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1

Extended Decentralized Linear-Quadratic-Gaussian Control  

NASA Technical Reports Server (NTRS)

A straightforward extension of a solution to the decentralized linear-Quadratic-Gaussian problem is proposed that allows its use for commonly encountered classes of problems that are currently solved with the extended Kalman filter. This extension allows the system to be partitioned in such a way as to exclude the nonlinearities from the essential algebraic relationships that allow the estimation and control to be optimally decentralized.

Carpenter, J. Russell

2000-01-01

2

Extended linear quadratic Gaussian control: Further extensions  

NASA Astrophysics Data System (ADS)

The extended linear quadratic Gaussian (ELQG) control method (Georgakakos and Marks, 1987) is a stochastic control algorithm for the optimal operation of multiobjective reservoirs. Mathematically, this method optimizes a general functional of a stochastic system in state-space form with upper and lower release constraints and probabilistic storage bounds. ELQG is a sequential algorithm which accounts for stochastic effects by preserving the first two statistical moments of the system's inputs and storages. In this paper, the method is first extended to handle nongaussian features which frequently characterize reservoir inputs. Second, ELQG's efficiency with respect to reliability storage constraints is discussed, and a new barrier function method is researched. These modifications are tested in case studies with the Savannah river system.

Georgakakos, Aristidis P.

1989-02-01

3

Jump linear quadratic Gaussian control in continuous time  

Microsoft Academic Search

The optimal quadratic control of continuous-time linear systems that possess randomly jumping parameters which can be described by finite-state Markov processes is addressed. The systems are also subject to Gaussian input and measurement noise. The optimal solution for the jump linear-quadratic-Gaussian (JLQC) problem is given. This solution is based on a separation theorem. The optimal state estimator is sample-path dependent.

Yuandong Ji; Howard J. Chizeck

1992-01-01

4

Linear quadratic Gaussian controller design for plasma current, position and shape control system in ITER  

Microsoft Academic Search

This paper is focused on the linear quadratic Gaussian (LQG) controller synthesis methodology for the ITER plasma current, position and shape control system as well as power derivative management system. It has been shown that some poloidal field (PF) coils have less influence on reference plasma-wall gaps control during plasma disturbances and hence they have been used to reduce total

V Belyakov; A Kavin; V Kharitonov; B Misenov; Y Mitrishkin; A Ovsyannikov; D Ovsyannikov; E Rumyantsev; E Veremei; A Zhabko

1999-01-01

5

Optimal quadratic control of jump linear systems with Gaussian noise in discrete-time  

Microsoft Academic Search

An optimal discrete-time jump linear quadratic Gaussian (JLQG) control problem is investigated. The system to be controlled is linear, except for randomly jumping parameters which obey a discrete-time finite-state Markov process. A quadratic expected cost is minimized, for systems subject to additive Gaussian input and measurement noise. It is assumed that the system structure (i.e. jumping parameters) is known at

Howard J. Chizeck; Yuandong Ji

1988-01-01

6

Optimal control design of fuel processing system by linear quadratic Gaussian and loop transfer recovery method  

Microsoft Academic Search

This paper presents an optimal control system which consists of both feedforward and state?feedback controllers designed using a well?developed linear quadratic Gaussian and loop transfer recovery (LQG\\/LTR) method for a fuel processing system (FPS). This FPS uses natural gas as fuel and reacts with atmospheric air through a catalytic partial oxidation (CPO) response. The control objective is focused on the

2008-01-01

7

Linear-quadratic-Gaussian torque control: Application to a flexible joint of a rehabilitation exoskeleton  

Microsoft Academic Search

A linear-quadratic-Gaussian regulator is proposed for the torque control of flexible robotic joints with built-in torque sensor. The regulator requires the joint-torque sensor information only and features: (1) a Kalman filter that, beside reducing the noise and evaluating the derivative of the torque sensor measure, is able to estimate all the external and internal torques acting on the joint; 2)

Rocco Vertechy; Antonio Frisoli; Massimiliano Solazzi; Andrea Dettori; Massimo Bergamasco

2010-01-01

8

Steering of Frequency Standards by the Use of Linear Quadratic Gaussian Control Theory  

NASA Technical Reports Server (NTRS)

Linear quadratic Gaussian control is a technique that uses Kalman filtering to estimate a state vector used for input into a control calculation. A control correction is calculated by minimizing a quadratic cost function that is dependent on both the state vector and the control amount. Different penalties, chosen by the designer, are assessed by the controller as the state vector and control amount vary from given optimal values. With this feature controllers can be designed to force the phase and frequency differences between two standards to zero either more or less aggressively depending on the application. Data will be used to show how using different parameters in the cost function analysis affects the steering and the stability of the frequency standards.

Koppang, Paul; Leland, Robert

1996-01-01

9

Neural network-based nonlinear model predictive control vs. linear quadratic gaussian control  

USGS Publications Warehouse

One problem with the application of neural networks to the multivariable control of mineral and extractive processes is determining whether and how to use them. The objective of this investigation was to compare neural network control to more conventional strategies and to determine if there are any advantages in using neural network control in terms of set-point tracking, rise time, settling time, disturbance rejection and other criteria. The procedure involved developing neural network controllers using both historical plant data and simulation models. Various control patterns were tried, including both inverse and direct neural network plant models. These were compared to state space controllers that are, by nature, linear. For grinding and leaching circuits, a nonlinear neural network-based model predictive control strategy was superior to a state space-based linear quadratic gaussian controller. The investigation pointed out the importance of incorporating state space into neural networks by making them recurrent, i.e., feeding certain output state variables into input nodes in the neural network. It was concluded that neural network controllers can have better disturbance rejection, set-point tracking, rise time, settling time and lower set-point overshoot, and it was also concluded that neural network controllers can be more reliable and easy to implement in complex, multivariable plants.

Cho, C.; Vance, R.; Mardi, N.; Qian, Z.; Prisbrey, K.

1997-01-01

10

Linear-quadratic-Gaussian control for adaptive optics systems using a hybrid model.  

PubMed

This paper presents a linear-quadratic-Gaussian (LQG) design based on the equivalent discrete-time model of an adaptive optics (AO) system. The design model incorporates deformable mirror dynamics, an asynchronous wavefront sensor and zero-order hold operation, and a continuous-time model of the incident wavefront. Using the structure of the discrete-time model, the dimensions of the Riccati equations to be solved are reduced. The LQG controller is shown to improve AO system performance under several conditions. PMID:19109596

Looze, Douglas P

2009-01-01

11

Experimental study on modified linear quadratic Gaussian control for adaptive optics.  

PubMed

To achieve high-resolution imaging the standard control algorithm used for classical adaptive optics (AO) is the simple but efficient proportional-integral (PI) controller. The goal is to minimize the rms error of the residual wave front. However, using the PI controller, it is not possible to do this. One possible way to minimize the rms error is to use linear quadratic Gaussian (LQG) control. In practice, however, this control algorithm still encounters an unexpected problem that leads to the divergence of control in AO. This paper proposes a modified LQG (MLQG) to solve this issue. The controller is analyzed explicitly. Laboratory tests shows strong stability and high precision compared to the classical control. PMID:24663418

Fu, Qiang; Pott, Jörg-Uwe; Peter, Diethard; Shen, Feng; Rao, Changhui; Li, Xinyang

2014-03-10

12

Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures  

NASA Technical Reports Server (NTRS)

An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

Gibson, J. S.; Adamian, A.

1988-01-01

13

Linear quadratic Gaussian and feedforward controllers for the DSS-13 antenna  

NASA Technical Reports Server (NTRS)

The controller development and the tracking performance evaluation for the DSS-13 antenna are presented. A trajectory preprocessor, linear quadratic Gaussian (LQG) controller, feedforward controller, and their combination were designed, built, analyzed, and tested. The antenna exhibits nonlinear behavior when the input to the antenna and/or the derivative of this input exceeds the imposed limits; for slewing and acquisition commands, these limits are typically violated. A trajectory preprocessor was designed to ensure that the antenna behaves linearly, just to prevent nonlinear limit cycling. The estimator model for the LQG controller was identified from the data obtained from the field test. Based on an LQG balanced representation, a reduced-order LQG controller was obtained. The feedforward controller and the combination of the LQG and feedforward controller were also investigated. The performance of the controllers was evaluated with the tracking errors (due to following a trajectory) and the disturbance errors (due to the disturbances acting on the antenna). The LQG controller has good disturbance rejection properties and satisfactory tracking errors. The feedforward controller has small tracking errors but poor disturbance rejection properties. The combined LQG and feedforward controller exhibits small tracking errors as well as good disturbance rejection properties. However, the cost for this performance is the complexity of the controller.

Gawronski, W. K.; Racho, C. S.; Mellstrom, J. A.

1994-01-01

14

Feasibility of Decentralized Linear-Quadratic-Gaussian Control of Autonomous Distributed Spacecraft  

NASA Technical Reports Server (NTRS)

A distributed satellite formation, modeled as an arbitrary number of fully connected nodes in a network, could be controlled using a decentralized controller framework that distributes operations in parallel over the network. For such problems, a solution that minimizes data transmission requirements, in the context of linear-quadratic-Gaussian (LQG) control theory, was given by Speyer. This approach is advantageous because it is non-hierarchical, detected failures gracefully degrade system performance, fewer local computations are required than for a centralized controller, and it is optimal with respect to the standard LQG cost function. Disadvantages of the approach are the need for a fully connected communications network, the total operations performed over all the nodes are greater than for a centralized controller, and the approach is formulated for linear time-invariant systems. To investigate the feasibility of the decentralized approach to satellite formation flying, a simple centralized LQG design for a spacecraft orbit control problem is adapted to the decentralized framework. The simple design uses a fixed reference trajectory (an equatorial, Keplerian, circular orbit), and by appropriate choice of coordinates and measurements is formulated as a linear time-invariant system.

Carpenter, J. Russell

1999-01-01

15

Antenna Linear-Quadratic-Gaussian (LQG) Controllers: Properties, Limits of Performance, and Tuning Procedure  

NASA Technical Reports Server (NTRS)

Wind gusts are the main disturbances that depreciate tracking precision of microwave antennas and radiotelescopes. The linear-quadratic-Gaussian (LQG) controllers - as compared with the proportional-and-integral (PI) controllers significantly improve the tracking precision in wind disturbances. However, their properties have not been satisfactorily understood; consequently, their tuning is a trial-and-error process. A control engineer has two tools to tune an LQG controller: the choice of coordinate system of the controller model and the selection of weights of the LQG performance index. This article analyzes properties of an open- and closed-loop antenna. It shows that the proper choice of coordinates of the open-loop model simplifies the shaping of the closed-loop performance. The closed-loop properties are influenced by the LQG weights. The article shows the impact of the weights on the antenna closed-loop bandwidth, disturbance rejection properties, and antenna acceleration. The bandwidth and the disturbance rejection characterize the antenna performance, while the acceleration represents the performance limit set by the antenna hardware (motors). The article presents the controller tuning procedure, based on the coordinate selection and the weight properties. The procedure rationally shapes the closed-loop performance, as an alternative to the trial-and-error approach.

Gawronski, W.

2004-01-01

16

ORACLS: A system for linear-quadratic-Gaussian control law design  

NASA Technical Reports Server (NTRS)

A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.

Armstrong, E. S.

1978-01-01

17

Practical gust load alleviation and flutter suppression control laws based on a LQG methodology. [Linear Quadratic Gaussian  

NASA Technical Reports Server (NTRS)

A modified linear quadratic Gaussian (LQG) synthesis procedure has been used to design low-order robust multiloop controllers for a flexible airplane. The introduction of properly constructed fictitious Gauss-Markov processes in the control loops allowed meeting classical frequency-domain stability criteria using the direct synthesis procedures of modern time-domain control theory. Model reduction was used to simplify the control laws to the point where they could be easily implemented on onboard flight computers. These control laws provided excellent gust load and flutter mode control with good stability margins and compared very favorably to other control laws synthesized by the classical root-locus technique.

Gangsaas, D.; Ly, U.; Norman, D. C.

1981-01-01

18

The role and use of the stochastic linear-quadratic-Gaussian problem in control system design.  

NASA Technical Reports Server (NTRS)

The role of the linear-quadratic stochastic control problem in engineering design is reviewed in tutorial fashion. The design approach is motivated by considering the control of a nonlinear uncertain plant about a desired input-output response. It is demonstrated how a design philosophy based on (1) deterministic perturbation control, (2) stochastic state estimation, and (3) linearized stochastic control leads to an overall closed-loop control system. The emphasis of the paper is on the philosophy of the design process, the modeling issue, and the formulation of the problem; the results are given for the sake of completeness, but no proofs are included. The systematic off-line nature of the design process is stressed throughout.

Athans, M.

1971-01-01

19

Linear-Quadratic-Gaussian Regulator Developed for a Magnetic Bearing  

NASA Technical Reports Server (NTRS)

Linear-Quadratic-Gaussian (LQG) control is a modern state-space technique for designing optimal dynamic regulators. It enables us to trade off regulation performance and control effort, and to take into account process and measurement noise. The Structural Mechanics and Dynamics Branch at the NASA Glenn Research Center has developed an LQG control for a fault-tolerant magnetic bearing suspension rig to optimize system performance and to reduce the sensor and processing noise. The LQG regulator consists of an optimal state-feedback gain and a Kalman state estimator. The first design step is to seek a state-feedback law that minimizes the cost function of regulation performance, which is measured by a quadratic performance criterion with user-specified weighting matrices, and to define the tradeoff between regulation performance and control effort. The next design step is to derive a state estimator using a Kalman filter because the optimal state feedback cannot be implemented without full state measurement. Since the Kalman filter is an optimal estimator when dealing with Gaussian white noise, it minimizes the asymptotic covariance of the estimation error.

Choi, Benjamin B.

2002-01-01

20

Integration of a Decentralized Linear-Quadratic-Gaussian Control into GSFC's Universal 3-D Autonomous Formation Flying Algorithm  

NASA Technical Reports Server (NTRS)

A decentralized control is investigated for applicability to the autonomous formation flying control algorithm developed by GSFC for the New Millenium Program Earth Observer-1 (EO-1) mission. This decentralized framework has the following characteristics: The approach is non-hierarchical, and coordination by a central supervisor is not required; Detected failures degrade the system performance gracefully; Each node in the decentralized network processes only its own measurement data, in parallel with the other nodes; Although the total computational burden over the entire network is greater than it would be for a single, centralized controller, fewer computations are required locally at each node; Requirements for data transmission between nodes are limited to only the dimension of the control vector, at the cost of maintaining a local additional data vector. The data vector compresses all past measurement history from all the nodes into a single vector of the dimension of the state; and The approach is optimal with respect to standard cost functions. The current approach is valid for linear time-invariant systems only. Similar to the GSFC formation flying algorithm, the extension to linear LQG time-varying systems requires that each node propagate its filter covariance forward (navigation) and controller Riccati matrix backward (guidance) at each time step. Extension of the GSFC algorithm to non-linear systems can also be accomplished via linearization about a reference trajectory in the standard fashion, or linearization about the current state estimate as with the extended Kalman filter. To investigate the feasibility of the decentralized integration with the GSFC algorithm, an existing centralized LQG design for a single spacecraft orbit control problem is adapted to the decentralized framework while using the GSFC algorithm's state transition matrices and framework. The existing GSFC design uses both reference trajectories of each spacecraft in formation and by appropriate choice of coordinates and simplified measurement modeling is formulated as a linear time-invariant system. Results for improvements to the GSFC algorithm and a multiple satellite formation will be addressed. The goal of this investigation is to progressively relax the assumptions that result in linear time-invariance, ultimately to the point of linearization of the non-linear dynamics about the current state estimate as in the extended Kalman filter. An assessment will then be made about the feasibility of the decentralized approach to the realistic formation flying application of the EO-1/Landsat 7 formation flying experiment.

Folta, David C.; Carpenter, J. Russell

1999-01-01

21

Design of a discrete Linear Quadratic Gaussian (DLQG) compensator for SSR damping using a sample invariant discrete model of TCSC  

Microsoft Academic Search

The paper presents the design of a discrete linear quadratic gaussian (DLQG) compensator for SSR damping which includes a full order Kalman filter to estimate all the states of the system and a full state feedback regulator. The controller is tested on IEEE First Benchmark model for SSR studies. A discrete linear-time invariant (LTI) model of a thyristor-controlled series capacitor

K. C. Sindhu Thampatty; E. P. Cheriyan; M. P. Nandakumar

2009-01-01

22

A quadratically constrained MAP classifier using the mixture of Gaussians models as a weight function.  

PubMed

In this paper, we propose classifiers derived from quadratically constrained maximum a posteriori (QCMAP) estimation. The QCMAP consists of the maximization of the expectation of a cost function, which is derived from the maximum a posteriori probability and a quadratic constraint. This criterion is highly general since its forms include least squares regressions and a support vector machine. Furthermore, the criterion provides a novel classifier, the "Gaussian QCMAP." The QCMAP procedure still has large theoretical interest and its full extensibility has yet to be explored. In this paper, we propose using the mixture of Gaussian distributions as the QCMAP weight function. The mixture of Gaussian distributions has wide-ranging applicability, and encompasses forms, such as a normal distribution model and a kernel density model. We propose four types of mixture of Gaussian functions for QCMAP classifiers, and conduct experiments to demonstrate their advantages. PMID:24808526

Yokota, Tatsuya; Yamashita, Yukihiko

2013-07-01

23

A user oriented microcomputer facility for designing linear quadratic Gaussian feedback compensators  

NASA Technical Reports Server (NTRS)

A laboratory design facility for digital microprocessor implementation of linear-quadratic-Gaussian feedback compensators is described. Outputs from user interactive programs for solving infinite time horizon LQ regulator and Kalman filter problems were conditioned for implementation on the laboratory microcomputer system. The software consisted of two parts: an offline high-level program for solving the LQ Ricatti equations and generating associated feedback and filter gains and a cross compiler/macro assembler which generates object code for the target microprocessor system. A PDP 11/70 with a UNIX operating system was used for all high level program and data management, and the target microprocessor system is an Intel MDS (8080-based processor). Application to the control of a two dimensional inverted pendulum is presented and issues in expanding the design/prototyping system to other target machine architectures are discussed.

Houpt, P. K.; Wahid, J.; Johnson, T. L.; Ward, S. A.

1978-01-01

24

Linear quadratic optimal learning control (LQL)  

Microsoft Academic Search

A learning control solution to the problem of finding a finite-time optimal control history that minimizes a quadratic cost is presented. Learning achieves optimization without requiring detailed knowledge of the system, which may be affected by unknown but repetitive disturbances. The optimal solution is synthesized one basis function at a time, reaching optimality in a finite number of trials. These

James A. Frueh; Minh Q. Phan

1998-01-01

25

Linear-quadratic-Gaussian synthesis with reduced parameter sensitivity  

NASA Technical Reports Server (NTRS)

We present a method for improving the tolerance of a conventional LQG controller to parameter errors in the plant model. The improvement is achieved by introducing additional terms reflecting the structure of the parameter errors into the LQR cost function, and also the process and measurement noise models. Adjusting the sizes of these additional terms permits a trade-off between robustness and nominal performance. Manipulation of some of the additional terms leads to high gain controllers while other terms lead to low gain controllers. Conditions are developed under which the high-gain approach asymptotically recovers the robustness of the corresponding full-state feedback design, and the low-gain approach makes the closed-loop poles asymptotically insensitive to parameter errors.

Lin, J. Y.; Mingori, D. L.

1992-01-01

26

Quadratic Programming for Allocating Control Effort  

NASA Technical Reports Server (NTRS)

A computer program calculates an optimal allocation of control effort in a system that includes redundant control actuators. The program implements an iterative (but otherwise single-stage) algorithm of the quadratic-programming type. In general, in the quadratic-programming problem, one seeks the values of a set of variables that minimize a quadratic cost function, subject to a set of linear equality and inequality constraints. In this program, the cost function combines control effort (typically quantified in terms of energy or fuel consumed) and control residuals (differences between commanded and sensed values of variables to be controlled). In comparison with prior control-allocation software, this program offers approximately equal accuracy but much greater computational efficiency. In addition, this program offers flexibility, robustness to actuation failures, and a capability for selective enforcement of control requirements. The computational efficiency of this program makes it suitable for such complex, real-time applications as controlling redundant aircraft actuators or redundant spacecraft thrusters. The program is written in the C language for execution in a UNIX operating system.

Singh, Gurkirpal

2005-01-01

27

Stochastic Linear Quadratic Optimal Control Problems  

SciTech Connect

This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) forward-backward stochastic differential equations are established. Some results involving Riccati equation are discussed as well.

Chen, S. [Department of Mathematics, Zhejiang University, Hangzhou 310027 (China); Yong, J. [Laboratory of Mathematics for Nonlinear Sciences, Department of Mathematics, and Institute of Mathematical Finance, Fudan University, Shanghai 200433 (China)

2001-07-01

28

Time evolution of a Gaussian class of quasi-distribution functions under quadratic Hamiltonian  

NASA Astrophysics Data System (ADS)

A Lie algebraic method for propagation of the Wigner quasi-distribution function under quadratic Hamiltonian was presented by Zoubi and Ben-Aryeh. We show that the same method can be used in order to propagate a rather general class of quasi distribution functions, which we call "Gaussian class". This class contains as special cases the well-known Wigner, Husimi, Glauber and Kirkwood-Rihaczek quasi-distribution functions. We present some examples of the calculation of the time-evolution of those functions.

Ginzburg, D.; Mann, A.

2014-03-01

29

Time evolution of a Gaussian class of quasi-distribution functions under quadratic Hamiltonian.  

PubMed

A Lie algebraic method for propagation of the Wigner quasi-distribution function (QDF) under quadratic Hamiltonian was presented by Zoubi and Ben-Aryeh. We show that the same method can be used in order to propagate a rather general class of QDFs, which we call the "Gaussian class." This class contains as special cases the well-known Wigner, Husimi, Glauber, and Kirkwood-Rihaczek QDFs. We present some examples of the calculation of the time evolution of those functions. PMID:24663423

Ginzburg, D; Mann, A

2014-03-10

30

Non-Gaussianity and gravitational waves from a quadratic and self-interacting curvaton  

SciTech Connect

In this paper we consider how non-Gaussianity of the primordial density perturbation and the amplitude of gravitational waves from inflation can be used to determine parameters of the curvaton scenario for the origin of structure. We show that in the simplest quadratic model, where the curvaton evolves as a free scalar field, measurement of the bispectrum relative to the power spectrum, f{sub NL}, and the tensor-to-scalar ratio can determine both the expectation value of the curvaton field during inflation and its dimensionless decay rate relative to the curvaton mass. We show how these predictions are altered by the introduction of self-interactions, in models where higher-order corrections are determined by a characteristic mass scale and discuss how additional information about primordial non-Gaussianity and scale dependence may constrain curvaton interactions.

Fonseca, Jose; Wands, David [Institute of Cosmology and Gravitation, Dennis Sciama Building, Burnaby Road, University of Portsmouth, Portsmouth, PO1 3FX (United Kingdom) and Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, 606-8502 (Japan)

2011-03-15

31

Discrete-Time Markovian Jump Linear Quadratic Optimal Control.  

National Technical Information Service (NTIS)

This paper is concerned with the optimal control of discrete-time linear systems that possess randomly jumping parameters described by finite state Markov processes. For problems having quadratic costs and perfect observations, the optimal control laws an...

H. J. Chizeck A. S. Willsky D. Castanon

1985-01-01

32

Quadratic Optimal Control of Abstract Linear Systems: The Stable Case.  

National Technical Information Service (NTIS)

The authors consider the infinite horizon quadratic cost minimization problem for a stable abstract linear control system, and show that it can be reduced to a spectral factorization problem in the (usually finite-dimensional) control space. More precisel...

O. J. Staffans

1995-01-01

33

A linear quadratic Gaussian with loop transfer recovery proximity operations autopilot for spacecraft. M.S. Thesis - MIT  

NASA Technical Reports Server (NTRS)

An automatic control scheme for spacecraft proximity operations is presented. The controller is capable of holding the vehicle at a prescribed location relative to a target, or maneuvering it to a different relative position using straight line-of-sight translations. The autopilot uses a feedforward loop to initiate and terminate maneuvers, and for operations at nonequilibrium set-points. A multivariate feedback loop facilitates precise position and velocity control in the presence of sensor noise. The feedback loop is formulated using the Linear Quadratic Gaussian (LQG) with Loop Transfer Recovery (LTR) design procedure. Linear models of spacecraft dynamics, adapted from Clohessey-Wiltshire Equations, are augmented and loop shaping techniques are applied to design a target feedback loop. The loop transfer recovery procedure is used to recover the frequency domain properties of the target feedback loop. The resulting compensator is integrated into an autopilot which is tested in a high fidelity Space Shuttle Simulator. The autopilot performance is evaluated for a variety of proximity operations tasks envisioned for future Shuttle flights.

Chen, George T.

1987-01-01

34

Analysis of integral controls in linear quadratic regulator design  

NASA Technical Reports Server (NTRS)

The application of linear optimal control to the design of systems with integral control action on specified outputs is considered. Using integral terms in a quadratic performance index, an asymptotic analysis is used to determine the effect of variable quadratic weights on the eigenvalues and eigenvectors of the closed loop system. It is shown that for small integral terms the placement of integrator poles and gain calculation can be effectively decoupled from placement of the primary system eigenvalues. This technique is applied to the design of integral controls for a STOL aircraft outer loop guidance system.

Slater, G. L.

1979-01-01

35

Tuning a fuzzy controller using quadratic response surfaces  

NASA Technical Reports Server (NTRS)

Response surface methodology, an alternative method to traditional tuning of a fuzzy controller, is described. An example based on a simulated inverted pendulum 'plant' shows that with (only) 15 trial runs, the controller can be calibrated using a quadratic form to approximate the response surface.

Schott, Brian; Whalen, Thomas

1992-01-01

36

Discrete-time markovian-jump linear quadratic optimal control  

Microsoft Academic Search

This paper is concerned with the optimal control of discrete-time linear systems that possess randomly jumping parameters described by finite-state Markov processes. For problems having quadratic costs and perfect observations, the optimal control laws and expected costs-to-go can be precomputed from a set of coupled Riccati-like matrix difference equations. Necessary and sufficient conditions are derived for the existence of optimal

H. J. CHIZECK; A. S. WILLSKY; D. CASTANON

1986-01-01

37

Discrete-time Markovian-jump linear quadratic optimal control  

NASA Technical Reports Server (NTRS)

This paper is concerned with the optimal control of discrete-time linear systems that possess randomly jumping parameters described by finite-state Markov processes. For problems having quadratic costs and perfect observations, the optimal control laws and expected costs-to-go can be precomputed from a set of coupled Riccati-like matrix difference equations. Necessary and sufficient conditions are derived for the existence of optimal constant control laws which stabilize the controlled system as the time horizon becomes infinite, with finite optimal expected cost.

Chizeck, H. J.; Willsky, A. S.; Castanon, D.

1986-01-01

38

Design of a linear Gaussian control law for an adaptive optics system  

NASA Astrophysics Data System (ADS)

This thesis considers the design of a linear quadratic Gaussian (LQG) controller for a ground-based adaptive-optics telescopes. The incoming aberrated image is reflected from a 97-element piezoelectric mirror, then measured with a Hartmann-type wavefront sensor. A Kalman filter processes the outputs of the wavefront sensor and obtains estimates of system states. A linear quadratic regulator processes these state estimates and determines an appropriate set of commands for the deformable mirror. Atmospheric distortion is modeled as a set of fourteen Zernike coefficients whose dynamic behavior is produced by excitation of a set of shaping filters by zero-mean Gaussian white noise. The response of the mirror to control voltages is modeled as a set of Zernike coefficients whose dynamics are modeled as deterministic first-order systems. The entire control system is simulated using the multimode simulation for optimal filter evaluation (MSOFE) software.

Vonbokern, Mark A.

1990-12-01

39

Frequency weighted system identification and linear quadratic controller design  

NASA Technical Reports Server (NTRS)

Application of filters for frequency weighting of Markov parameters (pulse response functions) is described in relation to system/observer identification. The time domain identification approach recovers a model which has a pulse response weighted according to frequency. The identified model is composed of the original system and filters. The augmented system is in a form which can be used directly for frequency weighted linear quadratic controller design. Data from either single or multiple experiments can be used to recover the Markov parameters. Measured acceleration signals from a truss structure are used for system identification and the model obtained is used for frequency weighted controller design. The procedure makes the identification and controler design complementary problems.

Horta, Lucas G.; Phan, Minh; Juang, Jer-Nan; Longman, Richard W.; Sulla, Jeffrey L.

1991-01-01

40

Gaussian2 theory: Use of higher level correlation methods, quadratic configuration interaction geometries, and second-order Møller-Plesset zero-point energies  

Microsoft Academic Search

The performance of Gaussian-2 theory is investigated when higher level theoretical methods are included for correlation effects, geometries, and zero-point energies. A higher level of correlation treatment is examined using Brueckner doubles [BD(T)] and coupled cluster [CCSD(T)] methods rather than quadratic configuration interaction [QCISD(T)]. The use of geometries optimized at the QCISD level rather than the second-order Moller--Plesset level (MP2)

Larry A. Curtiss; Krishnan Raghavachari; John A. Pople

1995-01-01

41

Gaussian2 theory: Use of higher level correlation methods, quadratic configuration interaction geometries, and second-order Mo&slash;ller–Plesset zero-point energies  

Microsoft Academic Search

The performance of Gaussian-2 theory is investigated when higher level theoretical methods are included for correlation effects, geometries, and zero-point energies. A higher level of correlation treatment is examined using Brueckner doubles [BD(T)] and coupled cluster [CCSD(T)] methods rather than quadratic configuration interaction [QCISD(T)]. The use of geometries optimized at the QCISD level rather than the second-order Mo&slash;ller–Plesset level (MP2)

Larry A. Curtiss; Krishnan Raghavachari; John A. Pople

1995-01-01

42

Dynamics and linear quadratic optimal control of flexible multibody systems  

NASA Astrophysics Data System (ADS)

An efficient algorithm for the modeling, dynamic analysis, and optimal control of flexible multibody systems (FMBS) is presented. The cantilevered Bernoulli-Euler beam model and the assumed mode method are used to represent flexibility of elastic bodies in 3D vibration problems. Centrifugal stiffening effects are introduced to correctly represent the dynamic response. The governing equations of motion are based on Kane's equations, adopting a recursive formulation and strategic positioning of the generalized coordinates. The linear quadratic optimization scheme is employed to formulate the vibration control problem. The solutions to the Riccati equation and the use of Kalman gain as optimal control feedbacks to the control of flexibility are also introduced. Based on the optimal control theory and the property of the built-in redundancy for flexible multibody systems, the performance index measure in the optimization control of such systems can be classified into two manifolds: (1) using the extra degrees of freedom resulting from redundancy as control inputs and choosing an integral-type performance index which results in a global optimization scheme and (2) using the joint forces and torques as control inputs and allowing the system output state to keep close track to a reference state while the performance index is kept minimum. Several numerical examples are presented to demonstrate the effectiveness of the methodologies developed.

Tung, Chin-Wei

1994-12-01

43

Quadratic Optimization in the Problems of Active Control of Sound  

NASA Technical Reports Server (NTRS)

We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulations of the problem. We have also obtained optimal solutions that minimize the overall absolute acoustic source strength of active control sources. These optimal solutions happen to be particular layers of monopoles on the perimeter of the protected region. Mathematically, minimization of acoustic source strength is equivalent to minimization in the sense of L(sub 1). By contrast. in the current paper we formulate and study optimization problems that involve quadratic functions of merit. Specifically, we minimize the L(sub 2) norm of the control sources, and we consider both the unconstrained and constrained minimization. The unconstrained L(sub 2) minimization is certainly the easiest problem to address numerically. On the other hand, the constrained approach allows one to analyze sophisticated geometries. In a special case, we call compare our finite-difference optimal solutions to the continuous optimal solutions obtained previously using a semi-analytic technique. We also show that the optima obtained in the sense of L(sub 2) differ drastically from those obtained in the sense of L(sub 1).

Loncaric, J.; Tsynkov, S. V.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

44

Controllability, observability and discrete-time markovian jump linear quadratic control  

Microsoft Academic Search

This paper is concerned with the controllability and observability of discrete-time linear systems that possess randomly jumping parameters described by finite-stale Markov processes, and the relationship between these properties and the solution of the infinite time jump linear quadratic (JLQ) optimal control problem. The solution of the markovian JLQ problem with finite or infinite time horizons is known. Necessary and

YUANDONG JI; HOWARD J. CHIZECK

1988-01-01

45

Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control  

Microsoft Academic Search

Consideration is given to the control of continuous-time linear systems that possess randomly jumping parameters which can be described by finite-state Markov processes. The relationship between appropriately defined controllability, stabilizability properties, and the solution of the infinite time jump linear quadratic (JLQ) optimal control problems is also examined. Although the solution of the continuous-time Markov JLQ problem with finite or

Y. Ji; H. J. Chizeck

1990-01-01

46

Central Control, Sewers and (0,1) quadratic programming  

NASA Astrophysics Data System (ADS)

We consider small sewer systems that combine foul water and storm water sewer functions in flat terrain. These systems are a combination of local gravity flow networks connected by pumps. The pumps are usually fixed speed, so they are on or off. We formulate a (0,1) quadratic programming problem, provide an overview of known solution methods and examine the relative speed of different solution methods.

Kolechkina, Alla; van Nooijen, Ronald

2013-04-01

47

Prompt critical control of the ACRR using a linear quadratic regulator design  

Microsoft Academic Search

This paper describes the application of linear control design techniques to the problem of nuclear reactor control. The control algorithm consists of generating a nominal trajectory within the control authority of the reactor rod drives, and then following this trajectory with a gain scheduled linear quadratic regulator (LQR). A controller based on this algorithm has generated power pulses up to

Gilkey

1992-01-01

48

Prompt critical control of the ACRR using a linear quadratic regulator design  

Microsoft Academic Search

This paper describes the application of ``Modern Control'' design techniques to the problem of nuclear reactor control. The control algorithm consists of generating a nominal trajectory within the control authority of the reactor rod drives, and then following this trajectory with a gain scheduled linear quadratic regulator (LQR). A controller based on this algorithm has generated power pulses up to

Jeffrey C. Gilkey

1993-01-01

49

Prompt critical control of the ACRR using a linear quadratic regulator design  

Microsoft Academic Search

This paper describes the application of ‘‘Modern Control’’ design techniques to the problem of nuclear reactor control. The control algorithm consists of generating a nominal trajectory within the control authority of the reactor rod drives, and then following this trajectory with a gain scheduled linear quadratic regulator (LQR). A controller based on this algorithm has generated power pulses up to

Jeffrey C. Gilkey

1993-01-01

50

Controllable gaussian-qubit interface for extremal quantum state engineering.  

PubMed

We study state engineering through bilinear interactions between two remote qubits and two-mode gaussian light fields. The attainable two-qubit states span the entire physically allowed region in the entanglement-versus-global-purity plane. Two-mode gaussian states with maximal entanglement at fixed global and marginal entropies produce maximally entangled two-qubit states in the corresponding entropic diagram. We show that a small set of parameters characterizing extremally entangled two-mode gaussian states is sufficient to control the engineering of extremally entangled two-qubit states, which can be realized in realistic matter-light scenarios. PMID:20867288

Adesso, Gerardo; Campbell, Steve; Illuminati, Fabrizio; Paternostro, Mauro

2010-06-18

51

An adaptive linear quadratic regulator with repetitive controller applied to uninterruptible power supplies  

Microsoft Academic Search

This paper proposes a discrete time adaptive linear quadratic regulator (LQR) with a repetitive controller (RP) for uninterruptible power supplies (UPS). In the controller design, the gains are determined by minimizing a cost function which reduces the tracking error and the control signal. A recursive least squares (RLS) estimator identifies the plant parameters at different load conditions. Then, the LQR

Vinicius Foletto Montagner; Emerson Giovani Carati; H. A. Grundling

2000-01-01

52

Sequential design of a linear quadratic controller for the Deep Space Network antennas  

Microsoft Academic Search

A new linear quadratic controller design procedure is proposed for the NASA\\/JPL Deep Space Network antennas. The antenna model is divided into a tracking subsystem and a flexible subsystem. Controllers for the flexible and tracking parts are designed separately by adjusting the performance index weights. Ad hoc weights are chosen for the tracking part of the controller and the weights

W. Gawronski

1992-01-01

53

A differential transformation based computational method for switched linear quadratic optimal control  

Microsoft Academic Search

A computational method based on differential transformation is proposed for solving switched linear quadratic (SLQ) optimal control problems with a predefined switching sequence. From the necessary conditions for optimality, the SLQ optimal control problem is first converted into a two-point boundary value problem (TPBVP) with additional transverse conditions at the switching times. Then we propose a differential transformation algorithm for

Jinhua Li; Dzung Du; Inseok Hwang

2007-01-01

54

Pointwise linear quadratic optimal control of a tandem cold rolling mill  

Microsoft Academic Search

The tandem cold rolling of metal strip is a complex nonlinear multivariable process whose optimization presents significant challenges to the control design. Existing systems using the present technology are limited in their capability for improvement in performance and robustness and therefore the need arises for a better approach. It is considered that a pointwise linear quadratic optimal control might fulfill

John Pittner; Marwan A. Simaan

2004-01-01

55

Approximating the linear quadratic optimal control law for hereditary systems with delays in the control  

NASA Technical Reports Server (NTRS)

The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary systems. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.

Milman, Mark H.

1987-01-01

56

Iterative Quadratic Optimization for the Bus Holding Control Problem  

Microsoft Academic Search

A multiple control-point strategy for holding control of a bus transit system is presented. The model developed is deterministic and assumes the availability of real-time information and historical data of the system. Stochastic effects are distur- bances to be compensated by the feedback nature of the control. The objective is to minimize total user delay, which is modeled by a

Luiz Alberto Koehler; Werner Kraus; Eduardo Camponogara

2011-01-01

57

Inverse Gaussian Control Charts for Monitoring Process Variability  

Microsoft Academic Search

Control charts for detecting shifts in process variability are constructed under the assumption that the quality characteristic under study follows the inverse Gaussian IG(?, ?) distribution with known parameter ?, and the location parameter ? is either known or unknown. The effects of the estimated probability limits on the performance of the proposed charts in detecting shifts in process variability are

C. H. Sim

2003-01-01

58

A new capability of cascaded quadratic processes: controllable red and blue shift of femtosecond pulses  

Microsoft Academic Search

We theoretically and experimentally demonstrate the controllable frequency shift of femtosecond pulses in quadratic media in the presence of group velocity mismatch. Applications of this new capability to the compensation of Raman scattering and high-energy pulse compression are discussed.

F. O. Ilday; K. Beckwitt; H. Lim; F. W. Wise

2003-01-01

59

Linear quadratic servo control of a reusable rocket engine  

NASA Technical Reports Server (NTRS)

A design method for a servo compensator is developed in the frequency domain using singular values. The method is applied to a reusable rocket engine. An intelligent control system for reusable rocket engines was proposed which includes a diagnostic system, a control system, and an intelligent coordinator which determines engine control strategies based on the identified failure modes. The method provides a means of generating various linear multivariable controllers capable of meeting performance and robustness specifications and accommodating failure modes identified by the diagnostic system. Command following with set point control is necessary for engine operation. A Kalman filter reconstructs the state while loop transfer recovery recovers the required degree of robustness while maintaining satisfactory rejection of sensor noise from the command error. The approach is applied to the design of a controller for a rocket engine satisfying performance constraints in the frequency domain. Simulation results demonstrate the performance of the linear design on a nonlinear engine model over all power levels during mainstage operation.

Musgrave, Jeffrey L.

1991-01-01

60

Gaussian Networks for Direct Adaptive Control  

Microsoft Academic Search

A direct adaptive tracking control architecture is proposed and evaluated for a class of continuous-time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible. The architecture employs a network of gausian radial basis functions to adaptively compensate for the plant nonlinearities. Under mild assumptions about the degree of smoothness

Robert M. Sanner; Jean-Jacques E. Slotine

1991-01-01

61

Sequential design of a linear quadratic controller for the deep space network antennas  

NASA Technical Reports Server (NTRS)

A linear quadratic controller design procedure is proposed for the NASA/JPL Deep Space Network antennas. The procedure is developed for an antenna model divided into tracking and flexible subsystems. Controllers for the flexible and tracking parts are designed separately by adjusting the performance index weights. The effect of weights on system performance is a crucial property, and is analytically described in this paper. The procedure is illustrated with the control system design for the DSS 13 antenna.

Gawronski, Wodek

1992-01-01

62

Optimal impulse control for cash management¶with quadratic holding-penalty costs  

Microsoft Academic Search

.   This paper studies optimal control for an infinite horizon cash management problem where the cash fund fluctuates as a Brownian\\u000a motion. Holding-penalty costs are assumed to be a quadratic function of the cash level and there are fixed and proportional\\u000a transaction costs. Using the “impulse technique”, we prove that optimal control exists and takes the form of a control

Stefano Baccarin

2002-01-01

63

Prompt critical control of the ACRR using a linear quadratic regulator design  

SciTech Connect

This paper describes the application of linear control design techniques to the problem of nuclear reactor control. The control algorithm consists of generating a nominal trajectory within the control authority of the reactor rod drives, and then following this trajectory with a gain scheduled linear quadratic regulator (LQR). A controller based on this algorithm has generated power pulses up to 100 MW on Sandia`s Annular Core Research Reactor (ACRR). Prompt critical control at $1.02 net reactivity and controlled start up rates over 350 DPM have also been demonstrated using tills controller.

Gilkey, J.C.

1992-09-01

64

Prompt critical control of the ACRR using a linear quadratic regulator design  

SciTech Connect

This paper describes the application of linear control design techniques to the problem of nuclear reactor control. The control algorithm consists of generating a nominal trajectory within the control authority of the reactor rod drives, and then following this trajectory with a gain scheduled linear quadratic regulator (LQR). A controller based on this algorithm has generated power pulses up to 100 MW on Sandia's Annular Core Research Reactor (ACRR). Prompt critical control at $1.02 net reactivity and controlled start up rates over 350 DPM have also been demonstrated using tills controller.

Gilkey, J.C.

1992-01-01

65

Learning control for minimizing a quadratic cost during repetitions of a task  

NASA Technical Reports Server (NTRS)

In many applications, control systems are asked to perform the same task repeatedly. Learning control laws have been developed over the last few years that allow the controller to improve its performance each repetition, and to converge to zero error in tracking a desired trajectory. This paper generates a new type of learning control law that learns to minimize a quadratic cost function for tracking. Besides being of interest in its own right, this objective alleviates the need to specify a desired trajectory that can actually be performed by the system. The approach used here is to adapt appropriate methods from numerical optimization theory in order to produce learning control algorithms that adjust the system command from repetition to repetition in order to converge to the quadratic cost optimal trajectory.

Longman, Richard W.; Chang, Chi-Kuang

1990-01-01

66

Linear quadratic servo control of a reusable rocket engine  

NASA Technical Reports Server (NTRS)

The paper deals with the development of a design method for a servo component in the frequency domain using singular values and its application to a reusable rocket engine. A general methodology used to design a class of linear multivariable controllers for intelligent control systems is presented. Focus is placed on performance and robustness characteristics, and an estimator design performed in the framework of the Kalman-filter formalism with emphasis on using a sensor set different from the commanded values is discussed. It is noted that loop transfer recovery modifies the nominal plant noise intensities in order to obtain the desired degree of robustness to uncertainty reflected at the plant input. Simulation results demonstrating the performance of the linear design on a nonlinear engine model over all power levels during mainstage operation are discussed.

Musgrave, Jeffrey L.

1991-01-01

67

Prompt critical control of the ACRR using a linear quadratic regulator design  

NASA Astrophysics Data System (ADS)

This paper describes the application of ``Modern Control'' design techniques to the problem of nuclear reactor control. The control algorithm consists of generating a nominal trajectory within the control authority of the reactor rod drives, and then following this trajectory with a gain scheduled linear quadratic regulator (LQR). A controller based on this algorithm has generated power pulses up to 100 mW on Sandia's Annular Core Research Reactor (ACRR). Prompt critical control at $1.02 net reactivity and at start-up rates over 350 decades per minute (DPM) has also been demonstrated using this controller.

Gilkey, Jeffrey C.

1993-01-01

68

Prompt critical control of the ACRR using a linear quadratic regulator design  

SciTech Connect

This paper describes the application of Modern Control'' design techniques to the problem of nuclear reactor control. The control algorithm consists of generating a nominal trajectory within the control authority of the reactor rod drives, and then following this trajectory with a gain scheduled linear quadratic regulator (LQR). A controller based on this algorithm has generated power pulses up to 100 mW on Sandia's Annular Core Research Reactor (ACRR). Prompt critical control at $1.02 net reactivity and at start-up rates over 350 decades per minute (DPM) has also been demonstrated using this controller.

Gilkey, J.C. (Exploratory Systems Development Center 9100, Sandia National Laboratories, Albuquerque, New Mexico 87185 (United States))

1993-01-20

69

The application of quadratic optimal cooperative control synthesis to a CH-47 helicopter  

NASA Technical Reports Server (NTRS)

A control-system design method, Quadratic Optimal Cooperative Control Synthesis (CCS), is applied to the design of a Stability and Control Augmentation Systems (SCAS). The CCS design method is different from other design methods in that it does not require detailed a priori design criteria, but instead relies on an explicit optimal pilot-model to create desired performance. The design model, which was developed previously for fixed-wing aircraft, is simplified and modified for application to a Boeing Vertol CH-47 helicopter. Two SCAS designs are developed using the CCS design methodology. The resulting CCS designs are then compared with designs obtained using classical/frequency-domain methods and Linear Quadratic Regulator (LQR) theory in a piloted fixed-base simulation. Results indicate that the CCS method, with slight modifications, can be used to produce controller designs which compare favorably with the frequency-domain approach.

Townsend, Barbara K.

1986-01-01

70

Controllability, observability and the jump linear quadratic problem in continuous time  

Microsoft Academic Search

This paper is concerned with the controllability and observability of continuous-time linear systems that possess randomly jumping parameters which can be described by finite-state Markov processes, and with the relationships between these properties and the solution of the infinite time jump linear quadratic (JLQ) optimal control problem. The solution of the continuous-time Markov JLQ problem with finite or infinite time

Yuandong Ji; Howard J. Chizeck

1987-01-01

71

Legendre-tau approximation for functional differential equations. II - The linear quadratic optimal control problem  

NASA Technical Reports Server (NTRS)

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Ito, Kazufumi; Teglas, Russell

1987-01-01

72

Legendre-tau approximation for functional differential equations. Part 2: The linear quadratic optimal control problem  

NASA Technical Reports Server (NTRS)

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Ito, K.; Teglas, R.

1984-01-01

73

Controllable self-steepening of ultrashort pulses in quadratic nonlinear media.  

PubMed

By analyzing ultrashort optical pulse propagation in quadratic nonlinear media beyond the slowly varying envelope approximation, we find that the sign and magnitude of self-steepening can be controlled through the wave vector mismatch. As an example of this phenomenon's impact on ultrashort pulse propagation, we show that it may be used to cancel the propagation effects of group-velocity mismatch. We obtain quantitative agreement between theory, simulations, and experiments. PMID:17026229

Moses, Jeffrey; Wise, Frank W

2006-08-18

74

Decoupled control analysis of a large flexible space antenna with linear quadratic regulator comparisons  

NASA Technical Reports Server (NTRS)

A decoupled-control analysis was performed for a large flexible space antenna. Control involved commanding changes in the rigid-body modes or nulling disturbances in the flexible modes. The study provides parametric-type data which could be useful in the final design of a large space antenna control system. Results are presented to illustrate the effect on control requirements of (1) the number of modes controlled; (2) the number, type, and location of control actuators; and (3) variations in the closed-loop dynamics of the control system. Comparisons are given between the decoupled-control results and those obtained by using a linear quadratic regulator approach. Time history responses are presented to illustrate the effects of the control procedures.

Young, J. W.; Hamer, H. A.; Johnson, K. G.

1984-01-01

75

Sensitivity Analysis of Linear Programming and Quadratic Programming Algorithms for Control Allocation  

NASA Technical Reports Server (NTRS)

The Next Generation (NextGen) transport aircraft configurations being investigated as part of the NASA Aeronautics Subsonic Fixed Wing Project have more control surfaces, or control effectors, than existing transport aircraft configurations. Conventional flight control is achieved through two symmetric elevators, two antisymmetric ailerons, and a rudder. The five effectors, reduced to three command variables, produce moments along the three main axes of the aircraft and enable the pilot to control the attitude and flight path of the aircraft. The NextGen aircraft will have additional redundant control effectors to control the three moments, creating a situation where the aircraft is over-actuated and where a simple relationship does not exist anymore between the required effector deflections and the desired moments. NextGen flight controllers will incorporate control allocation algorithms to determine the optimal effector commands and attain the desired moments, taking into account the effector limits. Approaches to solving the problem using linear programming and quadratic programming algorithms have been proposed and tested. It is of great interest to understand their relative advantages and disadvantages and how design parameters may affect their properties. In this paper, we investigate the sensitivity of the effector commands with respect to the desired moments and show on some examples that the solutions provided using the l2 norm of quadratic programming are less sensitive than those using the l1 norm of linear programming.

Frost, Susan A.; Bodson, Marc; Acosta, Diana M.

2009-01-01

76

Space shuttle active-pogo-suppressor control design using linear quadratic regulator techniques  

NASA Technical Reports Server (NTRS)

Two methods of active pogo suppression (stabilization) for the space shuttle vehicle were studied analytically. The basis for both approaches was the linear quadratic regulator, state space technique. The first approach minimized root-mean-square pump inlet pressure by using either fullstate feedback, partial-state feedback, or output feedback with a Kalman filter. The second approach increased the modal damping associated with the critical structural modes by using either full-state feedback or reconstructed state feedback. A number of implementable controls were found by both approaches. The designs were analyzed with respect to sensitivity, complexity, and controller energy requirements, as well as controller performance. Practical controllers resulting from the two design approaches tended to use pressure and flow as feedback variables for the minimum-rms method and structural accelerations or velocities for the modal control method. Both approaches are suitable for the design of active pogo-suppression controllers.

Lehtinen, B.; Lorenz, C. F.

1979-01-01

77

A new approach to approximating the linear quadratic optimal control law for hereditary systems with control delays  

NASA Technical Reports Server (NTRS)

A factorization approach is presented for deriving approximations to the optimal feedback gain for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the feedback kernels.

Milman, M. H.

1985-01-01

78

Singular linear-quadratic control problem for systems with linear delay  

NASA Astrophysics Data System (ADS)

A singular linear-quadratic optimization problem on the trajectories of non-autonomous linear differential equations with linear delay is considered. The peculiarity of this problem is the fact that this problem has no solution in the class of integrable controls. To ensure the existence of solutions is required to expand the class of controls including controls with impulse components. Dynamical systems with linear delay are used to describe the motion of pantograph from the current collector with electric traction, biology, etc. It should be noted that for practical problems fact singularity criterion of quality is quite commonly occurring, and therefore the study of these problems is surely important. For the problem under discussion optimal programming control contained impulse components at the initial and final moments of time is constructed under certain assumptions on the functional and the right side of the control system.

Sesekin, A. N.

2013-12-01

79

Intelligent, Robust Control of Deteriorated Turbofan Engines via Linear Parameter Varying Quadratic Lyapunov Function Design  

NASA Technical Reports Server (NTRS)

A method for accommodating engine deterioration via a scheduled Linear Parameter Varying Quadratic Lyapunov Function (LPVQLF)-Based controller is presented. The LPVQLF design methodology provides a means for developing unconditionally stable, robust control of Linear Parameter Varying (LPV) systems. The controller is scheduled on the Engine Deterioration Index, a function of estimated parameters that relate to engine health, and is computed using a multilayer feedforward neural network. Acceptable thrust response and tight control of exhaust gas temperature (EGT) is accomplished by adjusting the performance weights on these parameters for different levels of engine degradation. Nonlinear simulations demonstrate that the controller achieves specified performance objectives while being robust to engine deterioration as well as engine-to-engine variations.

Turso, James A.; Litt, Jonathan S.

2004-01-01

80

CAD of control systems: Application of nonlinear programming to a linear quadratic formulation  

NASA Technical Reports Server (NTRS)

The familiar suboptimal regulator design approach is recast as a constrained optimization problem and incorporated in a Computer Aided Design (CAD) package where both design objective and constraints are quadratic cost functions. This formulation permits the separate consideration of, for example, model following errors, sensitivity measures and control energy as objectives to be minimized or limits to be observed. Efficient techniques for computing the interrelated cost functions and their gradients are utilized in conjunction with a nonlinear programming algorithm. The effectiveness of the approach and the degree of insight into the problem which it affords is illustrated in a helicopter regulation design example.

Fleming, P.

1983-01-01

81

Realization theory and quadratic optimal controllers for systems defined over Banach and Frechet algebras  

NASA Technical Reports Server (NTRS)

It is noted that recent work by Kamen (1979) on the stability of half-plane digital filters shows that the problem of the existence of a feedback law also arises for other Banach algebras in applications. This situation calls for a realization theory and stabilizability criteria for systems defined over Banach for Frechet algebra A. Such a theory is developed here, with special emphasis placed on the construction of finitely generated realizations, the existence of coprime factorizations for T(s) defined over A, and the solvability of the quadratic optimal control problem and the associated algebraic Riccati equation over A.

Byrnes, C. I.

1980-01-01

82

Sequencing batch-reactor control using Gaussian-process models.  

PubMed

This paper presents a Gaussian-process (GP) model for the design of sequencing batch-reactor (SBR) control for wastewater treatment. The GP model is a probabilistic, nonparametric model with uncertainty predictions. In the case of SBR control, it is used for the on-line optimisation of the batch-phases duration. The control algorithm follows the course of the indirect process variables (pH, redox potential and dissolved oxygen concentration) and recognises the characteristic patterns in their time profile. The control algorithm uses GP-based regression to smooth the signals and GP-based classification for the pattern recognition. When tested on the signals from an SBR laboratory pilot plant, the control algorithm provided a satisfactory agreement between the proposed completion times and the actual termination times of the biodegradation processes. In a set of tested batches the final ammonia and nitrate concentrations were below 1 and 0.5 mg L(-1), respectively, while the aeration time was shortened considerably. PMID:23597762

Kocijan, Juš; Hvala, Nadja

2013-06-01

83

Sequential design of a linear quadratic controller for the Deep Space Network antennas  

NASA Technical Reports Server (NTRS)

A new linear quadratic controller design procedure is proposed for the NASA/JPL Deep Space Network antennas. The antenna model is divided into a tracking subsystem and a flexible subsystem. Controllers for the flexible and tracking parts are designed separately by adjusting the performance index weights. Ad hoc weights are chosen for the tracking part of the controller and the weights of the flexible part are adjusted. Next, the gains of the tracking part are determined, followed by the flexible controller final tune-up. In addition, the controller for the flexible part is designed separately for each mode; thus the design procedure consists of weight adjustment for small-size subsystems. Since the controller gains are obtained by adjusting the performance index weights, determination of the weight effect on system performance is a crucial task. A method of determining this effect that allows an on-line improvement of the tracking performance is presented in this article. The procedure is illustrated with the control system design for the Deep Space Station (DSS)-13 antenna.

Gawronski, W.

1992-01-01

84

Sequential design of a linear quadratic controller for the Deep Space Network antennas  

NASA Technical Reports Server (NTRS)

A new linear quadratic controller design procedure is proposed for the NASA/JPL Deep Space Network antennas. The antenna model is divided into a tracking subsystem and a flexible subsystem. Controllers for the flexible and tracking parts are designed separately by adjusting the performance index weights. Ad hoc weights are chosen for the tracking part of the controller and the weights of the flexible part are adjusted. Next, the gains of the tracking part are determined, followed by the flexible controller final tune-up. In addition, the controller for the flexible part is designed separately for each mode; thus the design procedure consists of weight adjustment for small-size subsystems. Since the controller gains are obtained by adjusting the performance index weights, determination of the weight effect on system performance is a crucial task. A method of determining this effect that allows an on-line improvement of the tracking performance is presented in this article. The procedure is illustrated with the control system design for the DSS-13 antenna.

Gawronski, W.

1992-01-01

85

Quadratic and cubic neural units for identification and fast state feedback control of unknown nonlinear dynamic systems  

Microsoft Academic Search

The main goal is to introduce quadratic and cubic neural units (QNU, CNU) as appropriate neural units for fast state feedback control of unknown, unstable, nonlinear systems and depict their ability to provide a more robust and faster response than as it is in the case of a common linear state feedback controllers. The concepts of CNU and QNU are

Ivo Bukovsky; Sanjeevakumar Redlapalli; Madan M. Gupta

2003-01-01

86

Linear-quadratic-regulator pointing control system design for a high-altitude balloon payload  

SciTech Connect

A pointing control system design for the science package of a NASA high-altitude research balloon is described. The balloon assembly consists of a single helium balloon connected to a payload recovery parachute, payload gondola, and ballast hopper. Pointing of the scientific payload is accomplished via an arrangement of drive motors and a flywheel. Linear quadratic regulator (LQR) synthesis techniques are employed to produce the azimuth and elevation controller designs. The use of LQR synthesis is motivated by the azimuthal dynamic coupling encountered between the balloon and gondola. Two control devices are employed in azimuth, one of which is a decoupler motor and the other a flywheel. The decoupler motor is intended to isolate the gondola from the balloon such that the flywheel can be accelerated or decelerated about a steady-state angular velocity to provide precise azimuthal pointing. The multiple-input/multiple-output nature of the azimuth pointing problem is best handled in a matrix synthesis procedure such as LQR. The controller design methodology is explained, and a combination of time responses and singular value analyses are used to analytically evaluate the performance of the control system. 11 refs., 17 figs.

White, J.E.; Etter, J.R.

1987-11-01

87

Quadratic formula  

NSDL National Science Digital Library

The quadratic formula is easy to solve, yet sufficiently sophisticated that it provides insight into oscillations of masses connected by springs, as well as insight into chemical bonds between atoms. The purpose of this video is to illustrate what it means to find the "zeros" or "roots" of the quadratic equation, both using a graphical description, as well as by analytically completing the square to obtain the famous quadratic formula.

Liao, David

88

Quadratic Damping  

ERIC Educational Resources Information Center

Quadratic friction involves a discontinuous damping term in equations of motion in order that the frictional force always opposes the direction of the motion. Perhaps for this reason this topic is usually omitted from beginning texts in differential equations and physics. However, quadratic damping is more realistic than viscous damping in many…

Fay, Temple H.

2012-01-01

89

Optimal Linear Quadratic Regulators for Control of Nonlinear Mechanical Systems with Redundant Degrees-of-Freedom  

NASA Astrophysics Data System (ADS)

An optimal regulator problem for endpoint position control of a robot arm with (or without) redundancy in its total degrees-of-freedom (DOF) is solved by combining Riemannian geometry with nonlinear control theory. Given a target point, within the task-space, that the arm endpoint should reach, a task-space position feedback with joint damping is shown to asymptotically stabilize reaching movements even if the number of DOF of the arm is greater than the dimension of the task space and thereby the inverse kinematics is ill-posed. Usually the speed of convergence of the endpoint trajectory is unsatisfactory, depending on the choice of feedback gains for joint damping. Hence, to speed up the convergence without incurring further energy consumption, an optimal control design for minimizing a performance index composed of an integral of joint dissipation energy plus a linear quadratic form of the task-space control input and output is introduced. It is then shown that the Hamilton-Jacobi-Bellman equation derived from the principle of optimality is solvable in control variables and the Hamilton-Jacobi equation itself has an explicit solution. Although the state of the original dynamics (the Euler-Lagrange equation) with DOF-redundancy contains uncontrollable and unobservable manifolds, the dynamics satisfies a nonlinear version of the Kalman-Yakubovich-Popov lemma and the task-space input-output passivity. An inverse problem of optimal regulator design for robotic arms under the effect of gravity is also tackled by combining Riemannian geometry with passivity-based control theory.

Arimoto, Suguru

90

The quadratic stabilization resilient guaranteed cost control for a class of uncertain discrete-time switched linear systems  

Microsoft Academic Search

This paper focuses on the problem of resilient hybrid guaranteed cost control for a class of uncertain discrete-time switched linear systems. The controller gain to be designed is assumed to have additive and multiplicative gain variations. Based on multiple-Lyapunov function technique, the design of resilient hybrid guaranteed cost controllers is derived to make the corresponding closed-loop system quadratic stable for

Sun Wenan; Zhang Qiang; Feng Jiaxin

2008-01-01

91

Quantum Optimal Control of Single Harmonic Oscillator under Quadratic Controls together with Linear Dipole Polarizability: A Fluctuation Free Expectation Value Dynamical Perspective  

SciTech Connect

In this study, the optimal control equations for one dimensional quantum harmonic oscillator under the quadratic control operators together with linear dipole polarizability effects are constructed in the sense of Heisenberg equation of motion. A numerical technique based on the approximation to the non-commuting quantum mechanical operators from the fluctuation free expectation value dynamics perspective in the classical limit is also proposed for the solution of optimal control equations which are ODEs with accompanying boundary conditions. The dipole interaction of the system is considered to be linear, and the observable whose expectation value will be suppressed during the control process is considered to be quadratic in terms of position operator x. The objective term operator is also assumed to be quadratic.

Ayvaz, Muzaffer; Demiralp, Metin [Istanbul Technical University, Informatics Institute, Maslak, 34469, Istanbul (Turkey)

2011-09-14

92

Robust Hinfinity output feedback control design for fuzzy dynamic systems with quadratic D stability constraints: An LMI approach  

Microsoft Academic Search

This paper addresses the problem of designing a robust output feedback controller for a class of fuzzy uncertain dynamic systems that guarantees (i) the L2-gain from an exogenous input to a regulated output is less or equal to a prescribed value and (ii) the closed-loop fuzzy system to be quadratically stable within a pre-specified LMI stability region. Based on an

Sing Kiong Nguang; Peng Shi

2006-01-01

93

A Quadratic Programming Formulation of a Moving Ball Interception and Shooting Behaviour, and Its Application to Neural Network Control  

Microsoft Academic Search

A desirable elementary behaviour for a robot soccer player is the moving ball interception and shooting behaviour, but generating\\u000a smooth, fast motion for a mobile robot in a changing environment is a difficult problem. We address this problem by formulating\\u000a the specifications of this behaviour as a quadratic programming optimisation problem, and by training a neural network controller\\u000a on the

Frédéric Maire; Doug Taylor

2000-01-01

94

Research on main stream temperature control system in power plant based on CMAC neural network and the single-neuron PID controller with quadratic index  

Microsoft Academic Search

The main steam temperature control system is necessary to ensure high efficiency and high load-following capability in the operation of modern power plant, which has the characteristics of large inertia, large time-delay and time-varying, etc. Thus conventional PID control strategy cannot achieve good control performance. The quadratic index was introduced into single-neuron PID controller and then the optimal controller was

Yang Xue; Zhen-Jie Yan

2010-01-01

95

A quadratic stability result for singular switched systems with application to anti-windup control  

Microsoft Academic Search

In this note we consider the problem of determining necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a pair of stable linear time-invariant systems whose system matrices are of the form A, A-ghT, and where one of the matrices is singular. We then apply this result in a study of a feedback system with

R. Shorten; M. Corless; R. Middleton; S. Klinge; K. Wulff

2009-01-01

96

LQG and Feedforward Controllers for the Deep Space Network Antennas  

NASA Technical Reports Server (NTRS)

The controller development and the tracking performance evaluation for NASA's Deep Space Network antenna are presented. A trajectory preprocessor, LQG (Linear Quadratic Gaussian) controller, feedforward controller, and their combination are designed, built, analyzed, and tested.

Gawronski, W. K.; Racho, C. S.; Mellstrom, J. A.

1994-01-01

97

Active Flutter Control for Flexible Vehicles, Volume 1.  

National Technical Information Service (NTIS)

An active flutter control methodology based on linear quadratic gaussian theory and its application to the control of a super critical wing is presented. Results of control surface and sensor position optimization are discussed. Both frequency response ma...

J. K. Mahesh W. L. Garrard C. R. Stones P. D. Hausman

1979-01-01

98

Real Time Control of Reservoir Systems.  

National Technical Information Service (NTIS)

The development of a new method for the real time operation of reservoir systems is described. The method, called Extended Linear Quadratic Gaussian (ELQG) controller, draws on and extends stochastic control theory results, and is well suited for the opti...

A. P. Georgakakos D. H. Marks

1985-01-01

99

Towards Fault-Tolerant Optimal Control.  

National Technical Information Service (NTIS)

Questions regarding the design of fault-tolerant controllers that may endow systems with dynamic reliability are addressed. Results for jump linear quadratic Gaussian (JLQG) control problems are extended to include random jump costs, trajectory discontinu...

H. J. Chizeck A. S. Willsky

1977-01-01

100

Improved single neuron controller for multivariable stochastic systems with non-Gaussianities and unmodeled dynamics.  

PubMed

In this paper, a new adaptive control approach is presented for multivariate nonlinear non-Gaussian systems with unknown models. A more general and systematic statistical measure, called (h,?)-entropy, is adopted here to characterize the uncertainty of the considered systems. By using the "sliding window" technique, the non-parameter estimate of the (h,?)-entropy is formulated. Then, the improved neuron based controllers are developed for multivariate nonlinear non-Gaussian systems by minimizing the entropies of the tracking errors in closed loops. The condition to guarantee the strictly decreasing entropy of tracking error is presented. Moreover, the convergence in the mean-square sense has been analyzed for all the weights in the neural controllers. Finally, the comparative simulation results are presented to show that the performance of the proposed algorithm is superior to that of PID control strategy. PMID:23910156

Zhang, Jianhua; Jiang, Man; Ren, Mifeng; Hou, Guolian; Xu, Jinliang

2013-11-01

101

Acceleration-Augmented LQG Control of an Active Magnetic Bearing.  

National Technical Information Service (NTIS)

A linear-quadratic-gaussian (LQG) regulator controller design for an acceleration-augmented active magnetic bearing (AMB) is outlined. Acceleration augmentation is a key feature in providing improved dynamic performance of the controller. The optimal cont...

J. J. Feeley

1993-01-01

102

A posteriori error estimates for mixed finite element approximation of nonlinear quadratic optimal control problems  

Microsoft Academic Search

In this paper, we obtain an a posteriori error analysis for mixed finite element approximation of convex optimal control problems governed by a nonlinear second-order elliptic equation. Our results are based on the approximation for both the coupled state variables and the control variable. We propose to improve the error estimates, which can be used to construct an adaptive finite

Yanping Chen; Zuliang Lu; Min Fu

2012-01-01

103

Quadratic Optimal Control Theory for Viscoelastically Damped Structures Using a Fractional Derivative Viscoelasticity Model.  

National Technical Information Service (NTIS)

The objective of this thesis is to develop a control law for structures incorporating both passive damping via viscoelastic materials modelled by a fractional calculus stress strain law and active damping by applied forces and torques. To achieve this, qu...

R. N. Walker

1988-01-01

104

Vibration control of large linear quadratic symmetric systems. Ph.D. Thesis  

NASA Technical Reports Server (NTRS)

Some unique properties on a class of the second order lambda matrices were found and applied to determine a damping matrix of the decoupled subsystem in such a way that the damped system would have preassigned eigenvalues without disturbing the stiffness matrix. The resulting system was realized as a time invariant velocity only feedback control system with desired poles. Another approach using optimal control theory was also applied to the decoupled system in such a way that the mode spillover problem could be eliminated. The procedures were tested successfully by numerical examples.

Jeon, G. J.

1983-01-01

105

Direct dynamics using variational Gaussian wavepackets. Application to the intelligent control of benzene photochemistry  

NASA Astrophysics Data System (ADS)

The direct dynamics variational multi-configuration Gaussian wavepacket (DD-vMCG) method is based on the multi-configuration time-dependent Hartree (MCTDH) algorithm. It uses a time-dependent basis set of parameterised Gaussian functions, which are coupled so as to variationally provide the best possible representation of the wavepacket. This approach is designed to treat quantum effects in large molecules with on-the-fly calculation of the potential energy surface performed by an interfaced quantum chemistry program. Here, we apply this method to the study of the non-adiabatic photochemistry of benzene. Our aim is to rationalise how the way the wavepacket crosses the S1/S0 seam may modify the branching ratio Dewar benzene : benzvalene and enhance their production rather than non-radiative decay back to benzene. This study is intended to identify realistic non-radiative decay pathways that lead to alternative photochemical reactivity and to find corresponding targets that can be reached by optimal control experiments.

Lasorne, Benjamin; Bearpark, Michael J.; Robb, Michael A.; Worth, Graham A.

2007-03-01

106

Lesson 14: Quadratic Formula  

NSDL National Science Digital Library

Completing the square is applied to the general quadratic to derive the quadratic formula. Before an area application example is given there is a quick review of the four methods that have been presented for solving quadratic equations. Complex numbers are introduced before the discriminant is presented.

2011-01-01

107

Quadratic Functions: Workshop 4  

NSDL National Science Digital Library

Lesson 1 of two lessons requires students to explore quadratic functions by examining the family of functions described by y = a (x - h)squared+ k. In Lesson 2 students explore quadratic functions by using a motion detector known as a Calculator Based Ranger (CBR) to examine the heights of the different bounces of a ball. Students will represent each bounce with a quadratic function of the form y = a (x - h)squared + k. Background information, resources, references and videos of the lessons are included. Students work in teams of four.

Annenberg Media, Insights into Algebra, Teaching for Learning

2009-12-23

108

Generation of a controllable optical cage by focusing a Laguerre-Gaussian correlated Schell-model beam.  

PubMed

We analyze the intensity of a Laguerre-Gaussian correlated Schell-model (LGCSM) beam focused by a thin lens near the focal region, and it is found that a controllable optical cage can be formed through varying the initial spatial coherence width. Furthermore, we carry out experimental measurement of the intensity of a focused LGCSM beam, and we observe that the optical cage is indeed formed in experiment. Our results will be useful for trapping particles or atoms. PMID:24784042

Chen, Yahong; Cai, Yangjian

2014-05-01

109

A line-of-sight performance criterion for controller design of a proposed laboratory model  

NASA Technical Reports Server (NTRS)

A line-of-sight performance criterion is derived for a proposed Controls Structures Interaction model, and its many uses in the control design process for fine pointing control are illustrated. A linearized line-of-sight (LOS) criterion is used for direct controller design and as a performance measure to judge different control methodologies. Numerical simulation results are shown where the three approaches: linear quadratic Gaussian theory, robust eigensystem assignment, and local velocity feedback are used for vibration control. Results indicate that the linear quadratic Gaussian controller, which incorporates a linearized LOS weighting matrix directly, yields good performance without wasting energy to control motions that have no influence on the LOS.

Lim, Kyong B.; Horta, Lucas G.

1990-01-01

110

Comparison of wind turbine LQG controllers using Individual Pitch Control to alleviate fatigue loads  

Microsoft Academic Search

This paper focuses on the design of Linear Quadratic Gaussian (LQG) controllers for variable-speed horizontal axis Wind Turbines (WT). These turbines use blade pitch angle and electromagnetic torque control variables to meet specified objectives for Full Load (FL) zone. The main control objectives are to reduce structural dynamic loads and to regulate the power of the WT. The controllers are

S. Nourdine; H. Camblong; I. Vechiu; G. Tapia

2010-01-01

111

A connection between half-quadratic criteria and EM algorithms  

Microsoft Academic Search

Iteratively Reweighted Least Squares (IRLS) and Residual Steepest descent (RSD) algorithms of robust statistics arise as special cases of half-quadratic schemes . Here, we adopt a statistical framework and we show that both algorithms are instances of the EM algorithm. The augmented dataset respectively involves a scale and a location mixture of Gaussians. The sufficient conditions for the construction cover

Frédéric Champagnat; Jérôme Idier

2004-01-01

112

Acceleration-Augmented LQG Control of an Active Magnetic Bearing  

NASA Technical Reports Server (NTRS)

A linear-quadratic-gaussian (LQG) regulator controller design for an acceleration-augmented active magnetic bearing (AMB) is outlined. Acceleration augmentation is a key feature in providing improved dynamic performance of the controller. The optimal control formulation provides a convenient method of trading-off fast transient response and force attenuation as control objectives.

Feeley, Joseph J.

1993-01-01

113

Acceleration-augmented LQG control of an active magnetic bearing  

NASA Astrophysics Data System (ADS)

A linear-quadratic-gaussian (LQG) regulator controller design for an acceleration-augmented active magnetic bearing (AMB) is outlined. Acceleration augmentation is a key feature in providing improved dynamic performance of the controller. The optimal control formulation provides a convenient method of trading-off fast transient response and force attenuation as control objectives.

Feeley, Joseph J.

114

The Quadratic Assignment Problem  

Microsoft Academic Search

This paper aims at describing the state of the art on quadratic assignment problems (QAPs). It discusses the most important developments in all aspects of the QAP such as linearizations, QAP polyhedra, algorithms to solve the problem to optimality, heuristics, polynomially solvable special cases, and asymptotic behavior. Moreover, it also considers problems related to the QAP, e.g. the biquadratic assignment

Rainer E. Burkard; Eranda Cela; Panos M. Pardalos; Leonidas S. Pitsoulis

1998-01-01

115

A Quadratic Spring Equation  

ERIC Educational Resources Information Center

Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…

Fay, Temple H.

2010-01-01

116

Extension of Karmarkar's algorithm onto convex quadratically constrained quadratic problems  

Microsoft Academic Search

Convex quadratically constrained quadratic problems are considered. It is shown that such problems can be transformed to aconic form. The feasible set of the conic form is the intersection of a direct product of standard quadratic cones intersected with\\u000a a hyperplane (the analogue of a simplex), and a linear subspace. For a problem of such form, the analogue of Karmarkar's

Arkadii Nemirovskii; Katya Scheinberg

1996-01-01

117

A dynamic feedforward neural network based on gaussian particle swarm optimization and its application for predictive control.  

PubMed

A dynamic feedforward neural network (DFNN) is proposed for predictive control, whose adaptive parameters are adjusted by using Gaussian particle swarm optimization (GPSO) in the training process. Adaptive time-delay operators are added in the DFNN to improve its generalization for poorly known nonlinear dynamic systems with long time delays. Furthermore, GPSO adopts a chaotic map with Gaussian function to balance the exploration and exploitation capabilities of particles, which improves the computational efficiency without compromising the performance of the DFNN. The stability of the particle dynamics is analyzed, based on the robust stability theory, without any restrictive assumption. A stability condition for the GPSO+DFNN model is derived, which ensures a satisfactory global search and quick convergence, without the need for gradients. The particle velocity ranges could change adaptively during the optimization process. The results of a comparative study show that the performance of the proposed algorithm can compete with selected algorithms on benchmark problems. Additional simulation results demonstrate the effectiveness and accuracy of the proposed combination algorithm in identifying and controlling nonlinear systems with long time delays. PMID:21803682

Han, Min; Fan, Jianchao; Wang, Jun

2011-09-01

118

Towards fault-tolerant optimal control  

NASA Technical Reports Server (NTRS)

The paper considers the design of fault-tolerant controllers that may endow systems with dynamic reliability. Results for jump linear quadratic Gaussian control problems are extended to include random jump costs, trajectory discontinuities, and a simple case of non-Markovian mode transitions.

Chizeck, H. J.; Willsky, A. S.

1979-01-01

119

Towards fault-tolerant optimal control  

Microsoft Academic Search

Questions regarding the design of fault-tolerant controllers that may endow systems with dynamic reliability are addressed here. Results for jump linear quadratic Gaussian (JLQG) control problems are extended to include random jump costs, trajectory discontinuities, and a simple case of non-Markovian mode transitions.

Howard J. Chizeck; Alan S. Willsky

1978-01-01

120

Approximation in LQG control of a thermoelastic rod  

NASA Technical Reports Server (NTRS)

Control and estimator gains are computed for linear-quadratic-Gaussian (LQG) optimal control of the axial vibrations of a thermoelastic rod. The computations are based on a modal approximation of the partial differential equations representing the rod, and convergence of the approximations to control and estimator gains is the main issue.

Gibson, J. S.; Rosen, I. G.; Tao, G.

1989-01-01

121

Direct adaptive control of wind energy conversion systems using Gaussian networks  

Microsoft Academic Search

Grid connected wind energy conversion systems (WECS) present interesting control demands, due to the intrinsic nonlinear characteristics of windmills and electric generators. In this paper a direct adaptive control strategy for WECS control is proposed. It is based on the combination of two control actions: a radial basis function network-based adaptive controller, which drives the tracking error to zero with

Miguel Angel Mayosky; Gustavo I. E. Cancelo

1999-01-01

122

Design of a candidate flutter suppression control law for DAST ARW-2  

NASA Technical Reports Server (NTRS)

A control law is developed to suppress symmetric flutter for a mathematical model of an aeroelastic research vehicle. An implementable control law is attained by including modified LQC (Linear Quadratic Gaussian) design techniques, controller order reduction, and gain scheduling. An alternate (complementary) design approach is illustrated for one flight condition wherein nongradient-based constrained optimization techniques are applied to maximize controller robustness.

Adams, W. M., Jr.; Tiffany, S. H.

1984-01-01

123

Direct adaptive control of wind energy conversion systems using Gaussian networks.  

PubMed

Grid connected wind energy conversion systems (WECS) present interesting control demands, due to the intrinsic nonlinear characteristics of windmills and electric generators. In this paper a direct adaptive control strategy for WECS control is proposed. It is based on the combination of two control actions: a radial basis zfunction network-based adaptive controller, which drives the tracking error to zero with user specified dynamics, and a supervisory controller, based on crude bounds of the system's nonlinearities. The supervisory controller fires when the finite neural-network approximation properties cannot be guaranteed. The form of the supervisor control and the adaptation law for the neural controller are derived from a Lyapunov analysis of stability. The results are applied to a typical turbine/generator pair, showing the feasibility of the proposed solution. PMID:18252585

Mayosky, M A; Cancelo, I E

1999-01-01

124

Lesson 17: Quadratic Inequalities  

NSDL National Science Digital Library

The lesson begins with using graphs to solve quadratic inequalities. AN equation modeling the height of a rocket is graphed along with a second equation that represents the minimum height at which the rocket can legally and safely be exploded. The intersections of the graphs provide the solution interval. A second method is then presented where the inequality is put into standard form and then solved for its x-intercepts. Interval notation and union of sets is reviewed before a purely algebraic procedure for solving the inequalities is presented. The lesson concludes with an application problem.

2011-01-01

125

Fluctuation estimates for sub-quadratic gradient field actions  

NASA Astrophysics Data System (ADS)

In this article we estimate fluctuations of the scalar field ? for a special class of sub-quadratic actions which grow like |??|2?, 0 < ? < 1. In particular if ? = 1/2 we show that in three dimensions is bounded for ? small. For each edge (jk) we introduce an auxiliary field tjk?R to express the action as a superposition of Gaussian free fields. The effective action which arises from integrating over the Gaussian field is shown to be convex in t. The Brascamp-Lieb inequality is then applied to obtain the desired estimates on a nonuniformly elliptic Green's function.

Brydges, David; Spencer, Thomas

2012-09-01

126

Estimation and Control for Linear Systems with Additive Cauchy Noise.  

National Technical Information Service (NTIS)

A new class of scalar and vector-state estimators and stochastic controllers for linear dynamic systems with additive Cauchy process and measurement noises has been developed. The Kalman filter and the linear- quadratic-Gaussian controller have been the m...

J. L. Speyer

2013-01-01

127

A Gaussian copula approach for the analysis of secondary phenotypes in case-control genetic association studies.  

PubMed

In many case-control genetic association studies, a set of correlated secondary phenotypes that may share common genetic factors with disease status are collected. Examination of these secondary phenotypes can yield valuable insights about the disease etiology and supplement the main studies. However, due to unequal sampling probabilities between cases and controls, standard regression analysis that assesses the effect of SNPs (single nucleotide polymorphisms) on secondary phenotypes using cases only, controls only, or combined samples of cases and controls can yield inflated type I error rates when the test SNP is associated with the disease. To solve this issue, we propose a Gaussian copula-based approach that efficiently models the dependence between disease status and secondary phenotypes. Through simulations, we show that our method yields correct type I error rates for the analysis of secondary phenotypes under a wide range of situations. To illustrate the effectiveness of our method in the analysis of real data, we applied our method to a genome-wide association study on high-density lipoprotein cholesterol (HDL-C), where "cases" are defined as individuals with extremely high HDL-C level and "controls" are defined as those with low HDL-C level. We treated 4 quantitative traits with varying degrees of correlation with HDL-C as secondary phenotypes and tested for association with SNPs in LIPG, a gene that is well known to be associated with HDL-C. We show that when the correlation between the primary and secondary phenotypes is >0.2, the P values from case-control combined unadjusted analysis are much more significant than methods that aim to correct for ascertainment bias. Our results suggest that to avoid false-positive associations, it is important to appropriately model secondary phenotypes in case-control genetic association studies. PMID:21933777

He, Jing; Li, Hongzhe; Edmondson, Andrew C; Rader, Daniel J; Li, Mingyao

2012-07-01

128

Classical adaptive optics: disturbance rejection control  

Microsoft Academic Search

This paper addresses the residual wavefront variance minimization by means of a linear quadratic gaussian control methodology. The proposed approach emphasizes the ability of the adaptive optics loop to reject the atmospheric aberration. We derive a diagonal state space system which clearly separates the dynamics of the plant (deformable mirror & wavefront sensor) from the disturbance dynamics (atmospheric model). This

Jean-Pierre Folcher; Andrea Abelli; André Ferrari; Marcel Carbillet

2010-01-01

129

Design of a candidate flutter suppression control law for DAST ARW-2. [Drones for Aerodynamic and Structural Testing Aeroelastic Research Wing  

NASA Technical Reports Server (NTRS)

A control law is developed to suppress symmetric flutter for a mathematical model of an aeroelastic research vehicle. An implementable control law is attained by including modified LQG (linear quadratic Gaussian) design techniques, controller order reduction, and gain scheduling. An alternate (complementary) design approach is illustrated for one flight condition wherein nongradient-based constrained optimization techniques are applied to maximize controller robustness.

Adams, W. M., Jr.; Tiffany, S. H.

1983-01-01

130

The general quadratic Radon transform  

NASA Astrophysics Data System (ADS)

The general quadratic Radon transform in two dimensions is investigated. Whereas the classical Radon transform of a smooth function represents the integration over all lines, the general quadratic Radon transform integrates over all conic sections. First, the parabolic isofocal Radon transform, i.e. the restriction of the general quadratic Radon transform to all parabolae with focus in the origin, is defined and illustrated. We show its intense relation to the classical Radon transform, deduce a support theorem, formulate an extension of the support theorem and derive an inversion formula. The natural extension to a more general class of isofocal quadratic Radon transforms is outlined. We show how the general quadratic Radon transform can be derived from the integrals over all parabolae by solving the related Cauchy problem. Finally, we introduce an entirely geometrical definition of a generalized Radon transform, the oriented generalized Radon transform.

Denecker, Koen; Van Overloop, Jeroen; Sommen, Frank

1998-06-01

131

Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, H? control theory, and linear matrix inequalities  

Microsoft Academic Search

This paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems, First, a stability condition for Takagi and Sugeno's fuzzy model is given in terms of Lyapunov stability theory. Next, new stability conditions for a generalized class of uncertain systems are derived from robust control

Kazuo Tanaka; T. Ikeda; H. O. Wang

1996-01-01

132

Optimal Estimation and Attitude Control of a Solar Electric Propulsion Spacecraft  

Microsoft Academic Search

Established procedures of linear, quadratic, Gaussian optimal estimation and control are developed and interpreted for their application ion to the problem of attitude control of spacecraft with dycallyamially significant elastic appendages. Results are presented both in general terms and for specific application to a solar electric spacecraft. aft. Comparisons are made between alternative coordinattems, systems, and a realistic range of

Victor Larson; Peter Likins; Elbert Marsh

1977-01-01

133

Shape Control of Plates with Piezo Actuators and Collocated Position/Rate Sensors  

NASA Technical Reports Server (NTRS)

This paper treats the control problem of shaping the surface deformation of a circular plate using embedded piezo-electric actuator and collocated rate sensors. An explicit Linear Quadratic Gaussian (LQG) optimizer stability augmentation compensator is derived as well as the optimal feed-forward control. Corresponding performance evaluation formulas are also derived.

Balakrishnan, A. V.

1994-01-01

134

Control Systems Design for Large Flexible Space Structures.  

National Technical Information Service (NTIS)

Several approaches for the design of reduced-order linear-quadratic-Gaussian type controllers for large space structures were proposed and evaluated using a continuous model of a long free-free beam. Sufficient conditions were derived for the asymptotic s...

S. M. Joshi A. S. Roberts

1980-01-01

135

Homotopy Algorithm for Digital Optimal Projection Control Gasd-Hadoc.  

National Technical Information Service (NTIS)

The linear-quadratic-gaussian (LQG) compensator was developed to facilitate the design of control laws for multi-input, multi-output (MIMO) systems. The compensator is computed by solving two algebraic equations for which standard closed-loop solutions ex...

E. G. Collins S. Richter L. D. Davis

1993-01-01

136

Issues in modeling and controlling the SCOLE configuration  

NASA Technical Reports Server (NTRS)

The parametric study of the in-plane Spacecraft Control Laboratory Experiment (SCOLE) system, the Floquet Stability Analysis, and three dimensional formulations of the SCOLE system dynamics are examined. Control issues are discussed, such as: control of large structures with delayed input in continuous time; control with delayed input in discrete time; control law design for SCOLE using Linear Quadratic Gaussian (LQC)/TRR technique; and optimal torque control for SCOLE slewing maneuvers.

Bainum, Peter M.; Reddy, A. S. S. R.; Diarra, Cheick Modibo; Li, Feiyue

1987-01-01

137

Strong self-focusing of laser beam in a medium with quadratic nonlinear response  

NASA Astrophysics Data System (ADS)

We compare self-focusing of laser beam with Gaussian, super-Gaussian and ring profile in a medium with quadratic nonlinear response due to cascading SHG. The duration of the light pulse under consideration is about microsecond. Nevertheless, the dispersion of group velocity is also taken into account. We demonstrate a possibility of strong growth for intensity of the laser radiation without changing the pulse shape and Gaussian profile of the beam. For initial super- Gaussian and ring profile the Gaussian profile appears due to the diffraction of laser beam at certain section of nonlinear medium. Then, the optical radiation undergoes self-focusing without changing the Gaussian intensity distribution till appearance of the first nonlinear focus. This phenomenon has various practical applications. For example, it can be used for developing the laser system in microsecond range of pulse duration which operates in the regime similar to KLM regime for femtosecond laser system.

Trofimov, Vyacheslav A.; Lysak, Tatiana M.

2012-10-01

138

Quadratic as Parametric Linear Programming.  

National Technical Information Service (NTIS)

The paper describes an approximate solution procedure for quadratic programming problems using parametric linear programming. Limited computational experience suggests that the approximation can be expected to be good. (Author)

R. J. Townsley W. Candler

1972-01-01

139

Vibration analysis and optimal control of rotating pre-twisted thin-walled beams using MFC actuators and sensors  

Microsoft Academic Search

Structural modeling of rotating pre-twisted thin-walled composite beams with embedded macro fiber composite (MFC) actuators and sensors using higher shear deformation theory (HSDT) is presented in the present work. The governing system of equations is derived from Hamilton's principle and solution is obtained by extended Galerkin's method. Optimal control problem is solved using linear quadratic Gaussian (LQG) control algorithm. Vibration

D. N. Vadiraja; A. D. Sahasrabudhe

2009-01-01

140

Linear quadratic stationkeeping on travelling ellipses  

NASA Technical Reports Server (NTRS)

An automatic controller for Space Shuttle stationkeeping or formationkeeping is presented. The controller, which is a candidate for future on-orbit autopilot enhancement, uses a fuel 'optimized' limit cycle trajectory in a feedforward loop for precise control at nonequilibrium set points. Disturbance rejection is accomplished by a discrete time, linear quadratic regulator, which is employed for tracking of the feedforward model. Feedback gain selection is done to provide good limit cycling performance and low fuel consumption. Velocity correlations are carried out by use of a pseudo 6 degree-of-freedom jet selection scheme. Results indicate that 20 ft precision can be achieved using current sensors.

Adams, Neil J.; Redding, David C.; Cox, Kenneth J.

1987-01-01

141

Active flutter control for flexible vehicles, volume 1  

NASA Technical Reports Server (NTRS)

An active flutter control methodology based on linear quadratic gaussian theory and its application to the control of a super critical wing is presented. Results of control surface and sensor position optimization are discussed. Both frequency response matching and residualization used to obtain practical flutter controllers are examined. The development of algorithms and computer programs for flutter modeling and active control design procedures is reported.

Mahesh, J. K.; Garrard, W. L.; Stones, C. R.; Hausman, P. D.

1979-01-01

142

Semi-Huber Quadratic Function and Comparative Study of Some MRFs for Bayesian Image Restoration  

NASA Astrophysics Data System (ADS)

The present work introduces an alternative method to deal with digital image restoration into a Bayesian framework, particularly, the use of a new half-quadratic function is proposed which performance is satisfactory compared with respect to some other functions in existing literature. The bayesian methodology is based on the prior knowledge of some information that allows an efficient modelling of the image acquisition process. The edge preservation of objects into the image while smoothing noise is necessary in an adequate model. Thus, we use a convexity criteria given by a semi-Huber function to obtain adequate weighting of the cost functions (half-quadratic) to be minimized. The principal objective when using Bayesian methods based on the Markov Random Fields (MRF) in the context of image processing is to eliminate those effects caused by the excessive smoothness on the reconstruction process of image which are rich in contours or edges. A comparison between the new introduced scheme and other three existing schemes, for the cases of noise filtering and image deblurring, is presented. This collection of implemented methods is inspired of course on the use of MRFs such as the semi-Huber, the generalized Gaussian, the Welch, and Tukey potential functions with granularity control. The obtained results showed a satisfactory performance and the effectiveness of the proposed estimator with respect to other three estimators.

De la Rosa, J. I.; Villa-Hernández, J.; González-Ramírez, E.; De la Rosa, M. E.; Gutiérrez, O.; Olvera-Olvera, C.; Castañeda-Miranda, R.; Fleury, G.

2013-10-01

143

Ab initio quadratic configuration interaction calculations of isotropic hyperfine coupling constants  

Microsoft Academic Search

Results are presented from quadratic configuration interaction (QCISD) calculations of the isotropic component of the magnetic hyperfine coupling in the electronic ground states of the atoms B-F and of some radicals and radical cations derived from associated diatomic hydrides. Moderately large basis sets of contracted Gaussian functions are employed. Starting from unrestricted Hartree-Fock (UHF) reference spaces the unpaired spin density

Ian Carmichael

1991-01-01

144

Tiltrotor Control Law Design for Rotor Loads Alleviation Using Modern Control Techniques  

Microsoft Academic Search

A weighted least-squares eigenstructure assignment technique and a balanced singular value Linear Quadratic Gaussian with Loop Transfer Recovery (LQG\\/LTR) technique are used to develop rotor loads alleviation control laws for the V-22 Osprey aircraft. These techniques were applied to alleviate rotor yoke chord loads as part of a comprehensive Bell-Boeing structural loads limiting control law design effort. The control laws

David G. Miller; Terry M. Black; Mukund Joglekar

1991-01-01

145

Solving Quadratic Equations by Factoring  

NSDL National Science Digital Library

This video explains how to solve quadratic equations with the factoring method. In 4 minutes 23 seconds, the two narrators explain in detail the steps required. Additionally, how these equations relate to objects and events in the real world such as roller coasters is covered.

2012-08-06

146

Gaussian quadrature for sums  

NASA Astrophysics Data System (ADS)

Gaussian quadrature is a well-known technique for numerical integration. Recently Gaussian quadrature with respect to discrete measures corresponding to finite sums has found some new interest. In this paper we apply these ideas to infinite sums in general and give an explicit construction for the weights and abscissae of Gaussian formulas. The abscissae of the Gaussian summation have a very interesting asymptotic distribution function with a kink singularity. We apply the Gaussian summation technique to two problems which have been discussed in the literature. We find that the Gaussian summation has a very rapid convergence rate for the Hardy-Littlewood sum for a large range of parameters.

Monien, H.

2010-04-01

147

A Method for Determining the Nominal Occular Hazard Zone for Gaussian Beam Laser Rangers with a Firmware Controlled Variable Focal Length  

NASA Technical Reports Server (NTRS)

LIDAR systems that maintain a constant beam spot size on a retroreflector in order to increase the accuracy of bearing and ranging data must use a software controlled variable position lens. These systems periodically update the estimated range and set the position of the focusing lens accordingly. In order to precisely calculate the r NOHD for such a system, the software method for setting the variable position lens and gaussian laser propagation can be used to calculate the irradiance at any point given the range estimation. NASA s Space Shuttle LIDAR, called the Trajectory Control Sensor (TCS), uses this configuration. Analytical tools were developed using Excel and VBA to determine the radiant energy to the International Space Station (ISS) crewmembers eyes while viewing the shuttle on approach and departure. Various viewing scenarios are considered including the use of through-the-lens imaging optics and the window transmissivity at the TCS wavelength. The methodology incorporates the TCS system control logic, gaussian laser propagation, potential failure mode end states, and guidance from American National Standard for the Safe Use of Lasers (ANSI Z136.1-2007). This approach can be adapted for laser safety analyses of similar LIDAR systems.

Picco, C. E.; Shavers, M. R.; Victor, J. M.; Duron, J. L.; Bowers, W. h.; Gillis, D. B.; VanBaalen, M.

2009-01-01

148

Quadratic Forms and Manifold Normal Distributions.  

National Technical Information Service (NTIS)

The distribution of quadratic forms in matrix normal variables is considered. An application of the distribution of quadratic forms is given by deriving distributions on manifolds of multivariate normal distributions. Special cases are, for instance, the ...

D. J. Dewaal

1982-01-01

149

Robust controller synthesis for large flexible space structures  

NASA Technical Reports Server (NTRS)

The application of a multivariable frequency domain method for the attitude control and vibration suppression of large flexible space structures is discussed. Results of application of the linear-quadratic-Gaussian/loop transfer recovery method to the cases of a hop/column antenna, a wrap-rib antenna, and the Spacecraft Control Laboratory Experiment are presented. Controller order reduction is implemented using the balanced realization method, a Hankel-norm-based method, and a method based on stable factorization.

Joshi, S. M.; Rowell, L. F.; Armstrong, E. S.

1988-01-01

150

Gaussian Quantum Discord  

Microsoft Academic Search

We extend the quantum discord to continuous variable systems and evaluate Gaussian quantum discord C(varrho) for bipartite Gaussian states. In particular, for squeezed-thermal states, we explicitly maximize the extractable information over Gaussian measurements: C(varrho) is minimized by a generalized measurement rather than a projective one. Almost all squeezed-thermal states have nonzero Gaussian discord: They may be either separable or entangled

Paolo Giorda; Matteo G. A. Paris

2010-01-01

151

Natural Exponential Families with Quadratic Variance Functions  

Microsoft Academic Search

The normal, Poisson, gamma, binomial, and negative binomial distributions are univariate natural exponential families with quadratic variance functions (the variance is at most a quadratic function of the mean). Only one other such family exists. Much theory is unified for these six natural exponential families by appeal to their quadratic variance property, including infinite divisibility, cumulants, orthogonal polynomials, large deviations,

Carl N. Morris

1982-01-01

152

Bayesian Quadratic Network Game Filters  

NASA Astrophysics Data System (ADS)

A repeated network game where agents have quadratic utilities that depend on information externalities -- an unknown underlying state -- as well as payoff externalities -- the actions of all other agents in the network -- is considered. Agents play Bayesian Nash Equilibrium strategies with respect to their beliefs on the state of the world and the actions of all other nodes in the network. These beliefs are refined over subsequent stages based on the observed actions of neighboring peers. This paper introduces the Quadratic Network Game (QNG) filter that agents can run locally to update their beliefs, select corresponding optimal actions, and eventually learn a sufficient statistic of the network's state. The QNG filter is demonstrated on a Cournot market competition game and a coordination game to implement navigation of an autonomous team.

Eksin, Ceyhun; Molavi, Pooya; Ribeiro, Alejandro; Jadbabaie, Ali

2014-05-01

153

Deblurring Gaussian Blur.  

National Technical Information Service (NTIS)

Gaussian blur, or convolution against a Gaussian kernel, is a common model for image and signal degradation. In general, the process of reversing Gaussian blur is unstable, and cannot be represented as a convolution filter in the spatial domain. If we res...

R. Hummel B. Kimia S. W. Zucker

1986-01-01

154

Geometrical Solutions of Quadratic Equations.  

ERIC Educational Resources Information Center

Demonstrates that the equation of a circle (x-h)2 + (y-k)2 = r2 with center (h; k) and radius r reduces to a quadratic equation x2-2xh + (h2 + k2 -r2) = O at the intersection with the x-axis. Illustrates how to determine the center of a circle as well as a point on a circle. (Author/ASK)

Grewal, A. S.; Godloza, L.

1999-01-01

155

Signatures of non-Gaussianity in the curvaton model  

SciTech Connect

We discuss the signatures of non-Gaussianity in the curvaton model where the potential includes also a non-quadratic term. In such a case the non-linearity parameter f{sub NL} can become very small, and we show that non-Gaussianity is then encoded in the non-reducible non-linearity parameter g{sub NL} of the trispectrum, which can be very large. Thus the place to look for the non-Gaussianity in the curvaton model may be the trispectrum rather than the bispectrum. We also show that g{sub NL} measures directly the deviation of the curvaton potential from the purely quadratic form. While g{sub NL} depends on the strength of the non-quadratic terms relative to the quadratic one, we find that for reasonable cases roughly g{sub NL}{approx}O(-10{sup 4})-O(-10{sup 5}), which are values that may well be accessible by future observations.

Enqvist, Kari [Helsinki Institute of Physics, University of Helsinki, PO Box 64, FIN-00014 (Finland)] [Helsinki Institute of Physics, University of Helsinki, PO Box 64, FIN-00014 (Finland); Takahashi, Tomo, E-mail: kari.enqvist@helsinki.fi, E-mail: tomot@cc.saga-u.ac.jp [Department of Physics, Saga University, Saga 840-8502 (Japan)] [Department of Physics, Saga University, Saga 840-8502 (Japan)

2008-09-15

156

Smart base-isolated benchmark building Part III: a sample controller for bilinear isolation  

Microsoft Academic Search

This paper presents a sample control design for the base isolated benchmark building with bilinear hys- teretic bearings ( e.g. , lead-rubber bearings). Since there is no well-defined control strategy for nonlinear structures, and available linear strategies are well-known among the civil engineering community, a linear quadratic Gaussian (LQG) controller is selected for this purpose. To utilize an LQG controller,

Baris Erkus; Erik A. Johnson

2006-01-01

157

Linear state feedback, quadratic weights, and closed loop eigenstructures. M.S. Thesis  

NASA Technical Reports Server (NTRS)

Results are given on the relationships between closed loop eigenstructures, state feedback gain matrices of the linear state feedback problem, and quadratic weights of the linear quadratic regulator. Equations are derived for the angles of general multivariable root loci and linear quadratic optimal root loci, including angles of departure and approach. The generalized eigenvalue problem is used for the first time to compute angles of approach. Equations are also derived to find the sensitivity of closed loop eigenvalues and the directional derivatives of closed loop eigenvectors (with respect to a scalar multiplying the feedback gain matrix or the quadratic control weight). An equivalence class of quadratic weights that produce the same asymptotic eigenstructure is defined, sufficient conditions to be in it are given, a canonical element is defined, and an algorithm to find it is given. The behavior of the optimal root locus in the nonasymptotic region is shown to be different for quadratic weights with the same asymptotic properties.

Thompson, P. M.

1979-01-01

158

Tethered systems control  

NASA Technical Reports Server (NTRS)

Viewgraphs on tethered systems control are presented. Topics covered include: rigid body simplifications; feedback control; quadratic optimal nonlinear control; quadratic optimal nonlinear controllers; Lyapunov-based nonlinear controllers; sensor/actuator options; tether control; and fuzzy logic control.

Nowlan, Dan

1990-01-01

159

Clustered Self Organising Migrating Algorithm for the Quadratic Assignment Problem  

NASA Astrophysics Data System (ADS)

An approach of population dynamics and clustering for permutative problems is presented in this paper. Diversity indicators are created from solution ordering and its mapping is shown as an advantage for population control in metaheuristics. Self Organising Migrating Algorithm (SOMA) is modified using this approach and vetted with the Quadratic Assignment Problem (QAP). Extensive experimentation is conducted on benchmark problems in this area.

Davendra, Donald; Zelinka, Ivan; Senkerik, Roman

2009-08-01

160

Linear-Quadratic Problems and the Riccati Equation.  

National Technical Information Service (NTIS)

An overview of the results relating the Riccati equation with the Linear Quadratic (LQ) control problem is given. It is demonstrated that the LQ problem can be solved by using the Riccati equation or its generalization, the dissipation inequality. The sin...

A. H. W. Geerts M. L. J. Hautus

1989-01-01

161

Gaussian quantum discord.  

PubMed

We extend the quantum discord to continuous variable systems and evaluate Gaussian quantum discord C(?) for bipartite Gaussian states. In particular, for squeezed-thermal states, we explicitly maximize the extractable information over Gaussian measurements: C(?) is minimized by a generalized measurement rather than a projective one. Almost all squeezed-thermal states have nonzero Gaussian discord: They may be either separable or entangled if the discord is below the threshold C(?) = 1, whereas they are all entangled above the threshold. We elucidate the general role of state parameters in determining the discord and discuss its evolution in noisy channels. PMID:20867693

Giorda, Paolo; Paris, Matteo G A

2010-07-01

162

Skin-friction Drag Reduction Via Robust Reduced-order Linear Feedback Control  

Microsoft Academic Search

A successful application of a linear controller to a two-dimensional channel flow is presented. An optimal and robust reduced-order linear feedback controller is derived by using multi-variable linear-quadratic-Gaussian synthesis, or, in modern term, H2 synthesis, combined with model reduction techniques. This controller based on a reduced-model of the linearized Navier-Stokes equations is applied to suppress finite-amplitude near-wall disturbances in a

L. CORTELEZZI; K. H. LEE; J. KIM; J. L. SPEYER

1998-01-01

163

Suppressed non-Gaussianity in the curvaton model  

NASA Astrophysics Data System (ADS)

We show that the local type non-Gaussianity in a class of curvaton models is suppressed, i.e., the nonlinearity parameters fNL and those related with higher order statistics can be at most O(1), even if the curvaton energy density is subdominant at the decay. This situation is naturally realized in a very simple curvaton potential with quadratic term plus quartic term.

Mukaida, Kyohei; Nakayama, Kazunori; Takimoto, Masahiro

2014-06-01

164

Generalized Gaussian process models  

Microsoft Academic Search

We propose a generalized Gaussian process model (GGPM), which is a unifying framework that encompasses many existing Gaussian process (GP) models, such as GP regression, classification, and counting. In the GGPM framework, the observation likelihood of the GP model is itself parameterized using the exponential family distribution. By deriving approximate inference algorithms for the generalized GP model, we are able

Antoni B. Chan; Daxiang Dong

2011-01-01

165

Decentered elliptical Gaussian beam  

NASA Astrophysics Data System (ADS)

A new kind of laser beam, called a decentered elliptical Gaussian beam (DEGB), is defined by a tensor method. The propagation formula for a DEGB passing through an axially nonsymmetrical paraxial optical system is derived through vector integration. The derived formula can be reduced to the formula for a fundamental elliptical Gaussian beam and a decentered Gaussian beam under certain conditions. As an example application of the derived formula, the propagation characteristics of a DEGB in free space are calculated and discussed. As another example we study the properties of a generalized laser beam array constructed by use of a DEGB as the fundamental mode.

Cai, Yangjian; Lin, Qiang

2002-07-01

166

A quadratically convergent VBSCF method  

NASA Astrophysics Data System (ADS)

A quadratically convergent valence bond self-consistent field method is described where the simultaneous optimisation of orbitals and the coefficients of the configurations (VB structures) is based on a Newton-Raphson scheme. The applicability of the method is demonstrated in actual calculations. The convergence and efficiency are compared with the Super-CI method. A necessary condition to achieve convergence in the Newton-Raphson method is that the Hessian is positive definite. When this is not the case, a combination of the Super-CI and Newton-Raphson methods is shown to be an optimal choice instead of shifting the eigenvalues of the Hessian to make it positive definite. In the combined method, the first few iterations are performed with the Super-CI method and then the Newton-Raphson scheme is switched on based on an internal indicator. This approach is found computationally a more economical choice than using either the Newton-Raphson or Super-CI method alone to perform a full optimisation of the nonorthogonal orbitals.

Rashid, Zahid; van Lenthe, Joop H.

2013-02-01

167

A comparison of controller designs for an experimental flexible structure  

NASA Technical Reports Server (NTRS)

Control systems design and hardware testing are addressed for an experimental structure that displays the characteristics of a typical flexible spacecraft. The results of designing and implementing various control design methodologies are described. The design methodologies under investigation include linear quadratic Gaussian control, static and dynamic dissipative controls, and H-infinity optimal control. Among the three controllers considered, it is shown, through computer simulation and laboratory experiments on the evolutionary structure, that the dynamic dissipative controller gave the best results in terms of vibration suppression and robustness with respect to modeling errors.

Lim, K. B.; Maghami, P. G.; Joshi, S. M.

1991-01-01

168

Some Like It Gaussian  

Microsoft Academic Search

In Hidden Markov models, speech features are modeled by Gaussian distributions. In this paper, we propose to gaussianize the\\u000a features to better fit to this modeling. A distribution of the data is estimated and a transform function is derived. We have\\u000a tested two methods of the transform estimation (global and speaker based). The results are reported on recognition of isolated

Pavel Matejka; Petr Schwarz; Martin Karafiát; Jan Cernocký

2002-01-01

169

Hollow vortex Gaussian beams  

NASA Astrophysics Data System (ADS)

A kind of hollow vortex Gaussian beam is introduced. Based on the Collins integral, an analytical propagation formula of a hollow vortex Gaussian beam through a paraxial ABCD optical system is derived. Due to the special distribution of the optical field, which is caused by the initial vortex phase, the dark region of a hollow vortex Gaussian beam will not disappear upon propagation. The analytical expressions for the beam propagation factor, the kurtosis parameter, and the orbital angular momentum density of a hollow vortex Gaussian beam passing through a paraxial ABCD optical system are also derived, respectively. The beam propagation factor is determined by the beam order and the topological charge. The kurtosis parameter and the orbital angular momentum density depend on beam order n, topological charge m, parameter ?, and transfer matrix elements A and D. As a numerical example, the propagation properties of a hollow vortex Gaussian beam in free space are demonstrated. The hollow vortex Gaussian beam has eminent propagation stability and has crucial application prospects in optical micromanipulation.

Zhou, GuoQuan; Cai, YangJian; Dai, ChaoQing

2013-05-01

170

Schur Stability Regions for Complex Quadratic Polynomials  

ERIC Educational Resources Information Center

Given a quadratic polynomial with complex coefficients, necessary and sufficient conditions are found in terms of the coefficients such that all its roots have absolute values less than 1. (Contains 3 figures.)

Cheng, Sui Sun; Huang, Shao Yuan

2010-01-01

171

Quadratic Functionals with General Boundary Conditions  

SciTech Connect

The purpose of this paper is to give the Reid 'Roundabout Theorem' for quadratic functionals with general boundary conditions. In particular, we describe the so-called coupled point and regularity condition introduced in terms of Riccati equation solutions.

Dosla, Z.; Dosly, O. [Department of Mathematics, Masaryk University, Janackovo nam. 2a, 66295 Brno (Czech Republic)

1997-11-15

172

Quadratic trianqular element for diffuse optical tomography  

NASA Astrophysics Data System (ADS)

Finite element method is a general approach for diffuse optical tomography, and the accuracy of which is closely related to the type of elements used. In this paper, we investigate the differences between linear element and quadratic triangular element in the forward problem of diffuse optical tomography. The results show that quadratic element is a better compromise between high accuracy and low time consumption compared to the linear element. This means high order element is a better choice for the diffuse optical tomography.

Zhang, Xuanxuan; Deng, Yong; Xu, Jun; Luo, Zhaoyang; Gong, Hui; Luo, Qingming

2012-12-01

173

Optimal power flow using sequential quadratic programming  

NASA Astrophysics Data System (ADS)

Optimal power flow (OPF) is an operational as well as a planning tool used by electric utilities to help them operate their network in the most economic and secure mode of operation. Various algorithms to solve the OPF problem evolved over the past three decades; linear programming (LP) techniques were among the major mathematical programming methods utilized. The linear models of the objective function and the linearization of the constraints are the main features of these techniques. The main advantages of the LP approach are simplicity and speed. Nonlinear programming techniques have been applied to OPF solution. The major drawback is the expensive solution of large sparse systems of equations. This research is concerned with the development of a new OPF solution algorithm using sequential quadratic programming (SQP). In this formulation, a small dense system the size of which is equal to the number of control variables is solved in an inner loop. The Jacobian and Hessian terms are calculated in an outer loop. The total number of outer loop iterations is comparable to those in an ordinary load flow in contrast to 20--30 iterations in other nonlinear methods. In addition, the total number of floating point operations is less than that encountered in direct methods by two orders of magnitude. We also model dispatch over a twenty four-hour time horizon in a transmission constrained power network that includes price-responsive loads where large energy customers can operate their loads in time intervals with lowest spot prices.

Nejdawi, Imad M.

1999-11-01

174

Bound entangled Gaussian states.  

PubMed

We discuss the entanglement properties of bipartite states with Gaussian Wigner functions. For the separability, and the positivity of the partial transpose, we establish explicit necessary and sufficient criteria in terms of the covariance matrix of the state. It is shown that, for systems composed of a single oscillator for Alice and an arbitrary number for Bob, positivity of the partial transpose implies separability. However, this implication fails with two oscillators on each side, as we show by constructing a five parameter family of bound entangled Gaussian states. PMID:11328047

Werner, R F; Wolf, M M

2001-04-16

175

Bioluminescence tomography with Gaussian prior  

PubMed Central

Parameterizing the bioluminescent source globally in Gaussians provides several advantages over voxel representation in bioluminescence tomography. It is mathematically unique to recover Gaussians [Med. Phys. 31(8), 2289 (2004)] and practically sufficient to approximate various shapes by Gaussians in diffusive medium. The computational burden is significantly reduced since much fewer unknowns are required. Besides, there are physiological evidences that the source can be modeled by Gaussians. The simulations show that the proposed model and algorithm significantly improves accuracy and stability in the presence of Gaussian or non- Gaussian sources, noisy data or the optical background mismatch. It is also validated through in vivo experimental data.

Gao, Hao; Zhao, Hongkai; Cong, Wenxiang; Wang, Ge

2010-01-01

176

Sequential design of discrete linear quadratic regulators via optimal root-locus techniques  

NASA Technical Reports Server (NTRS)

A sequential method employing classical root-locus techniques has been developed in order to determine the quadratic weighting matrices and discrete linear quadratic regulators of multivariable control systems. At each recursive step, an intermediate unity rank state-weighting matrix that contains some invariant eigenvectors of that open-loop matrix is assigned, and an intermediate characteristic equation of the closed-loop system containing the invariant eigenvalues is created.

Shieh, Leang S.; Yates, Robert E.; Ganesan, Sekar

1989-01-01

177

Optical Gaussian Convolvers.  

National Technical Information Service (NTIS)

The variable Gaussian convolution of an optical image is performed using a transparency, a focusing lens, a TV camera and a mechanism which moves the camera. The transparency has pattern inscribed on it which diffracts the light of the image with a Gaussi...

J. P. Sage

1986-01-01

178

Gaussian Processes for Regression  

Microsoft Academic Search

The Bayesian analysis of neural networks is difficult because a simpleprior over weights implies a complex prior distribution overfunctions. In this paper we investigate the use of Gaussian processpriors over functions, which permit the predictive Bayesian analysisfor fixed values of hyperparameters to be carried out exactlyusing matrix operations. Two methods, using optimization and averaging(via Hybrid Monte Carlo) over hyperparameters have

Carl Edward Rasmussen; Christopher K. I. Williams

1996-01-01

179

Optimal Gaussian entanglement swapping  

SciTech Connect

We consider entanglement swapping with general mixed two-mode Gaussian states and calculate the optimal gains for a broad class of such states including those states most relevant in communication scenarios. We show that, for this class of states, entanglement swapping adds no additional mixedness; that is, the ensemble-average output state has the same purity as the input states. This implies that, by using intermediate entanglement swapping steps, it is, in principle, possible to distribute entangled two-mode Gaussian states of higher purity as compared to direct transmission. We then apply the general results on optimal Gaussian swapping to the problem of quantum communication over a lossy fiber and demonstrate that, in contrast to the negative conclusions in the literature, swapping-based schemes in fact often perform better than direct transmission for high input squeezing. However, an effective transmission analysis reveals that the hope for improved performance based on optimal Gaussian entanglement swapping is spurious since the swapping does not lead to an enhancement of the effective transmission. This implies that the same or better results can always be obtained using direct transmission in combination with, in general, less squeezing.

Hoelscher-Obermaier, Jason; Loock, Peter van [Optical Quantum Information Theory Group, Max Planck Institute for the Science of Light, Guenther-Scharowsky-Str. 1/Bau 26, D-91058 Erlangen (Germany) and Institute of Theoretical Physics I, Universitaet Erlangen-Nuernberg, Staudtstr. 7/B2, D-91058 Erlangen (Germany)

2011-01-15

180

Truncated Gaussians as Tolerance Sets.  

National Technical Information Service (NTIS)

This work focuses on the use of truncated Gaussian distributions as models for bounded data - measurements that are constrained to appear between fixed limits. We prove that the truncated Gaussian can be viewed as a maximum entropy distribution for trunca...

F. Cozman E. Krotkov

1994-01-01

181

Binning in Gaussian Kernel Regularization.  

National Technical Information Service (NTIS)

Gaussian kernel regularization is widely used in the machine learning literature and proven successful in many empirical experiments. The periodic version of the Gaussian kernel regularization has been shown to be minimax rate optimal in estimating functi...

B. Yu T. Shi

2005-01-01

182

Nonlinear dynamics of quadratically cubic systems  

NASA Astrophysics Data System (ADS)

We propose a modified form of the well-known nonlinear dynamic equations with quadratic relations used to model a cubic nonlinearity. We show that such quadratically cubic equations sometimes allow exact solutions and sometimes make the original problem easier to analyze qualitatively. Occasionally, exact solutions provide a useful tool for studying new phenomena. Examples considered include nonlinear ordinary differential equations and Hopf, Burgers, Korteweg-de Vries, and nonlinear Schrödinger partial differential equations. Some problems are solved exactly in the space-time and spectral representations. Unsolved problems potentially solvable by the proposed approach are listed.

Rudenko, O. V.

2013-07-01

183

Indirect quantum tomography of quadratic Hamiltonians  

NASA Astrophysics Data System (ADS)

A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.

Burgarth, Daniel; Maruyama, Koji; Nori, Franco

2011-01-01

184

Gaussian Processes For Machine Learning  

Microsoft Academic Search

Gaussian processes (GPs) are natural generalisations of multivariate Gaussian ran- dom variables to innite (countably or continuous) index sets. GPs have been applied in a large number of elds to a diverse range of ends, and very many deep theoretical anal- yses of various properties are available. This paper gives an introduction to Gaussian processes on a fairly elementary level

Matthias Seeger

2004-01-01

185

Robust power system controller design based on measured models  

SciTech Connect

This paper presents combined system identification and controller design methods to dampen low-frequency oscillations in multimachine power systems. An iterative closed-loop identification method is used to find a linear model for the power system. Linear quadratic Gaussian controller design with loop transfer recovery (LQG/LTR), based on a generalized technique for the nonminimum phase (NMP) power system model, is used to design controllers. Simulation results are presented to demonstrate the robustness of controllers based on closed-loop identified plant models and the amount of loop transfer recovery that is possible for NMP plant models.

Fatehi, F.; Smith, J.R.; Pierre, D.A. [Montana State Univ., Bozeman, MT (United States). Electrical Engineering Dept.] [Montana State Univ., Bozeman, MT (United States). Electrical Engineering Dept.

1996-05-01

186

Identification of second-order Volterra filters driven by non-Gaussian stationary processes  

NASA Astrophysics Data System (ADS)

Some recent results relating to system identification are described and illustrated in this contribution. The system considered is nonlinear and time-invariant, being represented by a Volterra series up to second order. Closed-form expressions for the transfer functions of first and second order are derived for a class of non-Gaussian stationary input processes. It is shown that the obtained parameters are optimum in the mean square sense. Once the system is identified, we derive a closed-form expression for the quadratic coherence that is a measure of the goodness of fit of the quadratic model. It is shown that this expression simplifies to well known results when the system is linear or its input is Gaussian. Furthermore, we develop estimates for the transfer functions and the quadratic coherence from spectral and bispectral estimates, based on averaged periodograms and biperiodograms of data stretches of the observed input and output of the system. This method is tested and validated by using simulated input-output data of a known quadratically nonlinear system, with known input signal statistic, Finally, we discuss the problem of testing a specified value of the quadratic coherence.

Zoubir, Abdelhak M.

1992-11-01

187

Quantum entanglement beyond Gaussian criteria.  

PubMed

Most of the attention given to continuous variable systems for quantum information processing has traditionally been focused on Gaussian states. However, non-Gaussianity is an essential requirement for universal quantum computation and entanglement distillation, and can improve the efficiency of other quantum information tasks. Here we report the experimental observation of genuine non-Gaussian entanglement using spatially entangled photon pairs. The quantum correlations are invisible to all second-order tests, which identify only Gaussian entanglement, and are revealed only under application of a higher-order entanglement criterion. Thus, the photons exhibit a variety of entanglement that cannot be reproduced by Gaussian states. PMID:19995963

Gomes, R M; Salles, A; Toscano, F; Souto Ribeiro, P H; Walborn, S P

2009-12-22

188

Quantum entanglement beyond Gaussian criteria  

PubMed Central

Most of the attention given to continuous variable systems for quantum information processing has traditionally been focused on Gaussian states. However, non-Gaussianity is an essential requirement for universal quantum computation and entanglement distillation, and can improve the efficiency of other quantum information tasks. Here we report the experimental observation of genuine non-Gaussian entanglement using spatially entangled photon pairs. The quantum correlations are invisible to all second-order tests, which identify only Gaussian entanglement, and are revealed only under application of a higher-order entanglement criterion. Thus, the photons exhibit a variety of entanglement that cannot be reproduced by Gaussian states.

Gomes, R. M.; Salles, A.; Toscano, F.; Souto Ribeiro, P. H.; Walborn, S. P.

2009-01-01

189

Aeroelastic control of oblique-wing aircraft  

NASA Technical Reports Server (NTRS)

The U.S. Navy and NASA are currently involved in the design and development of an unsymmetric-skew-wing aircraft capable of 65 deg wing sweep and flight at Mach 1.6. A generic skew-wing aircraft model was developed for 45 deg wing skew at a flight condition of Mach 0.70 and 3048 m altitude. At this flight condition the aircraft has a wing flutter mode. An active implementable control law was developed using the linear quadratic Gaussian design technique. A method of modal residualization was used to reduce the order of the controller used for flutter suppression.

Burken, J. J.; Alag, G. S.; Gilyard, G. B.

1986-01-01

190

Multiplicative Updates for Nonnegative Quadratic Programming  

Microsoft Academic Search

Many problems in neural computation and statistical learning involve optimizations with nonnegativity constraints. In this paper, we study convex problems in quadratic program- ming where the optimization is confined to an axis-aligned region in the nonnegative orthant. For these problems, we derive multiplicative updates that improve the value of the objective function at each iteration and converge monotonically to the

Fei Sha; Yuanqing Lin; Lawrence K. Saul; Daniel D. Lee

2007-01-01

191

Transfer function with quadratic detection - Coherent illumination  

NASA Astrophysics Data System (ADS)

The visibility of the interference terms over the image irradiance of a complex amplitude object immersed in a uniform background is described by an interference transfer function (ITF). It is shown that the ITF is the linear transfer function for coherent optical systems with quadratic detection when the test object either has low contrast or is periodic.

Ojeda-Castaneda, J.; Jara, E.

1980-04-01

192

Curious Consequences of a Miscopied Quadratic  

ERIC Educational Resources Information Center

The starting point of this article is a search for pairs of quadratic polynomials x[superscript 2] + bx plus or minus c with the property that they both factor over the integers. The search leads quickly to some number theory in the form of primitive Pythagorean triples, and this paper develops the connection between these two topics.

Poet, Jeffrey L.; Vestal, Donald L., Jr.

2005-01-01

193

Mating Non-Renormalizable Quadratic Polynomials  

NASA Astrophysics Data System (ADS)

In this paper we prove the existence and uniqueness of matings of the basilica with any quadratic polynomial which lies outside of the 1/2-limb of {mathcal {M}} , is non- renormalizable, and does not have any non-repelling periodic orbits.

Aspenberg, Magnus; Yampolsky, Michael

2009-04-01

194

Mammogram enhancement using alpha weighted quadratic filter  

Microsoft Academic Search

Mammograms are widely used to detect breast cancer in women. The quality of the image may suffer from poor resolution or low contrast due to the limitations of the X-ray hardware systems. Image enhancement is a powerful tool to improve the visual quality of mammograms. This paper introduces a new powerful nonlinear filter called the alpha weighted quadratic filter for

Yicong Zhou; Karen Panetta; Sos Agaian

2009-01-01

195

Quadratic Gabor filters for object detection  

Microsoft Academic Search

We present a new class of quadratic filters that are capable of creating spherical, elliptical, hyperbolic and linear decision surfaces which result in better detection and classification capabilities than the linear decision surfaces obtained from correlation filters. Each filter comprises of a number of separately designed linear basis filters. These filters are linearly combined into several macro filters; the output

David M. Weber; David P. Casasent

2001-01-01

196

Probabilistic robust design with linear quadratic regulators  

Microsoft Academic Search

In this paper, we study robust design of uncertain systems in a probabilistic setting by means of linear quadratic regulators. We consider systems affected by random bounded nonlinear uncertainty so that classical optimization methods based on linear matrix inequalities cannot be used without conservatism. The approach followed here is a blend of randomization techniques for the uncertainty together with convex

B. T. Polyak; R. Tempo

2000-01-01

197

Probabilistic robust design with linear quadratic regulators  

Microsoft Academic Search

In this paper, we study robust design of uncertain systems in a probabilistic setting by means of linear quadratic regulators (LQR). We consider systems affected by random bounded nonlinear uncertainty so that classical optimization methods based on linear matrix inequalities cannot be used without conservatism. The approach followed here is a blend of randomization techniques for the uncertainty together with

B. T. Polyak; R. Tempo

2001-01-01

198

Integration of the Quadratic Function and Generalization  

ERIC Educational Resources Information Center

We will first recall useful formulas in integration that simplify the calculation of certain definite integrals with the quadratic function. A main formula relies only on the coefficients of the function. We will then explore a geometric proof of one of these formulas. Finally, we will extend the formulas to more general cases. (Contains 3…

Mitsuma, Kunio

2011-01-01

199

Image enhancement based on quadratic programming  

Microsoft Academic Search

In this paper, a simple but efficient image enhancement algorithm is proposed. We model the image enhancement problem as a quadratic programming problem, and the cost function of the optimization problem is formulated based on local gradients of an image. By adjusting the definitions of gain function and weighting function in the cost function, we can derive various kinds of

Tzu-cheng Jen; Sheng-jyh Wang

2008-01-01

200

Quadratic engel curves and consumer demand  

Microsoft Academic Search

This paper presents a model of consumer demand that is consistent with the observed expenditure patterns of individual consumers in a long time series of expenditure surveys and is also able to provide a detailed welfare analysis of shifts in relative prices. A nonparametric analysis of consumer expenditure patterns suggests that Engel curves require quadratic terms in the logarithm of

James Banks; Richard Blundell; Arthur Lewbel

1997-01-01

201

Approximation of the Quadratic Set Covering problem  

Microsoft Academic Search

We study in this article the polynomial approximation properties of the Quadratic Set Covering problem. This problem, which arises in many applications, is a natural generalization of the usual Set Covering problem. We show that this problem is very hard to approximate in the general case, and even in classical subcases (when the size of each set or when the

Bruno Escoffier; Peter L. Hammer

2007-01-01

202

Non-Gaussianity in axion N-flation models.  

PubMed

We study perturbations in the multifield axion N-flation model, taking account of the full cosine potential. We find significant differences from previous analyses which made a quadratic approximation to the potential. The tensor-to-scalar ratio and the scalar spectral index move to lower values, which nevertheless provide an acceptable fit to observation. Most significantly, we find that the bispectrum non-Gaussianity parameter f{NL} may be large, typically of order 10 for moderate values of the axion decay constant, increasing to of order 100 for decay constants slightly smaller than the Planck scale. Such a non-Gaussian fraction is detectable. We argue that this property is generic in multifield models of hilltop inflation. PMID:21231095

Kim, Soo A; Liddle, Andrew R; Seery, David

2010-10-29

203

Wind turbine power tracking using an improved multimodel quadratic approach.  

PubMed

In this paper, an improved multimodel optimal quadratic control structure for variable speed, pitch regulated wind turbines (operating at high wind speeds) is proposed in order to integrate high levels of wind power to actively provide a primary reserve for frequency control. On the basis of the nonlinear model of the studied plant, and taking into account the wind speed fluctuations, and the electrical power variation, a multimodel linear description is derived for the wind turbine, and is used for the synthesis of an optimal control law involving a state feedback, an integral action and an output reference model. This new control structure allows a rapid transition of the wind turbine generated power between different desired set values. This electrical power tracking is ensured with a high-performance behavior for all other state variables: turbine and generator rotational speeds and mechanical shaft torque; and smooth and adequate evolution of the control variables. PMID:20434153

Khezami, Nadhira; Benhadj Braiek, Naceur; Guillaud, Xavier

2010-07-01

204

Reliable design of H-2 optimal reduced-order controllers via a homotopy algorithm  

NASA Technical Reports Server (NTRS)

Due to control processor limitations, the design of reduced-order controllers is an active area of research. Suboptimal methods based on truncating the order of the corresponding linear-quadratic-Gaussian (LQG) compensator tend to fail if the requested controller dimension is sufficiently small and/or the requested controller authority is sufficiently high. Also, traditional parameter optimization approaches have only local convergence properties. This paper discusses a homotopy algorithm for optimal reduced-order control that has global convergence properties. The exposition is for discrete-time systems. The algorithm has been implemented in MATLAB and is applied to a benchmark problem.

Collins, Emmanuel G.; Richter, Stephen; Davis, Larry D.

1992-01-01

205

Geometric Approaches to Quadratic Equations from Other Times and Places.  

ERIC Educational Resources Information Center

Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)

Allaire, Patricia R.; Bradley, Robert E.

2001-01-01

206

Linear State Feedback, Quadratic Weights, and Closed Loop Eigenstructures.  

National Technical Information Service (NTIS)

Results are given on the relationships between closed loop eigenstructures, state feedback gain matrices of the linear state feedback problem, and quadratic weights of the linear quadratic regulator. Equations are derived for the angles of general multiva...

P. M. Thompson

1979-01-01

207

Truncated Gaussians as tolerance sets  

NASA Technical Reports Server (NTRS)

This work focuses on the use of truncated Gaussian distributions as models for bounded data measurements that are constrained to appear between fixed limits. The authors prove that the truncated Gaussian can be viewed as a maximum entropy distribution for truncated bounded data, when mean and covariance are given. The characteristic function for the truncated Gaussian is presented; from this, algorithms are derived for calculation of mean, variance, summation, application of Bayes rule and filtering with truncated Gaussians. As an example of the power of their methods, a derivation of the disparity constraint (used in computer vision) from their models is described. The authors' approach complements results in Statistics, but their proposal is not only to use the truncated Gaussian as a model for selected data; they propose to model measurements as fundamentally in terms of truncated Gaussians.

Cozman, Fabio; Krotkov, Eric

1994-01-01

208

Quadratic divergences and quantum gravitational contributions to gauge coupling constants  

Microsoft Academic Search

The calculation of quadratic divergences in Einstein-Maxwell theory with a possible cosmological constant is considered. We describe a method of calculation, using the background-field method, that is sensitive to quadratic divergences, is respectful of gauge invariance, and is independent of gauge conditions. A standard renormalization group analysis is applied to the result where it is shown that the quadratic divergences

David J. Toms

2011-01-01

209

Quadratic Spline Models for Producer's Supply and Demand Functions  

Microsoft Academic Search

In this paper, the authors propose and estimate a system of producer output supply and input demand functions that generalizes the standard normalized quadratic form. The generalization adds either linear or quadratic splines in a time (or technical change) variable, yet retains the main attractive property of the normalized quadratic, which is that it can provide a local second order

W. E. Diewert; T. J. Wales

1992-01-01

210

Linear and quadratic time-frequency signal representations  

Microsoft Academic Search

A tutorial review of both linear and quadratic representations is given. The linear representations discussed are the short-time Fourier transform and the wavelet transform. The discussion of quadratic representations concentrates on the Wigner distribution, the ambiguity function, smoothed versions of the Wigner distribution, and various classes of quadratic time-frequency representations. Examples of the application of these representations to typical problems

F. Hlawatsch; G. F. Boudreaux-Bartels

1992-01-01

211

Quadratic harmonic morphisms and O-systems  

Microsoft Academic Search

We introduce O-systems (Definition \\\\ref{DO}) of orthogonal transformations of ${\\\\Bbb R}^{m}$, and establish $1-1$ correspondences both between equivalence classes of Clifford systems and that of O-systems, and between O-systems and orthogonal multiplications of the form $\\\\mu :{\\\\Bbb R}^{n} \\\\times {\\\\Bbb R}^{m} \\\\longrightarrow {\\\\Bbb R}^{m} $, which allow us to solve the existence problems both for O-systems and for umbilical quadratic

Ye-lin Ou

1995-01-01

212

Quadratic stability and singular SISO switching systems  

Microsoft Academic Search

In this note we consider the problem of determining necessary and su-cient condi- tions for the existence of a common quadratic Lyapunov function for a pair of stable linear time-invariant systems whose system matrices are of the form A, A ¡ ghT, and where one of the matrices is singular. A necessary and su-cient condition for the existence of such

R. Shorten; M. Corless; S. Klinge; R. Middleton

2008-01-01

213

Quadratic Stability and Singular SISO Switching Systems  

Microsoft Academic Search

In this note, we consider the problem of determining necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a pair of stable linear time-invariant systems whose system matrices are of the form A, A-ghT, and where one of the matrices is singular. A necessary and sufficient condition for the existence of such a function is

Robert Shorten; Martin Corless; Kai Wulff; Steffi Klinge; Richard Middleton

2009-01-01

214

Monotone and convex quadratic spline interpolation  

NASA Technical Reports Server (NTRS)

A method for producing interpolants that preserve the monotonicity and convexity of discrete data is described. It utilizes the quadratic spline proposed by Schumaker (1983) which was subsequently characterized by De Vore and Yan (1986). The selection of first order derivatives at the given data points is essential to this spline. An observation made by De Vore and Yan is generalized, and an improved method to select these derivatives is proposed. The resulting spline is completely local, efficient, and simple to implement.

Lam, Maria H.

1990-01-01

215

Characterization of a Quadratic Function in Rn  

ERIC Educational Resources Information Center

It is proved that a scalar-valued function "f"(x) defined in "n"-dimensional space must be quadratic, if the intersection of tangent planes at x[subscript 1] and x[subscript 2] always contains the midpoint of the line joining x[subscript 1] and x[subscript 2]. This is the converse of a result of Stenlund proved in this JOURNAL in 2001.

Xu, Conway

2010-01-01

216

Robust generation, properties and potential applications of quadratic spatial solitons generated by optical parametric amplification  

Microsoft Academic Search

Quadratic spatial solitary waves are predicted and observed experimentally near degeneracy for Type II optical parametric amplification in bulk KTP, by seeding an intense pump optical field with a control signal at half the pump wave frequency. The self-trapping of light at the two wavelengths has been shown to be insensitive to phase, polarization and magnitude of the control input,

R. A. Fuerst; M. T. G. Canva; G. I. Stegeman; G. Leo; G. Assanto

1998-01-01

217

Constrained quadratic correlation filters for target detection.  

PubMed

A method for designing and implementing quadratic correlation filters (QCFs) for shift-invariant target detection in imagery is presented. The QCFs are quadratic classifiers that operate directly on the image data without feature extraction or segmentation. In this sense the QCFs retain the main advantages of conventional linear correlation filters while offering significant improvements in other respects. Not only is more processing required for detection of peaks in the outputs of multiple linear filters but choosing the most suitable among them is an error-prone task. All channels in a QCF work together to optimize the same performance metric and to produce a combined output that leads to considerable simplification of the postprocessing scheme. The QCFs that are developed involve hard constraints on the output of the filter. Inasmuch as this design methodology is indicative of the synthetic discriminant function (SDF) approach for linear filters, the filters that we develop here are referred to as quadratic SDFs (QSDFs). Two methods for designing QSDFs are presented, an efficient architecture for achieving them is discussed, and results from the Moving and Stationary Target Acquisition and Recognition synthetic aperture radar data set are presented. PMID:14735950

Muise, Robert; Mahalanobis, Abhijit; Mohapatra, Ram; Li, Xin; Han, Deguang; Mikhael, Wasfy

2004-01-10

218

Constrained quadratic correlation filters for target detection  

NASA Astrophysics Data System (ADS)

A method for designing and implementing quadratic correlation filters (QCFs) for shift-invariant target detection in imagery is presented. The QCFs are quadratic classifiers that operate directly on the image data without feature extraction or segmentation. In this sense the QCFs retain the main advantages of conventional linear correlation filters while offering significant improvements in other respects. Not only is more processing required for detection of peaks in the outputs of multiple linear filters but choosing the most suitable among them is an error-prone task. All channels in a QCF work together to optimize the same performance metric and to produce a combined output that leads to considerable simplification of the postprocessing scheme. The QCFs that are developed involve hard constraints on the output of the filter. Inasmuch as this design methodology is indicative of the synthetic discriminant function (SDF) approach for linear filters, the filters that we develop here are referred to as quadratic SDFs (QSDFs). Two methods for designing QSDFs are presented, an efficient architecture for achieving them is discussed, and results from the Moving and Stationary Target Acquisition and Recognition synthetic aperture radar data set are presented.

Muise, Robert; Mahalanobis, Abhijit; Mohapatra, Ram; Li, Xin; Han, Deguang; Mikhael, Wasfy

2004-01-01

219

Explicit Solution to a Certain Non-ELQG Risk-sensitive Stochastic Control Problem  

SciTech Connect

A risk-sensitive stochastic control problem with finite/infinite horizon is studied with a 1-dimensional controlled process defined by a linear SDE with a linear control-term in the drift. In the criterion function, a non-linear/quadratic term is introduced by using the solution to a Riccati differential equation, and hence, the problem is not ELQG (Exponential Linear Quadratic Gaussian) in general. For the problem, optimal value and control are calculated in explicit forms and the set of admissible risk-sensitive parameters is given in a concrete form. As applications, two types of large deviations control problems, i.e., maximizing an upside large deviations probability and minimizing a downside large deviations probability, are mentioned.

Hata, Hiroaki, E-mail: hata@math.sinica.edu.t [Academia Sinica, Institute of Mathematics (China); Sekine, Jun, E-mail: sekine@kier.kyoto-u.ac.j [Kyoto University, Institute of Economic Research (Japan)

2010-12-15

220

Reduced-Order Model Based Feedback Control For Modified Hasegawa-Wakatani Model  

SciTech Connect

In this work, the development of model-based feedback control that stabilizes an unstable equilibrium is obtained for the Modi ed Hasegawa-Wakatani (MHW) equations, a classic model in plasma turbulence. First, a balanced truncation (a model reduction technique that has proven successful in ow control design problems) is applied to obtain a low dimensional model of the linearized MHW equation. Then a modelbased feedback controller is designed for the reduced order model using linear quadratic regulators (LQR). Finally, a linear quadratic gaussian (LQG) controller, which is more resistant to disturbances is deduced. The controller is applied on the non-reduced, nonlinear MHW equations to stabilize the equilibrium and suppress the transition to drift-wave induced turbulence.

I.R. Goumiri, C.W. Rowley, Z. Ma, D.A. Gates, J.A. Krommes and J.B. Parker

2013-01-28

221

Analytic Minkowski functionals of the cosmic microwave background: Second-order non-Gaussianity with bispectrum and trispectrum  

SciTech Connect

Analytic formulas of Minkowski functionals in two-dimensional random fields are derived, including effects of second-order non-Gaussianity in the presence of both the bispectrum and trispectrum. The set of formulas provides a promising method to constrain the primordial non-Gaussianity of the universe by temperature fluctuations in the cosmic microwave background radiation. In a case of local-type non-Gaussianity, the Minkowski functionals are analytically given by powers of quadratic and cubic parameters, f{sub NL} and g{sub NL} (and {tau}{sub NL}). Our formulas are not restricted to this particular model, and applicable to a wide class of non-Gaussian models. The analytic formulas are compared to numerical evaluations from non-Gaussian realizations of temperature maps, showing very good agreement.

Matsubara, Takahiko [Department of Physics, Nagoya University, Chikusa, Nagoya, 464-8602 (Japan)

2010-04-15

222

Semi-Supervised Learning: From Gaussian Fields to Gaussian Processes  

Microsoft Academic Search

Abstract: We show that the Gaussian random fields and harmonic energy minimizing function framework for semi-supervised learning can be viewed in terms of Gaussian processes, with covariance matrices derived from the graph Laplacian. We derive hyperparameter learning with evidence maximization, and give an empirical study of various ways to parameterize the graph weights.

Xiaojin Zhu; John Lafferty; Zoubin Ghahramani

2003-01-01

223

Reduced order models for closed loop control: comparison between POD, BPOD, and global modes  

NASA Astrophysics Data System (ADS)

Linear Quadratic Gaussian (LQG) control is a promising tool to control flows. Initially developed for systems of moderate size, it is not directly applicable to fluid mechanics problems, requiring a reduced model. Three popular ways of reducing the system will be presented and their ability to control the global instability of an incompressible cavity flow will be studied. A comparison between reduced models based on global modes, Proper Orthogonal Decomposition (POD) modes and Balanced POD (BPOD) modes permits to discuss the relevant quantities to be captured by the reduced model to insure a successful control.

Barbagallo, A.; Sipp, D.; Schmid, P. J.

2012-01-01

224

Active control of random vibrations of stiffened composite panels using intelligent materials  

NASA Astrophysics Data System (ADS)

Piezoelectric devices and electrorheological fluids are used to control structural vibrations of stiffened composite panels subjected to random loads. The surface-bonded piezoelectric devices first sense the strain-rate of the panel and then generate a localized control moment. The electrorheological fluid, located in the core of each sandwich-beam stiffener, alters the overall stiffness and damping properties of the structure in response to applied voltage. The transfer matrix method, modal analysis, and optimal control theory are used to determine the vibration response of the panel system. The relative effectiveness of the intelligent materials is investigated and collocated velocity feedback is compared to linear quadratic Gaussian control.

Poulin, Kevin Christopher

225

Roll plus maneuver load alleviation control system designs for the active flexible wing wind-tunnel model  

NASA Technical Reports Server (NTRS)

Three designs for controlling loads while rolling for the Active Flexible Wing (AFW) are discussed. The goal is to provide good roll control while simultaneously limiting the torsion and bending loads experienced by the wing. The first design uses Linear Quadratic Gaussian/Loop Transfer Recovery (LQG/LTR) modern control methods to control roll rate and torsional loads at four different wing locations. The second design uses a nonlinear surface command function to produce surface position commands as a function of current roll rate and commanded roll rate. The final design is a flutter suppression control system. This system stabilizes both symmetric and axisymmetric flutter modes of the AFW.

Moore, Douglas B.; Miller, Gerald D.; Klepl, Martin J.

1991-01-01

226

Armendariz rings and gaussian rings  

Microsoft Academic Search

We prove a number of results concerning Armendariz rings and Gaussian rings. Recall that a (commutative) ring R is (Gaussian) Armendariz if for two polynomials f,g?R[X] (the ideal of R generated by the coefficients of f g is the product of the ideals generated by the coefficients of f and g) fg = 0 implies aibj=0 for each coefficient ai

D. D. Anderson; Victor Camillo

1998-01-01

227

Moments for general quadratic densities in n dimensions  

SciTech Connect

We present the calculation of the generating functions and the rth-order correlations for densities of the form {rho}(x) {proportional_to} where g(s) is a non-negative function of the quadratic ''action'' s(x)={summation}{sub i,j}H{sub ij}x{sub i}x{sub j}, where x = (x{sub 1},x{sub 2}...,x{sub n}) is a real n-dimensional vector and H is a real, symmetric n x n matrix whose eigenvalues are strictly positive. In particular, we find the connection between the (r+2)th-order and rth-order correlations, which constitutes a generalization of the Gaussian moment theorem, which corresponds to the particular choice g(s)=e{sup -s/2}. We present several examples for specific choices for g(s), including the explicit expression for the generating function for each case and the subspace projection of {rho}(x) in a few cases. We also provide the straightforward generalizations to: (1) the case where g=g(s(x)+a {center_dot} x), where a=(a{sub 1},a{sub 2},...,a{sub n}) is an arbitrary real n-dimensional vector, and (2) the complex case, in which the action is of the form s(z) = {summation}{sub i,j}H{sub ij}z{sup *}{sub i} z{sub j} where z=(z{sub 1},z{sub 2}...z{sub n}) is an n-dimensional complex vector and H is a Hermitian n x n matrix whose eigenvalues are strictly positive.

Furman, Miguel A.

2002-03-20

228

Criteria for correction of quadratic field-dependent aberrations.  

PubMed

Aberrations of imaging systems can be described by using a polynomial expansion of the dependence on field position, or the off-axis distance of a point object. On-axis, or zero-order, aberrations can be calculated directly. It is well-known that aberrations with linear field dependence can be calculated and controlled by using the Abbe sine condition, which evaluates only on-axis behavior. We present a new set of relationships that fully describe the aberrations that depend on the second power of the field. A simple set of equations is derived by using Hamilton's characteristic functions and simplified by evaluating astigmatism in the pupil. The equations, which we call the pupil astigmatism criteria, use on-axis behavior to evaluate and control all aberrations with quadratic dependence on the field and arbitrary dependence on the pupil. These relations are explained and are validated by using several specific optical designs. PMID:12413132

Zhao, Chunyu; Burge, James H

2002-11-01

229

Oscillations of a quadratically damped pendulum  

NASA Astrophysics Data System (ADS)

A physical pendulum consisting of a circular disk at the end of a thin metal rod is connected to a low-friction rotary motion sensor, so that its angular position and velocity can be accurately measured. The disk can be oriented either perpendicular or parallel to the plane of swing to give significant or negligible air drag, respectively. The motion is analytically modeled in phase space. A quadratic dependence of the damping torque on the angular velocity fits the results. This laboratory experiment is suitable for undergraduate physics majors taking a first or second course in classical mechanics.

Mungan, Carl E.; Lipscombe, Trevor C.

2013-09-01

230

Efficient entanglement criteria beyond Gaussian limits using Gaussian measurements.  

PubMed

We present a formalism to derive entanglement criteria beyond the Gaussian regime that can be readily tested by only homodyne detection. The measured observable is the Einstein-Podolsky-Rosen (EPR) correlation. Its arbitrary functional form enables us to detect non-Gaussian entanglement even when an entanglement test based on second-order moments fails. We illustrate the power of our experimentally friendly criteria for a broad class of non-Gaussian states under realistic conditions. We also show rigorously that quantum teleportation for continuous variables employs a specific functional form of EPR correlation. PMID:22400723

Nha, Hyunchul; Lee, Su-Yong; Ji, Se-Wan; Kim, M S

2012-01-20

231

A Wavelet Bicoherence-Based Quadratic Nonlinearity Feature for Translational Axis Condition Monitoring  

PubMed Central

The translational axis is one of the most important subsystems in modern machine tools, as its degradation may result in the loss of the product qualification and lower the control precision. Condition-based maintenance (CBM) has been considered as one of the advanced maintenance schemes to achieve effective, reliable and cost-effective operation of machine systems, however, current vibration-based maintenance schemes cannot be employed directly in the translational axis system, due to its complex structure and the inefficiency of commonly used condition monitoring features. In this paper, a wavelet bicoherence-based quadratic nonlinearity feature is proposed for translational axis condition monitoring by using the torque signature of the drive servomotor. Firstly, the quadratic nonlinearity of the servomotor torque signature is discussed, and then, a biphase randomization wavelet bicoherence is introduced for its quadratic nonlinear detection. On this basis, a quadratic nonlinearity feature is proposed for condition monitoring of the translational axis. The properties of the proposed quadratic nonlinearity feature are investigated by simulations. Subsequently, this feature is applied to the real-world servomotor torque data collected from the X-axis on a high precision vertical machining centre. All the results show that the performance of the proposed feature is much better than that of original condition monitoring features.

Li, Yong; Wang, Xiufeng; Lin, Jing; Shi, Shengyu

2014-01-01

232

An application of nonlinear programming to the design of regulators of a linear-quadratic formulation  

NASA Technical Reports Server (NTRS)

A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a nonlinear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer. One concerns helicopter longitudinal dynamics and the other the flight dynamics of an aerodynamically unstable aircraft.

Fleming, P.

1983-01-01

233

Non-Gaussian spin dephasing  

NASA Astrophysics Data System (ADS)

We address spin dephasing induced by stochastic transitions between different precession frequencies. A very famous analytical approximation is the Gaussian approximation presented by [Anderson and Weiss, Rev. Mod. Phys. 25, 269 (1953)]. It states that independent from the transition dynamics, a Gaussian frequency distribution implies a Gaussian distribution of the phase angles, which provides a simple analytical result for the transverse magnetization decay. In contrast we find that (i) the assumption of Gaussian dephasing restricts the stochastic dynamics to a very limited class, (ii) the Anderson-Weiss model is applicable only in a special case of fluctuations, i.e., if and only if the Green’s function G(?2,?1,?t) describing the transition probability between two frequencies ?1??2 is Gaussian, and (iii) the exact time course of magnetization decay is dependent on the relaxation time in the motional narrowing limit and the correlation time describing the correlation function of the local frequencies. In contrast to previous publications, we conclude that a Gaussian equilibrium distribution of local frequencies does not imply a Gaussian-distributed phase angle. The general theory is illustrated by calculating the Green’s function of the transition dynamics for a stochastic process in the strong collision approximation. The result is highly relevant for describing relaxation processes in the presence of local field inhomogeneities.

Bauer, W. R.; Ziener, C. H.; Jakob, P. M.

2005-05-01

234

The accuracy of the Gaussian-and-finite-element-Coulomb (GFC) method for the calculation of Coulomb integrals.  

PubMed

We analyze the accuracy of the Coulomb energy calculated using the Gaussian-and-finite-element-Coulomb (GFC) method. In this approach, the electrostatic potential associated with the molecular electronic density is obtained by solving the Poisson equation and then used to calculate matrix elements of the Coulomb operator. The molecular electrostatic potential is expanded in a mixed Gaussian-finite-element (GF) basis set consisting of Gaussian functions of s symmetry centered on the nuclei (with exponents obtained from a full optimization of the atomic potentials generated by the atomic densities from symmetry-averaged restricted open-shell Hartree-Fock theory) and shape functions defined on uniform finite elements. The quality of the GF basis is controlled by means of a small set of parameters; for a given width of the finite elements d, the highest accuracy is achieved at smallest computational cost when tricubic (n = 3) elements are used in combination with two (?(H) = 2) and eight (?(1st) = 8) Gaussians on hydrogen and first-row atoms, respectively, with exponents greater than a given threshold (?min (G)=0.5). The error in the calculated Coulomb energy divided by the number of atoms in the system depends on the system type but is independent of the system size or the orbital basis set, vanishing approximately like d(4) with decreasing d. If the boundary conditions for the Poisson equation are calculated in an approximate way, the GFC method may lose its variational character when the finite elements are too small; with larger elements, it is less sensitive to inaccuracies in the boundary values. As it is possible to obtain accurate boundary conditions in linear time, the overall scaling of the GFC method for large systems is governed by another computational step-namely, the generation of the three-center overlap integrals with three Gaussian orbitals. The most unfavorable (nearly quadratic) scaling is observed for compact, truly three-dimensional systems; however, this scaling can be reduced to linear by introducing more effective techniques for recognizing significant three-center overlap distributions. PMID:23927250

Przybytek, Michal; Helgaker, Trygve

2013-08-01

235

The accuracy of the Gaussian-and-finite-element-Coulomb (GFC) method for the calculation of Coulomb integrals  

NASA Astrophysics Data System (ADS)

We analyze the accuracy of the Coulomb energy calculated using the Gaussian-and-finite-element-Coulomb (GFC) method. In this approach, the electrostatic potential associated with the molecular electronic density is obtained by solving the Poisson equation and then used to calculate matrix elements of the Coulomb operator. The molecular electrostatic potential is expanded in a mixed Gaussian-finite-element (GF) basis set consisting of Gaussian functions of s symmetry centered on the nuclei (with exponents obtained from a full optimization of the atomic potentials generated by the atomic densities from symmetry-averaged restricted open-shell Hartree-Fock theory) and shape functions defined on uniform finite elements. The quality of the GF basis is controlled by means of a small set of parameters; for a given width of the finite elements d, the highest accuracy is achieved at smallest computational cost when tricubic (n = 3) elements are used in combination with two (?H = 2) and eight (?1st = 8) Gaussians on hydrogen and first-row atoms, respectively, with exponents greater than a given threshold (?minG=0.5). The error in the calculated Coulomb energy divided by the number of atoms in the system depends on the system type but is independent of the system size or the orbital basis set, vanishing approximately like d4 with decreasing d. If the boundary conditions for the Poisson equation are calculated in an approximate way, the GFC method may lose its variational character when the finite elements are too small; with larger elements, it is less sensitive to inaccuracies in the boundary values. As it is possible to obtain accurate boundary conditions in linear time, the overall scaling of the GFC method for large systems is governed by another computational step--namely, the generation of the three-center overlap integrals with three Gaussian orbitals. The most unfavorable (nearly quadratic) scaling is observed for compact, truly three-dimensional systems; however, this scaling can be reduced to linear by introducing more effective techniques for recognizing significant three-center overlap distributions.

Przybytek, Michal; Helgaker, Trygve

2013-08-01

236

Flutter suppression digital control law design and testing for the AFW wind-tunnel model  

NASA Technical Reports Server (NTRS)

Design of a control law for simultaneously suppressing the symmetric and antisymmetric flutter modes of a string mounted fixed-in-roll aeroelastic wind tunnel model is described. The flutter suppression control law was designed using linear quadratic Gaussian theory and involved control law order reduction, a gain root-locus study, and the use of previous experimental results. A 23 percent increase in open-loop flutter dynamic pressure was demonstrated during the wind tunnel test. Rapid roll maneuvers at 11 percent above the symmetric flutter boundary were also performed when the model was in a free-to-roll configuration.

Mukhopadhyay, Vivek

1992-01-01

237

Flutter suppression digital control law design and testing for the AFW wind tunnel model  

NASA Technical Reports Server (NTRS)

The design of a control law for simultaneously suppressing the symmetric and antisymmetric flutter modes of a sting mounted fixed-in-roll aeroelastic wind-tunnel model is described. The flutter suppression control law was designed using linear quadratic Gaussian theory, and it also involved control law order reduction, a gain root-locus study, and use of previous experimental results. A 23 percent increase in the open-loop flutter dynamic pressure was demonstrated during the wind-tunnel test. Rapid roll maneuvers at 11 percent above the symmetric flutter boundary were also performed when the model was in a free-to-roll configuration.

Mukhopadhyay, Vivek

1994-01-01

238

Flutter suppression digital control law design and testing for the AFW wind tunnel model  

NASA Technical Reports Server (NTRS)

Design of a control law for simultaneously suppressing the symmetric and antisymmetric flutter modes of a sting mounted fixed-in-roll aeroelastic wind tunnel model is described. The flutter suppression control law was designed using linear quadratic Gaussian theory, and involved control law order reduction, a gain root-locus study and use of previous experimental results. A 23 percent increase in the open-loop flutter dynamic pressure was demonstrated during the wind tunnel test. Rapid roll maneuvers at 11 percent above the symmetric flutter boundary were also performed when the model was in a free-to-roll configuration.

Mukhopadhyay, Vivek

1992-01-01

239

On the classification of quadratic harmonic morphisms between Euclidean spaces  

Microsoft Academic Search

We give a classification of quadratic harmonic morphisms between Euclidean spaces (Theorem 2.4) after proving a Rank Lemma. We also find a correspondence between umbilical (Definition 2.7) quadratic harmonic morphisms and Clifford systems. In the case $ {\\\\Bbb R}^{4}\\\\longrightarrow {\\\\Bbb R}^{3} $, we determine all quadratic harmonic morphisms and show that, up to a constant factor, they are all bi-equivalent

Ye-lin Ou; J. C. Wood

1995-01-01

240

Hollow Gaussian beams and their propagation properties.  

PubMed

A new mathematical model, described as hollow Gaussian beams (HGBs), is proposed to describe a dark hollow laser beam (DHB). The area of the dark region across the HGBs can easily be controlled by proper choice of the beam parameters. Based on the Collins integral, an analytical propagation formula for the HGBs through a paraxial optical system is derived. The HGBs also can be expressed as a superposition of a series of Lagurerre-Gaussian modes by use of a polynomial expansion. As a numerical example, the propagation properties of a DHB in free space are illustrated graphically. The HGBs provide a convenient and powerful way to describe and treat the propagation of DHBs and can be used conveniently to analyze atoms manipulated with a DHB. PMID:12879915

Cai, Yangjian; Lu, Xuanhui; Lin, Qiang

2003-07-01

241

The Gaussian parallel relay network  

Microsoft Academic Search

We introduce the real, discrete-time Gaussian parallel relay network. This simple network is theoretically important in the context of network information theory. We present upper and lower bounds to capacity and explain where they coincide

B. Schein; R. Gallager

2000-01-01

242

Steller Structure Treatment of Quadratic Gravity  

NASA Astrophysics Data System (ADS)

A scheme for considering stellar structure by taking advantage of the quadratic theory of gravitation in four-dimensions is proposed, citing the fact that the possible deviation of gravity in astrophysical systems from the Newtonian inverse square law can be explained through the use of this theory. A modified Lane-Emden equation is derived by making use of the linearized static field equation of quadratic gravity and the polytropic equation of state for a fluid. The influence on stellar structure of the additional force included in quadratic gravity is investigated. It is shown that the additional force can be treated as a perturbation of a bound system by solutions of the modified Lane-Emden equation and an order-of-magnitude analysis. %ZY. Fujii, Nature (London) 234 (1971), 5; Phys. Rev. D9 (1974), 874. D. R. Long, Phys. Rev. D 9 (1974), 850. J. O'Hanlon, Phys. Rev. Lett. 29 (1972), 137. D. R. Mikkelson and M. J. Newman, Phys. Rev. D 16 (1977), 919. R. V. Wagoner, Phys. Rev. D 1 (1970), 3209. J. Z. Xu and Y. H. Chen, Gen. Relat. Gravit. J. 23 (1991), 169. K. S. Stelle, Gen. Relat. Gravit. J. 8 (1978), 631. C. Xu and G. F. R. Ellis, Class. Quant. Grav. 8 (1991), 1747. A. Eddington, The Mathematical Theory of Relativity, 2nd ed. (Cambridge University Press, Cambridge, 1924). W. Pauli, Theory of Relativity (Pergamon Press, New York, 1921). H. A. Buchdahl, Proc. Edinburgh Math. Soc. 8 (1948), 89. J. D. Barrow and A. C. Ottewill, J. of Phys. A 16 (1983), 2757. M. B. Mijic, M. S. Morris and W. M. Suen, Phys. Rev. D 34 (1986), 2934. A. L. Berkin, Phys. Rev. D 42 (1990), 1017. N. D. Birrell and P. C. W. Davies, Quantum Field in Curved Space (Cambridge University Press, 1982). E. T. Tomboulis, Quantum Theory of Gravity, ed. S. M. Christensen (Bristol: Adam Hilger 1984). H. J. Treder, Ann. der Phys. 32 (1975), 383. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley, New York 1972). E. N. Glass and G. Szamosi, Phys. Rev. D 35 (1987), 1205.

Chen, Y.; Shao, C.; Chen, X.

2001-07-01

243

Propagation and focusing of Gaussian beams generated by Gaussian mirror resonators.  

PubMed

The propagation and focusing properties of a class of Gaussian beams generated by optical resonators with Gaussian reflectivity mirrors are investigated. Attention is concentrated on the following two beams in this class: (a) the annular Gaussian beam (the Gaussian doughnut mode) and (b) the flat-topped Gaussian beam. A class of flat-topped Gaussian beams is introduced. All analysis is limited to a coherent superposition scheme of the lowest-order Gaussian modes (TEM00) that have different parameters. PMID:12216877

Li, Yajun

2002-09-01

244

Decentralized Control of Sound Radiation using a High-Authority/Low-Authority Control Strategy with Anisotropic Actuators  

NASA Technical Reports Server (NTRS)

This paper describes a combined control strategy designed to reduce sound radiation from stiffened aircraft-style panels. The control architecture uses robust active damping in addition to high-authority linear quadratic Gaussian (LQG) control. Active damping is achieved using direct velocity feedback with triangularly shaped anisotropic actuators and point velocity sensors. While active damping is simple and robust, stability is guaranteed at the expense of performance. Therefore the approach is often referred to as low-authority control. In contrast, LQG control strategies can achieve substantial reductions in sound radiation. Unfortunately, the unmodeled interaction between neighboring control units can destabilize decentralized control systems. Numerical simulations show that combining active damping and decentralized LQG control can be beneficial. In particular, augmenting the in-bandwidth damping supplements the performance of the LQG control strategy and reduces the destabilizing interaction between neighboring control units.

Schiller, Noah H.; Cabell, Randolph H.; Fuller, Chris R.

2008-01-01

245

Mammogram enhancement using alpha weighted quadratic filter.  

PubMed

Mammograms are widely used to detect breast cancer in women. The quality of the image may suffer from poor resolution or low contrast due to the limitations of the X-ray hardware systems. Image enhancement is a powerful tool to improve the visual quality of mammograms. This paper introduces a new powerful nonlinear filter called the alpha weighted quadratic filter for mammogram enhancement. The user has the flexibility to design the filter by selecting all of the parameters manually or using an existing quantitative measure to select the optimal enhancement parameters. Computer simulations show that excellent enhancement results can be obtained with no apriori knowledge of the mammogram contents. The filter can also be used for automatic segmentation. PMID:19965002

Zhou, Yicong; Panetta, Karen; Agaian, Sos

2009-01-01

246

Photon blockade in quadratically coupled optomechanical systems  

NASA Astrophysics Data System (ADS)

We study the steady-state photon statistics of a quadratically coupled optomechanical cavity, which is weakly driven by a monochromatic laser field. We examine the photon blockade by evaluating the second-order correlation function of the cavity photons. By restricting the system within the zero-, one-, and two-photon subspace, we obtain an approximate analytical expression for the correlation function. We also numerically investigate the correlation function by solving the quantum master equation including both optical and mechanical dissipations. The results show that, in the deep-resolved-sideband and single-photon strong-coupling regimes, the single-photon resonant driving will induce a photon blockade, which is limited by the thermal noise of the mechanical environment.

Liao, Jie-Qiao; Nori, Franco

2013-08-01

247

Quadratic quantum cosmology with Schutz' perfect fluid  

NASA Astrophysics Data System (ADS)

We study the classical and quantum models of a Friedmann-Robertson-Walker (FRW) cosmology, coupled to a perfect fluid, in the context of the f(R) gravity. Using Schutz' representation for the perfect fluid, we show that, under a particular gauge choice, it may lead to the identification of a time parameter for the corresponding dynamical system. Moreover, this formalism gives rise to a Schrödinger-Wheeler-DeWitt (SWD) equation for the quantum-mechanical description of the model under consideration, the eigenfunctions of which can be used to construct the wavefunction of the universe. In the case of f(R) = R2 (pure quadratic model), for some particular choices of the perfect fluid source, exact solutions to the SWD equation can be obtained and the corresponding results are compared to the usual f(R) = R model.

Vakili, Babak

2010-01-01

248

Linear stability analysis of dynamical quadratic gravity  

NASA Astrophysics Data System (ADS)

We study the linear stability of dynamical, quadratic gravity, focusing on two particular subclasses (the even-parity sector, exemplified by Einstein-Dilaton-Gauss-Bonnet gravity, and the odd-parity sector, exemplified by dynamical Chern-Simons modified gravity) in the high-frequency, geometric optics approximation. This analysis is carried out by studying gravitational and scalar modes propagating on spherically symmetric and axially symmetric, vacuum solutions of the theory and finding the associated dispersion relations. These relations are solved in two separate cases (the scalar regime and the gravitational wave regime, defined by requiring the ratio of the amplitude of the perturbations to be much greater or smaller than unity) and found in both cases to not lead to exponential growth of the propagating modes, suggesting linearly stability. The modes are found to propagate at subluminal and superluminal speeds, depending on the propagating modes' direction relative to the background geometry, just as in dynamical Chern-Simons gravity.

Ayzenberg, Dimitry; Yagi, Kent; Yunes, Nicolás

2014-02-01

249

Non-Gaussian State Generation from Linear Elements via Feedback  

NASA Astrophysics Data System (ADS)

We present a feedback scheme to produce quantum non-Gaussian states from linear optical elements. Instead of traditional additive control methods, we introduce a mutiplicative feedback control and apply it to the deterministic generation of quantum superposition states. The protocol of feedback control is based on quantum nondemolition measurement of a quadrature, multifeedback structure, and Lyapunov stability for feedback design.

Yanagisawa, Masahiro

2009-11-01

250

Non-Gaussian state generation from linear elements via feedback.  

PubMed

We present a feedback scheme to produce quantum non-Gaussian states from linear optical elements. Instead of traditional additive control methods, we introduce a mutiplicative feedback control and apply it to the deterministic generation of quantum superposition states. The protocol of feedback control is based on quantum nondemolition measurement of a quadrature, multifeedback structure, and Lyapunov stability for feedback design. PMID:20365982

Yanagisawa, Masahiro

2009-11-13

251

Optimal controllers for finite wordlength implementation  

NASA Technical Reports Server (NTRS)

When a controller is implemented in a digital computer, with A/D and D/A conversion, the numerical errors of the computation can drastically affect the performance of the control system. There exists realizations of a given controller transfer function yielding arbitrarily large effects from computational errors. Since, in general, there is no upper bound, it is important to have a systematic way of reducing these effects. Optimum controller designs are developed which take account of the digital round-off errors in the controller implementation and in the A/D and D/A converters. These results provide a natural extension to the Linear Quadratic Gaussian (LQG) theory since they reduce to the standard LQG controller when infinite precision computation is used. But for finite precision the separation principle does not hold.

Liu, K.; Skelton, R.

1991-01-01

252

The Development of a Dsp-Based Active Small Amplitude Vibration Control System for Flexible Beams by Using the Lqg Algorithms and Intelligent Materials  

NASA Astrophysics Data System (ADS)

An active vibration control system is proposed for suppressing the small amplitude random vibrations in flexible beams. Intelligent materials such as the piezoelectric ceramic PZT are used as the actuator and the piezoelectric plastic PVDF is used as the sensor. The characteristics of the physical system are identified by a parametric modelling technique. The linear quadratic Gaussian (LQG) algorithm is employed for the controller design. The controller is implemented on the basis of a floating-point digital signal processor. The experimental results obtained by using the active vibration control system show significant attenuation of white noise disturbance in the frequency range of approximately 100-800 Hz.

Bai, M. R.; Lin, G. M.

1996-12-01

253

On the Approximation of Correlated Non-Gaussian Noise Pdfs using Gaussian Mixture Models  

Microsoft Academic Search

Gaussian mixture probability density functions (pdfs) have been popular for modeling non- Gaussian noise. The majority of non-Gaussian noise research has been restri cted to independent and identically distributed observation sequences due to the difficulty i n characterizing multidimen- sional pdf's. There has been very few studies on the ability of Gaussian m ixture pdfs to model correlated non-Gaussian noise

R. S. Blum; Y. Zhang; B. M. Sadler; R. J. Kozick

1999-01-01

254

Theory of exciton transport with quadratic exciton-phonon coupling  

Microsoft Academic Search

The coupling of excitons with phonons is an important process determining the mechanism of exciton transport in molecular crystals. Although linear exciton–phonon coupling has been extensively treated before, there has been little work on quadratic coupling. In this paper the theory of exciton transport is extended to take weak quadratic coupling into account, and the diffusion constant computed for a

R. W. Munn; R. Silbey

1978-01-01

255

PARAMETRIC QUADRATIC PROGRAMMING METHOD FOR ELASTIC CONTACT FRACTURE ANALYSIS  

Microsoft Academic Search

A solution procedure for elastic contact fracture mechanics has been proposed in this paper. The procedure is based on the quadratic programming and finite element method (FEM). In this paper, parametric quadratic programming method for two-dimensional contact mechanics analysis is applied to the crack problems involving the crack surfaces in frictional contact. Based on a linear complementary contact condition, the

R. K. L. SU; Y. ZHU; A. Y. T. LEUNG

2002-01-01

256

Parametric quadratic programming method for elastic contact fracture analysis  

Microsoft Academic Search

A solution procedure for elastic contact fracture mechanics has been proposed in this paper. The procedure is based on the quadratic programming and finite element method (FEM). In this paper, parametric quadratic programming method for two-dimensional contact mechanics analysis is applied to the crack problems involving the crack surfaces in frictional contact. Based on a linear complementary contact condition, the

R. K. L. Su; Y. Zhu; A. Y. T. Leung

2002-01-01

257

Quadratic finite element methods for unilateral contact problems  

Microsoft Academic Search

The present paper is concerned with the frictionless unilateral contact problem between two elastic bodies in a bidimensional context. We consider a mixed formulation in which the unknowns are the displacement field and the contact pressure. We introduce a finite element method using quadratic elements and continuous piecewise quadratic multipliers on the contact zone. The discrete unilateral non-interpenetration condition is

Patrick Hild; Patrick Laborde

2002-01-01

258

On copositive programming and standard quadratic optimization problems  

Microsoft Academic Search

A standard quadratic problem consists of finding global maximizers of a quadratic form over the standard simplex. In this paper, the usual semidefinite programming relaxation is strengthened by replacing the cone of positive semidefinite matrices by the cone of completely positive matrices (the positive semidefinite matrices which allow a factorization FFT whereF is some non-negative matrix). The dual of this

Immanuel M. Bomze; Mirjam Dür; Etienne de Klerk; Cornelis Roos; Arie J. Quist; Tamás Terlaky

2000-01-01

259

Design and application of quadratic correlation filters for target detection  

Microsoft Academic Search

We introduce a method for designing and implementing quadratic correlation filters (QCFs) for shift-invariant target detection in imagery. The QCFs are a quadratic classifier that operates directly on the image data without feature extraction or segmentation. In this sense, the QCFs retain the main advantages of conventional linear correlation filters while offering significant improvements in other respects. Not only is

ABHIJIT MAHALANOBIS; ROBERT R. MUISE; S. R. Stanfill; A. Van Nevel

2004-01-01

260

Tangent Lines without Derivatives for Quadratic and Cubic Equations  

ERIC Educational Resources Information Center

In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)

Carroll, William J.

2009-01-01

261

Natural Exponential Families with Quadratic Variance Functions: Statistical Theory  

Microsoft Academic Search

The normal, Poisson, gamma, binomial, negative binomial, and NEFGHS distributions are the six univariate natural exponential families (NEF) with quadratic variance functions (QVF). This sequel to Morris (1982) treats certain statistical topics that can be handled within this unified NEF-QVF formulation, including unbiased estimation, Bhattacharyya and Cramer-Rao lower bounds, conditional distributions and moments, quadratic regression, conjugate prior distributions, moments of

Carl N. Morris

1983-01-01

262

Quadratic divergences and quantum gravitational contributions to gauge coupling constants  

NASA Astrophysics Data System (ADS)

The calculation of quadratic divergences in Einstein-Maxwell theory with a possible cosmological constant is considered. We describe a method of calculation, using the background-field method, that is sensitive to quadratic divergences, is respectful of gauge invariance, and is independent of gauge conditions. A standard renormalization group analysis is applied to the result where it is shown that the quadratic divergences do lead to asymptotic freedom as found in the original paper of Robinson and Wilczek. The role and nature of these quadratic divergences is critically evaluated in light of recent criticism. Within the context of the background-field method, it is shown that it is possible to define the charge in a physically motivated way in which the quadratic divergences do not play a role. This latter view is studied in more depth in a toy model described in an appendix.

Toms, David J.

2011-10-01

263

Quadratic divergences and quantum gravitational contributions to gauge coupling constants  

SciTech Connect

The calculation of quadratic divergences in Einstein-Maxwell theory with a possible cosmological constant is considered. We describe a method of calculation, using the background-field method, that is sensitive to quadratic divergences, is respectful of gauge invariance, and is independent of gauge conditions. A standard renormalization group analysis is applied to the result where it is shown that the quadratic divergences do lead to asymptotic freedom as found in the original paper of Robinson and Wilczek. The role and nature of these quadratic divergences is critically evaluated in light of recent criticism. Within the context of the background-field method, it is shown that it is possible to define the charge in a physically motivated way in which the quadratic divergences do not play a role. This latter view is studied in more depth in a toy model described in an appendix.

Toms, David J. [School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne, NE1 7RU (United Kingdom)

2011-10-15

264

Information geometry of Gaussian channels  

SciTech Connect

We define a local Riemannian metric tensor in the manifold of Gaussian channels and the distance that it induces. We adopt an information-geometric approach and define a metric derived from the Bures-Fisher metric for quantum states. The resulting metric inherits several desirable properties from the Bures-Fisher metric and is operationally motivated by distinguishability considerations: It serves as an upper bound to the attainable quantum Fisher information for the channel parameters using Gaussian states, under generic constraints on the physically available resources. Our approach naturally includes the use of entangled Gaussian probe states. We prove that the metric enjoys some desirable properties like stability and covariance. As a by-product, we also obtain some general results in Gaussian channel estimation that are the continuous-variable analogs of previously known results in finite dimensions. We prove that optimal probe states are always pure and bounded in the number of ancillary modes, even in the presence of constraints on the reduced state input in the channel. This has experimental and computational implications. It limits the complexity of optimal experimental setups for channel estimation and reduces the computational requirements for the evaluation of the metric: Indeed, we construct a converging algorithm for its computation. We provide explicit formulas for computing the multiparametric quantum Fisher information for dissipative channels probed with arbitrary Gaussian states and provide the optimal observables for the estimation of the channel parameters (e.g., bath couplings, squeezing, and temperature).

Monras, Alex [Dipartimento di Matematica e Informatica, Universita degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (Italy); CNR-INFM Coherentia, Napoli (Italy); CNISM Unita di Salerno (Italy) and INFN Sezione di Napoli, Gruppo collegato di Salerno, Baronissi (Italy); Illuminati, Fabrizio [Dipartimento di Matematica e Informatica, Universita degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (Italy); CNR-INFM Coherentia, Napoli (Italy) and CNISM Unita di Salerno; and INFN Sezione di Napoli, Gruppo collegato di Salerno, Baronissi (Italy); ISI Foundation for Scientific Interchange, Villa Gualino, Viale Settimio Severo 65, I-10133 Torino (Italy)

2010-06-15

265

Suboptimal security solution of a linear-quadratic pursuit-evasion game with mixed noises  

Microsoft Academic Search

The discrete-time, linear-quadratic pursuit-evasion game is considered in this paper. The difference system contains the state-dependent, control-dependent, and additive noises. In addition, each player has additive noises in his own measurement vector, and he is restricted to implement a linear estimator based on his measurements. Each player's philosophy is not to run a risk but to adopt a security control

J. Y. S. Luh; M. Maguiraga

1971-01-01

266

Users manual for flight control design programs  

NASA Technical Reports Server (NTRS)

Computer programs for the design of analog and digital flight control systems are documented. The program DIGADAPT uses linear-quadratic-gaussian synthesis algorithms in the design of command response controllers and state estimators, and it applies covariance propagation analysis to the selection of sampling intervals for digital systems. Program SCHED executes correlation and regression analyses for the development of gain and trim schedules to be used in open-loop explicit-adaptive control laws. A linear-time-varying simulation of aircraft motions is provided by the program TVHIS, which includes guidance and control logic, as well as models for control actuator dynamics. The programs are coded in FORTRAN and are compiled and executed on both IBM and CDC computers.

Nalbandian, J. Y.

1975-01-01

267

Integrated structure/control law design by multilevel optimization  

NASA Technical Reports Server (NTRS)

A new approach to integrated structure/control law design based on multilevel optimization is presented. This new approach is applicable to aircraft and spacecraft and allows for the independent design of the structure and control law. Integration of the designs is achieved through use of an upper level coordination problem formulation within the multilevel optimization framework. The method requires the use of structure and control law design sensitivity information. A general multilevel structure/control law design problem formulation is given, and the use of Linear Quadratic Gaussian (LQG) control law design and design sensitivity methods within the formulation is illustrated. Results of three simple integrated structure/control law design examples are presented. These results show the capability of structure and control law design tradeoffs to improve controlled system performance within the multilevel approach.

Gilbert, Michael G.; Schmidt, David K.

1989-01-01

268

Cooling and squeezing via quadratic optomechanical coupling  

SciTech Connect

We explore the physics of optomechanical systems in which an optical cavity mode is coupled parametrically to the square of the position of a mechanical oscillator. We derive an effective master equation describing two-phonon cooling of the mechanical oscillator. We show that for high temperatures and weak coupling, the steady-state phonon number distribution is nonthermal (Gaussian) and that even for strong cooling the mean phonon number remains finite. Moreover, we demonstrate how to achieve mechanical squeezing by driving the cavity with two beams. Finally, we calculate the optical output and squeezing spectra. Implications for optomechanics experiments with the membrane-in-the-middle geometry or ultracold atoms in optical resonators are discussed.

Nunnenkamp, A.; Boerkje, K.; Harris, J. G. E.; Girvin, S. M. [Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520 (United States)

2010-08-15

269

AESOP- INTERACTIVE DESIGN OF LINEAR QUADRATIC REGULATORS AND KALMAN FILTERS  

NASA Technical Reports Server (NTRS)

AESOP was developed to solve a number of problems associated with the design of controls and state estimators for linear time-invariant systems. The systems considered are modeled in state-variable form by a set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are the linear quadratic regulator (LQR) design problem and the steady-state Kalman filter design problem. AESOP is designed to be used in an interactive manner. The user can solve design problems and analyze the solutions in a single interactive session. Both numerical and graphical information are available to the user during the session. The AESOP program is structured around a list of predefined functions. Each function performs a single computation associated with control, estimation, or system response determination. AESOP contains over sixty functions and permits the easy inclusion of user defined functions. The user accesses these functions either by inputting a list of desired functions in the order they are to be performed, or by specifying a single function to be performed. The latter case is used when the choice of function and function order depends on the results of previous functions. The available AESOP functions are divided into several general areas including: 1) program control, 2) matrix input and revision, 3) matrix formation, 4) open-loop system analysis, 5) frequency response, 6) transient response, 7) transient function zeros, 8) LQR and Kalman filter design, 9) eigenvalues and eigenvectors, 10) covariances, and 11) user-defined functions. The most important functions are those that design linear quadratic regulators and Kalman filters. The user interacts with AESOP when using these functions by inputting design weighting parameters and by viewing displays of designed system response. Support functions obtain system transient and frequency responses, transfer functions, and covariance matrices. AESOP can also provide the user with open-loop system information including stability, controllability, and observability. The AESOP program is written in FORTRAN IV for interactive execution and has been implemented on an IBM 3033 computer using TSS 370. As currently configured, AESOP has a central memory requirement of approximately 2 Megs of 8 bit bytes. Memory requirements can be reduced by redimensioning arrays in the AESOP program. Graphical output requires adaptation of the AESOP plot routines to whatever device is available. The AESOP program was developed in 1984.

Lehtinen, B.

1994-01-01

270

Gaussian-mixture umbrella sampling  

PubMed Central

We introduce the Gaussian-mixture umbrella sampling method (GAMUS), a biased molecular dynamics technique based on adaptive umbrella sampling that efficiently escapes free energy minima in multi-dimensional problems. The prior simulation data are reweighted with a maximum likelihood formulation, and the new approximate probability density is fit to a Gaussian-mixture model, augmented by information about the unsampled areas. The method can be used to identify free energy minima in multi-dimensional reaction coordinates. To illustrate GAMUS, we apply it to the alanine dipeptide (2D reaction coordinate) and tripeptide (4D reaction coordinate).

van der Vaart, Arjan; Karplus, Martin

2009-01-01

271

Non-Gaussianity from symmetry  

SciTech Connect

We point out that a light scalar field fluctuating around a symmetry-enhanced point can generate large non-Gaussianity in density fluctuations. We name such a particle an 'ungaussiton', a scalar field dominantly produced by the quantum fluctuations, generating sizable non-Gaussianity in the density fluctuations. We derive a consistency relation between the bispectrum and the trispectrum, {tau}{sub NL}{approx}10{sup 3}{center_dot}f{sub NL}{sup 4/3}, which can be extended to arbitrarily high order correlation functions. If such a relation is confirmed by future observations, it will strongly support this mechanism.

Suyama, Teruaki [Institute for Cosmic Ray Research, University of Tokyo, Kashiwa 277 8582 (Japan)] [Institute for Cosmic Ray Research, University of Tokyo, Kashiwa 277 8582 (Japan); Takahashi, Fuminobu, E-mail: suyama@icrr.u-tokyo.ac.jp, E-mail: fuminobu.takahashi@ipmu.jp [Institute for the Physics and Mathematics of the Universe, University of Tokyo, Chiba 277-8568 (Japan)] [Institute for the Physics and Mathematics of the Universe, University of Tokyo, Chiba 277-8568 (Japan)

2008-09-15

272

Second-order spectra for quadratic nonlinear systems by Volterra functional series: Analytical description and numerical simulation  

NASA Astrophysics Data System (ADS)

Higher-order spectral analysis techniques are often used to identify nonlinearities in complex dynamical systems. More specifically, the auto- and cross-bispectrum have proven to be useful tools in testing for the presence of quadratic nonlinearities based on knowledge of a system's input and output. In this paper, analytical expressions for the auto- and cross-bispectrum are developed using a Volterra functional approach under the assumption of a zero-mean, stationary Gaussian input; proper simplifications are presented when the whiteness of the input signal is also imposed. These formulae show the contributions of the bispectrum in terms of the system frequency response function and elementary physical properties of the system. Simulations based on a stochastic numerical integration technique accompany the analytical solutions for a mechanical mass-spring-damper system possessing quadratic damping and stiffness coefficients and subjected to Gaussian white noise excitation. Subsequent estimates of the bispectrum based on the simulated signals show excellent agreement with theory. These results show how modes may interact nonlinearly producing intermodulation components at the sum and/or difference frequency of the fundamental modes of oscillation. The presence and extent of nonlinear interactions between frequency components are identified. Advantages of using higher-order spectra techniques will be revealed and pertinent conclusions will be outlined.

Marzocca, P.; Nichols, J. M.; Milanese, A.; Seaver, M.; Trickey, S. T.

2008-11-01

273

Propagation properties of Airy-Gaussian beams  

NASA Astrophysics Data System (ADS)

The propagation of the Airy-Gaussian beams is studied in strongly nonlocal nonlinear media analytically and numerically. The linear momentum of the analytical Airy-Gaussian beam solution of the Snyder-Mitchell model is not conservational, which is the reason that results in the disagreement between the analytical Airy-Gaussian beam solution and the numerical simulations of the nonlocal nonlinear Schrödinger equation in the case of strong nonlocality. The quasi-Airy-Gaussian soliton in the Gaussian-shaped response material can be obtained when the parameter ? 0 is large enough, and the patterns of Airy-Gaussian beams are variable periodically in liquid crystal material during propagation.

Deng, D.; Li, H.

2012-03-01

274

Models for the 3D singular isotropic oscillator quadratic algebra  

SciTech Connect

We give the first explicit construction of the quadratic algebra for a 3D quantum superintegrable system with nondegenerate (4-parameter) potential together with realizations of irreducible representations of the quadratic algebra in terms of differential-differential or differential-difference and difference-difference operators in two variables. The example is the singular isotropic oscillator. We point out that the quantum models arise naturally from models of the Poisson algebras for the corresponding classical superintegrable system. These techniques extend to quadratic algebras for superintegrable systems in n dimensions and are closely related to Hecke algebras and multivariable orthogonal polynomials.

Kalnins, E. G., E-mail: math0236@waikato.ac.n [University of Waikato, Department of Mathematics (New Zealand); Miller, W.; Post, S. [University of Minnesota, School of Mathematics (United States)

2010-02-15

275

Gaussian laser beam profile shaping  

Microsoft Academic Search

A method for converting single-mode Gaussian beams into beams with uniform irradiance profiles is described. The design is based on a Fourier transform relation between the input and output beam functions. The efficacy of the solution is shown to depend on a parameter that contains the product of the widths of the input and output beams. Problems associated with errors

Fred M. Dickey; S. C. Holswade

1996-01-01

276

Non-gaussian shape recognition  

NASA Astrophysics Data System (ADS)

A detection of primordial non-Gaussianity could transform our understanding of the fundamental theory of inflation. The precision promised by upcoming cosmic microwave background (CMB) and large-scale structure (LSS) surveys raises a natural question: if a detection given a particular template is made, what does this truly tell us about the underlying theory? Even in the case of non-detections and upper bounds on deviations from Gaussianity, what can we then infer about the viable theories that remain? In this paper we present a systematic way to constrain a wide range of non-Gaussian shapes, including general single and multi-field models and models with excited initial states. We present a separable, divergent basis able to recreate many shapes in the literature to high accuracy with between three and seven basis functions. The basis allows shapes to be grouped into broad ''template classes'', satisfying theoretically-relevant priors on their divergence properties in the squeezed limit. We forecast how well a Planck-like CMB survey could not only detect a general non-Gaussian signal but discern more about its shape, using existing templates and new ones we propose. This approach offers an opportunity to tie together minimal theoretical priors with observational constraints on the shape in general, and in the squeezed limit, to gain a deeper insight into what drove inflation.

Byun, Joyce; Bean, Rachel

2013-09-01

277

Connectivity of a Gaussian network  

Microsoft Academic Search

Following Etherington, Hoge and Parkes, we consider a network consisting of (approximately) N transceivers in the plane R2 distributed randomly with density given by a Gaussian distribution about the origin, and assume each transceiver can communicate with all other transceivers within distance s. We give bounds for the distance from the origin to the furthest transceiver connected to the origin,

Paul N. Balister; Béla Bollobás; Amites Sarkar; Mark Walters

2008-01-01

278

Gaussian Wave Packet: Step Scattering  

NSDL National Science Digital Library

The Gaussian Wave Packet: Step Scattering model simulates the time evolution of a free Gaussian wave packet in position space when it is incident on a potential energy step.  The position-space wave functions are depicted using three colors on the graph: black which depicts the absolute square of the wave function, blue which depicts the real part of the wave function, and red which depicts the imaginary part of the wave function. The user may change the height of the potential step or the wave packet energy by dragging circles on the energy graph. The initial width of the packet may also be changed. Also shown are the theoretical and calculated transmission and reflection coefficients. The Gaussian Wave Packet: Step Scattering model was created using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_qm_gaussian_step.jar file will run the program if Java is installed.

Palop, Jose I.

2010-12-13

279

Combined control-structure optimization  

NASA Technical Reports Server (NTRS)

An approach for combined control-structure optimization keyed to enhancing early design trade-offs is outlined and illustrated by numerical examples. The approach employs a homotopic strategy and appears to be effective for generating families of designs that can be used in these early trade studies. Analytical results were obtained for classes of structure/control objectives with linear quadratic Gaussian (LQG) and linear quadratic regulator (LQR) costs. For these, researchers demonstrated that global optima can be computed for small values of the homotopy parameter. Conditions for local optima along the homotopy path were also given. Details of two numerical examples employing the LQR control cost were given showing variations of the optimal design variables along the homotopy path. The results of the second example suggest that introducing a second homotopy parameter relating the two parts of the control index in the LQG/LQR formulation might serve to enlarge the family of Pareto optima, but its effect on modifying the optimal structural shapes may be analogous to the original parameter lambda.

Salama, M.; Milman, M.; Bruno, R.; Scheid, R.; Gibson, S.

1989-01-01

280

The period function of reversible quadratic centers  

NASA Astrophysics Data System (ADS)

In this paper we investigate the bifurcation diagram of the period function associated to a family of reversible quadratic centers, namely the dehomogenized Loud's systems. The local bifurcation diagram of the period function at the center is fully understood using the results of Chicone and Jacobs [C. Chicone, M. Jacobs, Bifurcation of critical periods for plane vector fields, Trans. Amer. Math. Soc. 312 (1989) 433-486]. Most of the present paper deals with the local bifurcation diagram at the polycycle that bounds the period annulus of the center. The techniques that we use here are different from the ones in [C. Chicone, M. Jacobs, Bifurcation of critical periods for plane vector fields, Trans. Amer. Math. Soc. 312 (1989) 433-486] because, while the period function extends analytically at the center, it has no smooth extension to the polycycle. At best one can hope that it has some asymptotic expansion. Another major difficulty is that the asymptotic development has to be uniform with respect to the parameters, in order to prove that a parameter is not a bifurcation value. We study also the bifurcations in the interior of the period annulus and we show that there exist three germs of curves in the parameter space that correspond to this type of bifurcation. Moreover we determine some regions in the parameter space for which the corresponding period function has at least one or two critical periods. Finally we propose a complete conjectural bifurcation diagram of the period function of the dehomogenized Loud's systems. Our results can also be viewed as a contribution to the proof of Chicone's conjecture [C. Chicone, review in MathSciNet, ref. 94h:58072].

Mardeši?, P.; Marín, D.; Villadelprat, J.

281

GAUSSIAN BEAM LASER RESONATOR PROGRAM  

NASA Technical Reports Server (NTRS)

In designing a laser cavity, the laser engineer is frequently concerned with more than the stability of the resonator. Other considerations include the size of the beam at various optical surfaces within the resonator or the performance of intracavity line-narrowing or other optical elements. Laser resonators obey the laws of Gaussian beam propagation, not geometric optics. The Gaussian Beam Laser Resonator Program models laser resonators using Gaussian ray trace techniques. It can be used to determine the propagation of radiation through laser resonators. The algorithm used in the Gaussian Beam Resonator program has three major components. First, the ray transfer matrix for the laser resonator must be calculated. Next calculations of the initial beam parameters, specifically, the beam stability, the beam waist size and location for the resonator input element, and the wavefront curvature and beam radius at the input surface to the first resonator element are performed. Finally the propagation of the beam through the optical elements is computed. The optical elements can be modeled as parallel plates, lenses, mirrors, dummy surfaces, or Gradient Index (GRIN) lenses. A Gradient Index lens is a good approximation of a laser rod operating under a thermal load. The optical system may contain up to 50 elements. In addition to the internal beam elements the optical system may contain elements external to the resonator. The Gaussian Beam Resonator program was written in Microsoft FORTRAN (Version 4.01). It was developed for the IBM PS/2 80-071 microcomputer and has been implemented on an IBM PC compatible under MS DOS 3.21. The program was developed in 1988 and requires approximately 95K bytes to operate.

Cross, P. L.

1994-01-01

282

Basic Tools: Integration by Gaussian Quadrature.  

ERIC Educational Resources Information Center

Provides examples of nested subroutines, focusing on the Gaussian quadrature function and test program (program listings included). Nested subroutines, features of the Gaussian quadrature, and when not to use it are considered. (JN)

Thompson, H. Bradford; Tuttle, Caroline

1984-01-01

283

Hole Gratings and Diffraction of Gaussian Beams.  

National Technical Information Service (NTIS)

Methods for the determination of waist size and position for Gaussian beams are summarized and an alternative method which applies to pulse systems was proposed and tested. The general theory of Fraunhofer diffraction of Gaussian beams was developed which...

T. A. Wiggins

1986-01-01

284

Gaussian 3X (G3X) theory using coupled cluster and Brueckner doubles energies.  

SciTech Connect

Variations of Gaussian-3X (G3X) theory are presented having the quadratic configuration interaction (QCISD(T)) energy calculation replaced by either a coupled cluster (CCSD(T)) or Brueckner (BD(T)) energy. This modification is reported for several G3X methods including G3X, G3X(MP3), G3X(MP2), G3SX, and G3SX(MP3). In most cases the replacement of the QCISD(T) energy by one of these alternative energies results in a slight improvement in the accuracy of these methods as assessed on the G3/99 test set of molecules. These new G3X methods are useful alternatives to the G3X methods based on quadratic configuration interaction.

Curtiss, L. A.; Redfern, P. C.; Raghavachari, K.; Pople, J. A.; Agere Systems; Northwestern Univ.

2002-06-27

285

How many eigenvalues of a Gaussian random matrix are positive?  

SciTech Connect

We study the probability distribution of the index N{sub +}, i.e., the number of positive eigenvalues of an NxN Gaussian random matrix. We show analytically that, for large N and large N{sub +} with the fraction 0{<=}c=N{sub +}/N{<=}1 of positive eigenvalues fixed, the index distribution P(N{sub +}=cN,N){approx}exp[-{beta}N{sup 2}{Phi}(c)] where {beta} is the Dyson index characterizing the Gaussian ensemble. The associated large deviation rate function {Phi}(c) is computed explicitly for all 0{<=}c{<=}1. It is independent of {beta} and displays a quadratic form modulated by a logarithmic singularity around c=1/2. As a consequence, the distribution of the index has a Gaussian form near the peak, but with a variance {Delta}(N) of index fluctuations growing as {Delta}(N){approx}lnN/{beta}{pi}{sup 2} for large N. For {beta}=2, this result is independently confirmed against an exact finite-N formula, yielding {Delta}(N)=lnN/2{pi}{sup 2}+C+O(N{sup -1}) for large N, where the constant C for even N has the nontrivial value C=({gamma}+1+3ln2)/2{pi}{sup 2}{approx_equal}0.185 248... and {gamma}=0.5772... is the Euler constant. We also determine for large N the probability that the interval [{zeta}{sub 1},{zeta}{sub 2}] is free of eigenvalues. Some of these results have been announced in a recent letter [Phys. Rev. Lett. 103, 220603 (2009)].

Majumdar, Satya N.; Nadal, Celine [Laboratoire de Physique Theorique et Modeles Statistiques (UMR 8626 du CNRS), Universite Paris-Sud, Batiment 100, 91405 Orsay Cedex (France); Scardicchio, Antonello [Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste (Italy); INFN, Sezione di Trieste, Strada Costiera 11, 34151 Trieste (Italy); Vivo, Pierpaolo [Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste (Italy)

2011-04-15

286

Regular zeros of quadratic maps and their application  

SciTech Connect

Sufficient conditions for the existence of regular zeros of quadratic maps are obtained. Their applications are indicated to certain problems of analysis related to the inverse function theorem in a neighbourhood of an abnormal point. Bibliography: 13 titles.

Arutyunov, Aram V; Karamzin, Dmitry Yu

2011-06-30

287

Integrable Hamiltonian systems and interactions through quadratic constraints  

Microsoft Academic Search

On-invariant classical relativistic field theories in one time and one space dimension with interactions that are entirely due to quadratic constraints are shown to be closely related to integrable Hamiltonian systems.

K. Pohlmeyer

1976-01-01

288

Linear State Feedback, Quadratic Weights, and Closed Loop Eigenstructures.  

National Technical Information Service (NTIS)

Equations are derived for the angles of general multivariable root loci and linear quadratic optimal root loci, including angles of departure and approach. The generalized eigenvalue problem is used to compute angles of approach. Equations are also derive...

P. M. Thompson

1980-01-01

289

Piecewise-quadratic and piecewise-linear Lyapunov functions for discontinuous systems  

Microsoft Academic Search

This paper develops necessary and sufficient conditions for the existence of Lyapunov functions of tho Lur'e type (‘ piecewise-quadratic ’) for relay-control systems and gives explicit formulae- for ‘optimum ’functions of this form for estimating regions of asymptotic stability in special cases, comparing these with results of numerical optimization. Certain similarities and advantages of ‘piecewise-linear ’Lyapunov functions are discussed. Among

STEIN WEISSENBERGER

1969-01-01

290

Mobility of Discrete Solitons in Quadratically Nonlinear Media  

Microsoft Academic Search

We study the mobility of solitons in lattices with quadratic (chi(2), alias second-harmonic-generating) nonlinearity. Using the notion of the Peierls-Nabarro potential and systematic numerical simulations, we demonstrate that, in contrast with their cubic (chi(3)) counterparts, the discrete quadratic solitons are mobile not only in the one-dimensional (1D) setting, but also in two dimensions (2D), in any direction. We identify parametric

H. Susanto; P. G. Kevrekidis; R. Carretero-González; B. A. Malomed; D. J. Frantzeskakis

2007-01-01

291

Bipartite and Multipartite Entanglement of Gaussian States  

Microsoft Academic Search

In this chapter we review the characterization of entanglement in Gaussian states of continuous variable systems. For two-mode Gaussian states, we discuss how their bipartite entanglement can be accurately quantified in terms of the global and local amounts of mixedness, and efficiently estimated by direct measurements of the associated purities. For multimode Gaussian states endowed with local symmetry with respect

Gerardo Adesso; Fabrizio Illuminati

2005-01-01

292

Monogamy Inequality for Distributed Gaussian Entanglement  

Microsoft Academic Search

We show that for all n-mode Gaussian states of continuous variable systems, the entanglement shared among n parties exhibits the fundamental monogamy property. The monogamy inequality is proven by introducing the Gaussian tangle, an entanglement monotone under Gaussian local operations and classical communication, which is defined in terms of the squared negativity in complete analogy with the case of n-qubit

Tohya Hiroshima; Gerardo Adesso; Fabrizio Illuminati

2007-01-01

293

Gaussian statistics for palaeomagnetic vectors  

USGS Publications Warehouse

With the aim of treating the statistics of palaeomagnetic directions and intensities jointly and consistently, we represent the mean and the variance of palaeomagnetic vectors, at a particular site and of a particular polarity, by a probability density function in a Cartesian three-space of orthogonal magnetic-field components consisting of a single (unimoda) non-zero mean, spherically-symmetrical (isotropic) Gaussian function. For palaeomagnetic data of mixed polarities, we consider a bimodal distribution consisting of a pair of such symmetrical Gaussian functions, with equal, but opposite, means and equal variances. For both the Gaussian and bi-Gaussian distributions, and in the spherical three-space of intensity, inclination, and declination, we obtain analytical expressions for the marginal density functions, the cumulative distributions, and the expected values and variances for each spherical coordinate (including the angle with respect to the axis of symmetry of the distributions). The mathematical expressions for the intensity and off-axis angle are closed-form and especially manageable, with the intensity distribution being Rayleigh-Rician. In the limit of small relative vectorial dispersion, the Gaussian (bi-Gaussian) directional distribution approaches a Fisher (Bingham) distribution and the intensity distribution approaches a normal distribution. In the opposite limit of large relative vectorial dispersion, the directional distributions approach a spherically-uniform distribution and the intensity distribution approaches a Maxwell distribution. We quantify biases in estimating the properties of the vector field resulting from the use of simple arithmetic averages, such as estimates of the intensity or the inclination of the mean vector, or the variances of these quantities. With the statistical framework developed here and using the maximum-likelihood method, which gives unbiased estimates in the limit of large data numbers, we demonstrate how to formulate the inverse problem, and how to estimate the mean and variance of the magnetic vector field, even when the data consist of mixed combinations of directions and intensities. We examine palaeomagnetic secular-variation data from Hawaii and Re??union, and although these two sites are on almost opposite latitudes, we find significant differences in the mean vector and differences in the local vectorial variances, with the Hawaiian data being particularly anisotropic. These observations are inconsistent with a description of the mean field as being a simple geocentric axial dipole and with secular variation being statistically symmetrical with respect to reflection through the equatorial plane. Finally, our analysis of palaeomagnetic acquisition data from the 1960 Kilauea flow in Hawaii and the Holocene Xitle flow in Mexico, is consistent with the widely held suspicion that directional data are more accurate than intensity data.

Love, J. J.; Constable, C. G.

2003-01-01

294

Roundoff noise and scaling in the digital implementation of control compensators  

NASA Technical Reports Server (NTRS)

Researchers in digital signal processing have examined at length the effects of finite wordlength in the design of digital filters. The issues that have been considered apply to any digital system. In particular, the design of digital control systems must consider these issues. The paper will use, adapt, and extend the ideas developed in digital signal processing to the issue of roundoff noise in digital linear-quadratic-Gaussian (LQG) compensators. The roundoff noise effects for a particular LQG example and several different implementation structures will be then examined.

Moroney, P.; Willsky, A. S.; Houpt, P. K.

1983-01-01

295

Turbofan engine control system design using the LQG/LTR methodology  

NASA Technical Reports Server (NTRS)

Application of the linear-quadratic-Gaussian with loop-transfer-recovery methodology to design of a control system for a simplified turbofan engine model is considered. The importance of properly scaling the plant to achieve the desired target feedback loop is emphasized. The steps involved in the application of the methodology are discussed via an example, and evaluation results are presented for a reduced-order compensator. The effect of scaling the plant on the stability robustness evaluation of the closed-loop system is studied in detail.

Garg, Sanjay

1989-01-01

296

Turbofan engine control system design using the LQG/LTR methodology  

NASA Technical Reports Server (NTRS)

Application of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery methodology to design of a control system for a simplified turbofan engine model is considered. The importance of properly scaling the plant to achieve the desired Target-Feedback-Loop is emphasized. The steps involved in the application of the methodology are discussed via an example, and evaluation results are presented for a reduced-order compensator. The effect of scaling the plant on the stability robustness evaluation of the closed-loop system is studied in detail.

Garg, Sanjay

1989-01-01

297

Overview of computational control research at UT Austin  

NASA Technical Reports Server (NTRS)

An overview of current research activities at UT Austin is presented to discuss certain technical issues in the following areas: (1) Computer-Aided Nonlinear Control Design: In this project, the describing function method is employed for the nonlinear control analysis and design of a flexible spacecraft equipped with pulse modulated reaction jets. INCA program has been enhanced to allow the numerical calculation of describing functions as well as the nonlinear limit cycle analysis capability in the frequency domain; (2) Robust Linear Quadratic Gaussian (LQG) Compensator Synthesis: Robust control design techniques and software tools are developed for flexible space structures with parameter uncertainty. In particular, an interactive, robust multivariable control design capability is being developed for INCA program; and (3) LQR-Based Autonomous Control System for the Space Station: In this project, real time implementation of LQR-based autonomous control system is investigated for the space station with time-varying inertias and with significant multibody dynamic interactions.

Bong, Wie

1989-01-01

298

Selecting Knots Locally for Curve Interpolation with Quadratic Precision  

NASA Astrophysics Data System (ADS)

There are several prevailing methods for selecting knots for curve interpolation. A desirable criterion for knot selection is whether the knots can assist an interpolation scheme to achieve the reproduction of polynomial curves of certain degree if the data points to be interpolated are taken from such a curve. For example, if the data points are sampled from an underlying quadratic polynomial curve, one would wish to have the knots selected such that the resulting interpolation curve reproduces the underlying quadratic curve; and in this case the knot selection scheme is said to have quadratic precision. In this paper we propose a local method for determining knots with quadratic precision. This method improves on upon our previous method that entails the solution of a global equation to produce a knot sequence with quadratic precision. We show that this new knot selection scheme results in better interpolation error than other existing methods, including the chord-length method, the centripetal method and Foley's method, which do not possess quadratic precision.

Caiming, Zhang; Wenping, Wang; Jiaye, Wang; Xuemei, Li

299

Analytically reduced form of multicenter integrals from Gaussian transforms. [in atomic and molecular physics  

NASA Technical Reports Server (NTRS)

The four-dimensional Fourier-Feynman transformations previously used in analytically reducing the general class of integrals containing multicenter products of 1s hydrogenic orbitals, Coulomb or Yukawa potentials, and plane waves, are replaced by the one-dimensional Gaussian transformation. This reduces the previously required double-diagonalization of the quadratic form of the multicenter integrals to only one diagonalization, yielding a simpler reduced form of the integral. The present work also extends the result to include all s states and pairs of states with l not equal to zero summed over the m quantum number.

Straton, Jack C.

1989-01-01

300

Issues in the digital implementation of control compensators. Ph.D. Thesis  

NASA Technical Reports Server (NTRS)

Techniques developed for the finite-precision implementation of digital filters were used, adapted, and extended for digital feedback compensators, with particular emphasis on steady state, linear-quadratic-Gaussian compensators. Topics covered include: (1) the linear-quadratic-Gaussian problem; (2) compensator structures; (3) architectural issues: serialism, parallelism, and pipelining; (4) finite wordlength effects: quantization noise, quantizing the coefficients, and limit cycles; and (5) the optimization of structures.

Moroney, P.

1979-01-01

301

Gaussian Sum PHD Filtering Algorithm for Nonlinear Non-Gaussian Models  

Microsoft Academic Search

A new multi-target filtering algorithm, termed as the Gaussian sum probability hypothesis density (GSPHD) filter, is proposed for nonlinear non-Gaussian tracking models. Provided that the initial prior intensity of the states is Gaussian or can be identified as a Gaus-sian sum, the analytical results of the algorithm show that the posterior intensity at any subsequent time step remains a Gaussian

Yin Jianjun; Zhang Jianqiu; Zhuang Zesen

2008-01-01

302

Quantum versus classical correlations in Gaussian states.  

PubMed

Quantum discord, a measure of genuinely quantum correlations, is generalized to continuous variable systems. For all two-mode Gaussian states, we calculate analytically the quantum discord and a related measure of classical correlations, solving an optimization over all Gaussian measurements. Almost all two-mode Gaussian states are shown to have quantum correlations, while for separable states, the discord is smaller than unity. For a given amount of entanglement, it admits tight upper and lower bounds. Via a duality between entanglement and classical correlations, we derive a closed formula for the Gaussian entanglement of formation of a family of three-mode Gaussian states. PMID:20867753

Adesso, Gerardo; Datta, Animesh

2010-07-16

303

Dissipation-induced pure Gaussian state  

NASA Astrophysics Data System (ADS)

This paper provides some necessary and sufficient conditions for a general Markovian Gaussian master equation to have a unique pure steady state. The conditions are described by simple matrix equations; thus the so-called environment engineering problem for pure-Gaussian-state preparation can be straightforwardly dealt with in the linear algebraic framework. In fact, based on one of those conditions, for an arbitrary given pure Gaussian state, we obtain a complete parametrization of the Gaussian master equation having that state as a unique steady state; this leads to a systematic procedure for engineering a desired dissipative system. We demonstrate some examples including Gaussian cluster states.

Koga, Kei; Yamamoto, Naoki

2012-02-01

304

Spatial superpositions of Gaussian beams  

NASA Astrophysics Data System (ADS)

We explore an interferometric beam shaping technique that considers the coaxial superposition of two Gaussian beams. This technique is traditionally implemented in a Mach-Zehnder interferometer; however, to avoid phase shift drift due to vibrations and thermal effects we employ amplitude and phase modulation with a spatial light modulator (SLM) to achieve the beam shaping. We consider two Gaussian beams of equal but opposite curvature that possess the same phase and width incident on a focusing lens. At the plane of the lens we obtain a multi-ringed beam with a central intensity maximum which develops into a multi-ringed beam with a central null at the focal plane of the lens. The interesting feature of this beam is that it possesses two focal spots on either side of the focal plane of the lens. We investigate obstructing the beam at the focal plane of the lens and by carefully selecting the free parameters we obtain an unobstructed second focus while the equivalent Gaussian beam is sufficiently obstructed.

Naidoo, Darryl; Godin, Thomas; Fromager, Michael; Aît-Ameur, Kamel; Forbes, Andrew

2014-02-01

305

Gradient-Based Adaptation of General Gaussian Kernels  

Microsoft Academic Search

Gradient-based optimizing of gaussian kernel functions is considered. The gradient for the adaptation of scaling and rotation of the input space is computed to achieve invariance against linear transformations. This is done by using the exponential map as a parameterization of the kernel parameter manifold. By restricting the optimization to a constant trace subspace, the kernel size can be controlled.

Tobias Glasmachers; Christian Igel

2005-01-01

306

A linear quadratic regulator approach to the stabilization of uncertain linear systems  

NASA Technical Reports Server (NTRS)

This paper presents a linear quadratic regulator approach to the stabilization of uncertain linear systems. The uncertain systems under consideration are described by state equations with the presence of time-varying unknown-but-bounded uncertainty matrices. The method is based on linear quadratic regulator (LQR) theory and Liapunov stability theory. The robust stabilizing control law for a given uncertain system can be easily constructed from the symmetric positive-definite solution of the associated augmented Riccati equation. The proposed approach can be applied to matched and/or mismatched systems with uncertainty matrices in which only their matrix norms are bounded by some prescribed values and/or their entries are bounded by some prescribed constraint sets. Several numerical examples are presented to illustrate the results.

Shieh, L. S.; Sunkel, J. W.; Wang, Y. J.

1990-01-01

307

Ellipsometric investigation of quadratic electrooptic and electrostrictive effects with anodic niobium pentoxide films.  

PubMed

Anodic oxide films on niobium were studied in situ during formation using a computer-controlled ellipsometer at a wavelength of 6328 A. They were found to be optically homogeneous, isotropic, and nonabsorbing with no field applied but to become anisotropic (optically uniaxial with optic axis normal to the film surface) with field applied. The ordinary and extraordinary indices decreased, and the thickness increased quadratically with applied field. Values are reported for the refractive index of niobium and of the oxide, and these are compared with previous reports. The quadratic electrooptic coefficients for the oxide are reported and are of the same order of magnitude as those for oxygen-octahedra ferroelectrics and somewhat greater than the values for tantalum pentoxide films. PMID:20154823

Yee, K K; Young, L

1975-06-01

308

Spatial Gaussian process regression with mobile sensor networks.  

PubMed

This paper presents a method of using Gaussian process regression to model spatial functions for mobile wireless sensor networks. A distributed Gaussian process regression (DGPR) approach is developed by using a sparse Gaussian process regression method and a compactly supported covariance function. The resultant formulation of the DGPR approach only requires neighbor-to-neighbor communication, which enables each sensor node within a network to produce the regression result independently. The collective motion control is implemented by using a locational optimization algorithm, which utilizes the information entropy from the DGPR result. The collective mobility of sensor networks plus the online learning capability of the DGPR approach also enables the mobile sensor network to adapt to spatiotemporal functions. Simulation results are provided to show the performance of the proposed approach in modeling stationary spatial functions and spatiotemporal functions. PMID:24807524

Gu, Dongbing; Hu, Huosheng

2012-08-01

309

Computational methods for optimal linear-quadratic compensators for infinite dimensional discrete-time systems  

NASA Technical Reports Server (NTRS)

An abstract approximation theory and computational methods are developed for the determination of optimal linear-quadratic feedback control, observers and compensators for infinite dimensional discrete-time systems. Particular attention is paid to systems whose open-loop dynamics are described by semigroups of operators on Hilbert spaces. The approach taken is based on the finite dimensional approximation of the infinite dimensional operator Riccati equations which characterize the optimal feedback control and observer gains. Theoretical convergence results are presented and discussed. Numerical results for an example involving a heat equation with boundary control are presented and used to demonstrate the feasibility of the method.

Gibson, J. S.; Rosen, I. G.

1986-01-01

310

Gaussianity of LISA's confusion backgrounds  

SciTech Connect

Data analysis for the proposed Laser Interferometer Space Antenna (LISA) will be complicated by the huge number of sources in the LISA band. In the frequency band {approx}10{sup -4}-2x10{sup -3} Hz, galactic white dwarf binaries (GWDBs) are sufficiently dense in frequency space that it will be impossible to resolve most of them, and ''confusion noise'' from the unresolved Galactic binaries will dominate over instrumental noise in determining LISA's sensitivity to other sources in that band. Confusion noise from unresolved extreme-mass-ratio inspirals (EMRIs) could also contribute significantly to LISA's total noise curve. To date, estimates of the effect of LISA's confusion noise on matched-filter searches and their detection thresholds have generally approximated the noise as Gaussian, based on the central limit theorem. However in matched-filter searches, the appropriate detection threshold for a given class of signals may be located rather far out on the tail of the signal-to-noise probability distribution, where a priori it is unclear whether the Gaussian approximation is reliable. Using the Edgeworth expansion and the theory of large deviations, we investigate the probability distribution of the usual matched-filter detection statistic, far out on the tail of the distribution. We apply these tools to four somewhat idealized versions of LISA data searches: searches for EMRI signals buried in GWDB confusion noise, and searches for massive black hole binary signals buried in (i) GWDB noise, (ii) EMRI noise, and (iii) a sum of EMRI noise and Gaussian noise. Assuming reasonable short-distance cutoffs in the populations of confusion sources (since the very closest and hence strongest sources will be individually resolvable), modifications to the appropriate detection threshold, due to the non-Gaussianity of the confusion noise, turn out to be quite small for realistic cases. The smallness of the correction is partly due to the fact that these three types of sources evolve on quite different time scales, so no single background source closely resembles any search template. We also briefly discuss other types of LISA searches where the non-Gaussianity of LISA's confusion backgrounds could perhaps have a much greater impact on search reliability and efficacy.

Racine, Etienne [Department of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, California 91125 (United States); Cutler, Curt [Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109 (United States)

2007-12-15

311

A transient, quadratic nodal method for triangular-Z geometry  

SciTech Connect

Many systematically-derived nodal methods have been developed for Cartesian geometry due to the extensive interest in Light Water Reactors. These methods typically model the transverse-integrated flux as either an analytic or low order polynomial function of position within the node. Recently, quadratic nodal methods have been developed for R-Z and hexagonal geometry. A static and transient quadratic nodal method is developed for triangular-Z geometry. This development is particularly challenging because the quadratic expansion in each node must be performed between the node faces and the triangular points. As a consequence, in the 2-D plane, the flux and current at the points of the triangles must be treated. Quadratic nodal equations are solved using a non-linear iteration scheme, which utilizes the corrected, mesh-centered finite difference equations, and forces these equations to match the quadratic equations by computing discontinuity factors during the solution. Transient nodal equations are solved using the improved quasi-static method, which has been shown to be a very efficient solution method for transient problems. Several static problems are used to compare the quadratic nodal method to the Coarse Mesh Finite Difference (CMFD) method. The quadratic method is shown to give more accurate node-averaged fluxes. However, it appears that the method has difficulty predicting node leakages near reactor boundaries and severe material interfaces. The consequence is that the eigenvalue may be poorly predicted for certain reactor configurations. The transient methods are tested using a simple analytic test problem, a heterogeneous heavy water reactor benchmark problem, and three thermal hydraulic test problems. Results indicate that the transient methods have been implemented correctly.

DeLorey, T.F.

1993-06-01

312

A non-linear programming approach to the computer-aided design of regulators using a linear-quadratic formulation  

NASA Technical Reports Server (NTRS)

A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a non-linear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer-aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer.

Fleming, P.

1985-01-01

313

Gaussian, Hermite-Gaussian, and Laguerre-Gaussian beams: A primer  

Microsoft Academic Search

The paper aims at presenting a didactic and self-contained overview of Gauss-Hermite and Gauss-Laguerre laser beam modes. The usual textbook approach for deriving these modes is to solve the Helmoltz electromagnetic wave equation within the paraxial approximation. Here, a different technique is presented: Using the plane wave representation of the fundamental Gaussian mode as seed function, all higher-order beam modes

Francesco Pampaloni; Joerg Enderlein

2004-01-01

314

Solving POMDPs using quadratically constrained linear programs  

Microsoft Academic Search

Developing scalable algorithms for solving partially observ- able Markov decision processes (POMDPs) is an important challenge. One promising approach is based on representing POMDP policies as finite-state controllers. This method has been used successfully to address the intractable memory re- quirements of POMDP algorithms. We illustrate some fun- damental theoretical limitations of existing techniques that use controllers. We then propose

Christopher Amato; Daniel S. Bernstein; Shlomo Zilberstein

2006-01-01

315

Non-Gaussianity in the cosmic microwave background induced by dipolar dark matter  

NASA Astrophysics Data System (ADS)

In previous work [L. Blanchet and A. Le Tiec, Phys. Rev. D 80 (2009) 023524], motivated by the phenomenology of dark matter at galactic scales, a model of dipolar dark matter (DDM) was introduced. At linear order in cosmological perturbations, the dynamics of the DDM was shown to be identical to that of standard cold dark matter (CDM). In this paper, the DDM model is investigated at second order in cosmological perturbation theory. We find that the internal energy of the DDM fluid modifies the curvature perturbation generated by CDM with a term quadratic in the dipole field. This correction induces a new type of non-Gaussianity in the bispectrum of the curvature perturbation with respect to standard CDM. Leaving unspecified the primordial amplitude of the dipole field, which could in principle be determined by a more fundamental description of DDM, we find that, in contrast with usual models of primordial non-Gaussianities, the non-Gaussianity induced by DDM increases with time after the radiation-matter equality on super-Hubble scales. This distinctive feature of the DDM model, as compared with standard CDM, could thus provide a specific signature in the CMB and large-scale structure probes of non-Gaussianity.

Blanchet, Luc; Langlois, David; Le Tiec, Alexandre; Marsat, Sylvain

2013-02-01

316

Integrated optimization of actuator placement and vibration control for piezoelectric adaptive trusses  

NASA Astrophysics Data System (ADS)

In this paper, the integrated optimization of actuator placement and vibration control for piezoelectric adaptive truss is studied. Based on the dynamic finite element (FE) model and a linear-quadratic-Gaussian (LQG) model of vibration control for an adaptive truss, an integrated optimization model is built in which an improved quadratic performance index is adopted as the objective function and the mode closed-loop damping ratio, modal controllability and actuator number are selected as the constraints. A layered optimization strategy is implemented to address this optimization problem with discrete-continuous design variable. To prevent the optimization process from converging to the local optimal solution, the genetic algorithm (GA) for outside-layer optimization is extended with an improved penalty function. Numerical examples and the vibration control experiments for piezoelectric adaptive truss were used to validate the efficiency of the proposed method. The following conclusions were drawn from the results. (1) The improved penalty function can orient the optimization process to the global optimal solution. (2) Although the number of struts on the truss is large, the optimization computation time is short because of the high efficiency of the proposed method. (3) In the experiment, the quadratic performance index, modal response and sensor signals for the present paper's optimal actuator placement scheme are better than those described in the literature, but the placement requires more energy, which is consistent with the numerical results.

Li, W. P.; Huang, H.

2013-01-01

317

Quadratic Integrate-and-Fire Neuron Network Model  

NSDL National Science Digital Library

The Quadratic Integrate-and-Fire Neuron Network Model uses a network of Quadratic Integrate-and-Fire neurons to demonstrate how connectivity influences network synchrony. The user selects the number of neurons and the degree of connectivity, and can see how the neurons synchronize over time. In addition, the user can watch the potential of a single neuron. Although the dynamics of a single neuron do not change, the network architecture has a dramatic effect on how quickly the neurons will synchronize. The Quadratic Integrate-and-Fire Neuron Network Model was developed using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the jar file will run the program if Java is installed. You can modify this simulation if you have EJS installed by right-clicking within the map and selecting "Open Ejs Model" from the pop-up menu item.

Thomson, Colin F.

2012-12-22

318

Quadratic algebra approach to relativistic quantum Smorodinsky-Winternitz systems  

SciTech Connect

There exists a relation between the Klein-Gordon and the Dirac equations with scalar and vector potentials of equal magnitude and the Schroedinger equation. We obtain the relativistic energy spectrum for the four relativistic quantum Smorodinsky-Winternitz systems from their quasi-Hamiltonian and the quadratic algebras studied by Daskaloyannis in the nonrelativistic context. We also apply the quadratic algebra approach directly to the initial Dirac equation for these four systems and show that the quadratic algebras obtained are the same than those obtained from the quasi-Hamiltonians. We point out how results obtained in context of quantum superintegrable systems and their polynomial algebras can be applied to the quantum relativistic case.

Marquette, Ian [Department of Mathematics, University of York, Heslington, York YO10 5DD (United Kingdom)

2011-04-15

319

Optofluidic generation of Laguerre-Gaussian beams  

PubMed Central

Laguerre-Gaussian (LG) beams have been extensively studied due to their unique structure, characterized by a phase singularity at the center of the beam. Common methods for generating such beams include the use of diffractive optical elements and spatial light modulators, which although offering excellent versatility, suffers from several drawbacks, including in many cases a low power damage threshold as well as complexity and expense. This paper presents a simple, low cost method for the generation of high-fidelity LG beams using rapid prototyping techniques. Our approach is based on a fluidic-hologram concept, whereby the properties of the LG beam can be finely controlled by varying the refractive-index of the fluid that flows through the hologram. This simple approach, while optimized here for LG beam generation, is also expected to find applications in the production of tunable fluidic optical trains.

Jeffries, Gavin D. M.; Milne, Graham; Zhao, Yiqiong; Lopez-Mariscal, Carlos; Chiu, Daniel T.

2010-01-01

320

Modelling geomagnetic reversals as a Gaussian Cox Process  

NASA Astrophysics Data System (ADS)

The mean rate of reversal of the geomagnetic field, as recorded in the Geomagnetic Polarity Time Scale (GPTS), has long been an object of study. The significance of the apparent long-term variations in the mean rate of reversals - including the occurrence of superchrons - has been debated, as has the possible origins of these variations in external control of the geodynamo (e.g. by the time-varying boundary conditions imposed by mantle convection). Here we model the long-term variations in the reversal rate nonparametrically, in terms of an inhomogeneous Poisson process. Specifically, we consider a Gaussian Cox process, a type of doubly-stochastic Poisson process where the mean rate (or intensity) is modelled in terms of a Gaussian process. Such processes are amenable to likelihood-based inference using Bayesian Markov Chain Monte-Carlo (MCMC) methods, which we employ to provide posterior distributions of the model parameters. The specification of a Gaussian process requires a covariance function, relating the intensity at nearby times; crucially, however, the timescale of the covariance function is not prescribed, but appears as a model hyperparameter, whose posterior distribution is an important output of the analysis. For the geodynamo, this hyperparameter should robustly characterise the timescale of long-term variations. Two different types of Gaussian Cox process are considered: a Log Gaussian Cox Process, applied to binned reversal data; and a Sigmoidal Gaussian Cox Process, applied to the discrete reversal data using a technique involving latent variables. Different MCMC algorithms for sampling the posterior distribution of the model parameters are investigated for both types of process, to check (and to optimise) the convergence of the MCMC chains. This analysis is applied to different records of the GPTS, including those of Cande & Kent (1995) and Gradstein & Ogg (1996). The implications of this analysis for the geodynamo, and the possibility of comparable analysis of the output of numerical geodynamo simulations, are discussed.

Sarson, Graeme; Boys, Richard; Golightly, Andrew; Henderson, Daniel

2013-04-01

321

A High-Authority/Low-Authority Control Strategy for Coupled Aircraft-Style Bays  

NASA Technical Reports Server (NTRS)

This paper presents a numerical investigation of an active structural acoustic control strategy for coupled aircraft-style bays. While structural coupling can destabilize or limit the performance of some model-based decentralized control systems, fullycoupled centralized control strategies are impractical for typical aircraft containing several hundred bays. An alternative is to use classical rate feedback with matched, collocated transducer pairs to achieve active damping. Unfortunately, due to the conservative nature of this strategy, stability is guaranteed at the expense of achievable noise reduction. Therefore, this paper describes the development of a combined control strategy using robust active damping in addition to a high-authority controller based on linear quadratic Gaussian (LQG) theory. The combined control system is evaluated on a tensioned, two-bay model using piezoceramic actuators and ideal point velocity sensors. Transducer placement on the two-bay structure is discussed, and the advantages of a combined control strategy are presented.

Schiller, N. H.; Fuller, C. R.; Cabell, R. H.

2006-01-01

322

Gaussian mass optimization for kernel PCA parameters  

NASA Astrophysics Data System (ADS)

This paper proposes a novel kernel parameter optimization method based on Gaussian mass, which aims to overcome the current brute force parameter optimization method in a heuristic way. Generally speaking, the choice of kernel parameter should be tightly related to the target objects while the variance between the samples, the most commonly used kernel parameter, doesn't possess much features of the target, which gives birth to Gaussian mass. Gaussian mass defined in this paper has the property of the invariance of rotation and translation and is capable of depicting the edge, topology and shape information. Simulation results show that Gaussian mass leads a promising heuristic optimization boost up for kernel method. In MNIST handwriting database, the recognition rate improves by 1.6% compared with common kernel method without Gaussian mass optimization. Several promising other directions which Gaussian mass might help are also proposed at the end of the paper.

Liu, Yong; Wang, Zulin

2011-10-01

323

Mobility of Discrete Solitons in Quadratically Nonlinear Media  

NASA Astrophysics Data System (ADS)

We study the mobility of solitons in lattices with quadratic (?(2), alias second-harmonic-generating) nonlinearity. Using the notion of the Peierls-Nabarro potential and systematic numerical simulations, we demonstrate that, in contrast with their cubic (?(3)) counterparts, the discrete quadratic solitons are mobile not only in the one-dimensional (1D) setting, but also in two dimensions (2D), in any direction. We identify parametric regions where an initial kick applied to a soliton leads to three possible outcomes: staying put, persistent motion, or destruction. On the 2D lattice, the solitons survive the largest kick and attain the largest speed along the diagonal direction.

Susanto, H.; Kevrekidis, P. G.; Carretero-González, R.; Malomed, B. A.; Frantzeskakis, D. J.

2007-11-01

324

Selectable linear or quadratic coupling in an optomechanical system  

NASA Astrophysics Data System (ADS)

There has been much interest recently in the analysis of optomechanical systems incorporating dielectric nano- or microspheres inside a cavity field. We analyze here the situation when one of the mirrors of the cavity itself is also allowed to move. We reveal that the interplay between the two oscillators yields a cross-coupling that results in, e.g., appreciable cooling and squeezing of the motion of the sphere, despite its nominal quadratic coupling. We also discuss a simple modification that would allow this cross-coupling to be removed at will, thereby yielding a purely quadratic coupling for the sphere.

Xuereb, André; Paternostro, Mauro

2013-02-01

325

Remarks on quadratic bundles related to Hermitian symmetric spaces  

NASA Astrophysics Data System (ADS)

We consider quadratic bundles related to Hermitian symmetric spaces of the type SU(m+n)/S(U(m)×U(n)). We discuss the spectral properties of scattering operator, develop the direct scattering problem associated with it and stress on the effect of reduction on these. By applying a modification of Zakharov-Shabat's dressing procedure we demonstrate how one can obtain reflectionless potentials. That way one is able to generate soliton solutions to the nonlinear evolution equations belonging to the integrable hierarchy associated with quadratic bundles under study.

Valchev, Tihomir

2014-03-01

326

Monogamy inequality for distributed gaussian entanglement.  

PubMed

We show that for all n-mode Gaussian states of continuous variable systems, the entanglement shared among n parties exhibits the fundamental monogamy property. The monogamy inequality is proven by introducing the Gaussian tangle, an entanglement monotone under Gaussian local operations and classical communication, which is defined in terms of the squared negativity in complete analogy with the case of n-qubit systems. Our results elucidate the structure of quantum correlations in many-body harmonic lattice systems. PMID:17358836

Hiroshima, Tohya; Adesso, Gerardo; Illuminati, Fabrizio

2007-02-01

327

Quark and Lepton Masses from Gaussian Landscapes  

Microsoft Academic Search

The flavor structure of the Standard Model might arise from random selection\\u000aon a landscape. We propose a class of simple models, ``Gaussian landscapes,''\\u000awhere Yukawa couplings derive from overlap integrals of Gaussian wavefunctions\\u000aon extra-dimensions. Statistics of vacua are generated by scanning the peak\\u000apositions of these zero-modes, giving probability distributions for all flavor\\u000aobservables. Gaussian landscapes can broadly

Lawrence J. Hall; Michael P. Salem; Taizan Watari

2008-01-01

328

A Dynamical Systems Analysis of Semidefinite Programming with Application to Quadratic Optimization with Pure Quadratic Equality Constraints  

SciTech Connect

This paper considers the problem of minimizing a quadratic cost subject to purely quadratic equality constraints. This problem is tackled by first relating it to a standard semidefinite programming problem. The approach taken leads to a dynamical systems analysis of semidefinite programming and the formulation of a gradient descent flow which can be used to solve semidefinite programming problems. Though the reformulation of the initial problem as a semidefinite pro- gramming problem does not in general lead directly to a solution of the original problem, the initial problem is solved by using a modified flow incorporating a penalty function.

Orsi, R. J. [Department of Electrical and Electronic Engineering, University of Melbourne, Parkville, VIC 3052 (Australia); Mahony, R. E. [Heudiasyc - UTC UMR 6599, Centre de Recherche de Royallieu, BP 20529, 60205 Compiegne Cedex (France); Moore, J. B. [Department of Systems Engineering, RSISE, Australian National University, Canberra, ACT 0200 (Australia)

1999-09-15

329

Optimal and suboptimal detection of Gaussian signals in noise: asymptotic relative efficiency  

NASA Astrophysics Data System (ADS)

The performance of Bayesian detection of Gaussian signals using noisy observations is investigated via the error exponent for the average error probability. Under unknown signal correlation structure or limited processing capability it is reasonable to use the simple quadratic detector that is optimal in the case of an independent and identically distributed (i.i.d.) signal. Using the large deviations principle, the performance of this detector (which is suboptimal for non-i.i.d. signals) is compared with that of the optimal detector for correlated signals via the asymptotic relative efficiency defined as the ratio between sample sizes of two detectors required for the same performance in the large-sample-size regime. The effects of SNR on the ARE are investigated. It is shown that the asymptotic efficiency of the simple quadratic detector relative to the optimal detector converges to one as the SNR increases without bound for any bounded spectrum, and that the simple quadratic detector performs as well as the optimal detector for a wide range of the correlation values at high SNR.

Sung, Youngchul; Tong, Lang; Poor, H. V.

2005-08-01

330

Analytic solution of flat-top Gaussian and Laguerre-Gaussian laser field components.  

PubMed

We generalized the nonparaxial field components of Laguerre-Gaussian and flattened Gaussian beams obtained using the angular spectrum method to include symmetric radial and angular expansions and simplified them using an approximate evaluation of the integral equations for the field components. These field components possess series expressions in orders of a natural expansion parameter, which clarifies the physical interpretation of the series expansion. A connection between Laguerre-Gaussian and flat-top Gaussian profiles is obtained. PMID:20967101

Cerjan, Alexander; Cerjan, Charles

2010-10-15

331

Gaussian mixture PHD filter for jump Markov models based on best-fitting Gaussian approximation  

Microsoft Academic Search

A new Gaussian mixture probability hypothesis density (PHD) filter is developed for tracking multiple maneuvering targets that follow jump Markov models. This approach is based on the best-fitting Gaussian approximation which has been shown to be an accurate predictor of the interacting multiple model (IMM) performance. Compared with the existing Gaussian mixture multiple model PHD filter without interacting, simulations show

Wenling Li; Yingmin Jia

2011-01-01

332

A formal approach to the design of multibunch feedback systems: LQG controllers  

SciTech Connect

We formulate the multibunch feedback problem as a standard control-systems design problem and solve it using Linear Quadratic Gaussian (LQG) regulator theory. Use of a specific optimality criterion allows quantitative evaluation of different controllers and leads to the design of optimal LQG controllers. Computer simulations are used to show that, as compared to the existing Finite Impulse Response (FIR) control, LQG control can provide the same closed-loop damping for less peak power, thus making more effective use of limited kicker power. Furthermore, LQG control enables us to use more power to provide better damping without the problem of driving instabilities with higher loop gains. The code for the LQG filters described has been written for the Quick prototype installed at ALS.

Hindi, H.; Fox, J.; Prabhaker, S.; Sapozhnikov, L.; Oxoby, G.; Linscott, I.; Teytelman, D.

1994-06-01

333

Multivariable control of a forward swept wing aircraft. M.S. Thesis  

NASA Technical Reports Server (NTRS)

The impact of independent canard and flaperon control of the longitudinal axis of a generic forward swept wing aircraft is examined. The Linear Quadratic Gaussian (LQG)/Loop Transfer Recovery (LTR) method is used to design three compensators: two single-input-single-output (SISO) systems, one with angle of attack as output and canard as control, the other with pitch attitude as output and canard as control, and a two-input-two-output system with both canard and flaperon controlling both the pitch attitude and angle of attack. The performances of the three systems are compared showing the addition of flaperon control allows the aircraft to perform in the precision control modes with very little loss of command following accuracy.

Quinn, W. W.

1986-01-01

334

Frequency domain control design of large space structures: A practical approach  

NASA Technical Reports Server (NTRS)

Requirements indicate the need for much larger, more accurate, and in some cases, very dynamic satellites. Large control system bandwidths are needed to meet accuracy and response requirements while maintaining tight control over appendage oscillations. Studies in recent years have shown that linear quadratic Gaussian (LQG) controllers can achieve the desired performance if the system is linearized and if the system model is accurate. Results of an LQG controller applied to a single axis satellite with large solar arrays, are given. A reduced order model (ROM) comprises rigid body motion with dominant structural modes. Optimal control and estimation gains are calculated based on an extremely conservative 0.0005 critical damping ratio. In order to examine stability characteristics, single-input single-output (SISO) frequency response concepts are generalized to develop a method of displaying open loop frequency response of multi-input multi-output (MIMO) control system.

Harding, R.; Das, A.

1985-01-01

335

Relativistic nuclear matter with a quadratic scalar coupling  

Microsoft Academic Search

A coupling between the nucleon and the scalar meson, quadratic in the scalar field, has been added to the standard Walecka Lagrangian. The coupling constants have been determined to reproduce the binding energy and Fermi momentum of the empirical saturation point and the compression modulus of nuclear matter. Since this latter quantity has not yet been precisely determined, the model

J. C. Caillon; J. Labarsouque

1999-01-01

336

Quadratic phase coupling analysis for infrasound vehicle detection  

Microsoft Academic Search

The low attenuation characteristic of infrasound enables it to propagate long distances making it possible for the detection of infrasound sources. In this paper, a comparison in terms of the detection range between an acoustic microphone and an infrasound sensor in the context of vehicle detection is made. We propose to employ the bispectrum based quadratic phase coupling (QPC) analysis

Renshi Li; Vinod V. Reddy; Andy W. H. Khong

2010-01-01

337

An efficient method for quadratic Riccati differential equation  

NASA Astrophysics Data System (ADS)

In this paper, a new form of homotopy perturbation method (NHPM) has been adopted for solving the quadratic Riccati differential equation. In this technique, the solution is considered as a Taylor series expansion converges rapidly to the exact solution of the nonlinear equation. Having found the exact solution of the Riccati equation, the capability and the simplicity of the proposed technique is clarified.

Aminikhah, Hossein; Hemmatnezhad, Milad

2010-04-01

338

Efficient Color Histogram Indexing for Quadratic Form Distance Functions  

Microsoft Academic Search

In image retrieval based on color, the weighted distance between color histograms of two images, represented as a quadratic form, may be defined as a match measure. However, this distance measure is computationally expensive and it operates on high dimensional features (O(N)). We propose the use of low-dimensional, simple to compute distance measures between the color distributions, and show that

James L. Hafner; Harpreet S. Sawhney; William Equitz; Myron Flickner; Wayne Niblack

1995-01-01

339

ECONOMIC ACCEPTANCE SAMPLING BY VARIABLES WITH QUADRATIC QUALITY COSTS  

Microsoft Academic Search

An economic model is developed, to assist in the selection of minimum cost acceptance sampling plans by variables. The quadratic Taguchi loss function is adopted to model the cost of accepting items, with quality characteristics deviating from the target value. The case of a normally distributed quality characteristic with known variance is examined, and a simple and efficient optimization algorithm

GEORGE TAGARAS

1994-01-01

340

Velocity-locked solitary waves in quadratic media.  

PubMed

We demonstrate experimentally the existence of three-wave resonant interaction solitary triplets in quadratic media. Stable velocity-locked bright-dark-bright spatial solitary triplets, determined by the balance between the energy exchange rates and the velocity mismatch between the interacting waves, are excited in a KTP crystal. PMID:20366477

Baronio, Fabio; Conforti, Matteo; De Angelis, Costantino; Degasperis, Antonio; Andreana, Marco; Couderc, Vincent; Barthélémy, Alain

2010-03-19

341

Quadratically gated mixture of experts for incomplete data classification  

Microsoft Academic Search

We introduce quadratically gated mixture of experts (QGME), a statistical model for multi-class nonlinear classiflcation. The QGME is formulated in the setting of incom- plete data, where the data values are partially observed. We show that the missing val- ues entail joint estimation of the data mani- fold and the classifler, which allows adaptive imputation during classifler learning. The expectation

Xuejun Liao; Hui Li; Lawrence Carin

2007-01-01

342

Parallel Ant Colonies for the quadratic assignment problem  

Microsoft Academic Search

Ant Colonies optimization take inspiration from the behavior of real ant colonies to solve optimization problems. This paper presents a parallel model for ant colonies to solve the quadratic assignment problem (QAP). The cooperation between simulated ants is provided by a pheromone matrix that plays the role of a global memory. The exploration of the search space is guided by

El-ghazali Talbi; Olivier H. Roux; Cyril Fonlupt; Denis Robillard

2001-01-01

343

A Unified Approach to Teaching Quadratic and Cubic Equations.  

ERIC Educational Resources Information Center

Presents a simple method for teaching the algebraic solution of cubic equations via completion of the cube. Shows that this method is readily accepted by students already familiar with completion of the square as a method for quadratic equations. (Author/KHR)

Ward, A. J. B.

2003-01-01

344

Quadratic Expressions by Means of "Summing All the Matchsticks"  

ERIC Educational Resources Information Center

This note presents demonstrations of quadratic expressions that come about when particular problems are posed with respect to matchsticks that form regular triangles, squares, pentagons and so on. Usually when such "matchstick" problems are used as ways to foster algebraic thinking, the expressions for the number of matchstick quantities are…

Gierdien, M. Faaiz

2012-01-01

345

Least Squares Quadratic (LSQ) Approximation to Lognormal Sum Distributions  

Microsoft Academic Search

In this paper, least squares (LS) approximation approach is used to solve the approximation problem of a sum of lognormal random variables. It is shown that least squares quadratic (LSQ) approximation exhibits an excellent match with the simulation results in a wide range of the distributions of the summands. Using the coefficients obtained from the LSQ method, closed-form expressions for

Lian Zhao; Jiu Ding

2006-01-01

346

Quadrat Sampling: A Computer-Generated Laboratory Exercise  

NSDL National Science Digital Library

Obtaining spatial distributions by quadrat sampling can be difficult because field work tends to yield inconclusive data. This article describes a computer program that generates different spatial patterns for two species. It produces meaningful comparisons between two or more different habitats and uses cluster points which determine the interactions within and between species.

Boyer, John F.

2010-02-16

347

How Big the Set of Infinitely Renormalizable Quadratics Is.  

National Technical Information Service (NTIS)

The Mandelbrot set M is the bifurcation diagram of the complex quadratic family P(sub c): z -> z(squared) + c viewed dynamically. Despite the one line definition (see below), this set has quite a complicated structure, so that there is a little change to ...

M. Lyubich

1996-01-01

348

Homotopy analysis method for quadratic Riccati differential equation  

Microsoft Academic Search

In this paper, the quadratic Riccati differential equation is solved by means of an analytic technique, namely the homotopy analysis method (HAM). Comparisons are made between Adomian’s decomposition method (ADM), homotopy perturbation method (HPM) and the exact solution and the homotopy analysis method. The results reveal that the proposed method is very effective and simple.

Yue Tan; Saeid Abbasbandy

2008-01-01

349

Robust Estimation and Tests based on Quadratic Inference Function 1  

Microsoft Academic Search

Robust estimators and tests based on the quadratic inference function (QIF) are considered. The QIF enables one to combine a set of extended score functions effi- ciently. For example,one can create an adaptive estimator between the mean and median that is fully efficient at the normal model but is highly robust,with a 25% asymptotic breakdown point. In addition to providing

Chanseok Park; Bruce G. Lindsay

1999-01-01

350

Binary Mosaics and Point Quadrat Sampling in Ecology.  

National Technical Information Service (NTIS)

Point quadrat sampling is a method for estimating the proportional cover p of a plant species over a planar region, whereby the presence or absence of the species is recorded at each of N sample points. Then, if n is the number of points at which the spec...

C. J. F. ter Braak

1980-01-01

351

NON-GAUSSIANITIES IN THE LOCAL CURVATURE OF THE FIVE-YEAR WMAP DATA  

SciTech Connect

Using the five-year WMAP data, we re-investigate claims of non-Gaussianities and asymmetries detected in local curvature statistics of the one-year WMAP data. In Hansen et al., it was found that the northern ecliptic hemisphere was non-Gaussian at the {approx}1% level testing the densities of hill, lake, and saddle points based on the second derivatives of the cosmic microwave background temperature map. The five-year WMAP data have a much lower noise level and better control of systematics. Using these, we find that the anomalies are still present at a consistent level. Also the direction of maximum non-Gaussianity remains. Due to limited availability of computer resources, Hansen et al. were unable to calculate the full covariance matrix for the {chi}{sup 2}-test used. Here, we apply the full covariance matrix instead of the diagonal approximation and find that the non-Gaussianities disappear and there is no preferred non-Gaussian direction. We compare with simulations of weak lensing to see if this may cause the observed non-Gaussianity when using a diagonal covariance matrix. We conclude that weak lensing does not produce non-Gaussianity in the local curvature statistics at the scales investigated in this paper. The cause of the non-Gaussian detection in the case of a diagonal matrix remains unclear.

Rudjord, Oeystein; Groeneboom, Nicolaas E.; Hansen, Frode K. [Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, N-0315 Oslo (Norway); Cabella, Paolo, E-mail: oystein.rudjord@astro.uio.n [Dipartimento di Fisica, Universita di Roma 'Tor Vergata', Via della Ricerca Scientifica 1, I-00133, Roma (Italy)

2010-07-20

352

Displacement measurement on specimens subjected to non-Gaussian random vibrations in fatigue life tests  

NASA Astrophysics Data System (ADS)

High-cycle fatigue life tests conducted using controlled random vibrations are commonly used to evaluate failure in components and structures. In most cases, a Gaussian distribution of both the input vibration and the stress response is assumed, while real-life loads may be non-Gaussian causing the response to be non-Gaussian as well. Generating non-Gaussian drive signals with high kurtosis and a given power spectral density, however, does not always guarantee that the stress response will actually be non-Gaussian, because this depends on the adherence of the tested system to the Central Limit Theorem. On the other side, suitable measurement methods need to be developed in order to estimate the stress amplitude response at critical failure locations, and therefore to evaluate and select input loads. In this paper, a simple test rig with a notched cantilevered specimen was developed to measure the response and examine the kurtosis values in the case of stationary Gaussian, stationary non-Gaussian, and non-stationary non-Gaussian excitation signals. The Laser Doppler Vibrometry (LDV) technique was used for the first time in this type of test, to estimate the specimen stress amplitude response in terms of differential displacement at the notch section ends. A method based on the use of accelerometers to correct for the occasional signal drops occurring during the experiment is described and the results are discussed with respect to the ability of the test procedure to evaluate the output signal.

Troncossi, M.; Di Sante, R.; Rivola, A.

2014-05-01

353

Cylindrical quasi-Gaussian beams.  

PubMed

Making use of the complex-source-point method in cylindrical coordinates, an exact solution representing a cylindrical quasi-Gaussian beam of arbitrary waist w(0) satisfying both the Helmholtz and Maxwell's equations is introduced. The Cartesian components of the electromagnetic field are derived stemming from different polarizations of the magnetic and electric vector potentials based on Maxwell's vectorial equations and Lorenz's gauge condition, without any approximations. Computations illustrate the theory for tightly focused and quasi-collimated cylindrical beams. The results are particularly useful in beam-forming design using high-aperture or collimated cylindrical laser beams in imaging microscopy, particle manipulation, optical tweezers, and the study of scattering, radiation forces, and torque on cylindrical structures. PMID:24322117

Mitri, F G

2013-11-15

354

Testing Gaussianity on Archeops data  

NASA Astrophysics Data System (ADS)

Aims:We performed a Gaussianity analysis using a goodness-of-fit test and the Minkowski functionals on the sphere to study the measured Archeops Cosmic Microwave Background (CMB) temperature anisotropy data for a 143 GHz Archeops bolometer. We consider large angular scales, greater than 1.8 degrees, and a large fraction of the North Galactic hemisphere, around 16%, with a galactic latitude b > 15 degrees. Methods: The considered goodness-of-fit test, first proposed by Rayner & Best (1989, Smooth Tests of Goodness of Fit), was applied to the data after a signal-to-noise decomposition. The three Minkowski functionals on the sphere were used to construct a ?2 statistic using different thresholds. The former method was calibrated using simulations of Archeops data containing the CMB signal and instrumental noise in order to check its asymptotic convergence. Two kind of maps produced with two different map-making techniques (coaddition and Mirage) are analysed. Results: Archeops maps for both Mirage and coaddition map-making, are compatible with Gaussianity. From these results we can exclude a dust and atmospheric contamination larger than 7.8% (90% CL). Also the non-linear coupling parameter f_nl can be constrained to be f_nl = 200-800+1100 at the 95% CL and on angular scales of 1.8 degrees. For comparison, the same method was applied to data from the NASA WMAP satellite in the same region of sky. The 1-year and 3-year releases were used. Results are compatible with those obtained with Archeops, implying in particular an upper limit for f_nl on degree angular scales.

Curto, A.; Aumont, J.; Macías-Pérez, J. F.; Martínez-González, E.; Barreiro, R. B.; Santos, D.; Désert, F. X.; Tristram, M.

2007-10-01

355

Laser-matter interaction at solid-gas interface in the A?· p? gauge: linear, surface and quadratic terms  

NASA Astrophysics Data System (ADS)

At gas-solid interface the electron density, the dielectric function and the electric field of the photon vary sharply. Therefore, the usually assumed approximation of the spatially independent field of the photon does not hold anymore. In this paper we approximate the spatial variation of the vector potential A? perpendicular to the surface from the dielectric function, itself related to the electron density in a jellium model, and the Fresnel relations at abrupt interface. The resulted vector potential A? is then included in the laser-matter interaction Hamiltonian written in the A?· p? gauge (notation Ap) with zero scalar potential. For p polarization our detailed theoretical analysis unravel four terms linear in A?: a term perpendicular, two terms parallel and a surface term perpendicular to the surface, all four varying at the interface. There are also two terms quadratic in A?: a term perpendicular and a term parallel to the surface, again all varying at the interface. Using this interaction operator, we calculate all the laser-matter interaction terms for a (0 0 1) metallic surface lightened by a laser of 2 eV. The results for several metals, calculated with an elementary wave function product of a sum of Gaussian functions normal to the surface and plane waves perpendicular to it, show at nondestructive fluences a comparable relative importance for one linear term parallel to the surface and one surface term perpendicular to it but a negligible contribution of the quadratic term.

Ra?eev, G.; Bejan, D.

2003-03-01

356

Structured Gaussian Components for Hyperspectral Image Classification  

Microsoft Academic Search

The large number of bands in hyperspectral images leads to a large number of parameters to estimate. It has been argued in the literature that class-conditional distributions of hyperspectral images are non-Gaussian; thus, multiple components might be needed to describe the classes accurately. In this paper, we propose to represent the Gaussian components in the classifier with a smaller number

Asbjørn Berge; Anne H. Schistad Solberg

2006-01-01

357

Particle swarm optimization with Gaussian mutation  

Microsoft Academic Search

In this paper we present particle swarm optimization with Gaussian mutation combining the idea of the particle swarm with concepts from evolutionary algorithms. This method combines the traditional velocity and position update rules with the ideas of Gaussian mutation. This model is tested and compared with the standard PSO and standard GA. The comparative experiments have been conducted on unimodal

Natsuki Higashi; Hitoshi Iba

2003-01-01

358

Hole gratings and diffraction of Gaussian beams  

Microsoft Academic Search

Methods for the determination of waist size and position for Gaussian beams are summarized and an alternative method which applies to pulse systems was proposed and tested. The general theory of Fraunhofer diffraction of Gaussian beams was developed which permitted a new method for location of laser waists. An extension to Fresnel diffraction was proposed. The use of hole gratings

T. A. Wiggins

1986-01-01

359

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem  

NASA Technical Reports Server (NTRS)

An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

Gibson, J. S.; Rosen, I. G.

1988-01-01

360

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem  

NASA Technical Reports Server (NTRS)

An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

Gibson, J. S.; Rosen, I. G.

1986-01-01

361

Modification on static responses of a nano-oscillator by quadratic optomechanical couplings  

NASA Astrophysics Data System (ADS)

A quadratic coupling enabled parametric oscillation in an optomechanical system is used to modify the nonlinear static responses of a mechanical oscillator with a normal linear coupling. The mean value study showed that the modification of the static response on a mechanical oscillator is extremely sensitive and useful, which can readily enhance or suppress the nonlinear displacement response from a bistability case to singlet or triplet well case, freely bifurcating the equilibrium position from one to two or three. The static equilibria structure and the stability regions for mean-value controls on nano-oscillator were analyzed under the possible modification parameters.

Zhang, Lin; Song, ZhangDai

2014-05-01

362

Quadrotor UAV Control for Vision-based Moving Target Tracking Task  

NASA Astrophysics Data System (ADS)

The problem of stand-off tracking of a moving target using a quadrotor unmanned aerial vehicle (UAV) based on vision-sensing is investigated. A PID (Proportional-Integral-Derivative) controller is implemented for attitude stabilization of the quadrotor. An LQG-based (Linear-Quadratic-Gaussian) control law is designed and implemented for position control of the quadrotor for a moving target tracking task. A novel vision-based estimation algorithm is developed, enabling estimation of quadrotor's position, altitude and yaw relative to the target based on limited information about the target. Two image processing algorithms are implemented and compared for the task of feature detection and feature tracking in a series of images. Image processing algorithms are integrated with quadrotor control and experiments are performed to validate proposed control and estimation approaches.

Bohdanov, Denys

363

Asymmetric Gaussian harmonic steering in second-harmonic generation  

NASA Astrophysics Data System (ADS)

Intracavity second-harmonic generation is one of the simplest of the quantum optical processes and is well within the expertise of most optical laboratories. It is well understood and characterized, both theoretically and experimentally. We show that it can be a source of continuous-variable asymmetric Gaussian harmonic steering with fields which have a coherent excitation, hence combining the important effects of harmonic entanglement and asymmetric steering in one easily controllable device, adjustable by the simple means of tuning the cavity loss rates at the fundamental and harmonic frequencies. We find that whether quantum steering is available via the standard measurements of the Einstein-Podolsky-Rosen correlations can depend on which quadrature measurements are inferred from output spectral measurements of the fundamental and the harmonic. Altering the ratios of the cavity loss rates can be used to tune the regions where symmetric steering is available, with the results becoming asymmetric over all frequencies as the cavity damping at the fundamental frequency becomes significantly greater than at the harmonic. This asymmetry and its functional dependence on frequency is a potential new tool for experimental quantum information science, with possible utility for quantum key distribution. Although we show the effect here for Gaussian measurements of the quadratures, and cannot rule out a return of the steering symmetry for some class of non-Gaussian measurements, we note here that the system obeys Gaussian statistics in the operating regime investigated and Gaussian inference is at least as accurate as any other method for calculating the necessary correlations. Perhaps most importantly, this system is simpler than any other methods we are aware of which have been used or proposed to create asymmetric steering.

Olsen, M. K.

2013-11-01

364

Asymmetric Wiener Control.  

National Technical Information Service (NTIS)

A one-dimensional Wiener control problem with integral discounted quadratic cost function and asymmetric bounds on the control is considered, with infinite horizon. The optimal control is explicitly found. Bellman equations and Ito integrals are used to s...

H. Weiner

1983-01-01

365

On classical state space realisability of quadratic input–output differential equations  

Microsoft Academic Search

This article studies the realisability property of continuous-time quadratic input–output (i\\/o) equations in the classical state space form. Constraints on the parameters of the quadratic i\\/o model are suggested that lead to realisable models. The complete list of second- and third-order realisable i\\/o quadratic models is given and two subclasses of the n-th order realisable i\\/o quadratic systems are suggested.

Ü. Kotta; P. Kotta; M. Tõnso; A. S. I. Zinober

2009-01-01

366

Observational Quantification of Non-Gaussian Errors Within a Humidity-Temperature 1DVAR Retrieval System Over Japan  

NASA Astrophysics Data System (ADS)

A basic and simplifying assumption in variational and ensemble based assimilation systems is that the background and observational errors follow a Gaussian distribution. By incorporating both a lognormal transform and lognormal distribution into a 1DVAR retrieval system, specifically CIRA 1-Dimensional Optimal Estimator (C1DOE), more accurate retrievals are obtained for positive definite variables that are non-Gaussian in nature. We verify the non-Gaussian methodology in a controlled environment by analysing simulated data that is known to contain a lognormal signal. To quantify the non-Gaussian distribution spatially and seasonally a dense network of GPS sites near Japan which measure total precipitable water (tpw) will be analysed.

Kliewer, A.; Fletcher, S. J.; Jones, A. S.; Forsythe, J. M.

2013-12-01

367

Multichannel adaptive signal detection in space-time colored compound-gaussian autoregressive processes  

NASA Astrophysics Data System (ADS)

In this article, we consider the problem of adaptive detection for a multichannel signal in the presence of spatially and temporally colored compound-Gaussian disturbance. By modeling the disturbance as a multichannel autoregressive (AR) process, we first derive a parametric generalized likelihood ratio test against compound-Gaussian disturbance (CG-PGLRT) assuming that the true multichannel AR parameters are perfectly known. For the two-step GLRT design criterion, we combine the multichannel AR parameter estimation algorithm with three covariance matrix estimation strategies for compound-Gaussian environment, then obtain three adaptive CG-PGLRT detectors by replacing the ideal multichannel AR parameters with their estimates. Owing to treating the random texture components of disturbance as deterministic unknown parameters, all of the proposed detectors require no a priori knowledge about the disturbance statistics. The performance assessments are conducted by means of Monte Carlo trials. We focus on the issues of constant false alarm rate (CFAR) behavior, detection and false alarm probabilities. Numerical results show that the proposed adaptive CG-PGLRT detectors have dramatically ease the training and computational burden compared to the generalized likelihood ratio test-linear quadratic (GLRT-LQ) which is referred to as covariance matrix based detector and relies more heavily on training.

Xu, Qi; Ma, Xiaochuan; Yan, Shefeng; Hao, Chengpeng; Shi, Bo

2012-12-01

368

Applicability of quadratic and threshold models to motion discrimination in the rabbit retina  

Microsoft Academic Search

Computational and behavioral studies suggest that visual motion discrimination is based on quadratic nonlinearities. This raises the question of whether the behavior of motion sensitive neurons early in the visual system is actually quadratic. Theoretical studies show that mechanisms proposed for retinal directional selectivity do not behave quadratically at high stimulus contrast. However, for low contrast stimuli, models for these

Norberto M. Grzywacz; F. R. Amthor; L. A. Mistler

1990-01-01

369

Single-molecule orientation measurements with a quadrated pupil  

NASA Astrophysics Data System (ADS)

We present a means of measuring the dipole orientation of a fluorescent, rotationally fixed single molecule (SM), using a specially designed phase mask, termed a "quadrated pupil," conjugate to the back focal plane of a conventional widefield microscope. In comparison to image-fitting techniques that infer orientation by matching simulations to defocused or excessively magnified images, the quadrated pupil approach is more robust to minor modeling discrepancies, defocus, and optical aberrations. Precision on the order of 1°-5° is achieved in proofof- concept experiments for both azimuthal (?) and polar (?) angles. Since the phase mask is implemented on a liquid-crystal spatial light modulator (SLM) that may be deactivated without any mechanical perturbation of the sample or imaging system, the technique may be readily integrated into conventional imaging studies.

Backer, Adam S.; Backlund, Mikael P.; Lew, Matthew D.; Diezmann, Alexander R.; Sahl, Steffen J.; Moerner, W. E.

2014-03-01

370

Tableau-based protein substructure search using quadratic programming  

PubMed Central

Background Searching for proteins that contain similar substructures is an important task in structural biology. The exact solution of most formulations of this problem, including a recently published method based on tableaux, is too slow for practical use in scanning a large database. Results We developed an improved method for detecting substructural similarities in proteins using tableaux. Tableaux are compared efficiently by solving the quadratic program (QP) corresponding to the quadratic integer program (QIP) formulation of the extraction of maximally-similar tableaux. We compare the accuracy of the method in classifying protein folds with some existing techniques. Conclusion We find that including constraints based on the separation of secondary structure elements increases the accuracy of protein structure search using maximally-similar subtableau extraction, to a level where it has comparable or superior accuracy to existing techniques. We demonstrate that our implementation is able to search a structural database in a matter of hours on a standard PC.

Stivala, Alex; Wirth, Anthony; Stuckey, Peter J

2009-01-01

371

Quadratic nonlinear Klein-Gordon equation in one dimension  

NASA Astrophysics Data System (ADS)

We study the initial value problem for the quadratic nonlinear Klein-Gordon equation vtt + v - vxx = ?v2, t ? R, x ? R, with initial conditions v(0, x) = v0(x), vt(0, x) = v1(x), x ? R, where v0 and v1 are real-valued functions, ? ? R. Using the method of normal forms of Shatah [``Normal forms and quadratic nonlinear Klein-Gordon equations,'' Commun. Pure Appl. Math. 38, 685-696 (1985)], we obtain a sharp asymptotic behavior of small solutions without the condition of a compact support on the initial data, which was assumed in the previous work of J.-M. Delort [``Existence globale et comportement asymptotique pour l'équation de Klein-Gordon quasi-linéaire á données petites en dimension 1,'' Ann. Sci. Ec. Normale Super. 34(4), 1-61 (2001)].

Hayashi, Nakao; Naumkin, Pavel I.

2012-10-01

372

Optical continuous-variable quadratic phase gate via Faraday interaction.  

PubMed

The continuous-variable (CV) quadratic phase gate is one of the most fundamental CV quantum gates for universal CV quantum computation, while its experimental realization still remains a challenge. Here we propose a novel and experimentally feasible scheme to realize optical CV quadratic phase gate via Faraday interaction in an atomic ensemble. The gate is performed by simply sending an optical beam three times through an atomic medium prepared in coherent spin state. The fidelity of the gate can ideally run up to one. We show that the scheme also works well as a device to generate optical polarization squeezing. Considering the noise effects due to atomic decoherence and light losses, we find that the observed fidelities of gate operation and the attainable degree of polarization squeezing are still quite high. PMID:24787808

Wang, Ming-Feng; Jiang, Nian-Quan; Zheng, Yi-Zhuang

2014-04-21

373

Quasi-Gaussian electromagnetic beams  

NASA Astrophysics Data System (ADS)

A class of Maxwellian beams, which is an exact solution of the vector wave equation (Helmholtz equation) and Maxwell's equations, is introduced. The solution, termed a quasi-Gaussian electromagnetic (EM) beam, is formed from a superposition of sources and sinks with complex coordinates, and is characterized by an arbitrary waist w0 and a diffraction convergence length known as the Rayleigh range zR. An attractive feature of this beam is the description of strongly focused (or strongly divergent) EM-optical wave fields for kw0?1, where k is the wave number. A vector wave analysis is developed to determine and compute the spatial Cartesian components of the electric and magnetic fields (valid in the near field and the far field) stemming from Maxwell's vector equations and the Lorenz gauge condition, with particular emphasis on the parameter kw0 and the polarization states of the vector potentials used to derive the EM field's components. The results are potentially useful in the study of the axial and/or arbitrary wave scattering, radiation force, and torque in lasers operating with strongly focused (or strongly divergent) beams for particle manipulation in optical tweezers and imaging applications.

Mitri, F. G.

2013-03-01

374

Evidence for quadratic tidal tensor bias from the halo bispectrum  

NASA Astrophysics Data System (ADS)

The relation between the clustering properties of luminous matter in the form of galaxies and the underlying dark matter distribution is of fundamental importance for the interpretation of ongoing and upcoming galaxy surveys. The so-called local bias model, where galaxy density is a function of local matter density, is frequently discussed as a means to infer the matter power spectrum or correlation function from the measured galaxy correlation. However, gravitational evolution generates a term quadratic in the tidal tensor and thus nonlocal in the Eulerian density field, even if this term is absent in the initial conditions (Lagrangian space). Because the term is quadratic, it contributes as a loop correction to the power spectrum, so the standard linear bias picture still applies on very large scales; however, it contributes at leading order to the bispectrum for which it is significant on all scales. Such a term could also be present in Lagrangian space if halo formation were influenced by the tidal field. We measure the corresponding coupling strengths from the matter-matter-halo bispectrum in numerical simulations and find a nonvanishing coefficient for the tidal tensor term. We find no scale dependence of the inferred bias parameters up to k˜0.1hMpc-1 and that the tidal effect is increasing with halo mass. While the local Lagrangian bias picture is a better description of our results than the local Eulerian bias picture, our results suggest that there might be a tidal tensor bias already in the initial conditions. We also find that the coefficients of the quadratic density term deviate quite strongly from the theoretical predictions based on the spherical collapse model and a universal mass function. Both quadratic density and tidal tensor bias terms must be included in the modeling of galaxy clustering of current and future surveys if one wants to achieve the high precision cosmology promise of these data sets.

Baldauf, Tobias; Seljak, Uroš; Desjacques, Vincent; McDonald, Patrick

2012-10-01

375

Quantum integrals of motion for variable quadratic Hamiltonians  

SciTech Connect

We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic Hamiltonians. An extension of the Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy-related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application.

Cordero-Soto, Ricardo, E-mail: ricardojavier81@gmail.co [Mathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, AZ 85287-1804 (United States); Suazo, Erwin, E-mail: erwin.suazo@upr.ed [Department of Mathematical Sciences, University of Puerto Rico, Mayaquez, call box 9000, PR 00681-9000 (Puerto Rico); Suslov, Sergei K., E-mail: sks@asu.ed [School of Mathematical and Statistical Sciences and Mathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, AZ 85287-1804 (United States)

2010-09-15

376

Stability of Julia sets for a quadratic random dynamical system  

Microsoft Academic Search

For a sequence (cn) of complex numbers, the quadratic polynomials fcn:= z2 + Cn and the sequence (Fn) of iterates Fn: = fcn ? ? ? fc1 are considered. The Fatou set F(Cn) is defined as the set of all\\u000a $$z \\\\in \\\\hat {\\\\mathbb{C}}: = {\\\\mathbb{C}} \\\\cup \\\\left\\\\{ \\\\infty \\\\right\\\\}$$\\u000a such that (Fn) is normal in some neighbourhood of z,

Gong Zhimin; Qiu Weiyuan; Wang Jian

2002-01-01

377

Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality  

NASA Technical Reports Server (NTRS)

We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.

Acikmese, Ahmet Behcet; Corless, Martin

2004-01-01

378

DISTINGUISHED REPRESENTATIONS AND QUADRATIC BASE CHANGE FOR GL(3)  

Microsoft Academic Search

Let E=F be a quadratic extension of number elds. Suppose that every real place of F splits in E and let H be the unitary group in 3 variables. Suppose that is an automorphic cuspidal representation of GL(3;EA). We prove that there is a form in the space of such that the integral of over H(F )nH(FA) is non zero.

HERVE JACQUET; YANGBO YE

379

Periodic solutions of quadratic Weyl fractional integral equations  

NASA Astrophysics Data System (ADS)

In this paper, we study periodic solutions of quadratic Weyl fractional integral equations. We derive the convergence, periodicity, continuity and boundedness of Weyl kernel. With the help of these basic properties, we prove the existence of 2?-periodic solutions of the desired equation by using a technique of measure of noncompactness via Schauder fixed point theorem. Moreover, we obtain uniform local attractivity of the 2?-periodic solutions. Finally, an example is given to illustrate the obtained results.

Chen, Qian; Wang, JinRong; Chen, Fulai; Zhang, Yuruo

2014-06-01

380

Gaussian measures of entanglement versus negativities: Ordering of two-mode Gaussian states  

SciTech Connect

We study the entanglement of general (pure or mixed) two-mode Gaussian states of continuous-variable systems by comparing the two available classes of computable measures of entanglement: entropy-inspired Gaussian convex-roof measures and positive partial transposition-inspired measures (negativity and logarithmic negativity). We first review the formalism of Gaussian measures of entanglement, adopting the framework introduced in M. M. Wolf et al., Phys. Rev. A 69, 052320 (2004), where the Gaussian entanglement of formation was defined. We compute explicitly Gaussian measures of entanglement for two important families of nonsymmetric two-mode Gaussian state: namely, the states of extremal (maximal and minimal) negativities at fixed global and local purities, introduced in G. Adesso et al., Phys. Rev. Lett. 92, 087901 (2004). This analysis allows us to compare the different orderings induced on the set of entangled two-mode Gaussian states by the negativities and by the Gaussian measures of entanglement. We find that in a certain range of values of the global and local purities (characterizing the covariance matrix of the corresponding extremal states), states of minimum negativity can have more Gaussian entanglement of formation than states of maximum negativity. Consequently, Gaussian measures and negativities are definitely inequivalent measures of entanglement on nonsymmetric two-mode Gaussian states, even when restricted to a class of extremal states. On the other hand, the two families of entanglement measures are completely equivalent on symmetric states, for which the Gaussian entanglement of formation coincides with the true entanglement of formation. Finally, we show that the inequivalence between the two families of continuous-variable entanglement measures is somehow limited. Namely, we rigorously prove that, at fixed negativities, the Gaussian measures of entanglement are bounded from below. Moreover, we provide some strong evidence suggesting that they are as well bounded from above.

Adesso, Gerardo; Illuminati, Fabrizio [Dipartimento di Fisica 'E. R. Caianiello', Universita di Salerno, CNR-Coherentia, Gruppo di Salerno (Italy); INFN Sezione di Napoli-Gruppo Collegato di Salerno, Via S. Allende, 84081 Baronissi, SA (Italy)

2005-09-15

381

Theory and application of explicitly correlated Gaussians  

NASA Astrophysics Data System (ADS)

The variational method complemented with the use of explicitly correlated Gaussian basis functions is one of the most powerful approaches currently used for calculating the properties of few-body systems. Despite its conceptual simplicity, the method offers great flexibility, high accuracy, and can be used to study diverse quantum systems, ranging from small atoms and molecules to light nuclei, hadrons, quantum dots, and Efimov systems. The basic theoretical foundations are discussed, recent advances in the applications of explicitly correlated Gaussians in physics and chemistry are reviewed, and the strengths and weaknesses of the explicitly correlated Gaussians approach are compared with other few-body techniques.

Mitroy, Jim; Bubin, Sergiy; Horiuchi, Wataru; Suzuki, Yasuyuki; Adamowicz, Ludwik; Cencek, Wojciech; Szalewicz, Krzysztof; Komasa, Jacek; Blume, D.; Varga, Kálmán

2013-04-01

382

Gaussian Mixture Model of Heart Rate Variability  

PubMed Central

Heart rate variability (HRV) is an important measure of sympathetic and parasympathetic functions of the autonomic nervous system and a key indicator of cardiovascular condition. This paper proposes a novel method to investigate HRV, namely by modelling it as a linear combination of Gaussians. Results show that three Gaussians are enough to describe the stationary statistics of heart variability and to provide a straightforward interpretation of the HRV power spectrum. Comparisons have been made also with synthetic data generated from different physiologically based models showing the plausibility of the Gaussian mixture parameters.

Costa, Tommaso; Boccignone, Giuseppe; Ferraro, Mario

2012-01-01

383

Quark and lepton masses from Gaussian landscapes.  

PubMed

The flavor structure of the standard model (SM) might arise from random selection on a landscape. We propose a class of simple models, "Gaussian landscapes," where Yukawa couplings derive from overlap integrals of Gaussian wave functions on extra-dimensions. Statistics of vacua are generated by scanning the peak positions of these zero-modes, giving probability distributions for all flavor observables. Gaussian landscapes can account for all observed flavor patterns with few free parameters. Although they give broad probability distributions, the predictions are correlated and accounting for measured parameters sharpens the distributions of future neutrino measurements. PMID:18518022

Hall, Lawrence J; Salem, Michael P; Watari, Taizan

2008-04-11

384

Non-Gaussianity from isocurvature perturbations  

SciTech Connect

We develop a formalism for studying non-Gaussianity in both curvature and isocurvature perturbations. It is shown that non-Gaussianity in the isocurvature perturbation between dark matter and photons leaves distinct signatures in the cosmic microwave background temperature fluctuations, which may be confirmed in future experiments, or possibly even in the currently available observational data. As an explicit example, we consider the quantum chromodynamics axion and show that it can actually induce sizable non-Gaussianity for the inflationary scale, H{sub inf} = O(10{sup 9}-10{sup 11}) GeV.

Kawasaki, Masahiro; Nakayama, Kazunori; Sekiguchi, Toyokazu; Suyama, Teruaki [Institute for Cosmic Ray Research, University of Tokyo, Kashiwa 277-8582 (Japan)] [Institute for Cosmic Ray Research, University of Tokyo, Kashiwa 277-8582 (Japan); Takahashi, Fuminobu, E-mail: kawasaki@icrr.u-tokyo.ac.jp, E-mail: nakayama@icrr.u-tokyo.ac.jp, E-mail: sekiguti@icrr.u-tokyo.ac.jp, E-mail: suyama@icrr.u-tokyo.ac.jp, E-mail: fuminobu.takahashi@ipmu.jp [Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa 277-8568 (Japan)] [Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa 277-8568 (Japan)

2008-11-15

385

Quadratic mutual information for dimensionality reduction and classification  

NASA Astrophysics Data System (ADS)

A research area based on the application of information theory to machine learning has attracted considerable interest in the last few years. This research area has been coined information-theoretic learning within the community. In this paper we apply elements of information-theoretic learning to the problem of automatic target recognition (ATR). A number of researchers have previously shown the benefits of designing classifiers based on maximizing the mutual information between the class data and the class labels. Following prior research in information-theoretic learning, in the current results we show that quadratic mutual information, derived using a special case of the more general Renyi's entropy, can be used for classifier design. In this implementation, a simple subspace projection classifier is formulated to find the optimal projection weights such that the quadratic mutual information between the class data and the class labels is maximized. This subspace projection accomplishes a dimensionality reduction of the raw data set wherein information about the class membership is retained while irrelevant information is discarded. A subspace projection based on this criterion preserves as much class discriminability as possible within the subspace. For this paper, laser radar images are used to demonstrate the results. Classification performance against this data set is compared for a gradient descent MLP classifier and a quadratic mutual information MLP classifier.

Gray, David M.; Principe, José C.

2010-04-01

386

RANDOM CLUSTERING BASED ON THE CONDITIONAL INVERSE GAUSSIAN-POISSON DISTRIBUTION  

Microsoft Academic Search

The present article describes a Conditional Inverse Gaussian-Poisson (CIGP) distribution, obtained by conditioning an inverse Gaussian-Poisson population model on its total frequency.This CIGP distribution is equivalent to random partitioning of positive integers, with the possibility for a number of applications in statistical ecology, linguistics and statistical disclosure control to name a few.After showing the marginal moments of the distribution, parameter

Nobuaki Hoshino

2003-01-01

387

Modern CACSD using the Robust-Control Toolbox  

NASA Technical Reports Server (NTRS)

The Robust-Control Toolbox is a collection of 40 M-files which extend the capability of PC/PRO-MATLAB to do modern multivariable robust control system design. Included are robust analysis tools like singular values and structured singular values, robust synthesis tools like continuous/discrete H(exp 2)/H infinity synthesis and Linear Quadratic Gaussian Loop Transfer Recovery methods and a variety of robust model reduction tools such as Hankel approximation, balanced truncation and balanced stochastic truncation, etc. The capabilities of the toolbox are described and illustated with examples to show how easily they can be used in practice. Examples include structured singular value analysis, H infinity loop-shaping and large space structure model reduction.

Chiang, Richard Y.; Safonov, Michael G.

1989-01-01

388

Nonlinear and non-Gaussian Bayesian based handwriting beautification  

NASA Astrophysics Data System (ADS)

A framework is proposed in this paper to effectively and efficiently beautify handwriting by means of a novel nonlinear and non-Gaussian Bayesian algorithm. In the proposed framework, format and size of handwriting image are firstly normalized, and then typeface in computer system is applied to optimize vision effect of handwriting. The Bayesian statistics is exploited to characterize the handwriting beautification process as a Bayesian dynamic model. The model parameters to translate, rotate and scale typeface in computer system are controlled by state equation, and the matching optimization between handwriting and transformed typeface is employed by measurement equation. Finally, the new typeface, which is transformed from the original one and gains the best nonlinear and non-Gaussian optimization, is the beautification result of handwriting. Experimental results demonstrate the proposed framework provides a creative handwriting beautification methodology to improve visual acceptance.

Shi, Cao; Xiao, Jianguo; Xu, Canhui; Jia, Wenhua

2013-03-01

389

Gaussian surfaces and nullcone dual surfaces of null curves in a three-dimensional nullcone with index 2  

NASA Astrophysics Data System (ADS)

In this paper, we consider the null curves in the 3-nullcone with index 2 and we investigate these curves in the framework of the theory of Legendrian dualities between nullcones. The sufficient and necessary conditions for the classifications of the singularities of both Gaussian surfaces and those nullcone dual surfaces that are associated with a null curve are given; these conditions are closely related to several new geometric invariants. In addition, we reveal the relationships between these geometric invariants and the order of contact for the 2nd principal normal curve n(s) of a null curve ?(s) with quadratic surfaces. Finally, two examples, namely, a Gaussian surface and a nullcone dual surface, are used to demonstrate our theoretical results.

Wang, Zhigang; Pei, Donghe; Kong, Lingling

2013-11-01

390

LQG controller design using GUI: application to antennas and radio-telescopes  

PubMed

The Linear Quadratic Gaussian (LQG) algorithm has been used to control the JPL's beam wave-guide, and 70-m antennas. This algorithm significantly improves tracking precision in a wind disturbed environment. Based on this algorithm and the implementation experience a Matlab based Graphical User Interface (GUI) was developed to design the LQG controllers applicable to antennas and radiotelescopes. The GUI is described in this paper. It consists of two parts the basic LQG design and the fine-tuning of the basic design using a constrained optimization algorithm. The presented GUI was developed to simplify the design process, to make the design process user-friendly, and to enable design of an LQG controller for one with a limited control engineering background. The user is asked to manipulate the GUI sliders and radio buttons to watch the antenna performance. Simple rules are given at the GUI display. PMID:10871218

Maneri; Gawronski

2000-01-01

391

Why Should We Pivot in Gaussian Elimination?  

ERIC Educational Resources Information Center

The article discusses the use of computers to teacher college level mathematics. In particular, the Gaussian elimination procedure for solving a system of n linear equations in n unknowns, using a computer, is examined. (PK)

Rozema, Edward

1988-01-01

392

Improved Gaussian Beam-Scattering Algorithm  

NASA Technical Reports Server (NTRS)

The localized model of the beam-shape coefficients for Gaussian beam-scattering theory by a spherical particle provides a great simplification in the numerical implementation of the theory. We derive an alternative form for the localized coefficients that is more convenient for computer computations and that provides physical insight into the details of the scattering process. We construct a FORTRAN program for Gaussian beam scattering with the localized model and compare its computer run time on a personal computer with that of a traditional Mie scattering program and with three other published methods for computing Gaussian beam scattering. We show that the analytical form of the beam-shape coefficients makes evident the fact that the excitation rate of morphology-dependent resonances is greatly enhanced for far off-axis incidence of the Gaussian beam.

Lock, James A.

1995-01-01

393

Gaussian laser beam shaping: Test and evaluation.  

National Technical Information Service (NTIS)

A method for converting single mode Gaussian beams into beams with uniform irradiance profiles is described. This technique has application to laser cutting and welding, laser ablation, semiconductor mask fabrication, and other tasks. Currently, designs f...

S. C. Holswade F. M. Dickey

1996-01-01

394

Monthly streamflow forecasting using Gaussian Process Regression  

NASA Astrophysics Data System (ADS)

Gaussian Process Regression (GPR) is applied to monthly streamflow forecasting.The efficacy of GPR is demonstrated for over 400 stations in the continental U.S.Budyko framework is used to examine dependence of prediction skill on aridity index.

Sun, Alexander Y.; Wang, Dingbao; Xu, Xianli

2014-04-01

395

Decentered elliptical Hermite-Gaussian beam.  

PubMed

A new kind of laser beam called the decentered elliptical Hermite-Gaussian beam (DEHGB) is defined by use of a tensor method. The propagation formula of the DEHGB passing through a nonsymmetrical paraxial optical system is derived through vector integration. The derived formula can be easily reduced to the propagation formula of an aligned elliptical Hermite-Gaussian beam and that of a decentered elliptical Gaussian beam under certain conditions. By use of this formula, the propagation characteristics of the DEHGB through free space are presented graphically. As application examples, we construct a generalized laser array using the DEHGB as the fundamental mode. We also obtain the decentered elliptical flattened Gaussian beam by expressing it as superposition of a series of DEHGBs by using polynomial expansion. PMID:12801179

Cai, Yangjian; Lin, Qiang

2003-06-01

396

Remote transfer of Gaussian quantum discord.  

PubMed

Quantum discord quantifies quantum correlation between quantum systems, which has potential application in quantum information processing. In this paper, we propose a scheme realizing the remote transfer of Gaussian quantum discord, in which another quantum discordant state or an Einstein-Podolsky-Rosen entangled state serves as ancillary state. The calculation shows that two independent optical modes that without direct interaction become quantum correlated after the transfer. The output Gaussian quantum discord can be higher than the initial Gaussian quantum discord when optimal gain of the classical channel and the ancillary state are chosen. The physical reason for this result comes from the fact that the quantum discord of an asymmetric Gaussian quantum discordant state can be higher than that of a symmetric one. The presented scheme has potential application in quantum information network. PMID:24977844

Ma, Lingyu; Su, Xiaolong

2014-06-30

397

Evaluation of Derivatives of Gaussian Integrals.  

National Technical Information Service (NTIS)

We show that by a suitable change of variables, the derivatives of molecular integrals over Gaussian-type functions required for analytic energy derivatives can be evaluated with significantly less computational effort than current formulations. The reduc...

T. Helgaker P. R. Taylor

1992-01-01

398

Homodyne estimation of Gaussian quantum discord.  

PubMed

We address the experimental estimation of Gaussian quantum discord for a two-mode squeezed thermal state, and demonstrate a measurement scheme based on a pair of homodyne detectors assisted by Bayesian analysis, which provides nearly optimal estimation for small value of discord. In addition, though homodyne detection is not optimal for Gaussian discord, the noise ratio to the ultimate quantum limit, as dictated by the quantum Cramer-Rao bound, is limited to about 10 dB. PMID:23215259

Blandino, Rémi; Genoni, Marco G; Etesse, Jean; Barbieri, Marco; Paris, Matteo G A; Grangier, Philippe; Tualle-Brouri, Rosa

2012-11-01

399

Fuzzy Gaussian mixture models for speaker recognition  

Microsoft Academic Search

Abstract The Gaussian mixture model (GMM) is an important application of statistical clustering to speaker ,recognition. A number,of prototypes,are generated,from the training feature vectors by representing,the feature space as a mixture of Gaussian distributions. Each prototype consists of a model parameter set including mean vector, covariance matrix and mixture weight. In fuzzy clustering, the fuzzy c-means (FCM) method is the

Dat Tran; Tu Van Le; Michael Wagner

1998-01-01

400

Unitarily localizable entanglement of Gaussian states  

Microsoft Academic Search

We consider generic (m×n) -mode bipartitions of continuous-variable systems, and study the associated bisymmetric multimode Gaussian states. They are defined as (m+n) -mode Gaussian states invariant under local mode permutations on the m -mode and n -mode subsystems. We prove that such states are equivalent, under local unitary transformations, to the tensor product of a two-mode state and of m+n-2

Alessio Serafini; Gerardo Adesso; Fabrizio Illuminati

2005-01-01

401

Gaussian-Beam Laser-Resonator Program  

NASA Technical Reports Server (NTRS)

Gaussian Beam Laser Resonator Program models laser resonators by use of Gaussian-beam-propagation techniques. Used to determine radii of beams as functions of position in laser resonators. Algorithm used in program has three major components. First, ray-transfer matrix for laser resonator must be calculated. Next, initial parameters of beam calculated. Finally, propagation of beam through optical elements computed. Written in Microsoft FORTRAN (Version 4.01).

Cross, Patricia L.; Bair, Clayton H.; Barnes, Norman

1989-01-01

402

The Gaussian rank correlation estimator: robustness properties  

Microsoft Academic Search

The Gaussian rank correlation equals the usual correlation coefficient computed from the normal scores of the data. Although\\u000a its influence function is unbounded, it still has attractive robustness properties. In particular, its breakdown point is\\u000a above 12%. Moreover, the estimator is consistent and asymptotically efficient at the normal distribution. The correlation\\u000a matrix obtained from pairwise Gaussian rank correlations is always

Kris Boudt; Jonathan Cornelissen; Christophe Croux

2010-01-01

403

Bit error rate analysis of Gaussian, annular Gaussian, cos Gaussian, and cosh Gaussian beams with the help of random phase screens.  

PubMed

Using the random phase screen approach, we carry out a simulation analysis of the probability of error performance of Gaussian, annular Gaussian, cos Gaussian, and cosh Gaussian beams. In our scenario, these beams are intensity-modulated by the randomly generated binary symbols of an electrical message signal and then launched from the transmitter plane in equal powers. They propagate through a turbulent atmosphere modeled by a series of random phase screens. Upon arriving at the receiver plane, detection is performed in a circuitry consisting of a pin photodiode and a matched filter. The symbols detected are compared with the transmitted ones, errors are counted, and from there the probability of error is evaluated numerically. Within the range of source and propagation parameters tested, the lowest probability of error is obtained for the annular Gaussian beam. Our investigation reveals that there is hardly any difference between the aperture-averaged scintillations of the beams used, and the distinctive advantage of the annular Gaussian beam lies in the fact that the receiver aperture captures the maximum amount of power when this particular beam is launched from the transmitter plane. PMID:24921142

Eyyubo?lu, Halil T

2014-06-10

404

Block-based noise estimation using adaptive Gaussian filtering  

Microsoft Academic Search

This paper proposes a fast noise estimation algorithm using a Gaussian filter. It is based on block-based noise estimation, in which an input image is assumed to be contaminated by the additive white Gaussian noise and a filtering process is performed by an adaptive Gaussian filter. Coefficients of a Gaussian filter are selected as functions of the standard deviation of

Dong-Hyuk Shin; Rae-Hong Park; Seungjoon Yang; Jae-Han Jung

2005-01-01

405

Piezoelectric Active Vibration Control of Damped Sandwich Beams  

NASA Astrophysics Data System (ADS)

This work presents the design and analysis of the piezoelectric active control of damped sandwich beams. This is done using a specific finite element, able to handle sandwich beams with piezoelectric laminated surface layers and viscoelastic core. The piezoelectric direct and converse effects are accounted for through additional electrical degrees of freedom, condensed at the element level. The frequency dependence of the viscoelastic material properties is modelled using additional dissipative variables resulting from an anelastic displacement fields model. A complex-based modal reduction is then proposed and an equivalent real representation of the reduced-order system is constructed. The control design and performance are then evaluated using three control algorithms applied to the reduced-order model, namely, linear quadratic regulator (LQR), linear quadratic gaussian (LQG) and derivative feedback. To guarantee control feasibility and prevent piezoelectric material depoling, these algorithms are used in an iterative form to account for maximum control voltage. Parametric analyses of an actively controlled damped sandwich beam indicate that LQR controllers improve some selected modal dampings, while retaining the passive damping of uncontrolled modes. Derivative feedback controllers are less effective than an LQR one, but their well-known spillover destabilizing effects are attenuated by the increase of stability margins provided by the viscoelastic damping. It is also shown that LQG controllers may perform as well as LQR ones. Moreover, the delay effect induced by the state estimation of LQG associated with the passive attenuation lead to a damping performance similar to that of LQR with less control voltage. The parametric analyses and the comparative study of control strategies for the active control of damped sandwich beams, accounting for frequency dependence of viscoelastic material properties, are some of the originalities of this work. The others are the analysis of the LQG algorithm and the state space real representation of complex modal reduced models for hybrid piezoelectric-active viscoelastic-passive vibration control which are presented for the first time.

TRINDADE, M. A.; BENJEDDOU, A.; OHAYON, R.

2001-09-01

406

Self-sustained oscillation and harmonic generation in optomechanical systems with quadratic couplings  

NASA Astrophysics Data System (ADS)

Many works are based on the steady-state analysis of mean-value dynamics in electro- or optomechanical systems to explore vibration cooling, squeezing, and quantum-state controlling of massive objects. These studies are always conducted in a red-detuned pumping field under a lower power to maintain a stable situation. In this paper we consider self-sustained oscillations of a cavity-field-driven oscillator combined with quadratic coupling in a blue-detuned regime above a pumping threshold. Our study finds that the oscillator will be far away from its steady-state behavior by conducting a self-sustained oscillation with a discrete amplitude locking effect producing a rich energy-balanced structure. The dynamical backaction of this self-oscillation on the field mode induces a multipeak field spectrum, which implies an efficient harmonic generation with its intensity modified not only by the displacement x0 but also by the amplitude A of the mechanical oscillation. The corresponding nonlinear field spectrum and its magnitude are analytically analyzed with quadratic coupling when the mechanical oscillator is dynamically locked to a self-sustained oscillation.

Zhang, Lin; Kong, Hong-Yan

2014-02-01

407

Topics in Statistical Process Control.  

National Technical Information Service (NTIS)

The inverse gaussian distribution can be used to model processes with skewed output. In this thesis, several Shewhard and CUSUM control schemes are developed for the inverse gaussian distribution. The behavior of these schemes is described. A new type of ...

D. H. Olwell

1996-01-01

408

Regions of attraction and ultimate boundedness for linear quadratic regulators with nonlinearities  

NASA Technical Reports Server (NTRS)

The closed-loop stability of multivariable linear time-invariant systems controlled by optimal linear quadratic (LQ) regulators is investigated for the case when the feedback loops have nonlinearities N(sigma) that violate the standard stability condition, sigma N(sigma) or = 0.5 sigma(2). The violations of the condition are assumed to occur either (1) for values of sigma away from the origin (sigma = 0) or (2) for values of sigma in a neighborhood of the origin. It is proved that there exists a region of attraction for case (1) and a region of ultimate boundedness for case (2), and estimates are obtained for these regions. The results provide methods for selecting the performance function parameters to design LQ regulators with better tolerance to nonlinearities. The results are demonstrated by application to the problem of attitude and vibration control of a large, flexible space antenna in the presence of actuator nonlinearities.

Joshi, S. M.

1984-01-01

409

Mobility of Discrete Solitons in Quadratically Nonlinear Media  

Microsoft Academic Search

We study the mobility of solitons in second-harmonic-generating lattices.\\u000aContrary to what is known for their cubic counterparts, discrete quadratic\\u000asolitons are mobile not only in the one-dimensional (1D) setting, but also in\\u000atwo dimensions (2D). We identify parametric regions where an initial kick\\u000aapplied to a soliton leads to three possible outcomes, namely, staying put,\\u000apersistent motion, or destruction.

H. Susanto; P. G. Kevrekidis; R. Carretero-Gonzalez; Boris A. Malomed; D. J. Frantzeskakis

2007-01-01

410

Relativistic Stellar Model Admitting a Quadratic Equation of State  

NASA Astrophysics Data System (ADS)

A class of solutions describing the interior of a static spherically symmetric compact anisotropic star is reported. The analytic solution has been obtained by utilizing the Finch and Skea [Class. Quantum Grav.6 (1989) 467] ansatz for the metric potential grr which has a clear geometric interpretation for the associated background spacetime. Based on physical grounds, appropriate bounds on the model parameters have been obtained and it has been shown that the model admits an equation of state (EOS) which is quadratic in nature.

Sharma, R.; Ratanpal, B. S.

2013-11-01

411

Nios II hardware acceleration of the epsilon quadratic sieve algorithm  

NASA Astrophysics Data System (ADS)

The quadratic sieve (QS) algorithm is one of the most powerful algorithms to factor large composite primes used to break RSA cryptographic systems. The hardware structure of the QS algorithm seems to be a good fit for FPGA acceleration. Our new ?-QS algorithm further simplifies the hardware architecture making it an even better candidate for C2H acceleration. This paper shows our design results in FPGA resource and performance when implementing very long arithmetic on the Nios microprocessor platform with C2H acceleration for different libraries (GMP, LIP, FLINT, NRMP) and QS architecture choices for factoring 32-2048 bit RSA numbers.

Meyer-Bäse, Uwe; Botella, Guillermo; Castillo, Encarnacion; García, Antonio

2010-04-01

412

Rigorous performance bounds for quadratic and nested dynamical decoupling  

SciTech Connect

We present rigorous performance bounds for the quadratic dynamical decoupling pulse sequence which protects a qubit from general decoherence, and for its nested generalization to an arbitrary number of qubits. Our bounds apply under the assumptions of instantaneous pulses and of bounded perturbing environment and qubit-environment Hamiltonians such as those realized by baths of nuclear spins in quantum dots. We prove that if the total sequence time is fixed then the trace-norm distance between the unperturbed and protected system states can be made arbitrarily small by increasing the number of applied pulses.

Xia, Yuhou; Uhrig, Goetz S.; Lidar, Daniel A. [Department of Mathematics and Department of Physics, Haverford College, Haverford, Pennsylvania 19041 (United States); Lehrstuhl fuer Theoretische Physik I, Technische Universitaet Dortmund, Otto-Hahn Strasse 4, D-44221 Dortmund (Germany); Department of Electrical Engineering, Department of Chemistry, and Department of Physics, Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089 (United States)

2011-12-15

413

Pulse propagation in an elastic medium with quadratic nonlinearity (L).  

PubMed

This letter examines the propagation of an acoustic pulse in an elastic medium with weak quadratic nonlinearity. Both a displacement pulse and a stress pulse of arbitrary shapes are used to generate the wave motion in the solid. By obtaining the explicit solutions for arbitrary pulse shapes, it is shown that for a sinusoidal tone-burst, in addition to a second order harmonic field, a radiation induced static strain field is also generated. These results help clarify some confusion in the recent literature regarding the shape of the propagating static displacement pulse. PMID:22423681

Qu, Jianmin; Nagy, Peter B; Jacobs, Laurence J

2012-03-01

414

Analysis of electroperforated materials using the quadrat counts method  

NASA Astrophysics Data System (ADS)

The electroperforation distribution in thin porous materials is investigated using the quadrat counts method (QCM), a classical statistical technique aimed to evaluate the deviation from complete spatial randomness (CSR). Perforations are created by means of electrical discharges generated by needle-like tungsten electrodes. The objective of perforating a thin porous material is to enhance its air permeability, a critical issue in many industrial applications involving paper, plastics, textiles, etc. Using image analysis techniques and specialized statistical software it is shown that the perforation locations follow, beyond a certain length scale, a homogeneous 2D Poisson distribution.

Miranda, E.; Garzón, C.; Martínez-Cisneros, C.; Alonso, J.; García-García, J.

2011-06-01

415

A-REI A Linear and Quadratic System  

NSDL National Science Digital Library

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Consider the linear and quadratic functions appearing in the figure below. What are the coordinates of the point Q? Show step-by-step algebra work. Wha...

416

Evaluation of a photovoltaic energy mechatronics system with a built-in quadratic maximum power point tracking algorithm  

SciTech Connect

The historically high cost of crude oil price is stimulating research into solar (green) energy as an alternative energy source. In general, applications with large solar energy output require a maximum power point tracking (MPPT) algorithm to optimize the power generated by the photovoltaic effect. This work aims to provide a stand-alone solution for solar energy applications by integrating a DC/DC buck converter to a newly developed quadratic MPPT algorithm along with its appropriate software and hardware. The quadratic MPPT method utilizes three previously used duty cycles with their corresponding power outputs. It approaches the maximum value by using a second order polynomial formula, which converges faster than the existing MPPT algorithm. The hardware implementation takes advantage of the real-time controller system from National Instruments, USA. Experimental results have shown that the proposed solar mechatronics system can correctly and effectively track the maximum power point without any difficulties. (author)

Chao, R.M.; Ko, S.H.; Lin, I.H. [Department of Systems and Naval Mechatronics Engineering, National Cheng Kung University, Tainan, Taiwan 701 (China); Pai, F.S. [Department of Electronic Engineering, National University of Tainan (China); Chang, C.C. [Department of Environment and Energy, National University of Tainan (China)

2009-12-15

417

Linear Quadratic Tracking Design for a Generic Transport Aircraft with Structural Load Constraints  

NASA Technical Reports Server (NTRS)

When designing control laws for systems with constraints added to the tracking performance, control allocation methods can be utilized. Control allocations methods are used when there are more command inputs than controlled variables. Constraints that require allocators are such task as; surface saturation limits, structural load limits, drag reduction constraints or actuator failures. Most transport aircraft have many actuated surfaces compared to the three controlled variables (such as angle of attack, roll rate & angle of side slip). To distribute the control effort among the redundant set of actuators a fixed mixer approach can be utilized or online control allocation techniques. The benefit of an online allocator is that constraints can be considered in the design whereas the fixed mixer cannot. However, an online control allocator mixer has a disadvantage of not guaranteeing a surface schedule, which can then produce ill defined loads on the aircraft. The load uncertainty and complexity has prevented some controller designs from using advanced allocation techniques. This paper considers actuator redundancy management for a class of over actuated systems with real-time structural load limits using linear quadratic tracking applied to the generic transport model. A roll maneuver example of an artificial load limit constraint is shown and compared to the same no load limitation maneuver.

Burken, John J.; Frost, Susan A.; Taylor, Brian R.

2011-01-01

418

Robust multivariable controller design for flexible spacecraft  

NASA Technical Reports Server (NTRS)

Large, flexible spacecraft are typically characterized by a large number of significant elastic modes with very small inherent damping, low, closely spaced natural frequencies, and the lack of accurate knowledge of the structural parameters. Summarized here is some recent research on the design of robust controllers for such spacecraft, which will maintain stability, and possible performance, despite these problems. Two types of controllers are considered, the first being the linear-quadratic-Gaussian-(LQG)-type. The second type utilizes output feedback using collocated sensors and actuators. The problem of designing robust LQG-type controllers using the frequency domain loop transfer recovery (LTR) method is considered, and the method is applied to a large antenna model. Analytical results regarding the regions of stability for LQG-type controllers in the presence of actuator nonlinearities are also presented. The results obtained for the large antenna indicate that the LQG/LTR method is a promising approach for control system design for flexible spacecraft. For the second type of controllers (collocated controllers), it is proved that the stability is maintained in the presence of certain commonly encountered nonlinearities and first-order actuator dynamics. These results indicate that collocated controllers are good candidates for robust control in situations where model errors are large.

Joshi, Suresh M.; Armstrong, Ernest S.

1986-01-01

419

Non-Gaussianity and gravitational wave background in curvaton with a double well potential  

NASA Astrophysics Data System (ADS)

We study the density perturbation by a curvaton with a double well potential and give analytical expressions for the observables such as nonlinear parameters fNL, gNL and tensor-to-scalar ratio rT with emphasizing the differences from the simple quadratic potential. We show that the level of non-Gaussianity and the tensor-to-scalar ratio depends crucially on the reheating temperature as well as the curvaton self-coupling constant for a given initial amplitude of the curvaton. We find that for a large initial field the nonlinear parameters fNL can be 10-20 and the gravitational wave background also is observable in the Planck satellite.

Choi, Ki-Young; Seto, Osamu

2010-11-01

420

Non-Gaussianity and gravitational wave background in curvaton with a double well potential  

SciTech Connect

We study the density perturbation by a curvaton with a double well potential and give analytical expressions for the observables such as nonlinear parameters f{sub NL}, g{sub NL} and tensor-to-scalar ratio r{sub T} with emphasizing the differences from the simple quadratic potential. We show that the level of non-Gaussianity and the tensor-to-scalar ratio depends crucially on the reheating temperature as well as the curvaton self-coupling constant for a given initial amplitude of the curvaton. We find that for a large initial field the nonlinear parameters f{sub NL} can be 10-20 and the gravitational wave background also is observable in the Planck satellite.

Choi, Ki-Young; Seto, Osamu [Department of Physics, Pusan National University, Busan 609-735 (Korea, Republic of); Department of Architecture and Building Engineering, Hokkai-Gakuen University, Sapporo 062-8605 (Japan)

2010-11-15

421

Reliable fusion of control and sensing in intelligent machines. Thesis  

NASA Technical Reports Server (NTRS)

Although robotics research has produced a wealth of sophisticated control and sensing algorithms, very little research has been aimed at reliably combining these control and sensing strategies so that a specific task can be executed. To improve the reliability of robotic systems, analytic techniques are developed for calculating the probability that a particular combination of control and sensing algorithms will satisfy the required specifications. The probability can then be used to assess the reliability of the design. An entropy formulation is first used to quickly eliminate designs not capable of meeting the specifications. Next, a framework for analyzing reliability based on the first order second moment methods of structural engineering is proposed. To ensure performance over an interval of time, lower bounds on the reliability of meeting a set of quadratic specifications with a Gaussian discrete time invariant control system are derived. A case study analyzing visual positioning in robotic system is considered. The reliability of meeting timing and positioning specifications in the presence of camera pixel truncation, forward and inverse kinematic errors, and Gaussian joint measurement noise is determined. This information is used to select a visual sensing strategy, a kinematic algorithm, and a discrete compensator capable of accomplishing the desired task. Simulation results using PUMA 560 kinematic and dynamic characteristics are presented.

Mcinroy, John E.

1991-01-01

422

A simplified general design procedure for beam shaper converting Gaussian to super-Gaussian profile  

SciTech Connect

This paper introduces a simplified general design procedure for designing laser beam shapers capable of redistributing an arbitrary beam profile into any desired output profile. Both geometrical and diffractive optical modelings are performed on a practical single lens shaper converting Gaussian to super-Gaussian profile that shows significant reduction of destructive effects on the beam uniformity over the sharp edge shapers.

Liu, Chuyu; Zhang, Shukui

2008-08-01

423

Control Law Synthesis for Vertical Fin Buffeting Alleviation Using Strain Actuation  

NASA Technical Reports Server (NTRS)

In the present investigation, the results obtained during the ground test of a closed-loop control system conducted on a full-scale fighter to attenuate vertical fin buffeting response using strain actuation are presented. Two groups of actuators consisting of piezoelectric elements distributed over the structure were designed to achieve authority over the first and second modes of the vertical fin. The control laws were synthesized using the Linear Quadratic Gaussian (LQG) method for a time-invariant control system. Three different pairs of sensors including strain gauges and accelerometers at different locations were used to close the feedback loop. The results demonstrated that measurable reductions in the root-mean-square (RMS) values of the fin dynamic response identified by the strain transducer at the critical point for fatigue at the root were achieved under the most severe buffet condition. For less severe buffet conditions, reductions of up to 58% were achieved.

Nitzsche, F.; Zimcik, D. G.; Ryall, T. G.; Moses, R. W.; Henderson, D. A.

1999-01-01

424

The complete Gaussian class of quasiprobabilities and its relation to squeezed states and their discrete excitations  

NASA Astrophysics Data System (ADS)

The requirements on the general structure of quasiprobabilities for a single boson mode are investigated. The complete Gaussian class of quasiprobabilities, which can be obtained by convolutions of the Wigner quasiprobability with the complete class of normalized Gaussian functions, is represented by a three-dimensional complex vector parameter 1355-5111/8/2/003/img1 with the property of additivity when composing convolutions and meaning that the transition between two quasiprobabilities with the vector parameters r and s is given by the convolution with a Gaussian function belonging to the vector parameter r- s. The scalar product 1355-5111/8/2/003/img2 of r with itself is related to the determinant of the second-rank symmetric tensor of the quadratic form in the exponent of the Gaussian functions. This is obtained by a mapping with the two symmetric Pauli spin matrices and the unity matrix. The Wigner quasiprobability takes on the central position within this Gaussian class with the vector parameter r = (0,0,0). The class of s-ordered quasiprobabilities is described by the vector parameters 1355-5111/8/2/003/img3 with 1355-5111/8/2/003/img4 and its diagonalization is connected with displaced Fock states 1355-5111/8/2/003/img5. The class of quasiprobabilities corresponding to the linear interpolation between standard and antistandard ordering belongs to the vector parameter 1355-5111/8/2/003/img6 with 1355-5111/8/2/003/img7. Its diagonalization is connected with discrete series of excitations of the eigenstates of the canonical operators Q and P. The diagonalization of the complete Gaussian class of quasiprobabilities with real vector parameter 1355-5111/8/2/003/img8 and 1355-5111/8/2/003/img9 leads to dual systems of discrete excitations of squeezed coherent states with mutually orthogonal squeezing axes and properties of orthogonality and completeness and provides a possible generalization of the displaced Fock states. The diagonalization is basically different for real and complex vector parameters r. A generalization of the coherent-state quasiprobability, which uses squeezed coherent states instead of coherent states, belongs to a vector parameter 1355-5111/8/2/003/img8 with real 1355-5111/8/2/003/img11 and imaginary 1355-5111/8/2/003/img12 and 1355-5111/8/2/003/img13 and with 1355-5111/8/2/003/img14. New representations of special classes of quasiprobabilities are derived.

Wünsche, Alfred

1996-04-01

425

Simulator evaluation of system identification with on-line control law update for the controls and astrophysics experiment in space  

NASA Technical Reports Server (NTRS)

A procedure for optimizing the performance of large flexible spacecraft that require active vibration suppression to achieve required performance is presented. The procedure is to conduct on-orbit testing and system identification followed by a control system design. It is applied via simulation to a spacecraft configuration currently being considered for flight test by NASA - the Controls, Astrophysics, and Structures Experiment in Space (CASES). The system simulator is based on a NASTRAN finite element structural model. A finite number of modes is used to represent the structural dynamics. The system simulator also includes models of the electronics, actuators, sensors, the digital controller, and the internal and external disturbances. Nonlinearities caused by quantization are included in the study to examine tolerance of the procedure to modelling errors. Disturbance and sensor noise is modelled as a Gaussian process. For system identification, the system is excited using sinusoidal inputs at the resonant frequencies of the structure using each actuator. Mode shapes, frequencies, and damping ratios are identified from the unforced response sensor data after each excitation. Then, the excitation data is used to identify the actuator influence coefficients. The results of the individual parameter identification analyses are assembled into an aggregate system model. The control design is accomplished based only on the identified model using multi-input/output linear quadratic Gaussian theory. Its performance is evaluated based on time-to-damp as compared with the uncontrolled structure.

Montgomery, Raymond C.; Ghosh, Dave; Scott, Michael A.; Warnaar, Dirk

1991-01-01

426

Hydraulic conductivity fields: Gaussian or not?  

NASA Astrophysics Data System (ADS)

Hydraulic conductivity (K) fields are used to parameterize groundwater flow and transport models. Numerical simulations require a detailed representation of the K field, synthesized to interpolate between available data. Several recent studies introduced high-resolution K data (HRK) at the Macro Dispersion Experiment (MADE) site, and used ground-penetrating radar (GPR) to delineate the main structural features of the aquifer. This paper describes a statistical analysis of these data, and the implications for K field modeling in alluvial aquifers. Two striking observations have emerged from this analysis. The first is that a simple fractional difference filter can have a profound effect on data histograms, organizing non-Gaussian ln K data into a coherent distribution. The second is that using GPR facies allows us to reproduce the significantly non-Gaussian shape seen in real HRK data profiles, using a simulated Gaussian ln K field in each facies. This illuminates a current controversy in the literature, between those who favor Gaussian ln K models, and those who observe non-Gaussian ln K fields. Both camps are correct, but at different scales.

Meerschaert, Mark M.; Dogan, Mine; Dam, Remke L.; Hyndman, David W.; Benson, David A.

2013-08-01

427

Graphical calculus for Gaussian pure states  

SciTech Connect

We provide a unified graphical calculus for all Gaussian pure states, including graph transformation rules for all local and semilocal Gaussian unitary operations, as well as local quadrature measurements. We then use this graphical calculus to analyze continuous-variable (CV) cluster states, the essential resource for one-way quantum computing with CV systems. Current graphical approaches to CV cluster states are only valid in the unphysical limit of infinite squeezing, and the associated graph transformation rules only apply when the initial and final states are of this form. Our formalism applies to all Gaussian pure states and subsumes these rules in a natural way. In addition, the term 'CV graph state' currently has several inequivalent definitions in use. Using this formalism we provide a single unifying definition that encompasses all of them. We provide many examples of how the formalism may be used in the context of CV cluster states: defining the 'closest' CV cluster state to a given Gaussian pure state and quantifying the error in the approximation due to finite squeezing; analyzing the optimality of certain methods of generating CV cluster states; drawing connections between this graphical formalism and bosonic Hamiltonians with Gaussian ground states, including those useful for CV one-way quantum computing; and deriving a graphical measure of bipartite entanglement for certain classes of CV cluster states. We mention other possible applications of this formalism and conclude with a brief note on fault tolerance in CV one-way quantum computing.

Menicucci, Nicolas C.; Flammia, Steven T. [Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5 (Canada); Loock, Peter van [Optical Quantum Information Theory Group, Max Planck Institute for the Science of Light, Guenther-Scharowsky-Str. 1, Building 26, D-91058 Erlangen (Germany); Institute of Theoretical Physics I, Universitaet Erlangen-Nuernberg, Staudtstr. 7/B2, D-91058 Erlangen (Germany)

2011-04-15

428

A new adaptive control approach for aerospace vehicles with parameter uncertainties  

NASA Technical Reports Server (NTRS)

A new stochastic adaptive control structure is developed for the problem of combined parameter estimation and control of aerospace vehicles with changing parameters. Parameter uncertainties are modeled as first-order Gauss-Markov processes, and are introduced to the system dynamics through a small parameter. It is assumed that an accurate inertial measurement unit gives perfect measurements of the state variables. Since the stochastic system is assumed to be Gauss-Markov, the density function of the parameters given these measurements is conditionally Gaussian. Based on this conditionally Gaussian density, the problem of minimizing a quadratic cost over an infinite time horizon can be set up within the framework of stochastic optimal control theory. The optimal feedback control law is derived from a straightforward expansion of the Hamilton-Jacobi-Bellman equation, based on the LQG solution. The resulting nonlinear controller is applied to the pitch axis control of a space platform with uncertain moments of inertia and is shown to produce marked improvement over a fixed controller.

Hahn, Yungsun; Speyer, Jason L.

1989-01-01

429

An Instability Index Theory for Quadratic Pencils and Applications  

NASA Astrophysics Data System (ADS)

Primarily motivated by the stability analysis of nonlinear waves in second-order in time Hamiltonian systems, in this paper we develop an instability index theory for quadratic operator pencils acting on a Hilbert space. In an extension of the known theory for linear pencils, explicit connections are made between the number of eigenvalues of a given quadratic operator pencil with positive real parts to spectral information about the individual operators comprising the coefficients of the spectral parameter in the pencil. As an application, we apply the general theory developed here to yield spectral and nonlinear stability/instability results for abstract second-order in time wave equations. More specifically, we consider the problem of the existence and stability of spatially periodic waves for the "good" Boussinesq equation. In the analysis our instability index theory provides an explicit, and somewhat surprising, connection between the stability of a given periodic traveling wave solution of the "good" Boussinesq equation and the stability of the same periodic profile, but with different wavespeed, in the nonlinear dynamics of a related generalized Korteweg-de Vries equation.

Bronski, Jared; Johnson, Mathew A.; Kapitula, Todd

2014-04-01

430

Quadratic Reciprocity and the Group Orders of Particle States  

SciTech Connect

The construction of inverse states in a finite field F{sub P{sub P{alpha}}} enables the organization of the mass scale by associating particle states with residue class designations. With the assumption of perfect flatness ({Omega}total = 1.0), this approach leads to the derivation of a cosmic seesaw congruence which unifies the concepts of space and mass. The law of quadratic reciprocity profoundly constrains the subgroup structure of the multiplicative group of units F{sub P{sub {alpha}}}* defined by the field. Four specific outcomes of this organization are (1) a reduction in the computational complexity of the mass state distribution by a factor of {approximately}10{sup 30}, (2) the extension of the genetic divisor concept to the classification of subgroup orders, (3) the derivation of a simple numerical test for any prospective mass number based on the order of the integer, and (4) the identification of direct biological analogies to taxonomy and regulatory networks characteristic of cellular metabolism, tumor suppression, immunology, and evolution. It is generally concluded that the organizing principle legislated by the alliance of quadratic reciprocity with the cosmic seesaw creates a universal optimized structure that functions in the regulation of a broad range of complex phenomena.

DAI,YANG; BORISOV,ALEXEY B.; LONGWORTH,JAMES W.; BOYER,KEITH; RHODES,CHARLES K.

2001-06-01

431

Half-quadratic based Iterative Minimization for Robust Sparse Representation.  

PubMed

Robust sparse representation has shown significant potential in solving challenging problems in computer vision such as biometrics and visual surveillance. Although several robust sparse models have been proposed and promising results have been obtained, they are either for error correction or for error detection, and learning a general framework that systematically unifies these two aspects and explore their relation is still an open problem. In this paper, we develop a half-quadratic (HQ) framework to solve the robust sparse representation problem. By defining different kinds of half-quadratic functions, the proposed HQ framework is applicable to performing both error correction and error detection. More specifically, by using the additive form of HQ, we propose an L1-regularized error correction method by iteratively recovering corrupted data from errors incurred by noises and outliers; by using the multiplicative form of HQ, we propose an L1-regularized error detection method by learning from uncorrupted data iteratively. We also show that the L1-regularization solved by soft-thresholding function has a dual relationship to Huber M-estimator, which theoretically guarantees the performance of robust sparse representation in terms of M-estimation. Experiments on robust face recognition under severe occlusion and corruption validate our framework and findings. PMID:23712994

He, Ran; Zheng, Wei-Shi; Tan, Tieniu; Sun, Zhenan

2013-05-21

432

Integrated structural control design of large space structures  

SciTech Connect

Active control of structures has been under intensive development for the last ten years. Reference 2 reviews much of the identification and control technology for structural control developed during this time. The technology was initially focused on space structure and weapon applications; however, recently the technology is also being directed toward applications in manufacturing and transportation. Much of this technology focused on multiple-input/multiple-output (MIMO) identification and control methodology because many of the applications require a coordinated control involving multiple disturbances and control objectives where multiple actuators and sensors are necessary for high performance. There have been many optimal robust control methods developed for the design of MIMO robust control laws; however, there appears to be a significant gap between the theoretical development and experimental evaluation of control and identification methods to address structural control applications. Many methods have been developed for MIMO identification and control of structures, such as the Eigensystem Realization Algorithm (ERA), Q-Markov Covariance Equivalent Realization (Q-Markov COVER) for identification; and, Linear Quadratic Gaussian (LQG), Frequency Weighted LQG and H-/ii-synthesis methods for control. Upon implementation, many of the identification and control methods have shown limitations such as the excitation of unmodelled dynamics and sensitivity to system parameter variations. As a result, research on methods which address these problems have been conducted.

Allen, J.J.; Lauffer, J.P.

1995-01-01

433

Non-Gaussianity in island cosmology  

SciTech Connect

In this paper we fully calculate the non-Gaussianity of primordial curvature perturbation of the island universe by using the second order perturbation equation. We find that for the spectral index n{sub s}{approx_equal}0.96, which is favored by current observations, the non-Gaussianity level f{sub NL} seen in an island will generally lie between 30 and 60, which may be tested by the coming observations. In the landscape, the island universe is one of anthropically acceptable cosmological histories. Thus the results obtained in some sense mean the coming observations, especially the measurement of non-Gaussianity, will be significant to clarify how our position in the landscape is populated.

Piao Yunsong [College of Physical Sciences, Graduate School of Chinese Academy of Sciences, Beijing 100049 (China)

2009-04-15

434

Variational learning for Gaussian mixture models.  

PubMed

This paper proposes a joint maximum likelihood and Bayesian methodology for estimating Gaussian mixture models. In Bayesian inference, the distributions of parameters are modeled, characterized by hyperparameters. In the case of Gaussian mixtures, the distributions of parameters are considered as Gaussian for the mean, Wishart for the covariance, and Dirichlet for the mixing probability. The learning task consists of estimating the hyperparameters characterizing these distributions. The integration in the parameter space is decoupled using an unsupervised variational methodology entitled variational expectation-maximization (VEM). This paper introduces a hyperparameter initialization procedure for the training algorithm. In the first stage, distributions of parameters resulting from successive runs of the expectation-maximization algorithm are formed. Afterward, maximum-likelihood estimators are applied to find appropriate initial values for the hyperparameters. The proposed initialization provides faster convergence, more accurate hyperparameter estimates, and better generalization for the VEM training algorithm. The proposed methodology is applied in blind signal detection and in color image segmentation. PMID:16903369

Nasios, Nikolaos; Bors, Adrian G

2006-08-01

435

Number counts and non-Gaussianity  

NASA Astrophysics Data System (ADS)

We describe a general procedure for using number counts of any object to constrain the probability distribution of the primordial fluctuations, allowing for generic weak non-Gaussianity. We apply this procedure to use limits on the abundance of primordial black holes and dark matter ultracompact minihalos to characterize the allowed statistics of primordial fluctuations on very small scales. We present constraints on the power spectrum and the amplitude of the skewness for two different families of non-Gaussian distributions, distinguished by the relative importance of higher moments. Although primordial black holes probe the smallest scales, ultracompact minihalos provide significantly stronger constraints on the power spectrum and so are more likely to eventually provide small-scale constraints on non-Gaussianity.

Shandera, Sarah; Erickcek, Adrienne L.; Scott, Pat; Galarza, Jhon Yana

2013-11-01

436

A multiloop, digital flutter suppression control law synthesis case study  

NASA Technical Reports Server (NTRS)

A methodology for obtaining a digital low-order, multiloop, robust control law for aeroelastic application from a full-state Linear Quadratic Gaussian design is presented. As part of the design methodology, the multivariable system robustness at the plant input and output is evaluated using singular value properties and improved using constrained optimization procedures. To validate the methodology, a digital flutter suppression system has been designed for the full-span Active Flexible Wing (AFW) wind-tunnel model as part of a collaborative effort between the NASA Langley Research Center and Rockwell International. Preliminary results for a low-order discrete, symmetric flutter suppression system design that significantly improved the AFW model stability are provided and the experiences gained during the design process are discussed.

Mukhopadhyay, Vivek; Perry, Boyd, III; Noll, Thomas E.

1989-01-01

437

Robust controller synthesis for a large flexible space antenna  

NASA Technical Reports Server (NTRS)

The linear-quadratic Gaussian/loop-transfer-recovery method is used to synthesize a fine-pointing control system for a large space antenna. A finite-element model for the 122-m hoop/column antenna is employed, and a compensator, utilizing attitudes sensors and torque actuators, is designed which achieves pointing performance while maintaining stability robustness to unmodeled dynamics. Inclusion of the rigid-body modes plus the first three elastic modes is found to be necessary to achieve a 0.1-rad/s bandwidth. Results are obtained by employing a modification of the standard robustness recovery procedure, which reduces the conservative nature of the design methodology. Performance degradation is encountered due to the presence of unavoidable invariant zeros within the design bandwidth.

Sundararajan, N.; Joshi, S. M.; Armstrong, E. S.

1987-01-01

438

A methodology for designing robust multivariable nonlinear feedback control systems  

NASA Technical Reports Server (NTRS)

This paper presents an outline of a methodology for the design of nonlinear dynamic compensators for nonlinear multivariable systems with guarantees of closed-loop stability, robustness, and performance. The method is an extension of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery (LQG/LTR) methodology for linear systems, thus hinging upon the idea of constructing an approximate nonlinear inverse operator for the plant. A major feature of the method is a unification of both the state-space and Input-Output formulations. The major results of the paper are: (1) Properties of the solution of certain optimal control problems; (2) New results on nonlinear estimation, including a new nonlinear observer with certain guaranteed properties; (3) The Loop Operator Recovery (LOR) procedure, and (4) Inclusion of command-following and disturbance rejection with a goal of a closed-loop stable, robust system.

Grunberg, D. B.; Athans, M.

1985-01-01

439

Gaussian-state description of squeezed light  

SciTech Connect

We present a Gaussian-state description of squeezed light generated in an optical parametric oscillator. Using the Gaussian-state description we describe the dynamics of the system conditioned on homodyne detection on the output field. Our theory shows that the output field is squeezed only if observed for long enough times or by a detector with finite bandwidth. As an application of the present approach we consider the use of finite bandwidth squeezed light together with a sample of spin-polarized atoms to estimate a magnetic field.

Petersen, Vivi; Moelmer, Klaus [QUANTOP-Danish National Research Foundation Center for Quantum Optics, University of Aarhus, DK-8000 Aarhus C (Denmark); Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C (Denmark); Madsen, Lars Bojer [Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C (Denmark)

2005-11-15

440

Primordial non-Gaussianity in multiscalar inflation  

SciTech Connect

We give a concise formula for the non-Gaussianity of the primordial curvature perturbation generated on superhorizon scales in the multiscalar inflation model without assuming slow-roll conditions. This is an extension of our previous work. Using this formula, we study the generation of non-Gaussianity for the double inflation models in which the slow-roll conditions are temporarily violated after horizon exit, and we show that the nonlinear parameter f{sub NL} for such models is suppressed by the slow-roll parameters evaluated at the time of horizon exit.

Yokoyama, Shuichiro; Tanaka, Takahiro [Department of Physics, Kyoto University, Kyoto 606-8502 (Japan); Suyama, Teruaki [Institute for Cosmic Ray Research, University of Tokyo, Kashiwa 277-8582 (Japan)

2008-04-15

441

Invariant measures on multimode quantum Gaussian states  

SciTech Connect

We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom-the symplectic eigenvalues-which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.

Lupo, C. [School of Science and Technology, Universita di Camerino, I-62032 Camerino (Italy); Mancini, S. [School of Science and Technology, Universita di Camerino, I-62032 Camerino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, I-06123 Perugia (Italy); De Pasquale, A. [NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa (Italy); Facchi, P. [Dipartimento di Matematica and MECENAS, Universita di Bari, I-70125 Bari (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Florio, G. [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi, Piazza del Viminale 1, I-00184 Roma (Italy); Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy); Pascazio, S. [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy)

2012-12-15

442

Quantum Filtering and Optimal Control  

NASA Astrophysics Data System (ADS)

Quantum mechanical systems exhibit an inherently probabilistic nature upon measurement which excludes in principle the singular direct observability case. Quantum theory of time continuous measurements and quantum filtering developed by VPB on the basis of semi-Markov independent increment models for quantum noise and quantum nondemolition (QND) observability is generalized for demolition indirect measurements of quantum unstable systems satisfying the microcausality principle. The reduced quantum feedback-controlled dynamics is described both by linear semi-Markov and nonlinear conditionally-Markov stochastic master equations. Using this scheme for diffusive and counting measurement to describe the stochastic evolution of the open quantum system under the continuous indirect observation and working in parallel with classical indeterministic control theory, we show the conditionally-Markov Bellman equations for optimal feedback control of the a posteriori stochastic quantum states conditioned upon these measurements. The resulting Bellman equation for the diffusive observation is then applied to the explicitly solvable quantum linear-quadratic-Gaussian (LQG) problem which emphasizes many similarities with the corresponding classical control problem.

Belavkin, Viacheslav P.; Edwards, Simon

2008-08-01

443

A Robust Gaussian Filter Corresponding to the Transmisson Characterisic of the Gaussian Filter  

NASA Astrophysics Data System (ADS)

A surface roughness profile of an object can be measured by extracting a mean line of the long wavelength component from the primary profile, and by subtracting it from the primary profile. This mean line is usually computed by convolving the traditional Gaussian filter (GF) and the primary profile. However, if an outlier exists in the primary profile, the output of a Gaussian filter will be greatly affected by the outlier. To solve the outlier problem, several schemes of robust Gaussian filter have been proposed. However there are several fatal problems that a mean line determined with respect to the measurement data containing no outliers does not agree with the mean line of the Gaussian filter output. To solve these problems, this paper proposes a new robust Gaussian filter based on a fast M-estimation method (FMGF) and the performance of the new robust Gaussian filter was experimentally clarified. As a result, if an outlier exist, the proposed method behaves a robust performance. If no outlier exists, the output wave pattern, RMSE and transmission characteristic accorded mutually with Gaussian filter.

Kondo, Yuki; Numada, Munetoshi; Koshimizu, Hiroyasu

2014-03-01

444

Equivalent total doses for different fractionation schemes, based on the linear quadratic model  

SciTech Connect

A majority of patients receiving radical radiation therapy are treated with 1.8-2.0-Gy fractions, a dose that has evolved from clinical experience. However, other fractionation schemes can be advantageous. When fractionation is altered, the total dose prescribed should lead to equivalent or higher tumor control with the same or less tissue toxicity. To facilitate the use of different fractionation schemes, the authors compiled tables for equivalent biologic doses for late toxicity in normal tissues and tumoricidal doses for epithelial tumors, for various fraction sizes. The linear quadratic model according to Fowler was used. It is shown how these tables should be modified for proliferation of tumors during the course of radiation therapy. The tables make the use of different fractionation schemes easy. They also allow adjustment of total dose if fractionation needs to be changed during the course of treatment.

Muller-Runkel, R.; Vijayakumar, S. (St. Margaret Hospital and Health Centers, Hammond, IN (USA))

1991-05-01

445

Normalized Intensity Variance of a Single-Mode Laser Driven by Quadratic Pump Noise  

NASA Astrophysics Data System (ADS)

A single-mode laser noise model driven by quadratic pump noise is proposed. The approximation Fokker-Planck equation (AFPE) and steady probability distribution of the laser intensity for the model are derived. It is found that the AFPE is symmetrical with respect to the sign of ?. This point leads to some symmetrical features for the statistical properties of the system. As an important application of the above-mentioned results, the normalized intensity variance NIV is derived. It is found that the NIV is controlled intensively by the cross-correlation between the real and imaginary parts of pump noise. For the NIV versus a curves an interest cross-correlation effect, the two directions of the NIV versus a curves, is found.

Cao, Li; Wu, Da-Jin

446

Rays of Small Integer Solutions of Homogeneous Ternary Quadratic Equations  

NASA Astrophysics Data System (ADS)

We have dealt with the general ternary quadratic equation: ax2 + by^ {2} + cz2 + dxy + exz + fyz = 0 with integer coefficients. After giving a matrix-reduction formula for a quadratic equation in any number of variables, of which the reduction of the above ternary equation is an easy consequence, we have devoted our attention to the reduced equation: ax^ {2} + by2 + cz^{2 } = 0. We have devised an algorithm for reducing Dirichlet's possibly larger solutions to this prescribed range of Holzer's. Then we have generalized Holzer's theorem to the case of the ternary equation: ax^{2 } + by2 + cz2 + dxy + exz + fyz = 0, giving in this context a new range called the CM-range, of which the Holzer's range is a particular case when d = e = f = 0. We have described an algorithm for getting a solution of the general ternary within this CM-range. After that we have devised an algorithm for getting all the solutions of the Legendre's equation ax 2 + by2 + cz^ {2} = 0 within the Holzer's range--and have shown that if we regard this Legendre's equation as a double cone, these solutions within the Holzer's range lie along some definite rays, here called the CM-rays, which are completely determined by the prime factors of the coefficients a, b and c. After giving an algorithm for detecting these CM-rays of the reduced equation: ax^2 + by^2 + cz^2 = 0, we have shown how one can produce some similar rays of solutions of the above general ternary quadratic equation: ax2 + by2 + cz2 + dxy + exz + fyz = 0. Note that apart from the method of exhausting all the possibilities, so far there has been no precisely stated algorithm to find the minimum solutions of the above ternary equations. Towards the end, observing in the context of our main result an inequality involving two functions, namely C and PCM from doubz_sp{*} {3} to doubz_+, and simultaneously presenting some tables of these positive CM-rays or PCM-rays lying in the positive octant, we have concluded this work with a number of hints for some possible future investigations. (Abstract shortened with permission of author.).

Mishra, Sudhakara

1991-02-01

447

Approximating gaussian mixture model or radial basis function network with multilayer perceptron.  

PubMed

Gaussian mixture models (GMMs) and multilayer perceptron (MLP) are both popular pattern classification techniques. This brief shows that a multilayer perceptron with quadratic inputs (MLPQ) can accurately approximate GMMs with diagonal covariance matrices. The mapping equations between the parameters of GMM and the weights of MLPQ are presented. A similar approach is applied to radial basis function networks (RBFNs) to show that RBFNs with Gaussian basis functions and Euclidean norm can be approximated accurately with MLPQ. The mapping equations between RBFN and MLPQ weights are presented. There are well-established training procedures for GMMs, such as the expectation maximization (EM) algorithm. The GMM parameters obtained by the EM algorithm can be used to generate a set of initial weights of MLPQ. Similarly, a trained RBFN can be used to generate a set of initial weights of MLPQ. MLPQ training can be continued further with gradient-descent based methods, which can lead to improvement in performance compared to the GMM or RBFN from which it is initialized. Thus, the MLPQ can always perform as well as or better than the GMM or RBFN. PMID:24808530

Patrikar, A M

2013-07-01

448

Self focusing of a quadruple Gaussian laser beam in a plasma  

NASA Astrophysics Data System (ADS)

The self focusing of a quadruple Gaussian laser beam, comprising four coherent identical Gaussian beams with axes parallel to ? but shifted from z-axis by -x0?,x0?,-x0?,x0? in a collisionless plasma, is investigated in the paraxial ray approximation. The nonlinearity arises through the ponderomotive force led plasma density redistribution. As the beam propagates, it maintains the shape of its intensity profile with spot size r0 of each of the four distributions modified from r0 to r0f, x0, modified to x0f and the axial intensity enhanced by 1/f2, where f is the beam width parameter. In the regime of quadratic nonlinearity, the threshold beam power for self focusing, Pth, increases with x0 as the laser intensity gradient decreases and the ponderomotive force becomes weaker. At beam power greater than Pth, the beam focuses in an oscillatory manner, i.e., f varies periodically with z due to the saturating effect of nonlinearity. The locations of intensity maxima of the four beams also vary periodically with z. As x0 increases from 0 to 0.6r0, the transverse intensity gradient becomes weaker and the rate of self focusing, i.e., the rate of variation of f with z decreases.

Sati, Priti; Sharma, Anamika; Tripathi, V. K.

2012-09-01

449

Gof Tests for the Inverse Gaussian Distribution  

Microsoft Academic Search

This paper provides some new goodness of fit tests which can be used for assessing the appropriateness of both discrete and continuous distributions. The main focus is on the inverse Gaussian distribution. The first test statistic uses a standardized version of the logarithm of the empirical moment generating function in order to construct plots which are equivalent to a goodness-of-fit

Ioannis A. Koutrouvelis; Alex Karagrigoriou

450

Nonlinear Bayesian estimation using Gaussian sum approximations  

Microsoft Academic Search

Knowledge of the probability density function of the state conditioned on all available measurement data provides the most complete possible description of the state, and from this density any of the common types of estimates (e.g., minimum variance or maximum a posteriori) can be determined. Except in the linear Gaussian case, it is extremely difficult to determine this density function.

D. L. Alspach; H. W. Sorenson

1972-01-01

451

Advanced LIGO: non-Gaussian beams  

Microsoft Academic Search

By using non-Gaussian, flat-topped beams in the advanced gravitational wave interferometers currently being designed, one can reduce the impact on the interferometer sensitivity of a variety of fundamental disturbances (thermoelastic noise, noise in mirror coatings, thermal lensing, etc). This may make beating the standard quantum limit an achievable goal.

Erika D'Ambrosio; Richard O'Shaugnessy; Kip Thorne; Phil Willems; Sergey Strigin; Sergey Vyatchanin

2004-01-01

452

Non-Gaussianity effects in petrophysical quantities  

NASA Astrophysics Data System (ADS)

It has been proved that there are many indicators (petrophysical quantities) for the estimation of petroleum reservoirs. The value of information contained in each indicator is yet to be addressed. In this work, the most famous and applicable petrophysical quantities for a reservoir, which are the gamma emission (GR), sonic transient time (DT), neutron porosity (NPHI), bulk density (RHOB), and deep induced resistivity (ILD), have been analyzed in order to characterize a reservoir. The implemented technique is the well-logging method. Based on the log-normal model defined in random multiplicative processes, the probability distribution function (PDF) for the data sets is described. The shape of the PDF depends on the parameter ?2 which determines the efficiency of non-Gaussianity. When non-Gaussianity appears, it is a sign of uncertainty and phase transition in the critical regime. The large value and scale-invariant behavior of the non-Gaussian parameter ?2 is an indication of a new phase which proves adequate for the existence of petroleum reservoirs. Our results show that one of the indicators (GR) is more non-Gaussian than the other indicators, scale wise. This means that GR is a continuously critical indicator. But by moving windows with various scales, the estimated ?2 shows that the most appropriate indicator for distinguishing the critical regime is ILD, which shows an increase at the end of the measured region of the well.

Koohi Lai, Z.; Jafari, G. R.

2013-10-01

453

Halo clustering with nonlocal non-Gaussianity  

SciTech Connect

We show how the peak-background split (PBS) can be generalized to predict the effect of nonlocal primordial non-Gaussianity on the clustering of halos. Our approach is applicable to arbitrary primordial bispectra. We show that the scale dependence of halo clustering predicted in the peak-background split agrees with that of the local-biasing model on large scales. On smaller scales, k > or approx. 0.01h Mpc{sup -1}, the predictions diverge, a consequence of the assumption of separation of scales in the peak-background split. Even on large scales, PBS and local biasing do not generally agree on the amplitude of the effect outside of the high-peak limit. The scale dependence of the biasing - the effect that provides strong constraints to the local-model bispectrum - is far weaker for the equilateral and self-ordering-scalar-field models of non-Gaussianity. The bias scale dependence for the orthogonal and folded models is weaker than in the local model ({approx}k{sup -1}), but likely still strong enough to be constraining. We show that departures from scale-invariance of the primordial power spectrum may lead to order-unity corrections, relative to predictions made assuming scale-invariance--to the non-Gaussian bias in some of these nonlocal models for non-Gaussianity. An Appendix shows that a nonlocal model can produce the local-model bispectrum, a mathematical curiosity we uncovered in the course of this investigation.

Schmidt, Fabian; Kamionkowski, Marc [California Institute of Technology, Mail Code 350-17, Pasadena, California 91125 (United States)

2010-11-15

454

Speech Enhancement Using Gaussian Scale Mixture Models  

PubMed Central

This paper presents a novel probabilistic approach to speech enhancement. Instead of a deterministic logarithmic relationship, we assume a probabilistic relationship between the frequency coefficients and the log-spectra. The speech model in the log-spectral domain is a Gaussian mixture model (GMM). The frequency coefficients obey a zero-mean Gaussian whose covariance equals to the exponential of the log-spectra. This results in a Gaussian scale mixture model (GSMM) for the speech signal in the frequency domain, since the log-spectra can be regarded as scaling factors. The probabilistic relation between frequency coefficients and log-spectra allows these to be treated as two random variables, both to be estimated from the noisy signals. Expectation-maximization (EM) was used to train the GSMM and Bayesian inference was used to compute the posterior signal distribution. Because exact inference of this full probabilistic model is computationally intractable, we developed two approaches to enhance the efficiency: the Laplace method and a variational approximation. The proposed methods were applied to enhance speech corrupted by Gaussian noise and speech-shaped noise (SSN). For both approximations, signals reconstructed from the estimated frequency coefficients provided higher signal-to-noise ratio (SNR) and those reconstructed from the estimated log-spectra produced lower word recognition error rate because the log-spectra fit the inputs to the recognizer better. Our algorithms effectively reduced the SSN, which algorithms based on spectral analysis were not able to suppress.

Hao, Jiucang; Lee, Te-Won; Sejnowski, Terrence J.

2011-01-01

455

Gaussian Filtering using State Decomposition Methods  

Microsoft Academic Search

State estimation for nonlinear systems generally requires approximations of the system or the probability densities, as the occurring prediction and filtering equations cannot be solved in closed form. For instance, Linear Regression Kalman Filters like the Unscented Kalman Filter or the considered Gaussian Filter propagate a small set of sample points through the system to approximate the posterior mean and

Frederik Beutler; Marco F. Huber; Uwe D. Hanebeck

2009-01-01

456

Detecting drug promiscuity using Gaussian ensemble screening.  

PubMed

Polypharmacology describes the binding of a ligand to multiple protein targets (a promiscuous ligand) or multiple diverse ligands binding to a given target (a promiscuous target). Pharmaceutical companies are discovering increasing numbers of both promiscuous drugs and drug targets. Hence, polypharmacology is now recognized as an important aspect of drug design. Here, we describe a new and fast way to predict polypharmacological relationships between drug classes quantitatively, which we call Gaussian Ensemble Screening (GES). This approach represents a cluster of molecules with similar spherical harmonic surface shapes as a Gaussian distribution with respect to a selected center molecule. Calculating the Gaussian overlap between pairs of such clusters allows the similarity between drug classes to be calculated analytically without requiring thousands of bootstrap comparisons, as in current promiscuity prediction approaches. We find that such cluster similarity scores also follow a Gaussian distribution. Hence, a cluster similarity score may be transformed into a probability value, or "p-value", in order to quantify the relationships between drug classes. We present results obtained when using the GES approach to predict relationships between drug classes in a subset of the MDL Drug Data Report (MDDR) database. Our results indicate that GES is a useful way to study polypharmacology relationships, and it could provide a novel way to propose new targets for drug repositioning. PMID:22747187

Pérez-Nueno, Violeta I; Venkatraman, Vishwesh; Mavridis, Lazaros; Ritchie, David W

2012-08-27

457

Radon-Nikodym Derivatives of Gaussian Measures  

Microsoft Academic Search

We give simple necessary and sufficient conditions on the mean and covariance for a Gaussian measure to be equivalent to Wiener measure. This was formerly an unsolved problem [26]. An unsolved problem is to obtain the Radom-Nikodym derivative $d\\\\mu\\/d\\\

L. A. Shepp

1966-01-01

458

The Gaussian entropy of fermionic systems  

SciTech Connect

We consider the entropy and decoherence in fermionic quantum systems. By making a Gaussian Ansatz for the density operator of a collection of fermions we study statistical 2-point correlators and express the entropy of a system fermion in terms of these correlators. In a simple case when a set of N thermalised environmental fermionic oscillators interacts bi-linearly with the system fermion we can study its time dependent entropy, which also represents a quantitative measure for decoherence and classicalization. We then consider a relativistic fermionic quantum field theory and take a mass mixing term as a simple model for the Yukawa interaction. It turns out that even in this Gaussian approximation, the fermionic system decoheres quite effectively, such that in a large coupling and high temperature regime the system field approaches the temperature of the environmental fields. - Highlights: Black-Right-Pointing-Pointer We construct the Gaussian density operator for relativistic fermionic systems. Black-Right-Pointing-Pointer The Gaussian entropy of relativistic fermionic systems is described in terms of 2-point correlators. Black-Right-Pointing-Pointer We explicitly show the growth of entropy for fermionic fields mixing with a thermal fermionic environment.

Prokopec, Tomislav, E-mail: T.Prokopec@uu.nl [Institute for Theoretical Physics (ITP) and Spinoza Institute, Utrecht University, Postbus 80195, 3508 TD Utrecht (Netherlands)] [Institute for Theoretical Physics (ITP) and Spinoza Institute, Utrecht University, Postbus 80195, 3508 TD Utrecht (Netherlands); Schmidt, Michael G., E-mail: M.G.Schmidt@thphys.uni-heidelberg.de [Institut fuer Theoretische Physik, Heidelberg University, Philosophenweg 16, D-69120 Heidelberg (Germany); Weenink, Jan, E-mail: J.G.Weenink@uu.nl [Institute for Theoretical Physics (ITP) and Spinoza Institute, Utrecht University, Postbus 80195, 3508 TD Utrecht (Netherlands)] [Institute for Theoretical Physics (ITP) and Spinoza Institute, Utrecht University, Postbus 80195, 3508 TD Utrecht (Netherlands)

2012-12-15

459

Conditions for Gaussian long term manufacturing processes  

Microsoft Academic Search

The manufacturing community defines capability indices for manufacturing processes applicable time-wise for both long term and short term processes. The long term process distribution can be constructed from the consolidation of the data sets that was used to estimate the multiple short term distributions. There is a tendency for Gaussian distributed short-term processes to exhibit time sensitive random variation in

R. J. Pieper; Nikhil T. Satyala

2009-01-01

460

Gaussian Process modeling of large scale terrain  

Microsoft Academic Search

This paper addresses the problem of large scale terrain modeling for a mobile robot. Building a model of large scale terrain data that can adequately handle uncertainty and incompleteness in a statistically sound way is a very challenging problem. This work proposes the use of Gaussian Processes as models of large scale terrain. The proposed model naturally provides a multi-resolution

Shrihari Vasudevan; Fabio T. Ramos; Eric Nettleton; Hugh F. Durrant-whyte; Allan Blair

2009-01-01

461

Dislocation parity effects in crystals with quadratic nonlinear response.  

PubMed

The effect of edge topological dislocations on the phase matching spectrum of quadratic nonlinear photonic crystals was studied theoretically and experimentally. We have found that the parity of the dislocation's topological charge governs the transfer of energy between an input wave and its second harmonic. A dislocation with an odd topological charge nulls the efficiency of the otherwise optimal phase matched wavelength, whereas high conversion is now achieved at new wavelengths that exhibited low efficiency without the dislocation. However, when the topological charge is an even number, the dislocation has a negligible effect on the efficiency curve. This effect is observed in periodically poled crystals having a single peak in the phase matching spectrum, as well as in phase-reversed and quasiperiodic nonlinear photonic crystals that are characterized by multiple efficiency peaks, where a dimple is imprinted on each spectral peak. PMID:24580591

Sharabi, Shani; Voloch-Bloch, Noa; Juwiler, Irit; Arie, Ady

2014-02-01

462

A Fixed-Point Iteration Method with Quadratic Convergence  

SciTech Connect

The fixed-point iteration algorithm is turned into a quadratically convergent scheme for a system of nonlinear equations. Most of the usual methods for obtaining the roots of a system of nonlinear equations rely on expanding the equation system about the roots in a Taylor series, and neglecting the higher order terms. Rearrangement of the resulting truncated system then results in the usual Newton-Raphson and Halley type approximations. In this paper the introduction of unit root functions avoids the direct expansion of the nonlinear system about the root, and relies, instead, on approximations which enable the unit root functions to considerably widen the radius of convergence of the iteration method. Methods for obtaining higher order rates of convergence and larger radii of convergence are discussed.

Walker, Kevin P. [Engineering Science Software, Inc.; Sham, Sam [ORNL

2012-01-01

463

Lensless imaging by entangled photons from quadratic nonlinear photonic crystals  

NASA Astrophysics Data System (ADS)

Lenses play a key role in quantum imaging but inevitably constrain the spatial resolution and working wavelength. In this work we develop and demonstrate a lensless quantum ghost imaging by engineering quadratic nonlinear photonic crystals. With a transverse parabolic domain modulation introduced into the lithium tantalate crystal, the entangled photon pairs generated from parametric down-conversion will self-focus. Therefore we can dispense with additional lenses to construct imaging in a nonlocal way. The lensless imaging is found to follow a specific imaging formula where the effective focal length is determined by the domain modulation and pump wavelength. Additionally, two nonlocal images can be retrieved when the entangled photon pair is generated under two concurrent noncollinear phase-matching geometries. Our work provides a principle and method to realize lensless ghost imaging, which may be extended to other wavelengths and stimulate new types of practical quantum technologies.

Xu, P.; Leng, H. Y.; Zhu, Z. H.; Bai, Y. F.; Jin, H.; Gong, Y. X.; Yu, X. Q.; Xie, Z. D.; Mu, S. Y.; Zhu, S. N.

2012-07-01

464

Robust multivariable control of an active acoustic grillage: Modeling, design and implementation  

NASA Astrophysics Data System (ADS)

Active Noise Control has found wide application in recent years due to availability of fast computers, embedded and data acquisition systems. An Active Acoustic Grillage (AAG) is an array of sound sources and microphones forming an acoustic barrier trapping sound but allowing air and light to pass through. The objective of research reported in this dissertation is to apply multi-input- multi-output (MIMO) design methods and increase the system robustness while retaining or improving the performance in comparison with single-input-single-output (SISO) design. The AAG concept can be used for noise cancellation in ducts with relatively large cross- section. Although previously available distributed single-input-single-output (SISO) design provides an inexpensive and expandable system, the MIMO approach significantly improves stability and robustness of the AAG. Methods considered for controller design include Linear Quadratic Gaussian (LQG) and H? mixed sensitivity optimization. Serious challenges are imposed by the non-minimum phase behavior and lightly damped acoustic modes. Several linear quadratic and robust controllers have been developed that provide 10-15 dB attenuation in the frequency range of 100-300 Hz. Benefits of MIM0 design are demonstrated on a test grillage. These results can be applied to other noise control systems with multiple sensors and actuators where cross coupling is significant.

Sepp, Kalev

2001-11-01

465

H2, fixed architecture, control design for large scale systems. Ph.D. Thesis  

NASA Technical Reports Server (NTRS)

The H2, fixed architecture, control problem is a classic linear quadratic Gaussian (LQG) problem whose solution is constrained to be a linear time invariant compensator with a decentralized processing structure. The compensator can be made of p independent subcontrollers, each of which has a fixed order and connects selected sensors to selected actuators. The H2, fixed architecture, control problem allows the design of simplified feedback systems needed to control large scale systems. Its solution becomes more complicated, however, as more constraints are introduced. This work derives the necessary conditions for optimality for the problem and studies their properties. It is found that the filter and control problems couple when the architecture constraints are introduced, and that the different subcontrollers must be coordinated in order to achieve global system performance. The problem requires the simultaneous solution of highly coupled matrix equations. The use of homotopy is investigated as a numerical tool, and its convergence properties studied. It is found that the general constrained problem may have multiple stabilizing solutions, and that these solutions may be local minima or saddle points for the quadratic cost. The nature of the solution is not invariant when the parameters of the system are changed. Bifurcations occur, and a solution may continuously transform into a nonstabilizing compensator. Using a modified homotopy procedure, fixed architecture compensators are derived for models of large flexible structures to help understand the properties of the constrained solutions and compare them to the corresponding unconstrained ones.

Mercadal, Mathieu

1990-01-01

466

Spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity  

SciTech Connect

We present a brief review of the results of fifty years of development efforts in spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity. The recent original results obtained by the authors show the fundamental possibility of determining, from experimental data, the coordinate dependences of complex quadratic susceptibility tensor components of a onedimensionally inhomogeneous (along the z axis) medium with an arbitrary frequency dispersion, if the linear dielectric properties of the medium also vary along the z axis and are described by a diagonal tensor of the linear dielectric constant. It is assumed that the medium in question has the form of a plane-parallel plate, whose surfaces are perpendicular to the direction of the inhomogeneity. Using the example of several components of the tensors X{sup (2)}(z, {omega}{sub 1} {+-} {omega}{sub 2}; {omega}{sub 1}, {+-} {omega}{sub 2}), we describe two methods for finding their spatial profiles, which differ in the interaction geometry of plane monochromatic fundamental waves with frequencies {omega}{sub 1} and {omega}{sub 2}. The both methods are based on assessing the intensity of the waves propagating from the plate at the sum or difference frequency and require measurements over a range of angles of incidence of the fundamental waves. Such measurements include two series of additional estimates of the intensities of the waves generated under special conditions by using the test and additional reference plates, which eliminates the need for complicated phase measurements of the complex amplitudes of the waves at the sum (difference) frequency.

Golubkov, A A; Makarov, Vladimir A

2011-11-30

467

a Distributed Gaussian Discrete Variable Representation  

NASA Astrophysics Data System (ADS)

In this work a discrete variable representation (DVR) is constructed from a distributed Gaussian basis (DGB). A DGB is a finite or infinite chain of uniformly distributed Gaussians g_{n}(x) = e^{-c^2(x/d-n)^2} where n takes integer values. There are three main parts of this thesis. In the first part (Chapter III) the finite chain distributed Gaussian DVR (Finite Chain DG-DVR) is derived. In order to accomplish this, the distributed Gaussian orthogonal polynomials are introduced. The connection of these polynomials to Stieltjes-Wigert polynomials is shown. The recurrence relation for these orthogonal polynomials is derived. Tested recipes are given to calculate the quadrature points and weights and to construct the corresponding Lagrange functions which are analogs of Lagrange interpolation polynomials. The symmetries of quadrature points, weights, and Lagrange functions are derived. Limit cases ctoinfty and cto 0 are studied. In the second part (Chapter IV)the infinite chain limit DG-DVR is derived from a limit of the finite chain DG-DVR. The quadrature points and weights and the Lagrange functions are found in this limit and kinetic energy operator is constructed. It is shown that in the limit c to 0 the infinite chain DG-DVR reduces to Colbert and Miller's DVR. A discussion of ability of a distributed Gaussian basis to represent an arbitrary function is given. The results of this treatment yield a possible explanation of surprising accuracy of Colbert-Miller DVR. In the third part construction of the DG-DVR is given when one point is chosen arbitrarily. Some interesting identities and integral representations for the b _{n} and sigma_ {n} coefficients that are introduced in the second part are found.

Karabulut, Hasan

468

Quantifying non-Gaussianity for quantum information  

SciTech Connect

We address the quantification of non-Gaussianity (nG) of states and operations in continuous-variable systems and its use in quantum information. We start by illustrating in detail the properties and the relationships of two recently proposed measures of nG based on the Hilbert-Schmidt distance and the quantum relative entropy (QRE) between the state under examination and a reference Gaussian state. We then evaluate the non-Gaussianities of several families of non-Gaussian quantum states and show that the two measures have the same basic properties and also share the same qualitative behavior in most of the examples taken into account. However, we also show that they introduce a different relation of order; that is, they are not strictly monotone to each other. We exploit the nG measures for states in order to introduce a measure of nG for quantum operations, to assess Gaussification and de-Gaussification protocols, and to investigate in detail the role played by nG in entanglement-distillation protocols. Besides, we exploit the QRE-based nG measure to provide different insight on the extremality of Gaussian states for some entropic quantities such as conditional entropy, mutual information, and the Holevo bound. We also deal with parameter estimation and present a theorem connecting the QRE nG to the quantum Fisher information. Finally, since evaluation of the QRE nG measure requires the knowledge of the full density matrix, we derive some experimentally friendly lower bounds to nG for some classes of states and by considering the possibility of performing on the states only certain efficient or inefficient measurements.

Genoni, Marco G.; Paris, Matteo G. A. [Consorzio Nazionale Interuniversitario per le Scienze Fisiche della Materia, UdR Milano, I-20133 Milano (Italy); Dipartimento di Fisica, Universita degli Studi di Milano, I-20133 Milano (Italy)

2010-11-15