturn 5/S1-C dry workshop and Saturn 5/S1-C Skylab.

Joint Transmitter and Receiver Power Allocation under Minimax MSE Criterion with Perfect and Imperfect CSI for MC-CDMA Transmissions

NASA Astrophysics Data System (ADS)

Kotchasarn, Chirawat; Saengudomlert, Poompat

We investigate the problem of joint transmitter and receiver power allocation with the minimax mean square error (MSE) criterion for uplink transmissions in a multi-carrier code division multiple access (MC-CDMA) system. The objective of power allocation is to minimize the maximum MSE among all users each of which has limited transmit power. This problem is a nonlinear optimization problem. Using the Lagrange multiplier method, we derive the Karush-Kuhn-Tucker (KKT) conditions which are necessary for a power allocation to be optimal. Numerical results indicate that, compared to the minimum total MSE criterion, the minimax MSE criterion yields a higher total MSE but provides a fairer treatment across the users. The advantages of the minimax MSE criterion are more evident when we consider the bit error rate (BER) estimates. Numerical results show that the minimax MSE criterion yields a lower maximum BER and a lower average BER. We also observe that, with the minimax MSE criterion, some users do not transmit at full power. For comparison, with the minimum total MSE criterion, all users transmit at full power. In addition, we investigate robust joint transmitter and receiver power allocation where the channel state information (CSI) is not perfect. The CSI error is assumed to be unknown but bounded by a deterministic value. This problem is formulated as a semidefinite programming (SDP) problem with bilinear matrix inequality (BMI) constraints. Numerical results show that, with imperfect CSI, the minimax MSE criterion also outperforms the minimum total MSE criterion in terms of the maximum and average BERs.

Viète's Formula and an Error Bound without Taylor's Theorem

ERIC Educational Resources Information Center

Boucher, Chris

2018-01-01

This note presents a derivation of Viète's classic product approximation of pi that relies on only the Pythagorean Theorem. We also give a simple error bound for the approximation that, while not optimal, still reveals the exponential convergence of the approximation and whose derivation does not require Taylor's Theorem.

Correcting Coefficient Alpha for Correlated Errors: Is [alpha][K]a Lower Bound to Reliability?

ERIC Educational Resources Information Center

Rae, Gordon

2006-01-01

When errors of measurement are positively correlated, coefficient alpha may overestimate the "true" reliability of a composite. To reduce this inflation bias, Komaroff (1997) has proposed an adjusted alpha coefficient, ak. This article shows that ak is only guaranteed to be a lower bound to reliability if the latter does not include correlated…

An Inverse Neural Controller Based on the Applicability Domain of RBF Network Models

PubMed Central

Alexandridis, Alex; Stogiannos, Marios; Papaioannou, Nikolaos; Zois, Elias; Sarimveis, Haralambos

2018-01-01

This paper presents a novel methodology of generic nature for controlling nonlinear systems, using inverse radial basis function neural network models, which may combine diverse data originating from various sources. The algorithm starts by applying the particle swarm optimization-based non-symmetric variant of the fuzzy means (PSO-NSFM) algorithm so that an approximation of the inverse system dynamics is obtained. PSO-NSFM offers models of high accuracy combined with small network structures. Next, the applicability domain concept is suitably tailored and embedded into the proposed control structure in order to ensure that extrapolation is avoided in the controller predictions. Finally, an error correction term, estimating the error produced by the unmodeled dynamics and/or unmeasured external disturbances, is included to the control scheme to increase robustness. The resulting controller guarantees bounded input-bounded state (BIBS) stability for the closed loop system when the open loop system is BIBS stable. The proposed methodology is evaluated on two different control problems, namely, the control of an experimental armature-controlled direct current (DC) motor and the stabilization of a highly nonlinear simulated inverted pendulum. For each one of these problems, appropriate case studies are tested, in which a conventional neural controller employing inverse models and a PID controller are also applied. The results reveal the ability of the proposed control scheme to handle and manipulate diverse data through a data fusion approach and illustrate the superiority of the method in terms of faster and less oscillatory responses. PMID:29361781

Improving Bayesian credibility intervals for classifier error rates using maximum entropy empirical priors.

PubMed

Gustafsson, Mats G; Wallman, Mikael; Wickenberg Bolin, Ulrika; Göransson, Hanna; Fryknäs, M; Andersson, Claes R; Isaksson, Anders

2010-06-01

Successful use of classifiers that learn to make decisions from a set of patient examples require robust methods for performance estimation. Recently many promising approaches for determination of an upper bound for the error rate of a single classifier have been reported but the Bayesian credibility interval (CI) obtained from a conventional holdout test still delivers one of the tightest bounds. The conventional Bayesian CI becomes unacceptably large in real world applications where the test set sizes are less than a few hundred. The source of this problem is that fact that the CI is determined exclusively by the result on the test examples. In other words, there is no information at all provided by the uniform prior density distribution employed which reflects complete lack of prior knowledge about the unknown error rate. Therefore, the aim of the study reported here was to study a maximum entropy (ME) based approach to improved prior knowledge and Bayesian CIs, demonstrating its relevance for biomedical research and clinical practice. It is demonstrated how a refined non-uniform prior density distribution can be obtained by means of the ME principle using empirical results from a few designs and tests using non-overlapping sets of examples. Experimental results show that ME based priors improve the CIs when employed to four quite different simulated and two real world data sets. An empirically derived ME prior seems promising for improving the Bayesian CI for the unknown error rate of a designed classifier. Copyright 2010 Elsevier B.V. All rights reserved.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baker, Kyri; Dall'Anese, Emiliano; Summers, Tyler

This paper outlines a data-driven, distributionally robust approach to solve chance-constrained AC optimal power flow problems in distribution networks. Uncertain forecasts for loads and power generated by photovoltaic (PV) systems are considered, with the goal of minimizing PV curtailment while meeting power flow and voltage regulation constraints. A data- driven approach is utilized to develop a distributionally robust conservative convex approximation of the chance-constraints; particularly, the mean and covariance matrix of the forecast errors are updated online, and leveraged to enforce voltage regulation with predetermined probability via Chebyshev-based bounds. By combining an accurate linear approximation of the AC power flowmore » equations with the distributionally robust chance constraint reformulation, the resulting optimization problem becomes convex and computationally tractable.« less

Analysis of basic clustering algorithms for numerical estimation of statistical averages in biomolecules.

PubMed

Anandakrishnan, Ramu; Onufriev, Alexey

2008-03-01

In statistical mechanics, the equilibrium properties of a physical system of particles can be calculated as the statistical average over accessible microstates of the system. In general, these calculations are computationally intractable since they involve summations over an exponentially large number of microstates. Clustering algorithms are one of the methods used to numerically approximate these sums. The most basic clustering algorithms first sub-divide the system into a set of smaller subsets (clusters). Then, interactions between particles within each cluster are treated exactly, while all interactions between different clusters are ignored. These smaller clusters have far fewer microstates, making the summation over these microstates, tractable. These algorithms have been previously used for biomolecular computations, but remain relatively unexplored in this context. Presented here, is a theoretical analysis of the error and computational complexity for the two most basic clustering algorithms that were previously applied in the context of biomolecular electrostatics. We derive a tight, computationally inexpensive, error bound for the equilibrium state of a particle computed via these clustering algorithms. For some practical applications, it is the root mean square error, which can be significantly lower than the error bound, that may be more important. We how that there is a strong empirical relationship between error bound and root mean square error, suggesting that the error bound could be used as a computationally inexpensive metric for predicting the accuracy of clustering algorithms for practical applications. An example of error analysis for such an application-computation of average charge of ionizable amino-acids in proteins-is given, demonstrating that the clustering algorithm can be accurate enough for practical purposes.

Multipole Algorithms for Molecular Dynamics Simulation on High Performance Computers.

NASA Astrophysics Data System (ADS)

Elliott, William Dewey

1995-01-01

A fundamental problem in modeling large molecular systems with molecular dynamics (MD) simulations is the underlying N-body problem of computing the interactions between all pairs of N atoms. The simplest algorithm to compute pair-wise atomic interactions scales in runtime {cal O}(N^2), making it impractical for interesting biomolecular systems, which can contain millions of atoms. Recently, several algorithms have become available that solve the N-body problem by computing the effects of all pair-wise interactions while scaling in runtime less than {cal O}(N^2). One algorithm, which scales {cal O}(N) for a uniform distribution of particles, is called the Greengard-Rokhlin Fast Multipole Algorithm (FMA). This work describes an FMA-like algorithm called the Molecular Dynamics Multipole Algorithm (MDMA). The algorithm contains several features that are new to N-body algorithms. MDMA uses new, efficient series expansion equations to compute general 1/r^{n } potentials to arbitrary accuracy. In particular, the 1/r Coulomb potential and the 1/r^6 portion of the Lennard-Jones potential are implemented. The new equations are based on multivariate Taylor series expansions. In addition, MDMA uses a cell-to-cell interaction region of cells that is closely tied to worst case error bounds. The worst case error bounds for MDMA are derived in this work also. These bounds apply to other multipole algorithms as well. Several implementation enhancements are described which apply to MDMA as well as other N-body algorithms such as FMA and tree codes. The mathematics of the cell -to-cell interactions are converted to the Fourier domain for reduced operation count and faster computation. A relative indexing scheme was devised to locate cells in the interaction region which allows efficient pre-computation of redundant information and prestorage of much of the cell-to-cell interaction. Also, MDMA was integrated into the MD program SIgMA to demonstrate the performance of the program over several simulation timesteps. One MD application described here highlights the utility of including long range contributions to Lennard-Jones potential in constant pressure simulations. Another application shows the time dependence of long range forces in a multiple time step MD simulation.

Feedback attitude sliding mode regulation control of spacecraft using arm motion

NASA Astrophysics Data System (ADS)

Shi, Ye; Liang, Bin; Xu, Dong; Wang, Xueqian; Xu, Wenfu

2013-09-01

The problem of spacecraft attitude regulation based on the reaction of arm motion has attracted extensive attentions from both engineering and academic fields. Most of the solutions of the manipulator’s motion tracking problem just achieve asymptotical stabilization performance, so that these controllers cannot realize precise attitude regulation because of the existence of non-holonomic constraints. Thus, sliding mode control algorithms are adopted to stabilize the tracking error with zero transient process. Due to the switching effects of the variable structure controller, once the tracking error reaches the designed hyper-plane, it will be restricted to this plane permanently even with the existence of external disturbances. Thus, precise attitude regulation can be achieved. Furthermore, taking the non-zero initial tracking errors and chattering phenomenon into consideration, saturation functions are used to replace sign functions to smooth the control torques. The relations between the upper bounds of tracking errors and the controller parameters are derived to reveal physical characteristic of the controller. Mathematical models of free-floating space manipulator are established and simulations are conducted in the end. The results show that the spacecraft’s attitude can be regulated to the position as desired by using the proposed algorithm, the steady state error is 0.000 2 rad. In addition, the joint tracking trajectory is smooth, the joint tracking errors converges to zero quickly with a satisfactory continuous joint control input. The proposed research provides a feasible solution for spacecraft attitude regulation by using arm motion, and improves the precision of the spacecraft attitude regulation.

Topics in quantum cryptography, quantum error correction, and channel simulation

NASA Astrophysics Data System (ADS)

Luo, Zhicheng

In this thesis, we mainly investigate four different topics: efficiently implementable codes for quantum key expansion [51], quantum error-correcting codes based on privacy amplification [48], private classical capacity of quantum channels [44], and classical channel simulation with quantum side information [49, 50]. For the first topic, we propose an efficiently implementable quantum key expansion protocol, capable of increasing the size of a pre-shared secret key by a constant factor. Previously, the Shor-Preskill proof [64] of the security of the Bennett-Brassard 1984 (BB84) [6] quantum key distribution protocol relied on the theoretical existence of good classical error-correcting codes with the "dual-containing" property. But the explicit and efficiently decodable construction of such codes is unknown. We show that we can lift the dual-containing constraint by employing the non-dual-containing codes with excellent performance and efficient decoding algorithms. For the second topic, we propose a construction of Calderbank-Shor-Steane (CSS) [19, 68] quantum error-correcting codes, which are originally based on pairs of mutually dual-containing classical codes, by combining a classical code with a two-universal hash function. We show, using the results of Renner and Koenig [57], that the communication rates of such codes approach the hashing bound on tensor powers of Pauli channels in the limit of large block-length. For the third topic, we prove a regularized formula for the secret key assisted capacity region of a quantum channel for transmitting private classical information. This result parallels the work of Devetak on entanglement assisted quantum communication capacity. This formula provides a new family protocol, the private father protocol, under the resource inequality framework that includes the private classical communication without the assisted secret keys as a child protocol. For the fourth topic, we study and solve the problem of classical channel simulation with quantum side information at the receiver. Our main theorem has two important corollaries: rate-distortion theory with quantum side information and common randomness distillation. Simple proofs of achievability of classical multi-terminal source coding problems can be made via a unified approach using the channel simulation theorem as building blocks. The fully quantum generalization of the problem is also conjectured with outer and inner bounds on the achievable rate pairs.

Quantifying the impact of material-model error on macroscale quantities-of-interest using multiscale a posteriori error-estimation techniques

DOE PAGES

Brown, Judith A.; Bishop, Joseph E.

2016-07-20

An a posteriori error-estimation framework is introduced to quantify and reduce modeling errors resulting from approximating complex mesoscale material behavior with a simpler macroscale model. Such errors may be prevalent when modeling welds and additively manufactured structures, where spatial variations and material textures may be present in the microstructure. We consider a case where a <100> fiber texture develops in the longitudinal scanning direction of a weld. Transversely isotropic elastic properties are obtained through homogenization of a microstructural model with this texture and are considered the reference weld properties within the error-estimation framework. Conversely, isotropic elastic properties are considered approximatemore » weld properties since they contain no representation of texture. Errors introduced by using isotropic material properties to represent a weld are assessed through a quantified error bound in the elastic regime. Lastly, an adaptive error reduction scheme is used to determine the optimal spatial variation of the isotropic weld properties to reduce the error bound.« less

Mismeasurement and the resonance of strong confounders: uncorrelated errors.

PubMed

Marshall, J R; Hastrup, J L

1996-05-15

Greenland first documented (Am J Epidemiol 1980; 112:564-9) that error in the measurement of a confounder could resonate--that it could bias estimates of other study variables, and that the bias could persist even with statistical adjustment for the confounder as measured. An important question is raised by this finding: can such bias be more than trivial within the bounds of realistic data configurations? The authors examine several situations involving dichotomous and continuous data in which a confounder and a null variable are measured with error, and they assess the extent of resultant bias in estimates of the effect of the null variable. They show that, with continuous variables, measurement error amounting to 40% of observed variance in the confounder could cause the observed impact of the null study variable to appear to alter risk by as much as 30%. Similarly, they show, with dichotomous independent variables, that 15% measurement error in the form of misclassification could lead the null study variable to appear to alter risk by as much as 50%. Such bias would result only from strong confounding. Measurement error would obscure the evidence that strong confounding is a likely problem. These results support the need for every epidemiologic inquiry to include evaluations of measurement error in each variable considered.

Divergences and estimating tight bounds on Bayes error with applications to multivariate Gaussian copula and latent Gaussian copula

NASA Astrophysics Data System (ADS)

Thelen, Brian J.; Xique, Ismael J.; Burns, Joseph W.; Goley, G. Steven; Nolan, Adam R.; Benson, Jonathan W.

2017-04-01

In Bayesian decision theory, there has been a great amount of research into theoretical frameworks and information- theoretic quantities that can be used to provide lower and upper bounds for the Bayes error. These include well-known bounds such as Chernoff, Battacharrya, and J-divergence. Part of the challenge of utilizing these various metrics in practice is (i) whether they are "loose" or "tight" bounds, (ii) how they might be estimated via either parametric or non-parametric methods, and (iii) how accurate the estimates are for limited amounts of data. In general what is desired is a methodology for generating relatively tight lower and upper bounds, and then an approach to estimate these bounds efficiently from data. In this paper, we explore the so-called triangle divergence which has been around for a while, but was recently made more prominent in some recent research on non-parametric estimation of information metrics. Part of this work is motivated by applications for quantifying fundamental information content in SAR/LIDAR data, and to help in this, we have developed a flexible multivariate modeling framework based on multivariate Gaussian copula models which can be combined with the triangle divergence framework to quantify this information, and provide approximate bounds on Bayes error. In this paper we present an overview of the bounds, including those based on triangle divergence and verify that under a number of multivariate models, the upper and lower bounds derived from triangle divergence are significantly tighter than the other common bounds, and often times, dramatically so. We also propose some simple but effective means for computing the triangle divergence using Monte Carlo methods, and then discuss estimation of the triangle divergence from empirical data based on Gaussian Copula models.

Adaptive Neural Output Feedback Control for Nonstrict-Feedback Stochastic Nonlinear Systems With Unknown Backlash-Like Hysteresis and Unknown Control Directions.

PubMed

Yu, Zhaoxu; Li, Shugang; Yu, Zhaosheng; Li, Fangfei

2018-04-01

This paper investigates the problem of output feedback adaptive stabilization for a class of nonstrict-feedback stochastic nonlinear systems with both unknown backlashlike hysteresis and unknown control directions. A new linear state transformation is applied to the original system, and then, control design for the new system becomes feasible. By combining the neural network's (NN's) parameterization, variable separation technique, and Nussbaum gain function method, an input-driven observer-based adaptive NN control scheme, which involves only one parameter to be updated, is developed for such systems. All closed-loop signals are bounded in probability and the error signals remain semiglobally bounded in the fourth moment (or mean square). Finally, the effectiveness and the applicability of the proposed control design are verified by two simulation examples.

Assessment of the relative merits of a few methods to detect evolutionary trends.

PubMed

Laurin, Michel

2010-12-01

Some of the most basic questions about the history of life concern evolutionary trends. These include determining whether or not metazoans have become more complex over time, whether or not body size tends to increase over time (the Cope-Depéret rule), or whether or not brain size has increased over time in various taxa, such as mammals and birds. Despite the proliferation of studies on such topics, assessment of the reliability of results in this field is hampered by the variability of techniques used and the lack of statistical validation of these methods. To solve this problem, simulations are performed using a variety of evolutionary models (gradual Brownian motion, speciational Brownian motion, and Ornstein-Uhlenbeck), with or without a drift of variable amplitude, with variable variance of tips, and with bounds placed close or far from the starting values and final means of simulated characters. These are used to assess the relative merits (power, Type I error rate, bias, and mean absolute value of error on slope estimate) of several statistical methods that have recently been used to assess the presence of evolutionary trends in comparative data. Results show widely divergent performance of the methods. The simple, nonphylogenetic regression (SR) and variance partitioning using phylogenetic eigenvector regression (PVR) with a broken stick selection procedure have greatly inflated Type I error rate (0.123-0.180 at a 0.05 threshold), which invalidates their use in this context. However, they have the greatest power. Most variants of Felsenstein's independent contrasts (FIC; five of which are presented) have adequate Type I error rate, although two have a slightly inflated Type I error rate with at least one of the two reference trees (0.064-0.090 error rate at a 0.05 threshold). The power of all contrast-based methods is always much lower than that of SR and PVR, except under Brownian motion with a strong trend and distant bounds. Mean absolute value of error on slope of all FIC methods is slightly higher than that of phylogenetic generalized least squares (PGLS), SR, and PVR. PGLS performs well, with low Type I error rate, low error on regression coefficient, and power comparable with some FIC methods. Four variants of skewness analysis are examined, and a new method to assess significance of results is presented. However, all have consistently low power, except in rare combinations of trees, trend strength, and distance between final means and bounds. Globally, the results clearly show that FIC-based methods and PGLS are globally better than nonphylogenetic methods and variance partitioning with PVR. FIC methods and PGLS are sensitive to the model of evolution (and, hence, to branch length errors). Our results suggest that regressing raw character contrasts against raw geological age contrasts yields a good combination of power and Type I error rate. New software to facilitate batch analysis is presented.

Adaptive Resampling Particle Filters for GPS Carrier-Phase Navigation and Collision Avoidance System

NASA Astrophysics Data System (ADS)

Hwang, Soon Sik

This dissertation addresses three problems: 1) adaptive resampling technique (ART) for Particle Filters, 2) precise relative positioning using Global Positioning System (GPS) Carrier-Phase (CP) measurements applied to nonlinear integer resolution problem for GPS CP navigation using Particle Filters, and 3) collision detection system based on GPS CP broadcasts. First, Monte Carlo filters, called Particle Filters (PF), are widely used where the system is non-linear and non-Gaussian. In real-time applications, their estimation accuracies and efficiencies are significantly affected by the number of particles and the scheduling of relocating weights and samples, the so-called resampling step. In this dissertation, the appropriate number of particles is estimated adaptively such that the error of the sample mean and variance stay in bounds. These bounds are given by the confidence interval of a normal probability distribution for a multi-variate state. Two required number of samples maintaining the mean and variance error within the bounds are derived. The time of resampling is determined when the required sample number for the variance error crosses the required sample number for the mean error. Second, the PF using GPS CP measurements with adaptive resampling is applied to precise relative navigation between two GPS antennas. In order to make use of CP measurements for navigation, the unknown number of cycles between GPS antennas, the so called integer ambiguity, should be resolved. The PF is applied to this integer ambiguity resolution problem where the relative navigation states estimation involves nonlinear observations and nonlinear dynamics equation. Using the PF, the probability density function of the states is estimated by sampling from the position and velocity space and the integer ambiguities are resolved without using the usual hypothesis tests to search for the integer ambiguity. The ART manages the number of position samples and the frequency of the resampling step for real-time kinematics GPS navigation. The experimental results demonstrate the performance of the ART and the insensitivity of the proposed approach to GPS CP cycle-slips. Third, the GPS has great potential for the development of new collision avoidance systems and is being considered for the next generation Traffic alert and Collision Avoidance System (TCAS). The current TCAS equipment, is capable of broadcasting GPS code information to nearby airplanes, and also, the collision avoidance system using the navigation information based on GPS code has been studied by researchers. In this dissertation, the aircraft collision detection system using GPS CP information is addressed. The PF with position samples is employed for the CP based relative position estimation problem and the same algorithm can be used to determine the vehicle attitude if multiple GPS antennas are used. For a reliable and enhanced collision avoidance system, three dimensional trajectories are projected using the estimates of the relative position, velocity, and the attitude. It is shown that the performance of GPS CP based collision detecting algorithm meets the accuracy requirements for a precise approach of flight for auto landing with significantly less unnecessary collision false alarms and no miss alarms.

Distribution-Preserving Stratified Sampling for Learning Problems.

PubMed

Cervellera, Cristiano; Maccio, Danilo

2017-06-09

The need for extracting a small sample from a large amount of real data, possibly streaming, arises routinely in learning problems, e.g., for storage, to cope with computational limitations, obtain good training/test/validation sets, and select minibatches for stochastic gradient neural network training. Unless we have reasons to select the samples in an active way dictated by the specific task and/or model at hand, it is important that the distribution of the selected points is as similar as possible to the original data. This is obvious for unsupervised learning problems, where the goal is to gain insights on the distribution of the data, but it is also relevant for supervised problems, where the theory explains how the training set distribution influences the generalization error. In this paper, we analyze the technique of stratified sampling from the point of view of distances between probabilities. This allows us to introduce an algorithm, based on recursive binary partition of the input space, aimed at obtaining samples that are distributed as much as possible as the original data. A theoretical analysis is proposed, proving the (greedy) optimality of the procedure together with explicit error bounds. An adaptive version of the algorithm is also introduced to cope with streaming data. Simulation tests on various data sets and different learning tasks are also provided.

The presence of English and Spanish dyslexia in the Web

NASA Astrophysics Data System (ADS)

Rello, Luz; Baeza-Yates, Ricardo

2012-09-01

In this study we present a lower bound of the prevalence of dyslexia in the Web for English and Spanish. On the basis of analysis of corpora written by dyslexic people, we propose a classification of the different kinds of dyslexic errors. A representative data set of dyslexic words is used to calculate this lower bound in web pages containing English and Spanish dyslexic errors. We also present an analysis of dyslexic errors in major Internet domains, social media sites, and throughout English- and Spanish-speaking countries. To show the independence of our estimations from the presence of other kinds of errors, we compare them with the overall lexical quality of the Web and with the error rate of noncorrected corpora. The presence of dyslexic errors in the Web motivates work in web accessibility for dyslexic users.

Decoy-state quantum key distribution with more than three types of photon intensity pulses

NASA Astrophysics Data System (ADS)

Chau, H. F.

2018-04-01

The decoy-state method closes source security loopholes in quantum key distribution (QKD) using a laser source. In this method, accurate estimates of the detection rates of vacuum and single-photon events plus the error rate of single-photon events are needed to give a good enough lower bound of the secret key rate. Nonetheless, the current estimation method for these detection and error rates, which uses three types of photon intensities, is accurate up to about 1 % relative error. Here I report an experimentally feasible way that greatly improves these estimates and hence increases the one-way key rate of the BB84 QKD protocol with unbiased bases selection by at least 20% on average in realistic settings. The major tricks are the use of more than three types of photon intensities plus the fact that estimating bounds of the above detection and error rates is numerically stable, although these bounds are related to the inversion of a high condition number matrix.

Tracking control of a closed-chain five-bar robot with two degrees of freedom by integration of an approximation-based approach and mechanical design.

PubMed

Cheng, Long; Hou, Zeng-Guang; Tan, Min; Zhang, W J

2012-10-01

The trajectory tracking problem of a closed-chain five-bar robot is studied in this paper. Based on an error transformation function and the backstepping technique, an approximation-based tracking algorithm is proposed, which can guarantee the control performance of the robotic system in both the stable and transient phases. In particular, the overshoot, settling time, and final tracking error of the robotic system can be all adjusted by properly setting the parameters in the error transformation function. The radial basis function neural network (RBFNN) is used to compensate the complicated nonlinear terms in the closed-loop dynamics of the robotic system. The approximation error of the RBFNN is only required to be bounded, which simplifies the initial "trail-and-error" configuration of the neural network. Illustrative examples are given to verify the theoretical analysis and illustrate the effectiveness of the proposed algorithm. Finally, it is also shown that the proposed approximation-based controller can be simplified by a smart mechanical design of the closed-chain robot, which demonstrates the promise of the integrated design and control philosophy.

Numerical and analytical bounds on threshold error rates for hypergraph-product codes

NASA Astrophysics Data System (ADS)

Kovalev, Alexey A.; Prabhakar, Sanjay; Dumer, Ilya; Pryadko, Leonid P.

2018-06-01

We study analytically and numerically decoding properties of finite-rate hypergraph-product quantum low density parity-check codes obtained from random (3,4)-regular Gallager codes, with a simple model of independent X and Z errors. Several nontrivial lower and upper bounds for the decodable region are constructed analytically by analyzing the properties of the homological difference, equal minus the logarithm of the maximum-likelihood decoding probability for a given syndrome. Numerical results include an upper bound for the decodable region from specific heat calculations in associated Ising models and a minimum-weight decoding threshold of approximately 7 % .

Consistent Tolerance Bounds for Statistical Distributions

NASA Technical Reports Server (NTRS)

Mezzacappa, M. A.

1983-01-01

Assumption that sample comes from population with particular distribution is made with confidence C if data lie between certain bounds. These "confidence bounds" depend on C and assumption about distribution of sampling errors around regression line. Graphical test criteria using tolerance bounds are applied in industry where statistical analysis influences product development and use. Applied to evaluate equipment life.

Robustness of linear quadratic state feedback designs in the presence of system uncertainty. [application to Augmentor Wing Jet STOL Research Aircraft flare control autopilot design

NASA Technical Reports Server (NTRS)

Patel, R. V.; Toda, M.; Sridhar, B.

1977-01-01

The paper deals with the problem of expressing the robustness (stability) property of a linear quadratic state feedback (LQSF) design quantitatively in terms of bounds on the perturbations (modeling errors or parameter variations) in the system matrices so that the closed-loop system remains stable. Nonlinear time-varying and linear time-invariant perturbations are considered. The only computation required in obtaining a measure of the robustness of an LQSF design is to determine the eigenvalues of two symmetric matrices determined when solving the algebraic Riccati equation corresponding to the LQSF design problem. Results are applied to a complex dynamic system consisting of the flare control of a STOL aircraft. The design of the flare control is formulated as an LQSF tracking problem.

Uncertainties in extracted parameters of a Gaussian emission line profile with continuum background.

PubMed

Minin, Serge; Kamalabadi, Farzad

2009-12-20

We derive analytical equations for uncertainties in parameters extracted by nonlinear least-squares fitting of a Gaussian emission function with an unknown continuum background component in the presence of additive white Gaussian noise. The derivation is based on the inversion of the full curvature matrix (equivalent to Fisher information matrix) of the least-squares error, chi(2), in a four-variable fitting parameter space. The derived uncertainty formulas (equivalent to Cramer-Rao error bounds) are found to be in good agreement with the numerically computed uncertainties from a large ensemble of simulated measurements. The derived formulas can be used for estimating minimum achievable errors for a given signal-to-noise ratio and for investigating some aspects of measurement setup trade-offs and optimization. While the intended application is Fabry-Perot spectroscopy for wind and temperature measurements in the upper atmosphere, the derivation is generic and applicable to other spectroscopy problems with a Gaussian line shape.

An approach to get thermodynamic properties from speed of sound

NASA Astrophysics Data System (ADS)

Núñez, M. A.; Medina, L. A.

2017-01-01

An approach for estimating thermodynamic properties of gases from the speed of sound u, is proposed. The square u2, the compression factor Z and the molar heat capacity at constant volume C V are connected by two coupled nonlinear partial differential equations. Previous approaches to solving this system differ in the conditions used on the range of temperature values [Tmin,Tmax]. In this work we propose the use of Dirichlet boundary conditions at Tmin, Tmax. The virial series of the compression factor Z = 1+Bρ+Cρ2+… and other properties leads the problem to the solution of a recursive set of linear ordinary differential equations for the B, C. Analytic solutions of the B equation for Argon are used to study the stability of our approach and previous ones under perturbation errors of the input data. The results show that the approach yields B with a relative error bounded basically by that of the boundary values and the error of other approaches can be some orders of magnitude lager.

Observer-based distributed adaptive fault-tolerant containment control of multi-agent systems with general linear dynamics.

PubMed

Ye, Dan; Chen, Mengmeng; Li, Kui

2017-11-01

In this paper, we consider the distributed containment control problem of multi-agent systems with actuator bias faults based on observer method. The objective is to drive the followers into the convex hull spanned by the dynamic leaders, where the input is unknown but bounded. By constructing an observer to estimate the states and bias faults, an effective distributed adaptive fault-tolerant controller is developed. Different from the traditional method, an auxiliary controller gain is designed to deal with the unknown inputs and bias faults together. Moreover, the coupling gain can be adjusted online through the adaptive mechanism without using the global information. Furthermore, the proposed control protocol can guarantee that all the signals of the closed-loop systems are bounded and all the followers converge to the convex hull with bounded residual errors formed by the dynamic leaders. Finally, a decoupled linearized longitudinal motion model of the F-18 aircraft is used to demonstrate the effectiveness. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Branch and bound algorithm for accurate estimation of analytical isotropic bidirectional reflectance distribution function models.

PubMed

Yu, Chanki; Lee, Sang Wook

2016-05-20

We present a reliable and accurate global optimization framework for estimating parameters of isotropic analytical bidirectional reflectance distribution function (BRDF) models. This approach is based on a branch and bound strategy with linear programming and interval analysis. Conventional local optimization is often very inefficient for BRDF estimation since its fitting quality is highly dependent on initial guesses due to the nonlinearity of analytical BRDF models. The algorithm presented in this paper employs L₁-norm error minimization to estimate BRDF parameters in a globally optimal way and interval arithmetic to derive our feasibility problem and lower bounding function. Our method is developed for the Cook-Torrance model but with several normal distribution functions such as the Beckmann, Berry, and GGX functions. Experiments have been carried out to validate the presented method using 100 isotropic materials from the MERL BRDF database, and our experimental results demonstrate that the L₁-norm minimization provides a more accurate and reliable solution than the L₂-norm minimization.

Robustness of linear quadratic state feedback designs in the presence of system uncertainty. [applied to STOL autopilot design

NASA Technical Reports Server (NTRS)

Patel, R. V.; Toda, M.; Sridhar, B.

1977-01-01

In connection with difficulties concerning an accurate mathematical representation of a linear quadratic state feedback (LQSF) system, it is often necessary to investigate the robustness (stability) of an LQSF design in the presence of system uncertainty and obtain some quantitative measure of the perturbations which such a design can tolerate. A study is conducted concerning the problem of expressing the robustness property of an LQSF design quantitatively in terms of bounds on the perturbations (modeling errors or parameter variations) in the system matrices. Bounds are obtained for the general case of nonlinear, time-varying perturbations. It is pointed out that most of the presented results are readily applicable to practical situations for which a designer has estimates of the bounds on the system parameter perturbations. Relations are provided which help the designer to select appropriate weighting matrices in the quadratic performance index to attain a robust design. The developed results are employed in the design of an autopilot logic for the flare maneuver of the Augmentor Wing Jet STOL Research Aircraft.

Discriminating quantum-optical beam-splitter channels with number-diagonal signal states: Applications to quantum reading and target detection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nair, Ranjith

2011-09-15

We consider the problem of distinguishing, with minimum probability of error, two optical beam-splitter channels with unequal complex-valued reflectivities using general quantum probe states entangled over M signal and M' idler mode pairs of which the signal modes are bounced off the beam splitter while the idler modes are retained losslessly. We obtain a lower bound on the output state fidelity valid for any pure input state. We define number-diagonal signal (NDS) states to be input states whose density operator in the signal modes is diagonal in the multimode number basis. For such input states, we derive series formulas formore » the optimal error probability, the output state fidelity, and the Chernoff-type upper bounds on the error probability. For the special cases of quantum reading of a classical digital memory and target detection (for which the reflectivities are real valued), we show that for a given input signal photon probability distribution, the fidelity is minimized by the NDS states with that distribution and that for a given average total signal energy N{sub s}, the fidelity is minimized by any multimode Fock state with N{sub s} total signal photons. For reading of an ideal memory, it is shown that Fock state inputs minimize the Chernoff bound. For target detection under high-loss conditions, a no-go result showing the lack of appreciable quantum advantage over coherent state transmitters is derived. A comparison of the error probability performance for quantum reading of number state and two-mode squeezed vacuum state (or EPR state) transmitters relative to coherent state transmitters is presented for various values of the reflectances. While the nonclassical states in general perform better than the coherent state, the quantitative performance gains differ depending on the values of the reflectances. The experimental outlook for realizing nonclassical gains from number state transmitters with current technology at moderate to high values of the reflectances is argued to be good.« less

A regularization method for extrapolation of solar potential magnetic fields

NASA Technical Reports Server (NTRS)

Gary, G. A.; Musielak, Z. E.

1992-01-01

The mathematical basis of a Tikhonov regularization method for extrapolating the chromospheric-coronal magnetic field using photospheric vector magnetograms is discussed. The basic techniques show that the Cauchy initial value problem can be formulated for potential magnetic fields. The potential field analysis considers a set of linear, elliptic partial differential equations. It is found that, by introducing an appropriate smoothing of the initial data of the Cauchy potential problem, an approximate Fourier integral solution is found, and an upper bound to the error in the solution is derived. This specific regularization technique, which is a function of magnetograph measurement sensitivities, provides a method to extrapolate the potential magnetic field above an active region into the chromosphere and low corona.

Computation and analysis for a constrained entropy optimization problem in finance

NASA Astrophysics Data System (ADS)

He, Changhong; Coleman, Thomas F.; Li, Yuying

2008-12-01

In [T. Coleman, C. He, Y. Li, Calibrating volatility function bounds for an uncertain volatility model, Journal of Computational Finance (2006) (submitted for publication)], an entropy minimization formulation has been proposed to calibrate an uncertain volatility option pricing model (UVM) from market bid and ask prices. To avoid potential infeasibility due to numerical error, a quadratic penalty function approach is applied. In this paper, we show that the solution to the quadratic penalty problem can be obtained by minimizing an objective function which can be evaluated via solving a Hamilton-Jacobian-Bellman (HJB) equation. We prove that the implicit finite difference solution of this HJB equation converges to its viscosity solution. In addition, we provide computational examples illustrating accuracy of calibration.

Fundamental Bounds for Sequence Reconstruction from Nanopore Sequencers.

PubMed

Magner, Abram; Duda, Jarosław; Szpankowski, Wojciech; Grama, Ananth

2016-06-01

Nanopore sequencers are emerging as promising new platforms for high-throughput sequencing. As with other technologies, sequencer errors pose a major challenge for their effective use. In this paper, we present a novel information theoretic analysis of the impact of insertion-deletion (indel) errors in nanopore sequencers. In particular, we consider the following problems: (i) for given indel error characteristics and rate, what is the probability of accurate reconstruction as a function of sequence length; (ii) using replicated extrusion (the process of passing a DNA strand through the nanopore), what is the number of replicas needed to accurately reconstruct the true sequence with high probability? Our results provide a number of important insights: (i) the probability of accurate reconstruction of a sequence from a single sample in the presence of indel errors tends quickly (i.e., exponentially) to zero as the length of the sequence increases; and (ii) replicated extrusion is an effective technique for accurate reconstruction. We show that for typical distributions of indel errors, the required number of replicas is a slow function (polylogarithmic) of sequence length - implying that through replicated extrusion, we can sequence large reads using nanopore sequencers. Moreover, we show that in certain cases, the required number of replicas can be related to information-theoretic parameters of the indel error distributions.

Estimation of errors in the inverse modeling of accidental release of atmospheric pollutant: Application to the reconstruction of the cesium-137 and iodine-131 source terms from the Fukushima Daiichi power plant

NASA Astrophysics Data System (ADS)

Winiarek, Victor; Bocquet, Marc; Saunier, Olivier; Mathieu, Anne

2012-03-01

A major difficulty when inverting the source term of an atmospheric tracer dispersion problem is the estimation of the prior errors: those of the atmospheric transport model, those ascribed to the representativity of the measurements, those that are instrumental, and those attached to the prior knowledge on the variables one seeks to retrieve. In the case of an accidental release of pollutant, the reconstructed source is sensitive to these assumptions. This sensitivity makes the quality of the retrieval dependent on the methods used to model and estimate the prior errors of the inverse modeling scheme. We propose to use an estimation method for the errors' amplitude based on the maximum likelihood principle. Under semi-Gaussian assumptions, it takes into account, without approximation, the positivity assumption on the source. We apply the method to the estimation of the Fukushima Daiichi source term using activity concentrations in the air. The results are compared to an L-curve estimation technique and to Desroziers's scheme. The total reconstructed activities significantly depend on the chosen method. Because of the poor observability of the Fukushima Daiichi emissions, these methods provide lower bounds for cesium-137 and iodine-131 reconstructed activities. These lower bound estimates, 1.2 × 1016 Bq for cesium-137, with an estimated standard deviation range of 15%-20%, and 1.9 - 3.8 × 1017 Bq for iodine-131, with an estimated standard deviation range of 5%-10%, are of the same order of magnitude as those provided by the Japanese Nuclear and Industrial Safety Agency and about 5 to 10 times less than the Chernobyl atmospheric releases.

Analysis of real-time numerical integration methods applied to dynamic clamp experiments.

PubMed

Butera, Robert J; McCarthy, Maeve L

2004-12-01

Real-time systems are frequently used as an experimental tool, whereby simulated models interact in real time with neurophysiological experiments. The most demanding of these techniques is known as the dynamic clamp, where simulated ion channel conductances are artificially injected into a neuron via intracellular electrodes for measurement and stimulation. Methodologies for implementing the numerical integration of the gating variables in real time typically employ first-order numerical methods, either Euler or exponential Euler (EE). EE is often used for rapidly integrating ion channel gating variables. We find via simulation studies that for small time steps, both methods are comparable, but at larger time steps, EE performs worse than Euler. We derive error bounds for both methods, and find that the error can be characterized in terms of two ratios: time step over time constant, and voltage measurement error over the slope factor of the steady-state activation curve of the voltage-dependent gating variable. These ratios reliably bound the simulation error and yield results consistent with the simulation analysis. Our bounds quantitatively illustrate how measurement error restricts the accuracy that can be obtained by using smaller step sizes. Finally, we demonstrate that Euler can be computed with identical computational efficiency as EE.

Doppler-shift estimation of flat underwater channel using data-aided least-square approach

NASA Astrophysics Data System (ADS)

Pan, Weiqiang; Liu, Ping; Chen, Fangjiong; Ji, Fei; Feng, Jing

2015-06-01

In this paper we proposed a dada-aided Doppler estimation method for underwater acoustic communication. The training sequence is non-dedicate, hence it can be designed for Doppler estimation as well as channel equalization. We assume the channel has been equalized and consider only flat-fading channel. First, based on the training symbols the theoretical received sequence is composed. Next the least square principle is applied to build the objective function, which minimizes the error between the composed and the actual received signal. Then an iterative approach is applied to solve the least square problem. The proposed approach involves an outer loop and inner loop, which resolve the channel gain and Doppler coefficient, respectively. The theoretical performance bound, i.e. the Cramer-Rao Lower Bound (CRLB) of estimation is also derived. Computer simulations results show that the proposed algorithm achieves the CRLB in medium to high SNR cases.

Fuzzy Adaptive Compensation Control of Uncertain Stochastic Nonlinear Systems With Actuator Failures and Input Hysteresis.

PubMed

Wang, Jianhui; Liu, Zhi; Chen, C L Philip; Zhang, Yun

2017-10-12

Hysteresis exists ubiquitously in physical actuators. Besides, actuator failures/faults may also occur in practice. Both effects would deteriorate the transient tracking performance, and even trigger instability. In this paper, we consider the problem of compensating for actuator failures and input hysteresis by proposing a fuzzy control scheme for stochastic nonlinear systems. Compared with the existing research on stochastic nonlinear uncertain systems, it is found that how to guarantee a prescribed transient tracking performance when taking into account actuator failures and hysteresis simultaneously also remains to be answered. Our proposed control scheme is designed on the basis of the fuzzy logic system and backstepping techniques for this purpose. It is proven that all the signals remain bounded and the tracking error is ensured to be within a preestablished bound with the failures of hysteretic actuator. Finally, simulations are provided to illustrate the effectiveness of the obtained theoretical results.

Sanity check for NN bound states in lattice QCD with Lüscher's finite volume formula - Disclosing Symptoms of Fake Plateaux -

NASA Astrophysics Data System (ADS)

Aoki, Sinya; Doi, Takumi; Iritani, Takumi

2018-03-01

The sanity check is to rule out certain classes of obviously false results, not to catch every possible error. After reviewing such a sanity check for NN bound states with the Lüscher's finite volume formula [1-3], we give further evidences for the operator dependence of plateaux, a symptom of the fake plateau problem, against the claim [4]. We then present our critical comments on [5] by NPLQCD: (i) Operator dependences of plateaux in NPL2013 [6, 7] exist with the P value of 4-5%. (ii) The volume independence of plateaux in NPL2013 does not prove their correctness. (iii) Effective range expansions (EREs) in NPL2013 violate the physical pole condition. (iv) Their comment is partly based on new data and analysis different from the original ones. (v) Their new ERE does not satisfy the Lüscher's finite volume formula.

Fuzzy Adaptive Control Design and Discretization for a Class of Nonlinear Uncertain Systems.

PubMed

Zhao, Xudong; Shi, Peng; Zheng, Xiaolong

2016-06-01

In this paper, tracking control problems are investigated for a class of uncertain nonlinear systems in lower triangular form. First, a state-feedback controller is designed by using adaptive backstepping technique and the universal approximation ability of fuzzy logic systems. During the design procedure, a developed method with less computation is proposed by constructing one maximum adaptive parameter. Furthermore, adaptive controllers with nonsymmetric dead-zone are also designed for the systems. Then, a sampled-data control scheme is presented to discretize the obtained continuous-time controller by using the forward Euler method. It is shown that both proposed continuous and discrete controllers can ensure that the system output tracks the target signal with a small bounded error and the other closed-loop signals remain bounded. Two simulation examples are presented to verify the effectiveness and applicability of the proposed new design techniques.

Consideration of plant behaviour in optimal servo-compensator design

NASA Astrophysics Data System (ADS)

Moase, W. H.; Manzie, C.

2016-07-01

Where the most prevalent optimal servo-compensator formulations penalise the behaviour of an error system, this paper considers the problem of additionally penalising the actual states and inputs of the plant. Doing so has the advantage of enabling the penalty function to better resemble an economic cost. This is especially true of problems where control effort needs to be sensibly allocated across weakly redundant inputs or where one wishes to use penalties to soft-constrain certain states or inputs. It is shown that, although the resulting cost function grows unbounded as its horizon approaches infinity, it is possible to formulate an equivalent optimisation problem with a bounded cost. The resulting optimisation problem is similar to those in earlier studies but has an additional 'correction term' in the cost function, and a set of equality constraints that arise when there are redundant inputs. A numerical approach to solve the resulting optimisation problem is presented, followed by simulations on a micro-macro positioner that illustrate the benefits of the proposed servo-compensator design approach.

Event-triggered resilient filtering with stochastic uncertainties and successive packet dropouts via variance-constrained approach

NASA Astrophysics Data System (ADS)

Jia, Chaoqing; Hu, Jun; Chen, Dongyan; Liu, Yurong; Alsaadi, Fuad E.

2018-07-01

In this paper, we discuss the event-triggered resilient filtering problem for a class of time-varying systems subject to stochastic uncertainties and successive packet dropouts. The event-triggered mechanism is employed with hope to reduce the communication burden and save network resources. The stochastic uncertainties are considered to describe the modelling errors and the phenomenon of successive packet dropouts is characterized by a random variable obeying the Bernoulli distribution. The aim of the paper is to provide a resilient event-based filtering approach for addressed time-varying systems such that, for all stochastic uncertainties, successive packet dropouts and filter gain perturbation, an optimized upper bound of the filtering error covariance is obtained by designing the filter gain. Finally, simulations are provided to demonstrate the effectiveness of the proposed robust optimal filtering strategy.

Measurement accuracies in band-limited extrapolation

NASA Technical Reports Server (NTRS)

Kritikos, H. N.

1982-01-01

The problem of numerical instability associated with extrapolation algorithms is addressed. An attempt is made to estimate the bounds for the acceptable errors and to place a ceiling on the measurement accuracy and computational accuracy needed for the extrapolation. It is shown that in band limited (or visible angle limited) extrapolation the larger effective aperture L' that can be realized from a finite aperture L by over sampling is a function of the accuracy of measurements. It is shown that for sampling in the interval L/b absolute value of xL, b1 the signal must be known within an error e sub N given by e sub N squared approximately = 1/4(2kL') cubed (e/8b L/L')(2kL') where L is the physical aperture, L' is the extrapolated aperture, and k = 2pi lambda.

Multilevel sequential Monte Carlo: Mean square error bounds under verifiable conditions

DOE PAGES

Del Moral, Pierre; Jasra, Ajay; Law, Kody J. H.

2017-01-09

We consider the multilevel sequential Monte Carlo (MLSMC) method of Beskos et al. (Stoch. Proc. Appl. [to appear]). This technique is designed to approximate expectations w.r.t. probability laws associated to a discretization. For instance, in the context of inverse problems, where one discretizes the solution of a partial differential equation. The MLSMC approach is especially useful when independent, coupled sampling is not possible. Beskos et al. show that for MLSMC the computational effort to achieve a given error, can be less than independent sampling. In this article we significantly weaken the assumptions of Beskos et al., extending the proofs tomore » non-compact state-spaces. The assumptions are based upon multiplicative drift conditions as in Kontoyiannis and Meyn (Electron. J. Probab. 10 [2005]: 61–123). The assumptions are verified for an example.« less

Multilevel sequential Monte Carlo: Mean square error bounds under verifiable conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Del Moral, Pierre; Jasra, Ajay; Law, Kody J. H.

We consider the multilevel sequential Monte Carlo (MLSMC) method of Beskos et al. (Stoch. Proc. Appl. [to appear]). This technique is designed to approximate expectations w.r.t. probability laws associated to a discretization. For instance, in the context of inverse problems, where one discretizes the solution of a partial differential equation. The MLSMC approach is especially useful when independent, coupled sampling is not possible. Beskos et al. show that for MLSMC the computational effort to achieve a given error, can be less than independent sampling. In this article we significantly weaken the assumptions of Beskos et al., extending the proofs tomore » non-compact state-spaces. The assumptions are based upon multiplicative drift conditions as in Kontoyiannis and Meyn (Electron. J. Probab. 10 [2005]: 61–123). The assumptions are verified for an example.« less

Observer-Based Adaptive NN Control for a Class of Uncertain Nonlinear Systems With Nonsymmetric Input Saturation.

PubMed

Yong-Feng Gao; Xi-Ming Sun; Changyun Wen; Wei Wang

2017-07-01

This paper is concerned with the problem of adaptive tracking control for a class of uncertain nonlinear systems with nonsymmetric input saturation and immeasurable states. The radial basis function of neural network (NN) is employed to approximate unknown functions, and an NN state observer is designed to estimate the immeasurable states. To analyze the effect of input saturation, an auxiliary system is employed. By the aid of adaptive backstepping technique, an adaptive tracking control approach is developed. Under the proposed adaptive tracking controller, the boundedness of all the signals in the closed-loop system is achieved. Moreover, distinct from most of the existing references, the tracking error can be bounded by an explicit function of design parameters and saturation input error. Finally, an example is given to show the effectiveness of the proposed method.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Duchaineau, M.; Wolinsky, M.; Sigeti, D.E.

Terrain visualization is a difficult problem for applications requiring accurate images of large datasets at high frame rates, such as flight simulation and ground-based aircraft testing using synthetic sensor stimulation. On current graphics hardware, the problem is to maintain dynamic, view-dependent triangle meshes and texture maps that produce good images at the required frame rate. We present an algorithm for constructing triangle meshes that optimizes flexible view-dependent error metrics, produces guaranteed error bounds, achieves specified triangle counts directly, and uses frame-to-frame coherence to operate at high frame rates for thousands of triangles per frame. Our method, dubbed Real-time Optimally Adaptingmore » Meshes (ROAM), uses two priority queues to drive split and merge operations that maintain continuous triangulations built from pre-processed bintree triangles. We introduce two additional performance optimizations: incremental triangle stripping and priority-computation deferral lists. ROAM execution time is proportionate to the number of triangle changes per frame, which is typically a few percent of the output mesh size, hence ROAM performance is insensitive to the resolution and extent of the input terrain. Dynamic terrain and simple vertex morphing are supported.« less

Bounds on Block Error Probability for Multilevel Concatenated Codes

NASA Technical Reports Server (NTRS)

Lin, Shu; Moorthy, Hari T.; Stojanovic, Diana

1996-01-01

Maximum likelihood decoding of long block codes is not feasable due to large complexity. Some classes of codes are shown to be decomposable into multilevel concatenated codes (MLCC). For these codes, multistage decoding provides good trade-off between performance and complexity. In this paper, we derive an upper bound on the probability of block error for MLCC. We use this bound to evaluate difference in performance for different decompositions of some codes. Examples given show that a significant reduction in complexity can be achieved when increasing number of stages of decoding. Resulting performance degradation varies for different decompositions. A guideline is given for finding good m-level decompositions.

Fundamental performance of transverse wind estimator from Shack-Hartmann wave-front sensor measurements.

PubMed

Li, Zhenghan; Li, Xinyang

2018-04-30

Real time transverse wind estimation contributes to predictive correction which is used to compensate for the time delay error in the control systems of adaptive optics (AO) system. Many methods that apply Shack-Hartmann wave-front sensor to wind profile measurement have been proposed. One of the obvious problems is the lack of a fundamental benchmark to compare the various methods. In this work, we present the fundamental performance limits for transverse wind estimator from Shack-Hartmann wave-front sensor measurements using Cramér-Rao lower bound (CRLB). The bound provides insight into the nature of the transverse wind estimation, thereby suggesting how to design and improve the estimator in the different application scenario. We analyze the theoretical bound and find that factors such as slope measurement noise, wind velocity and atmospheric coherence length r 0 have important influence on the performance. Then, we introduced the non-iterative gradient-based transverse wind estimator. The source of the deterministic bias of the gradient-based transverse wind estimators is analyzed for the first time. Finally, we derived biased CRLB for the gradient-based transverse wind estimators from Shack-Hartmann wave-front sensor measurements and the bound can predict the performance of estimator more accurately.

Open Systems with Error Bounds: Spin-Boson Model with Spectral Density Variations.

PubMed

Mascherpa, F; Smirne, A; Huelga, S F; Plenio, M B

2017-03-10

In the study of open quantum systems, one of the most common ways to describe environmental effects on the reduced dynamics is through the spectral density. However, in many models this object cannot be computed from first principles and needs to be inferred on phenomenological grounds or fitted to experimental data. Consequently, some uncertainty regarding its form and parameters is unavoidable; this in turn calls into question the accuracy of any theoretical predictions based on a given spectral density. Here, we focus on the spin-boson model as a prototypical open quantum system, find two error bounds on predicted expectation values in terms of the spectral density variation considered, and state a sufficient condition for the strongest one to apply. We further demonstrate an application of our result, by bounding the error brought about by the approximations involved in the hierarchical equations of motion resolution method for spin-boson dynamics.

An internal reference model-based PRF temperature mapping method with Cramer-Rao lower bound noise performance analysis.

PubMed

Li, Cheng; Pan, Xinyi; Ying, Kui; Zhang, Qiang; An, Jing; Weng, Dehe; Qin, Wen; Li, Kuncheng

2009-11-01

The conventional phase difference method for MR thermometry suffers from disturbances caused by the presence of lipid protons, motion-induced error, and field drift. A signal model is presented with multi-echo gradient echo (GRE) sequence using a fat signal as an internal reference to overcome these problems. The internal reference signal model is fit to the water and fat signals by the extended Prony algorithm and the Levenberg-Marquardt algorithm to estimate the chemical shifts between water and fat which contain temperature information. A noise analysis of the signal model was conducted using the Cramer-Rao lower bound to evaluate the noise performance of various algorithms, the effects of imaging parameters, and the influence of the water:fat signal ratio in a sample on the temperature estimate. Comparison of the calculated temperature map and thermocouple temperature measurements shows that the maximum temperature estimation error is 0.614 degrees C, with a standard deviation of 0.06 degrees C, confirming the feasibility of this model-based temperature mapping method. The influence of sample water:fat signal ratio on the accuracy of the temperature estimate is evaluated in a water-fat mixed phantom experiment with an optimal ratio of approximately 0.66:1. (c) 2009 Wiley-Liss, Inc.

Generating moment matching scenarios using optimization techniques

DOE PAGES

Mehrotra, Sanjay; Papp, Dávid

2013-05-16

An optimization based method is proposed to generate moment matching scenarios for numerical integration and its use in stochastic programming. The main advantage of the method is its flexibility: it can generate scenarios matching any prescribed set of moments of the underlying distribution rather than matching all moments up to a certain order, and the distribution can be defined over an arbitrary set. This allows for a reduction in the number of scenarios and allows the scenarios to be better tailored to the problem at hand. The method is based on a semi-infinite linear programming formulation of the problem thatmore » is shown to be solvable with polynomial iteration complexity. A practical column generation method is implemented. The column generation subproblems are polynomial optimization problems; however, they need not be solved to optimality. It is found that the columns in the column generation approach can be efficiently generated by random sampling. The number of scenarios generated matches a lower bound of Tchakaloff's. The rate of convergence of the approximation error is established for continuous integrands, and an improved bound is given for smooth integrands. Extensive numerical experiments are presented in which variants of the proposed method are compared to Monte Carlo and quasi-Monte Carlo methods on both numerical integration problems and stochastic optimization problems. The benefits of being able to match any prescribed set of moments, rather than all moments up to a certain order, is also demonstrated using optimization problems with 100-dimensional random vectors. Here, empirical results show that the proposed approach outperforms Monte Carlo and quasi-Monte Carlo based approaches on the tested problems.« less

Soft-decision decoding techniques for linear block codes and their error performance analysis

NASA Technical Reports Server (NTRS)

Lin, Shu

1996-01-01

The first paper presents a new minimum-weight trellis-based soft-decision iterative decoding algorithm for binary linear block codes. The second paper derives an upper bound on the probability of block error for multilevel concatenated codes (MLCC). The bound evaluates difference in performance for different decompositions of some codes. The third paper investigates the bit error probability code for maximum likelihood decoding of binary linear codes. The fourth and final paper included in this report is concerns itself with the construction of multilevel concatenated block modulation codes using a multilevel concatenation scheme for the frequency non-selective Rayleigh fading channel.

Adaptive NN controller design for a class of nonlinear MIMO discrete-time systems.

PubMed

Liu, Yan-Jun; Tang, Li; Tong, Shaocheng; Chen, C L Philip

2015-05-01

An adaptive neural network tracking control is studied for a class of multiple-input multiple-output (MIMO) nonlinear systems. The studied systems are in discrete-time form and the discretized dead-zone inputs are considered. In addition, the studied MIMO systems are composed of N subsystems, and each subsystem contains unknown functions and external disturbance. Due to the complicated framework of the discrete-time systems, the existence of the dead zone and the noncausal problem in discrete-time, it brings about difficulties for controlling such a class of systems. To overcome the noncausal problem, by defining the coordinate transformations, the studied systems are transformed into a special form, which is suitable for the backstepping design. The radial basis functions NNs are utilized to approximate the unknown functions of the systems. The adaptation laws and the controllers are designed based on the transformed systems. By using the Lyapunov method, it is proved that the closed-loop system is stable in the sense that the semiglobally uniformly ultimately bounded of all the signals and the tracking errors converge to a bounded compact set. The simulation examples and the comparisons with previous approaches are provided to illustrate the effectiveness of the proposed control algorithm.

Automatic optimal filament segmentation with sub-pixel accuracy using generalized linear models and B-spline level-sets

PubMed Central

Xiao, Xun; Geyer, Veikko F.; Bowne-Anderson, Hugo; Howard, Jonathon; Sbalzarini, Ivo F.

2016-01-01

Biological filaments, such as actin filaments, microtubules, and cilia, are often imaged using different light-microscopy techniques. Reconstructing the filament curve from the acquired images constitutes the filament segmentation problem. Since filaments have lower dimensionality than the image itself, there is an inherent trade-off between tracing the filament with sub-pixel accuracy and avoiding noise artifacts. Here, we present a globally optimal filament segmentation method based on B-spline vector level-sets and a generalized linear model for the pixel intensity statistics. We show that the resulting optimization problem is convex and can hence be solved with global optimality. We introduce a simple and efficient algorithm to compute such optimal filament segmentations, and provide an open-source implementation as an ImageJ/Fiji plugin. We further derive an information-theoretic lower bound on the filament segmentation error, quantifying how well an algorithm could possibly do given the information in the image. We show that our algorithm asymptotically reaches this bound in the spline coefficients. We validate our method in comprehensive benchmarks, compare with other methods, and show applications from fluorescence, phase-contrast, and dark-field microscopy. PMID:27104582

A Physiologically Based Pharmacokinetic Model to Predict the Pharmacokinetics of Highly Protein-Bound Drugs and Impact of Errors in Plasma Protein Binding

PubMed Central

Ye, Min; Nagar, Swati; Korzekwa, Ken

2015-01-01

Predicting the pharmacokinetics of highly protein-bound drugs is difficult. Also, since historical plasma protein binding data was often collected using unbuffered plasma, the resulting inaccurate binding data could contribute to incorrect predictions. This study uses a generic physiologically based pharmacokinetic (PBPK) model to predict human plasma concentration-time profiles for 22 highly protein-bound drugs. Tissue distribution was estimated from in vitro drug lipophilicity data, plasma protein binding, and blood: plasma ratio. Clearance was predicted with a well-stirred liver model. Underestimated hepatic clearance for acidic and neutral compounds was corrected by an empirical scaling factor. Predicted values (pharmacokinetic parameters, plasma concentration-time profile) were compared with observed data to evaluate model accuracy. Of the 22 drugs, less than a 2-fold error was obtained for terminal elimination half-life (t1/2, 100% of drugs), peak plasma concentration (Cmax, 100%), area under the plasma concentration-time curve (AUC0–t, 95.4%), clearance (CLh, 95.4%), mean retention time (MRT, 95.4%), and steady state volume (Vss, 90.9%). The impact of fup errors on CLh and Vss prediction was evaluated. Errors in fup resulted in proportional errors in clearance prediction for low-clearance compounds, and in Vss prediction for high-volume neutral drugs. For high-volume basic drugs, errors in fup did not propagate to errors in Vss prediction. This is due to the cancellation of errors in the calculations for tissue partitioning of basic drugs. Overall, plasma profiles were well simulated with the present PBPK model. PMID:26531057

Fuel Burn Estimation Model

NASA Technical Reports Server (NTRS)

Chatterji, Gano

2011-01-01

Conclusions: Validated the fuel estimation procedure using flight test data. A good fuel model can be created if weight and fuel data are available. Error in assumed takeoff weight results in similar amount of error in the fuel estimate. Fuel estimation error bounds can be determined.

Minimum Error Bounded Efficient L1 Tracker with Occlusion Detection (PREPRINT)

DTIC Science & Technology

2011-01-01

Minimum Error Bounded Efficient `1 Tracker with Occlusion Detection Xue Mei\\ ∗ Haibin Ling† Yi Wu†[ Erik Blasch‡ Li Bai] \\Assembly Test Technology...proposed BPR-L1 tracker is tested on several challenging benchmark sequences involving chal- lenges such as occlusion and illumination changes. In all...point method de - pends on the value of the regularization parameter λ. In the experiments, we found that the total number of PCG is a few hundred. The

Trimming and procrastination as inversion techniques

NASA Astrophysics Data System (ADS)

Backus, George E.

1996-12-01

By examining the processes of truncating and approximating the model space (trimming it), and by committing to neither the objectivist nor the subjectivist interpretation of probability (procrastinating), we construct a formal scheme for solving linear and non-linear geophysical inverse problems. The necessary prior information about the correct model xE can be either a collection of inequalities or a probability measure describing where xE was likely to be in the model space X before the data vector y0 was measured. The results of the inversion are (1) a vector z0 that estimates some numerical properties zE of xE; (2) an estimate of the error δz = z0 - zE. As y0 is finite dimensional, so is z0, and hence in principle inversion cannot describe all of xE. The error δz is studied under successively more specialized assumptions about the inverse problem, culminating in a complete analysis of the linear inverse problem with a prior quadratic bound on xE. Our formalism appears to encompass and provide error estimates for many of the inversion schemes current in geomagnetism, and would be equally applicable in geodesy and seismology if adequate prior information were available there. As an idealized example we study the magnetic field at the core-mantle boundary, using satellite measurements of field elements at sites assumed to be almost uniformly distributed on a single spherical surface. Magnetospheric currents are neglected and the crustal field is idealized as a random process with rotationally invariant statistics. We find that an appropriate data compression diagonalizes the variance matrix of the crustal signal and permits an analytic trimming of the idealized problem.

Imaginary-frequency polarizability and van der Waals force constants of two-electron atoms, with rigorous bounds

NASA Technical Reports Server (NTRS)

Glover, R. M.; Weinhold, F.

1977-01-01

Variational functionals of Braunn and Rebane (1972) for the imagery-frequency polarizability (IFP) have been generalized by the method of Gramian inequalities to give rigorous upper and lower bounds, valid even when the true (but unknown) unperturbed wavefunction must be represented by a variational approximation. Using these formulas in conjunction with flexible variational trial functions, tight error bounds are computed for the IFP and the associated two- and three-body van der Waals interaction constants of the ground 1(1S) and metastable 2(1,3S) states of He and Li(+). These bounds generally establish the ground-state properties to within a fraction of a per cent and metastable properties to within a few per cent, permitting a comparative assessment of competing theoretical methods at this level of accuracy. Unlike previous 'error bounds' for these properties, the present results have a completely a priori theoretical character, with no empirical input data.

Distribution-Agnostic Stochastic Optimal Power Flow for Distribution Grids: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baker, Kyri; Dall'Anese, Emiliano; Summers, Tyler

2016-09-01

This paper outlines a data-driven, distributionally robust approach to solve chance-constrained AC optimal power flow problems in distribution networks. Uncertain forecasts for loads and power generated by photovoltaic (PV) systems are considered, with the goal of minimizing PV curtailment while meeting power flow and voltage regulation constraints. A data- driven approach is utilized to develop a distributionally robust conservative convex approximation of the chance-constraints; particularly, the mean and covariance matrix of the forecast errors are updated online, and leveraged to enforce voltage regulation with predetermined probability via Chebyshev-based bounds. By combining an accurate linear approximation of the AC power flowmore » equations with the distributionally robust chance constraint reformulation, the resulting optimization problem becomes convex and computationally tractable.« less

Scope of Gradient and Genetic Algorithms in Multivariable Function Optimization

NASA Technical Reports Server (NTRS)

Shaykhian, Gholam Ali; Sen, S. K.

2007-01-01

Global optimization of a multivariable function - constrained by bounds specified on each variable and also unconstrained - is an important problem with several real world applications. Deterministic methods such as the gradient algorithms as well as the randomized methods such as the genetic algorithms may be employed to solve these problems. In fact, there are optimization problems where a genetic algorithm/an evolutionary approach is preferable at least from the quality (accuracy) of the results point of view. From cost (complexity) point of view, both gradient and genetic approaches are usually polynomial-time; there are no serious differences in this regard, i.e., the computational complexity point of view. However, for certain types of problems, such as those with unacceptably erroneous numerical partial derivatives and those with physically amplified analytical partial derivatives whose numerical evaluation involves undesirable errors and/or is messy, a genetic (stochastic) approach should be a better choice. We have presented here the pros and cons of both the approaches so that the concerned reader/user can decide which approach is most suited for the problem at hand. Also for the function which is known in a tabular form, instead of an analytical form, as is often the case in an experimental environment, we attempt to provide an insight into the approaches focusing our attention toward accuracy. Such an insight will help one to decide which method, out of several available methods, should be employed to obtain the best (least error) output. *

Performance Bounds on Two Concatenated, Interleaved Codes

NASA Technical Reports Server (NTRS)

Moision, Bruce; Dolinar, Samuel

2010-01-01

A method has been developed of computing bounds on the performance of a code comprised of two linear binary codes generated by two encoders serially concatenated through an interleaver. Originally intended for use in evaluating the performances of some codes proposed for deep-space communication links, the method can also be used in evaluating the performances of short-block-length codes in other applications. The method applies, more specifically, to a communication system in which following processes take place: At the transmitter, the original binary information that one seeks to transmit is first processed by an encoder into an outer code (Co) characterized by, among other things, a pair of numbers (n,k), where n (n > k)is the total number of code bits associated with k information bits and n k bits are used for correcting or at least detecting errors. Next, the outer code is processed through either a block or a convolutional interleaver. In the block interleaver, the words of the outer code are processed in blocks of I words. In the convolutional interleaver, the interleaving operation is performed bit-wise in N rows with delays that are multiples of B bits. The output of the interleaver is processed through a second encoder to obtain an inner code (Ci) characterized by (ni,ki). The output of the inner code is transmitted over an additive-white-Gaussian- noise channel characterized by a symbol signal-to-noise ratio (SNR) Es/No and a bit SNR Eb/No. At the receiver, an inner decoder generates estimates of bits. Depending on whether a block or a convolutional interleaver is used at the transmitter, the sequence of estimated bits is processed through a block or a convolutional de-interleaver, respectively, to obtain estimates of code words. Then the estimates of the code words are processed through an outer decoder, which generates estimates of the original information along with flags indicating which estimates are presumed to be correct and which are found to be erroneous. From the perspective of the present method, the topic of major interest is the performance of the communication system as quantified in the word-error rate and the undetected-error rate as functions of the SNRs and the total latency of the interleaver and inner code. The method is embodied in equations that describe bounds on these functions. Throughout the derivation of the equations that embody the method, it is assumed that the decoder for the outer code corrects any error pattern of t or fewer errors, detects any error pattern of s or fewer errors, may detect some error patterns of more than s errors, and does not correct any patterns of more than t errors. Because a mathematically complete description of the equations that embody the method and of the derivation of the equations would greatly exceed the space available for this article, it must suffice to summarize by reporting that the derivation includes consideration of several complex issues, including relationships between latency and memory requirements for block and convolutional codes, burst error statistics, enumeration of error-event intersections, and effects of different interleaving depths. In a demonstration, the method was used to calculate bounds on the performances of several communication systems, each based on serial concatenation of a (63,56) expurgated Hamming code with a convolutional inner code through a convolutional interleaver. The bounds calculated by use of the method were compared with results of numerical simulations of performances of the systems to show the regions where the bounds are tight (see figure).

Sliding mode output feedback control based on tracking error observer with disturbance estimator.

PubMed

Xiao, Lingfei; Zhu, Yue

2014-07-01

For a class of systems who suffers from disturbances, an original output feedback sliding mode control method is presented based on a novel tracking error observer with disturbance estimator. The mathematical models of the systems are not required to be with high accuracy, and the disturbances can be vanishing or nonvanishing, while the bounds of disturbances are unknown. By constructing a differential sliding surface and employing reaching law approach, a sliding mode controller is obtained. On the basis of an extended disturbance estimator, a creative tracking error observer is produced. By using the observation of tracking error and the estimation of disturbance, the sliding mode controller is implementable. It is proved that the disturbance estimation error and tracking observation error are bounded, the sliding surface is reachable and the closed-loop system is robustly stable. The simulations on a servomotor positioning system and a five-degree-of-freedom active magnetic bearings system verify the effect of the proposed method. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

FSMRank: feature selection algorithm for learning to rank.

PubMed

Lai, Han-Jiang; Pan, Yan; Tang, Yong; Yu, Rong

2013-06-01

In recent years, there has been growing interest in learning to rank. The introduction of feature selection into different learning problems has been proven effective. These facts motivate us to investigate the problem of feature selection for learning to rank. We propose a joint convex optimization formulation which minimizes ranking errors while simultaneously conducting feature selection. This optimization formulation provides a flexible framework in which we can easily incorporate various importance measures and similarity measures of the features. To solve this optimization problem, we use the Nesterov's approach to derive an accelerated gradient algorithm with a fast convergence rate O(1/T(2)). We further develop a generalization bound for the proposed optimization problem using the Rademacher complexities. Extensive experimental evaluations are conducted on the public LETOR benchmark datasets. The results demonstrate that the proposed method shows: 1) significant ranking performance gain compared to several feature selection baselines for ranking, and 2) very competitive performance compared to several state-of-the-art learning-to-rank algorithms.

A Constrained Least Squares Approach to Mobile Positioning: Algorithms and Optimality

NASA Astrophysics Data System (ADS)

Cheung, KW; So, HC; Ma, W.-K.; Chan, YT

2006-12-01

The problem of locating a mobile terminal has received significant attention in the field of wireless communications. Time-of-arrival (TOA), received signal strength (RSS), time-difference-of-arrival (TDOA), and angle-of-arrival (AOA) are commonly used measurements for estimating the position of the mobile station. In this paper, we present a constrained weighted least squares (CWLS) mobile positioning approach that encompasses all the above described measurement cases. The advantages of CWLS include performance optimality and capability of extension to hybrid measurement cases (e.g., mobile positioning using TDOA and AOA measurements jointly). Assuming zero-mean uncorrelated measurement errors, we show by mean and variance analysis that all the developed CWLS location estimators achieve zero bias and the Cramér-Rao lower bound approximately when measurement error variances are small. The asymptotic optimum performance is also confirmed by simulation results.

A Lyapunov and Sacker–Sell spectral stability theory for one-step methods

DOE PAGES

Steyer, Andrew J.; Van Vleck, Erik S.

2018-04-13

Approximation theory for Lyapunov and Sacker–Sell spectra based upon QR techniques is used to analyze the stability of a one-step method solving a time-dependent (nonautonomous) linear ordinary differential equation (ODE) initial value problem in terms of the local error. Integral separation is used to characterize the conditioning of stability spectra calculations. The stability of the numerical solution by a one-step method of a nonautonomous linear ODE using real-valued, scalar, nonautonomous linear test equations is justified. This analysis is used to approximate exponential growth/decay rates on finite and infinite time intervals and establish global error bounds for one-step methods approximating uniformly,more » exponentially stable trajectories of nonautonomous and nonlinear ODEs. A time-dependent stiffness indicator and a one-step method that switches between explicit and implicit Runge–Kutta methods based upon time-dependent stiffness are developed based upon the theoretical results.« less

A Lyapunov and Sacker–Sell spectral stability theory for one-step methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Steyer, Andrew J.; Van Vleck, Erik S.

Approximation theory for Lyapunov and Sacker–Sell spectra based upon QR techniques is used to analyze the stability of a one-step method solving a time-dependent (nonautonomous) linear ordinary differential equation (ODE) initial value problem in terms of the local error. Integral separation is used to characterize the conditioning of stability spectra calculations. The stability of the numerical solution by a one-step method of a nonautonomous linear ODE using real-valued, scalar, nonautonomous linear test equations is justified. This analysis is used to approximate exponential growth/decay rates on finite and infinite time intervals and establish global error bounds for one-step methods approximating uniformly,more » exponentially stable trajectories of nonautonomous and nonlinear ODEs. A time-dependent stiffness indicator and a one-step method that switches between explicit and implicit Runge–Kutta methods based upon time-dependent stiffness are developed based upon the theoretical results.« less

Experimental study of adaptive pointing and tracking for large flexible space structures

NASA Technical Reports Server (NTRS)

Boussalis, D.; Bayard, D. S.; Ih, C.; Wang, S. J.; Ahmed, A.

1991-01-01

This paper describes an experimental study of adaptive pointing and tracking control for flexible spacecraft conducted on a complex ground experiment facility. The algorithm used in this study is based on a multivariable direct model reference adaptive control law. Several experimental validation studies were performed earlier using this algorithm for vibration damping and robust regulation, with excellent results. The current work extends previous studies by addressing the pointing and tracking problem. As is consistent with an adaptive control framework, the plant is assumed to be poorly known to the extent that only system level knowledge of its dynamics is available. Explicit bounds on the steady-state pointing error are derived as functions of the adaptive controller design parameters. It is shown that good tracking performance can be achieved in an experimental setting by adjusting adaptive controller design weightings according to the guidelines indicated by the analytical expressions for the error.

Adaptive neural control for dual-arm coordination of humanoid robot with unknown nonlinearities in output mechanism.

PubMed

Liu, Zhi; Chen, Ci; Zhang, Yun; Chen, C L P

2015-03-01

To achieve an excellent dual-arm coordination of the humanoid robot, it is essential to deal with the nonlinearities existing in the system dynamics. The literatures so far on the humanoid robot control have a common assumption that the problem of output hysteresis could be ignored. However, in the practical applications, the output hysteresis is widely spread; and its existing limits the motion/force performances of the robotic system. In this paper, an adaptive neural control scheme, which takes the unknown output hysteresis and computational efficiency into account, is presented and investigated. In the controller design, the prior knowledge of system dynamics is assumed to be unknown. The motion error is guaranteed to converge to a small neighborhood of the origin by Lyapunov's stability theory. Simultaneously, the internal force is kept bounded and its error can be made arbitrarily small.

Representations of Intervals and Optimal Error Bounds.

DTIC Science & Technology

1980-07-01

OAA629-8O-C-0ONI UNCLASS I FI IEDMRC TSR-2098 NL 11111L 3 -2 11111 ~ 13.6 1111 125 .4 111.6 MCROCOPY RESOLUTION TEST CHART NATIONA’ 13UREAU OF STANDARDS...geometric and harmonic means, Excess width Work Unit Number 3 (Numerical Analysis and Computer Science) Sponsored by the United States Army under...example in the next section, following which the general theory will be dis- cussed. 3 . An example of an optimal point and error bound. A simple

Approximation of Bit Error Rates in Digital Communications

DTIC Science & Technology

2007-06-01

and Technology Organisation DSTO—TN—0761 ABSTRACT This report investigates the estimation of bit error rates in digital communi- cations, motivated by...recent work in [6]. In the latter, bounds are used to construct estimates for bit error rates in the case of differentially coherent quadrature phase

Permanence analysis of a concatenated coding scheme for error control

NASA Technical Reports Server (NTRS)

Costello, D. J., Jr.; Lin, S.; Kasami, T.

1983-01-01

A concatenated coding scheme for error control in data communications is analyzed. In this scheme, the inner code is used for both error correction and detection, however, the outer code is used only for error detection. A retransmission is requested if the outer code detects the presence of errors after the inner code decoding. Probability of undetected error is derived and bounded. A particular example, proposed for the planetary program, is analyzed.

Probability of undetected error after decoding for a concatenated coding scheme

NASA Technical Reports Server (NTRS)

Costello, D. J., Jr.; Lin, S.

1984-01-01

A concatenated coding scheme for error control in data communications is analyzed. In this scheme, the inner code is used for both error correction and detection, however the outer code is used only for error detection. A retransmission is requested if the outer code detects the presence of errors after the inner code decoding. Probability of undetected error is derived and bounded. A particular example, proposed for NASA telecommand system is analyzed.

Galerkin v. discrete-optimal projection in nonlinear model reduction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carlberg, Kevin Thomas; Barone, Matthew Franklin; Antil, Harbir

Discrete-optimal model-reduction techniques such as the Gauss{Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible ow problems where standard Galerkin techniques have failed. However, there has been limited comparative analysis of the two approaches. This is due in part to difficulties arising from the fact that Galerkin techniques perform projection at the time-continuous level, while discrete-optimal techniques do so at the time-discrete level. This work provides a detailed theoretical and experimental comparison of the two techniques for two common classes of time integrators: linear multistep schemes and Runge{Kutta schemes.more » We present a number of new ndings, including conditions under which the discrete-optimal ROM has a time-continuous representation, conditions under which the two techniques are equivalent, and time-discrete error bounds for the two approaches. Perhaps most surprisingly, we demonstrate both theoretically and experimentally that decreasing the time step does not necessarily decrease the error for the discrete-optimal ROM; instead, the time step should be `matched' to the spectral content of the reduced basis. In numerical experiments carried out on a turbulent compressible- ow problem with over one million unknowns, we show that increasing the time step to an intermediate value decreases both the error and the simulation time of the discrete-optimal reduced-order model by an order of magnitude.« less

Scoring-and-unfolding trimmed tree assembler: concepts, constructs and comparisons.

PubMed

Narzisi, Giuseppe; Mishra, Bud

2011-01-15

Mired by its connection to a well-known -complete combinatorial optimization problem-namely, the Shortest Common Superstring Problem (SCSP)-historically, the whole-genome sequence assembly (WGSA) problem has been assumed to be amenable only to greedy and heuristic methods. By placing efficiency as their first priority, these methods opted to rely only on local searches, and are thus inherently approximate, ambiguous or error prone, especially, for genomes with complex structures. Furthermore, since choice of the best heuristics depended critically on the properties of (e.g. errors in) the input data and the available long range information, these approaches hindered designing an error free WGSA pipeline. We dispense with the idea of limiting the solutions to just the approximated ones, and instead favor an approach that could potentially lead to an exhaustive (exponential-time) search of all possible layouts. Its computational complexity thus must be tamed through a constrained search (Branch-and-Bound) and quick identification and pruning of implausible overlays. For his purpose, such a method necessarily relies on a set of score functions (oracles) that can combine different structural properties (e.g. transitivity, coverage, physical maps, etc.). We give a detailed description of this novel assembly framework, referred to as Scoring-and-Unfolding Trimmed Tree Assembler (SUTTA), and present experimental results on several bacterial genomes using next-generation sequencing technology data. We also report experimental evidence that the assembly quality strongly depends on the choice of the minimum overlap parameter k. SUTTA's binaries are freely available to non-profit institutions for research and educational purposes at http://www.bioinformatics.nyu.edu.

Bounded Error Schemes for the Wave Equation on Complex Domains

NASA Technical Reports Server (NTRS)

Abarbanel, Saul; Ditkowski, Adi; Yefet, Amir

1998-01-01

This paper considers the application of the method of boundary penalty terms ("SAT") to the numerical solution of the wave equation on complex shapes with Dirichlet boundary conditions. A theory is developed, in a semi-discrete setting, that allows the use of a Cartesian grid on complex geometries, yet maintains the order of accuracy with only a linear temporal error-bound. A numerical example, involving the solution of Maxwell's equations inside a 2-D circular wave-guide demonstrates the efficacy of this method in comparison to others (e.g. the staggered Yee scheme) - we achieve a decrease of two orders of magnitude in the level of the L2-error.

Determining Type I and Type II Errors when Applying Information Theoretic Change Detection Metrics for Data Association and Space Situational Awareness

NASA Astrophysics Data System (ADS)

Wilkins, M.; Moyer, E. J.; Hussein, Islam I.; Schumacher, P. W., Jr.

Correlating new detections back to a large catalog of resident space objects (RSOs) requires solving one of three types of data association problems: observation-to-track, track-to-track, or observation-to-observation. The authors previous work has explored the use of various information divergence metrics for solving these problems: Kullback-Leibler (KL) divergence, mutual information, and Bhattacharrya distance. In addition to approaching the data association problem strictly from the metric tracking aspect, we have explored fusing metric and photometric data using Bayesian probabilistic reasoning for RSO identification to aid in our ability to correlate data to specific RS Os. In this work, we will focus our attention on the KL Divergence, which is a measure of the information gained when new evidence causes the observer to revise their beliefs. We can apply the Principle of Minimum Discrimination Information such that new data produces as small an information gain as possible and this information change is bounded by ɛ. Choosing an appropriate value for ɛ for both convergence and change detection is a function of your risk tolerance. Small ɛ for change detection increases alarm rates while larger ɛ for convergence means that new evidence need not be identical in information content. We need to understand what this change detection metric implies for Type I α and Type II β errors when we are forced to make a decision on whether new evidence represents a true change in characterization of an object or is merely within the bounds of our measurement uncertainty. This is unclear for the case of fusing multiple kinds and qualities of characterization evidence that may exist in different metric spaces or are even semantic statements. To this end, we explore the use of Sequential Probability Ratio Testing where we suppose that we may need to collect additional evidence before accepting or rejecting the null hypothesis that a change has occurred. In this work, we will explore the effects of choosing ɛ as a function of α and β. Our intent is that this work will help bridge understanding between the well-trodden grounds of Type I and Type II errors and changes in information theoretic content.

Investigation of several aspects of LANDSAT-4 data quality

NASA Technical Reports Server (NTRS)

Wrigley, R. C. (Principal Investigator)

1983-01-01

No insurmountable problems in change detection analysis were found when portions of scenes collected simultaneously by LANDSAT 4 MSS and either LANDSAT 2 or 3. The cause of the periodic noise in LANDSAT 4 MSS images which had a RMS value of approximately 2DN should be corrected in the LANDSAT D instrument before its launch. Analysis of the P-tape of the Arkansas scene shows bands within the same focal plane very well registered except for the thermal band which was misregistered by approximately three 28.5 meter pixels in both directions. It is possible to derive tight confidence bounds for the registration errors. Preliminary analyses of the Sacramento and Arkansas scenes reveals a very high degree of consistency with earlier results for bands 3 vs 1, 3 vs 4, and 3 vs 5. Results are presented in table form. It is suggested that attention be given to the standard deviations of registrations errors to judge whether or not they will be within specification once any known mean registration errors are corrected. Techniques used for MTF analysis of a Washington scene produced noisy results.

A physiologically based pharmacokinetic model to predict the pharmacokinetics of highly protein-bound drugs and the impact of errors in plasma protein binding.

PubMed

Ye, Min; Nagar, Swati; Korzekwa, Ken

2016-04-01

Predicting the pharmacokinetics of highly protein-bound drugs is difficult. Also, since historical plasma protein binding data were often collected using unbuffered plasma, the resulting inaccurate binding data could contribute to incorrect predictions. This study uses a generic physiologically based pharmacokinetic (PBPK) model to predict human plasma concentration-time profiles for 22 highly protein-bound drugs. Tissue distribution was estimated from in vitro drug lipophilicity data, plasma protein binding and the blood: plasma ratio. Clearance was predicted with a well-stirred liver model. Underestimated hepatic clearance for acidic and neutral compounds was corrected by an empirical scaling factor. Predicted values (pharmacokinetic parameters, plasma concentration-time profile) were compared with observed data to evaluate the model accuracy. Of the 22 drugs, less than a 2-fold error was obtained for the terminal elimination half-life (t1/2 , 100% of drugs), peak plasma concentration (Cmax , 100%), area under the plasma concentration-time curve (AUC0-t , 95.4%), clearance (CLh , 95.4%), mean residence time (MRT, 95.4%) and steady state volume (Vss , 90.9%). The impact of fup errors on CLh and Vss prediction was evaluated. Errors in fup resulted in proportional errors in clearance prediction for low-clearance compounds, and in Vss prediction for high-volume neutral drugs. For high-volume basic drugs, errors in fup did not propagate to errors in Vss prediction. This is due to the cancellation of errors in the calculations for tissue partitioning of basic drugs. Overall, plasma profiles were well simulated with the present PBPK model. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

A Very Efficient Transfer Function Bounding Technique on Bit Error Rate for Viterbi Decoded, Rate 1/N Convolutional Codes

NASA Technical Reports Server (NTRS)

Lee, P. J.

1984-01-01

For rate 1/N convolutional codes, a recursive algorithm for finding the transfer function bound on bit error rate (BER) at the output of a Viterbi decoder is described. This technique is very fast and requires very little storage since all the unnecessary operations are eliminated. Using this technique, we find and plot bounds on the BER performance of known codes of rate 1/2 with K 18, rate 1/3 with K 14. When more than one reported code with the same parameter is known, we select the code that minimizes the required signal to noise ratio for a desired bit error rate of 0.000001. This criterion of determining goodness of a code had previously been found to be more useful than the maximum free distance criterion and was used in the code search procedures of very short constraint length codes. This very efficient technique can also be used for searches of longer constraint length codes.

AveBoost2: Boosting for Noisy Data

NASA Technical Reports Server (NTRS)

Oza, Nikunj C.

2004-01-01

AdaBoost is a well-known ensemble learning algorithm that constructs its constituent or base models in sequence. A key step in AdaBoost is constructing a distribution over the training examples to create each base model. This distribution, represented as a vector, is constructed to be orthogonal to the vector of mistakes made by the pre- vious base model in the sequence. The idea is to make the next base model's errors uncorrelated with those of the previous model. In previous work, we developed an algorithm, AveBoost, that constructed distributions orthogonal to the mistake vectors of all the previous models, and then averaged them to create the next base model s distribution. Our experiments demonstrated the superior accuracy of our approach. In this paper, we slightly revise our algorithm to allow us to obtain non-trivial theoretical results: bounds on the training error and generalization error (difference between training and test error). Our averaging process has a regularizing effect which, as expected, leads us to a worse training error bound for our algorithm than for AdaBoost but a superior generalization error bound. For this paper, we experimented with the data that we used in both as originally supplied and with added label noise-a small fraction of the data has its original label changed. Noisy data are notoriously difficult for AdaBoost to learn. Our algorithm's performance improvement over AdaBoost is even greater on the noisy data than the original data.

Bounded state variables and the calculus of variations

NASA Technical Reports Server (NTRS)

Hanafy, L. M.

1972-01-01

An optimal control problem with bounded state variables is transformed into a Lagrange problem by means of differentiable mappings which take some Euclidean space onto the control and state regions. Whereas all such mappings lead to a Lagrange problem, it is shown that only those which are defined as acceptable pairs of transformations are suitable in the sense that solutions to the transformed Lagrange problem will lead to solutions to the original bounded state problem and vice versa. In particular, an acceptable pair of transformations is exhibited for the case when the control and state regions are right parallelepipeds. Finally, a description of the necessary conditions for the bounded state problem which were obtained by this method is given.

The Theory and Practice of Estimating the Accuracy of Dynamic Flight-Determined Coefficients

NASA Technical Reports Server (NTRS)

Maine, R. E.; Iliff, K. W.

1981-01-01

Means of assessing the accuracy of maximum likelihood parameter estimates obtained from dynamic flight data are discussed. The most commonly used analytical predictors of accuracy are derived and compared from both statistical and simplified geometrics standpoints. The accuracy predictions are evaluated with real and simulated data, with an emphasis on practical considerations, such as modeling error. Improved computations of the Cramer-Rao bound to correct large discrepancies due to colored noise and modeling error are presented. The corrected Cramer-Rao bound is shown to be the best available analytical predictor of accuracy, and several practical examples of the use of the Cramer-Rao bound are given. Engineering judgement, aided by such analytical tools, is the final arbiter of accuracy estimation.

Numerical Error Estimation with UQ

NASA Astrophysics Data System (ADS)

Ackmann, Jan; Korn, Peter; Marotzke, Jochem

2014-05-01

Ocean models are still in need of means to quantify model errors, which are inevitably made when running numerical experiments. The total model error can formally be decomposed into two parts, the formulation error and the discretization error. The formulation error arises from the continuous formulation of the model not fully describing the studied physical process. The discretization error arises from having to solve a discretized model instead of the continuously formulated model. Our work on error estimation is concerned with the discretization error. Given a solution of a discretized model, our general problem statement is to find a way to quantify the uncertainties due to discretization in physical quantities of interest (diagnostics), which are frequently used in Geophysical Fluid Dynamics. The approach we use to tackle this problem is called the "Goal Error Ensemble method". The basic idea of the Goal Error Ensemble method is that errors in diagnostics can be translated into a weighted sum of local model errors, which makes it conceptually based on the Dual Weighted Residual method from Computational Fluid Dynamics. In contrast to the Dual Weighted Residual method these local model errors are not considered deterministically but interpreted as local model uncertainty and described stochastically by a random process. The parameters for the random process are tuned with high-resolution near-initial model information. However, the original Goal Error Ensemble method, introduced in [1], was successfully evaluated only in the case of inviscid flows without lateral boundaries in a shallow-water framework and is hence only of limited use in a numerical ocean model. Our work consists in extending the method to bounded, viscous flows in a shallow-water framework. As our numerical model, we use the ICON-Shallow-Water model. In viscous flows our high-resolution information is dependent on the viscosity parameter, making our uncertainty measures viscosity-dependent. We will show that we can choose a sensible parameter by using the Reynolds-number as a criteria. Another topic, we will discuss is the choice of the underlying distribution of the random process. This is especially of importance in the scope of lateral boundaries. We will present resulting error estimates for different height- and velocity-based diagnostics applied to the Munk gyre experiment. References [1] F. RAUSER: Error Estimation in Geophysical Fluid Dynamics through Learning; PhD Thesis, IMPRS-ESM, Hamburg, 2010 [2] F. RAUSER, J. MAROTZKE, P. KORN: Ensemble-type numerical uncertainty quantification from single model integrations; SIAM/ASA Journal on Uncertainty Quantification, submitted

Spectral Regularization Algorithms for Learning Large Incomplete Matrices.

PubMed

Mazumder, Rahul; Hastie, Trevor; Tibshirani, Robert

2010-03-01

We use convex relaxation techniques to provide a sequence of regularized low-rank solutions for large-scale matrix completion problems. Using the nuclear norm as a regularizer, we provide a simple and very efficient convex algorithm for minimizing the reconstruction error subject to a bound on the nuclear norm. Our algorithm Soft-Impute iteratively replaces the missing elements with those obtained from a soft-thresholded SVD. With warm starts this allows us to efficiently compute an entire regularization path of solutions on a grid of values of the regularization parameter. The computationally intensive part of our algorithm is in computing a low-rank SVD of a dense matrix. Exploiting the problem structure, we show that the task can be performed with a complexity linear in the matrix dimensions. Our semidefinite-programming algorithm is readily scalable to large matrices: for example it can obtain a rank-80 approximation of a 10(6) × 10(6) incomplete matrix with 10(5) observed entries in 2.5 hours, and can fit a rank 40 approximation to the full Netflix training set in 6.6 hours. Our methods show very good performance both in training and test error when compared to other competitive state-of-the art techniques.

Spectral Regularization Algorithms for Learning Large Incomplete Matrices

PubMed Central

Mazumder, Rahul; Hastie, Trevor; Tibshirani, Robert

2010-01-01

We use convex relaxation techniques to provide a sequence of regularized low-rank solutions for large-scale matrix completion problems. Using the nuclear norm as a regularizer, we provide a simple and very efficient convex algorithm for minimizing the reconstruction error subject to a bound on the nuclear norm. Our algorithm Soft-Impute iteratively replaces the missing elements with those obtained from a soft-thresholded SVD. With warm starts this allows us to efficiently compute an entire regularization path of solutions on a grid of values of the regularization parameter. The computationally intensive part of our algorithm is in computing a low-rank SVD of a dense matrix. Exploiting the problem structure, we show that the task can be performed with a complexity linear in the matrix dimensions. Our semidefinite-programming algorithm is readily scalable to large matrices: for example it can obtain a rank-80 approximation of a 106 × 106 incomplete matrix with 105 observed entries in 2.5 hours, and can fit a rank 40 approximation to the full Netflix training set in 6.6 hours. Our methods show very good performance both in training and test error when compared to other competitive state-of-the art techniques. PMID:21552465

Distributed Optimal Consensus Control for Multiagent Systems With Input Delay.

PubMed

Zhang, Huaipin; Yue, Dong; Zhao, Wei; Hu, Songlin; Dou, Chunxia; Huaipin Zhang; Dong Yue; Wei Zhao; Songlin Hu; Chunxia Dou; Hu, Songlin; Zhang, Huaipin; Dou, Chunxia; Yue, Dong; Zhao, Wei

2018-06-01

This paper addresses the problem of distributed optimal consensus control for a continuous-time heterogeneous linear multiagent system subject to time varying input delays. First, by discretization and model transformation, the continuous-time input-delayed system is converted into a discrete-time delay-free system. Two delicate performance index functions are defined for these two systems. It is shown that the performance index functions are equivalent and the optimal consensus control problem of the input-delayed system can be cast into that of the delay-free system. Second, by virtue of the Hamilton-Jacobi-Bellman (HJB) equations, an optimal control policy for each agent is designed based on the delay-free system and a novel value iteration algorithm is proposed to learn the solutions to the HJB equations online. The proposed adaptive dynamic programming algorithm is implemented on the basis of a critic-action neural network (NN) structure. Third, it is proved that local consensus errors of the two systems and weight estimation errors of the critic-action NNs are uniformly ultimately bounded while the approximated control policies converge to their target values. Finally, two simulation examples are presented to illustrate the effectiveness of the developed method.

Error Estimates for Numerical Integration Rules

ERIC Educational Resources Information Center

Mercer, Peter R.

2005-01-01

The starting point for this discussion of error estimates is the fact that integrals that arise in Fourier series have properties that can be used to get improved bounds. This idea is extended to more general situations.

Adaptive neural network backstepping control for a class of uncertain fractional-order chaotic systems with unknown backlash-like hysteresis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Yimin; Lv, Hui, E-mail: lvhui207@gmail.com

In this paper, we consider the control problem of a class of uncertain fractional-order chaotic systems preceded by unknown backlash-like hysteresis nonlinearities based on backstepping control algorithm. We model the hysteresis by using a differential equation. Based on the fractional Lyapunov stability criterion and the backstepping algorithm procedures, an adaptive neural network controller is driven. No knowledge of the upper bound of the disturbance and system uncertainty is required in our controller, and the asymptotical convergence of the tracking error can be guaranteed. Finally, we give two simulation examples to confirm our theoretical results.

Graph Theory-Based Pinning Synchronization of Stochastic Complex Dynamical Networks.

PubMed

Li, Xiao-Jian; Yang, Guang-Hong

2017-02-01

This paper is concerned with the adaptive pinning synchronization problem of stochastic complex dynamical networks (CDNs). Based on algebraic graph theory and Lyapunov theory, pinning controller design conditions are derived, and the rigorous convergence analysis of synchronization errors in the probability sense is also conducted. Compared with the existing results, the topology structures of stochastic CDN are allowed to be unknown due to the use of graph theory. In particular, it is shown that the selection of nodes for pinning depends on the unknown lower bounds of coupling strengths. Finally, an example on a Chua's circuit network is given to validate the effectiveness of the theoretical results.

Adaptive relative pose control of spacecraft with model couplings and uncertainties

NASA Astrophysics Data System (ADS)

Sun, Liang; Zheng, Zewei

2018-02-01

The spacecraft pose tracking control problem for an uncertain pursuer approaching to a space target is researched in this paper. After modeling the nonlinearly coupled dynamics for relative translational and rotational motions between two spacecraft, position tracking and attitude synchronization controllers are developed independently by using a robust adaptive control approach. The unknown kinematic couplings, parametric uncertainties, and bounded external disturbances are handled with adaptive updating laws. It is proved via Lyapunov method that the pose tracking errors converge to zero asymptotically. Spacecraft close-range rendezvous and proximity operations are introduced as an example to validate the effectiveness of the proposed control approach.

A duality approach for solving bounded linear programming problems with fuzzy variables based on ranking functions and its application in bounded transportation problems

NASA Astrophysics Data System (ADS)

Ebrahimnejad, Ali

2015-08-01

There are several methods, in the literature, for solving fuzzy variable linear programming problems (fuzzy linear programming in which the right-hand-side vectors and decision variables are represented by trapezoidal fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings a new method based on the bounded dual simplex method is proposed to determine the fuzzy optimal solution of that kind of fuzzy variable linear programming problems in which some or all variables are restricted to lie within lower and upper bounds. To illustrate the proposed method, an application example is solved and the obtained results are given. The advantages of the proposed method over existing methods are discussed. Also, one application of this algorithm in solving bounded transportation problems with fuzzy supplies and demands is dealt with. The proposed method is easy to understand and to apply for determining the fuzzy optimal solution of bounded fuzzy variable linear programming problems occurring in real-life situations.

Approximation-Based Discrete-Time Adaptive Position Tracking Control for Interior Permanent Magnet Synchronous Motors.

PubMed

Yu, Jinpeng; Shi, Peng; Yu, Haisheng; Chen, Bing; Lin, Chong

2015-07-01

This paper considers the problem of discrete-time adaptive position tracking control for a interior permanent magnet synchronous motor (IPMSM) based on fuzzy-approximation. Fuzzy logic systems are used to approximate the nonlinearities of the discrete-time IPMSM drive system which is derived by direct discretization using Euler method, and a discrete-time fuzzy position tracking controller is designed via backstepping approach. In contrast to existing results, the advantage of the scheme is that the number of the adjustable parameters is reduced to two only and the problem of coupling nonlinearity can be overcome. It is shown that the proposed discrete-time fuzzy controller can guarantee the tracking error converges to a small neighborhood of the origin and all the signals are bounded. Simulation results illustrate the effectiveness and the potentials of the theoretic results obtained.

Quantum optimization for training support vector machines.

PubMed

Anguita, Davide; Ridella, Sandro; Rivieccio, Fabio; Zunino, Rodolfo

2003-01-01

Refined concepts, such as Rademacher estimates of model complexity and nonlinear criteria for weighting empirical classification errors, represent recent and promising approaches to characterize the generalization ability of Support Vector Machines (SVMs). The advantages of those techniques lie in both improving the SVM representation ability and yielding tighter generalization bounds. On the other hand, they often make Quadratic-Programming algorithms no longer applicable, and SVM training cannot benefit from efficient, specialized optimization techniques. The paper considers the application of Quantum Computing to solve the problem of effective SVM training, especially in the case of digital implementations. The presented research compares the behavioral aspects of conventional and enhanced SVMs; experiments in both a synthetic and real-world problems support the theoretical analysis. At the same time, the related differences between Quadratic-Programming and Quantum-based optimization techniques are considered.

Adaptive control of a quadrotor aerial vehicle with input constraints and uncertain parameters

NASA Astrophysics Data System (ADS)

Tran, Trong-Toan; Ge, Shuzhi Sam; He, Wei

2018-05-01

In this paper, we address the problem of adaptive bounded control for the trajectory tracking of a Quadrotor Aerial Vehicle (QAV) while the input saturations and uncertain parameters with the known bounds are simultaneously taken into account. First, to deal with the underactuated property of the QAV model, we decouple and construct the QAV model as a cascaded structure which consists of two fully actuated subsystems. Second, to handle the input constraints and uncertain parameters, we use a combination of the smooth saturation function and smooth projection operator in the control design. Third, to ensure the stability of the overall system of the QAV, we develop the technique for the cascaded system in the presence of both the input constraints and uncertain parameters. Finally, the region of stability of the closed-loop system is constructed explicitly, and our design ensures the asymptotic convergence of the tracking errors to the origin. The simulation results are provided to illustrate the effectiveness of the proposed method.

Decentralized stabilization for a class of continuous-time nonlinear interconnected systems using online learning optimal control approach.

PubMed

Liu, Derong; Wang, Ding; Li, Hongliang

2014-02-01

In this paper, using a neural-network-based online learning optimal control approach, a novel decentralized control strategy is developed to stabilize a class of continuous-time nonlinear interconnected large-scale systems. First, optimal controllers of the isolated subsystems are designed with cost functions reflecting the bounds of interconnections. Then, it is proven that the decentralized control strategy of the overall system can be established by adding appropriate feedback gains to the optimal control policies of the isolated subsystems. Next, an online policy iteration algorithm is presented to solve the Hamilton-Jacobi-Bellman equations related to the optimal control problem. Through constructing a set of critic neural networks, the cost functions can be obtained approximately, followed by the control policies. Furthermore, the dynamics of the estimation errors of the critic networks are verified to be uniformly and ultimately bounded. Finally, a simulation example is provided to illustrate the effectiveness of the present decentralized control scheme.

Lossless Brownian Information Engine

NASA Astrophysics Data System (ADS)

Paneru, Govind; Lee, Dong Yun; Tlusty, Tsvi; Pak, Hyuk Kyu

2018-01-01

We report on a lossless information engine that converts nearly all available information from an error-free feedback protocol into mechanical work. Combining high-precision detection at a resolution of 1 nm with ultrafast feedback control, the engine is tuned to extract the maximum work from information on the position of a Brownian particle. We show that the work produced by the engine achieves a bound set by a generalized second law of thermodynamics, demonstrating for the first time the sharpness of this bound. We validate a generalized Jarzynski equality for error-free feedback-controlled information engines.

Lossless Brownian Information Engine.

PubMed

Paneru, Govind; Lee, Dong Yun; Tlusty, Tsvi; Pak, Hyuk Kyu

2018-01-12

We report on a lossless information engine that converts nearly all available information from an error-free feedback protocol into mechanical work. Combining high-precision detection at a resolution of 1 nm with ultrafast feedback control, the engine is tuned to extract the maximum work from information on the position of a Brownian particle. We show that the work produced by the engine achieves a bound set by a generalized second law of thermodynamics, demonstrating for the first time the sharpness of this bound. We validate a generalized Jarzynski equality for error-free feedback-controlled information engines.

Majorana Braiding with Thermal Noise.

PubMed

Pedrocchi, Fabio L; DiVincenzo, David P

2015-09-18

We investigate the self-correcting properties of a network of Majorana wires, in the form of a trijunction, in contact with a parity-preserving thermal environment. As opposed to the case where Majorana bound states are immobile, braiding Majorana bound states within a trijunction introduces dangerous error processes that we identify. Such errors prevent the lifetime of the memory from increasing with the size of the system. We confirm our predictions with Monte Carlo simulations. Our findings put a restriction on the degree of self-correction of this specific quantum computing architecture.

Duffing's Equation and Nonlinear Resonance

ERIC Educational Resources Information Center

Fay, Temple H.

2003-01-01

The phenomenon of nonlinear resonance (sometimes called the "jump phenomenon") is examined and second-order van der Pol plane analysis is employed to indicate that this phenomenon is not a feature of the equation, but rather the result of accumulated round-off error, truncation error and algorithm error that distorts the true bounded solution onto…

Sloppy-slotted ALOHA

NASA Technical Reports Server (NTRS)

Crozier, Stewart N.

1990-01-01

Random access signaling, which allows slotted packets to spill over into adjacent slots, is investigated. It is shown that sloppy-slotted ALOHA can always provide higher throughput than conventional slotted ALOHA. The degree of improvement depends on the timing error distribution. Throughput performance is presented for Gaussian timing error distributions, modified to include timing error corrections. A general channel capacity lower bound, independent of the specific timing error distribution, is also presented.

Bounded-Angle Iterative Decoding of LDPC Codes

NASA Technical Reports Server (NTRS)

Dolinar, Samuel; Andrews, Kenneth; Pollara, Fabrizio; Divsalar, Dariush

2009-01-01

Bounded-angle iterative decoding is a modified version of conventional iterative decoding, conceived as a means of reducing undetected-error rates for short low-density parity-check (LDPC) codes. For a given code, bounded-angle iterative decoding can be implemented by means of a simple modification of the decoder algorithm, without redesigning the code. Bounded-angle iterative decoding is based on a representation of received words and code words as vectors in an n-dimensional Euclidean space (where n is an integer).

Optimized tomography of continuous variable systems using excitation counting

NASA Astrophysics Data System (ADS)

Shen, Chao; Heeres, Reinier W.; Reinhold, Philip; Jiang, Luyao; Liu, Yi-Kai; Schoelkopf, Robert J.; Jiang, Liang

2016-11-01

We propose a systematic procedure to optimize quantum state tomography protocols for continuous variable systems based on excitation counting preceded by a displacement operation. Compared with conventional tomography based on Husimi or Wigner function measurement, the excitation counting approach can significantly reduce the number of measurement settings. We investigate both informational completeness and robustness, and provide a bound of reconstruction error involving the condition number of the sensing map. We also identify the measurement settings that optimize this error bound, and demonstrate that the improved reconstruction robustness can lead to an order-of-magnitude reduction of estimation error with given resources. This optimization procedure is general and can incorporate prior information of the unknown state to further simplify the protocol.

Insights into the Earth System mass variability from CSR-RL05 GRACE gravity fields

NASA Astrophysics Data System (ADS)

Bettadpur, S.

2012-04-01

The next-generation Release-05 GRACE gravity field data products are the result of extensive effort applied to the improvements to the GRACE Level-1 (tracking) data products, and to improvements in the background gravity models and processing methodology. As a result, the squared-error upper-bound in RL05 fields is half or less than the squared-error upper-bound in RL04 fields. The CSR-RL05 field release consists of unconstrained gravity fields as well as a regularized gravity field time-series that can be used for several applications without any post-processing error reduction. This paper will describe the background and the nature of these improvements in the data products, and provide an error characterization. We will describe the insights these new series offer in measuring the mass flux due to diverse Hydrologic, Oceanographic and Cryospheric processes.

Termination Proofs for String Rewriting Systems via Inverse Match-Bounds

NASA Technical Reports Server (NTRS)

Butler, Ricky (Technical Monitor); Geser, Alfons; Hofbauer, Dieter; Waldmann, Johannes

2004-01-01

Annotating a letter by a number, one can record information about its history during a reduction. A string rewriting system is called match-bounded if there is a global upper bound to these numbers. In earlier papers we established match-boundedness as a strong sufficient criterion for both termination and preservation of regular languages. We show now that the string rewriting system whose inverse (left and right hand sides exchanged) is match-bounded, also have exceptional properties, but slightly different ones. Inverse match-bounded systems effectively preserve context-free languages; their sets of normalized strings and their sets of immortal strings are effectively regular. These sets of strings can be used to decide the normalization, the termination and the uniform termination problems of inverse match-bounded systems. We also show that the termination problem is decidable in linear time, and that a certain strong reachability problem is deciable, thus solving two open problems of McNaughton's.

New bounding and decomposition approaches for MILP investment problems: Multi-area transmission and generation planning under policy constraints

DOE PAGES

Munoz, F. D.; Hobbs, B. F.; Watson, J. -P.

2016-02-01

A novel two-phase bounding and decomposition approach to compute optimal and near-optimal solutions to large-scale mixed-integer investment planning problems is proposed and it considers a large number of operating subproblems, each of which is a convex optimization. Our motivating application is the planning of power transmission and generation in which policy constraints are designed to incentivize high amounts of intermittent generation in electric power systems. The bounding phase exploits Jensen’s inequality to define a lower bound, which we extend to stochastic programs that use expected-value constraints to enforce policy objectives. The decomposition phase, in which the bounds are tightened, improvesmore » upon the standard Benders’ algorithm by accelerating the convergence of the bounds. The lower bound is tightened by using a Jensen’s inequality-based approach to introduce an auxiliary lower bound into the Benders master problem. Upper bounds for both phases are computed using a sub-sampling approach executed on a parallel computer system. Numerical results show that only the bounding phase is necessary if loose optimality gaps are acceptable. But, the decomposition phase is required to attain optimality gaps. Moreover, use of both phases performs better, in terms of convergence speed, than attempting to solve the problem using just the bounding phase or regular Benders decomposition separately.« less

New bounding and decomposition approaches for MILP investment problems: Multi-area transmission and generation planning under policy constraints

DOE Office of Scientific and Technical Information (OSTI.GOV)

Munoz, F. D.; Hobbs, B. F.; Watson, J. -P.

A novel two-phase bounding and decomposition approach to compute optimal and near-optimal solutions to large-scale mixed-integer investment planning problems is proposed and it considers a large number of operating subproblems, each of which is a convex optimization. Our motivating application is the planning of power transmission and generation in which policy constraints are designed to incentivize high amounts of intermittent generation in electric power systems. The bounding phase exploits Jensen’s inequality to define a lower bound, which we extend to stochastic programs that use expected-value constraints to enforce policy objectives. The decomposition phase, in which the bounds are tightened, improvesmore » upon the standard Benders’ algorithm by accelerating the convergence of the bounds. The lower bound is tightened by using a Jensen’s inequality-based approach to introduce an auxiliary lower bound into the Benders master problem. Upper bounds for both phases are computed using a sub-sampling approach executed on a parallel computer system. Numerical results show that only the bounding phase is necessary if loose optimality gaps are acceptable. But, the decomposition phase is required to attain optimality gaps. Moreover, use of both phases performs better, in terms of convergence speed, than attempting to solve the problem using just the bounding phase or regular Benders decomposition separately.« less

Thermodynamics of natural selection III: Landauer's principle in computation and chemistry.

PubMed

Smith, Eric

2008-05-21

This is the third in a series of three papers devoted to energy flow and entropy changes in chemical and biological processes, and their relations to the thermodynamics of computation. The previous two papers have developed reversible chemical transformations as idealizations for studying physiology and natural selection, and derived bounds from the second law of thermodynamics, between information gain in an ensemble and the chemical work required to produce it. This paper concerns the explicit mapping of chemistry to computation, and particularly the Landauer decomposition of irreversible computations, in which reversible logical operations generating no heat are separated from heat-generating erasure steps which are logically irreversible but thermodynamically reversible. The Landauer arrangement of computation is shown to produce the same entropy-flow diagram as that of the chemical Carnot cycles used in the second paper of the series to idealize physiological cycles. The specific application of computation to data compression and error-correcting encoding also makes possible a Landauer analysis of the somewhat different problem of optimal molecular recognition, which has been considered as an information theory problem. It is shown here that bounds on maximum sequence discrimination from the enthalpy of complex formation, although derived from the same logical model as the Shannon theorem for channel capacity, arise from exactly the opposite model for erasure.

Automatic optimal filament segmentation with sub-pixel accuracy using generalized linear models and B-spline level-sets.

PubMed

Xiao, Xun; Geyer, Veikko F; Bowne-Anderson, Hugo; Howard, Jonathon; Sbalzarini, Ivo F

2016-08-01

Biological filaments, such as actin filaments, microtubules, and cilia, are often imaged using different light-microscopy techniques. Reconstructing the filament curve from the acquired images constitutes the filament segmentation problem. Since filaments have lower dimensionality than the image itself, there is an inherent trade-off between tracing the filament with sub-pixel accuracy and avoiding noise artifacts. Here, we present a globally optimal filament segmentation method based on B-spline vector level-sets and a generalized linear model for the pixel intensity statistics. We show that the resulting optimization problem is convex and can hence be solved with global optimality. We introduce a simple and efficient algorithm to compute such optimal filament segmentations, and provide an open-source implementation as an ImageJ/Fiji plugin. We further derive an information-theoretic lower bound on the filament segmentation error, quantifying how well an algorithm could possibly do given the information in the image. We show that our algorithm asymptotically reaches this bound in the spline coefficients. We validate our method in comprehensive benchmarks, compare with other methods, and show applications from fluorescence, phase-contrast, and dark-field microscopy. Copyright © 2016 The Authors. Published by Elsevier B.V. All rights reserved.

Scalable L-infinite coding of meshes.

PubMed

Munteanu, Adrian; Cernea, Dan C; Alecu, Alin; Cornelis, Jan; Schelkens, Peter

2010-01-01

The paper investigates the novel concept of local-error control in mesh geometry encoding. In contrast to traditional mesh-coding systems that use the mean-square error as target distortion metric, this paper proposes a new L-infinite mesh-coding approach, for which the target distortion metric is the L-infinite distortion. In this context, a novel wavelet-based L-infinite-constrained coding approach for meshes is proposed, which ensures that the maximum error between the vertex positions in the original and decoded meshes is lower than a given upper bound. Furthermore, the proposed system achieves scalability in L-infinite sense, that is, any decoding of the input stream will correspond to a perfectly predictable L-infinite distortion upper bound. An instantiation of the proposed L-infinite-coding approach is demonstrated for MESHGRID, which is a scalable 3D object encoding system, part of MPEG-4 AFX. In this context, the advantages of scalable L-infinite coding over L-2-oriented coding are experimentally demonstrated. One concludes that the proposed L-infinite mesh-coding approach guarantees an upper bound on the local error in the decoded mesh, it enables a fast real-time implementation of the rate allocation, and it preserves all the scalability features and animation capabilities of the employed scalable mesh codec.

Guaranteed convergence of the Hough transform

NASA Astrophysics Data System (ADS)

Soffer, Menashe; Kiryati, Nahum

1995-01-01

The straight-line Hough Transform using normal parameterization with a continuous voting kernel is considered. It transforms the colinearity detection problem to a problem of finding the global maximum of a two dimensional function above a domain in the parameter space. The principle is similar to robust regression using fixed scale M-estimation. Unlike standard M-estimation procedures the Hough Transform does not rely on a good initial estimate of the line parameters: The global optimization problem is approached by exhaustive search on a grid that is usually as fine as computationally feasible. The global maximum of a general function above a bounded domain cannot be found by a finite number of function evaluations. Only if sufficient a-priori knowledge about the smoothness of the objective function is available, convergence to the global maximum can be guaranteed. The extraction of a-priori information and its efficient use are the main challenges in real global optimization problems. The global optimization problem in the Hough Transform is essentially how fine should the parameter space quantization be in order not to miss the true maximum. More than thirty years after Hough patented the basic algorithm, the problem is still essentially open. In this paper an attempt is made to identify a-priori information on the smoothness of the objective (Hough) function and to introduce sufficient conditions for the convergence of the Hough Transform to the global maximum. An image model with several application dependent parameters is defined. Edge point location errors as well as background noise are accounted for. Minimal parameter space quantization intervals that guarantee convergence are obtained. Focusing policies for multi-resolution Hough algorithms are developed. Theoretical support for bottom- up processing is provided. Due to the randomness of errors and noise, convergence guarantees are probabilistic.

Asymptotic Analysis Of The Total Least Squares ESPRIT Algorithm'

NASA Astrophysics Data System (ADS)

Ottersten, B. E.; Viberg, M.; Kailath, T.

1989-11-01

This paper considers the problem of estimating the parameters of multiple narrowband signals arriving at an array of sensors. Modern approaches to this problem often involve costly procedures for calculating the estimates. The ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) algorithm was recently proposed as a means for obtaining accurate estimates without requiring a costly search of the parameter space. This method utilizes an array invariance to arrive at a computationally efficient multidimensional estimation procedure. Herein, the asymptotic distribution of the estimation error is derived for the Total Least Squares (TLS) version of ESPRIT. The Cramer-Rao Bound (CRB) for the ESPRIT problem formulation is also derived and found to coincide with the variance of the asymptotic distribution through numerical examples. The method is also compared to least squares ESPRIT and MUSIC as well as to the CRB for a calibrated array. Simulations indicate that the theoretic expressions can be used to accurately predict the performance of the algorithm.

A Theoretical Analysis: Physical Unclonable Functions and The Software Protection Problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nithyanand, Rishab; Solis, John H.

2011-09-01

Physical Unclonable Functions (PUFs) or Physical One Way Functions (P-OWFs) are physical systems whose responses to input stimuli (i.e., challenges) are easy to measure (within reasonable error bounds) but hard to clone. This property of unclonability is due to the accepted hardness of replicating the multitude of uncontrollable manufacturing characteristics and makes PUFs useful in solving problems such as device authentication, software protection, licensing, and certified execution. In this paper, we focus on the effectiveness of PUFs for software protection and show that traditional non-computational (black-box) PUFs cannot solve the problem against real world adversaries in offline settings. Our contributionsmore » are the following: We provide two real world adversary models (weak and strong variants) and present definitions for security against the adversaries. We continue by proposing schemes secure against the weak adversary and show that no scheme is secure against a strong adversary without the use of trusted hardware. Finally, we present a protection scheme secure against strong adversaries based on trusted hardware.« less

L1-norm kernel discriminant analysis via Bayes error bound optimization for robust feature extraction.

PubMed

Zheng, Wenming; Lin, Zhouchen; Wang, Haixian

2014-04-01

A novel discriminant analysis criterion is derived in this paper under the theoretical framework of Bayes optimality. In contrast to the conventional Fisher's discriminant criterion, the major novelty of the proposed one is the use of L1 norm rather than L2 norm, which makes it less sensitive to the outliers. With the L1-norm discriminant criterion, we propose a new linear discriminant analysis (L1-LDA) method for linear feature extraction problem. To solve the L1-LDA optimization problem, we propose an efficient iterative algorithm, in which a novel surrogate convex function is introduced such that the optimization problem in each iteration is to simply solve a convex programming problem and a close-form solution is guaranteed to this problem. Moreover, we also generalize the L1-LDA method to deal with the nonlinear robust feature extraction problems via the use of kernel trick, and hereafter proposed the L1-norm kernel discriminant analysis (L1-KDA) method. Extensive experiments on simulated and real data sets are conducted to evaluate the effectiveness of the proposed method in comparing with the state-of-the-art methods.

High dimensional linear regression models under long memory dependence and measurement error

NASA Astrophysics Data System (ADS)

Kaul, Abhishek

This dissertation consists of three chapters. The first chapter introduces the models under consideration and motivates problems of interest. A brief literature review is also provided in this chapter. The second chapter investigates the properties of Lasso under long range dependent model errors. Lasso is a computationally efficient approach to model selection and estimation, and its properties are well studied when the regression errors are independent and identically distributed. We study the case, where the regression errors form a long memory moving average process. We establish a finite sample oracle inequality for the Lasso solution. We then show the asymptotic sign consistency in this setup. These results are established in the high dimensional setup (p> n) where p can be increasing exponentially with n. Finally, we show the consistency, n½ --d-consistency of Lasso, along with the oracle property of adaptive Lasso, in the case where p is fixed. Here d is the memory parameter of the stationary error sequence. The performance of Lasso is also analysed in the present setup with a simulation study. The third chapter proposes and investigates the properties of a penalized quantile based estimator for measurement error models. Standard formulations of prediction problems in high dimension regression models assume the availability of fully observed covariates and sub-Gaussian and homogeneous model errors. This makes these methods inapplicable to measurement errors models where covariates are unobservable and observations are possibly non sub-Gaussian and heterogeneous. We propose weighted penalized corrected quantile estimators for the regression parameter vector in linear regression models with additive measurement errors, where unobservable covariates are nonrandom. The proposed estimators forgo the need for the above mentioned model assumptions. We study these estimators in both the fixed dimension and high dimensional sparse setups, in the latter setup, the dimensionality can grow exponentially with the sample size. In the fixed dimensional setting we provide the oracle properties associated with the proposed estimators. In the high dimensional setting, we provide bounds for the statistical error associated with the estimation, that hold with asymptotic probability 1, thereby providing the ℓ1-consistency of the proposed estimator. We also establish the model selection consistency in terms of the correctly estimated zero components of the parameter vector. A simulation study that investigates the finite sample accuracy of the proposed estimator is also included in this chapter.

Galerkin v. least-squares Petrov–Galerkin projection in nonlinear model reduction

DOE PAGES

Carlberg, Kevin Thomas; Barone, Matthew F.; Antil, Harbir

2016-10-20

Least-squares Petrov–Galerkin (LSPG) model-reduction techniques such as the Gauss–Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible flow problems where standard Galerkin techniques have failed. Furthermore, there has been limited comparative analysis of the two approaches. This is due in part to difficulties arising from the fact that Galerkin techniques perform optimal projection associated with residual minimization at the time-continuous level, while LSPG techniques do so at the time-discrete level. This work provides a detailed theoretical and computational comparison of the two techniques for two common classes of timemore » integrators: linear multistep schemes and Runge–Kutta schemes. We present a number of new findings, including conditions under which the LSPG ROM has a time-continuous representation, conditions under which the two techniques are equivalent, and time-discrete error bounds for the two approaches. Perhaps most surprisingly, we demonstrate both theoretically and computationally that decreasing the time step does not necessarily decrease the error for the LSPG ROM; instead, the time step should be ‘matched’ to the spectral content of the reduced basis. In numerical experiments carried out on a turbulent compressible-flow problem with over one million unknowns, we show that increasing the time step to an intermediate value decreases both the error and the simulation time of the LSPG reduced-order model by an order of magnitude.« less

Galerkin v. least-squares Petrov–Galerkin projection in nonlinear model reduction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carlberg, Kevin Thomas; Barone, Matthew F.; Antil, Harbir

Least-squares Petrov–Galerkin (LSPG) model-reduction techniques such as the Gauss–Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible flow problems where standard Galerkin techniques have failed. Furthermore, there has been limited comparative analysis of the two approaches. This is due in part to difficulties arising from the fact that Galerkin techniques perform optimal projection associated with residual minimization at the time-continuous level, while LSPG techniques do so at the time-discrete level. This work provides a detailed theoretical and computational comparison of the two techniques for two common classes of timemore » integrators: linear multistep schemes and Runge–Kutta schemes. We present a number of new findings, including conditions under which the LSPG ROM has a time-continuous representation, conditions under which the two techniques are equivalent, and time-discrete error bounds for the two approaches. Perhaps most surprisingly, we demonstrate both theoretically and computationally that decreasing the time step does not necessarily decrease the error for the LSPG ROM; instead, the time step should be ‘matched’ to the spectral content of the reduced basis. In numerical experiments carried out on a turbulent compressible-flow problem with over one million unknowns, we show that increasing the time step to an intermediate value decreases both the error and the simulation time of the LSPG reduced-order model by an order of magnitude.« less

Reformulation of the covering and quantizer problems as ground states of interacting particles.

PubMed

Torquato, S

2010-11-01

It is known that the sphere-packing problem and the number-variance problem (closely related to an optimization problem in number theory) can be posed as energy minimizations associated with an infinite number of point particles in d-dimensional Euclidean space R(d) interacting via certain repulsive pair potentials. We reformulate the covering and quantizer problems as the determination of the ground states of interacting particles in R(d) that generally involve single-body, two-body, three-body, and higher-body interactions. This is done by linking the covering and quantizer problems to certain optimization problems involving the "void" nearest-neighbor functions that arise in the theory of random media and statistical mechanics. These reformulations, which again exemplify the deep interplay between geometry and physics, allow one now to employ theoretical and numerical optimization techniques to analyze and solve these energy minimization problems. The covering and quantizer problems have relevance in numerous applications, including wireless communication network layouts, the search of high-dimensional data parameter spaces, stereotactic radiation therapy, data compression, digital communications, meshing of space for numerical analysis, and coding and cryptography, among other examples. In the first three space dimensions, the best known solutions of the sphere-packing and number-variance problems (or their "dual" solutions) are directly related to those of the covering and quantizer problems, but such relationships may or may not exist for d≥4 , depending on the peculiarities of the dimensions involved. Our reformulation sheds light on the reasons for these similarities and differences. We also show that disordered saturated sphere packings provide relatively thin (economical) coverings and may yield thinner coverings than the best known lattice coverings in sufficiently large dimensions. In the case of the quantizer problem, we derive improved upper bounds on the quantizer error using sphere-packing solutions, which are generally substantially sharper than an existing upper bound in low to moderately large dimensions. We also demonstrate that disordered saturated sphere packings yield relatively good quantizers. Finally, we remark on possible applications of our results for the detection of gravitational waves.

Reformulation of the covering and quantizer problems as ground states of interacting particles

NASA Astrophysics Data System (ADS)

Torquato, S.

2010-11-01

It is known that the sphere-packing problem and the number-variance problem (closely related to an optimization problem in number theory) can be posed as energy minimizations associated with an infinite number of point particles in d -dimensional Euclidean space Rd interacting via certain repulsive pair potentials. We reformulate the covering and quantizer problems as the determination of the ground states of interacting particles in Rd that generally involve single-body, two-body, three-body, and higher-body interactions. This is done by linking the covering and quantizer problems to certain optimization problems involving the “void” nearest-neighbor functions that arise in the theory of random media and statistical mechanics. These reformulations, which again exemplify the deep interplay between geometry and physics, allow one now to employ theoretical and numerical optimization techniques to analyze and solve these energy minimization problems. The covering and quantizer problems have relevance in numerous applications, including wireless communication network layouts, the search of high-dimensional data parameter spaces, stereotactic radiation therapy, data compression, digital communications, meshing of space for numerical analysis, and coding and cryptography, among other examples. In the first three space dimensions, the best known solutions of the sphere-packing and number-variance problems (or their “dual” solutions) are directly related to those of the covering and quantizer problems, but such relationships may or may not exist for d≥4 , depending on the peculiarities of the dimensions involved. Our reformulation sheds light on the reasons for these similarities and differences. We also show that disordered saturated sphere packings provide relatively thin (economical) coverings and may yield thinner coverings than the best known lattice coverings in sufficiently large dimensions. In the case of the quantizer problem, we derive improved upper bounds on the quantizer error using sphere-packing solutions, which are generally substantially sharper than an existing upper bound in low to moderately large dimensions. We also demonstrate that disordered saturated sphere packings yield relatively good quantizers. Finally, we remark on possible applications of our results for the detection of gravitational waves.

Eigenvalues of the Wentzell-Laplace operator and of the fourth order Steklov problems

NASA Astrophysics Data System (ADS)

Xia, Changyu; Wang, Qiaoling

2018-05-01

We prove a sharp upper bound and a lower bound for the first nonzero eigenvalue of the Wentzell-Laplace operator on compact manifolds with boundary and an isoperimetric inequality for the same eigenvalue in the case where the manifold is a bounded domain in a Euclidean space. We study some fourth order Steklov problems and obtain isoperimetric upper bound for the first eigenvalue of them. We also find all the eigenvalues and eigenfunctions for two kind of fourth order Steklov problems on a Euclidean ball.

Quantum Optimization of Fully Connected Spin Glasses

NASA Astrophysics Data System (ADS)

Venturelli, Davide; Mandrà, Salvatore; Knysh, Sergey; O'Gorman, Bryan; Biswas, Rupak; Smelyanskiy, Vadim

2015-07-01

Many NP-hard problems can be seen as the task of finding a ground state of a disordered highly connected Ising spin glass. If solutions are sought by means of quantum annealing, it is often necessary to represent those graphs in the annealer's hardware by means of the graph-minor embedding technique, generating a final Hamiltonian consisting of coupled chains of ferromagnetically bound spins, whose binding energy is a free parameter. In order to investigate the effect of embedding on problems of interest, the fully connected Sherrington-Kirkpatrick model with random ±1 couplings is programmed on the D-Wave TwoTM annealer using up to 270 qubits interacting on a Chimera-type graph. We present the best embedding prescriptions for encoding the Sherrington-Kirkpatrick problem in the Chimera graph. The results indicate that the optimal choice of embedding parameters could be associated with the emergence of the spin-glass phase of the embedded problem, whose presence was previously uncertain. This optimal parameter setting allows the performance of the quantum annealer to compete with (and potentially outperform, in the absence of analog control errors) optimized simulated annealing algorithms.

Parallel algorithms for the molecular conformation problem

NASA Astrophysics Data System (ADS)

Rajan, Kumar

Given a set of objects, and some of the pairwise distances between them, the problem of identifying the positions of the objects in the Euclidean space is referred to as the molecular conformation problem. This problem is known to be computationally difficult. One of the most important applications of this problem is the determination of the structure of molecules. In the case of molecular structure determination, usually only the lower and upper bounds on some of the interatomic distances are available. The process of obtaining a tighter set of bounds between all pairs of atoms, using the available interatomic distance bounds is referred to as bound-smoothing . One method for bound-smoothing is to use the limits imposed by the triangle inequality. The distance bounds so obtained can often be tightened further by applying the tetrangle inequality---the limits imposed on the six pairwise distances among a set of four atoms (instead of three for the triangle inequalities). The tetrangle inequality is expressed by the Cayley-Menger determinants. The sequential tetrangle-inequality bound-smoothing algorithm considers a quadruple of atoms at a time, and tightens the bounds on each of its six distances. The sequential algorithm is computationally expensive, and its application is limited to molecules with up to a few hundred atoms. Here, we conduct an experimental study of tetrangle-inequality bound-smoothing and reduce the sequential time by identifying the most computationally expensive portions of the process. We also present a simple criterion to determine which of the quadruples of atoms are likely to be tightened the most by tetrangle-inequality bound-smoothing. This test could be used to enhance the applicability of this process to large molecules. We map the problem of parallelizing tetrangle-inequality bound-smoothing to that of generating disjoint packing designs of a certain kind. We map this, in turn, to a regular-graph coloring problem, and present a simple, parallel algorithm for tetrangle-inequality bound-smoothing. We implement the parallel algorithm on the Intel Paragon X/PS, and apply it to real-life molecules. Our results show that with this parallel algorithm, tetrangle inequality can be applied to large molecules in a reasonable amount of time. We extend the regular graph to represent more general packing designs, and present a coloring algorithm for this graph. This can be used to generate constant-weight binary codes in parallel. Once a tighter set of distance bounds is obtained, the molecular conformation problem is usually formulated as a non-linear optimization problem, and a global optimization algorithm is then used to solve the problem. Here we present a parallel, deterministic algorithm for the optimization problem based on Interval Analysis. We implement our algorithm, using dynamic load balancing, on a network of Sun Ultra-Sparc workstations. Our experience with this algorithm shows that its application is limited to small instances of the molecular conformation problem, where the number of measured, pairwise distances is close to the maximum value. However, since the interval method eliminates a substantial portion of the initial search space very quickly, it can be used to prune the search space before any of the more efficient, nondeterministic methods can be applied.

Bias estimation for moving optical sensor measurements with targets of opportunity

NASA Astrophysics Data System (ADS)

Belfadel, Djedjiga; Osborne, Richard W.; Bar-Shalom, Yaakov

2014-06-01

Integration of space based sensors into a Ballistic Missile Defense System (BMDS) allows for detection and tracking of threats over a larger area than ground based sensors [1]. This paper examines the effect of sensor bias error on the tracking quality of a Space Tracking and Surveillance System (STSS) for the highly non-linear problem of tracking a ballistic missile. The STSS constellation consists of two or more satellites (on known trajectories) for tracking ballistic targets. Each satellite is equipped with an IR sensor that provides azimuth and elevation to the target. The tracking problem is made more difficult due to a constant or slowly varying bias error present in each sensor's line of sight measurements. It is important to correct for these bias errors so that the multiple sensor measurements and/or tracks can be referenced as accurately as possible to a common tracking coordinate system. The measurements provided by these sensors are assumed time-coincident (synchronous) and perfectly associated. The line of sight (LOS) measurements from the sensors can be fused into measurements which are the Cartesian target position, i.e., linear in the target state. We evaluate the Cramér-Rao Lower Bound (CRLB) on the covariance of the bias estimates, which serves as a quantification of the available information about the biases. Statistical tests on the results of simulations show that this method is statistically efficient, even for small sample sizes (as few as two sensors and six points on the (unknown) trajectory of a single target of opportunity). We also show that the RMS position error is significantly improved with bias estimation compared with the target position estimation using the original biased measurements.

Analysis of the Bayesian Cramér-Rao lower bound in astrometry. Studying the impact of prior information in the location of an object

NASA Astrophysics Data System (ADS)

Echeverria, Alex; Silva, Jorge F.; Mendez, Rene A.; Orchard, Marcos

2016-10-01

Context. The best precision that can be achieved to estimate the location of a stellar-like object is a topic of permanent interest in the astrometric community. Aims: We analyze bounds for the best position estimation of a stellar-like object on a CCD detector array in a Bayesian setting where the position is unknown, but where we have access to a prior distribution. In contrast to a parametric setting where we estimate a parameter from observations, the Bayesian approach estimates a random object (I.e., the position is a random variable) from observations that are statistically dependent on the position. Methods: We characterize the Bayesian Cramér-Rao (CR) that bounds the minimum mean square error (MMSE) of the best estimator of the position of a point source on a linear CCD-like detector, as a function of the properties of detector, the source, and the background. Results: We quantify and analyze the increase in astrometric performance from the use of a prior distribution of the object position, which is not available in the classical parametric setting. This gain is shown to be significant for various observational regimes, in particular in the case of faint objects or when the observations are taken under poor conditions. Furthermore, we present numerical evidence that the MMSE estimator of this problem tightly achieves the Bayesian CR bound. This is a remarkable result, demonstrating that all the performance gains presented in our analysis can be achieved with the MMSE estimator. Conclusions: The Bayesian CR bound can be used as a benchmark indicator of the expected maximum positional precision of a set of astrometric measurements in which prior information can be incorporated. This bound can be achieved through the conditional mean estimator, in contrast to the parametric case where no unbiased estimator precisely reaches the CR bound.

Real-time hydraulic interval state estimation for water transport networks: a case study

NASA Astrophysics Data System (ADS)

Vrachimis, Stelios G.; Eliades, Demetrios G.; Polycarpou, Marios M.

2018-03-01

Hydraulic state estimation in water distribution networks is the task of estimating water flows and pressures in the pipes and nodes of the network based on some sensor measurements. This requires a model of the network as well as knowledge of demand outflow and tank water levels. Due to modeling and measurement uncertainty, standard state estimation may result in inaccurate hydraulic estimates without any measure of the estimation error. This paper describes a methodology for generating hydraulic state bounding estimates based on interval bounds on the parametric and measurement uncertainties. The estimation error bounds provided by this method can be applied to determine the existence of unaccounted-for water in water distribution networks. As a case study, the method is applied to a modified transport network in Cyprus, using actual data in real time.

Adaptive Output-Feedback Neural Control of Switched Uncertain Nonlinear Systems With Average Dwell Time.

PubMed

Long, Lijun; Zhao, Jun

2015-07-01

This paper investigates the problem of adaptive neural tracking control via output-feedback for a class of switched uncertain nonlinear systems without the measurements of the system states. The unknown control signals are approximated directly by neural networks. A novel adaptive neural control technique for the problem studied is set up by exploiting the average dwell time method and backstepping. A switched filter and different update laws are designed to reduce the conservativeness caused by adoption of a common observer and a common update law for all subsystems. The proposed controllers of subsystems guarantee that all closed-loop signals remain bounded under a class of switching signals with average dwell time, while the output tracking error converges to a small neighborhood of the origin. As an application of the proposed design method, adaptive output feedback neural tracking controllers for a mass-spring-damper system are constructed.

Optimisation algorithms for ECG data compression.

PubMed

Haugland, D; Heber, J G; Husøy, J H

1997-07-01

The use of exact optimisation algorithms for compressing digital electrocardiograms (ECGs) is demonstrated. As opposed to traditional time-domain methods, which use heuristics to select a small subset of representative signal samples, the problem of selecting the subset is formulated in rigorous mathematical terms. This approach makes it possible to derive algorithms guaranteeing the smallest possible reconstruction error when a bounded selection of signal samples is interpolated. The proposed model resembles well-known network models and is solved by a cubic dynamic programming algorithm. When applied to standard test problems, the algorithm produces a compressed representation for which the distortion is about one-half of that obtained by traditional time-domain compression techniques at reasonable compression ratios. This illustrates that, in terms of the accuracy of decoded signals, existing time-domain heuristics for ECG compression may be far from what is theoretically achievable. The paper is an attempt to bridge this gap.

SURBAL: computerized metes and bounds surveying

Treesearch

Roger N. Baughman; James H. Patric

1970-01-01

A computer program has been developed at West Virginia University for use in metes and bounds surveying. Stations, slope distances, slope angles, and bearings are primary information needed for this program. Other information needed may include magnetic deviation, acceptable closure error, desired map scale, and title designation. SURBAL prints out latitudes and...

Simulation techniques for estimating error in the classification of normal patterns

NASA Technical Reports Server (NTRS)

Whitsitt, S. J.; Landgrebe, D. A.

1974-01-01

Methods of efficiently generating and classifying samples with specified multivariate normal distributions were discussed. Conservative confidence tables for sample sizes are given for selective sampling. Simulation results are compared with classified training data. Techniques for comparing error and separability measure for two normal patterns are investigated and used to display the relationship between the error and the Chernoff bound.

Improved segmentation of occluded and adjoining vehicles in traffic surveillance videos

NASA Astrophysics Data System (ADS)

Juneja, Medha; Grover, Priyanka

2013-12-01

Occlusion in image processing refers to concealment of any part of the object or the whole object from view of an observer. Real time videos captured by static cameras on roads often encounter overlapping and hence, occlusion of vehicles. Occlusion in traffic surveillance videos usually occurs when an object which is being tracked is hidden by another object. This makes it difficult for the object detection algorithms to distinguish all the vehicles efficiently. Also morphological operations tend to join the close proximity vehicles resulting in formation of a single bounding box around more than one vehicle. Such problems lead to errors in further video processing, like counting of vehicles in a video. The proposed system brings forward efficient moving object detection and tracking approach to reduce such errors. The paper uses successive frame subtraction technique for detection of moving objects. Further, this paper implements the watershed algorithm to segment the overlapped and adjoining vehicles. The segmentation results have been improved by the use of noise and morphological operations.

Synchronization of multiple 3-DOF helicopters under actuator faults and saturations with prescribed performance.

PubMed

Yang, Huiliao; Jiang, Bin; Yang, Hao; Liu, Hugh H T

2018-04-01

The distributed cooperative control strategy is proposed to make the networked nonlinear 3-DOF helicopters achieve the attitude synchronization in the presence of actuator faults and saturations. Based on robust adaptive control, the proposed control method can both compensate the uncertain partial loss of control effectiveness and deal with the system uncertainties. To address actuator saturation problem, the control scheme is designed to ensure that the saturation constraint on the actuation will not be violated during the operation in spite of the actuator faults. It is shown that with the proposed control strategy, both the tracking errors of the leading helicopter and the attitude synchronization errors of each following helicopter are bounded in the existence of faulty actuators and actuator saturations. Moreover, the state responses of the entire group would not exceed the predesigned performance functions which are totally independent from the underlaying interaction topology. Simulation results illustrate the effectiveness of the proposed control scheme. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

A new accuracy measure based on bounded relative error for time series forecasting

PubMed Central

Twycross, Jamie; Garibaldi, Jonathan M.

2017-01-01

Many accuracy measures have been proposed in the past for time series forecasting comparisons. However, many of these measures suffer from one or more issues such as poor resistance to outliers and scale dependence. In this paper, while summarising commonly used accuracy measures, a special review is made on the symmetric mean absolute percentage error. Moreover, a new accuracy measure called the Unscaled Mean Bounded Relative Absolute Error (UMBRAE), which combines the best features of various alternative measures, is proposed to address the common issues of existing measures. A comparative evaluation on the proposed and related measures has been made with both synthetic and real-world data. The results indicate that the proposed measure, with user selectable benchmark, performs as well as or better than other measures on selected criteria. Though it has been commonly accepted that there is no single best accuracy measure, we suggest that UMBRAE could be a good choice to evaluate forecasting methods, especially for cases where measures based on geometric mean of relative errors, such as the geometric mean relative absolute error, are preferred. PMID:28339480

A new accuracy measure based on bounded relative error for time series forecasting.

PubMed

Chen, Chao; Twycross, Jamie; Garibaldi, Jonathan M

2017-01-01

Many accuracy measures have been proposed in the past for time series forecasting comparisons. However, many of these measures suffer from one or more issues such as poor resistance to outliers and scale dependence. In this paper, while summarising commonly used accuracy measures, a special review is made on the symmetric mean absolute percentage error. Moreover, a new accuracy measure called the Unscaled Mean Bounded Relative Absolute Error (UMBRAE), which combines the best features of various alternative measures, is proposed to address the common issues of existing measures. A comparative evaluation on the proposed and related measures has been made with both synthetic and real-world data. The results indicate that the proposed measure, with user selectable benchmark, performs as well as or better than other measures on selected criteria. Though it has been commonly accepted that there is no single best accuracy measure, we suggest that UMBRAE could be a good choice to evaluate forecasting methods, especially for cases where measures based on geometric mean of relative errors, such as the geometric mean relative absolute error, are preferred.

Evaluating the effects of modeling errors for isolated finite three-dimensional targets

NASA Astrophysics Data System (ADS)

Henn, Mark-Alexander; Barnes, Bryan M.; Zhou, Hui

2017-10-01

Optical three-dimensional (3-D) nanostructure metrology utilizes a model-based metrology approach to determine critical dimensions (CDs) that are well below the inspection wavelength. Our project at the National Institute of Standards and Technology is evaluating how to attain key CD and shape parameters from engineered in-die capable metrology targets. More specifically, the quantities of interest are determined by varying the input parameters for a physical model until the simulations agree with the actual measurements within acceptable error bounds. As in most applications, establishing a reasonable balance between model accuracy and time efficiency is a complicated task. A well-established simplification is to model the intrinsically finite 3-D nanostructures as either periodic or infinite in one direction, reducing the computationally expensive 3-D simulations to usually less complex two-dimensional (2-D) problems. Systematic errors caused by this simplified model can directly influence the fitting of the model to the measurement data and are expected to become more apparent with decreasing lengths of the structures. We identify these effects using selected simulation results and present experimental setups, e.g., illumination numerical apertures and focal ranges, that can increase the validity of the 2-D approach.

An Effective Terrain Aided Navigation for Low-Cost Autonomous Underwater Vehicles.

PubMed

Zhou, Ling; Cheng, Xianghong; Zhu, Yixian; Dai, Chenxi; Fu, Jinbo

2017-03-25

Terrain-aided navigation is a potentially powerful solution for obtaining submerged position fixes for autonomous underwater vehicles. The application of terrain-aided navigation with high-accuracy inertial navigation systems has demonstrated meter-level navigation accuracy in sea trials. However, available sensors may be limited depending on the type of the mission. Such limitations, especially for low-grade navigation sensors, not only degrade the accuracy of traditional navigation systems, but further impact the ability to successfully employ terrain-aided navigation. To address this problem, a tightly-coupled navigation is presented to successfully estimate the critical sensor errors by incorporating raw sensor data directly into an augmented navigation system. Furthermore, three-dimensional distance errors are calculated, providing measurement updates through the particle filter for absolute and bounded position error. The development of the terrain aided navigation system is elaborated for a vehicle equipped with a non-inertial-grade strapdown inertial navigation system, a 4-beam Doppler Velocity Log range sensor and a sonar altimeter. Using experimental data for navigation performance evaluation in areas with different terrain characteristics, the experiment results further show that the proposed method can be successfully applied to the low-cost AUVs and significantly improves navigation performance.

An Effective Terrain Aided Navigation for Low-Cost Autonomous Underwater Vehicles

PubMed Central

Zhou, Ling; Cheng, Xianghong; Zhu, Yixian; Dai, Chenxi; Fu, Jinbo

2017-01-01

Terrain-aided navigation is a potentially powerful solution for obtaining submerged position fixes for autonomous underwater vehicles. The application of terrain-aided navigation with high-accuracy inertial navigation systems has demonstrated meter-level navigation accuracy in sea trials. However, available sensors may be limited depending on the type of the mission. Such limitations, especially for low-grade navigation sensors, not only degrade the accuracy of traditional navigation systems, but further impact the ability to successfully employ terrain-aided navigation. To address this problem, a tightly-coupled navigation is presented to successfully estimate the critical sensor errors by incorporating raw sensor data directly into an augmented navigation system. Furthermore, three-dimensional distance errors are calculated, providing measurement updates through the particle filter for absolute and bounded position error. The development of the terrain aided navigation system is elaborated for a vehicle equipped with a non-inertial-grade strapdown inertial navigation system, a 4-beam Doppler Velocity Log range sensor and a sonar altimeter. Using experimental data for navigation performance evaluation in areas with different terrain characteristics, the experiment results further show that the proposed method can be successfully applied to the low-cost AUVs and significantly improves navigation performance. PMID:28346346

An extension of the receiver operating characteristic curve and AUC-optimal classification.

PubMed

Takenouchi, Takashi; Komori, Osamu; Eguchi, Shinto

2012-10-01

While most proposed methods for solving classification problems focus on minimization of the classification error rate, we are interested in the receiver operating characteristic (ROC) curve, which provides more information about classification performance than the error rate does. The area under the ROC curve (AUC) is a natural measure for overall assessment of a classifier based on the ROC curve. We discuss a class of concave functions for AUC maximization in which a boosting-type algorithm including RankBoost is considered, and the Bayesian risk consistency and the lower bound of the optimum function are discussed. A procedure derived by maximizing a specific optimum function has high robustness, based on gross error sensitivity. Additionally, we focus on the partial AUC, which is the partial area under the ROC curve. For example, in medical screening, a high true-positive rate to the fixed lower false-positive rate is preferable and thus the partial AUC corresponding to lower false-positive rates is much more important than the remaining AUC. We extend the class of concave optimum functions for partial AUC optimality with the boosting algorithm. We investigated the validity of the proposed method through several experiments with data sets in the UCI repository.

Distributed cooperative H∞ optimal tracking control of MIMO nonlinear multi-agent systems in strict-feedback form via adaptive dynamic programming

NASA Astrophysics Data System (ADS)

Luy, N. T.

2018-04-01

The design of distributed cooperative H∞ optimal controllers for multi-agent systems is a major challenge when the agents' models are uncertain multi-input and multi-output nonlinear systems in strict-feedback form in the presence of external disturbances. In this paper, first, the distributed cooperative H∞ optimal tracking problem is transformed into controlling the cooperative tracking error dynamics in affine form. Second, control schemes and online algorithms are proposed via adaptive dynamic programming (ADP) and the theory of zero-sum differential graphical games. The schemes use only one neural network (NN) for each agent instead of three from ADP to reduce computational complexity as well as avoid choosing initial NN weights for stabilising controllers. It is shown that despite not using knowledge of cooperative internal dynamics, the proposed algorithms not only approximate values to Nash equilibrium but also guarantee all signals, such as the NN weight approximation errors and the cooperative tracking errors in the closed-loop system, to be uniformly ultimately bounded. Finally, the effectiveness of the proposed method is shown by simulation results of an application to wheeled mobile multi-robot systems.

An analysis of spectral envelope-reduction via quadratic assignment problems

NASA Technical Reports Server (NTRS)

George, Alan; Pothen, Alex

1994-01-01

A new spectral algorithm for reordering a sparse symmetric matrix to reduce its envelope size was described. The ordering is computed by associating a Laplacian matrix with the given matrix and then sorting the components of a specified eigenvector of the Laplacian. In this paper, we provide an analysis of the spectral envelope reduction algorithm. We described related 1- and 2-sum problems; the former is related to the envelope size, while the latter is related to an upper bound on the work involved in an envelope Cholesky factorization scheme. We formulate the latter two problems as quadratic assignment problems, and then study the 2-sum problem in more detail. We obtain lower bounds on the 2-sum by considering a projected quadratic assignment problem, and then show that finding a permutation matrix closest to an orthogonal matrix attaining one of the lower bounds justifies the spectral envelope reduction algorithm. The lower bound on the 2-sum is seen to be tight for reasonably 'uniform' finite element meshes. We also obtain asymptotically tight lower bounds for the envelope size for certain classes of meshes.

Generalization Performance of Regularized Ranking With Multiscale Kernels.

PubMed

Zhou, Yicong; Chen, Hong; Lan, Rushi; Pan, Zhibin

2016-05-01

The regularized kernel method for the ranking problem has attracted increasing attentions in machine learning. The previous regularized ranking algorithms are usually based on reproducing kernel Hilbert spaces with a single kernel. In this paper, we go beyond this framework by investigating the generalization performance of the regularized ranking with multiscale kernels. A novel ranking algorithm with multiscale kernels is proposed and its representer theorem is proved. We establish the upper bound of the generalization error in terms of the complexity of hypothesis spaces. It shows that the multiscale ranking algorithm can achieve satisfactory learning rates under mild conditions. Experiments demonstrate the effectiveness of the proposed method for drug discovery and recommendation tasks.

The method of fundamental solutions for computing acoustic interior transmission eigenvalues

NASA Astrophysics Data System (ADS)

Kleefeld, Andreas; Pieronek, Lukas

2018-03-01

We analyze the method of fundamental solutions (MFS) in two different versions with focus on the computation of approximate acoustic interior transmission eigenvalues in 2D for homogeneous media. Our approach is mesh- and integration free, but suffers in general from the ill-conditioning effects of the discretized eigenoperator, which we could then successfully balance using an approved stabilization scheme. Our numerical examples cover many of the common scattering objects and prove to be very competitive in accuracy with the standard methods for PDE-related eigenvalue problems. We finally give an approximation analysis for our framework and provide error estimates, which bound interior transmission eigenvalue deviations in terms of some generalized MFS output.

QMR: A Quasi-Minimal Residual method for non-Hermitian linear systems

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Nachtigal, Noel M.

1990-01-01

The biconjugate gradient (BCG) method is the natural generalization of the classical conjugate gradient algorithm for Hermitian positive definite matrices to general non-Hermitian linear systems. Unfortunately, the original BCG algorithm is susceptible to possible breakdowns and numerical instabilities. A novel BCG like approach is presented called the quasi-minimal residual (QMR) method, which overcomes the problems of BCG. An implementation of QMR based on a look-ahead version of the nonsymmetric Lanczos algorithm is proposed. It is shown how BCG iterates can be recovered stably from the QMR process. Some further properties of the QMR approach are given and an error bound is presented. Finally, numerical experiments are reported.

Regularization by Functions of Bounded Variation and Applications to Image Enhancement

DOE Office of Scientific and Technical Information (OSTI.GOV)

Casas, E.; Kunisch, K.; Pola, C.

1999-09-15

Optimization problems regularized by bounded variation seminorms are analyzed. The optimality system is obtained and finite-dimensional approximations of bounded variation function spaces as well as of the optimization problems are studied. It is demonstrated that the choice of the vector norm in the definition of the bounded variation seminorm is of special importance for approximating subspaces consisting of piecewise constant functions. Algorithms based on a primal-dual framework that exploit the structure of these nondifferentiable optimization problems are proposed. Numerical examples are given for denoising of blocky images with very high noise.

Bounding Averages Rigorously Using Semidefinite Programming: Mean Moments of the Lorenz System

NASA Astrophysics Data System (ADS)

Goluskin, David

2018-04-01

We describe methods for proving bounds on infinite-time averages in differential dynamical systems. The methods rely on the construction of nonnegative polynomials with certain properties, similarly to the way nonlinear stability can be proved using Lyapunov functions. Nonnegativity is enforced by requiring the polynomials to be sums of squares, a condition which is then formulated as a semidefinite program (SDP) that can be solved computationally. Although such computations are subject to numerical error, we demonstrate two ways to obtain rigorous results: using interval arithmetic to control the error of an approximate SDP solution, and finding exact analytical solutions to relatively small SDPs. Previous formulations are extended to allow for bounds depending analytically on parametric variables. These methods are illustrated using the Lorenz equations, a system with three state variables ( x, y, z) and three parameters (β ,σ ,r). Bounds are reported for infinite-time averages of all eighteen moments x^ly^mz^n up to quartic degree that are symmetric under (x,y)\\mapsto (-x,-y). These bounds apply to all solutions regardless of stability, including chaotic trajectories, periodic orbits, and equilibrium points. The analytical approach yields two novel bounds that are sharp: the mean of z^3 can be no larger than its value of (r-1)^3 at the nonzero equilibria, and the mean of xy^3 must be nonnegative. The interval arithmetic approach is applied at the standard chaotic parameters to bound eleven average moments that all appear to be maximized on the shortest periodic orbit. Our best upper bound on each such average exceeds its value on the maximizing orbit by less than 1%. Many bounds reported here are much tighter than would be possible without computer assistance.

Security of a semi-quantum protocol where reflections contribute to the secret key

NASA Astrophysics Data System (ADS)

Krawec, Walter O.

2016-05-01

In this paper, we provide a proof of unconditional security for a semi-quantum key distribution protocol introduced in a previous work. This particular protocol demonstrated the possibility of using X basis states to contribute to the raw key of the two users (as opposed to using only direct measurement results) even though a semi-quantum participant cannot directly manipulate such states. In this work, we provide a complete proof of security by deriving a lower bound of the protocol's key rate in the asymptotic scenario. Using this bound, we are able to find an error threshold value such that for all error rates less than this threshold, it is guaranteed that A and B may distill a secure secret key; for error rates larger than this threshold, A and B should abort. We demonstrate that this error threshold compares favorably to several fully quantum protocols. We also comment on some interesting observations about the behavior of this protocol under certain noise scenarios.

Analysis of uncertainties and convergence of the statistical quantities in turbulent wall-bounded flows by means of a physically based criterion

NASA Astrophysics Data System (ADS)

Andrade, João Rodrigo; Martins, Ramon Silva; Thompson, Roney Leon; Mompean, Gilmar; da Silveira Neto, Aristeu

2018-04-01

The present paper provides an analysis of the statistical uncertainties associated with direct numerical simulation (DNS) results and experimental data for turbulent channel and pipe flows, showing a new physically based quantification of these errors, to improve the determination of the statistical deviations between DNSs and experiments. The analysis is carried out using a recently proposed criterion by Thompson et al. ["A methodology to evaluate statistical errors in DNS data of plane channel flows," Comput. Fluids 130, 1-7 (2016)] for fully turbulent plane channel flows, where the mean velocity error is estimated by considering the Reynolds stress tensor, and using the balance of the mean force equation. It also presents how the residual error evolves in time for a DNS of a plane channel flow, and the influence of the Reynolds number on its convergence rate. The root mean square of the residual error is shown in order to capture a single quantitative value of the error associated with the dimensionless averaging time. The evolution in time of the error norm is compared with the final error provided by DNS data of similar Reynolds numbers available in the literature. A direct consequence of this approach is that it was possible to compare different numerical results and experimental data, providing an improved understanding of the convergence of the statistical quantities in turbulent wall-bounded flows.

Statistical inference with quantum measurements: methodologies for nitrogen vacancy centers in diamond

NASA Astrophysics Data System (ADS)

Hincks, Ian; Granade, Christopher; Cory, David G.

2018-01-01

The analysis of photon count data from the standard nitrogen vacancy (NV) measurement process is treated as a statistical inference problem. This has applications toward gaining better and more rigorous error bars for tasks such as parameter estimation (e.g. magnetometry), tomography, and randomized benchmarking. We start by providing a summary of the standard phenomenological model of the NV optical process in terms of Lindblad jump operators. This model is used to derive random variables describing emitted photons during measurement, to which finite visibility, dark counts, and imperfect state preparation are added. NV spin-state measurement is then stated as an abstract statistical inference problem consisting of an underlying biased coin obstructed by three Poisson rates. Relevant frequentist and Bayesian estimators are provided, discussed, and quantitatively compared. We show numerically that the risk of the maximum likelihood estimator is well approximated by the Cramér-Rao bound, for which we provide a simple formula. Of the estimators, we in particular promote the Bayes estimator, owing to its slightly better risk performance, and straightforward error propagation into more complex experiments. This is illustrated on experimental data, where quantum Hamiltonian learning is performed and cross-validated in a fully Bayesian setting, and compared to a more traditional weighted least squares fit.

Face recognition using total margin-based adaptive fuzzy support vector machines.

PubMed

Liu, Yi-Hung; Chen, Yen-Ting

2007-01-01

This paper presents a new classifier called total margin-based adaptive fuzzy support vector machines (TAF-SVM) that deals with several problems that may occur in support vector machines (SVMs) when applied to the face recognition. The proposed TAF-SVM not only solves the overfitting problem resulted from the outlier with the approach of fuzzification of the penalty, but also corrects the skew of the optimal separating hyperplane due to the very imbalanced data sets by using different cost algorithm. In addition, by introducing the total margin algorithm to replace the conventional soft margin algorithm, a lower generalization error bound can be obtained. Those three functions are embodied into the traditional SVM so that the TAF-SVM is proposed and reformulated in both linear and nonlinear cases. By using two databases, the Chung Yuan Christian University (CYCU) multiview and the facial recognition technology (FERET) face databases, and using the kernel Fisher's discriminant analysis (KFDA) algorithm to extract discriminating face features, experimental results show that the proposed TAF-SVM is superior to SVM in terms of the face-recognition accuracy. The results also indicate that the proposed TAF-SVM can achieve smaller error variances than SVM over a number of tests such that better recognition stability can be obtained.

A tight Cramér-Rao bound for joint parameter estimation with a pure two-mode squeezed probe

NASA Astrophysics Data System (ADS)

Bradshaw, Mark; Assad, Syed M.; Lam, Ping Koy

2017-08-01

We calculate the Holevo Cramér-Rao bound for estimation of the displacement experienced by one mode of an two-mode squeezed vacuum state with squeezing r and find that it is equal to 4 exp ⁡ (- 2 r). This equals the sum of the mean squared error obtained from a dual homodyne measurement, indicating that the bound is tight and that the dual homodyne measurement is optimal.

A Posteriori Finite Element Bounds for Sensitivity Derivatives of Partial-Differential-Equation Outputs. Revised

NASA Technical Reports Server (NTRS)

Lewis, Robert Michael; Patera, Anthony T.; Peraire, Jaume

1998-01-01

We present a Neumann-subproblem a posteriori finite element procedure for the efficient and accurate calculation of rigorous, 'constant-free' upper and lower bounds for sensitivity derivatives of functionals of the solutions of partial differential equations. The design motivation for sensitivity derivative error control is discussed; the a posteriori finite element procedure is described; the asymptotic bounding properties and computational complexity of the method are summarized; and illustrative numerical results are presented.

Critical bounds on noise and SNR for robust estimation of real-time brain activity from functional near infra-red spectroscopy.

PubMed

Aqil, Muhammad; Jeong, Myung Yung

2018-04-24

The robust characterization of real-time brain activity carries potential for many applications. However, the contamination of measured signals by various instrumental, environmental, and physiological sources of noise introduces a substantial amount of signal variance and, consequently, challenges real-time estimation of contributions from underlying neuronal sources. Functional near infra-red spectroscopy (fNIRS) is an emerging imaging modality whose real-time potential is yet to be fully explored. The objectives of the current study are to (i) validate a time-dependent linear model of hemodynamic responses in fNIRS, and (ii) test the robustness of this approach against measurement noise (instrumental and physiological) and mis-specification of the hemodynamic response basis functions (amplitude, latency, and duration). We propose a linear hemodynamic model with time-varying parameters, which are estimated (adapted and tracked) using a dynamic recursive least square algorithm. Owing to the linear nature of the activation model, the problem of achieving robust convergence to an accurate estimation of the model parameters is recast as a problem of parameter error stability around the origin. We show that robust convergence of the proposed method is guaranteed in the presence of an acceptable degree of model misspecification and we derive an upper bound on noise under which reliable parameters can still be inferred. We also derived a lower bound on signal-to-noise-ratio over which the reliable parameters can still be inferred from a channel/voxel. Whilst here applied to fNIRS, the proposed methodology is applicable to other hemodynamic-based imaging technologies such as functional magnetic resonance imaging. Copyright © 2018 Elsevier Inc. All rights reserved.

Solving Open Job-Shop Scheduling Problems by SAT Encoding

NASA Astrophysics Data System (ADS)

Koshimura, Miyuki; Nabeshima, Hidetomo; Fujita, Hiroshi; Hasegawa, Ryuzo

This paper tries to solve open Job-Shop Scheduling Problems (JSSP) by translating them into Boolean Satisfiability Testing Problems (SAT). The encoding method is essentially the same as the one proposed by Crawford and Baker. The open problems are ABZ8, ABZ9, YN1, YN2, YN3, and YN4. We proved that the best known upper bounds 678 of ABZ9 and 884 of YN1 are indeed optimal. We also improved the upper bound of YN2 and lower bounds of ABZ8, YN2, YN3 and YN4.

Local Improvement Results for Anderson Acceleration with Inaccurate Function Evaluations

DOE PAGES

Toth, Alex; Ellis, J. Austin; Evans, Tom; ...

2017-10-26

Here, we analyze the convergence of Anderson acceleration when the fixed point map is corrupted with errors. We also consider uniformly bounded errors and stochastic errors with infinite tails. We prove local improvement results which describe the performance of the iteration up to the point where the accuracy of the function evaluation causes the iteration to stagnate. We illustrate the results with examples from neutronics.

Local Improvement Results for Anderson Acceleration with Inaccurate Function Evaluations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Toth, Alex; Ellis, J. Austin; Evans, Tom

Here, we analyze the convergence of Anderson acceleration when the fixed point map is corrupted with errors. We also consider uniformly bounded errors and stochastic errors with infinite tails. We prove local improvement results which describe the performance of the iteration up to the point where the accuracy of the function evaluation causes the iteration to stagnate. We illustrate the results with examples from neutronics.

Percolation bounds for decoding thresholds with correlated erasures in quantum LDPC codes

NASA Astrophysics Data System (ADS)

Hamilton, Kathleen; Pryadko, Leonid

Correlations between errors can dramatically affect decoding thresholds, in some cases eliminating the threshold altogether. We analyze the existence of a threshold for quantum low-density parity-check (LDPC) codes in the case of correlated erasures. When erasures are positively correlated, the corresponding multi-variate Bernoulli distribution can be modeled in terms of cluster errors, where qubits in clusters of various size can be marked all at once. In a code family with distance scaling as a power law of the code length, erasures can be always corrected below percolation on a qubit adjacency graph associated with the code. We bound this correlated percolation transition by weighted (uncorrelated) percolation on a specially constructed cluster connectivity graph, and apply our recent results to construct several bounds for the latter. This research was supported in part by the NSF Grant PHY-1416578 and by the ARO Grant W911NF-14-1-0272.

Hardware-efficient bosonic quantum error-correcting codes based on symmetry operators

NASA Astrophysics Data System (ADS)

Niu, Murphy Yuezhen; Chuang, Isaac L.; Shapiro, Jeffrey H.

2018-03-01

We establish a symmetry-operator framework for designing quantum error-correcting (QEC) codes based on fundamental properties of the underlying system dynamics. Based on this framework, we propose three hardware-efficient bosonic QEC codes that are suitable for χ(2 )-interaction based quantum computation in multimode Fock bases: the χ(2 ) parity-check code, the χ(2 ) embedded error-correcting code, and the χ(2 ) binomial code. All of these QEC codes detect photon-loss or photon-gain errors by means of photon-number parity measurements, and then correct them via χ(2 ) Hamiltonian evolutions and linear-optics transformations. Our symmetry-operator framework provides a systematic procedure for finding QEC codes that are not stabilizer codes, and it enables convenient extension of a given encoding to higher-dimensional qudit bases. The χ(2 ) binomial code is of special interest because, with m ≤N identified from channel monitoring, it can correct m -photon-loss errors, or m -photon-gain errors, or (m -1 )th -order dephasing errors using logical qudits that are encoded in O (N ) photons. In comparison, other bosonic QEC codes require O (N2) photons to correct the same degree of bosonic errors. Such improved photon efficiency underscores the additional error-correction power that can be provided by channel monitoring. We develop quantum Hamming bounds for photon-loss errors in the code subspaces associated with the χ(2 ) parity-check code and the χ(2 ) embedded error-correcting code, and we prove that these codes saturate their respective bounds. Our χ(2 ) QEC codes exhibit hardware efficiency in that they address the principal error mechanisms and exploit the available physical interactions of the underlying hardware, thus reducing the physical resources required for implementing their encoding, decoding, and error-correction operations, and their universal encoded-basis gate sets.

Certified dual-corrected radiation patterns of phased antenna arrays by offline–online order reduction of finite-element models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sommer, A., E-mail: a.sommer@lte.uni-saarland.de; Farle, O., E-mail: o.farle@lte.uni-saarland.de; Dyczij-Edlinger, R., E-mail: edlinger@lte.uni-saarland.de

2015-10-15

This paper presents a fast numerical method for computing certified far-field patterns of phased antenna arrays over broad frequency bands as well as wide ranges of steering and look angles. The proposed scheme combines finite-element analysis, dual-corrected model-order reduction, and empirical interpolation. To assure the reliability of the results, improved a posteriori error bounds for the radiated power and directive gain are derived. Both the reduced-order model and the error-bounds algorithm feature offline–online decomposition. A real-world example is provided to demonstrate the efficiency and accuracy of the suggested approach.

A new learning strategy for the two-time-scale neural controller with its application to the tracking control of rigid arms

NASA Technical Reports Server (NTRS)

Cheng, W.; Wen, J. T.

1992-01-01

A novel fast learning rule with fast weight identification is proposed for the two-time-scale neural controller, and a two-stage learning strategy is developed for the proposed neural controller. The results of the stability analysis show that both the tracking error and the fast weight error will be uniformly bounded and converge to a bounded region which depends only on the accuracy of the slow learning if the system is sufficiently excited. The efficiency of the two-stage learning is also demonstrated by a simulation of a two-link arm.

Noncommuting observables in quantum detection and estimation theory

NASA Technical Reports Server (NTRS)

Helstrom, C. W.

1972-01-01

Basing decisions and estimates on simultaneous approximate measurements of noncommuting observables in a quantum receiver is shown to be equivalent to measuring commuting projection operators on a larger Hilbert space than that of the receiver itself. The quantum-mechanical Cramer-Rao inequalities derived from right logarithmic derivatives and symmetrized logarithmic derivatives of the density operator are compared, and it is shown that the latter give superior lower bounds on the error variances of individual unbiased estimates of arrival time and carrier frequency of a coherent signal. For a suitably weighted sum of the error variances of simultaneous estimates of these, the former yield the superior lower bound under some conditions.

An Algorithm for the Weighted Earliness-Tardiness Unconstrained Project Scheduling Problem

NASA Astrophysics Data System (ADS)

Afshar Nadjafi, Behrouz; Shadrokh, Shahram

This research considers a project scheduling problem with the object of minimizing weighted earliness-tardiness penalty costs, taking into account a deadline for the project and precedence relations among the activities. An exact recursive method has been proposed for solving the basic form of this problem. We present a new depth-first branch and bound algorithm for extended form of the problem, which time value of money is taken into account by discounting the cash flows. The algorithm is extended with two bounding rules in order to reduce the size of the branch and bound tree. Finally, some test problems are solved and computational results are reported.

Intelligent robust tracking control for a class of uncertain strict-feedback nonlinear systems.

PubMed

Chang, Yeong-Chan

2009-02-01

This paper addresses the problem of designing robust tracking controls for a large class of strict-feedback nonlinear systems involving plant uncertainties and external disturbances. The input and virtual input weighting matrices are perturbed by bounded time-varying uncertainties. An adaptive fuzzy-based (or neural-network-based) dynamic feedback tracking controller will be developed such that all the states and signals of the closed-loop system are bounded and the trajectory tracking error should be as small as possible. First, the adaptive approximators with linearly parameterized models are designed, and a partitioned procedure with respect to the developed adaptive approximators is proposed such that the implementation of the fuzzy (or neural network) basis functions depends only on the state variables but does not depend on the tuning approximation parameters. Furthermore, we extend to design the nonlinearly parameterized adaptive approximators. Consequently, the intelligent robust tracking control schemes developed in this paper possess the properties of computational simplicity and easy implementation. Finally, simulation examples are presented to demonstrate the effectiveness of the proposed control algorithms.

Derivative-free generation and interpolation of convex Pareto optimal IMRT plans

NASA Astrophysics Data System (ADS)

Hoffmann, Aswin L.; Siem, Alex Y. D.; den Hertog, Dick; Kaanders, Johannes H. A. M.; Huizenga, Henk

2006-12-01

In inverse treatment planning for intensity-modulated radiation therapy (IMRT), beamlet intensity levels in fluence maps of high-energy photon beams are optimized. Treatment plan evaluation criteria are used as objective functions to steer the optimization process. Fluence map optimization can be considered a multi-objective optimization problem, for which a set of Pareto optimal solutions exists: the Pareto efficient frontier (PEF). In this paper, a constrained optimization method is pursued to iteratively estimate the PEF up to some predefined error. We use the property that the PEF is convex for a convex optimization problem to construct piecewise-linear upper and lower bounds to approximate the PEF from a small initial set of Pareto optimal plans. A derivative-free Sandwich algorithm is presented in which these bounds are used with three strategies to determine the location of the next Pareto optimal solution such that the uncertainty in the estimated PEF is maximally reduced. We show that an intelligent initial solution for a new Pareto optimal plan can be obtained by interpolation of fluence maps from neighbouring Pareto optimal plans. The method has been applied to a simplified clinical test case using two convex objective functions to map the trade-off between tumour dose heterogeneity and critical organ sparing. All three strategies produce representative estimates of the PEF. The new algorithm is particularly suitable for dynamic generation of Pareto optimal plans in interactive treatment planning.

High order local absorbing boundary conditions for acoustic waves in terms of farfield expansions

NASA Astrophysics Data System (ADS)

Villamizar, Vianey; Acosta, Sebastian; Dastrup, Blake

2017-03-01

We devise a new high order local absorbing boundary condition (ABC) for radiating problems and scattering of time-harmonic acoustic waves from obstacles of arbitrary shape. By introducing an artificial boundary S enclosing the scatterer, the original unbounded domain Ω is decomposed into a bounded computational domain Ω- and an exterior unbounded domain Ω+. Then, we define interface conditions at the artificial boundary S, from truncated versions of the well-known Wilcox and Karp farfield expansion representations of the exact solution in the exterior region Ω+. As a result, we obtain a new local absorbing boundary condition (ABC) for a bounded problem on Ω-, which effectively accounts for the outgoing behavior of the scattered field. Contrary to the low order absorbing conditions previously defined, the error at the artificial boundary induced by this novel ABC can be easily reduced to reach any accuracy within the limits of the computational resources. We accomplish this by simply adding as many terms as needed to the truncated farfield expansions of Wilcox or Karp. The convergence of these expansions guarantees that the order of approximation of the new ABC can be increased arbitrarily without having to enlarge the radius of the artificial boundary. We include numerical results in two and three dimensions which demonstrate the improved accuracy and simplicity of this new formulation when compared to other absorbing boundary conditions.

An extended Reed Solomon decoder design

NASA Technical Reports Server (NTRS)

Chen, J.; Owsley, P.; Purviance, J.

1991-01-01

It has previously been shown that the Reed-Solomon (RS) codes can correct errors beyond the Singleton and Rieger Bounds with an arbitrarily small probability of a miscorrect. That is, an (n,k) RS code can correct more than (n-k)/2 errors. An implementation of such an RS decoder is presented in this paper. An existing RS decoder, the AHA4010, is utilized in this work. This decoder is especially useful for errors which are patterned with a long burst plus some random errors.

New Mathematical Strategy Using Branch and Bound Method

NASA Astrophysics Data System (ADS)

Tarray, Tanveer Ahmad; Bhat, Muzafar Rasool

In this paper, the problem of optimal allocation in stratified random sampling is used in the presence of nonresponse. The problem is formulated as a nonlinear programming problem (NLPP) and is solved using Branch and Bound method. Also the results are formulated through LINGO.

Design framework for spherical microphone and loudspeaker arrays in a multiple-input multiple-output system.

PubMed

Morgenstern, Hai; Rafaely, Boaz; Noisternig, Markus

2017-03-01

Spherical microphone arrays (SMAs) and spherical loudspeaker arrays (SLAs) facilitate the study of room acoustics due to the three-dimensional analysis they provide. More recently, systems that combine both arrays, referred to as multiple-input multiple-output (MIMO) systems, have been proposed due to the added spatial diversity they facilitate. The literature provides frameworks for designing SMAs and SLAs separately, including error analysis from which the operating frequency range (OFR) of an array is defined. However, such a framework does not exist for the joint design of a SMA and a SLA that comprise a MIMO system. This paper develops a design framework for MIMO systems based on a model that addresses errors and highlights the importance of a matched design. Expanding on a free-field assumption, errors are incorporated separately for each array and error bounds are defined, facilitating error analysis for the system. The dependency of the error bounds on the SLA and SMA parameters is studied and it is recommended that parameters should be chosen to assure matched OFRs of the arrays in MIMO system design. A design example is provided, demonstrating the superiority of a matched system over an unmatched system in the synthesis of directional room impulse responses.

Choosing the Number of Clusters in K-Means Clustering

ERIC Educational Resources Information Center

Steinley, Douglas; Brusco, Michael J.

2011-01-01

Steinley (2007) provided a lower bound for the sum-of-squares error criterion function used in K-means clustering. In this article, on the basis of the lower bound, the authors propose a method to distinguish between 1 cluster (i.e., a single distribution) versus more than 1 cluster. Additionally, conditional on indicating there are multiple…

Error analysis of mathematical problems on TIMSS: A case of Indonesian secondary students

NASA Astrophysics Data System (ADS)

Priyani, H. A.; Ekawati, R.

2018-01-01

Indonesian students’ competence in solving mathematical problems is still considered as weak. It was pointed out by the results of international assessment such as TIMSS. This might be caused by various types of errors made. Hence, this study aimed at identifying students’ errors in solving mathematical problems in TIMSS in the topic of numbers that considered as the fundamental concept in Mathematics. This study applied descriptive qualitative analysis. The subject was three students with most errors in the test indicators who were taken from 34 students of 8th graders. Data was obtained through paper and pencil test and student’s’ interview. The error analysis indicated that in solving Applying level problem, the type of error that students made was operational errors. In addition, for reasoning level problem, there are three types of errors made such as conceptual errors, operational errors and principal errors. Meanwhile, analysis of the causes of students’ errors showed that students did not comprehend the mathematical problems given.

Optimal joint measurements of complementary observables by a single trapped ion

NASA Astrophysics Data System (ADS)

Xiong, T. P.; Yan, L. L.; Ma, Z. H.; Zhou, F.; Chen, L.; Yang, W. L.; Feng, M.; Busch, P.

2017-06-01

The uncertainty relations, pioneered by Werner Heisenberg nearly 90 years ago, set a fundamental limitation on the joint measurability of complementary observables. This limitation has long been a subject of debate, which has been reignited recently due to new proposed forms of measurement uncertainty relations. The present work is associated with a new error trade-off relation for compatible observables approximating two incompatible observables, in keeping with the spirit of Heisenberg’s original ideas of 1927. We report the first direct test and confirmation of the tight bounds prescribed by such an error trade-off relation, based on an experimental realisation of optimal joint measurements of complementary observables using a single ultracold {}40{{{Ca}}}+ ion trapped in a harmonic potential. Our work provides a prototypical determination of ultimate joint measurement error bounds with potential applications in quantum information science for high-precision measurement and information security.

On the performance evaluation of LQAM-MPPM techniques over exponentiated Weibull fading free-space optical channels

NASA Astrophysics Data System (ADS)

Khallaf, Haitham S.; Elfiqi, Abdulaziz E.; Shalaby, Hossam M. H.; Sampei, Seiichi; Obayya, Salah S. A.

2018-06-01

We investigate the performance of hybrid L-ary quadrature-amplitude modulation-multi-pulse pulse-position modulation (LQAM-MPPM) techniques over exponentiated Weibull (EW) fading free-space optical (FSO) channel, considering both weather and pointing-error effects. Upper bound and approximate-tight upper bound expressions for the bit-error rate (BER) of LQAM-MPPM techniques over EW FSO channels are obtained, taking into account the effects of fog, beam divergence, and pointing-error. Setup block diagram for both the transmitter and receiver of the LQAM-MPPM/FSO system are introduced and illustrated. The BER expressions are evaluated numerically and the results reveal that LQAM-MPPM technique outperforms ordinary LQAM and MPPM schemes under different fading levels and weather conditions. Furthermore, the effect of modulation-index is investigated and it turned out that a modulation-index greater than 0.4 is required in order to optimize the system performance. Finally, the effect of pointing-error introduces a great power penalty on the LQAM-MPPM system performance. Specifically, at a BER of 10-9, pointing-error introduces power penalties of about 45 and 28 dB for receiver aperture sizes of DR = 50 and 200 mm, respectively.

Measurement uncertainty relations: characterising optimal error bounds for qubits

NASA Astrophysics Data System (ADS)

Bullock, T.; Busch, P.

2018-07-01

In standard formulations of the uncertainty principle, two fundamental features are typically cast as impossibility statements: two noncommuting observables cannot in general both be sharply defined (for the same state), nor can they be measured jointly. The pioneers of quantum mechanics were acutely aware and puzzled by this fact, and it motivated Heisenberg to seek a mitigation, which he formulated in his seminal paper of 1927. He provided intuitive arguments to show that the values of, say, the position and momentum of a particle can at least be unsharply defined, and they can be measured together provided some approximation errors are allowed. Only now, nine decades later, a working theory of approximate joint measurements is taking shape, leading to rigorous and experimentally testable formulations of associated error tradeoff relations. Here we briefly review this new development, explaining the concepts and steps taken in the construction of optimal joint approximations of pairs of incompatible observables. As a case study, we deduce measurement uncertainty relations for qubit observables using two distinct error measures. We provide an operational interpretation of the error bounds and discuss some of the first experimental tests of such relations.

Set membership experimental design for biological systems.

PubMed

Marvel, Skylar W; Williams, Cranos M

2012-03-21

Experimental design approaches for biological systems are needed to help conserve the limited resources that are allocated for performing experiments. The assumptions used when assigning probability density functions to characterize uncertainty in biological systems are unwarranted when only a small number of measurements can be obtained. In these situations, the uncertainty in biological systems is more appropriately characterized in a bounded-error context. Additionally, effort must be made to improve the connection between modelers and experimentalists by relating design metrics to biologically relevant information. Bounded-error experimental design approaches that can assess the impact of additional measurements on model uncertainty are needed to identify the most appropriate balance between the collection of data and the availability of resources. In this work we develop a bounded-error experimental design framework for nonlinear continuous-time systems when few data measurements are available. This approach leverages many of the recent advances in bounded-error parameter and state estimation methods that use interval analysis to generate parameter sets and state bounds consistent with uncertain data measurements. We devise a novel approach using set-based uncertainty propagation to estimate measurement ranges at candidate time points. We then use these estimated measurements at the candidate time points to evaluate which candidate measurements furthest reduce model uncertainty. A method for quickly combining multiple candidate time points is presented and allows for determining the effect of adding multiple measurements. Biologically relevant metrics are developed and used to predict when new data measurements should be acquired, which system components should be measured and how many additional measurements should be obtained. The practicability of our approach is illustrated with a case study. This study shows that our approach is able to 1) identify candidate measurement time points that maximize information corresponding to biologically relevant metrics and 2) determine the number at which additional measurements begin to provide insignificant information. This framework can be used to balance the availability of resources with the addition of one or more measurement time points to improve the predictability of resulting models.

Set membership experimental design for biological systems

PubMed Central

2012-01-01

Background Experimental design approaches for biological systems are needed to help conserve the limited resources that are allocated for performing experiments. The assumptions used when assigning probability density functions to characterize uncertainty in biological systems are unwarranted when only a small number of measurements can be obtained. In these situations, the uncertainty in biological systems is more appropriately characterized in a bounded-error context. Additionally, effort must be made to improve the connection between modelers and experimentalists by relating design metrics to biologically relevant information. Bounded-error experimental design approaches that can assess the impact of additional measurements on model uncertainty are needed to identify the most appropriate balance between the collection of data and the availability of resources. Results In this work we develop a bounded-error experimental design framework for nonlinear continuous-time systems when few data measurements are available. This approach leverages many of the recent advances in bounded-error parameter and state estimation methods that use interval analysis to generate parameter sets and state bounds consistent with uncertain data measurements. We devise a novel approach using set-based uncertainty propagation to estimate measurement ranges at candidate time points. We then use these estimated measurements at the candidate time points to evaluate which candidate measurements furthest reduce model uncertainty. A method for quickly combining multiple candidate time points is presented and allows for determining the effect of adding multiple measurements. Biologically relevant metrics are developed and used to predict when new data measurements should be acquired, which system components should be measured and how many additional measurements should be obtained. Conclusions The practicability of our approach is illustrated with a case study. This study shows that our approach is able to 1) identify candidate measurement time points that maximize information corresponding to biologically relevant metrics and 2) determine the number at which additional measurements begin to provide insignificant information. This framework can be used to balance the availability of resources with the addition of one or more measurement time points to improve the predictability of resulting models. PMID:22436240

The Aharonov-Bohm effect and Tonomura et al. experiments: Rigorous results

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ballesteros, Miguel; Weder, Ricardo

The Aharonov-Bohm effect is a fundamental issue in physics. It describes the physically important electromagnetic quantities in quantum mechanics. Its experimental verification constitutes a test of the theory of quantum mechanics itself. The remarkable experiments of Tonomura et al. ['Observation of Aharonov-Bohm effect by electron holography', Phys. Rev. Lett 48, 1443 (1982) and 'Evidence for Aharonov-Bohm effect with magnetic field completely shielded from electron wave', Phys. Rev. Lett 56, 792 (1986)] are widely considered as the only experimental evidence of the physical existence of the Aharonov-Bohm effect. Here we give the first rigorous proof that the classical ansatz of Aharonovmore » and Bohm of 1959 ['Significance of electromagnetic potentials in the quantum theory', Phys. Rev. 115, 485 (1959)], that was tested by Tonomura et al., is a good approximation to the exact solution to the Schroedinger equation. This also proves that the electron, that is, represented by the exact solution, is not accelerated, in agreement with the recent experiment of Caprez et al. in 2007 ['Macroscopic test of the Aharonov-Bohm effect', Phys. Rev. Lett. 99, 210401 (2007)], that shows that the results of the Tonomura et al. experiments can not be explained by the action of a force. Under the assumption that the incoming free electron is a Gaussian wave packet, we estimate the exact solution to the Schroedinger equation for all times. We provide a rigorous, quantitative error bound for the difference in norm between the exact solution and the Aharonov-Bohm Ansatz. Our bound is uniform in time. We also prove that on the Gaussian asymptotic state the scattering operator is given by a constant phase shift, up to a quantitative error bound that we provide. Our results show that for intermediate size electron wave packets, smaller than the ones used in the Tonomura et al. experiments, quantum mechanics predicts the results observed by Tonomura et al. with an error bound smaller than 10{sup -99}. It would be quite interesting to perform experiments with electron wave packets of intermediate size. Furthermore, we provide a physical interpretation of our error bound.« less

Communication complexity and information complexity

NASA Astrophysics Data System (ADS)

Pankratov, Denis

Information complexity enables the use of information-theoretic tools in communication complexity theory. Prior to the results presented in this thesis, information complexity was mainly used for proving lower bounds and direct-sum theorems in the setting of communication complexity. We present three results that demonstrate new connections between information complexity and communication complexity. In the first contribution we thoroughly study the information complexity of the smallest nontrivial two-party function: the AND function. While computing the communication complexity of AND is trivial, computing its exact information complexity presents a major technical challenge. In overcoming this challenge, we reveal that information complexity gives rise to rich geometrical structures. Our analysis of information complexity relies on new analytic techniques and new characterizations of communication protocols. We also uncover a connection of information complexity to the theory of elliptic partial differential equations. Once we compute the exact information complexity of AND, we can compute exact communication complexity of several related functions on n-bit inputs with some additional technical work. Previous combinatorial and algebraic techniques could only prove bounds of the form theta( n). Interestingly, this level of precision is typical in the area of information theory, so our result demonstrates that this meta-property of precise bounds carries over to information complexity and in certain cases even to communication complexity. Our result does not only strengthen the lower bound on communication complexity of disjointness by making it more exact, but it also shows that information complexity provides the exact upper bound on communication complexity. In fact, this result is more general and applies to a whole class of communication problems. In the second contribution, we use self-reduction methods to prove strong lower bounds on the information complexity of two of the most studied functions in the communication complexity literature: Gap Hamming Distance (GHD) and Inner Product mod 2 (IP). In our first result we affirm the conjecture that the information complexity of GHD is linear even under the uniform distribution. This strengthens the O(n) bound shown by Kerenidis et al. (2012) and answers an open problem by Chakrabarti et al. (2012). We also prove that the information complexity of IP is arbitrarily close to the trivial upper bound n as the permitted error tends to zero, again strengthening the O(n) lower bound proved by Braverman and Weinstein (2011). More importantly, our proofs demonstrate that self-reducibility makes the connection between information complexity and communication complexity lower bounds a two-way connection. Whereas numerous results in the past used information complexity techniques to derive new communication complexity lower bounds, we explore a generic way, in which communication complexity lower bounds imply information complexity lower bounds in a black-box manner. In the third contribution we consider the roles that private and public randomness play in the definition of information complexity. In communication complexity, private randomness can be trivially simulated by public randomness. Moreover, the communication cost of simulating public randomness with private randomness is well understood due to Newman's theorem (1991). In information complexity, the roles of public and private randomness are reversed: public randomness can be trivially simulated by private randomness. However, the information cost of simulating private randomness with public randomness is not understood. We show that protocols that use only public randomness admit a rather strong compression. In particular, efficient simulation of private randomness by public randomness would imply a version of a direct sum theorem in the setting of communication complexity. This establishes a yet another connection between the two areas. (Abstract shortened by UMI.).

Bounds on complex polarizabilities and a new perspective on scattering by a lossy inclusion

NASA Astrophysics Data System (ADS)

Milton, Graeme W.

2017-09-01

Here, we obtain explicit formulas for bounds on the complex electrical polarizability at a given frequency of an inclusion with known volume that follow directly from the quasistatic bounds of Bergman and Milton on the effective complex dielectric constant of a two-phase medium. We also describe how analogous bounds on the orientationally averaged bulk and shear polarizabilities at a given frequency can be obtained from bounds on the effective complex bulk and shear moduli of a two-phase medium obtained by Milton, Gibiansky, and Berryman, using the quasistatic variational principles of Cherkaev and Gibiansky. We also show how the polarizability problem and the acoustic scattering problem can both be reformulated in an abstract setting as "Y problems." In the acoustic scattering context, to avoid explicit introduction of the Sommerfeld radiation condition, we introduce auxiliary fields at infinity and an appropriate "constitutive law" there, which forces the Sommerfeld radiation condition to hold. As a consequence, we obtain minimization variational principles for acoustic scattering that can be used to obtain bounds on the complex backwards scattering amplitude. Some explicit elementary bounds are given.

The optimal modified variational iteration method for the Lane-Emden equations with Neumann and Robin boundary conditions

NASA Astrophysics Data System (ADS)

Singh, Randhir; Das, Nilima; Kumar, Jitendra

2017-06-01

An effective analytical technique is proposed for the solution of the Lane-Emden equations. The proposed technique is based on the variational iteration method (VIM) and the convergence control parameter h . In order to avoid solving a sequence of nonlinear algebraic or complicated integrals for the derivation of unknown constant, the boundary conditions are used before designing the recursive scheme for solution. The series solutions are found which converges rapidly to the exact solution. Convergence analysis and error bounds are discussed. Accuracy, applicability of the method is examined by solving three singular problems: i) nonlinear Poisson-Boltzmann equation, ii) distribution of heat sources in the human head, iii) second-kind Lane-Emden equation.

Fast state estimation subject to random data loss in discrete-time nonlinear stochastic systems

NASA Astrophysics Data System (ADS)

Mahdi Alavi, S. M.; Saif, Mehrdad

2013-12-01

This paper focuses on the design of the standard observer in discrete-time nonlinear stochastic systems subject to random data loss. By the assumption that the system response is incrementally bounded, two sufficient conditions are subsequently derived that guarantee exponential mean-square stability and fast convergence of the estimation error for the problem at hand. An efficient algorithm is also presented to obtain the observer gain. Finally, the proposed methodology is employed for monitoring the Continuous Stirred Tank Reactor (CSTR) via a wireless communication network. The effectiveness of the designed observer is extensively assessed by using an experimental tested-bed that has been fabricated for performance evaluation of the over wireless-network estimation techniques under realistic radio channel conditions.

Decentralized state estimation for a large-scale spatially interconnected system.

PubMed

Liu, Huabo; Yu, Haisheng

2018-03-01

A decentralized state estimator is derived for the spatially interconnected systems composed of many subsystems with arbitrary connection relations. An optimization problem on the basis of linear matrix inequality (LMI) is constructed for the computations of improved subsystem parameter matrices. Several computationally effective approaches are derived which efficiently utilize the block-diagonal characteristic of system parameter matrices and the sparseness of subsystem connection matrix. Moreover, this decentralized state estimator is proved to converge to a stable system and obtain a bounded covariance matrix of estimation errors under certain conditions. Numerical simulations show that the obtained decentralized state estimator is attractive in the synthesis of a large-scale networked system. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Model Error Estimation for the CPTEC Eta Model

NASA Technical Reports Server (NTRS)

Tippett, Michael K.; daSilva, Arlindo

1999-01-01

Statistical data assimilation systems require the specification of forecast and observation error statistics. Forecast error is due to model imperfections and differences between the initial condition and the actual state of the atmosphere. Practical four-dimensional variational (4D-Var) methods try to fit the forecast state to the observations and assume that the model error is negligible. Here with a number of simplifying assumption, a framework is developed for isolating the model error given the forecast error at two lead-times. Two definitions are proposed for the Talagrand ratio tau, the fraction of the forecast error due to model error rather than initial condition error. Data from the CPTEC Eta Model running operationally over South America are used to calculate forecast error statistics and lower bounds for tau.

Hamiltonian lattice field theory: Computer calculations using variational methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zako, Robert L.

1991-12-03

I develop a variational method for systematic numerical computation of physical quantities -- bound state energies and scattering amplitudes -- in quantum field theory. An infinite-volume, continuum theory is approximated by a theory on a finite spatial lattice, which is amenable to numerical computation. I present an algorithm for computing approximate energy eigenvalues and eigenstates in the lattice theory and for bounding the resulting errors. I also show how to select basis states and choose variational parameters in order to minimize errors. The algorithm is based on the Rayleigh-Ritz principle and Kato`s generalizations of Temple`s formula. The algorithm could bemore » adapted to systems such as atoms and molecules. I show how to compute Green`s functions from energy eigenvalues and eigenstates in the lattice theory, and relate these to physical (renormalized) coupling constants, bound state energies and Green`s functions. Thus one can compute approximate physical quantities in a lattice theory that approximates a quantum field theory with specified physical coupling constants. I discuss the errors in both approximations. In principle, the errors can be made arbitrarily small by increasing the size of the lattice, decreasing the lattice spacing and computing sufficiently long. Unfortunately, I do not understand the infinite-volume and continuum limits well enough to quantify errors due to the lattice approximation. Thus the method is currently incomplete. I apply the method to real scalar field theories using a Fock basis of free particle states. All needed quantities can be calculated efficiently with this basis. The generalization to more complicated theories is straightforward. I describe a computer implementation of the method and present numerical results for simple quantum mechanical systems.« less

Errors and Understanding: The Effects of Error-Management Training on Creative Problem-Solving

ERIC Educational Resources Information Center

Robledo, Issac C.; Hester, Kimberly S.; Peterson, David R.; Barrett, Jamie D.; Day, Eric A.; Hougen, Dean P.; Mumford, Michael D.

2012-01-01

People make errors in their creative problem-solving efforts. The intent of this article was to assess whether error-management training would improve performance on creative problem-solving tasks. Undergraduates were asked to solve an educational leadership problem known to call for creative thought where problem solutions were scored for…

On the spin- 1/2 Aharonov–Bohm problem in conical space: Bound states, scattering and helicity nonconservation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Andrade, F.M., E-mail: fmandrade@uepg.br; Silva, E.O., E-mail: edilbertoo@gmail.com; Pereira, M., E-mail: marciano@uepg.br

2013-12-15

In this work the bound state and scattering problems for a spin- 1/2 particle undergone to an Aharonov–Bohm potential in a conical space in the nonrelativistic limit are considered. The presence of a δ-function singularity, which comes from the Zeeman spin interaction with the magnetic flux tube, is addressed by the self-adjoint extension method. One of the advantages of the present approach is the determination of the self-adjoint extension parameter in terms of physics of the problem. Expressions for the energy bound states, phase-shift and S matrix are determined in terms of the self-adjoint extension parameter, which is explicitly determinedmore » in terms of the parameters of the problem. The relation between the bound state and zero modes and the failure of helicity conservation in the scattering problem and its relation with the gyromagnetic ratio g are discussed. Also, as an application, we consider the spin- 1/2 Aharonov–Bohm problem in conical space plus a two-dimensional isotropic harmonic oscillator. -- Highlights: •Planar dynamics of a spin- 1/2 neutral particle. •Bound state for Aharonov–Bohm systems. •Aharonov–Bohm scattering. •Helicity nonconservation. •Determination of the self-adjoint extension parameter.« less

Towards fault tolerant adiabatic quantum computation.

PubMed

Lidar, Daniel A

2008-04-25

I show how to protect adiabatic quantum computation (AQC) against decoherence and certain control errors, using a hybrid methodology involving dynamical decoupling, subsystem and stabilizer codes, and energy gaps. Corresponding error bounds are derived. As an example, I show how to perform decoherence-protected AQC against local noise using at most two-body interactions.

Quantum error correction of continuous-variable states against Gaussian noise

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ralph, T. C.

2011-08-15

We describe a continuous-variable error correction protocol that can correct the Gaussian noise induced by linear loss on Gaussian states. The protocol can be implemented using linear optics and photon counting. We explore the theoretical bounds of the protocol as well as the expected performance given current knowledge and technology.

A Simple Algorithm for the Metric Traveling Salesman Problem

NASA Technical Reports Server (NTRS)

Grimm, M. J.

1984-01-01

An algorithm was designed for a wire list net sort problem. A branch and bound algorithm for the metric traveling salesman problem is presented for this. The algorithm is a best bound first recursive descent where the bound is based on the triangle inequality. The bounded subsets are defined by the relative order of the first K of the N cities (i.e., a K city subtour). When K equals N, the bound is the length of the tour. The algorithm is implemented as a one page subroutine written in the C programming language for the VAX 11/750. Average execution times for randomly selected planar points using the Euclidean metric are 0.01, 0.05, 0.42, and 3.13 seconds for ten, fifteen, twenty, and twenty-five cities, respectively. Maximum execution times for a hundred cases are less than eleven times the averages. The speed of the algorithms is due to an initial ordering algorithm that is a N squared operation. The algorithm also solves the related problem where the tour does not return to the starting city and the starting and/or ending cities may be specified. It is possible to extend the algorithm to solve a nonsymmetric problem satisfying the triangle inequality.

Two-sided estimates of minimum-error distinguishability of mixed quantum states via generalized Holevo-Curlander bounds

NASA Astrophysics Data System (ADS)

Tyson, Jon

2009-03-01

We prove a concise factor-of-2 estimate for the failure rate of optimally distinguishing an arbitrary ensemble of mixed quantum states, generalizing work of Holevo [Theor. Probab. Appl. 23, 411 (1978)] and Curlander [Ph.D. Thesis, MIT, 1979]. A modification to the minimal principle of Cocha and Poor [Proceedings of the 6th International Conference on Quantum Communication, Measurement, and Computing (Rinton, Princeton, NJ, 2003)] is used to derive a suboptimal measurement which has an error rate within a factor of 2 of the optimal by construction. This measurement is quadratically weighted and has appeared as the first iterate of a sequence of measurements proposed by Ježek et al. [Phys. Rev. A 65, 060301 (2002)]. Unlike the so-called pretty good measurement, it coincides with Holevo's asymptotically optimal measurement in the case of nonequiprobable pure states. A quadratically weighted version of the measurement bound by Barnum and Knill [J. Math. Phys. 43, 2097 (2002)] is proven. Bounds on the distinguishability of syndromes in the sense of Schumacher and Westmoreland [Phys. Rev. A 56, 131 (1997)] appear as a corollary. An appendix relates our bounds to the trace-Jensen inequality.

Entanglement renormalization, quantum error correction, and bulk causality

NASA Astrophysics Data System (ADS)

Kim, Isaac H.; Kastoryano, Michael J.

2017-04-01

Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progres-sively more well-protected against erasure errors at larger length scales. In particular, an approximate variant of holographic quantum error correcting code emerges at low energy for critical systems. This implies that two operators that are largely separated in scales behave as if they are spatially separated operators, in the sense that they obey a Lieb-Robinson type locality bound under a time evolution generated by a local Hamiltonian.

Short-term prediction of rain attenuation level and volatility in Earth-to-Satellite links at EHF band

NASA Astrophysics Data System (ADS)

de Montera, L.; Mallet, C.; Barthès, L.; Golé, P.

2008-08-01

This paper shows how nonlinear models originally developed in the finance field can be used to predict rain attenuation level and volatility in Earth-to-Satellite links operating at the Extremely High Frequencies band (EHF, 20 50 GHz). A common approach to solving this problem is to consider that the prediction error corresponds only to scintillations, whose variance is assumed to be constant. Nevertheless, this assumption does not seem to be realistic because of the heteroscedasticity of error time series: the variance of the prediction error is found to be time-varying and has to be modeled. Since rain attenuation time series behave similarly to certain stocks or foreign exchange rates, a switching ARIMA/GARCH model was implemented. The originality of this model is that not only the attenuation level, but also the error conditional distribution are predicted. It allows an accurate upper-bound of the future attenuation to be estimated in real time that minimizes the cost of Fade Mitigation Techniques (FMT) and therefore enables the communication system to reach a high percentage of availability. The performance of the switching ARIMA/GARCH model was estimated using a measurement database of the Olympus satellite 20/30 GHz beacons and this model is shown to outperform significantly other existing models. The model also includes frequency scaling from the downlink frequency to the uplink frequency. The attenuation effects (gases, clouds and rain) are first separated with a neural network and then scaled using specific scaling factors. As to the resulting uplink prediction error, the error contribution of the frequency scaling step is shown to be larger than that of the downlink prediction, indicating that further study should focus on improving the accuracy of the scaling factor.

Skeletal Correlates for Body Mass Estimation in Modern and Fossil Flying Birds

PubMed Central

Field, Daniel J.; Lynner, Colton; Brown, Christian; Darroch, Simon A. F.

2013-01-01

Scaling relationships between skeletal dimensions and body mass in extant birds are often used to estimate body mass in fossil crown-group birds, as well as in stem-group avialans. However, useful statistical measurements for constraining the precision and accuracy of fossil mass estimates are rarely provided, which prevents the quantification of robust upper and lower bound body mass estimates for fossils. Here, we generate thirteen body mass correlations and associated measures of statistical robustness using a sample of 863 extant flying birds. By providing robust body mass regressions with upper- and lower-bound prediction intervals for individual skeletal elements, we address the longstanding problem of body mass estimation for highly fragmentary fossil birds. We demonstrate that the most precise proxy for estimating body mass in the overall dataset, measured both as coefficient determination of ordinary least squares regression and percent prediction error, is the maximum diameter of the coracoid’s humeral articulation facet (the glenoid). We further demonstrate that this result is consistent among the majority of investigated avian orders (10 out of 18). As a result, we suggest that, in the majority of cases, this proxy may provide the most accurate estimates of body mass for volant fossil birds. Additionally, by presenting statistical measurements of body mass prediction error for thirteen different body mass regressions, this study provides a much-needed quantitative framework for the accurate estimation of body mass and associated ecological correlates in fossil birds. The application of these regressions will enhance the precision and robustness of many mass-based inferences in future paleornithological studies. PMID:24312392

Stochastic control approaches for sensor management in search and exploitation

NASA Astrophysics Data System (ADS)

Hitchings, Darin Chester

Recent improvements in the capabilities of autonomous vehicles have motivated their increased use in such applications as defense, homeland security, environmental monitoring, and surveillance. To enhance performance in these applications, new algorithms are required to control teams of robots autonomously and through limited interactions with human operators. In this dissertation we develop new algorithms for control of robots performing information-seeking missions in unknown environments. These missions require robots to control their sensors in order to discover the presence of objects, keep track of the objects, and learn what these objects are, given a fixed sensing budget. Initially, we investigate control of multiple sensors, with a finite set of sensing options and finite-valued measurements, to locate and classify objects given a limited resource budget. The control problem is formulated as a Partially Observed Markov Decision Problem (POMDP), but its exact solution requires excessive computation. Under the assumption that sensor error statistics are independent and time-invariant, we develop a class of algorithms using Lagrangian Relaxation techniques to obtain optimal mixed strategies using performance bounds developed in previous research. We investigate alternative Receding Horizon (RH) controllers to convert the mixed strategies to feasible adaptive-sensing strategies and evaluate the relative performance of these controllers in simulation. The resulting controllers provide superior performance to alternative algorithms proposed in the literature and obtain solutions to large-scale POMDP problems several orders of magnitude faster than optimal Dynamic Programming (DP) approaches with comparable performance quality. We extend our results for finite action, finite measurement sensor control to scenarios with moving objects. We use Hidden Markov Models (HMMs) for the evolution of objects, according to the dynamics of a birth-death process. We develop a new lower bound on the performance of adaptive controllers in these scenarios, develop algorithms for computing solutions to this lower bound, and use these algorithms as part of a RH controller for sensor allocation in the presence of moving objects We also consider an adaptive Search problem where sensing actions are continuous and the underlying measurement space is also continuous. We extend our previous hierarchical decomposition approach based on performance bounds to this problem and develop novel implementations of Stochastic Dynamic Programming (SDP) techniques to solve this problem. Our algorithms are nearly two orders of magnitude faster than previously proposed approaches and yield solutions of comparable quality. For supervisory control, we discuss how human operators can work with and augment robotic teams performing these tasks. Our focus is on how tasks are partitioned among teams of robots and how a human operator can make intelligent decisions for task partitioning. We explore these questions through the design of a game that involves robot automata controlled by our algorithms and a human supervisor that partitions tasks based on different levels of support information. This game can be used with human subject experiments to explore the effect of information on quality of supervisory control.

Estimating Climatological Bias Errors for the Global Precipitation Climatology Project (GPCP)

NASA Technical Reports Server (NTRS)

Adler, Robert; Gu, Guojun; Huffman, George

2012-01-01

A procedure is described to estimate bias errors for mean precipitation by using multiple estimates from different algorithms, satellite sources, and merged products. The Global Precipitation Climatology Project (GPCP) monthly product is used as a base precipitation estimate, with other input products included when they are within +/- 50% of the GPCP estimates on a zonal-mean basis (ocean and land separately). The standard deviation s of the included products is then taken to be the estimated systematic, or bias, error. The results allow one to examine monthly climatologies and the annual climatology, producing maps of estimated bias errors, zonal-mean errors, and estimated errors over large areas such as ocean and land for both the tropics and the globe. For ocean areas, where there is the largest question as to absolute magnitude of precipitation, the analysis shows spatial variations in the estimated bias errors, indicating areas where one should have more or less confidence in the mean precipitation estimates. In the tropics, relative bias error estimates (s/m, where m is the mean precipitation) over the eastern Pacific Ocean are as large as 20%, as compared with 10%-15% in the western Pacific part of the ITCZ. An examination of latitudinal differences over ocean clearly shows an increase in estimated bias error at higher latitudes, reaching up to 50%. Over land, the error estimates also locate regions of potential problems in the tropics and larger cold-season errors at high latitudes that are due to snow. An empirical technique to area average the gridded errors (s) is described that allows one to make error estimates for arbitrary areas and for the tropics and the globe (land and ocean separately, and combined). Over the tropics this calculation leads to a relative error estimate for tropical land and ocean combined of 7%, which is considered to be an upper bound because of the lack of sign-of-the-error canceling when integrating over different areas with a different number of input products. For the globe the calculated relative error estimate from this study is about 9%, which is also probably a slight overestimate. These tropical and global estimated bias errors provide one estimate of the current state of knowledge of the planet's mean precipitation.

Graphs and matroids weighted in a bounded incline algebra.

PubMed

Lu, Ling-Xia; Zhang, Bei

2014-01-01

Firstly, for a graph weighted in a bounded incline algebra (or called a dioid), a longest path problem (LPP, for short) is presented, which can be considered the uniform approach to the famous shortest path problem, the widest path problem, and the most reliable path problem. The solutions for LPP and related algorithms are given. Secondly, for a matroid weighted in a linear matroid, the maximum independent set problem is studied.

Screening actuator locations for static shape control

NASA Technical Reports Server (NTRS)

Haftka, Raphael T.

1990-01-01

Correction of shape distortion due to zero-mean normally distributed errors in structural sizes which are random variables is examined. A bound on the maximum improvement in the expected value of the root-mean-square shape error is obtained. The shape correction associated with the optimal actuators is also characterized. An actuator effectiveness index is developed and shown to be helpful in screening actuator locations in the structure. The results are specialized to a simple form for truss structures composed of nominally identical members. The bound and effectiveness index are tested on a 55-m radiometer antenna truss structure. It is found that previously obtained results for optimum actuators had a performance close to the bound obtained here. Furthermore, the actuators associated with the optimum design are shown to have high effectiveness indices. Since only a small fraction of truss elements tend to have high effectiveness indices, the proposed screening procedure can greatly reduce the number of truss members that need to be considered as actuator sites.

Unified Computational Methods for Regression Analysis of Zero-Inflated and Bound-Inflated Data

PubMed Central

Yang, Yan; Simpson, Douglas

2010-01-01

Bounded data with excess observations at the boundary are common in many areas of application. Various individual cases of inflated mixture models have been studied in the literature for bound-inflated data, yet the computational methods have been developed separately for each type of model. In this article we use a common framework for computing these models, and expand the range of models for both discrete and semi-continuous data with point inflation at the lower boundary. The quasi-Newton and EM algorithms are adapted and compared for estimation of model parameters. The numerical Hessian and generalized Louis method are investigated as means for computing standard errors after optimization. Correlated data are included in this framework via generalized estimating equations. The estimation of parameters and effectiveness of standard errors are demonstrated through simulation and in the analysis of data from an ultrasound bioeffect study. The unified approach enables reliable computation for a wide class of inflated mixture models and comparison of competing models. PMID:20228950

ALPS: A Linear Program Solver

NASA Technical Reports Server (NTRS)

Ferencz, Donald C.; Viterna, Larry A.

1991-01-01

ALPS is a computer program which can be used to solve general linear program (optimization) problems. ALPS was designed for those who have minimal linear programming (LP) knowledge and features a menu-driven scheme to guide the user through the process of creating and solving LP formulations. Once created, the problems can be edited and stored in standard DOS ASCII files to provide portability to various word processors or even other linear programming packages. Unlike many math-oriented LP solvers, ALPS contains an LP parser that reads through the LP formulation and reports several types of errors to the user. ALPS provides a large amount of solution data which is often useful in problem solving. In addition to pure linear programs, ALPS can solve for integer, mixed integer, and binary type problems. Pure linear programs are solved with the revised simplex method. Integer or mixed integer programs are solved initially with the revised simplex, and the completed using the branch-and-bound technique. Binary programs are solved with the method of implicit enumeration. This manual describes how to use ALPS to create, edit, and solve linear programming problems. Instructions for installing ALPS on a PC compatible computer are included in the appendices along with a general introduction to linear programming. A programmers guide is also included for assistance in modifying and maintaining the program.

Adaptive neural network decentralized backstepping output-feedback control for nonlinear large-scale systems with time delays.

PubMed

Tong, Shao Cheng; Li, Yong Ming; Zhang, Hua-Guang

2011-07-01

In this paper, two adaptive neural network (NN) decentralized output feedback control approaches are proposed for a class of uncertain nonlinear large-scale systems with immeasurable states and unknown time delays. Using NNs to approximate the unknown nonlinear functions, an NN state observer is designed to estimate the immeasurable states. By combining the adaptive backstepping technique with decentralized control design principle, an adaptive NN decentralized output feedback control approach is developed. In order to overcome the problem of "explosion of complexity" inherent in the proposed control approach, the dynamic surface control (DSC) technique is introduced into the first adaptive NN decentralized control scheme, and a simplified adaptive NN decentralized output feedback DSC approach is developed. It is proved that the two proposed control approaches can guarantee that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded, and the observer errors and the tracking errors converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approaches.

Finite-time containment control of perturbed multi-agent systems based on sliding-mode control

NASA Astrophysics Data System (ADS)

Yu, Di; Ji, Xiang Yang

2018-01-01

Aimed at faster convergence rate, this paper investigates finite-time containment control problem for second-order multi-agent systems with norm-bounded non-linear perturbation. When topology between the followers are strongly connected, the nonsingular fast terminal sliding-mode error is defined, corresponding discontinuous control protocol is designed and the appropriate value range of control parameter is obtained by applying finite-time stability analysis, so that the followers converge to and move along the desired trajectories within the convex hull formed by the leaders in finite time. Furthermore, on the basis of the sliding-mode error defined, the corresponding distributed continuous control protocols are investigated with fast exponential reaching law and double exponential reaching law, so as to make the followers move to the small neighbourhoods of their desired locations and keep within the dynamic convex hull formed by the leaders in finite time to achieve practical finite-time containment control. Meanwhile, we develop the faster control scheme according to comparison of the convergence rate of these two different reaching laws. Simulation examples are given to verify the correctness of theoretical results.

Observer-Based Adaptive Fault-Tolerant Tracking Control of Nonlinear Nonstrict-Feedback Systems.

PubMed

Wu, Chengwei; Liu, Jianxing; Xiong, Yongyang; Wu, Ligang

2017-06-28

This paper studies an output-based adaptive fault-tolerant control problem for nonlinear systems with nonstrict-feedback form. Neural networks are utilized to identify the unknown nonlinear characteristics in the system. An observer and a general fault model are constructed to estimate the unavailable states and describe the fault, respectively. Adaptive parameters are constructed to overcome the difficulties in the design process for nonstrict-feedback systems. Meanwhile, dynamic surface control technique is introduced to avoid the problem of ''explosion of complexity''. Furthermore, based on adaptive backstepping control method, an output-based adaptive neural tracking control strategy is developed for the considered system against actuator fault, which can ensure that all the signals in the resulting closed-loop system are bounded, and the system output signal can be regulated to follow the response of the given reference signal with a small error. Finally, the simulation results are provided to validate the effectiveness of the control strategy proposed in this paper.

Constructing probabilistic scenarios for wide-area solar power generation

DOE PAGES

Woodruff, David L.; Deride, Julio; Staid, Andrea; ...

2017-12-22

Optimizing thermal generation commitments and dispatch in the presence of high penetrations of renewable resources such as solar energy requires a characterization of their stochastic properties. In this study, we describe novel methods designed to create day-ahead, wide-area probabilistic solar power scenarios based only on historical forecasts and associated observations of solar power production. Each scenario represents a possible trajectory for solar power in next-day operations with an associated probability computed by algorithms that use historical forecast errors. Scenarios are created by segmentation of historic data, fitting non-parametric error distributions using epi-splines, and then computing specific quantiles from these distributions.more » Additionally, we address the challenge of establishing an upper bound on solar power output. Our specific application driver is for use in stochastic variants of core power systems operations optimization problems, e.g., unit commitment and economic dispatch. These problems require as input a range of possible future realizations of renewables production. However, the utility of such probabilistic scenarios extends to other contexts, e.g., operator and trader situational awareness. Finally, we compare the performance of our approach to a recently proposed method based on quantile regression, and demonstrate that our method performs comparably to this approach in terms of two widely used methods for assessing the quality of probabilistic scenarios: the Energy score and the Variogram score.« less

Constructing probabilistic scenarios for wide-area solar power generation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Woodruff, David L.; Deride, Julio; Staid, Andrea

Optimizing thermal generation commitments and dispatch in the presence of high penetrations of renewable resources such as solar energy requires a characterization of their stochastic properties. In this study, we describe novel methods designed to create day-ahead, wide-area probabilistic solar power scenarios based only on historical forecasts and associated observations of solar power production. Each scenario represents a possible trajectory for solar power in next-day operations with an associated probability computed by algorithms that use historical forecast errors. Scenarios are created by segmentation of historic data, fitting non-parametric error distributions using epi-splines, and then computing specific quantiles from these distributions.more » Additionally, we address the challenge of establishing an upper bound on solar power output. Our specific application driver is for use in stochastic variants of core power systems operations optimization problems, e.g., unit commitment and economic dispatch. These problems require as input a range of possible future realizations of renewables production. However, the utility of such probabilistic scenarios extends to other contexts, e.g., operator and trader situational awareness. Finally, we compare the performance of our approach to a recently proposed method based on quantile regression, and demonstrate that our method performs comparably to this approach in terms of two widely used methods for assessing the quality of probabilistic scenarios: the Energy score and the Variogram score.« less

Error Suppression for Hamiltonian-Based Quantum Computation Using Subsystem Codes

NASA Astrophysics Data System (ADS)

Marvian, Milad; Lidar, Daniel A.

2017-01-01

We present general conditions for quantum error suppression for Hamiltonian-based quantum computation using subsystem codes. This involves encoding the Hamiltonian performing the computation using an error detecting subsystem code and the addition of a penalty term that commutes with the encoded Hamiltonian. The scheme is general and includes the stabilizer formalism of both subspace and subsystem codes as special cases. We derive performance bounds and show that complete error suppression results in the large penalty limit. To illustrate the power of subsystem-based error suppression, we introduce fully two-local constructions for protection against local errors of the swap gate of adiabatic gate teleportation and the Ising chain in a transverse field.

Error Suppression for Hamiltonian-Based Quantum Computation Using Subsystem Codes.

PubMed

Marvian, Milad; Lidar, Daniel A

2017-01-20

We present general conditions for quantum error suppression for Hamiltonian-based quantum computation using subsystem codes. This involves encoding the Hamiltonian performing the computation using an error detecting subsystem code and the addition of a penalty term that commutes with the encoded Hamiltonian. The scheme is general and includes the stabilizer formalism of both subspace and subsystem codes as special cases. We derive performance bounds and show that complete error suppression results in the large penalty limit. To illustrate the power of subsystem-based error suppression, we introduce fully two-local constructions for protection against local errors of the swap gate of adiabatic gate teleportation and the Ising chain in a transverse field.

Verifying the error bound of numerical computation implemented in computer systems

DOEpatents

Sawada, Jun

2013-03-12

A verification tool receives a finite precision definition for an approximation of an infinite precision numerical function implemented in a processor in the form of a polynomial of bounded functions. The verification tool receives a domain for verifying outputs of segments associated with the infinite precision numerical function. The verification tool splits the domain into at least two segments, wherein each segment is non-overlapping with any other segment and converts, for each segment, a polynomial of bounded functions for the segment to a simplified formula comprising a polynomial, an inequality, and a constant for a selected segment. The verification tool calculates upper bounds of the polynomial for the at least two segments, beginning with the selected segment and reports the segments that violate a bounding condition.

Worst error performance of continuous Kalman filters. [for deep space navigation and maneuvers

NASA Technical Reports Server (NTRS)

Nishimura, T.

1975-01-01

The worst error performance of estimation filters is investigated for continuous systems in this paper. The pathological performance study, without assuming any dynamical model such as Markov processes for perturbations, except for its bounded amplitude, will give practical and dependable criteria in establishing the navigation and maneuver strategy in deep space missions.

BCDP: Budget Constrained and Delay-Bounded Placement for Hybrid Roadside Units in Vehicular Ad Hoc Networks

PubMed Central

Li, Peng; Huang, Chuanhe; Liu, Qin

2014-01-01

In vehicular ad hoc networks, roadside units (RSUs) placement has been proposed to improve the the overall network performance in many ITS applications. This paper addresses the budget constrained and delay-bounded placement problem (BCDP) for roadside units in vehicular ad hoc networks. There are two types of RSUs: cable connected RSU (c-RSU) and wireless RSU (w-RSU). c-RSUs are interconnected through wired lines, and they form the backbone of VANETs, while w-RSUs connect to other RSUs through wireless communication and serve as an economical extension of the coverage of c-RSUs. The delay-bounded coverage range and deployment cost of these two cases are totally different. We are given a budget constraint and a delay bound, the problem is how to find the optimal candidate sites with the maximal delay-bounded coverage to place RSUs such that a message from any c-RSU in the region can be disseminated to the more vehicles within the given budget constraint and delay bound. We first prove that the BCDP problem is NP-hard. Then we propose several algorithms to solve the BCDP problem. Simulation results show the heuristic algorithms can significantly improve the coverage range and reduce the total deployment cost, compared with other heuristic methods. PMID:25436656

An internal pilot design for prospective cancer screening trials with unknown disease prevalence.

PubMed

Brinton, John T; Ringham, Brandy M; Glueck, Deborah H

2015-10-13

For studies that compare the diagnostic accuracy of two screening tests, the sample size depends on the prevalence of disease in the study population, and on the variance of the outcome. Both parameters may be unknown during the design stage, which makes finding an accurate sample size difficult. To solve this problem, we propose adapting an internal pilot design. In this adapted design, researchers will accrue some percentage of the planned sample size, then estimate both the disease prevalence and the variances of the screening tests. The updated estimates of the disease prevalence and variance are used to conduct a more accurate power and sample size calculation. We demonstrate that in large samples, the adapted internal pilot design produces no Type I inflation. For small samples (N less than 50), we introduce a novel adjustment of the critical value to control the Type I error rate. We apply the method to two proposed prospective cancer screening studies: 1) a small oral cancer screening study in individuals with Fanconi anemia and 2) a large oral cancer screening trial. Conducting an internal pilot study without adjusting the critical value can cause Type I error rate inflation in small samples, but not in large samples. An internal pilot approach usually achieves goal power and, for most studies with sample size greater than 50, requires no Type I error correction. Further, we have provided a flexible and accurate approach to bound Type I error below a goal level for studies with small sample size.

Quaternion-based adaptive output feedback attitude control of spacecraft using Chebyshev neural networks.

PubMed

Zou, An-Min; Dev Kumar, Krishna; Hou, Zeng-Guang

2010-09-01

This paper investigates the problem of output feedback attitude control of an uncertain spacecraft. Two robust adaptive output feedback controllers based on Chebyshev neural networks (CNN) termed adaptive neural networks (NN) controller-I and adaptive NN controller-II are proposed for the attitude tracking control of spacecraft. The four-parameter representations (quaternion) are employed to describe the spacecraft attitude for global representation without singularities. The nonlinear reduced-order observer is used to estimate the derivative of the spacecraft output, and the CNN is introduced to further improve the control performance through approximating the spacecraft attitude motion. The implementation of the basis functions of the CNN used in the proposed controllers depends only on the desired signals, and the smooth robust compensator using the hyperbolic tangent function is employed to counteract the CNN approximation errors and external disturbances. The adaptive NN controller-II can efficiently avoid the over-estimation problem (i.e., the bound of the CNNs output is much larger than that of the approximated unknown function, and hence, the control input may be very large) existing in the adaptive NN controller-I. Both adaptive output feedback controllers using CNN can guarantee that all signals in the resulting closed-loop system are uniformly ultimately bounded. For performance comparisons, the standard adaptive controller using the linear parameterization of spacecraft attitude motion is also developed. Simulation studies are presented to show the advantages of the proposed CNN-based output feedback approach over the standard adaptive output feedback approach.

Forward and back diffusion through argillaceous formations

NASA Astrophysics Data System (ADS)

Yang, Minjune; Annable, Michael D.; Jawitz, James W.

2017-05-01

The exchange of solutes between aquifers and lower-permeability argillaceous formations is of considerable interest for solute and contaminant fate and transport. We present a synthesis of analytical solutions for solute diffusion between aquifers and single aquitard systems, validated in well-controlled experiments, and applied to several data sets from laboratory and field-scale problems with diffusion time and length scales ranging from 10-2 to 108 years and 10-2 to 102 m. One-dimensional diffusion models were applied using the method of images to consider the general cases of a finite aquitard bounded by two aquifers at the top and bottom, or a semiinfinite aquitard bounded by an aquifer. The simpler semiinfinite equations are appropriate for all domains with dimensionless relative diffusion length, ZD < 0.7. At dimensionless length scales above this threshold, application of semiinfinite equations to aquitards of finite thickness leads to increasing errors and solutions based on the method of images are required. Measured resident solute concentration profiles in aquitards and flux-averaged solute concentrations in surrounding aquifers were accurately modeled by appropriately accounting for generalized dynamic aquifer-aquitard boundary conditions, including concentration gradient reversals. Dimensionless diffusion length scales were used to illustrate the transferability of these relatively simple models to physical systems with dimensions that spanned 10 orders of magnitude. The results of this study offer guidance on the application of a simplified analytical approach to environmentally important layered problems with one or two diffusion interfaces.

Estimation of uncertainty bounds for individual particle image velocimetry measurements from cross-correlation peak ratio

NASA Astrophysics Data System (ADS)

Charonko, John J.; Vlachos, Pavlos P.

2013-06-01

Numerous studies have established firmly that particle image velocimetry (PIV) is a robust method for non-invasive, quantitative measurements of fluid velocity, and that when carefully conducted, typical measurements can accurately detect displacements in digital images with a resolution well below a single pixel (in some cases well below a hundredth of a pixel). However, to date, these estimates have only been able to provide guidance on the expected error for an average measurement under specific image quality and flow conditions. This paper demonstrates a new method for estimating the uncertainty bounds to within a given confidence interval for a specific, individual measurement. Here, cross-correlation peak ratio, the ratio of primary to secondary peak height, is shown to correlate strongly with the range of observed error values for a given measurement, regardless of flow condition or image quality. This relationship is significantly stronger for phase-only generalized cross-correlation PIV processing, while the standard correlation approach showed weaker performance. Using an analytical model of the relationship derived from synthetic data sets, the uncertainty bounds at a 95% confidence interval are then computed for several artificial and experimental flow fields, and the resulting errors are shown to match closely to the predicted uncertainties. While this method stops short of being able to predict the true error for a given measurement, knowledge of the uncertainty level for a PIV experiment should provide great benefits when applying the results of PIV analysis to engineering design studies and computational fluid dynamics validation efforts. Moreover, this approach is exceptionally simple to implement and requires negligible additional computational cost.

Analysis of Online Composite Mirror Descent Algorithm.

PubMed

Lei, Yunwen; Zhou, Ding-Xuan

2017-03-01

We study the convergence of the online composite mirror descent algorithm, which involves a mirror map to reflect the geometry of the data and a convex objective function consisting of a loss and a regularizer possibly inducing sparsity. Our error analysis provides convergence rates in terms of properties of the strongly convex differentiable mirror map and the objective function. For a class of objective functions with Hölder continuous gradients, the convergence rates of the excess (regularized) risk under polynomially decaying step sizes have the order [Formula: see text] after [Formula: see text] iterates. Our results improve the existing error analysis for the online composite mirror descent algorithm by avoiding averaging and removing boundedness assumptions, and they sharpen the existing convergence rates of the last iterate for online gradient descent without any boundedness assumptions. Our methodology mainly depends on a novel error decomposition in terms of an excess Bregman distance, refined analysis of self-bounding properties of the objective function, and the resulting one-step progress bounds.

RaptorX-Angle: real-value prediction of protein backbone dihedral angles through a hybrid method of clustering and deep learning.

PubMed

Gao, Yujuan; Wang, Sheng; Deng, Minghua; Xu, Jinbo

2018-05-08

Protein dihedral angles provide a detailed description of protein local conformation. Predicted dihedral angles can be used to narrow down the conformational space of the whole polypeptide chain significantly, thus aiding protein tertiary structure prediction. However, direct angle prediction from sequence alone is challenging. In this article, we present a novel method (named RaptorX-Angle) to predict real-valued angles by combining clustering and deep learning. Tested on a subset of PDB25 and the targets in the latest two Critical Assessment of protein Structure Prediction (CASP), our method outperforms the existing state-of-art method SPIDER2 in terms of Pearson Correlation Coefficient (PCC) and Mean Absolute Error (MAE). Our result also shows approximately linear relationship between the real prediction errors and our estimated bounds. That is, the real prediction error can be well approximated by our estimated bounds. Our study provides an alternative and more accurate prediction of dihedral angles, which may facilitate protein structure prediction and functional study.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Omkar, S.; Srikanth, R., E-mail: srik@poornaprajna.org; Banerjee, Subhashish

A protocol based on quantum error correction based characterization of quantum dynamics (QECCD) is developed for quantum process tomography on a two-qubit system interacting dissipatively with a vacuum bath. The method uses a 5-qubit quantum error correcting code that corrects arbitrary errors on the first two qubits, and also saturates the quantum Hamming bound. The dissipative interaction with a vacuum bath allows for both correlated and independent noise on the two-qubit system. We study the dependence of the degree of the correlation of the noise on evolution time and inter-qubit separation.

Adaptive estimation of a time-varying phase with coherent states: Smoothing can give an unbounded improvement over filtering

NASA Astrophysics Data System (ADS)

Laverick, Kiarn T.; Wiseman, Howard M.; Dinani, Hossein T.; Berry, Dominic W.

2018-04-01

The problem of measuring a time-varying phase, even when the statistics of the variation is known, is considerably harder than that of measuring a constant phase. In particular, the usual bounds on accuracy, such as the 1 /(4 n ¯) standard quantum limit with coherent states, do not apply. Here, by restricting to coherent states, we are able to analytically obtain the achievable accuracy, the equivalent of the standard quantum limit, for a wide class of phase variation. In particular, we consider the case where the phase has Gaussian statistics and a power-law spectrum equal to κp -1/|ω| p for large ω , for some p >1 . For coherent states with mean photon flux N , we give the quantum Cramér-Rao bound on the mean-square phase error as [psin(π /p ) ] -1(4N /κ ) -(p -1 )/p . Next, we consider whether the bound can be achieved by an adaptive homodyne measurement in the limit N /κ ≫1 , which allows the photocurrent to be linearized. Applying the optimal filtering for the resultant linear Gaussian system, we find the same scaling with N , but with a prefactor larger by a factor of p . By contrast, if we employ optimal smoothing we can exactly obtain the quantum Cramér-Rao bound. That is, contrary to previously considered (p =2 ) cases of phase estimation, here the improvement offered by smoothing over filtering is not limited to a factor of 2 but rather can be unbounded by a factor of p . We also study numerically the performance of these estimators for an adaptive measurement in the limit where N /κ is not large and find a more complicated picture.

A linear programming approach to max-sum problem: a review.

PubMed

Werner, Tomás

2007-07-01

The max-sum labeling problem, defined as maximizing a sum of binary (i.e., pairwise) functions of discrete variables, is a general NP-hard optimization problem with many applications, such as computing the MAP configuration of a Markov random field. We review a not widely known approach to the problem, developed by Ukrainian researchers Schlesinger et al. in 1976, and show how it contributes to recent results, most importantly, those on the convex combination of trees and tree-reweighted max-product. In particular, we review Schlesinger et al.'s upper bound on the max-sum criterion, its minimization by equivalent transformations, its relation to the constraint satisfaction problem, the fact that this minimization is dual to a linear programming relaxation of the original problem, and the three kinds of consistency necessary for optimality of the upper bound. We revisit problems with Boolean variables and supermodular problems. We describe two algorithms for decreasing the upper bound. We present an example application for structural image analysis.

Poster error probability in the Mu-11 Sequential Ranging System

NASA Technical Reports Server (NTRS)

Coyle, C. W.

1981-01-01

An expression is derived for the posterior error probability in the Mu-2 Sequential Ranging System. An algorithm is developed which closely bounds the exact answer and can be implemented in the machine software. A computer simulation is provided to illustrate the improved level of confidence in a ranging acquisition using this figure of merit as compared to that using only the prior probabilities. In a simulation of 20,000 acquisitions with an experimentally determined threshold setting, the algorithm detected 90% of the actual errors and made false indication of errors on 0.2% of the acquisitions.

Modeling and control of beam-like structures

NASA Technical Reports Server (NTRS)

Hu, A.; Skelton, R. E.; Yang, T. Y.

1987-01-01

The most popular finite element codes are based upon appealing theories of convergence of modal frequencies. For example, the popularity of cubic elements for beam-like structures is due to the rapid convergence of modal frequencies and stiffness properties. However, for those problems in which the primary consideration is the accuracy of response of the structure at specified locations it is more important to obtain accuracy in the modal costs than in the modal frequencies. The modal cost represents the contribution of a mode in the norm of the response vector. This paper provides a complete modal cost analysis for beam-like continua. Upper bounds are developed for mode truncation errors in the model reduction process and modal cost analysis dictates which modes to retain in order to reduce the model for control design purposes.

Neural-Network-Based Adaptive Decentralized Fault-Tolerant Control for a Class of Interconnected Nonlinear Systems.

PubMed

Li, Xiao-Jian; Yang, Guang-Hong

2018-01-01

This paper is concerned with the adaptive decentralized fault-tolerant tracking control problem for a class of uncertain interconnected nonlinear systems with unknown strong interconnections. An algebraic graph theory result is introduced to address the considered interconnections. In addition, to achieve the desirable tracking performance, a neural-network-based robust adaptive decentralized fault-tolerant control (FTC) scheme is given to compensate the actuator faults and system uncertainties. Furthermore, via the Lyapunov analysis method, it is proven that all the signals of the resulting closed-loop system are semiglobally bounded, and the tracking errors of each subsystem exponentially converge to a compact set, whose radius is adjustable by choosing different controller design parameters. Finally, the effectiveness and advantages of the proposed FTC approach are illustrated with two simulated examples.

Exponential synchronization of neural networks with discrete and distributed delays under time-varying sampling.

PubMed

Wu, Zheng-Guang; Shi, Peng; Su, Hongye; Chu, Jian

2012-09-01

This paper investigates the problem of master-slave synchronization for neural networks with discrete and distributed delays under variable sampling with a known upper bound on the sampling intervals. An improved method is proposed, which captures the characteristic of sampled-data systems. Some delay-dependent criteria are derived to ensure the exponential stability of the error systems, and thus the master systems synchronize with the slave systems. The desired sampled-data controller can be achieved by solving a set of linear matrix inequalitys, which depend upon the maximum sampling interval and the decay rate. The obtained conditions not only have less conservatism but also have less decision variables than existing results. Simulation results are given to show the effectiveness and benefits of the proposed methods.

On the synchronizability and detectability of random PPM sequences

NASA Technical Reports Server (NTRS)

Georghiades, Costas N.; Lin, Shu

1987-01-01

The problem of synchronization and detection of random pulse-position-modulation (PPM) sequences is investigated under the assumption of perfect slot synchronization. Maximum-likelihood PPM symbol synchronization and receiver algorithms are derived that make decisions based both on soft as well as hard data; these algorithms are seen to be easily implementable. Bounds derived on the symbol error probability as well as the probability of false synchronization indicate the existence of a rather severe performance floor, which can easily be the limiting factor in the overall system performance. The performance floor is inherent in the PPM format and random data and becomes more serious as the PPM alphabet size Q is increased. A way to eliminate the performance floor is suggested by inserting special PPM symbols in the random data stream.

On the synchronizability and detectability of random PPM sequences

NASA Technical Reports Server (NTRS)

Georghiades, Costas N.

1987-01-01

The problem of synchronization and detection of random pulse-position-modulation (PPM) sequences is investigated under the assumption of perfect slot synchronization. Maximum likelihood PPM symbol synchronization and receiver algorithms are derived that make decisions based both on soft as well as hard data; these algorithms are seen to be easily implementable. Bounds were derived on the symbol error probability as well as the probability of false synchronization that indicate the existence of a rather severe performance floor, which can easily be the limiting factor in the overall system performance. The performance floor is inherent in the PPM format and random data and becomes more serious as the PPM alphabet size Q is increased. A way to eliminate the performance floor is suggested by inserting special PPM symbols in the random data stream.

Electrochemical state and internal variables estimation using a reduced-order physics-based model of a lithium-ion cell and an extended Kalman filter

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stetzel, KD; Aldrich, LL; Trimboli, MS

2015-03-15

This paper addresses the problem of estimating the present value of electrochemical internal variables in a lithium-ion cell in real time, using readily available measurements of cell voltage, current, and temperature. The variables that can be estimated include any desired set of reaction flux and solid and electrolyte potentials and concentrations at any set of one-dimensional spatial locations, in addition to more standard quantities such as state of charge. The method uses an extended Kalman filter along with a one-dimensional physics-based reduced-order model of cell dynamics. Simulations show excellent and robust predictions having dependable error bounds for most internal variables.more » (C) 2014 Elsevier B.V. All rights reserved.« less

Terminal Sliding Mode-Based Consensus Tracking Control for Networked Uncertain Mechanical Systems on Digraphs.

PubMed

Chen, Gang; Song, Yongduan; Guan, Yanfeng

2018-03-01

This brief investigates the finite-time consensus tracking control problem for networked uncertain mechanical systems on digraphs. A new terminal sliding-mode-based cooperative control scheme is developed to guarantee that the tracking errors converge to an arbitrarily small bound around zero in finite time. All the networked systems can have different dynamics and all the dynamics are unknown. A neural network is used at each node to approximate the local unknown dynamics. The control schemes are implemented in a fully distributed manner. The proposed control method eliminates some limitations in the existing terminal sliding-mode-based consensus control methods and extends the existing analysis methods to the case of directed graphs. Simulation results on networked robot manipulators are provided to show the effectiveness of the proposed control algorithms.

An Approximate Approach to Automatic Kernel Selection.

PubMed

Ding, Lizhong; Liao, Shizhong

2016-02-02

Kernel selection is a fundamental problem of kernel-based learning algorithms. In this paper, we propose an approximate approach to automatic kernel selection for regression from the perspective of kernel matrix approximation. We first introduce multilevel circulant matrices into automatic kernel selection, and develop two approximate kernel selection algorithms by exploiting the computational virtues of multilevel circulant matrices. The complexity of the proposed algorithms is quasi-linear in the number of data points. Then, we prove an approximation error bound to measure the effect of the approximation in kernel matrices by multilevel circulant matrices on the hypothesis and further show that the approximate hypothesis produced with multilevel circulant matrices converges to the accurate hypothesis produced with kernel matrices. Experimental evaluations on benchmark datasets demonstrate the effectiveness of approximate kernel selection.

Explicit bounds for the positive root of classes of polynomials with applications

NASA Astrophysics Data System (ADS)

Herzberger, Jürgen

2003-03-01

We consider a certain type of polynomial equations for which there exists--according to Descartes' rule of signs--only one simple positive root. These equations are occurring in Numerical Analysis when calculating or estimating the R-order or Q-order of convergence of certain iterative processes with an error-recursion of special form. On the other hand, these polynomial equations are very common as defining equations for the effective rate of return for certain cashflows like bonds or annuities in finance. The effective rate of interest i* for those cashflows is i*=q*-1, where q* is the unique positive root of such polynomial. We construct bounds for i* for a special problem concerning an ordinary simple annuity which is obtained by changing the conditions of such an annuity with given data applying the German rule (Preisangabeverordnung or short PAngV). Moreover, we consider a number of results for such polynomial roots in Numerical Analysis showing that by a simple variable transformation we can derive several formulas out of earlier results by applying this transformation. The same is possible in finance in order to generalize results to more complicated cashflows.

A Linear Kernel for Co-Path/Cycle Packing

NASA Astrophysics Data System (ADS)

Chen, Zhi-Zhong; Fellows, Michael; Fu, Bin; Jiang, Haitao; Liu, Yang; Wang, Lusheng; Zhu, Binhai

Bounded-Degree Vertex Deletion is a fundamental problem in graph theory that has new applications in computational biology. In this paper, we address a special case of Bounded-Degree Vertex Deletion, the Co-Path/Cycle Packing problem, which asks to delete as few vertices as possible such that the graph of the remaining (residual) vertices is composed of disjoint paths and simple cycles. The problem falls into the well-known class of 'node-deletion problems with hereditary properties', is hence NP-complete and unlikely to admit a polynomial time approximation algorithm with approximation factor smaller than 2. In the framework of parameterized complexity, we present a kernelization algorithm that produces a kernel with at most 37k vertices, improving on the super-linear kernel of Fellows et al.'s general theorem for Bounded-Degree Vertex Deletion. Using this kernel,and the method of bounded search trees, we devise an FPT algorithm that runs in time O *(3.24 k ). On the negative side, we show that the problem is APX-hard and unlikely to have a kernel smaller than 2k by a reduction from Vertex Cover.

Errors Analysis of Students in Mathematics Department to Learn Plane Geometry

NASA Astrophysics Data System (ADS)

Mirna, M.

2018-04-01

This article describes the results of qualitative descriptive research that reveal the locations, types and causes of student error in answering the problem of plane geometry at the problem-solving level. Answers from 59 students on three test items informed that students showed errors ranging from understanding the concepts and principles of geometry itself to the error in applying it to problem solving. Their type of error consists of concept errors, principle errors and operational errors. The results of reflection with four subjects reveal the causes of the error are: 1) student learning motivation is very low, 2) in high school learning experience, geometry has been seen as unimportant, 3) the students' experience using their reasoning in solving the problem is very less, and 4) students' reasoning ability is still very low.

Human-robot cooperative movement training: learning a novel sensory motor transformation during walking with robotic assistance-as-needed.

PubMed

Emken, Jeremy L; Benitez, Raul; Reinkensmeyer, David J

2007-03-28

A prevailing paradigm of physical rehabilitation following neurologic injury is to "assist-as-needed" in completing desired movements. Several research groups are attempting to automate this principle with robotic movement training devices and patient cooperative algorithms that encourage voluntary participation. These attempts are currently not based on computational models of motor learning. Here we assume that motor recovery from a neurologic injury can be modelled as a process of learning a novel sensory motor transformation, which allows us to study a simplified experimental protocol amenable to mathematical description. Specifically, we use a robotic force field paradigm to impose a virtual impairment on the left leg of unimpaired subjects walking on a treadmill. We then derive an "assist-as-needed" robotic training algorithm to help subjects overcome the virtual impairment and walk normally. The problem is posed as an optimization of performance error and robotic assistance. The optimal robotic movement trainer becomes an error-based controller with a forgetting factor that bounds kinematic errors while systematically reducing its assistance when those errors are small. As humans have a natural range of movement variability, we introduce an error weighting function that causes the robotic trainer to disregard this variability. We experimentally validated the controller with ten unimpaired subjects by demonstrating how it helped the subjects learn the novel sensory motor transformation necessary to counteract the virtual impairment, while also preventing them from experiencing large kinematic errors. The addition of the error weighting function allowed the robot assistance to fade to zero even though the subjects' movements were variable. We also show that in order to assist-as-needed, the robot must relax its assistance at a rate faster than that of the learning human. The assist-as-needed algorithm proposed here can limit error during the learning of a dynamic motor task. The algorithm encourages learning by decreasing its assistance as a function of the ongoing progression of movement error. This type of algorithm is well suited for helping people learn dynamic tasks for which large kinematic errors are dangerous or discouraging, and thus may prove useful for robot-assisted movement training of walking or reaching following neurologic injury.

Analysis of synchronous digital-modulation schemes for satellite communication

NASA Technical Reports Server (NTRS)

Takhar, G. S.; Gupta, S. C.

1975-01-01

The multipath communication channel for space communications is modeled as a multiplicative channel. This paper discusses the effects of multiplicative channel processes on the symbol error rate for quadrature modulation (QM) digital modulation schemes. An expression for the upper bound on the probability of error is derived and numerically evaluated. The results are compared with those obtained for additive channels.

Empirically Estimable Classification Bounds Based on a Nonparametric Divergence Measure

PubMed Central

Berisha, Visar; Wisler, Alan; Hero, Alfred O.; Spanias, Andreas

2015-01-01

Information divergence functions play a critical role in statistics and information theory. In this paper we show that a non-parametric f-divergence measure can be used to provide improved bounds on the minimum binary classification probability of error for the case when the training and test data are drawn from the same distribution and for the case where there exists some mismatch between training and test distributions. We confirm the theoretical results by designing feature selection algorithms using the criteria from these bounds and by evaluating the algorithms on a series of pathological speech classification tasks. PMID:26807014

Rotational relaxation of molecular hydrogen at moderate temperatures

NASA Technical Reports Server (NTRS)

Sharma, S. P.

1994-01-01

Using a coupled rotation-vibration-dissociation model the rotational relaxation times for molecular hydrogen as a function of final temperature (500-5000 K), in a hypothetical scenario of sudden compression, are computed. The theoretical model is based on a master equation solver. The bound-bound and bound-free transition rates have been computed using a quasiclassical trajectory method. A review of the available experimental data on the rotational relaxation of hydrogen is presented, with a critical overview of the method of measurements and data reduction, including the sources of errors. These experimental data are then compared with the computed results.

Exploring L1 model space in search of conductivity bounds for the MT problem

NASA Astrophysics Data System (ADS)

Wheelock, B. D.; Parker, R. L.

2013-12-01

Geophysical inverse problems of the type encountered in electromagnetic techniques are highly non-unique. As a result, any single inverted model, though feasible, is at best inconclusive and at worst misleading. In this paper, we use modified inversion methods to establish bounds on electrical conductivity within a model of the earth. Our method consists of two steps, each making use of the 1-norm in model regularization. Both 1-norm minimization problems are framed without approximation as non-negative least-squares (NNLS) problems. First, we must identify a parsimonious set of regions within the model for which upper and lower bounds on average conductivity will be sought. This is accomplished by minimizing the 1-norm of spatial variation, which produces a model with a limited number of homogeneous regions; in fact, the number of homogeneous regions will never be greater than the number of data, regardless of the number of free parameters supplied. The second step establishes bounds for each of these regions with pairs of inversions. The new suite of inversions also uses a 1-norm penalty, but applied to the conductivity values themselves, rather than the spatial variation thereof. In the bounding step we use the 1-norm of our model parameters because it is proportional to average conductivity. For a lower bound on average conductivity, the 1-norm within a bounding region is minimized. For an upper bound on average conductivity, the 1-norm everywhere outside a bounding region is minimized. The latter minimization has the effect of concentrating conductance into the bounding region. Taken together, these bounds are a measure of the uncertainty in the associated region of our model. Starting with a blocky inverse solution is key in the selection of the bounding regions. Of course, there is a tradeoff between resolution and uncertainty: an increase in resolution (smaller bounding regions), results in greater uncertainty (wider bounds). Minimization of the 1-norm of spatial variation delivers the fewest possible regions defined by a mean conductivity, the quantity we wish to bound. Thus, these regions present a natural set for which the most narrow and discriminating bounds can be found. For illustration, we apply these techniques to synthetic magnetotelluric (MT) data sets resulting from one-dimensional (1D) earth models. In each case we find that with realistic data coverage, any single inverted model can often stray from the truth, while the computed bounds on an encompassing region contain both the inverted and the true conductivities, indicating that our measure of model uncertainty is robust. Such estimates of uncertainty for conductivity can then be translated to bounds on important petrological parameters such as mineralogy, porosity, saturation, and fluid type.

Variationally consistent discretization schemes and numerical algorithms for contact problems

NASA Astrophysics Data System (ADS)

Wohlmuth, Barbara

We consider variationally consistent discretization schemes for mechanical contact problems. Most of the results can also be applied to other variational inequalities, such as those for phase transition problems in porous media, for plasticity or for option pricing applications from finance. The starting point is to weakly incorporate the constraint into the setting and to reformulate the inequality in the displacement in terms of a saddle-point problem. Here, the Lagrange multiplier represents the surface forces, and the constraints are restricted to the boundary of the simulation domain. Having a uniform inf-sup bound, one can then establish optimal low-order a priori convergence rates for the discretization error in the primal and dual variables. In addition to the abstract framework of linear saddle-point theory, complementarity terms have to be taken into account. The resulting inequality system is solved by rewriting it equivalently by means of the non-linear complementarity function as a system of equations. Although it is not differentiable in the classical sense, semi-smooth Newton methods, yielding super-linear convergence rates, can be applied and easily implemented in terms of a primal-dual active set strategy. Quite often the solution of contact problems has a low regularity, and the efficiency of the approach can be improved by using adaptive refinement techniques. Different standard types, such as residual- and equilibrated-based a posteriori error estimators, can be designed based on the interpretation of the dual variable as Neumann boundary condition. For the fully dynamic setting it is of interest to apply energy-preserving time-integration schemes. However, the differential algebraic character of the system can result in high oscillations if standard methods are applied. A possible remedy is to modify the fully discretized system by a local redistribution of the mass. Numerical results in two and three dimensions illustrate the wide range of possible applications and show the performance of the space discretization scheme, non-linear solver, adaptive refinement process and time integration.

Approximate solution of the p-median minimization problem

NASA Astrophysics Data System (ADS)

Il'ev, V. P.; Il'eva, S. D.; Navrotskaya, A. A.

2016-09-01

A version of the facility location problem (the well-known p-median minimization problem) and its generalization—the problem of minimizing a supermodular set function—is studied. These problems are NP-hard, and they are approximately solved by a gradient algorithm that is a discrete analog of the steepest descent algorithm. A priori bounds on the worst-case behavior of the gradient algorithm for the problems under consideration are obtained. As a consequence, a bound on the performance guarantee of the gradient algorithm for the p-median minimization problem in terms of the production and transportation cost matrix is obtained.

Insight and analysis problem solving in microbes to machines.

PubMed

Clark, Kevin B

2015-11-01

A key feature for obtaining solutions to difficult problems, insight is oftentimes vaguely regarded as a special discontinuous intellectual process and/or a cognitive restructuring of problem representation or goal approach. However, this nearly century-old state of art devised by the Gestalt tradition to explain the non-analytical or non-trial-and-error, goal-seeking aptitude of primate mentality tends to neglect problem-solving capabilities of lower animal phyla, Kingdoms other than Animalia, and advancing smart computational technologies built from biological, artificial, and composite media. Attempting to provide an inclusive, precise definition of insight, two major criteria of insight, discontinuous processing and problem restructuring, are here reframed using terminology and statistical mechanical properties of computational complexity classes. Discontinuous processing becomes abrupt state transitions in algorithmic/heuristic outcomes or in types of algorithms/heuristics executed by agents using classical and/or quantum computational models. And problem restructuring becomes combinatorial reorganization of resources, problem-type substitution, and/or exchange of computational models. With insight bounded by computational complexity, humans, ciliated protozoa, and complex technological networks, for example, show insight when restructuring time requirements, combinatorial complexity, and problem type to solve polynomial and nondeterministic polynomial decision problems. Similar effects are expected from other problem types, supporting the idea that insight might be an epiphenomenon of analytical problem solving and consequently a larger information processing framework. Thus, this computational complexity definition of insight improves the power, external and internal validity, and reliability of operational parameters with which to classify, investigate, and produce the phenomenon for computational agents ranging from microbes to man-made devices. Copyright © 2015 Elsevier Ltd. All rights reserved.

Large Eddy Simulation of Wall-Bounded Turbulent Flows with the Lattice Boltzmann Method: Effect of Collision Model, SGS Model and Grid Resolution

NASA Astrophysics Data System (ADS)

Pradhan, Aniruddhe; Akhavan, Rayhaneh

2017-11-01

Effect of collision model, subgrid-scale model and grid resolution in Large Eddy Simulation (LES) of wall-bounded turbulent flows with the Lattice Boltzmann Method (LBM) is investigated in turbulent channel flow. The Single Relaxation Time (SRT) collision model is found to be more accurate than Multi-Relaxation Time (MRT) collision model in well-resolved LES. Accurate LES requires grid resolutions of Δ+ <= 4 in the near-wall region, which is comparable to Δ+ <= 2 required in DNS. At larger grid resolutions SRT becomes unstable, while MRT remains stable but gives unacceptably large errors. LES with no model gave errors comparable to the Dynamic Smagorinsky Model (DSM) and the Wall Adapting Local Eddy-viscosity (WALE) model. The resulting errors in the prediction of the friction coefficient in turbulent channel flow at a bulk Reynolds Number of 7860 (Reτ 442) with Δ+ = 4 and no-model, DSM and WALE were 1.7%, 2.6%, 3.1% with SRT, and 8.3% 7.5% 8.7% with MRT, respectively. These results suggest that LES of wall-bounded turbulent flows with LBM requires either grid-embedding in the near-wall region, with grid resolutions comparable to DNS, or a wall model. Results of LES with grid-embedding and wall models will be discussed.

Approximating Multilinear Monomial Coefficients and Maximum Multilinear Monomials in Multivariate Polynomials

NASA Astrophysics Data System (ADS)

Chen, Zhixiang; Fu, Bin

This paper is our third step towards developing a theory of testing monomials in multivariate polynomials and concentrates on two problems: (1) How to compute the coefficients of multilinear monomials; and (2) how to find a maximum multilinear monomial when the input is a ΠΣΠ polynomial. We first prove that the first problem is #P-hard and then devise a O *(3 n s(n)) upper bound for this problem for any polynomial represented by an arithmetic circuit of size s(n). Later, this upper bound is improved to O *(2 n ) for ΠΣΠ polynomials. We then design fully polynomial-time randomized approximation schemes for this problem for ΠΣ polynomials. On the negative side, we prove that, even for ΠΣΠ polynomials with terms of degree ≤ 2, the first problem cannot be approximated at all for any approximation factor ≥ 1, nor "weakly approximated" in a much relaxed setting, unless P=NP. For the second problem, we first give a polynomial time λ-approximation algorithm for ΠΣΠ polynomials with terms of degrees no more a constant λ ≥ 2. On the inapproximability side, we give a n (1 - ɛ)/2 lower bound, for any ɛ> 0, on the approximation factor for ΠΣΠ polynomials. When the degrees of the terms in these polynomials are constrained as ≤ 2, we prove a 1.0476 lower bound, assuming Pnot=NP; and a higher 1.0604 lower bound, assuming the Unique Games Conjecture.

An Improved Neutron Transport Algorithm for Space Radiation

NASA Technical Reports Server (NTRS)

Heinbockel, John H.; Clowdsley, Martha S.; Wilson, John W.

2000-01-01

A low-energy neutron transport algorithm for use in space radiation protection is developed. The algorithm is based upon a multigroup analysis of the straight-ahead Boltzmann equation by using a mean value theorem for integrals. This analysis is accomplished by solving a realistic but simplified neutron transport test problem. The test problem is analyzed by using numerical and analytical procedures to obtain an accurate solution within specified error bounds. Results from the test problem are then used for determining mean values associated with rescattering terms that are associated with a multigroup solution of the straight-ahead Boltzmann equation. The algorithm is then coupled to the Langley HZETRN code through the evaporation source term. Evaluation of the neutron fluence generated by the solar particle event of February 23, 1956, for a water and an aluminum-water shield-target configuration is then compared with LAHET and MCNPX Monte Carlo code calculations for the same shield-target configuration. The algorithm developed showed a great improvement in results over the unmodified HZETRN solution. In addition, a two-directional solution of the evaporation source showed even further improvement of the fluence near the front of the water target where diffusion from the front surface is important.

Actor-critic-based optimal tracking for partially unknown nonlinear discrete-time systems.

PubMed

Kiumarsi, Bahare; Lewis, Frank L

2015-01-01

This paper presents a partially model-free adaptive optimal control solution to the deterministic nonlinear discrete-time (DT) tracking control problem in the presence of input constraints. The tracking error dynamics and reference trajectory dynamics are first combined to form an augmented system. Then, a new discounted performance function based on the augmented system is presented for the optimal nonlinear tracking problem. In contrast to the standard solution, which finds the feedforward and feedback terms of the control input separately, the minimization of the proposed discounted performance function gives both feedback and feedforward parts of the control input simultaneously. This enables us to encode the input constraints into the optimization problem using a nonquadratic performance function. The DT tracking Bellman equation and tracking Hamilton-Jacobi-Bellman (HJB) are derived. An actor-critic-based reinforcement learning algorithm is used to learn the solution to the tracking HJB equation online without requiring knowledge of the system drift dynamics. That is, two neural networks (NNs), namely, actor NN and critic NN, are tuned online and simultaneously to generate the optimal bounded control policy. A simulation example is given to show the effectiveness of the proposed method.

On the optimality of individual entangling-probe attacks against BB84 quantum key distribution

NASA Astrophysics Data System (ADS)

Herbauts, I. M.; Bettelli, S.; Hã¼bel, H.; Peev, M.

2008-02-01

Some MIT researchers [Phys. Rev. A 75, 042327 (2007)] have recently claimed that their implementation of the Slutsky-Brandt attack [Phys. Rev. A 57, 2383 (1998); Phys. Rev. A 71, 042312 (2005)] to the BB84 quantum-key-distribution (QKD) protocol puts the security of this protocol “to the test” by simulating “the most powerful individual-photon attack” [Phys. Rev. A 73, 012315 (2006)]. A related unfortunate news feature by a scientific journal [G. Brumfiel, Quantum cryptography is hacked, News @ Nature (april 2007); Nature 447, 372 (2007)] has spurred some concern in the QKD community and among the general public by misinterpreting the implications of this work. The present article proves the existence of a stronger individual attack on QKD protocols with encrypted error correction, for which tight bounds are shown, and clarifies why the claims of the news feature incorrectly suggest a contradiction with the established “old-style” theory of BB84 individual attacks. The full implementation of a quantum cryptographic protocol includes a reconciliation and a privacy-amplification stage, whose choice alters in general both the maximum extractable secret and the optimal eavesdropping attack. The authors of [Phys. Rev. A 75, 042327 (2007)] are concerned only with the error-free part of the so-called sifted string, and do not consider faulty bits, which, in the version of their protocol, are discarded. When using the provably superior reconciliation approach of encrypted error correction (instead of error discard), the Slutsky-Brandt attack is no more optimal and does not “threaten” the security bound derived by Lütkenhaus [Phys. Rev. A 59, 3301 (1999)]. It is shown that the method of Slutsky and collaborators [Phys. Rev. A 57, 2383 (1998)] can be adapted to reconciliation with error correction, and that the optimal entangling probe can be explicitly found. Moreover, this attack fills Lütkenhaus bound, proving that it is tight (a fact which was not previously known).

Backstepping Design of Adaptive Neural Fault-Tolerant Control for MIMO Nonlinear Systems.

PubMed

Gao, Hui; Song, Yongduan; Wen, Changyun

In this paper, an adaptive controller is developed for a class of multi-input and multioutput nonlinear systems with neural networks (NNs) used as a modeling tool. It is shown that all the signals in the closed-loop system with the proposed adaptive neural controller are globally uniformly bounded for any external input in . In our control design, the upper bound of the NN modeling error and the gains of external disturbance are characterized by unknown upper bounds, which is more rational to establish the stability in the adaptive NN control. Filter-based modification terms are used in the update laws of unknown parameters to improve the transient performance. Finally, fault-tolerant control is developed to accommodate actuator failure. An illustrative example applying the adaptive controller to control a rigid robot arm shows the validation of the proposed controller.In this paper, an adaptive controller is developed for a class of multi-input and multioutput nonlinear systems with neural networks (NNs) used as a modeling tool. It is shown that all the signals in the closed-loop system with the proposed adaptive neural controller are globally uniformly bounded for any external input in . In our control design, the upper bound of the NN modeling error and the gains of external disturbance are characterized by unknown upper bounds, which is more rational to establish the stability in the adaptive NN control. Filter-based modification terms are used in the update laws of unknown parameters to improve the transient performance. Finally, fault-tolerant control is developed to accommodate actuator failure. An illustrative example applying the adaptive controller to control a rigid robot arm shows the validation of the proposed controller.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, L; Han, Y; Jin, M

Purpose: To develop an iterative reconstruction method for X-ray CT, in which the reconstruction can quickly converge to the desired solution with much reduced projection views. Methods: The reconstruction is formulated as a convex feasibility problem, i.e. the solution is an intersection of three convex sets: 1) data fidelity (DF) set – the L2 norm of the difference of observed projections and those from the reconstructed image is no greater than an error bound; 2) non-negativity of image voxels (NN) set; and 3) piecewise constant (PC) set - the total variation (TV) of the reconstructed image is no greater thanmore » an upper bound. The solution can be found by applying projection onto convex sets (POCS) sequentially for these three convex sets. Specifically, the algebraic reconstruction technique and setting negative voxels as zero are used for projection onto the DF and NN sets, respectively, while the projection onto the PC set is achieved by solving a standard Rudin, Osher, and Fatemi (ROF) model. The proposed method is named as full sequential POCS (FS-POCS), which is tested using the Shepp-Logan phantom and the Catphan600 phantom and compared with two similar algorithms, TV-POCS and CP-TV. Results: Using the Shepp-Logan phantom, the root mean square error (RMSE) of reconstructed images changing along with the number of iterations is used as the convergence measurement. In general, FS- POCS converges faster than TV-POCS and CP-TV, especially with fewer projection views. FS-POCS can also achieve accurate reconstruction of cone-beam CT of the Catphan600 phantom using only 54 views, comparable to that of FDK using 364 views. Conclusion: We developed an efficient iterative reconstruction for sparse-view CT using full sequential POCS. The simulation and physical phantom data demonstrated the computational efficiency and effectiveness of FS-POCS.« less

An efficient method for generalized linear multiplicative programming problem with multiplicative constraints.

PubMed

Zhao, Yingfeng; Liu, Sanyang

2016-01-01

We present a practical branch and bound algorithm for globally solving generalized linear multiplicative programming problem with multiplicative constraints. To solve the problem, a relaxation programming problem which is equivalent to a linear programming is proposed by utilizing a new two-phase relaxation technique. In the algorithm, lower and upper bounds are simultaneously obtained by solving some linear relaxation programming problems. Global convergence has been proved and results of some sample examples and a small random experiment show that the proposed algorithm is feasible and efficient.

A fast numerical method for the valuation of American lookback put options

NASA Astrophysics Data System (ADS)

Song, Haiming; Zhang, Qi; Zhang, Ran

2015-10-01

A fast and efficient numerical method is proposed and analyzed for the valuation of American lookback options. American lookback option pricing problem is essentially a two-dimensional unbounded nonlinear parabolic problem. We reformulate it into a two-dimensional parabolic linear complementary problem (LCP) on an unbounded domain. The numeraire transformation and domain truncation technique are employed to convert the two-dimensional unbounded LCP into a one-dimensional bounded one. Furthermore, the variational inequality (VI) form corresponding to the one-dimensional bounded LCP is obtained skillfully by some discussions. The resulting bounded VI is discretized by a finite element method. Meanwhile, the stability of the semi-discrete solution and the symmetric positive definiteness of the full-discrete matrix are established for the bounded VI. The discretized VI related to options is solved by a projection and contraction method. Numerical experiments are conducted to test the performance of the proposed method.

Performance bounds for nonlinear systems with a nonlinear ℒ2-gain property

NASA Astrophysics Data System (ADS)

Zhang, Huan; Dower, Peter M.

2012-09-01

Nonlinear ℒ2-gain is a finite gain concept that generalises the notion of conventional (linear) finite ℒ2-gain to admit the application of ℒ2-gain analysis tools of a broader class of nonlinear systems. The computation of tight comparison function bounds for this nonlinear ℒ2-gain property is important in applications such as small gain design. This article presents an approximation framework for these comparison function bounds through the formulation and solution of an optimal control problem. Key to the solution of this problem is the lifting of an ℒ2-norm input constraint, which is facilitated via the introduction of an energy saturation operator. This admits the solution of the optimal control problem of interest via dynamic programming and associated numerical methods, leading to the computation of the proposed bounds. Two examples are presented to demonstrate this approach.

Determination and error analysis of emittance and spectral emittance measurements by remote sensing

NASA Technical Reports Server (NTRS)

Dejesusparada, N. (Principal Investigator); Kumar, R.

1977-01-01

The author has identified the following significant results. From the theory of remote sensing of surface temperatures, an equation of the upper bound of absolute error of emittance was determined. It showed that the absolute error decreased with an increase in contact temperature, whereas, it increased with an increase in environmental integrated radiant flux density. Change in emittance had little effect on the absolute error. A plot of the difference between temperature and band radiance temperature vs. emittance was provided for the wavelength intervals: 4.5 to 5.5 microns, 8 to 13.5 microns, and 10.2 to 12.5 microns.

Long-distance measurement-device-independent quantum key distribution with coherent-state superpositions.

PubMed

Yin, H-L; Cao, W-F; Fu, Y; Tang, Y-L; Liu, Y; Chen, T-Y; Chen, Z-B

2014-09-15

Measurement-device-independent quantum key distribution (MDI-QKD) with decoy-state method is believed to be securely applied to defeat various hacking attacks in practical quantum key distribution systems. Recently, the coherent-state superpositions (CSS) have emerged as an alternative to single-photon qubits for quantum information processing and metrology. Here, in this Letter, CSS are exploited as the source in MDI-QKD. We present an analytical method that gives two tight formulas to estimate the lower bound of yield and the upper bound of bit error rate. We exploit the standard statistical analysis and Chernoff bound to perform the parameter estimation. Chernoff bound can provide good bounds in the long-distance MDI-QKD. Our results show that with CSS, both the security transmission distance and secure key rate are significantly improved compared with those of the weak coherent states in the finite-data case.

Stochastic goal-oriented error estimation with memory

NASA Astrophysics Data System (ADS)

Ackmann, Jan; Marotzke, Jochem; Korn, Peter

2017-11-01

We propose a stochastic dual-weighted error estimator for the viscous shallow-water equation with boundaries. For this purpose, previous work on memory-less stochastic dual-weighted error estimation is extended by incorporating memory effects. The memory is introduced by describing the local truncation error as a sum of time-correlated random variables. The random variables itself represent the temporal fluctuations in local truncation errors and are estimated from high-resolution information at near-initial times. The resulting error estimator is evaluated experimentally in two classical ocean-type experiments, the Munk gyre and the flow around an island. In these experiments, the stochastic process is adapted locally to the respective dynamical flow regime. Our stochastic dual-weighted error estimator is shown to provide meaningful error bounds for a range of physically relevant goals. We prove, as well as show numerically, that our approach can be interpreted as a linearized stochastic-physics ensemble.

Errors analysis of problem solving using the Newman stage after applying cooperative learning of TTW type

NASA Astrophysics Data System (ADS)

Rr Chusnul, C.; Mardiyana, S., Dewi Retno

2017-12-01

Problem solving is the basis of mathematics learning. Problem solving teaches us to clarify an issue coherently in order to avoid misunderstanding information. Sometimes there may be mistakes in problem solving due to misunderstanding the issue, choosing a wrong concept or misapplied concept. The problem-solving test was carried out after students were given treatment on learning by using cooperative learning of TTW type. The purpose of this study was to elucidate student problem regarding to problem solving errors after learning by using cooperative learning of TTW type. Newman stages were used to identify problem solving errors in this study. The new research used a descriptive method to find out problem solving errors in students. The subject in this study were students of Vocational Senior High School (SMK) in 10th grade. Test and interview was conducted for data collection. Thus, the results of this study suggested problem solving errors in students after learning by using cooperative learning of TTW type for Newman stages.

Remediating Common Math Errors.

ERIC Educational Resources Information Center

Wagner, Rudolph F.

1981-01-01

Explanations and remediation suggestions for five types of mathematics errors due either to perceptual or cognitive difficulties are given. Error types include directionality problems, mirror writing, visually misperceived signs, diagnosed directionality problems, and mixed process errors. (CL)

Understanding Problem-Solving Errors by Students with Learning Disabilities in Standards-Based and Traditional Curricula

ERIC Educational Resources Information Center

Bouck, Emily C.; Bouck, Mary K.; Joshi, Gauri S.; Johnson, Linley

2016-01-01

Students with learning disabilities struggle with word problems in mathematics classes. Understanding the type of errors students make when working through such mathematical problems can further describe student performance and highlight student difficulties. Through the use of error codes, researchers analyzed the type of errors made by 14 sixth…

Assessment of averaging spatially correlated noise for 3-D radial imaging.

PubMed

Stobbe, Robert W; Beaulieu, Christian

2011-07-01

Any measurement of signal intensity obtained from an image will be corrupted by noise. If the measurement is from one voxel, an error bound associated with noise can be assigned if the standard deviation of noise in the image is known. If voxels are averaged together within a region of interest (ROI) and the image noise is uncorrelated, the error bound associated with noise will be reduced in proportion to the square root of the number of voxels in the ROI. However, when 3-D-radial images are created the image noise will be spatially correlated. In this paper, an equation is derived and verified with simulated noise for the computation of noise averaging when image noise is correlated, facilitating the assessment of noise characteristics for different 3-D-radial imaging methodologies. It is already known that if the radial evolution of projections are altered such that constant sampling density is produced in k-space, the signal-to-noise ratio (SNR) inefficiency of standard radial imaging (SR) can effectively be eliminated (assuming a uniform transfer function is desired). However, it is shown in this paper that the low-frequency noise power reduction of SR will produce beneficial (anti-) correlation of noise and enhanced noise averaging characteristics. If an ROI contains only one voxel a radial evolution altered uniform k-space sampling technique such as twisted projection imaging (TPI) will produce an error bound ~35% less with respect to noise than SR, however, for an ROI containing 16 voxels the SR methodology will facilitate an error bound ~20% less than TPI. If a filtering transfer function is desired, it is shown that designing sampling density to create the filter shape has both SNR and noise correlation advantages over sampling k-space uniformly. In this context SR is also beneficial. Two sets of 48 images produced from a saline phantom with sodium MRI at 4.7T are used to experimentally measure noise averaging characteristics of radial imaging and good agreement with theory is obtained.

Constrained binary classification using ensemble learning: an application to cost-efficient targeted PrEP strategies.

PubMed

Zheng, Wenjing; Balzer, Laura; van der Laan, Mark; Petersen, Maya

2018-01-30

Binary classification problems are ubiquitous in health and social sciences. In many cases, one wishes to balance two competing optimality considerations for a binary classifier. For instance, in resource-limited settings, an human immunodeficiency virus prevention program based on offering pre-exposure prophylaxis (PrEP) to select high-risk individuals must balance the sensitivity of the binary classifier in detecting future seroconverters (and hence offering them PrEP regimens) with the total number of PrEP regimens that is financially and logistically feasible for the program. In this article, we consider a general class of constrained binary classification problems wherein the objective function and the constraint are both monotonic with respect to a threshold. These include the minimization of the rate of positive predictions subject to a minimum sensitivity, the maximization of sensitivity subject to a maximum rate of positive predictions, and the Neyman-Pearson paradigm, which minimizes the type II error subject to an upper bound on the type I error. We propose an ensemble approach to these binary classification problems based on the Super Learner methodology. This approach linearly combines a user-supplied library of scoring algorithms, with combination weights and a discriminating threshold chosen to minimize the constrained optimality criterion. We then illustrate the application of the proposed classifier to develop an individualized PrEP targeting strategy in a resource-limited setting, with the goal of minimizing the number of PrEP offerings while achieving a minimum required sensitivity. This proof of concept data analysis uses baseline data from the ongoing Sustainable East Africa Research in Community Health study. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Parallel computers - Estimate errors caused by imprecise data

NASA Technical Reports Server (NTRS)

Kreinovich, Vladik; Bernat, Andrew; Villa, Elsa; Mariscal, Yvonne

1991-01-01

A new approach to the problem of estimating errors caused by imprecise data is proposed in the context of software engineering. A software device is used to produce an ideal solution to the problem, when the computer is capable of computing errors of arbitrary programs. The software engineering aspect of this problem is to describe a device for computing the error estimates in software terms and then to provide precise numbers with error estimates to the user. The feasibility of the program capable of computing both some quantity and its error estimate in the range of possible measurement errors is demonstrated.

Degenerate quantum codes and the quantum Hamming bound

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sarvepalli, Pradeep; Klappenecker, Andreas

2010-03-15

The parameters of a nondegenerate quantum code must obey the Hamming bound. An important open problem in quantum coding theory is whether the parameters of a degenerate quantum code can violate this bound for nondegenerate quantum codes. In this article we show that Calderbank-Shor-Steane (CSS) codes, over a prime power alphabet q{>=}5, cannot beat the quantum Hamming bound. We prove a quantum version of the Griesmer bound for the CSS codes, which allows us to strengthen the Rains' bound that an [[n,k,d

Discretization vs. Rounding Error in Euler's Method

ERIC Educational Resources Information Center

Borges, Carlos F.

2011-01-01

Euler's method for solving initial value problems is an excellent vehicle for observing the relationship between discretization error and rounding error in numerical computation. Reductions in stepsize, in order to decrease discretization error, necessarily increase the number of steps and so introduce additional rounding error. The problem is…

Computing an upper bound on contact stress with surrogate duality

NASA Astrophysics Data System (ADS)

Xuan, Zhaocheng; Papadopoulos, Panayiotis

2016-07-01

We present a method for computing an upper bound on the contact stress of elastic bodies. The continuum model of elastic bodies with contact is first modeled as a constrained optimization problem by using finite elements. An explicit formulation of the total contact force, a fraction function with the numerator as a linear function and the denominator as a quadratic convex function, is derived with only the normalized nodal contact forces as the constrained variables in a standard simplex. Then two bounds are obtained for the sum of the nodal contact forces. The first is an explicit formulation of matrices of the finite element model, derived by maximizing the fraction function under the constraint that the sum of the normalized nodal contact forces is one. The second bound is solved by first maximizing the fraction function subject to the standard simplex and then using Dinkelbach's algorithm for fractional programming to find the maximum—since the fraction function is pseudo concave in a neighborhood of the solution. These two bounds are solved with the problem dimensions being only the number of contact nodes or node pairs, which are much smaller than the dimension for the original problem, namely, the number of degrees of freedom. Next, a scheme for constructing an upper bound on the contact stress is proposed that uses the bounds on the sum of the nodal contact forces obtained on a fine finite element mesh and the nodal contact forces obtained on a coarse finite element mesh, which are problems that can be solved at a lower computational cost. Finally, the proposed method is verified through some examples concerning both frictionless and frictional contact to demonstrate the method's feasibility, efficiency, and robustness.

Modal cost analysis for simple continua

NASA Technical Reports Server (NTRS)

Hu, A.; Skelton, R. E.; Yang, T. Y.

1988-01-01

The most popular finite element codes are based upon appealing theories of convergence of modal frequencies. For example, the popularity of cubic elements for beam-like structures is due to the rapid convergence of modal frequencies and stiffness properties. However, for those problems in which the primary consideration is the accuracy of response of the structure at specified locations, it is more important to obtain accuracy in the modal costs than in the modal frequencies. The modal cost represents the contribution of a mode in the norm of the response vector. This paper provides a complete modal cost analysis for simple continua such as beam-like structures. Upper bounds are developed for mode truncation errors in the model reduction process and modal cost analysis dictates which modes to retain in order to reduce the model for control design purposes.

An interval precise integration method for transient unbalance response analysis of rotor system with uncertainty

NASA Astrophysics Data System (ADS)

Fu, Chao; Ren, Xingmin; Yang, Yongfeng; Xia, Yebao; Deng, Wangqun

2018-07-01

A non-intrusive interval precise integration method (IPIM) is proposed in this paper to analyze the transient unbalance response of uncertain rotor systems. The transfer matrix method (TMM) is used to derive the deterministic equations of motion of a hollow-shaft overhung rotor. The uncertain transient dynamic problem is solved by combing the Chebyshev approximation theory with the modified precise integration method (PIM). Transient response bounds are calculated by interval arithmetic of the expansion coefficients. Theoretical error analysis of the proposed method is provided briefly, and its accuracy is further validated by comparing with the scanning method in simulations. Numerical results show that the IPIM can keep good accuracy in vibration prediction of the start-up transient process. Furthermore, the proposed method can also provide theoretical guidance to other transient dynamic mechanical systems with uncertainties.

Near optimal discrimination of binary coherent signals via atom–light interaction

NASA Astrophysics Data System (ADS)

Han, Rui; Bergou, János A.; Leuchs, Gerd

2018-04-01

We study the discrimination of weak coherent states of light with significant overlaps by nondestructive measurements on the light states through measuring atomic states that are entangled to the coherent states via dipole coupling. In this way, the problem of measuring and discriminating coherent light states is shifted to finding the appropriate atom–light interaction and atomic measurements. We show that this scheme allows us to attain a probability of error extremely close to the Helstrom bound, the ultimate quantum limit for discriminating binary quantum states, through the simple Jaynes–Cummings interaction between the field and ancilla with optimized light–atom coupling and projective measurements on the atomic states. Moreover, since the measurement is nondestructive on the light state, information that is not detected by one measurement can be extracted from the post-measurement light states through subsequent measurements.

A hybrid approach to parameter identification of linear delay differential equations involving multiple delays

NASA Astrophysics Data System (ADS)

Marzban, Hamid Reza

2018-05-01

In this paper, we are concerned with the parameter identification of linear time-invariant systems containing multiple delays. The approach is based upon a hybrid of block-pulse functions and Legendre's polynomials. The convergence of the proposed procedure is established and an upper error bound with respect to the L2-norm associated with the hybrid functions is derived. The problem under consideration is first transformed into a system of algebraic equations. The least squares technique is then employed for identification of the desired parameters. Several multi-delay systems of varying complexity are investigated to evaluate the performance and capability of the proposed approximation method. It is shown that the proposed approach is also applicable to a class of nonlinear multi-delay systems. It is demonstrated that the suggested procedure provides accurate results for the desired parameters.

The Foraging Ecology of Royal and Sandwich Terns in North Carolina, USA

USGS Publications Warehouse

McGinnis, T.W.; Emslie, S.D.

2001-01-01

Population sizes of territorial male red-winged blackbirds (Agelaius phoeniceus) were determined with counts of territorial males (area count) and a Petersen-Lincoln Index method for roadsides (roadside estimate). Weather conditions and time of day did not influence either method. Combined roadside estimates had smaller error bounds than the individual transect estimates and were not hindered by the problem of zero recaptures. Roadside estimates were usually one-half as large as the area counts, presumably due to an observer bias for marked birds. The roadside estimate provides only an index of major changes in populations of territorial male redwings. When the roadside estimate is employed, the area count should be used to determine the amount and nature of observer bias. For small population surveys, the area count is probably more reliable and accurate than the roadside estimate.

Determining population size of territorial red-winged blackbirds

USGS Publications Warehouse

Albers, P.H.

1976-01-01

Population sizes of territorial male red-winged blackbirds (Agelaius phoeniceus) were determined with counts of territorial males (area count) and a Petersen-Lincoln Index method for roadsides (roadside estimate). Weather conditions and time of day did not influence either method. Combined roadside estimates had smaller error bounds than the individual transect estimates and were not hindered by the problem of zero recaptures. Roadside estimates were usually one-half as large as the area counts, presumably due to an observer bias for marked birds. The roadside estimate provides only an index of major changes in populations of territorial male redwings. When the roadside estimate is employed, the area count should be used to determine the amount and nature of observer bias. For small population surveys, the area count is probably more reliable and accurate than the roadside estimate.

Network problem threshold

NASA Technical Reports Server (NTRS)

Gejji, Raghvendra, R.

1992-01-01

Network transmission errors such as collisions, CRC errors, misalignment, etc. are statistical in nature. Although errors can vary randomly, a high level of errors does indicate specific network problems, e.g. equipment failure. In this project, we have studied the random nature of collisions theoretically as well as by gathering statistics, and established a numerical threshold above which a network problem is indicated with high probability.

Errors Made by Elementary Fourth Grade Students When Modelling Word Problems and the Elimination of Those Errors through Scaffolding

ERIC Educational Resources Information Center

Ulu, Mustafa

2017-01-01

This study aims to identify errors made by primary school students when modelling word problems and to eliminate those errors through scaffolding. A 10-question problem-solving achievement test was used in the research. The qualitative and quantitative designs were utilized together. The study group of the quantitative design comprises 248…

Panel Flutter Emulation Using a Few Concentrated Forces

NASA Astrophysics Data System (ADS)

Dhital, Kailash; Han, Jae-Hung

2018-04-01

The objective of this paper is to study the feasibility of panel flutter emulation using a few concentrated forces. The concentrated forces are considered to be equivalent to aerodynamic forces. The equivalence is carried out using surface spline method and principle of virtual work. The structural modeling of the plate is based on the classical plate theory and the aerodynamic modeling is based on the piston theory. The present approach differs from the linear panel flutter analysis in scheming the modal aerodynamics forces with unchanged structural properties. The solutions for the flutter problem are obtained numerically using the standard eigenvalue procedure. A few concentrated forces were considered with an optimization effort to decide their optimal locations. The optimization process is based on minimizing the error between the flutter bounds from emulated and linear flutter analysis method. The emulated flutter results for the square plate of four different boundary conditions using six concentrated forces are obtained with minimal error to the reference value. The results demonstrated the workability and viability of using concentrated forces in emulating real panel flutter. In addition, the paper includes the parametric studies of linear panel flutter whose proper literatures are not available.

Approximate Algorithms for Computing Spatial Distance Histograms with Accuracy Guarantees

PubMed Central

Grupcev, Vladimir; Yuan, Yongke; Tu, Yi-Cheng; Huang, Jin; Chen, Shaoping; Pandit, Sagar; Weng, Michael

2014-01-01

Particle simulation has become an important research tool in many scientific and engineering fields. Data generated by such simulations impose great challenges to database storage and query processing. One of the queries against particle simulation data, the spatial distance histogram (SDH) query, is the building block of many high-level analytics, and requires quadratic time to compute using a straightforward algorithm. Previous work has developed efficient algorithms that compute exact SDHs. While beating the naive solution, such algorithms are still not practical in processing SDH queries against large-scale simulation data. In this paper, we take a different path to tackle this problem by focusing on approximate algorithms with provable error bounds. We first present a solution derived from the aforementioned exact SDH algorithm, and this solution has running time that is unrelated to the system size N. We also develop a mathematical model to analyze the mechanism that leads to errors in the basic approximate algorithm. Our model provides insights on how the algorithm can be improved to achieve higher accuracy and efficiency. Such insights give rise to a new approximate algorithm with improved time/accuracy tradeoff. Experimental results confirm our analysis. PMID:24693210

Reconstruction of sparse-view X-ray computed tomography using adaptive iterative algorithms.

PubMed

Liu, Li; Lin, Weikai; Jin, Mingwu

2015-01-01

In this paper, we propose two reconstruction algorithms for sparse-view X-ray computed tomography (CT). Treating the reconstruction problems as data fidelity constrained total variation (TV) minimization, both algorithms adapt the alternate two-stage strategy: projection onto convex sets (POCS) for data fidelity and non-negativity constraints and steepest descent for TV minimization. The novelty of this work is to determine iterative parameters automatically from data, thus avoiding tedious manual parameter tuning. In TV minimization, the step sizes of steepest descent are adaptively adjusted according to the difference from POCS update in either the projection domain or the image domain, while the step size of algebraic reconstruction technique (ART) in POCS is determined based on the data noise level. In addition, projection errors are used to compare with the error bound to decide whether to perform ART so as to reduce computational costs. The performance of the proposed methods is studied and evaluated using both simulated and physical phantom data. Our methods with automatic parameter tuning achieve similar, if not better, reconstruction performance compared to a representative two-stage algorithm. Copyright © 2014 Elsevier Ltd. All rights reserved.

Proximity Navigation of Highly Constrained Spacecraft

NASA Technical Reports Server (NTRS)

Scarritt, S.; Swartwout, M.

2007-01-01

Bandit is a 3-kg automated spacecraft in development at Washington University in St. Louis. Bandit's primary mission is to demonstrate proximity navigation, including docking, around a 25-kg student-built host spacecraft. However, because of extreme constraints in mass, power and volume, traditional sensing and actuation methods are not available. In particular, Bandit carries only 8 fixed-magnitude cold-gas thrusters to control its 6 DOF motion. Bandit lacks true inertial sensing, and the ability to sense position relative to the host has error bounds that approach the size of the Bandit itself. Some of the navigation problems are addressed through an extremely robust, error-tolerant soft dock. In addition, we have identified a control methodology that performs well in this constrained environment: behavior-based velocity potential functions, which use a minimum-seeking method similar to Lyapunov functions. We have also adapted the discrete Kalman filter for use on Bandit for position estimation and have developed a similar measurement vs. propagation weighting algorithm for attitude estimation. This paper provides an overview of Bandit and describes the control and estimation approach. Results using our 6DOF flight simulator are provided, demonstrating that these methods show promise for flight use.

Volumetric breast density measurement: sensitivity analysis of a relative physics approach

PubMed Central

Lau, Susie; Abdul Aziz, Yang Faridah

2016-01-01

Objective: To investigate the sensitivity and robustness of a volumetric breast density (VBD) measurement system to errors in the imaging physics parameters including compressed breast thickness (CBT), tube voltage (kVp), filter thickness, tube current-exposure time product (mAs), detector gain, detector offset and image noise. Methods: 3317 raw digital mammograms were processed with Volpara® (Matakina Technology Ltd, Wellington, New Zealand) to obtain fibroglandular tissue volume (FGV), breast volume (BV) and VBD. Errors in parameters including CBT, kVp, filter thickness and mAs were simulated by varying them in the Digital Imaging and Communications in Medicine (DICOM) tags of the images up to ±10% of the original values. Errors in detector gain and offset were simulated by varying them in the Volpara configuration file up to ±10% from their default values. For image noise, Gaussian noise was generated and introduced into the original images. Results: Errors in filter thickness, mAs, detector gain and offset had limited effects on FGV, BV and VBD. Significant effects in VBD were observed when CBT, kVp, detector offset and image noise were varied (p < 0.0001). Maximum shifts in the mean (1.2%) and median (1.1%) VBD of the study population occurred when CBT was varied. Conclusion: Volpara was robust to expected clinical variations, with errors in most investigated parameters giving limited changes in results, although extreme variations in CBT and kVp could lead to greater errors. Advances in knowledge: Despite Volpara's robustness, rigorous quality control is essential to keep the parameter errors within reasonable bounds. Volpara appears robust within those bounds, albeit for more advanced applications such as tracking density change over time, it remains to be seen how accurate the measures need to be. PMID:27452264

Volumetric breast density measurement: sensitivity analysis of a relative physics approach.

PubMed

Lau, Susie; Ng, Kwan Hoong; Abdul Aziz, Yang Faridah

2016-10-01

To investigate the sensitivity and robustness of a volumetric breast density (VBD) measurement system to errors in the imaging physics parameters including compressed breast thickness (CBT), tube voltage (kVp), filter thickness, tube current-exposure time product (mAs), detector gain, detector offset and image noise. 3317 raw digital mammograms were processed with Volpara(®) (Matakina Technology Ltd, Wellington, New Zealand) to obtain fibroglandular tissue volume (FGV), breast volume (BV) and VBD. Errors in parameters including CBT, kVp, filter thickness and mAs were simulated by varying them in the Digital Imaging and Communications in Medicine (DICOM) tags of the images up to ±10% of the original values. Errors in detector gain and offset were simulated by varying them in the Volpara configuration file up to ±10% from their default values. For image noise, Gaussian noise was generated and introduced into the original images. Errors in filter thickness, mAs, detector gain and offset had limited effects on FGV, BV and VBD. Significant effects in VBD were observed when CBT, kVp, detector offset and image noise were varied (p < 0.0001). Maximum shifts in the mean (1.2%) and median (1.1%) VBD of the study population occurred when CBT was varied. Volpara was robust to expected clinical variations, with errors in most investigated parameters giving limited changes in results, although extreme variations in CBT and kVp could lead to greater errors. Despite Volpara's robustness, rigorous quality control is essential to keep the parameter errors within reasonable bounds. Volpara appears robust within those bounds, albeit for more advanced applications such as tracking density change over time, it remains to be seen how accurate the measures need to be.

A quantitative comparison of numerical methods for the compressible Euler equations: fifth-order WENO and piecewise-linear Godunov

NASA Astrophysics Data System (ADS)

Greenough, J. A.; Rider, W. J.

2004-05-01

A numerical study is undertaken comparing a fifth-order version of the weighted essentially non-oscillatory numerical (WENO5) method to a modern piecewise-linear, second-order, version of Godunov's (PLMDE) method for the compressible Euler equations. A series of one-dimensional test problems are examined beginning with classical linear problems and ending with complex shock interactions. The problems considered are: (1) linear advection of a Gaussian pulse in density, (2) Sod's shock tube problem, (3) the "peak" shock tube problem, (4) a version of the Shu and Osher shock entropy wave interaction and (5) the Woodward and Colella interacting shock wave problem. For each problem and method, run times, density error norms and convergence rates are reported for each method as produced from a common code test-bed. The linear problem exhibits the advertised convergence rate for both methods as well as the expected large disparity in overall error levels; WENO5 has the smaller errors and an enormous advantage in overall efficiency (in accuracy per unit CPU time). For the nonlinear problems with discontinuities, however, we generally see both first-order self-convergence of error as compared to an exact solution, or when an analytic solution is not available, a converged solution generated on an extremely fine grid. The overall comparison of error levels shows some variation from problem to problem. For Sod's shock tube, PLMDE has nearly half the error, while on the peak problem the errors are nearly the same. For the interacting blast wave problem the two methods again produce a similar level of error with a slight edge for the PLMDE. On the other hand, for the Shu-Osher problem, the errors are similar on the coarser grids, but favors WENO by a factor of nearly 1.5 on the finer grids used. In all cases holding mesh resolution constant though, PLMDE is less costly in terms of CPU time by approximately a factor of 6. If the CPU cost is taken as fixed, that is run times are equal for both numerical methods, then PLMDE uniformly produces lower errors than WENO for the fixed computation cost on the test problems considered here.

GUM Analysis for TIMS and SIMS Isotopic Ratios in Graphite

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heasler, Patrick G.; Gerlach, David C.; Cliff, John B.

2007-04-01

This report describes GUM calculations for TIMS and SIMS isotopic ratio measurements of reactor graphite samples. These isotopic ratios are used to estimate reactor burn-up, and currently consist of various ratios of U, Pu, and Boron impurities in the graphite samples. The GUM calculation is a propagation of error methodology that assigns uncertainties (in the form of standard error and confidence bound) to the final estimates.

Setting the Record Straight: Strong Positive Impacts Found from the National Evaluation of Upward Bound. Re-Analysis Documents Significant Positive Impacts Masked by Errors in Flawed Contractor Reports

ERIC Educational Resources Information Center

Cahalan, Margaret; Goodwin, David

2014-01-01

In January 2009, in the last week of the Bush Administration, the U.S. Department of Education (ED), upon orders from the departing political appointee staff, published the final report in a long running National Evaluation of Upward Bound (UB). The study was conducted by the contractor, Mathematica Policy Research. After more than a year in…

Finite-Time Attitude Tracking Control for Spacecraft Using Terminal Sliding Mode and Chebyshev Neural Network.

PubMed

An-Min Zou; Kumar, K D; Zeng-Guang Hou; Xi Liu

2011-08-01

A finite-time attitude tracking control scheme is proposed for spacecraft using terminal sliding mode and Chebyshev neural network (NN) (CNN). The four-parameter representations (quaternion) are used to describe the spacecraft attitude for global representation without singularities. The attitude state (i.e., attitude and velocity) error dynamics is transformed to a double integrator dynamics with a constraint on the spacecraft attitude. With consideration of this constraint, a novel terminal sliding manifold is proposed for the spacecraft. In order to guarantee that the output of the NN used in the controller is bounded by the corresponding bound of the approximated unknown function, a switch function is applied to generate a switching between the adaptive NN control and the robust controller. Meanwhile, a CNN, whose basis functions are implemented using only desired signals, is introduced to approximate the desired nonlinear function and bounded external disturbances online, and the robust term based on the hyperbolic tangent function is applied to counteract NN approximation errors in the adaptive neural control scheme. Most importantly, the finite-time stability in both the reaching phase and the sliding phase can be guaranteed by a Lyapunov-based approach. Finally, numerical simulations on the attitude tracking control of spacecraft in the presence of an unknown mass moment of inertia matrix, bounded external disturbances, and control input constraints are presented to demonstrate the performance of the proposed controller.

A computer program to calculate zeroes, extrema, and interval integrals for the associated Legendre functions. [for estimation of bounds of truncation error in spherical harmonic expansion of geopotential

NASA Technical Reports Server (NTRS)

Payne, M. H.

1973-01-01

A computer program is described for the calculation of the zeroes of the associated Legendre functions, Pnm, and their derivatives, for the calculation of the extrema of Pnm and also the integral between pairs of successive zeroes. The program has been run for all n,m from (0,0) to (20,20) and selected cases beyond that for n up to 40. Up to (20,20), the program (written in double precision) retains nearly full accuracy, and indications are that up to (40,40) there is still sufficient precision (4-5 decimal digits for a 54-bit mantissa) for estimation of various bounds and errors involved in geopotential modelling, the purpose for which the program was written.

Robust adaptive tracking control for nonholonomic mobile manipulator with uncertainties.

PubMed

Peng, Jinzhu; Yu, Jie; Wang, Jie

2014-07-01

In this paper, mobile manipulator is divided into two subsystems, that is, nonholonomic mobile platform subsystem and holonomic manipulator subsystem. First, the kinematic controller of the mobile platform is derived to obtain a desired velocity. Second, regarding the coupling between the two subsystems as disturbances, Lyapunov functions of the two subsystems are designed respectively. Third, a robust adaptive tracking controller is proposed to deal with the unknown upper bounds of parameter uncertainties and disturbances. According to the Lyapunov stability theory, the derived robust adaptive controller guarantees global stability of the closed-loop system, and the tracking errors and adaptive coefficient errors are all bounded. Finally, simulation results show that the proposed robust adaptive tracking controller for nonholonomic mobile manipulator is effective and has good tracking capacity. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Linear optical quantum metrology with single photons: Experimental errors, resource counting, and quantum Cramér-Rao bounds

NASA Astrophysics Data System (ADS)

Olson, Jonathan P.; Motes, Keith R.; Birchall, Patrick M.; Studer, Nick M.; LaBorde, Margarite; Moulder, Todd; Rohde, Peter P.; Dowling, Jonathan P.

2017-07-01

Quantum number-path entanglement is a resource for supersensitive quantum metrology and in particular provides for sub-shot-noise or even Heisenberg-limited sensitivity. However, such number-path entanglement is thought to have been resource intensive to create in the first place, typically requiring either very strong nonlinearities or nondeterministic preparation schemes with feedforward, which are difficult to implement. Recently [K. R. Motes et al., Phys. Rev. Lett. 114, 170802 (2015), 10.1103/PhysRevLett.114.170802], it was shown that number-path entanglement from a BosonSampling inspired interferometer can be used to beat the shot-noise limit. In this paper we compare and contrast different interferometric schemes, discuss resource counting, calculate exact quantum Cramér-Rao bounds, and study details of experimental errors.

An Analysis of a Finite Element Method for Convection-Diffusion Problems. Part II. A Posteriori Error Estimates and Adaptivity.

DTIC Science & Technology

1983-03-01

AN ANALYSIS OF A FINITE ELEMENT METHOD FOR CONVECTION- DIFFUSION PROBLEMS PART II: A POSTERIORI ERROR ESTIMATES AND ADAPTIVITY by W. G. Szymczak Y 6a...PERIOD COVERED AN ANALYSIS OF A FINITE ELEMENT METHOD FOR final life of the contract CONVECTION- DIFFUSION PROBLEM S. Part II: A POSTERIORI ERROR ...Element Method for Convection- Diffusion Problems. Part II: A Posteriori Error Estimates and Adaptivity W. G. Szvmczak and I. Babu~ka# Laboratory for

A Model-Free No-arbitrage Price Bound for Variance Options

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bonnans, J. Frederic, E-mail: frederic.bonnans@inria.fr; Tan Xiaolu, E-mail: xiaolu.tan@polytechnique.edu

2013-08-01

We suggest a numerical approximation for an optimization problem, motivated by its applications in finance to find the model-free no-arbitrage bound of variance options given the marginal distributions of the underlying asset. A first approximation restricts the computation to a bounded domain. Then we propose a gradient projection algorithm together with the finite difference scheme to solve the optimization problem. We prove the general convergence, and derive some convergence rate estimates. Finally, we give some numerical examples to test the efficiency of the algorithm.

Statistical image quantification toward optimal scan fusion and change quantification

NASA Astrophysics Data System (ADS)

Potesil, Vaclav; Zhou, Xiang Sean

2007-03-01

Recent advance of imaging technology has brought new challenges and opportunities for automatic and quantitative analysis of medical images. With broader accessibility of more imaging modalities for more patients, fusion of modalities/scans from one time point and longitudinal analysis of changes across time points have become the two most critical differentiators to support more informed, more reliable and more reproducible diagnosis and therapy decisions. Unfortunately, scan fusion and longitudinal analysis are both inherently plagued with increased levels of statistical errors. A lack of comprehensive analysis by imaging scientists and a lack of full awareness by physicians pose potential risks in clinical practice. In this paper, we discuss several key error factors affecting imaging quantification, studying their interactions, and introducing a simulation strategy to establish general error bounds for change quantification across time. We quantitatively show that image resolution, voxel anisotropy, lesion size, eccentricity, and orientation are all contributing factors to quantification error; and there is an intricate relationship between voxel anisotropy and lesion shape in affecting quantification error. Specifically, when two or more scans are to be fused at feature level, optimal linear fusion analysis reveals that scans with voxel anisotropy aligned with lesion elongation should receive a higher weight than other scans. As a result of such optimal linear fusion, we will achieve a lower variance than naïve averaging. Simulated experiments are used to validate theoretical predictions. Future work based on the proposed simulation methods may lead to general guidelines and error lower bounds for quantitative image analysis and change detection.

A fast and robust computational method for the ionization cross sections of the driven Schrödinger equation using an O (N) multigrid-based scheme

NASA Astrophysics Data System (ADS)

Cools, S.; Vanroose, W.

2016-03-01

This paper improves the convergence and robustness of a multigrid-based solver for the cross sections of the driven Schrödinger equation. Adding a Coupled Channel Correction Step (CCCS) after each multigrid (MG) V-cycle efficiently removes the errors that remain after the V-cycle sweep. The combined iterative solution scheme (MG-CCCS) is shown to feature significantly improved convergence rates over the classical MG method at energies where bound states dominate the solution, resulting in a fast and scalable solution method for the complex-valued Schrödinger break-up problem for any energy regime. The proposed solver displays optimal scaling; a solution is found in a time that is linear in the number of unknowns. The method is validated on a 2D Temkin-Poet model problem, and convergence results both as a solver and preconditioner are provided to support the O (N) scalability of the method. This paper extends the applicability of the complex contour approach for far field map computation (Cools et al. (2014) [10]).

Optimizing the learning rate for adaptive estimation of neural encoding models

PubMed Central

2018-01-01

Closed-loop neurotechnologies often need to adaptively learn an encoding model that relates the neural activity to the brain state, and is used for brain state decoding. The speed and accuracy of adaptive learning algorithms are critically affected by the learning rate, which dictates how fast model parameters are updated based on new observations. Despite the importance of the learning rate, currently an analytical approach for its selection is largely lacking and existing signal processing methods vastly tune it empirically or heuristically. Here, we develop a novel analytical calibration algorithm for optimal selection of the learning rate in adaptive Bayesian filters. We formulate the problem through a fundamental trade-off that learning rate introduces between the steady-state error and the convergence time of the estimated model parameters. We derive explicit functions that predict the effect of learning rate on error and convergence time. Using these functions, our calibration algorithm can keep the steady-state parameter error covariance smaller than a desired upper-bound while minimizing the convergence time, or keep the convergence time faster than a desired value while minimizing the error. We derive the algorithm both for discrete-valued spikes modeled as point processes nonlinearly dependent on the brain state, and for continuous-valued neural recordings modeled as Gaussian processes linearly dependent on the brain state. Using extensive closed-loop simulations, we show that the analytical solution of the calibration algorithm accurately predicts the effect of learning rate on parameter error and convergence time. Moreover, the calibration algorithm allows for fast and accurate learning of the encoding model and for fast convergence of decoding to accurate performance. Finally, larger learning rates result in inaccurate encoding models and decoders, and smaller learning rates delay their convergence. The calibration algorithm provides a novel analytical approach to predictably achieve a desired level of error and convergence time in adaptive learning, with application to closed-loop neurotechnologies and other signal processing domains. PMID:29813069

Optimizing the learning rate for adaptive estimation of neural encoding models.

PubMed

Hsieh, Han-Lin; Shanechi, Maryam M

2018-05-01

Closed-loop neurotechnologies often need to adaptively learn an encoding model that relates the neural activity to the brain state, and is used for brain state decoding. The speed and accuracy of adaptive learning algorithms are critically affected by the learning rate, which dictates how fast model parameters are updated based on new observations. Despite the importance of the learning rate, currently an analytical approach for its selection is largely lacking and existing signal processing methods vastly tune it empirically or heuristically. Here, we develop a novel analytical calibration algorithm for optimal selection of the learning rate in adaptive Bayesian filters. We formulate the problem through a fundamental trade-off that learning rate introduces between the steady-state error and the convergence time of the estimated model parameters. We derive explicit functions that predict the effect of learning rate on error and convergence time. Using these functions, our calibration algorithm can keep the steady-state parameter error covariance smaller than a desired upper-bound while minimizing the convergence time, or keep the convergence time faster than a desired value while minimizing the error. We derive the algorithm both for discrete-valued spikes modeled as point processes nonlinearly dependent on the brain state, and for continuous-valued neural recordings modeled as Gaussian processes linearly dependent on the brain state. Using extensive closed-loop simulations, we show that the analytical solution of the calibration algorithm accurately predicts the effect of learning rate on parameter error and convergence time. Moreover, the calibration algorithm allows for fast and accurate learning of the encoding model and for fast convergence of decoding to accurate performance. Finally, larger learning rates result in inaccurate encoding models and decoders, and smaller learning rates delay their convergence. The calibration algorithm provides a novel analytical approach to predictably achieve a desired level of error and convergence time in adaptive learning, with application to closed-loop neurotechnologies and other signal processing domains.

COMPLEX VARIABLE BOUNDARY ELEMENT METHOD: APPLICATIONS.

USGS Publications Warehouse

Hromadka, T.V.; Yen, C.C.; Guymon, G.L.

1985-01-01

The complex variable boundary element method (CVBEM) is used to approximate several potential problems where analytical solutions are known. A modeling result produced from the CVBEM is a measure of relative error in matching the known boundary condition values of the problem. A CVBEM error-reduction algorithm is used to reduce the relative error of the approximation by adding nodal points in boundary regions where error is large. From the test problems, overall error is reduced significantly by utilizing the adaptive integration algorithm.

Error Propagation Dynamics of PIV-based Pressure Field Calculations: How well does the pressure Poisson solver perform inherently?

PubMed

Pan, Zhao; Whitehead, Jared; Thomson, Scott; Truscott, Tadd

2016-08-01

Obtaining pressure field data from particle image velocimetry (PIV) is an attractive technique in fluid dynamics due to its noninvasive nature. The application of this technique generally involves integrating the pressure gradient or solving the pressure Poisson equation using a velocity field measured with PIV. However, very little research has been done to investigate the dynamics of error propagation from PIV-based velocity measurements to the pressure field calculation. Rather than measure the error through experiment, we investigate the dynamics of the error propagation by examining the Poisson equation directly. We analytically quantify the error bound in the pressure field, and are able to illustrate the mathematical roots of why and how the Poisson equation based pressure calculation propagates error from the PIV data. The results show that the error depends on the shape and type of boundary conditions, the dimensions of the flow domain, and the flow type.

Students’ errors in solving combinatorics problems observed from the characteristics of RME modeling

NASA Astrophysics Data System (ADS)

Meika, I.; Suryadi, D.; Darhim

2018-01-01

This article was written based on the learning evaluation results of students’ errors in solving combinatorics problems observed from the characteristics of Realistic Mathematics Education (RME); that is modeling. Descriptive method was employed by involving 55 students from two international-based pilot state senior high schools in Banten. The findings of the study suggested that the students still committed errors in simplifying the problem as much 46%; errors in making mathematical model (horizontal mathematization) as much 60%; errors in finishing mathematical model (vertical mathematization) as much 65%; and errors in interpretation as well as validation as much 66%.

Scattering and bound states of spinless particles in a mixed vector-scalar smooth step potential

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garcia, M.G.; Castro, A.S. de

2009-11-15

Scattering and bound states for a spinless particle in the background of a kink-like smooth step potential, added with a scalar uniform background, are considered with a general mixing of vector and scalar Lorentz structures. The problem is mapped into the Schroedinger-like equation with an effective Rosen-Morse potential. It is shown that the scalar uniform background present subtle and trick effects for the scattering states and reveals itself a high-handed element for formation of bound states. In that process, it is shown that the problem of solving a differential equation for the eigenenergies is transmuted into the simpler and moremore » efficient problem of solving an irrational algebraic equation.« less

Gender differences in the pathway from adverse life events to adolescent emotional and behavioural problems via negative cognitive errors.

PubMed

Flouri, Eirini; Panourgia, Constantina

2011-06-01

The aim of this study was to test for gender differences in how negative cognitive errors (overgeneralizing, catastrophizing, selective abstraction, and personalizing) mediate the association between adverse life events and adolescents' emotional and behavioural problems (measured with the Strengths and Difficulties Questionnaire). The sample consisted of 202 boys and 227 girls (aged 11-15 years) from three state secondary schools in disadvantaged areas in one county in the South East of England. Control variables were age, ethnicity, special educational needs, exclusion history, family structure, family socio-economic disadvantage, and verbal cognitive ability. Adverse life events were measured with Tiet et al.'s (1998) Adverse Life Events Scale. For both genders, we assumed a pathway from adverse life events to emotional and behavioural problems via cognitive errors. We found no gender differences in life adversity, cognitive errors, total difficulties, peer problems, or hyperactivity. In both boys and girls, even after adjustment for controls, cognitive errors were related to total difficulties and emotional symptoms, and life adversity was related to total difficulties and conduct problems. The life adversity/conduct problems association was not explained by negative cognitive errors in either gender. However, we found gender differences in how adversity and cognitive errors produced hyperactivity and internalizing problems. In particular, life adversity was not related, after adjustment for controls, to hyperactivity in girls and to peer problems and emotional symptoms in boys. Cognitive errors fully mediated the effect of life adversity on hyperactivity in boys and on peer and emotional problems in girls.

Fault-tolerant logical gates in quantum error-correcting codes

NASA Astrophysics Data System (ADS)

Pastawski, Fernando; Yoshida, Beni

2015-01-01

Recently, S. Bravyi and R. König [Phys. Rev. Lett. 110, 170503 (2013), 10.1103/PhysRevLett.110.170503] have shown that there is a trade-off between fault-tolerantly implementable logical gates and geometric locality of stabilizer codes. They consider locality-preserving operations which are implemented by a constant-depth geometrically local circuit and are thus fault tolerant by construction. In particular, they show that, for local stabilizer codes in D spatial dimensions, locality-preserving gates are restricted to a set of unitary gates known as the D th level of the Clifford hierarchy. In this paper, we explore this idea further by providing several extensions and applications of their characterization to qubit stabilizer and subsystem codes. First, we present a no-go theorem for self-correcting quantum memory. Namely, we prove that a three-dimensional stabilizer Hamiltonian with a locality-preserving implementation of a non-Clifford gate cannot have a macroscopic energy barrier. This result implies that non-Clifford gates do not admit such implementations in Haah's cubic code and Michnicki's welded code. Second, we prove that the code distance of a D -dimensional local stabilizer code with a nontrivial locality-preserving m th -level Clifford logical gate is upper bounded by O (LD +1 -m) . For codes with non-Clifford gates (m >2 ), this improves the previous best bound by S. Bravyi and B. Terhal [New. J. Phys. 11, 043029 (2009), 10.1088/1367-2630/11/4/043029]. Topological color codes, introduced by H. Bombin and M. A. Martin-Delgado [Phys. Rev. Lett. 97, 180501 (2006), 10.1103/PhysRevLett.97.180501; Phys. Rev. Lett. 98, 160502 (2007), 10.1103/PhysRevLett.98.160502; Phys. Rev. B 75, 075103 (2007), 10.1103/PhysRevB.75.075103], saturate the bound for m =D . Third, we prove that the qubit erasure threshold for codes with a nontrivial transversal m th -level Clifford logical gate is upper bounded by 1 /m . This implies that no family of fault-tolerant codes with transversal gates in increasing level of the Clifford hierarchy may exist. This result applies to arbitrary stabilizer and subsystem codes and is not restricted to geometrically local codes. Fourth, we extend the result of Bravyi and König to subsystem codes. Unlike stabilizer codes, the so-called union lemma does not apply to subsystem codes. This problem is avoided by assuming the presence of an error threshold in a subsystem code, and a conclusion analogous to that of Bravyi and König is recovered.

Trajectory specification for high capacity air traffic control

NASA Technical Reports Server (NTRS)

Paielli, Russell A. (Inventor)

2010-01-01

Method and system for analyzing and processing information on one or more aircraft flight paths, using a four-dimensional coordinate system including three Cartesian or equivalent coordinates (x, y, z) and a fourth coordinate .delta. that corresponds to a distance estimated along a reference flight path to a nearest reference path location corresponding to a present location of the aircraft. Use of the coordinate .delta., rather than elapsed time t, avoids coupling of along-track error into aircraft altitude and reduces effects of errors on an aircraft landing site. Along-track, cross-track and/or altitude errors are estimated and compared with a permitted error bounding space surrounding the reference flight path.

Closed-loop stability of linear quadratic optimal systems in the presence of modeling errors

NASA Technical Reports Server (NTRS)

Toda, M.; Patel, R.; Sridhar, B.

1976-01-01

The well-known stabilizing property of linear quadratic state feedback design is utilized to evaluate the robustness of a linear quadratic feedback design in the presence of modeling errors. Two general conditions are obtained for allowable modeling errors such that the resulting closed-loop system remains stable. One of these conditions is applied to obtain two more particular conditions which are readily applicable to practical situations where a designer has information on the bounds of modeling errors. Relations are established between the allowable parameter uncertainty and the weighting matrices of the quadratic performance index, thereby enabling the designer to select appropriate weighting matrices to attain a robust feedback design.

LS Bound based gene selection for DNA microarray data.

PubMed

Zhou, Xin; Mao, K Z

2005-04-15

One problem with discriminant analysis of DNA microarray data is that each sample is represented by quite a large number of genes, and many of them are irrelevant, insignificant or redundant to the discriminant problem at hand. Methods for selecting important genes are, therefore, of much significance in microarray data analysis. In the present study, a new criterion, called LS Bound measure, is proposed to address the gene selection problem. The LS Bound measure is derived from leave-one-out procedure of LS-SVMs (least squares support vector machines), and as the upper bound for leave-one-out classification results it reflects to some extent the generalization performance of gene subsets. We applied this LS Bound measure for gene selection on two benchmark microarray datasets: colon cancer and leukemia. We also compared the LS Bound measure with other evaluation criteria, including the well-known Fisher's ratio and Mahalanobis class separability measure, and other published gene selection algorithms, including Weighting factor and SVM Recursive Feature Elimination. The strength of the LS Bound measure is that it provides gene subsets leading to more accurate classification results than the filter method while its computational complexity is at the level of the filter method. A companion website can be accessed at http://www.ntu.edu.sg/home5/pg02776030/lsbound/. The website contains: (1) the source code of the gene selection algorithm; (2) the complete set of tables and figures regarding the experimental study; (3) proof of the inequality (9). ekzmao@ntu.edu.sg.

Chain representations of Open Quantum Systems and Lieb-Robinson like bounds for the dynamics

NASA Astrophysics Data System (ADS)

Woods, Mischa

2013-03-01

This talk is concerned with the mapping of the Hamiltonian of open quantum systems onto chain representations, which forms the basis for a rigorous theory of the interaction of a system with its environment. This mapping progresses as an interaction which gives rise to a sequence of residual spectral densities of the system. The rigorous mathematical properties of this mapping have been unknown so far. Here we develop the theory of secondary measures to derive an analytic, expression for the sequence solely in terms of the initial measure and its associated orthogonal polynomials of the first and second kind. These mappings can be thought of as taking a highly nonlocal Hamiltonian to a local Hamiltonian. In the latter, a Lieb-Robinson like bound for the dynamics of the open quantum system makes sense. We develop analytical bounds on the error to observables of the system as a function of time when the semi-infinite chain in truncated at some finite length. The fact that this is possible shows that there is a finite ``Speed of sound'' in these chain representations. This has many implications of the simulatability of open quantum systems of this type and demonstrates that a truncated chain can faithfully reproduce the dynamics at shorter times. These results make a significant and mathematically rigorous contribution to the understanding of the theory of open quantum systems; and pave the way towards the efficient simulation of these systems, which within the standard methods, is often an intractable problem. EPSRC CDT in Controlled Quantum Dynamics, EU STREP project and Alexander von Humboldt Foundation

Adaptive fuzzy-neural-network control for maglev transportation system.

PubMed

Wai, Rong-Jong; Lee, Jeng-Dao

2008-01-01

A magnetic-levitation (maglev) transportation system including levitation and propulsion control is a subject of considerable scientific interest because of highly nonlinear and unstable behaviors. In this paper, the dynamic model of a maglev transportation system including levitated electromagnets and a propulsive linear induction motor (LIM) based on the concepts of mechanical geometry and motion dynamics is developed first. Then, a model-based sliding-mode control (SMC) strategy is introduced. In order to alleviate chattering phenomena caused by the inappropriate selection of uncertainty bound, a simple bound estimation algorithm is embedded in the SMC strategy to form an adaptive sliding-mode control (ASMC) scheme. However, this estimation algorithm is always a positive value so that tracking errors introduced by any uncertainty will cause the estimated bound increase even to infinity with time. Therefore, it further designs an adaptive fuzzy-neural-network control (AFNNC) scheme by imitating the SMC strategy for the maglev transportation system. In the model-free AFNNC, online learning algorithms are designed to cope with the problem of chattering phenomena caused by the sign action in SMC design, and to ensure the stability of the controlled system without the requirement of auxiliary compensated controllers despite the existence of uncertainties. The outputs of the AFNNC scheme can be directly supplied to the electromagnets and LIM without complicated control transformations for relaxing strict constrains in conventional model-based control methodologies. The effectiveness of the proposed control schemes for the maglev transportation system is verified by numerical simulations, and the superiority of the AFNNC scheme is indicated in comparison with the SMC and ASMC strategies.

Error-correcting pairs for a public-key cryptosystem

NASA Astrophysics Data System (ADS)

Pellikaan, Ruud; Márquez-Corbella, Irene

2017-06-01

Code-based Cryptography (CBC) is a powerful and promising alternative for quantum resistant cryptography. Indeed, together with lattice-based cryptography, multivariate cryptography and hash-based cryptography are the principal available techniques for post-quantum cryptography. CBC was first introduced by McEliece where he designed one of the most efficient Public-Key encryption schemes with exceptionally strong security guarantees and other desirable properties that still resist to attacks based on Quantum Fourier Transform and Amplitude Amplification. The original proposal, which remains unbroken, was based on binary Goppa codes. Later, several families of codes have been proposed in order to reduce the key size. Some of these alternatives have already been broken. One of the main requirements of a code-based cryptosystem is having high performance t-bounded decoding algorithms which is achieved in the case the code has a t-error-correcting pair (ECP). Indeed, those McEliece schemes that use GRS codes, BCH, Goppa and algebraic geometry codes are in fact using an error-correcting pair as a secret key. That is, the security of these Public-Key Cryptosystems is not only based on the inherent intractability of bounded distance decoding but also on the assumption that it is difficult to retrieve efficiently an error-correcting pair. In this paper, the class of codes with a t-ECP is proposed for the McEliece cryptosystem. Moreover, we study the hardness of distinguishing arbitrary codes from those having a t-error correcting pair.

Comparing Consider-Covariance Analysis with Sigma-Point Consider Filter and Linear-Theory Consider Filter Formulations

NASA Technical Reports Server (NTRS)

Lisano, Michael E.

2007-01-01

Recent literature in applied estimation theory reflects growing interest in the sigma-point (also called unscented ) formulation for optimal sequential state estimation, often describing performance comparisons with extended Kalman filters as applied to specific dynamical problems [c.f. 1, 2, 3]. Favorable attributes of sigma-point filters are described as including a lower expected error for nonlinear even non-differentiable dynamical systems, and a straightforward formulation not requiring derivation or implementation of any partial derivative Jacobian matrices. These attributes are particularly attractive, e.g. in terms of enabling simplified code architecture and streamlined testing, in the formulation of estimators for nonlinear spaceflight mechanics systems, such as filter software onboard deep-space robotic spacecraft. As presented in [4], the Sigma-Point Consider Filter (SPCF) algorithm extends the sigma-point filter algorithm to the problem of consider covariance analysis. Considering parameters in a dynamical system, while estimating its state, provides an upper bound on the estimated state covariance, which is viewed as a conservative approach to designing estimators for problems of general guidance, navigation and control. This is because, whether a parameter in the system model is observable or not, error in the knowledge of the value of a non-estimated parameter will increase the actual uncertainty of the estimated state of the system beyond the level formally indicated by the covariance of an estimator that neglects errors or uncertainty in that parameter. The equations for SPCF covariance evolution are obtained in a fashion similar to the derivation approach taken with standard (i.e. linearized or extended) consider parameterized Kalman filters (c.f. [5]). While in [4] the SPCF and linear-theory consider filter (LTCF) were applied to an illustrative linear dynamics/linear measurement problem, in the present work examines the SPCF as applied to nonlinear sequential consider covariance analysis, i.e. in the presence of nonlinear dynamics and nonlinear measurements. A simple SPCF for orbit determination, exemplifying an algorithm hosted in the guidance, navigation and control (GN&C) computer processor of a hypothetical robotic spacecraft, was implemented, and compared with an identically-parameterized (standard) extended, consider-parameterized Kalman filter. The onboard filtering scenario examined is a hypothetical spacecraft orbit about a small natural body with imperfectly-known mass. The formulations, relative complexities, and performances of the filters are compared and discussed.

WHAMII - An enumeration and insertion procedure with binomial bounds for the stochastic time-constrained traveling salesman problem

NASA Technical Reports Server (NTRS)

Dahl, Roy W.; Keating, Karen; Salamone, Daryl J.; Levy, Laurence; Nag, Barindra; Sanborn, Joan A.

1987-01-01

This paper presents an algorithm (WHAMII) designed to solve the Artificial Intelligence Design Challenge at the 1987 AIAA Guidance, Navigation and Control Conference. The problem under consideration is a stochastic generalization of the traveling salesman problem in which travel costs can incur a penalty with a given probability. The variability in travel costs leads to a probability constraint with respect to violating the budget allocation. Given the small size of the problem (eleven cities), an approach is considered that combines partial tour enumeration with a heuristic city insertion procedure. For computational efficiency during both the enumeration and insertion procedures, precalculated binomial probabilities are used to determine an upper bound on the actual probability of violating the budget constraint for each tour. The actual probability is calculated for the final best tour, and additional insertions are attempted until the actual probability exceeds the bound.

Student Errors in Dynamic Mathematical Environments

ERIC Educational Resources Information Center

Brown, Molly; Bossé, Michael J.; Chandler, Kayla

2016-01-01

This study investigates the nature of student errors in the context of problem solving and Dynamic Math Environments. This led to the development of the Problem Solving Action Identification Framework; this framework captures and defines all activities and errors associated with problem solving in a dynamic math environment. Found are three…

Correcting quantum errors with entanglement.

PubMed

Brun, Todd; Devetak, Igor; Hsieh, Min-Hsiu

2006-10-20

We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard quantum error-correcting codes, thus allowing us to "quantize" all of classical linear coding theory. In particular, efficient modern classical codes that attain the Shannon capacity can be made into entanglement-assisted quantum codes attaining the hashing bound (closely related to the quantum capacity). For systems without large amounts of shared entanglement, these codes can also be used as catalytic codes, in which a small amount of initial entanglement enables quantum communication.

Asymptotic stability estimates near an equilibrium point

NASA Astrophysics Data System (ADS)

Dumas, H. Scott; Meyer, Kenneth R.; Palacián, Jesús F.; Yanguas, Patricia

2017-07-01

We use the error bounds for adiabatic invariants found in the work of Chartier, Murua and Sanz-Serna [3] to bound the solutions of a Hamiltonian system near an equilibrium over exponentially long times. Our estimates depend only on the linearized system and not on the higher order terms as in KAM theory, nor do we require any steepness or convexity conditions as in Nekhoroshev theory. We require that the equilibrium point where our estimate applies satisfy a type of formal stability called Lie stability.

The Problem of Limited Inter-rater Agreement in Modelling Music Similarity

PubMed Central

Flexer, Arthur; Grill, Thomas

2016-01-01

One of the central goals of Music Information Retrieval (MIR) is the quantification of similarity between or within pieces of music. These quantitative relations should mirror the human perception of music similarity, which is however highly subjective with low inter-rater agreement. Unfortunately this principal problem has been given little attention in MIR so far. Since it is not meaningful to have computational models that go beyond the level of human agreement, these levels of inter-rater agreement present a natural upper bound for any algorithmic approach. We will illustrate this fundamental problem in the evaluation of MIR systems using results from two typical application scenarios: (i) modelling of music similarity between pieces of music; (ii) music structure analysis within pieces of music. For both applications, we derive upper bounds of performance which are due to the limited inter-rater agreement. We compare these upper bounds to the performance of state-of-the-art MIR systems and show how the upper bounds prevent further progress in developing better MIR systems. PMID:28190932

GUM Analysis for SIMS Isotopic Ratios in BEP0 Graphite Qualification Samples, Round 2

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gerlach, David C.; Heasler, Patrick G.; Reid, Bruce D.

2009-01-01

This report describes GUM calculations for TIMS and SIMS isotopic ratio measurements of reactor graphite samples. These isotopic ratios are used to estimate reactor burn-up, and currently consist of various ratios of U, Pu, and Boron impurities in the graphite samples. The GUM calculation is a propagation of error methodology that assigns uncertainties (in the form of standard error and confidence bound) to the final estimates.

Integrated Data and Control Level Fault Tolerance Techniques for Signal Processing Computer Design

DTIC Science & Technology

1990-09-01

TOLERANCE TECHNIQUES FOR SIGNAL PROCESSING COMPUTER DESIGN G. Robert Redinbo I. INTRODUCTION High-speed signal processing is an important application of...techniques and mathematical approaches will be expanded later to the situation where hardware errors and roundoff and quantization noise affect all...detect errors equal in number to the degree of g(X), the maximum permitted by the Singleton bound [13]. Real cyclic codes, primarily applicable to

Using Fisher Information Criteria for Chemical Sensor Selection via Convex Optimization Methods

DTIC Science & Technology

2016-11-16

determinant of the inverse Fisher information matrix which is proportional to the global error volume. If a practitioner has a suitable...pro- ceeds from the determinant of the inverse Fisher information matrix which is proportional to the global error volume. If a practitioner has a...design of statistical estimators (i.e. sensors) as their respective inverses act as lower bounds to the (co)variances of the subject estimator, a property

Error Analysis of Wind Measurements for the University of Illinois Sodium Doppler Temperature System

NASA Technical Reports Server (NTRS)

Pfenninger, W. Matthew; Papen, George C.

1992-01-01

Four-frequency lidar measurements of temperature and wind velocity require accurate frequency tuning to an absolute reference and long term frequency stability. We quantify frequency tuning errors for the Illinois sodium system, to measure absolute frequencies and a reference interferometer to measure relative frequencies. To determine laser tuning errors, we monitor the vapor cell and interferometer during lidar data acquisition and analyze the two signals for variations as functions of time. Both sodium cell and interferometer are the same as those used to frequency tune the laser. By quantifying the frequency variations of the laser during data acquisition, an error analysis of temperature and wind measurements can be calculated. These error bounds determine the confidence in the calculated temperatures and wind velocities.

All the nonadiabatic (J=0) bound states of NO{sub 2}

DOE Office of Scientific and Technical Information (OSTI.GOV)

Salzgeber, R.F.; Mandelshtam, V.A.; Schlier, C.

1999-02-01

We calculated all 3170 A{sub 1} and B{sub 2} (J=0) vibronic bound states of the coupled electronic ground ({tilde X}&hthinsp;{sup 2}A{sub 1}) and the first excited ({tilde A}&hthinsp;{sup 2}B{sub 2}) surfaces of NO{sub 2}, using a modification of the {ital ab initio} potentials of Leonardi {ital et al.} [J. Chem. Phys. {bold 105}, 9051 (1996)]. The calculation was performed by harmonic inversion of the Chebyshev correlation function generated from a DVR Hamiltonian in Radau coordinates. The rms error of the eigenenergies is about 2.5 cm{sup {minus}1}, corresponding to a relative error of 10{sup {minus}4} near the dissociation energy. The resultsmore » are compared with the adiabatic and diabatic levels calculated from the same surfaces, with experimental data, and with some approximations for the number of states function N(E). The experimental levels are reproduced fairly well up to an energy of 12&hthinsp;000 cm{sup {minus}1} above the potential minimum while the total number of bound levels agrees to within 2{percent} with that calculated from the phase space volume. {copyright} {ital 1999 American Institute of Physics.}« less

A Posteriori Bounds for Linear-Functional Outputs of Crouzeix-Raviart Finite Element Discretizations of the Incompressible Stokes Problem

NASA Technical Reports Server (NTRS)

Patera, Anthony T.; Paraschivoiu, Marius

1998-01-01

We present a finite element technique for the efficient generation of lower and upper bounds to outputs which are linear functionals of the solutions to the incompressible Stokes equations in two space dimensions; the finite element discretization is effected by Crouzeix-Raviart elements, the discontinuous pressure approximation of which is central to our approach. The bounds are based upon the construction of an augmented Lagrangian: the objective is a quadratic "energy" reformulation of the desired output; the constraints are the finite element equilibrium equations (including the incompressibility constraint), and the intersubdomain continuity conditions on velocity. Appeal to the dual max-min problem for appropriately chosen candidate Lagrange multipliers then yields inexpensive bounds for the output associated with a fine-mesh discretization; the Lagrange multipliers are generated by exploiting an associated coarse-mesh approximation. In addition to the requisite coarse-mesh calculations, the bound technique requires solution only of local subdomain Stokes problems on the fine-mesh. The method is illustrated for the Stokes equations, in which the outputs of interest are the flowrate past, and the lift force on, a body immersed in a channel.

A tight upper bound for quadratic knapsack problems in grid-based wind farm layout optimization

NASA Astrophysics Data System (ADS)

Quan, Ning; Kim, Harrison M.

2018-03-01

The 0-1 quadratic knapsack problem (QKP) in wind farm layout optimization models possible turbine locations as nodes, and power loss due to wake effects between pairs of turbines as edges in a complete graph. The goal is to select up to a certain number of turbine locations such that the sum of selected node and edge coefficients is maximized. Finding the optimal solution to the QKP is difficult in general, but it is possible to obtain a tight upper bound on the QKP's optimal value which facilitates the use of heuristics to solve QKPs by giving a good estimate of the optimality gap of any feasible solution. This article applies an upper bound method that is especially well-suited to QKPs in wind farm layout optimization due to certain features of the formulation that reduce the computational complexity of calculating the upper bound. The usefulness of the upper bound was demonstrated by assessing the performance of the greedy algorithm for solving QKPs in wind farm layout optimization. The results show that the greedy algorithm produces good solutions within 4% of the optimal value for small to medium sized problems considered in this article.

Limits on estimating the width of thin tubular structures in 3D images.

PubMed

Wörz, Stefan; Rohr, Karl

2006-01-01

This work studies limits on estimating the width of thin tubular structures in 3D images. Based on nonlinear estimation theory we analyze the minimal stochastic error of estimating the width. Given a 3D analytic model of the image intensities of tubular structures, we derive a closed-form expression for the Cramér-Rao bound of the width estimate under image noise. We use the derived lower bound as a benchmark and compare it with three previously proposed accuracy limits for vessel width estimation. Moreover, by experimental investigations we demonstrate that the derived lower bound can be achieved by fitting a 3D parametric intensity model directly to the image data.

A passivity criterion for sampled-data bilateral teleoperation systems.

PubMed

Jazayeri, Ali; Tavakoli, Mahdi

2013-01-01

A teleoperation system consists of a teleoperator, a human operator, and a remote environment. Conditions involving system and controller parameters that ensure the teleoperator passivity can serve as control design guidelines to attain maximum teleoperation transparency while maintaining system stability. In this paper, sufficient conditions for teleoperator passivity are derived for when position error-based controllers are implemented in discrete-time. This new analysis is necessary because discretization causes energy leaks and does not necessarily preserve the passivity of the system. The proposed criterion for sampled-data teleoperator passivity imposes lower bounds on the teleoperator's robots dampings, an upper bound on the sampling time, and bounds on the control gains. The criterion is verified through simulations and experiments.

Human-robot cooperative movement training: Learning a novel sensory motor transformation during walking with robotic assistance-as-needed

PubMed Central

Emken, Jeremy L; Benitez, Raul; Reinkensmeyer, David J

2007-01-01

Background A prevailing paradigm of physical rehabilitation following neurologic injury is to "assist-as-needed" in completing desired movements. Several research groups are attempting to automate this principle with robotic movement training devices and patient cooperative algorithms that encourage voluntary participation. These attempts are currently not based on computational models of motor learning. Methods Here we assume that motor recovery from a neurologic injury can be modelled as a process of learning a novel sensory motor transformation, which allows us to study a simplified experimental protocol amenable to mathematical description. Specifically, we use a robotic force field paradigm to impose a virtual impairment on the left leg of unimpaired subjects walking on a treadmill. We then derive an "assist-as-needed" robotic training algorithm to help subjects overcome the virtual impairment and walk normally. The problem is posed as an optimization of performance error and robotic assistance. The optimal robotic movement trainer becomes an error-based controller with a forgetting factor that bounds kinematic errors while systematically reducing its assistance when those errors are small. As humans have a natural range of movement variability, we introduce an error weighting function that causes the robotic trainer to disregard this variability. Results We experimentally validated the controller with ten unimpaired subjects by demonstrating how it helped the subjects learn the novel sensory motor transformation necessary to counteract the virtual impairment, while also preventing them from experiencing large kinematic errors. The addition of the error weighting function allowed the robot assistance to fade to zero even though the subjects' movements were variable. We also show that in order to assist-as-needed, the robot must relax its assistance at a rate faster than that of the learning human. Conclusion The assist-as-needed algorithm proposed here can limit error during the learning of a dynamic motor task. The algorithm encourages learning by decreasing its assistance as a function of the ongoing progression of movement error. This type of algorithm is well suited for helping people learn dynamic tasks for which large kinematic errors are dangerous or discouraging, and thus may prove useful for robot-assisted movement training of walking or reaching following neurologic injury. PMID:17391527

On entanglement-assisted quantum codes achieving the entanglement-assisted Griesmer bound

NASA Astrophysics Data System (ADS)

Li, Ruihu; Li, Xueliang; Guo, Luobin

2015-12-01

The theory of entanglement-assisted quantum error-correcting codes (EAQECCs) is a generalization of the standard stabilizer formalism. Any quaternary (or binary) linear code can be used to construct EAQECCs under the entanglement-assisted (EA) formalism. We derive an EA-Griesmer bound for linear EAQECCs, which is a quantum analog of the Griesmer bound for classical codes. This EA-Griesmer bound is tighter than known bounds for EAQECCs in the literature. For a given quaternary linear code {C}, we show that the parameters of the EAQECC that EA-stabilized by the dual of {C} can be determined by a zero radical quaternary code induced from {C}, and a necessary condition under which a linear EAQECC may achieve the EA-Griesmer bound is also presented. We construct four families of optimal EAQECCs and then show the necessary condition for existence of EAQECCs is also sufficient for some low-dimensional linear EAQECCs. The four families of optimal EAQECCs are degenerate codes and go beyond earlier constructions. What is more, except four codes, our [[n,k,d_{ea};c

Theoretical Bound of CRLB for Energy Efficient Technique of RSS-Based Factor Graph Geolocation

NASA Astrophysics Data System (ADS)

Kahar Aziz, Muhammad Reza; Heriansyah; Saputra, EfaMaydhona; Musa, Ardiansyah

2018-03-01

To support the increase of wireless geolocation development as the key of the technology in the future, this paper proposes theoretical bound derivation, i.e., Cramer Rao lower bound (CRLB) for energy efficient of received signal strength (RSS)-based factor graph wireless geolocation technique. The theoretical bound derivation is crucially important to evaluate whether the energy efficient technique of RSS-based factor graph wireless geolocation is effective as well as to open the opportunity to further innovation of the technique. The CRLB is derived in this paper by using the Fisher information matrix (FIM) of the main formula of the RSS-based factor graph geolocation technique, which is lied on the Jacobian matrix. The simulation result shows that the derived CRLB has the highest accuracy as a bound shown by its lowest root mean squared error (RMSE) curve compared to the RMSE curve of the RSS-based factor graph geolocation technique. Hence, the derived CRLB becomes the lower bound for the efficient technique of RSS-based factor graph wireless geolocation.

On increasing stability in the two dimensional inverse source scattering problem with many frequencies

NASA Astrophysics Data System (ADS)

Entekhabi, Mozhgan Nora; Isakov, Victor

2018-05-01

In this paper, we will study the increasing stability in the inverse source problem for the Helmholtz equation in the plane when the source term is assumed to be compactly supported in a bounded domain Ω with a sufficiently smooth boundary. Using the Fourier transform in the frequency domain, bounds for the Hankel functions and for scattering solutions in the complex plane, improving bounds for the analytic continuation, and the exact observability for the wave equation led us to our goals which are a sharp uniqueness and increasing stability estimate when the wave number interval is growing.

Robust on-off pulse control of flexible space vehicles

NASA Technical Reports Server (NTRS)

Wie, Bong; Sinha, Ravi

1993-01-01

The on-off reaction jet control system is often used for attitude and orbital maneuvering of various spacecraft. Future space vehicles such as the orbital transfer vehicles, orbital maneuvering vehicles, and space station will extensively use reaction jets for orbital maneuvering and attitude stabilization. The proposed robust fuel- and time-optimal control algorithm is used for a three-mass spacing model of flexible spacecraft. A fuel-efficient on-off control logic is developed for robust rest-to-rest maneuver of a flexible vehicle with minimum excitation of structural modes. The first part of this report is concerned with the problem of selecting a proper pair of jets for practical trade-offs among the maneuvering time, fuel consumption, structural mode excitation, and performance robustness. A time-optimal control problem subject to parameter robustness constraints is formulated and solved. The second part of this report deals with obtaining parameter insensitive fuel- and time- optimal control inputs by solving a constrained optimization problem subject to robustness constraints. It is shown that sensitivity to modeling errors can be significantly reduced by the proposed, robustified open-loop control approach. The final part of this report deals with sliding mode control design for uncertain flexible structures. The benchmark problem of a flexible structure is used as an example for the feedback sliding mode controller design with bounded control inputs and robustness to parameter variations is investigated.

Map based navigation for autonomous underwater vehicles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tuohy, S.T.; Leonard, J.J.; Bellingham, J.G.

1995-12-31

In this work, a map based navigation algorithm is developed wherein measured geophysical properties are matched to a priori maps. The objectives is a complete algorithm applicable to a small, power-limited AUV which performs in real time to a required resolution with bounded position error. Interval B-Splines are introduced for the non-linear representation of two-dimensional geophysical parameters that have measurement uncertainty. Fine-scale position determination involves the solution of a system of nonlinear polynomial equations with interval coefficients. This system represents the complete set of possible vehicle locations and is formulated as the intersection of contours established on each map frommore » the simultaneous measurement of associated geophysical parameters. A standard filter mechanisms, based on a bounded interval error model, predicts the position of the vehicle and, therefore, screens extraneous solutions. When multiple solutions are found, a tracking mechanisms is applied until a unique vehicle location is determined.« less

A Dissimilarity Measure for Clustering High- and Infinite Dimensional Data that Satisfies the Triangle Inequality

NASA Technical Reports Server (NTRS)

Socolovsky, Eduardo A.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

The cosine or correlation measures of similarity used to cluster high dimensional data are interpreted as projections, and the orthogonal components are used to define a complementary dissimilarity measure to form a similarity-dissimilarity measure pair. Using a geometrical approach, a number of properties of this pair is established. This approach is also extended to general inner-product spaces of any dimension. These properties include the triangle inequality for the defined dissimilarity measure, error estimates for the triangle inequality and bounds on both measures that can be obtained with a few floating-point operations from previously computed values of the measures. The bounds and error estimates for the similarity and dissimilarity measures can be used to reduce the computational complexity of clustering algorithms and enhance their scalability, and the triangle inequality allows the design of clustering algorithms for high dimensional distributed data.

Potts glass reflection of the decoding threshold for qudit quantum error correcting codes

NASA Astrophysics Data System (ADS)

Jiang, Yi; Kovalev, Alexey A.; Pryadko, Leonid P.

We map the maximum likelihood decoding threshold for qudit quantum error correcting codes to the multicritical point in generalized Potts gauge glass models, extending the map constructed previously for qubit codes. An n-qudit quantum LDPC code, where a qudit can be involved in up to m stabilizer generators, corresponds to a ℤd Potts model with n interaction terms which can couple up to m spins each. We analyze general properties of the phase diagram of the constructed model, give several bounds on the location of the transitions, bounds on the energy density of extended defects (non-local analogs of domain walls), and discuss the correlation functions which can be used to distinguish different phases in the original and the dual models. This research was supported in part by the Grants: NSF PHY-1415600 (AAK), NSF PHY-1416578 (LPP), and ARO W911NF-14-1-0272 (LPP).

All the adiabatic bound states of NO{sub 2}

DOE Office of Scientific and Technical Information (OSTI.GOV)

Salzgeber, R.F.; Mandelshtam, V.; Schlier, C.

1998-07-01

We calculated all 2967 even and odd bound states of the adiabatic ground state of NO{sub 2}, using a modification of the abthinspinitio potential energy surface of Leonardi {ital et al.} [J. Chem. Phys. {bold 105}, 9051 (1996)]. The calculation was performed by harmonic inversion of the Chebyshev correlation function generated by a DVR Hamiltonian in Radau coordinates. The relative error for the computed eigenenergies (measured from the potential minimum), is 10{sup {minus}4} or better, corresponding to an absolute error of less than about 2.5thinspcm{sup {minus}1}. Near the dissociation threshold the average density of states is about 0.2/cm{sup {minus}1} formore » each symmetry. Statistical analysis of the states shows some interesting structure of the rigidity parameter {Delta}{sub 3} as a function of energy. {copyright} {ital 1998 American Institute of Physics.}« less

Software reliability: Additional investigations into modeling with replicated experiments

NASA Technical Reports Server (NTRS)

Nagel, P. M.; Schotz, F. M.; Skirvan, J. A.

1984-01-01

The effects of programmer experience level, different program usage distributions, and programming languages are explored. All these factors affect performance, and some tentative relational hypotheses are presented. An analytic framework for replicated and non-replicated (traditional) software experiments is presented. A method of obtaining an upper bound on the error rate of the next error is proposed. The method was validated empirically by comparing forecasts with actual data. In all 14 cases the bound exceeded the observed parameter, albeit somewhat conservatively. Two other forecasting methods are proposed and compared to observed results. Although demonstrated relative to this framework that stages are neither independent nor exponentially distributed, empirical estimates show that the exponential assumption is nearly valid for all but the extreme tails of the distribution. Except for the dependence in the stage probabilities, Cox's model approximates to a degree what is being observed.

Fault-tolerant clock synchronization validation methodology. [in computer systems

NASA Technical Reports Server (NTRS)

Butler, Ricky W.; Palumbo, Daniel L.; Johnson, Sally C.

1987-01-01

A validation method for the synchronization subsystem of a fault-tolerant computer system is presented. The high reliability requirement of flight-crucial systems precludes the use of most traditional validation methods. The method presented utilizes formal design proof to uncover design and coding errors and experimentation to validate the assumptions of the design proof. The experimental method is described and illustrated by validating the clock synchronization system of the Software Implemented Fault Tolerance computer. The design proof of the algorithm includes a theorem that defines the maximum skew between any two nonfaulty clocks in the system in terms of specific system parameters. Most of these parameters are deterministic. One crucial parameter is the upper bound on the clock read error, which is stochastic. The probability that this upper bound is exceeded is calculated from data obtained by the measurement of system parameters. This probability is then included in a detailed reliability analysis of the system.

On the capacity of ternary Hebbian networks

NASA Technical Reports Server (NTRS)

Baram, Yoram

1991-01-01

Networks of ternary neurons storing random vectors over the set -1,0,1 by the so-called Hebbian rule are considered. It is shown that the maximal number of stored patterns that are equilibrium states of the network with probability tending to one as N tends to infinity is at least on the order of (N exp 2-1/alpha)/K, where N is the number of neurons, K is the number of nonzero elements in a pattern, and t = alpha x K, alpha between 1/2 and 1, is the threshold in the neuron function. While, for small K, this bound is similar to that obtained for fully connected binary networks, the number of interneural connections required in the ternary case is considerably smaller. Similar bounds, incorporating error probabilities, are shown to guarantee, in the same probabilistic sense, the correction of errors in the nonzero elements and in the location of these elements.

A Generalization of the Simultaneous Diagonalization of Hermitian Matrices and its Relation to Quantum Estimation Theory

NASA Astrophysics Data System (ADS)

Nagaoka, Hiroshi

We study the problem of minimizing a quadratic quantity defined for given two Hermitian matrices X, Y and a positive-definite Hermitian matrix. This problem is reduced to the simultaneous diagonalization of X, Y when XY = YX. We derive a lower bound for the quantity, and in some special cases solve the problem by showing that the lower bound is achievable. This problem is closely related to a simultaneous measurement of quantum mechanical observables which are not commuting and has an application in the theory of quantum state estimation.

An improved nonparametric lower bound of species richness via a modified good-turing frequency formula.

PubMed

Chiu, Chun-Huo; Wang, Yi-Ting; Walther, Bruno A; Chao, Anne

2014-09-01

It is difficult to accurately estimate species richness if there are many almost undetectable species in a hyper-diverse community. Practically, an accurate lower bound for species richness is preferable to an inaccurate point estimator. The traditional nonparametric lower bound developed by Chao (1984, Scandinavian Journal of Statistics 11, 265-270) for individual-based abundance data uses only the information on the rarest species (the numbers of singletons and doubletons) to estimate the number of undetected species in samples. Applying a modified Good-Turing frequency formula, we derive an approximate formula for the first-order bias of this traditional lower bound. The approximate bias is estimated by using additional information (namely, the numbers of tripletons and quadrupletons). This approximate bias can be corrected, and an improved lower bound is thus obtained. The proposed lower bound is nonparametric in the sense that it is universally valid for any species abundance distribution. A similar type of improved lower bound can be derived for incidence data. We test our proposed lower bounds on simulated data sets generated from various species abundance models. Simulation results show that the proposed lower bounds always reduce bias over the traditional lower bounds and improve accuracy (as measured by mean squared error) when the heterogeneity of species abundances is relatively high. We also apply the proposed new lower bounds to real data for illustration and for comparisons with previously developed estimators. © 2014, The International Biometric Society.

Error Analysis for Arithmetic Word Problems--A Case Study of Primary Three Students in One Singapore School

ERIC Educational Resources Information Center

Cheng, Lu Pien

2015-01-01

In this study, ways in which 9-year old students from one Singapore school solved 1-step and 2-step word problems based on the three semantic structures were examined. The students' work and diagrams provided insights into the range of errors in word problem solving for 1- step and 2-step word problems. In particular, the errors provided some…

Camera calibration correction in shape from inconsistent silhouette

USDA-ARS?s Scientific Manuscript database

The use of shape from silhouette for reconstruction tasks is plagued by two types of real-world errors: camera calibration error and silhouette segmentation error. When either error is present, we call the problem the Shape from Inconsistent Silhouette (SfIS) problem. In this paper, we show how sm...

An hp-adaptivity and error estimation for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Bey, Kim S.

1995-01-01

This paper presents an hp-adaptive discontinuous Galerkin method for linear hyperbolic conservation laws. A priori and a posteriori error estimates are derived in mesh-dependent norms which reflect the dependence of the approximate solution on the element size (h) and the degree (p) of the local polynomial approximation. The a posteriori error estimate, based on the element residual method, provides bounds on the actual global error in the approximate solution. The adaptive strategy is designed to deliver an approximate solution with the specified level of error in three steps. The a posteriori estimate is used to assess the accuracy of a given approximate solution and the a priori estimate is used to predict the mesh refinements and polynomial enrichment needed to deliver the desired solution. Numerical examples demonstrate the reliability of the a posteriori error estimates and the effectiveness of the hp-adaptive strategy.

A Semi-Infinite Programming based algorithm for determining T-optimum designs for model discrimination

PubMed Central

Duarte, Belmiro P.M.; Wong, Weng Kee; Atkinson, Anthony C.

2016-01-01

T-optimum designs for model discrimination are notoriously difficult to find because of the computational difficulty involved in solving an optimization problem that involves two layers of optimization. Only a handful of analytical T-optimal designs are available for the simplest problems; the rest in the literature are found using specialized numerical procedures for a specific problem. We propose a potentially more systematic and general way for finding T-optimal designs using a Semi-Infinite Programming (SIP) approach. The strategy requires that we first reformulate the original minimax or maximin optimization problem into an equivalent semi-infinite program and solve it using an exchange-based method where lower and upper bounds produced by solving the outer and the inner programs, are iterated to convergence. A global Nonlinear Programming (NLP) solver is used to handle the subproblems, thus finding the optimal design and the least favorable parametric configuration that minimizes the residual sum of squares from the alternative or test models. We also use a nonlinear program to check the global optimality of the SIP-generated design and automate the construction of globally optimal designs. The algorithm is successfully used to produce results that coincide with several T-optimal designs reported in the literature for various types of model discrimination problems with normally distributed errors. However, our method is more general, merely requiring that the parameters of the model be estimated by a numerical optimization. PMID:27330230

A Semi-Infinite Programming based algorithm for determining T-optimum designs for model discrimination.

PubMed

Duarte, Belmiro P M; Wong, Weng Kee; Atkinson, Anthony C

2015-03-01

T-optimum designs for model discrimination are notoriously difficult to find because of the computational difficulty involved in solving an optimization problem that involves two layers of optimization. Only a handful of analytical T-optimal designs are available for the simplest problems; the rest in the literature are found using specialized numerical procedures for a specific problem. We propose a potentially more systematic and general way for finding T-optimal designs using a Semi-Infinite Programming (SIP) approach. The strategy requires that we first reformulate the original minimax or maximin optimization problem into an equivalent semi-infinite program and solve it using an exchange-based method where lower and upper bounds produced by solving the outer and the inner programs, are iterated to convergence. A global Nonlinear Programming (NLP) solver is used to handle the subproblems, thus finding the optimal design and the least favorable parametric configuration that minimizes the residual sum of squares from the alternative or test models. We also use a nonlinear program to check the global optimality of the SIP-generated design and automate the construction of globally optimal designs. The algorithm is successfully used to produce results that coincide with several T-optimal designs reported in the literature for various types of model discrimination problems with normally distributed errors. However, our method is more general, merely requiring that the parameters of the model be estimated by a numerical optimization.

The cost-constrained traveling salesman problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sokkappa, P.R.

1990-10-01

The Cost-Constrained Traveling Salesman Problem (CCTSP) is a variant of the well-known Traveling Salesman Problem (TSP). In the TSP, the goal is to find a tour of a given set of cities such that the total cost of the tour is minimized. In the CCTSP, each city is given a value, and a fixed cost-constraint is specified. The objective is to find a subtour of the cities that achieves maximum value without exceeding the cost-constraint. Thus, unlike the TSP, the CCTSP requires both selection and sequencing. As a consequence, most results for the TSP cannot be extended to the CCTSP.more » We show that the CCTSP is NP-hard and that no K-approximation algorithm or fully polynomial approximation scheme exists, unless P = NP. We also show that several special cases are polynomially solvable. Algorithms for the CCTSP, which outperform previous methods, are developed in three areas: upper bounding methods, exact algorithms, and heuristics. We found that a bounding strategy based on the knapsack problem performs better, both in speed and in the quality of the bounds, than methods based on the assignment problem. Likewise, we found that a branch-and-bound approach using the knapsack bound was superior to a method based on a common branch-and-bound method for the TSP. In our study of heuristic algorithms, we found that, when selecting modes for inclusion in the subtour, it is important to consider the neighborhood'' of the nodes. A node with low value that brings the subtour near many other nodes may be more desirable than an isolated node of high value. We found two types of repetition to be desirable: repetitions based on randomization in the subtour buildings process, and repetitions encouraging the inclusion of different subsets of the nodes. By varying the number and type of repetitions, we can adjust the computation time required by our method to obtain algorithms that outperform previous methods.« less

Application of GPS to Enable Launch Vehicle Upper Stage Heliocentric Disposal

NASA Technical Reports Server (NTRS)

Anzalone, Evan J.; Oliver, T. Emerson

2017-01-01

To properly dispose of the upper stage of the Space Launch System, the vehicle must perform a burn in Earth orbit to perform a close flyby of the Lunar surface to gain adequate energy to enter into heliocentric space. This architecture was selected to meet NASA requirements to limit orbital debris in the Earth-Moon system. The choice of a flyby for heliocentric disposal was driven by mission and vehicle constraints. This paper describes the SLS mission for Exploration Mission -1, a high level overview of the Block 1 vehicle, and the various disposal options considered. The research focuses on this analysis in terms of the mission design and navigation problem, focusing on the vehicle-level requirements that enable a successful mission. An inertial-only system is shown to be insufficient for heliocentric flyby due to large inertial integration errors from launch through disposal maneuver while on a trans-lunar trajectory. The various options for aiding the navigation system are presented and details are provided on the use of GPS to bound the state errors in orbit to improve the capability for stage disposal. The state estimation algorithm used is described as well as its capability in determination of the vehicle state at the start of the planned maneuver. This data, both dispersions on state and on errors, is then used to develop orbital targets to use for meeting the required Lunar flyby for entering onto a heliocentric trajectory. The effect of guidance and navigation errors on this capability is described as well as the identified constraints for achieving the disposal requirements. Additionally, discussion is provided on continued analysis and identification of system considerations that can drive the ability to integrate onto a vehicle intended for deep space.

A robust algorithm for automated target recognition using precomputed radar cross sections

NASA Astrophysics Data System (ADS)

Ehrman, Lisa M.; Lanterman, Aaron D.

2004-09-01

Passive radar is an emerging technology that offers a number of unique benefits, including covert operation. Many such systems are already capable of detecting and tracking aircraft. The goal of this work is to develop a robust algorithm for adding automated target recognition (ATR) capabilities to existing passive radar systems. In previous papers, we proposed conducting ATR by comparing the precomputed RCS of known targets to that of detected targets. To make the precomputed RCS as accurate as possible, a coordinated flight model is used to estimate aircraft orientation. Once the aircraft's position and orientation are known, it is possible to determine the incident and observed angles on the aircraft, relative to the transmitter and receiver. This makes it possible to extract the appropriate radar cross section (RCS) from our simulated database. This RCS is then scaled to account for propagation losses and the receiver's antenna gain. A Rician likelihood model compares these expected signals from different targets to the received target profile. We have previously employed Monte Carlo runs to gauge the probability of error in the ATR algorithm; however, generation of a statistically significant set of Monte Carlo runs is computationally intensive. As an alternative to Monte Carlo runs, we derive the relative entropy (also known as Kullback-Liebler distance) between two Rician distributions. Since the probability of Type II error in our hypothesis testing problem can be expressed as a function of the relative entropy via Stein's Lemma, this provides us with a computationally efficient method for determining an upper bound on our algorithm's performance. It also provides great insight into the types of classification errors we can expect from our algorithm. This paper compares the numerically approximated probability of Type II error with the results obtained from a set of Monte Carlo runs.

Annual Cost of U.S. Hospital Visits for Pediatric Abusive Head Trauma.

PubMed

Peterson, Cora; Xu, Likang; Florence, Curtis; Parks, Sharyn E

2015-08-01

We estimated the frequency and direct medical cost from the provider perspective of U.S. hospital visits for pediatric abusive head trauma (AHT). We identified treat-and-release hospital emergency department (ED) visits and admissions for AHT among patients aged 0-4 years in the Nationwide Emergency Department Sample and Nationwide Inpatient Sample (NIS), 2006-2011. We applied cost-to-charge ratios and estimated professional fee ratios from Truven Health MarketScan(®) to estimate per-visit and total population costs of AHT ED visits and admissions. Regression models assessed cost differences associated with selected patient and hospital characteristics. AHT was diagnosed during 6,827 (95% confidence interval [CI] [6,072, 7,582]) ED visits and 12,533 (95% CI [10,395, 14,671]) admissions (28% originating in the same hospital's ED) nationwide over the study period. The average medical cost per ED visit and admission were US$2,612 (error bound: 1,644-3,581) and US$31,901 (error bound: 29,266-34,536), respectively (2012 USD). The average total annual nationwide medical cost of AHT hospital visits was US$69.6 million (error bound: 56.9-82.3 million) over the study period. Factors associated with higher per-visit costs included patient age <1 year, males, coexisting chronic conditions, discharge to another facility, death, higher household income, public insurance payer, hospital trauma level, and teaching hospitals in urban locations. Study findings emphasize the importance of focused interventions to reduce this type of high-cost child abuse. © The Author(s) 2015.

Sampling-free Bayesian inversion with adaptive hierarchical tensor representations

NASA Astrophysics Data System (ADS)

Eigel, Martin; Marschall, Manuel; Schneider, Reinhold

2018-03-01

A sampling-free approach to Bayesian inversion with an explicit polynomial representation of the parameter densities is developed, based on an affine-parametric representation of a linear forward model. This becomes feasible due to the complete treatment in function spaces, which requires an efficient model reduction technique for numerical computations. The advocated perspective yields the crucial benefit that error bounds can be derived for all occuring approximations, leading to provable convergence subject to the discretization parameters. Moreover, it enables a fully adaptive a posteriori control with automatic problem-dependent adjustments of the employed discretizations. The method is discussed in the context of modern hierarchical tensor representations, which are used for the evaluation of a random PDE (the forward model) and the subsequent high-dimensional quadrature of the log-likelihood, alleviating the ‘curse of dimensionality’. Numerical experiments demonstrate the performance and confirm the theoretical results.

Detecting and locating light atoms from high-resolution STEM images: The quest for a single optimal design.

PubMed

Gonnissen, J; De Backer, A; den Dekker, A J; Sijbers, J; Van Aert, S

2016-11-01

In the present paper, the optimal detector design is investigated for both detecting and locating light atoms from high resolution scanning transmission electron microscopy (HR STEM) images. The principles of detection theory are used to quantify the probability of error for the detection of light atoms from HR STEM images. To determine the optimal experiment design for locating light atoms, use is made of the so-called Cramér-Rao Lower Bound (CRLB). It is investigated if a single optimal design can be found for both the detection and location problem of light atoms. Furthermore, the incoming electron dose is optimised for both research goals and it is shown that picometre range precision is feasible for the estimation of the atom positions when using an appropriate incoming electron dose under the optimal detector settings to detect light atoms. Copyright © 2016 Elsevier B.V. All rights reserved.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Sun Ung, E-mail: sunung@umich.edu; Monroe, Charles W., E-mail: cwmonroe@umich.edu

The inverse problem of parameterizing intermolecular potentials given macroscopic transport and thermodynamic data is addressed. Procedures are developed to create arbitrary-precision algorithms for transport collision integrals, using the Lennard-Jones (12–6) potential as an example. Interpolation formulas are produced that compute these collision integrals to four-digit accuracy over the reduced-temperature range 0.3≤T{sup ⁎}≤400, allowing very fast computation. Lennard-Jones parameters for neon, argon, and krypton are determined by simultaneously fitting the observed temperature dependences of their viscosities and second virial coefficients—one of the first times that a thermodynamic and a dynamic property have been used simultaneously for Lennard-Jones parameterization. In addition tomore » matching viscosities and second virial coefficients within the bounds of experimental error, the determined Lennard-Jones parameters are also found to predict the thermal conductivity and self-diffusion coefficient accurately, supporting the value of the Lennard-Jones (12–6) potential for noble-gas transport-property correlation.« less

Experimental quantum key distribution with source flaws

NASA Astrophysics Data System (ADS)

Xu, Feihu; Wei, Kejin; Sajeed, Shihan; Kaiser, Sarah; Sun, Shihai; Tang, Zhiyuan; Qian, Li; Makarov, Vadim; Lo, Hoi-Kwong

2015-09-01

Decoy-state quantum key distribution (QKD) is a standard technique in current quantum cryptographic implementations. Unfortunately, existing experiments have two important drawbacks: the state preparation is assumed to be perfect without errors and the employed security proofs do not fully consider the finite-key effects for general attacks. These two drawbacks mean that existing experiments are not guaranteed to be proven to be secure in practice. Here, we perform an experiment that shows secure QKD with imperfect state preparations over long distances and achieves rigorous finite-key security bounds for decoy-state QKD against coherent attacks in the universally composable framework. We quantify the source flaws experimentally and demonstrate a QKD implementation that is tolerant to channel loss despite the source flaws. Our implementation considers more real-world problems than most previous experiments, and our theory can be applied to general discrete-variable QKD systems. These features constitute a step towards secure QKD with imperfect devices.

New Operational Matrices for Solving Fractional Differential Equations on the Half-Line

PubMed Central

2015-01-01

In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order ν. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques. PMID:25996369

The Adiabatic Theorem and Linear Response Theory for Extended Quantum Systems

NASA Astrophysics Data System (ADS)

Bachmann, Sven; De Roeck, Wojciech; Fraas, Martin

2018-03-01

The adiabatic theorem refers to a setup where an evolution equation contains a time-dependent parameter whose change is very slow, measured by a vanishing parameter ɛ. Under suitable assumptions the solution of the time-inhomogenous equation stays close to an instantaneous fixpoint. In the present paper, we prove an adiabatic theorem with an error bound that is independent of the number of degrees of freedom. Our setup is that of quantum spin systems where the manifold of ground states is separated from the rest of the spectrum by a spectral gap. One important application is the proof of the validity of linear response theory for such extended, genuinely interacting systems. In general, this is a long-standing mathematical problem, which can be solved in the present particular case of a gapped system, relevant e.g. for the integer quantum Hall effect.

Standard representation and unified stability analysis for dynamic artificial neural network models.

PubMed

Kim, Kwang-Ki K; Patrón, Ernesto Ríos; Braatz, Richard D

2018-02-01

An overview is provided of dynamic artificial neural network models (DANNs) for nonlinear dynamical system identification and control problems, and convex stability conditions are proposed that are less conservative than past results. The three most popular classes of dynamic artificial neural network models are described, with their mathematical representations and architectures followed by transformations based on their block diagrams that are convenient for stability and performance analyses. Classes of nonlinear dynamical systems that are universally approximated by such models are characterized, which include rigorous upper bounds on the approximation errors. A unified framework and linear matrix inequality-based stability conditions are described for different classes of dynamic artificial neural network models that take additional information into account such as local slope restrictions and whether the nonlinearities within the DANNs are odd. A theoretical example shows reduced conservatism obtained by the conditions. Copyright © 2017. Published by Elsevier Ltd.

Distributed Adaptive Fuzzy Control for Nonlinear Multiagent Systems Via Sliding Mode Observers.

PubMed

Shen, Qikun; Shi, Peng; Shi, Yan

2016-12-01

In this paper, the problem of distributed adaptive fuzzy control is investigated for high-order uncertain nonlinear multiagent systems on directed graph with a fixed topology. It is assumed that only the outputs of each follower and its neighbors are available in the design of its distributed controllers. Equivalent output injection sliding mode observers are proposed for each follower to estimate the states of itself and its neighbors, and an observer-based distributed adaptive controller is designed for each follower to guarantee that it asymptotically synchronizes to a leader with tracking errors being semi-globally uniform ultimate bounded, in which fuzzy logic systems are utilized to approximate unknown functions. Based on algebraic graph theory and Lyapunov function approach, using Filippov-framework, the closed-loop system stability analysis is conducted. Finally, numerical simulations are provided to illustrate the effectiveness and potential of the developed design techniques.

Distributed neural network control for adaptive synchronization of uncertain dynamical multiagent systems.

PubMed

Peng, Zhouhua; Wang, Dan; Zhang, Hongwei; Sun, Gang

2014-08-01

This paper addresses the leader-follower synchronization problem of uncertain dynamical multiagent systems with nonlinear dynamics. Distributed adaptive synchronization controllers are proposed based on the state information of neighboring agents. The control design is developed for both undirected and directed communication topologies without requiring the accurate model of each agent. This result is further extended to the output feedback case where a neighborhood observer is proposed based on relative output information of neighboring agents. Then, distributed observer-based synchronization controllers are derived and a parameter-dependent Riccati inequality is employed to prove the stability. This design has a favorable decouple property between the observer and the controller designs for nonlinear multiagent systems. For both cases, the developed controllers guarantee that the state of each agent synchronizes to that of the leader with bounded residual errors. Two illustrative examples validate the efficacy of the proposed methods.

Distributed Adaptive Finite-Time Approach for Formation-Containment Control of Networked Nonlinear Systems Under Directed Topology.

PubMed

Wang, Yujuan; Song, Yongduan; Ren, Wei

2017-07-06

This paper presents a distributed adaptive finite-time control solution to the formation-containment problem for multiple networked systems with uncertain nonlinear dynamics and directed communication constraints. By integrating the special topology feature of the new constructed symmetrical matrix, the technical difficulty in finite-time formation-containment control arising from the asymmetrical Laplacian matrix under single-way directed communication is circumvented. Based upon fractional power feedback of the local error, an adaptive distributed control scheme is established to drive the leaders into the prespecified formation configuration in finite time. Meanwhile, a distributed adaptive control scheme, independent of the unavailable inputs of the leaders, is designed to keep the followers within a bounded distance from the moving leaders and then to make the followers enter the convex hull shaped by the formation of the leaders in finite time. The effectiveness of the proposed control scheme is confirmed by the simulation.

New operational matrices for solving fractional differential equations on the half-line.

PubMed

Bhrawy, Ali H; Taha, Taha M; Alzahrani, Ebraheem O; Alzahrani, Ebrahim O; Baleanu, Dumitru; Alzahrani, Abdulrahim A

2015-01-01

In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order ν. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques.

Retrieving the aerosol complex refractive index using PyMieScatt: A Mie computational package with visualization capabilities

NASA Astrophysics Data System (ADS)

Sumlin, Benjamin J.; Heinson, William R.; Chakrabarty, Rajan K.

2018-01-01

The complex refractive index m = n + ik of a particle is an intrinsic property which cannot be directly measured; it must be inferred from its extrinsic properties such as the scattering and absorption cross-sections. Bohren and Huffman called this approach "describing the dragon from its tracks", since the inversion of Lorenz-Mie theory equations is intractable without the use of computers. This article describes PyMieScatt, an open-source module for Python that contains functionality for solving the inverse problem for complex m using extensive optical and physical properties as input, and calculating regions where valid solutions may exist within the error bounds of laboratory measurements. Additionally, the module has comprehensive capabilities for studying homogeneous and coated single spheres, as well as ensembles of homogeneous spheres with user-defined size distributions, making it a complete tool for studying the optical behavior of spherical particles.

Adaptive Fuzzy Tracking Control for a Class of MIMO Nonlinear Systems in Nonstrict-Feedback Form.

PubMed

Chen, Bing; Lin, Chong; Liu, Xiaoping; Liu, Kefu

2015-12-01

This paper focuses on the problem of fuzzy adaptive control for a class of multiinput and multioutput (MIMO) nonlinear systems in nonstrict-feedback form, which contains the strict-feedback form as a special case. By the condition of variable partition, a new fuzzy adaptive backstepping is proposed for such a class of nonlinear MIMO systems. The suggested fuzzy adaptive controller guarantees that the proposed control scheme can guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking errors eventually converge to a small neighborhood around the origin. The main advantage of this paper is that a control approach is systematically derived for nonlinear systems with strong interconnected terms which are the functions of all states of the whole system. Simulation results further illustrate the effectiveness of the suggested approach.

Chance-Constrained AC Optimal Power Flow for Distribution Systems With Renewables

DOE Office of Scientific and Technical Information (OSTI.GOV)

DallAnese, Emiliano; Baker, Kyri; Summers, Tyler

This paper focuses on distribution systems featuring renewable energy sources (RESs) and energy storage systems, and presents an AC optimal power flow (OPF) approach to optimize system-level performance objectives while coping with uncertainty in both RES generation and loads. The proposed method hinges on a chance-constrained AC OPF formulation where probabilistic constraints are utilized to enforce voltage regulation with prescribed probability. A computationally more affordable convex reformulation is developed by resorting to suitable linear approximations of the AC power-flow equations as well as convex approximations of the chance constraints. The approximate chance constraints provide conservative bounds that hold for arbitrarymore » distributions of the forecasting errors. An adaptive strategy is then obtained by embedding the proposed AC OPF task into a model predictive control framework. Finally, a distributed solver is developed to strategically distribute the solution of the optimization problems across utility and customers.« less

Partial branch and bound algorithm for improved data association in multiframe processing

NASA Astrophysics Data System (ADS)

Poore, Aubrey B.; Yan, Xin

1999-07-01

A central problem in multitarget, multisensor, and multiplatform tracking remains that of data association. Lagrangian relaxation methods have shown themselves to yield near optimal answers in real-time. The necessary improvement in the quality of these solutions warrants a continuing interest in these methods. These problems are NP-hard; the only known methods for solving them optimally are enumerative in nature with branch-and-bound being most efficient. Thus, the development of methods less than a full branch-and-bound are needed for improving the quality. Such methods as K-best, local search, and randomized search have been proposed to improve the quality of the relaxation solution. Here, a partial branch-and-bound technique along with adequate branching and ordering rules are developed. Lagrangian relaxation is used as a branching method and as a method to calculate the lower bound for subproblems. The result shows that the branch-and-bound framework greatly improves the resolution quality of the Lagrangian relaxation algorithm and yields better multiple solutions in less time than relaxation alone.

Approximating the 0-1 Multiple Knapsack Problem with Agent Decomposition and Market Negotiation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smolinski, B.

The 0-1 multiple knapsack problem appears in many domains from financial portfolio management to cargo ship stowing. Methods for solving it range from approximate algorithms, such as greedy algorithms, to exact algorithms, such as branch and bound. Approximate algorithms have no bounds on how poorly they perform and exact algorithms can suffer from exponential time and space complexities with large data sets. This paper introduces a market model based on agent decomposition and market auctions for approximating the 0-1 multiple knapsack problem, and an algorithm that implements the model (M(x)). M(x) traverses the solution space rather than getting caught inmore » a local maximum, overcoming an inherent problem of many greedy algorithms. The use of agents ensures that infeasible solutions are not considered while traversing the solution space and that traversal of the solution space is not just random, but is also directed. M(x) is compared to a bound and bound algorithm (BB) and a simple greedy algorithm with a random shuffle (G(x)). The results suggest that M(x) is a good algorithm for approximating the 0-1 Multiple Knapsack problem. M(x) almost always found solutions that were close to optimal in a fraction of the time it took BB to run and with much less memory on large test data sets. M(x) usually performed better than G(x) on hard problems with correlated data.« less

Estimating the Standard Error of Robust Regression Estimates.

DTIC Science & Technology

1987-03-01

error is 0(n4/5). In another Monte Carlo study, McKean and Schrader (1984) found that the tests resulting from studentizing ; by _3d/1/2 with d =0(n4 /5...44 4 -:~~-~*v: -. *;~ ~ ~*t .~ # ~ 44 % * ~ .%j % % % * . ., ~ -%. -14- Sheather, S. J. and McKean, J. W. (1987). A comparison of testing and...Wiley, New York. Welsch, R. E. (1980). Regression Sensitivity Analysis and Bounded- Influence Estimation, in Evaluation of Econometric Models eds. J

Combined Uncertainty and A-Posteriori Error Bound Estimates for CFD Calculations: Theory and Implementation

NASA Technical Reports Server (NTRS)

Barth, Timothy J.

2014-01-01

Simulation codes often utilize finite-dimensional approximation resulting in numerical error. Some examples include, numerical methods utilizing grids and finite-dimensional basis functions, particle methods using a finite number of particles. These same simulation codes also often contain sources of uncertainty, for example, uncertain parameters and fields associated with the imposition of initial and boundary data,uncertain physical model parameters such as chemical reaction rates, mixture model parameters, material property parameters, etc.

Approximate error conjugation gradient minimization methods

DOEpatents

Kallman, Jeffrey S

2013-05-21

In one embodiment, a method includes selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, calculating an approximate error using the subset of rays, and calculating a minimum in a conjugate gradient direction based on the approximate error. In another embodiment, a system includes a processor for executing logic, logic for selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, logic for calculating an approximate error using the subset of rays, and logic for calculating a minimum in a conjugate gradient direction based on the approximate error. In other embodiments, computer program products, methods, and systems are described capable of using approximate error in constrained conjugate gradient minimization problems.

Output feedback control of a quadrotor UAV using neural networks.

PubMed

Dierks, Travis; Jagannathan, Sarangapani

2010-01-01

In this paper, a new nonlinear controller for a quadrotor unmanned aerial vehicle (UAV) is proposed using neural networks (NNs) and output feedback. The assumption on the availability of UAV dynamics is not always practical, especially in an outdoor environment. Therefore, in this work, an NN is introduced to learn the complete dynamics of the UAV online, including uncertain nonlinear terms like aerodynamic friction and blade flapping. Although a quadrotor UAV is underactuated, a novel NN virtual control input scheme is proposed which allows all six degrees of freedom (DOF) of the UAV to be controlled using only four control inputs. Furthermore, an NN observer is introduced to estimate the translational and angular velocities of the UAV, and an output feedback control law is developed in which only the position and the attitude of the UAV are considered measurable. It is shown using Lyapunov theory that the position, orientation, and velocity tracking errors, the virtual control and observer estimation errors, and the NN weight estimation errors for each NN are all semiglobally uniformly ultimately bounded (SGUUB) in the presence of bounded disturbances and NN functional reconstruction errors while simultaneously relaxing the separation principle. The effectiveness of proposed output feedback control scheme is then demonstrated in the presence of unknown nonlinear dynamics and disturbances, and simulation results are included to demonstrate the theoretical conjecture.

Navigation errors encountered using weather-mapping radar for helicopter IFR guidance to oil rigs

NASA Technical Reports Server (NTRS)

Phillips, J. D.; Bull, J. S.; Hegarty, D. M.; Dugan, D. C.

1980-01-01

In 1978 a joint NASA-FAA helicopter flight test was conducted to examine the use of weather-mapping radar for IFR guidance during landing approaches to oil rig helipads. The following navigation errors were measured: total system error, radar-range error, radar-bearing error, and flight technical error. Three problem areas were identified: (1) operational problems leading to pilot blunders, (2) poor navigation to the downwind final approach point, and (3) pure homing on final approach. Analysis of these problem areas suggests improvement in the radar equipment, approach procedure, and pilot training, and gives valuable insight into the development of future navigation aids to serve the off-shore oil industry.

Transforming graph states using single-qubit operations.

PubMed

Dahlberg, Axel; Wehner, Stephanie

2018-07-13

Stabilizer states form an important class of states in quantum information, and are of central importance in quantum error correction. Here, we provide an algorithm for deciding whether one stabilizer (target) state can be obtained from another stabilizer (source) state by single-qubit Clifford operations (LC), single-qubit Pauli measurements (LPM) and classical communication (CC) between sites holding the individual qubits. What is more, we provide a recipe to obtain the sequence of LC+LPM+CC operations which prepare the desired target state from the source state, and show how these operations can be applied in parallel to reach the target state in constant time. Our algorithm has applications in quantum networks, quantum computing, and can also serve as a design tool-for example, to find transformations between quantum error correcting codes. We provide a software implementation of our algorithm that makes this tool easier to apply. A key insight leading to our algorithm is to show that the problem is equivalent to one in graph theory, which is to decide whether some graph G ' is a vertex-minor of another graph G The vertex-minor problem is, in general, [Formula: see text]-Complete, but can be solved efficiently on graphs which are not too complex. A measure of the complexity of a graph is the rank-width which equals the Schmidt-rank width of a subclass of stabilizer states called graph states, and thus intuitively is a measure of entanglement. Here, we show that the vertex-minor problem can be solved in time O (| G | 3 ), where | G | is the size of the graph G , whenever the rank-width of G and the size of G ' are bounded. Our algorithm is based on techniques by Courcelle for solving fixed parameter tractable problems, where here the relevant fixed parameter is the rank width. The second half of this paper serves as an accessible but far from exhausting introduction to these concepts, that could be useful for many other problems in quantum information.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).

Uncertainty Quantification for Polynomial Systems via Bernstein Expansions

NASA Technical Reports Server (NTRS)

Crespo, Luis G.; Kenny, Sean P.; Giesy, Daniel P.

2012-01-01

This paper presents a unifying framework to uncertainty quantification for systems having polynomial response metrics that depend on both aleatory and epistemic uncertainties. The approach proposed, which is based on the Bernstein expansions of polynomials, enables bounding the range of moments and failure probabilities of response metrics as well as finding supersets of the extreme epistemic realizations where the limits of such ranges occur. These bounds and supersets, whose analytical structure renders them free of approximation error, can be made arbitrarily tight with additional computational effort. Furthermore, this framework enables determining the importance of particular uncertain parameters according to the extent to which they affect the first two moments of response metrics and failure probabilities. This analysis enables determining the parameters that should be considered uncertain as well as those that can be assumed to be constants without incurring significant error. The analytical nature of the approach eliminates the numerical error that characterizes the sampling-based techniques commonly used to propagate aleatory uncertainties as well as the possibility of under predicting the range of the statistic of interest that may result from searching for the best- and worstcase epistemic values via nonlinear optimization or sampling.

Charge renormalization at the large-D limit for N-electron atoms and weakly bound systems

NASA Astrophysics Data System (ADS)

Kais, S.; Bleil, R.

1995-05-01

We develop a systematic way to determine an effective nuclear charge ZRD such that the Hartree-Fock results will be significantly closer to the exact energies by utilizing the analytically known large-D limit energies. This method yields an expansion for the effective nuclear charge in powers of (1/D), which we have evaluated to the first order. This first order approximation to the desired effective nuclear charge has been applied to two-electron atoms with Z=2-20, and weakly bound systems such as H-. The errors for the two-electron atoms when compared with exact results were reduced from ˜0.2% for Z=2 to ˜0.002% for large Z. Although usual Hartree-Fock calculations for H- show this to be unstable, our results reduce the percent error of the Hartree-Fock energy from 7.6% to 1.86% and predicts the anion to be stable. For N-electron atoms (N=3-18, Z=3-28), using only the zeroth order approximation for the effective charge significantly reduces the error of Hartree-Fock calculations and recovers more than 80% of the correlation energy.

Modelling of the batch biosorption system: study on exchange of protons with cell wall-bound mineral ions.

PubMed

Mishra, Vishal

2015-01-01

The interchange of the protons with the cell wall-bound calcium and magnesium ions at the interface of solution/bacterial cell surface in the biosorption system at various concentrations of protons has been studied in the present work. A mathematical model for establishing the correlation between concentration of protons and active sites was developed and optimized. The sporadic limited residence time reactor was used to titrate the calcium and magnesium ions at the individual data point. The accuracy of the proposed mathematical model was estimated using error functions such as nonlinear regression, adjusted nonlinear regression coefficient, the chi-square test, P-test and F-test. The values of the chi-square test (0.042-0.017), P-test (<0.001-0.04), sum of square errors (0.061-0.016), root mean square error (0.01-0.04) and F-test (2.22-19.92) reported in the present research indicated the suitability of the model over a wide range of proton concentrations. The zeta potential of the bacterium surface at various concentrations of protons was observed to validate the denaturation of active sites.

Extracting Loop Bounds for WCET Analysis Using the Instrumentation Point Graph

NASA Astrophysics Data System (ADS)

Betts, A.; Bernat, G.

2009-05-01

Every calculation engine proposed in the literature of Worst-Case Execution Time (WCET) analysis requires upper bounds on loop iterations. Existing mechanisms to procure this information are either error prone, because they are gathered from the end-user, or limited in scope, because automatic analyses target very specific loop structures. In this paper, we present a technique that obtains bounds completely automatically for arbitrary loop structures. In particular, we show how to employ the Instrumentation Point Graph (IPG) to parse traces of execution (generated by an instrumented program) in order to extract bounds relative to any loop-nesting level. With this technique, therefore, non-rectangular dependencies between loops can be captured, allowing more accurate WCET estimates to be calculated. We demonstrate the improvement in accuracy by comparing WCET estimates computed through our HMB framework against those computed with state-of-the-art techniques.

The condition of a finite Markov chain and perturbation bounds for the limiting probabilities

NASA Technical Reports Server (NTRS)

Meyer, C. D., Jr.

1979-01-01

The inequalities bounding the relative error the norm of w- w squiggly/the norm of w are exhibited by a very simple function of E and A. Let T denote the transition matrix of an ergodic chain, C, and let A = I - T. Let E be a perturbation matrix such that T squiggly = T - E is also the transition matrix of an ergodic chain, C squiggly. Let w and w squiggly denote the limiting probability (row) vectors for C and C squiggly. The inequality is the best one possible. This bound can be significant in the numerical determination of the limiting probabilities for an ergodic chain. In addition to presenting a sharp bound for the norm of w-w squiggly/the norm of w an explicit expression for w squiggly will be derived in which w squiggly is given as a function of E, A, w and some other related terms.