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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

Adaptive continuous-time linear quadratic Gaussian control  

E-print Network

The adaptive linear quadratic Gaussian control problem, where the linear transformation of the state A and the linear transformation of the control B are unknown, is solved assuming only that (A, B) is controllable and (A, ...

Duncan, Tyrone E.; Guo, L.; Pasik-Duncan, Bozenna

1999-09-01

3

Robustness results in linear-quadratic Gaussian based multivariable control designs  

NASA Technical Reports Server (NTRS)

The robustness of control systems with respect to model uncertainty is considered using simple frequency domain criteria. Available and new results are derived under a common framework in which the minimum singular value of the return difference transfer matrix is the key quantity. In particular, robustness results associated with multivariable control systems designed on the basis of linear-quadratic (LQ) and the linear-quadratic Gaussian (LQG) design methodologies are presented.

Lehtomaki, N. A.; Athans, M.; Sandell, N. R., Jr.

1981-01-01

4

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

5

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

6

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

7

Experimental study on Modified Linear Quadratic Gaussian Control for Adaptive Optics  

E-print Network

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 root mean square (RMS) error of the residual wave front. However, with the PI controller one does not reach this minimum. A possibility to achieve is to use Linear Quadratic Gaussian Control (LQG). In practice, however this control algorithm still encounters one unexpected problem, leading to the divergence of control in AO. In this paper we propose a Modified LQG (MLQG) to solve this issue. The controller is analyzed explicitly. Test in the lab shows strong stability and high precision compared to the classical control.

Fu, Qiang; Dethard, Peter; Shen, Feng; Rao, Changhui; Li, Xinyang

2014-01-01

8

A Structured Linear Quadratic Gaussian Based Control Design Algorithm for Machine Tool Controllers Including Both Feed Drive and Process Dynamics  

Microsoft Academic Search

A new extension of the stochastic linear quadratic Gaussian (LQG) regulator problem is developed and used for the design of new suboptimal cross-coupling controllers for machine tool drives. This new extension allowed us to combine both the drive and the cutting dynamics into a unified model driven by the static and the dynamic portions of the cutting force. The dynamic

E. M. Elbeheiry; W. H. ELMARAGHY; H. A. ELMARAGHY

2005-01-01

9

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

10

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

11

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

12

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

13

CREATED ON MAY 31, 2013 1 Linear Quadratic Gaussian (LQG) Control of Wind  

E-print Network

navigation control systems, medical porocesses controllers and even nuclear power plants. It combines both wind trubines. Such control theories are not only capable of increasing the energy capture efficiency and maintenance costs associated with the system. In this paper, the general formulation of the Linear Quadratic

Lavaei, Javad

14

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

15

Optimal and suboptimal quadratic forms for noncentered Gaussian processes.  

PubMed

Individual random trajectories of stochastic processes are often analyzed by using quadratic forms such as time averaged (TA) mean square displacement (MSD) or velocity auto-correlation function (VACF). The appropriate quadratic form is expected to have a narrow probability distribution in order to reduce statistical uncertainty of a single measurement. We consider the problem of finding the optimal quadratic form that minimizes a chosen cumulant moment (e.g., the variance) of the probability distribution, under the constraint of fixed mean value. For discrete noncentered Gaussian processes, we construct the optimal quadratic form by using the spectral representation of cumulant moments. Moreover, we obtain a simple explicit formula for the smallest achievable cumulant moment that may serve as a quality benchmark for other quadratic forms. We illustrate the optimality issues by comparing the optimal variance with the variances of the TA MSD and TA VACF of fractional Brownian motion superimposed with a constant drift and independent Gaussian noise. PMID:24125246

Grebenkov, Denis S

2013-09-01

16

Optimal and suboptimal quadratic forms for noncentered Gaussian processes  

NASA Astrophysics Data System (ADS)

Individual random trajectories of stochastic processes are often analyzed by using quadratic forms such as time averaged (TA) mean square displacement (MSD) or velocity auto-correlation function (VACF). The appropriate quadratic form is expected to have a narrow probability distribution in order to reduce statistical uncertainty of a single measurement. We consider the problem of finding the optimal quadratic form that minimizes a chosen cumulant moment (e.g., the variance) of the probability distribution, under the constraint of fixed mean value. For discrete noncentered Gaussian processes, we construct the optimal quadratic form by using the spectral representation of cumulant moments. Moreover, we obtain a simple explicit formula for the smallest achievable cumulant moment that may serve as a quality benchmark for other quadratic forms. We illustrate the optimality issues by comparing the optimal variance with the variances of the TA MSD and TA VACF of fractional Brownian motion superimposed with a constant drift and independent Gaussian noise.

Grebenkov, Denis S.

2013-09-01

17

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

18

A tutorial on the LQG/LTR method. [Linear Quadratic Gaussian/Loop Transfer Recovery  

NASA Technical Reports Server (NTRS)

In this paper the so-called Linear-Quadratic-Gaussian method with Loop-Transfer-Recovery is surveyed. The objective is to provide a pragmatic exposition, with special emphasis on the step-by-step characteristics for designing multivariable feedback control systems.

Athans, M.

1986-01-01

19

Rate Region of the Quadratic Gaussian Two-Encoder Source-Coding Problem  

Microsoft Academic Search

We determine the rate region of the quadratic Gaussian two-encoder source-coding problem. This rate region is achieved by a simple archi- tecture that separates the analog and digital aspects of the compression. Furthermore, this architecture requires higher rates to send a Gaussian source than it does to send any other source with the same covariance. Our techniques can also be

Aaron B. Wagner; Saurabha Tavildar; Pramod Viswanath

2008-01-01

20

Rate Region of the Quadratic Gaussian Two-Encoder Source-Coding Problem  

Microsoft Academic Search

We determine the rate region of the quadratic Gaussian two-encoder source-coding problem with separate distortion constraints. This region is achieved by a simple architecture that separates the analog and digital aspects of the compression. Furthermore, this architecture requires higher rates to send a Gaussian source than it does to send any other source with the same covariance. The proof technique

Aaron B. Wagner; Saurabha Tavildar; Pramod Viswanath

2006-01-01

21

Rate Region of the Quadratic Gaussian Two-Terminal Source-Coding Problem  

Microsoft Academic Search

We determine the rate region of the quadratic Gaussian two-terminal source-coding problem. This rate region is achieved by a simple archi- tecture that separates the analog and digital aspects of the compression. Furthermore, this architecture requires higher rates to send a Gaussian source than it does to send any other source with the same covariance. The determination of the rate

Aaron B. Wagner; Saurabha Tavildar; Pramod Viswanath

2005-01-01

22

LaGuerre-Gaussian periodically focusing beams in a quadratic index medium  

SciTech Connect

The Hermite-Gaussian periodically focusing beam solutions of the scalar paraxial wave equation with quadratic index variations are appropriate for rectangular coordinates. One expects the solutions appropriate to cylindrical coordinates to be LaGuerre-Gaussian multifocussing beams. The phase shifts of these solutions appear not be available in the published literature. In this note, the authors present an expression for these phase shifts together with a sketch of its derivation.

Newstein, M.; Rudman, B.

1987-05-01

23

Time-averaged quadratic functionals of a Gaussian process.  

PubMed

The characterization of a stochastic process from its single random realization is a challenging problem for most single-particle tracking techniques which survey an individual trajectory of a tracer in a complex or viscoelastic medium. We consider two quadratic functionals of the trajectory: the time-averaged mean-square displacement (MSD) and the time-averaged squared root mean-square displacement (SRMS). For a large class of stochastic processes governed by the generalized Langevin equation with arbitrary frictional memory kernel and harmonic potential, the exact formulas for the mean and covariance of these functionals are derived. The formula for the mean value can be directly used for fitting experimental data, e.g., in optical tweezers microrheology. The formula for the variance (and covariance) allows one to estimate the intrinsic fluctuations of measured (or simulated) time-averaged MSD or SRMS for choosing the experimental setup appropriately. We show that the time-averaged SRMS has smaller fluctuations than the time-averaged MSD, in spite of much broader applications of the latter one. The theoretical results are successfully confirmed by Monte Carlo simulations of the Langevin dynamics. We conclude that the use of the time-averaged SRMS would result in a more accurate statistical analysis of individual trajectories and more reliable interpretation of experimental data. PMID:21797312

Grebenkov, Denis S

2011-06-01

24

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

25

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

26

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

27

Quadratic  

NSDL National Science Digital Library

Shows how the roots of a quadratic change as the b term in the equation changes. The equation was chosen to illustrate the fact that only real roots are seen as points where the curve crosses the x-axis. This can lead to a useful discussion of what is meant by a physically meaningful solution.

28

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

29

Controlling the disorder properties of quadratic nonlinear photonic crystals  

E-print Network

Controlling the disorder properties of quadratic nonlinear photonic crystals Idith Varon,* Gil demonstrate a modulation scheme for disordered nonlinear crystals that combines periodic modulation and disordered sections. The crystal is divided into a set of identical periodically poled building blocks

Arie, Ady

30

INDEFINITE STOCHASTIC LINEAR QUADRATIC CONTROL AND GENERALIZED DIFFERENTIAL RICCATI EQUATION  

E-print Network

INDEFINITE STOCHASTIC LINEAR QUADRATIC CONTROL AND GENERALIZED DIFFERENTIAL RICCATI EQUATION M. AIT in finance. However, there remains an outstanding open problem, which is to identify an appropriate Riccati Riccati equation, called the generalized (differential) Riccati equation, is introduced, which involves

Moore, John Barratt

31

Finding Optimal Gains In Linear-Quadratic Control Problems  

NASA Technical Reports Server (NTRS)

Analytical method based on Volterra factorization leads to new approximations for optimal control gains in finite-time linear-quadratic control problem of system having infinite number of dimensions. Circumvents need to analyze and solve Riccati equations and provides more transparent connection between dynamics of system and optimal gain.

Milman, Mark H.; Scheid, Robert E., Jr.

1990-01-01

32

Inertia-Controlling Methods for General Quadratic Programming  

Microsoft Academic Search

Active-set quadratic programming (QP) methods use a working set to define the search direction and multiplier estimates. In the method proposed by Fletcher in 1971, and in several subsequent mathematically equivalent methods, the working set is chosen to control the inertia of the reduced Hessian, which is never permitted to have more than one nonpositive eigenvalue. (We call such methods

PHILIP E. GILL; WALTER MURRAY; MICHAEL A. SAUNDERS

1991-01-01

33

Indefinite Stochastic Linear Quadratic Control and Generalized Differential Riccati Equation  

E-print Network

Indefinite Stochastic Linear Quadratic Control and Generalized Differential Riccati Equation M. Ait is to identify an appro- priate Riccati-type equation whose solvability is equivalent to the solvability of this possibly in- definite LQ problem. In this paper we intro- duce a new type of differential Riccati equation

Moore, John Barratt

34

Linear Quadratic State Feedback Optimal Control against Actuator Failures  

Microsoft Academic Search

This paper is concerned with the synthesis of a robust and optimal controller for open-loop unstable systems possessing actuator redundancy. The designed linear quadratic state feedback regulator can maintain the close-loop stability in the presence of some certain actuator failures. At the first design stage, a discriminance of actuator functional redundancy is given, which is the precondition to design the

Zhizhou Zhang; Zhiqiang Long; Longhua She; Wensen Chang

2007-01-01

35

Nonlinear Quadratic Pricing for Concavifiable Utilities in Network Rate Control  

E-print Network

with the non-elastic applications. Such applications, for example, voice/video over IP, have certain data rateNonlinear Quadratic Pricing for Concavifiable Utilities in Network Rate Control Quanyan Zhu objective function. We use a game- theoretical framework as well as a centralized optimization approach

Boutaba, Raouf

36

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

NASA Technical Reports Server (NTRS)

The LQG controllers significantly improve antenna tracking precision, but 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, and the selection of weights of the LQG performance index. The paper selects the coordinates of the open-loop model that simplify the shaping of the closed-loop performance. and analyzes the impact of thc weights on the antenna closed-loop bandwidth, disturbance rejection properties, and antenna acceleration. Finally, it presents the LQG controller tuning procedure that rationally shapes the closed-loop performance.

Gawronski, Wodek K.

2004-01-01

37

A Discrete Linear Adaptive Controller with a Linear Quadratic Regulator Derived Proportional Derivative Controller  

Microsoft Academic Search

Recently, a linear adaptive control strategy based on Discrete Disturbance Accommodating Control theory (DAC) has appeared in the literature. This approach permits an entirely linear controller with constant parameters. The adaptive DAC approach is combined with a Linear-Quadratic Regulator (LQR) derived Proportional-Derivative (PD) controller for setpoint control of a simulated Thermal Control System on board the Space Station Freedom (SSF).

Steve Rogers; Haik Biglari

1992-01-01

38

A decentralized linear quadratic control design method for flexible structures  

NASA Technical Reports Server (NTRS)

A decentralized suboptimal linear quadratic control design procedure which combines substructural synthesis, model reduction, decentralized control design, subcontroller synthesis, and controller reduction is proposed for the design of reduced-order controllers for flexible structures. The procedure starts with a definition of the continuum structure to be controlled. An evaluation model of finite dimension is obtained by the finite element method. Then, the finite element model is decomposed into several substructures by using a natural decomposition called substructuring decomposition. Each substructure, at this point, still has too large a dimension and must be reduced to a size that is Riccati-solvable. Model reduction of each substructure can be performed by using any existing model reduction method, e.g., modal truncation, balanced reduction, Krylov model reduction, or mixed-mode method. Then, based on the reduced substructure model, a subcontroller is designed by an LQ optimal control method for each substructure independently. After all subcontrollers are designed, a controller synthesis method called substructural controller synthesis is employed to synthesize all subcontrollers into a global controller. The assembling scheme used is the same as that employed for the structure matrices. Finally, a controller reduction scheme, called the equivalent impulse response energy controller (EIREC) reduction algorithm, is used to reduce the global controller to a reasonable size for implementation. The EIREC reduced controller preserves the impulse response energy of the full-order controller and has the property of matching low-frequency moments and low-frequency power moments. An advantage of the substructural controller synthesis method is that it relieves the computational burden associated with dimensionality. Besides that, the SCS design scheme is also a highly adaptable controller synthesis method for structures with varying configuration, or varying mass and stiffness properties.

Su, Tzu-Jeng; Craig, Roy R., Jr.

1990-01-01

39

Gaussian  

NSDL National Science Digital Library

Gaussian is a electronic structure program. Designed to model a broad range of molecular systems under a variety of conditions, it performs its computations starting from the basic laws of quantum mechanics.

40

Human-Inspired Control of Bipedal Robots via Control Lyapunov Functions and Quadratic Programs  

E-print Network

Human-Inspired Control of Bipedal Robots via Control Lyapunov Functions and Quadratic Programs walking through controller synthesis inspired by human locomotion. Motivated by the hierarchical con- trol present in humans, we begin by viewing the human as a "black box" and describe outputs, or virtual

Ames, Aaron

41

Structure preserving integrators for solving linear quadratic optimal control problems with applications to describe the flight of a quadrotor  

E-print Network

Structure preserving integrators for solving linear quadratic optimal control problems Valencia, Spain. Abstract We present structure preserving integrators for solving linear quadratic optimal control problems. This problem requires the numerical integration of matrix Riccati differential equations

Blanes, Sergio

42

Controllable Gaussian-qubit interface for extremal quantum state engineering  

E-print Network

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.

G. Adesso; S. Campbell; F. Illuminati; M. Paternostro

2010-03-11

43

Controllable Gaussian-Qubit Interface for Extremal Quantum State Engineering  

NASA Astrophysics Data System (ADS)

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.

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

2010-06-01

44

Gaussian mixture models-based control chart pattern recognition  

Microsoft Academic Search

Abnormal patterns exhibited in control charts can be associated with certain assignable causes for process variation. Hence, accurate and fast control chart pattern recognition (CCPR) is essential for significantly narrowing down the scope of possible causes that must be investigated, and speeds up the troubleshooting process. This study proposes a Gaussian mixture models (GMM)-based CCPR model that employs a collection

Jianbo Yu

2011-01-01

45

Linear matrix inequalities, Riccati equations, and indefinite stochastic linear quadratic controls  

Microsoft Academic Search

This paper deals with an optimal stochastic linear-quadratic (LQ) control problem in infinite time horizon, where the diffusion term in dynamics depends on both the state and the control variables. In contrast to the deterministic case, we allow the control and state weighting matrices in the cost functional to be indefinite. This leads to an indefinite LQ problem, which may

Mustapha Ait Rami; Xun Yu Zhou

2000-01-01

46

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

47

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 schemes. 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.

1988-01-01

48

New approaches to relaxed quadratic stability condition of fuzzy control systems  

Microsoft Academic Search

This paper deals with the quadratic stability conditions of fuzzy control systems that relax the existing conditions reported in the previous literatures. Two new conditions are proposed and shown to be useful in analyzing and designing fuzzy control systems. The first one employs the S-procedure to utilize information regarding the premise parts of the fuzzy systems. The next one enlarges

Euntai Kim; Heejin Lee

2000-01-01

49

Directional passability and quadratic steering logic for pyramid-type single gimbal control moment gyros  

NASA Astrophysics Data System (ADS)

Singularity analysis and the steering logic of pyramid-type single gimbal control moment gyros are studied. First, a new concept of directional passability in a specified direction is introduced to investigate the structure of an elliptic singular surface. The differences between passability and directional passability are discussed in detail and are visualized for 0H, 2H, and 4H singular surfaces. Second, quadratic steering logic (QSL), a new steering logic for passing the singular surface, is investigated. The algorithm is based on the quadratic constrained quadratic optimization problem and is reduced to the Newton method by using Gröbner bases. The proposed steering logic is demonstrated through numerical simulations for both constant torque maneuvering examples and attitude control examples.

Yamada, Katsuhiko; Jikuya, Ichiro

2014-09-01

50

On some dynamical and geometrical properties of the Maxwell-Bloch equations with a quadratic control  

E-print Network

In this paper, we analyze the stability of the real-valued Maxwell-Bloch equations with a control that depends on state variables quadratically. We also investigate the topological properties of the energy-Casimir map, as well as the existence of periodic orbits and explicitly construct the heteroclinic orbits.

Tudor Binzar; Cristian Lazureanu

2014-02-24

51

Augmented Lagrangians with Adaptive Precision Control for Quadratic Programming with Equality Constraints  

Microsoft Academic Search

In this paper we introduce an augmented Lagrangian type algorithm for strictly convex quadratic programming problems with equality constraints. The new feature of the proposed algorithm is the adaptive precision control of the solution of auxiliary problems in the inner loop of the basic algorithm. Global convergence and boundedness of the penalty parameter are proved and an error estimate is

Z. Dostál; A. Friedlander; S. A. Santos

1999-01-01

52

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

Microsoft Academic Search

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

J. E. White; J. R. Etter

1987-01-01

53

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

54

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

55

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

56

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

57

Searchless tuning of linear controllers for the minimum of quadratic criterion  

NASA Astrophysics Data System (ADS)

A searchless method of calculating the tunings of typical controllers is developed for linear plants with a time delay, the use of which makes it possible to minimize the quadratic criterion I 2 with respect to an internal disturbance. The basic idea of the method consists in obtaining the complex frequency response of a suboptimal linear controller, followed by approaching the characteristic of a typical controller to this frequency response in the essential frequency band using the least squares method. Recommendations on selecting the smoothing filter time constant and the suboptimal system's dynamic error are given for a system comprising a PID controller and a second-order plant with a time delay.

Pikina, G. A.; Burtseva, Yu. S.

2014-03-01

58

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

59

Submersible control using the Linear Quadratic Gaussian with Loop Transfer Recovery (LQG/LTR) method  

E-print Network

notation for describing submarine dynamics. The hydrodynamic equations of motion were developed for a submerged vehicle, Le. , the equations are not valid if any part of the vehicle is above the surface of the ocean The six equations of motion... notation for describing submarine dynamics. The hydrodynamic equations of motion were developed for a submerged vehicle, Le. , the equations are not valid if any part of the vehicle is above the surface of the ocean The six equations of motion...

Juul, Douglas Lawton

2012-06-07

60

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

61

Air-to-fuel ratio control of spark ignition engines using Gaussian network sliding control  

Microsoft Academic Search

This paper treats air-to-fuel ratio control of a spark ignition engine. A direct adaptive control method using Gaussian neural networks is developed to compensate transient fueling dynamics and the measurement bias of mass air flow rate into the manifold. The transient fueling compensation method is coupled with a dynamic sliding mode control technique that governs fueling rate when the throttle

Mooncheol Won; Seibum B. Choi; J. K. Hedrick

1998-01-01

62

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

63

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

64

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

65

A fuzzy-Gaussian neural network and its application to mobile robot control  

Microsoft Academic Search

A fuzzy-Gaussian neural network (FGNN) controller is described by applying a Gaussian function as an activation function. A specialized learning architecture is used so that membership function can be tuned without using expert's manipulated data. As an example of the application, a tracking control problem for the speed and azimuth of a mobile robot driven by two independent wheels is

Keigo Watanabe; Jun Tang; Masatoshi Nakamura; Shinji Koga; Toshio Fukuda

1996-01-01

66

Controllable Gaussian-Qubit Interface for Extremal Quantum State Engineering  

Microsoft Academic Search

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

Gerardo Adesso; Steve Campbell; Fabrizio Illuminati; Mauro Paternostro

2010-01-01

67

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

68

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

69

Soliton transmission control by super-Gaussian filters  

NASA Astrophysics Data System (ADS)

Bandwidth-limited filtering has been proven to overcome certain limitations in soliton transmission systems. We propose super-Gaussian filters instead of Butterworth filter response obtained with conventionally used Fabry-Perot etalons as a method to improve soliton stability and reduce dispersion degradation and theoretically demonstrate their practical implementation in the form of holographic fiber gratings.

Peral, E.; Capmany, J.; Marti, J.

1996-12-01

70

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

71

Unitarily manipulating in time and space a Gaussian wave-packet motional state of a single atom in a quadratic potential field  

Microsoft Academic Search

The paper first discusses theoretically the off-resonance selective excitation method that is dependent on the atomic internal states and used to generate approximately a standard coherent state of harmonic oscillator. The coherent average method then is proposed to construct the state-selective trigger pulse. A state-selective trigger pulse can keep Gaussian shape unchanged but change in an internal-state-dependent form the center-of-mass

Xijia Miao

2007-01-01

72

Optimal PHP control of multiple part-types on a failure-prone machine with quadratic buffer costs  

Microsoft Academic Search

We consider a single, failure-prone machine, producing multiple part-types. The goal is to minimize the expected sum of quadratic buffer costs. In general, the optimal solution to this problem is unknown. However, by restricting the allowable set of control policies to the class of prioritized hedging point policies, we are able to determine simple, analytical expressions for the optimal hedging

Chang Shu; James R. Perkins

1998-01-01

73

Decoupled and linear quadratic regulator control of a large, flexible space antenna with an observer in the control loop  

NASA Technical Reports Server (NTRS)

An analysis is performed to compare decoupled and linear quadratic regulator (LQR) procedures for the control of a large, flexible space antenna. Control objectives involve: (1) commanding changes in the rigid-body modes, (2) nulling initial disturbances in the rigid-body modes, or (3) nulling initial disturbances in the first three flexible modes. Control is achieved with two three-axis control-moment gyros located on the antenna column. Results are presented to illustrate various effects on control requirements for the two procedures. These effects include errors in the initial estimates of state variables, variations in the type, number, and location of sensors, and deletions of state-variable estimates for certain flexible modes after control activation. The advantages of incorporating a time lag in the control feedback are also illustrated. In addition, the effects of inoperative-control situations are analyzed with regard to control requirements and resultant modal responses. Comparisons are included which show the effects of perfect state feedback with no residual modes (ideal case). Time-history responses are presented to illustrate the various effects on the control procedures.

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

1985-01-01

74

Extremely narrow resonances in electromagnetically induced transparency and absorption using a Laguerre-Gaussian control beam  

E-print Network

We observe resonances with width 20 times below the natural linewidth for a probe laser on an optical transition, when the same transition is driven by a control laser with a Laguerre-Gaussian (LG) profile. The basic mechanism is the phenomenon of electromagnetically induced transparency and absorption (EITA). Aligning the Gaussian probe beam to the central hole in the LG control beam simultaneously allows a strong control intensity required for high signal-to-noise ratio and a low intensity in the probe region required to get narrow resonances. We observe these resonances on the $D_2$ line of Rb in a room-temperature vapor cell and show that the linewidth is reduced by a factor of 4 compared to the use of a Gaussian control beam, which should prove advantageous in all applications of EITA.

Chanu, Sapam Ranjita

2011-01-01

75

IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 11, NO. 1, JANUARY 2003 139 Experimental Characterization and Quadratic Programming-Based Control of  

E-print Network

-order modeling to velocity control design for permanent-magnet syn- chronous motors minimizing copper losses Characterization and Quadratic Programming-Based Control of Brushless-Motors Farhad Aghili, Martin Buehler, and John M. Hollerbach Abstract--A new torque control strategy for brushless motors is presented, which

Hollerbach, John M.

76

A feedback control strategy for the airfoil system under non-Gaussian colored noise excitation.  

PubMed

The stability of a binary airfoil with feedback control under stochastic disturbances, a non-Gaussian colored noise, is studied in this paper. First, based on some approximated theories and methods the non-Gaussian colored noise is simplified to an Ornstein-Uhlenbeck process. Furthermore, via the stochastic averaging method and the logarithmic polar transformation, one dimensional diffusion process can be obtained. At last by applying the boundary conditions, the largest Lyapunov exponent which can determine the almost-sure stability of the system and the effective region of control parameters is calculated. PMID:25273197

Huang, Yong; Tao, Gang

2014-09-01

77

An Efficient Sequential Linear Quadratic Algorithm for Solving Nonlinear Optimal Control Problems  

E-print Network

sequence of linear quadratic subproblems. Each subproblem is solved efficiently using the Riccati complex to compute analytically. Our algorithm is based on linearizing the system dynamics about a input by solving a Riccati difference equation. Algorithms similar in spirit are reported in [6], [7], [8], [9

Bobrow, James E.

78

Explicit Stochastic Predictive Control of Combustion Plants Based on Gaussian Process Models  

E-print Network

Energy production is one of the largest sources of air pollution. A feasible method to reduce the harmful). The objectives for the improvement of the power plant combustion process are energy saving, pollution reduction1 Explicit Stochastic Predictive Control of Combustion Plants Based on Gaussian Process Models

Johansen, Tor Arne

79

Multistage quadratic stochastic programming  

NASA Astrophysics Data System (ADS)

Quadratic stochastic programming (QSP) in which each subproblem is a convex piecewise quadratic program with stochastic data, is a natural extension of stochastic linear programming. This allows the use of quadratic or piecewise quadratic objective functions which are essential for controlling risk in financial and project planning. Two-stage QSP is a special case of extended linear-quadratic programming (ELQP). The recourse functions in QSP are piecewise quadratic convex and Lipschitz continuous. Moreover, they have Lipschitz gradients if each QP subproblem is strictly convex and differentiable. Using these properties, a generalized Newton algorithm exhibiting global and superlinear convergence has been proposed recently for the two stage case. We extend the generalized Newton algorithm to multistage QSP and show that it is globally and finitely convergent under suitable conditions. We present numerical results on randomly generated data and modified publicly available stochastic linear programming test sets. Efficiency schemes on different scenario tree structures are discussed. The large-scale deterministic equivalent of the multistage QSP is also generated and their accuracy compared.

Lau, Karen K.; Womersley, Robert S.

2001-04-01

80

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

81

Narrowing of resonances in electromagnetically induced transparency and absorption using a Laguerre-Gaussian control beam  

NASA Astrophysics Data System (ADS)

We study the phenomenon of electromagnetically induced transparency and absorption (EITA) using a control laser with a Laguerre-Gaussian (LG) profile instead of the usual Gaussian profile, and observe significant narrowing of the resonance widths. Aligning the probe beam to the central hole in the doughnut-shaped LG control beam allows simultaneously a strong control intensity required for high signal-to-noise ratio and a low intensity in the probe region required to get narrow resonances. Experiments with an expanded Gaussian control and a second-order LG control show that transit time and orbital angular momentum do not play a significant role. This explanation is borne out by a density-matrix analysis with a radially varying control Rabi frequency. We observe these resonances using degenerate two-level transitions in the D2 line of 87Rb in a room temperature vapor cell, and an EIA resonance with width up to 20 times below the natural linewidth for the F=2?F'=3 transition. Thus the use of LG beams should prove advantageous in all applications of EITA and other kinds of pump-probe spectroscopy as well.

Ranjita Chanu, Sapam; Natarajan, Vasant

2013-05-01

82

The application of LQR synthesis techniques to the turboshaft engine control problem. [Linear Quadratic Regulator  

NASA Technical Reports Server (NTRS)

A power turbine governor was designed for a recent-technology turboshaft engine coupled to a modern, articulated rotor system using Linear Quadratic Regulator (LQR) and Kalman Filter (KF) techniques. A linear, state-space model of the engine and rotor system was derived for six engine power settings from flight idle to maximum continuous. An integrator was appended to the fuel flow input to reduce the steady-state governor error to zero. Feedback gains were calculated for the system states at each power setting using the LQR technique. The main rotor tip speed state is not measurable, so a Kalman Filter of the rotor was used to estimate this state. The crossover of the system was increased to 10 rad/s compared to 2 rad/sec for a current governor. Initial computer simulations with a nonlinear engine model indicate a significant decrease in power turbine speed variation with the LQR governor compared to a conventional governor.

Pfeil, W. H.; De Los Reyes, G.; Bobula, G. A.

1985-01-01

83

Approximation of Gaussian basis functions in the problem of adaptive control of nonlinear objects  

Microsoft Academic Search

An approach to the development of a neurocontroller for controlling nonlinear dynamical objects on the basis of radial-basis\\u000a function neural networks is considered. Piecewise-linear approximation of Gaussian basis functions is proposed to simplify\\u000a the solution of the problem being considered. Simulation results show that the method allows one to reduce the time of construction\\u000a of an object model and calculation

O. G. Rudenko; A. A. Bezsonov; A. S. Liashenko; R. A. Sunna

2011-01-01

84

Local Gaussian Process Regression for Real Time Online Model Learning and Control  

Microsoft Academic Search

Learning in real-time applications, e.g., online approximation of the inverse dy- namics model for model-based robot control, requires fast online regression tech- niques. Inspired by local learning, we propose a method to speed up standard Gaussian process regression (GPR) with local GP models (LGP). The training data is partitioned in local regions, for each an individual GP model is trained.

Duy Nguyen-Tuong; Jan Peters; Matthias Seeger

85

QUADRATIC RECIPROCITY JORDAN SCHETTLER  

E-print Network

is a quadratic residue mod p -1 if n is a quadratic nonresidue mod p 0 if p|n. The law of quadratic reciprocityQUADRATIC RECIPROCITY JORDAN SCHETTLER Abstract. The goals of this project are to have the reader proof of Gauss's Theorema Aureum of quadratic reciprocity. 1. Quadratic Residues and Legendre Symbols

Bigelow, Stephen

86

Neural-genetic synthesis for state-space controllers based on linear quadratic regulator design for eigenstructure assignment.  

PubMed

Toward the synthesis of state-space controllers, a neural-genetic model based on the linear quadratic regulator design for the eigenstructure assignment of multivariable dynamic systems is presented. The neural-genetic model represents a fusion of a genetic algorithm and a recurrent neural network (RNN) to perform the selection of the weighting matrices and the algebraic Riccati equation solution, respectively. A fourth-order electric circuit model is used to evaluate the convergence of the computational intelligence paradigms and the control design method performance. The genetic search convergence evaluation is performed in terms of the fitness function statistics and the RNN convergence, which is evaluated by landscapes of the energy and norm, as a function of the parameter deviations. The control problem solution is evaluated in the time and frequency domains by the impulse response, singular values, and modal analysis. PMID:19661008

da Fonseca Neto, João Viana; Abreu, Ivanildo Silva; da Silva, Fábio Nogueira

2010-04-01

87

Quadratic double centralizers and quadratic multipliers  

Microsoft Academic Search

In this paper, we establish stability of quadratic double centralizers and quadratic multipliers on Banach algebras. We also\\u000a prove the super stability of quadratic double centralizers on Banach algebras which are weakly commutative and weakly without\\u000a order, and of quadratic multipliers on Banach algebras which are weakly without order.

M. Eshaghi Gordji; M. Ramezani; A. Ebadian

2011-01-01

88

Active noise control with on-line estimation of non-Gaussian noise characteristics  

NASA Astrophysics Data System (ADS)

Active noise control (ANC) is a methodology for attenuating noise based on adaptive signal processing algorithms. ANC is well assessed for the attenuation of Gaussian noise, but the rejection of non-Gaussian impulsive noise signals represents a much more critical task that may even impair algorithm convergence. To overcome this problem the adaptive filter weight update process must be modified by discarding or discounting samples associated with impulsive noise. This can be done either by modeling the impulsive noise with a non-Gaussian distribution such as the Symmetric ?-stable (S?S) distribution or by applying an outlier detection method. With both approaches the accuracy in the noise description appears to be crucial for effective noise reduction. This paper proposes two novel approaches for the attenuation of impulsive noise both for invariant and time-varying noise distributions. The first one is based on the on-line estimation of an S?S model of the noise probabilistic description. The second relies on a simple on-line recursive procedure that reliably estimates amplitude thresholds for outlier detection. Both methods compare favorably with competitor approaches, while maintaining a sufficiently low algorithm complexity. Several examples are shown to demonstrate the algorithms' effectiveness.

Bergamasco, Marco; Della Rossa, Fabio; Piroddi, Luigi

2012-01-01

89

Constrained nonlinear control allocation with singularity avoidance using sequential quadratic programming  

Microsoft Academic Search

Control allocation problems can be formulated as optimization problems, where the objective is typically to minimize the use of control effort (or power) subject to actuator rate and position constraints, and other operational constraints. Here we consider the additional objective of singularity avoidance, which is essential to avoid loss of controllability in some applications, leading to a nonconvex nonlinear program.

Tor A. Johansen; Thor I. Fossen; Svein P. Berge

2004-01-01

90

Dirichlet boundary control problems for parabolic equations with quadratic cost: Analyticity and riccati's feedback synthesis  

Microsoft Academic Search

Riccati type feedback synthesis of optimal controls for Dirichlet boundary parabolic equations is considered. The functional cost penalizes the L2 -energy over [0,T] of state and control action u and also final state y(T) at t=T. This latter fact, makes the functional cost discontinuous on the space of admissible controls: L2(); =[0T] × . After overcoming some technical difficulties related

Irena Lasiecka; Roberto Triggiani

91

A Fast Sequential Linear Quadratic Algorithm for Solving Unconstrained Nonlinear Optimal Control Problems  

E-print Network

using the Riccati difference equa- tion. We show that each iteration produces a descent direction with respect to the states and 1 #12;the controls are too complex to compute analytically. It should be noted

Bobrow, James E.

92

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

93

AIAA-2000-4043 MAGNETIC TORQUER ATTITUDE CONTROL VIA ASYMPTOTIC PERIODIC LINEAR QUADRATIC  

E-print Network

and b is the Earth's magnetic field. Equation (1) highlights the principal problem of magnetic vector. The system is controllable if the orbit is inclined because the Earth's magnetic field vector's magnetic field in order to determine the actual torque. Projection is necessary because the magnetic torque

Psiaki, Mark L.

94

Effects of model error on control of large flexible space antenna with comparisons of decoupled and linear quadratic regulator control procedures  

NASA Technical Reports Server (NTRS)

An analysis was performed to determine the effects of model error on the control of a large flexible space antenna. Control was achieved by employing two three-axis control-moment gyros (CMG's) located on the antenna column. State variables were estimated by including an observer in the control loop that used attitude and attitude-rate sensors on the column. Errors were assumed to exist in the individual model parameters: modal frequency, modal damping, mode slope (control-influence coefficients), and moment of inertia. Their effects on control-system performance were analyzed either for (1) nulling initial disturbances in the rigid-body modes, or (2) nulling initial disturbances in the first three flexible modes. The study includes the effects on stability, time to null, and control requirements (defined as maximum torque and total momentum), as well as on the accuracy of obtaining initial estimates of the disturbances. The effects on the transients of the undisturbed modes are also included. The results, which are compared for decoupled and linear quadratic regulator (LQR) control procedures, are shown in tabular form, parametric plots, and as sample time histories of modal-amplitude and control responses. Results of the analysis showed that the effects of model errors on the control-system performance were generally comparable for both control procedures. The effect of mode-slope error was the most serious of all model errors.

Hamer, H. A.; Johnson, K. G.

1986-01-01

95

Spatial solitons in a three-level atomic medium supported by a Laguerre-Gaussian control beam  

SciTech Connect

We investigate the existence and stability of various types of spatial solitons in a three-level atomic medium with Laguerre-Gaussian control beam. Radial and azimuthal modulations of the medium properties, introduced by the control beam, provide possibilities for existence of diverse soliton patterns and dynamics. Beam diffraction provides additional soliton controllability. All types of solitons can be generated at very low input energy at a few-photon level.

Hang Chao [Centro de Fisica Teorica e Computacional, Faculdade de Ciencias, Universidade de Lisboa, Avenida Professor Gama Pinto 2, Lisboa PT-1649-003 (Portugal); Department of Physics and State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai CN-200062 (China); Konotop, V. V. [Centro de Fisica Teorica e Computacional, Faculdade de Ciencias, Universidade de Lisboa, Avenida Professor Gama Pinto 2, Lisboa PT-1649-003 (Portugal); Departamento de Fisica, Faculdade de Ciencias, Universidade de Lisboa, Campo Grande, Ed. C8, Piso 6, Lisboa PT-1749-016 (Portugal)

2011-05-15

96

Self-Replicating Quadratics  

ERIC Educational Resources Information Center

We show that there are exactly four quadratic polynomials, Q(x) = x [superscript 2] + ax + b, such that (x[superscript 2] + ax + b) (x[superscript 2] - ax + b) = (x[superscript 4] + ax[superscript 2] + b). For n = 1, 2, ..., these quadratic polynomials can be written as the product of N = 2[superscript n] quadratic polynomials in x[superscript…

Withers, Christopher S.; Nadarajah, Saralees

2012-01-01

97

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

98

Gaussian Primes  

NSDL National Science Digital Library

This is an introduction to Gaussian primes, complex numbers with integers for real and imaginary parts that are divisible by themselves and 1, but no other complex numbers with integer coefficients. This shows calculations of the first few Gaussian primes.

Loy, Jim

2007-11-15

99

Robust solutions of uncertain quadratic and conic-quadratic problems  

E-print Network

Robust solutions of uncertain quadratic and conic-quadratic problems A. Ben-Tal y#3; A. Nemirovski birthday. Abstract We consider a conic-quadratic (and in particular a quadratically constrained conic-quadratic problem. Keywords: Semide#12;nite relaxation of NP-hard problems, (conic) quadratic

Roos, Kees

100

Multirate LQG controller applied to self-location and path-tracking in mobile robots  

Microsoft Academic Search

Presents an approach to solving the linear quadratic Gaussian problem for controlling MIMO multirate sampled-data systems. The problem is split into three parts: first a generalized discrete multirate model is computed, second the solution of the linear quadratic regulator problem is computed and then a multirate Kalman filter is obtained. The model is composed by a time invariant single rate

Josep Tornero; R. Piza; Pedro Albertos; Julian Salt

2001-01-01

101

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

102

Homotopy approach to optimal, linear quadratic, fixed architecture compensation  

NASA Technical Reports Server (NTRS)

Optimal linear quadratic Gaussian compensators with constrained architecture are a sensible way to generate good multivariable feedback systems meeting strict implementation requirements. The optimality conditions obtained from the constrained linear quadratic Gaussian are a set of highly coupled matrix equations that cannot be solved algebraically except when the compensator is centralized and full order. An alternative to the use of general parameter optimization methods for solving the problem is to use homotopy. The benefit of the method is that it uses the solution to a simplified problem as a starting point and the final solution is then obtained by solving a simple differential equation. This paper investigates the convergence properties and the limitation of such an approach and sheds some light on the nature and the number of solutions of the constrained linear quadratic Gaussian problem. It also demonstrates the usefulness of homotopy on an example of an optimal decentralized compensator.

Mercadal, Mathieu

1991-01-01

103

Excess noise control in Gaussian-modulated coherent state quantum key distribution system  

Microsoft Academic Search

A novel polarization-frequency-multiplexing scheme is implemented to suppress noise in a fiber-based Gaussian-modulated coherent-state quantum key distribution system. The achievable secrete key rate is 0.30 bit\\/pulse with a 5 km-fiber and 0.05 bit\\/pulse with a 20 km-fiber.

Bing Qi; Lei-Lei Huang; Yue-Meng Chi; Li Qian; Hoi-Kwong Lo

2008-01-01

104

PRIMES AND QUADRATIC RECIPROCITY  

Microsoft Academic Search

We discuss number theory with the ultimate goal of understanding quadratic reciprocity. We begin by discussing Fermat's Little Theorem, the Chinese Remainder Theorem, and Carmichael numbers. Then we dene the Legendre symbol and prove Gauss's Lemma. Finally, using Gauss's Lemma we prove the Law of Quadratic Reciprocity.

ANGELICA WONG

105

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

106

Robust solutions of uncertain quadratic and conic-quadratic problems  

E-print Network

Robust solutions of uncertain quadratic and conic-quadratic problems A. Ben-Tal A. Nemirovski C. Abstract We consider a conic-quadratic (and in particular a quadratically constrained) optimization problem on the quality of the approximation, which is essentially independent of the dimensions of the underlying conic

Nemirovski, Arkadi

107

Robust solutions of uncertain quadratic and conic-quadratic problems  

E-print Network

Robust solutions of uncertain quadratic and conic-quadratic problems A. Ben-Tal A. Nemirovski C. Abstract We consider a conic-quadratic (and in particular a quadratically constrained) optimization problem on the quality of the approximation, which is independent of the dimensions of the underlying conic

Roos, Kees

108

ROBUST SOLUTIONS OF UNCERTAIN QUADRATIC AND CONIC-QUADRATIC PROBLEMS  

E-print Network

ROBUST SOLUTIONS OF UNCERTAIN QUADRATIC AND CONIC-QUADRATIC PROBLEMS A. BEN-TAL, A. NEMIROVSKI­560 Dedicated to Jochem Zowe on the occasion of his 60th birthday. Abstract. We consider a conic-quadratic (and, which is essentially independent of the dimensions of the underlying conic-quadratic problem. Key words

Nemirovski, Arkadi

109

Optical Quadratic Measure Eigenmodes  

E-print Network

We report a mathematically rigorous technique which facilitates the optimization of various optical properties of electromagnetic fields. The technique exploits the linearity of electromagnetic fields along with the quadratic nature of their interaction with matter. In this manner we may decompose the respective fields into optical quadratic measure eigenmodes (QME). Key applications include the optimization of the size of a focused spot, the transmission through photonic devices, and the structured illumination of photonic and plasmonic structures. We verify the validity of the QME approach through a particular experimental realization where the size of a focused optical field is minimized using a superposition of Bessel beams.

Michael Mazilu; Joerg Baumgartl; Sebastian Kosmeier; Kishan Dholakia

2010-07-13

110

The linear quadratic optimal control problem for infinite dimensional systems over an infinite horizon - Survey and examples  

NASA Technical Reports Server (NTRS)

Available published results are surveyed for a special class of infinite-dimensional control systems whose evolution is characterized by a semigroup of operators of class C subscript zero. Emphasis is placed on an approach that clarifies the system-theoretic relationship among controllability, stabilizability, stability, and the existence of a solution to an associated operator equation of the Riccati type. Formulation of the optimal control problem is reviewed along with the asymptotic behavior of solutions to a general system of equations and several theorems concerning L2 stability. Examples are briefly discussed which involve second-order parabolic systems, first-order hyperbolic systems, and distributed boundary control.

Bensoussan, A.; Delfour, M. C.; Mitter, S. K.

1976-01-01

111

VTOL controls for shipboard landing. M.S.Thesis  

NASA Technical Reports Server (NTRS)

The problem of landing a VTOL aircraft on a small ship in rough seas using an automatic controller is examined. The controller design uses the linear quadratic Gaussian results of modern control theory. Linear time invariant dynamic models are developed for the aircraft, ship, and wave motions. A hover controller commands the aircraft to track position and orientation of the ship deck using only low levels of control power. Commands for this task are generated by the solution of the steady state linear quadratic gaussian regulator problem. Analytical performance and control requirement tradeoffs are obtained. A landing controller commands the aircraft from stationary hover along a smooth, low control effort trajectory, to a touchdown on a predicted crest of ship motion. The design problem is formulated and solved as an approximate finite-time linear quadratic stochastic regulator. Performance and control results are found by Monte Carlo simulations.

Mcmuldroch, C. G.

1979-01-01

112

The Mystical "Quadratic Formula."  

ERIC Educational Resources Information Center

Uses projectile motion to explain the two roots found when using the quadratic formula. An example is provided for finding the time of flight for a projectile which has a negative root implying a negative time of flight. This negative time of flight also has a useful physical meaning. (MVL)

March, Robert H.

1993-01-01

113

Supplementary material for nonparameteric adaptive control of time varying systems using gaussian processes  

E-print Network

Real-world dynamical variations make adaptive control of time-varying systems highly relevant. However, most adaptive control literature focuses on analyzing systems where the uncertainty is represented as a weighted linear ...

Chowdhary, Girish

2013-03-15

114

A new eddy current model for magnetic bearing control system design  

NASA Technical Reports Server (NTRS)

This paper describes a new VLSI-based controller for the implementation of a Linear-Quadratic-Gaussian (LQG) theory-based control system. Use of the controller is demonstrated by design of a controller for a magnetic bearing and its performance is evaluated by computer simulation.

Feeley, Joseph J.; Ahlstrom, Daniel J.

1992-01-01

115

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

116

An application of modern control theory to an elastic spacecraft  

NASA Technical Reports Server (NTRS)

Results are presented to illustrate the application of established procedures of linear, quadratic, Gaussian optimal estimation and control to a spacecraft with dynamically significant elastic appendages. Interpretations are provided in both time domain and frequency domain, and conclusions are drawn for a wide class of problems of flexible spacecraft attitude control.

Larson, V.; Likins, P. W.

1976-01-01

117

Gaussian beams in hollow metal waveguides  

PubMed

Various families of Gaussian beams have been explored previously to represent the propagation of nearly plane electromagnetic waves in media having at most quadratic transverse variations of the index of refraction and the gain or loss in the vicinity of the beam. However, such beams cannot directly represent the wave solutions for propagation in planar or rectangular waveguides, and sinusoidal mode functions are more commonly used for such waveguides. On the other hand, it is also useful to consider the possibility of recurring Gaussian beams that have an approximately Gaussian transverse profile at certain distinct planes along the propagation path. It is shown here that under some conditions recurring Gaussian beams can describe wave propagation in hollow metal waveguides, and they can also lead to efficient coupling between the waveguide fields and free-space beams. PMID:10850483

Casperson

2000-06-01

118

LQG\\/LTR robust control system design for low-pressure feedwater heater train  

Microsoft Academic Search

The linear quadratic Gaussian with loop transfer recovery (LQG\\/LTR) control system design method is used to obtain a level control system for a nuclear plant low-pressure feedwater heater train. A control system design for robustness at the plant output is developed. Its performance and stability robustness are evaluated for given specifications. The tools for analysis are the return ratio, return

G. V. Murphy; J. M. Bailey

1990-01-01

119

Quadratic spatial solitons  

NASA Astrophysics Data System (ADS)

Quadratic spatial solitons, beams that propagate unchanged in shape and magnitude, are supported by second order optical nonlinearities and can occur in all wave mixing processes under appropriate conditions. They are multi-component, consisting of all the frequency components that are coupled by a second order nonlinear interaction near a phase-matching condition. They have been observed in a number of bulk crystalline media, in LiNbO 3 slab waveguides and in arrays of parallel, weakly coupled, LiNbO 3 channel waveguides. The properties of the solitons and their excitation will be reviewed. To cite this article: G.I. Stegeman, C. R. Physique 8 (2007).

Stegeman, George I.

2007-03-01

120

Guises and Disguises of Quadratic Divergences  

E-print Network

In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale $\\lambda$. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.

Cherchiglia, A L; Hiller, Brigitte; Scarpelli, A P Baêta; Sampaio, Marcos

2014-01-01

121

Guises and Disguises of Quadratic Divergences  

E-print Network

In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale $\\lambda$. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.

A. L. Cherchiglia; A. R. Vieira; Brigitte Hiller; A. P. Baêta Scarpelli; Marcos Sampaio

2014-10-04

122

ASYMPTOTIC DISTRIBUTION OF QUADRATIC FORMS I F. G otze 1 and A. N. Tikhomirov 1;2  

E-print Network

distance between the distribution of Qn and the distribution of the same quadratic forms with X j replaced), Fox and Taqqu (1985, 1987) (limit theorems for quadratic forms G n of Gaussian r.v.'s with long­range m ff m (Y 2 m \\Gamma 1), where fff m g is a sequence of real numbers. Rotar' (1973) proved

Bielefeld, University of

123

The explicit linear quadratic regulator for constrained systems  

Microsoft Academic Search

We present a technique to compute the explicit state-feedback solution to both the xnite and inxnite horizon linear quadratic optimal control problem subject to state and input constraints. We show that this closed form solution is piecewise linear and continuous. As a practical consequence of the result, constrained linear quadratic regulation becomes attractive also for systems with high sampling rates,

Alberto Bemporad; Manfred Morari; Vivek Dua; Efstratios N. Pistikopoulos

2002-01-01

124

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

125

Quadratic spatial soliton interactions  

NASA Astrophysics Data System (ADS)

Quadratic spatial soliton interactions were investigated in this Dissertation. The first part deals with characterizing the principal features of multi-soliton generation and soliton self-reflection. The second deals with two beam processes leading to soliton interactions and collisions. These subjects were investigated both theoretically and experimentally. The experiments were performed by using potassium niobate (KNBO 3) and periodically poled potassium titanyl phosphate (KTP) crystals. These particular crystals were desirable for these experiments because of their large nonlinear coefficients and, more importantly, because the experiments could be performed under non-critical-phase-matching (NCPM) conditions. The single soliton generation measurements, performed on KNBO3 by launching the fundamental component only, showed a broad angular acceptance bandwidth which was important for the soliton collisions performed later. Furthermore, at high input intensities multi-soliton generation was observed for the first time. The influence on the multi-soliton patterns generated of the input intensity and beam symmetry was investigated. The combined experimental and theoretical efforts indicated that spatial and temporal noise on the input laser beam induced multi-soliton patterns. Another research direction pursued was intensity dependent soliton routing by using of a specially engineered quadratically nonlinear interface within a periodically poled KTP sample. This was the first time demonstration of the self-reflection phenomenon in a system with a quadratic nonlinearity. The feature investigated is believed to have a great potential for soliton routing and manipulation by engineered structures. A detailed investigation was conducted on two soliton interaction and collision processes. Birth of an additional soliton resulting from a two soliton collision was observed and characterized for the special case of a non-planar geometry. A small amount of spiraling, up to 30 degrees rotation, was measured in the experiments performed. The parameters relevant for characterizing soliton collision processes were also studied in detail. Measurements were performed for various collision angles (from 0.2 to 4 degrees), phase mismatch, relative phase between the solitons and the distance to the collision point within the sample (which affects soliton formation). Both the individual and combined effects of these collision variables were investigated. Based on the research conducted, several all-optical switching scenarios were proposed.

Jankovic, Ladislav

126

A Sequential Quadratically Constrained Quadratic Programming Method of Feasible Directions  

SciTech Connect

In this paper, a sequential quadratically constrained quadratic programming method of feasible directions is proposed for the optimization problems with nonlinear inequality constraints. At each iteration of the proposed algorithm, a feasible direction of descent is obtained by solving only one subproblem which consist of a convex quadratic objective function and simple quadratic inequality constraints without the second derivatives of the functions of the discussed problems, and such a subproblem can be formulated as a second-order cone programming which can be solved by interior point methods. To overcome the Maratos effect, an efficient higher-order correction direction is obtained by only one explicit computation formula. The algorithm is proved to be globally convergent and superlinearly convergent under some mild conditions without the strict complementarity. Finally, some preliminary numerical results are reported.

Jian Jinbao [Guangxi University, College of Mathematics and Informatics Science (China)], E-mail: jianjb@gxu.edu.cn; Hu Qingjie [Hunan Business College, Department of Information (China); Tang Chunming; Zheng Haiyan [Guangxi University, College of Mathematics and Informatics Science (China)

2007-12-15

127

Robust Solutions of Uncertain Quadratic and Conic-Quadratic Problems  

Microsoft Academic Search

We consider a conic-quadratic (and in particular a quadratically constrained) optimization problem with uncertain data, known only to reside in some uncertainty set U . The robust counterpart of such a problem leads usually to an NP-hard semidefinite problem; this is the case for example when U is given as intersection of ellipsoids, or as an n-dimensional box. For these

Aharon Ben-Tal; Arkadi Nemirovski; Cees Roos

2002-01-01

128

Computer-aided design of flight control systems  

NASA Technical Reports Server (NTRS)

A computer program is presented for facilitating the development and assessment of flight control systems, and application to a control design is discussed. The program is a computer-aided control-system design program based on direct digital synthesis of a proportional-integral-filter controller with scheduled linear-quadratic-Gaussian gains and command generator tracking of pilot inputs. The FlightCAD system concentrates on aircraft dynamics, flight-control systems, stability and performance, and has practical engineering applications.

Stengel, Robert F.; Sircar, Subrata

1991-01-01

129

An Investigation on Quadratic Equations.  

ERIC Educational Resources Information Center

Argues that exploring a familiar topic or examination question in a novel manner is a useful way to find topics for mathematical investigation in the classroom. The example used to illustrate the premise is a quadratic equation. (PK)

Hirst, Keith

1988-01-01

130

regularized sequential quadratic programming methods  

E-print Network

Oct 2, 2011 ... Research supported in part by National Science Foundation grants DMS- .... in the formulation of algorithms since the early 1960s (for a seminal reference, see .... is the solution (when it exists) of the convex quadratic program.

2011-10-30

131

Interface solitons in quadratic nonlinear photonic lattices  

SciTech Connect

We study the properties of two-color nonlinear localized modes which may exist at the interfaces separating two different periodic photonic lattices in quadratic media, focusing on the impact of phase mismatch of the photonic lattices on the properties, stability, and threshold power requirements for the generation of interface localized modes. We employ both an effective discrete model and continuum model with periodic potential and find good qualitative agreement between both models. Dynamic excitation of interface modes shows that a two-color interface twisted mode splits into two beams with different escaping angles and carrying different energies when entering a uniform medium from the quadratic photonic lattice. The output position and energy contents of each two-color interface solitons can be controlled by judicious tuning of the lattice parameters.

Xu Zhiyong; Kivshar, Yuri S. [Nonlinear Physics Center, Research School of Physics and Engineering, Australian National University, Canberra, Australian Capital Territory 0200 (Australia); Molina, Mario I. [Departmento de Fisica, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, 7800024 Nunoa, Santiago (Chile)

2009-07-15

132

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

133

Quadratic optomechanics in a cryogenic membrane-in-the-middle system  

E-print Network

Optomechanical experiments in the quantum regime have mostly been limited to the study of Gaussian states. This limitation is largely due to the linearity of the optomechanical coupling that is realized in most devices. In contrast, theoretical proposals show that non-Gaussian states and other striking quantum phenomena (such as quantum jumps between phonon number eigenstates) can be observed in optomechanical systems with large nonlinear coupling, provided that they operate in the resolved sideband regime, with very low damping, and in a sufficiently cold environment. Here we describe a device that meets these requirements. Specifically, we demonstrate a cryogenic, resolved sideband membrane-in-the-middle device with large quadratic optomechanical coupling. We present a thorough characterization of the classical dynamics that result from the quadratic coupling and find that these results agree with a simple model. We also use the quadratic coupling to monitor fluctuations of the intracavity laser power, in a...

Lee, Donghun; Mason, David; Shkarin, Alexey B; Hoch, Scott W; Harris, Jack G E

2014-01-01

134

Laguerre-Gaussian supercontinuum  

Microsoft Academic Search

We show what is believed to be the first coherent white-light optical vortices generated from supercontinuum that have the azimuthally varying phase structure consistent with a monochromatic Laguerre-Gaussian beam. Two methods of Laguerre-Gaussian supercontinuum generation are discussed and contrasted. We use a computer-generated hologram to convert a Gaussian white-light supercontinuum source into Laguerre-Gaussian supercontinuum.

H. I. Sztul; V. Kartazayev; R. R. Alfano

2006-01-01

135

Optimality of Gaussian Discord  

NASA Astrophysics Data System (ADS)

In this Letter we exploit the recently solved conjecture on the bosonic minimum output entropy to show the optimality of Gaussian discord, so that the computation of quantum discord for bipartite Gaussian states can be restricted to local Gaussian measurements. We prove such optimality for a large family of Gaussian states, including all two-mode squeezed thermal states, which are the most typical Gaussian states realized in experiments. Our family also includes other types of Gaussian states and spans their entire set in a suitable limit where they become Choi matrices of Gaussian channels. As a result, we completely characterize the quantum correlations possessed by some of the most important bosonic states in quantum optics and quantum information.

Pirandola, Stefano; Spedalieri, Gaetana; Braunstein, Samuel L.; Cerf, Nicolas J.; Lloyd, Seth

2014-10-01

136

A Quadratic Closure for Compressible Turbulence  

SciTech Connect

We have investigated a one-point closure model for compressible turbulence based on third- and higher order cumulant discard for systems undergoing rapid deformation, such as might occur downstream of a shock or other discontinuity. In so doing, we find the lowest order contributions of turbulence to the mean flow, which lead to criteria for Adaptive Mesh Refinement. Rapid distortion theory (RDT) as originally applied by Herring closes the turbulence hierarchy of moment equations by discarding third order and higher cumulants. This is similar to the fourth-order cumulant discard hypothesis of Millionshchikov, except that the Millionshchikov hypothesis was taken to apply to incompressible homogeneous isotropic turbulence generally, whereas RDT is applied only to fluids undergoing a distortion that is 'rapid' in the sense that the interaction of the mean flow with the turbulence overwhelms the interaction of the turbulence with itself. It is also similar to Gaussian closure, in which both second and fourth-order cumulants are retained. Motivated by RDT, we develop a quadratic one-point closure for rapidly distorting compressible turbulence, without regard to homogeneity or isotropy, and make contact with two equation turbulence models, especially the K-{var_epsilon} and K-L models, and with linear instability growth. In the end, we arrive at criteria for Adaptive Mesh Refinement in Finite Volume simulations.

Futterman, J A

2008-09-16

137

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

138

Neuromuscular stochastic optimal control of a tendon driven index finger model  

Microsoft Academic Search

Our long-term goal is to find control princi- ples to control robotic hands with dexterity and robustness comparable to that of the human hand. Here we explore a control strategy capable of accommodating the nonlinearities, high dimensionality and endogenous noise intrinsic to complex, tendon-driven biomechanical structures. We present the first stochastic optimal feedback controller (i.e., an iterative Linear Quadratic Gaussian

Evangelos Theodorou; Emanuel Todorov; Francisco J. Valero-Cuevas

2011-01-01

139

QUADRATIC RECIPROCITY IN ODD CHARACTERISTIC KEITH CONRAD  

E-print Network

+ T + 1? The answer to questions like this can be found with the quadratic reciprocity law in F[T]. It has a strong resemblance to the quadratic reciprocity law in Z. We restrict to F with odd characteristic the quadratic reciprocity law. The proof of the law is in Section 3. Some applications are given in Section 4

Lozano-Robledo, Alvaro

140

QUADRATIC RECIPROCITY IN CHARACTERISTIC 2 KEITH CONRAD  

E-print Network

. When F has odd characteristic, the quadratic reciprocity law in F[T] lets us decide whether . This is similar to the quadratic reciprocity law in Z. We want to develop an analogous reciprocity law when F has properties, and state the quadratic reciprocity law on F[T]. Section 3 defines the trace on finite fields

Lozano-Robledo, Alvaro

141

The law of quadratic reciprocity  

Microsoft Academic Search

Which famous mathematical theorem has been proved most often? Pythagoras would certainly be a good candidate or the fundamental\\u000a theorem of algebra, but the champion is without doubt the law of quadratic reciprocity in number theory. In an admirable monograph\\u000a Franz Lemmermeyer lists as of the year 2000 no fewer than 196 proofs. Many of them are of course only

Martin Aigner; Günter M. Ziegler

142

ORTHOGONAL POLYNOMIALS AND QUADRATIC TRANSFORMATIONS  

Microsoft Academic Search

Starting from a sequencefPngn‚0 of monic polynomials orthogonal with respect to a linear functional u, we flnd a linear functional v such that fQng‚0, with either Q2n(x) = Pn(T(x)) or Q2n+1(x) = (x¡a)Pn(T(x)) where T is a monic quadratic polynomial and a 2 C, is a sequence of monic orthogonal polynomials with respect to v. In particular, we discuss the

PORTUGALIAE MATHEMATICA; F. Marcellan; J. Petronilho

143

Quadratic Residues a is a quadratic residue mod m if x2  

E-print Network

a reciprocity law.) The law of quadratic reciprocity says: The congruences are either both solvable or both, a is a quadratic nonresidue. · Quadratic Reciprocity relates the solvability of the congruence x2 = p (mod q gave of quadratic reciprocity one of his crowning achievements; in fact, he gave 6 distinct proofs

Ikenaga, Bruce

144

Estimation of Clustering Parameters Using Gaussian Process Regression  

PubMed Central

We propose a method for estimating the clustering parameters in a Neyman-Scott Poisson process using Gaussian process regression. It is assumed that the underlying process has been observed within a number of quadrats, and from this sparse information the distribution is modelled as a Gaussian process. The clustering parameters are then estimated numerically by fitting to the covariance structure of the model. It is shown that the proposed method is resilient to any sampling regime. The method is applied to simulated two-dimensional clustered populations and the results are compared to a related method from the literature. PMID:25383766

Rigby, Paul; Pizarro, Oscar; Williams, Stefan B.

2014-01-01

145

Flutter control of a composite plate with piezoelectric multilayered actuators  

Microsoft Academic Search

Active flutter velocity enhancement scheme is presented for lifting surfaces, employing Linear Quadratic Gaussian based multi-input multi-output controller with multilayered piezoelectric actuators. To numerically test the developed concept, a composite plate wing, surface bonded with eight piezoelectric bender actuators and sensors has been considered. A modal flutter control model is formulated in state-space domain using coupled piezoelectric finite element procedures

S. Raja; A. A. Pashilkar; R. Sreedeep; J. V. Kamesh

2006-01-01

146

Robust power system controller design based on measured models  

Microsoft Academic Search

This paper presents combined power 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

F. Fatehi; J. R. Smith; D. A. Pierre

1996-01-01

147

Learning Mixtures of Gaussians  

Microsoft Academic Search

Mixtures of Gaussians are among the most fundamental and widely used statistical models. Current techniques for learning such mixtures from data are local search heuris- tics withweak performance guarantees. We present the first provably correct algorithm for learning a mixture of Gaus- sians. This algorithm is very simple and returns the true centers of the Gaussians to withinthe precision specified

Sanjoy Dasgupta

1999-01-01

148

Least square and Instrumental Variable system identification of ac servo position control system with fractional Gaussian noise  

Microsoft Academic Search

In this paper, the classical Least Square Estimator (LSE) and its improved version the Instrumental Variable (IV) estimator have been used for the identification of an ac servo motor position control system. The data for system identification has been collected from a practical test set-up for fixed command on the final angular position of the servo motor with varying level

Saptarshi Das; Abhishek Kumar; Indranil Pan; Anish Acharya; Shantanu Das; Amitava Gupta

2011-01-01

149

OPTICAL SOLITONS: Excitation of two-dimensional soliton matrices by fundamental Gaussian beams  

NASA Astrophysics Data System (ADS)

The excitation of two-dimensional periodic structures of fields of the first and second radiation harmonics due to the modulation instability of fundamental Gaussian beams is studied in a medium with a quadratic nonlinearity. The distances are found at which soliton matrix structures with a specified period are formed and destroyed. Optical gratings formed due to nonlinear aberration of broad Gaussian beams are considered.

Borovkova, O. V.; Chuprakov, D. A.; Sukhorukov, Anatolii P.

2005-01-01

150

Rocket ascent trajectory optimization via recursive quadratic programming  

Microsoft Academic Search

An algorithm for solving parameterized optimal control problems such as the ascent trajectory optimization problem of a multistage launch vehicle is developed. The implementation of this algorithm, designated as the Recursive Quadratic Programming Approach, for the pitch and yaw optimization of a multistage launch vehicle is discussed, and results are given for injection into a polar orbit from the Indian

K. H. Well; S. R. Tandon

1982-01-01

151

The eccentricity of conic sections formulated as rational Bézier quadratics  

Microsoft Academic Search

The eccentricity of rational quadratic Bézier curves is formulated directly in terms of their control-points and weights. Based on this expression, we analyze the range and extreme values of the eccentricity of conic sections expressed in this form. We also provide an explicit expression for the eccentricity of the osculating conic of a rational Bézier curve of high degree.

Chendong Xu; Tae-wan Kim; Gerald E. Farin

2010-01-01

152

Improving the Performance of MIQP Solvers for Quadratic Programs ...  

E-print Network

doctrine, a mean-variance optimizer should solve the following quadratic problem: min xT Qx ... with different risk measures and tracking error control. ...... the CVX Matlab codes and the C program codes in our numerical tests are available at.

2013-09-07

153

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

154

Free Gaussian Wave Packet  

NSDL National Science Digital Library

The Free Gaussian Wave Packet model simulates the time evolution of a free-particle Gaussian wave packet in position and k (momentum) space.  The position-space and k-space (momentum-space) wave functions are depicted using three colors on the graph to depict the absolute square of the wave function, the real part of the wave function, and the imaginary part of the wave function. The user may change the wave packet's initial width, its initial average position, and its initial average k value (momentum). The Free Gaussian Wave Packet 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_free_gaussian.jar file will run the program if Java is installed.

Palop, Jose I.

2010-07-16

155

Autonomous Gaussian Decomposition  

E-print Network

We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of Gaussian components in the data, and also their locations, widths, and amplitudes. We test AGD and find that it produces results comparable to human-derived solutions on 21cm absorption spectra from the 21cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the HI line completeness as a function of peak optical depth and velocity width for the 21-SPONGE data, and also show that the results of AGD are stable against varying observational noise intensity. The autonomy and computational efficiency of the method over traditional manual Gaussian fits allow for truly unbiased comparisons between observations and simulations, and for the ability to scale up and interpret the very large data volumes from the up...

Lindner, Robert R; Murray, Claire E; Stanimirovi?, Snežana; Babler, Brian L; Heiles, Carl; Hennebelle, Patrick; Goss, W M; Dickey, John

2014-01-01

156

Complex argument Hermite-Gaussian and Laguerre-Gaussian beams  

Microsoft Academic Search

Hermite-Gaussian and Laguerre-Gaussian beams with complex arguments of the type introduced by Siegman (J. Opt. Soc. Am. 63, 1093 (1973)) are shown to arise naturally in correction terms of a perturbation expansion whose leading term is the fundamental paraxial Gaussian beam. Additionally, they can all be expressed as derivatives of the fundamental Gaussian beam and as paraxial limits of multipole

Erich Zauderer

1986-01-01

157

Gaussian operations and privacy  

SciTech Connect

We consider the possibilities offered by Gaussian states and operations for two honest parties, Alice and Bob, to obtain privacy against a third eavesdropping party, Eve. We first extend the security analysis of the protocol proposed in [Navascues et al. Phys. Rev. Lett. 94, 010502 (2005)]. Then, we prove that a generalized version of this protocol does not allow one to distill a secret key out of bound entangled Gaussian states.

Navascues, Miguel; Acin, Antonio [ICFO-Institut de Ciencies Fotoniques, Jordi Girona 29, Edifici Nexus II, E-08034 Barcelona (Spain)

2005-07-15

158

Gaussian bridges Dario Gasbarra1  

E-print Network

Gaussian bridges Dario Gasbarra1 , Tommi Sottinen2 , and Esko Valkeila3 1 Department of Mathematics.valkeila@hut.fi Summary. We consider Gaussian bridges; in particular their dynamic representa- tions. We prove a Girsanov theorem between the law of Gaussian bridge and the original Gaussian process, which holds with natural

Sottinen, Tommi

159

Discriminative learning quadratic discriminant function for handwriting recognition.  

PubMed

In character string recognition integrating segmentation and classification, high classification accuracy and resistance to noncharacters are desired to the underlying classifier. In a previous evaluation study, the modified quadratic discriminant function (MQDF) proposed by Kimura et al. was shown to be superior in noncharacter resistance but inferior in classification accuracy to neural networks. This paper proposes a discriminative learning algorithm to optimize the parameters of MQDF with aim to improve the classification accuracy while preserving the superior noncharacter resistance. We refer to the resulting classifier as discriminative learning QDF (DLQDF). The parameters of DLQDF adhere to the structure of MQDF under the Gaussian density assumption and are optimized under the minimum classification error (MCE) criterion. The promise of DLQDF is justified in handwritten digit recognition and numeral string recognition, where the performance of DLQDF is comparable to or superior to that of neural classifiers. The results are also competitive to the best ones reported in the literature. PMID:15384535

Liu, Cheng-Lin; Sako, Hiroshi; Fujisawa, Hiromichi

2004-03-01

160

Single-photon quadratic optomechanics  

PubMed Central

We present exact analytical solutions to study the coherent interaction between a single photon and the mechanical motion of a membrane in quadratic optomechanics. We consider single-photon emission and scattering when the photon is initially inside the cavity and in the fields outside the cavity, respectively. Using our solutions, we calculate the single-photon emission and scattering spectra, and find relations between the spectral features and the system's inherent parameters, such as: the optomechanical coupling strength, the mechanical frequency, and the cavity-field decay rate. In particular, we clarify the conditions for the phonon sidebands to be visible. We also study the photon-phonon entanglement for the long-time emission and scattering states. The linear entropy is employed to characterize this entanglement by treating it as a bipartite one between a single mode of phonons and a single photon. PMID:25200128

Liao, Jie-Qiao; Nori, Franco

2014-01-01

161

Design of reduced-order, H2 optimal controllers using a homotopy algorithm  

Microsoft Academic Search

The minimal dimension of a linear-quadratic-gaussian (LQG) compensator is almost always equal to the dimension of the design plant. This deficiency can lead to implementation problems when considering control design for high-order systems such as flexible structures and has led to the development of methodologies for the design of optimal (or near optimal) controllers whose dimension is less than that

EMMANUEL G. COLLINS Jr; LARRY D. DAVIS; STEPHEN RICHTER

1995-01-01

162

Quadratic Equations: From Factored to Standard Form  

NSDL National Science Digital Library

This activity leads students to understand the utility in the factored form of a quadratic equation. Students then express quadratic equations in standard form in the corresponding factored form. The activity is concluded with four critical-thinking questions. website: http://www.mathedpage.org/ copyright information: http://www.mathedpage.org/rights.html

2011-01-01

163

Binary Quadratic Forms: A Historical View  

ERIC Educational Resources Information Center

We present an expository account of the development of the theory of binary quadratic forms. Beginning with the formulation and proof of the Two-Square Theorem, we show how the study of forms of the type x[squared] + ny[squared] led to the discovery of the Quadratic Reciprocity Law, and how this theorem, along with the concept of reduction relates…

Khosravani, Azar N.; Beintema, Mark B.

2006-01-01

164

Another Look at the Quadratic Formula.  

ERIC Educational Resources Information Center

An exploration of a problem called solving quadratic congruences modulo p is detailed and is built around an alternate method of deriving the quadratic formula. Three practical pedagogical values that have been experienced by students and instructor when the material was presented to classes are noted. (MP)

Obermeyer, Dean D.

1982-01-01

165

Dynamics of quadratic polynomials II: rigidity  

Microsoft Academic Search

This is a continuation of the series of notes on the dynamics of quadratic polynomials. We show the following Rigidity Theorem: Any combinatorial class contains at most one quadratic polynomial satisfying the secondary limbs condition with a-priori bounds. As a corollary, such maps are combinatorially and topologically rigid, and as a consequence, the Mandelbrot set is locally connected at the

Mikhail Lyubich

1995-01-01

166

An Unexpected Influence on a Quadratic  

ERIC Educational Resources Information Center

Using technology to explore the coefficients of a quadratic equation can lead to an unexpected result. This article describes an investigation that involves sliders and dynamically linked representations. It guides students to notice the effect that the parameter "a" has on the graphical representation of a quadratic function in the form…

Davis, Jon D.

2013-01-01

167

Free-space propagation of second harmonic Laguerre Gaussian beams carrying phase singularity  

Microsoft Academic Search

The vorticity of a free propagating second harmonic (SH) beam produced in a nonlinear quadratic crystal by a combined beam composed of two coaxial Laguerre-Gaussian vortex beams is analysed. In the near field of the SH radiation an aligned vortical structure with a number of double-charge vortices is created. The diffraction of the SH beam under free propagation is also

S. Orlov; K. Regelskis; V. Smilgevicius; A. Stabinis

2004-01-01

168

A quadratically convergent VBSCF method.  

PubMed

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. PMID:23406096

Rashid, Zahid; van Lenthe, Joop H

2013-02-01

169

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

170

Seven Wonders of the Ancient and Modern Quadratic World.  

ERIC Educational Resources Information Center

Presents four methods for solving a quadratic equation using graphing calculator technology: (1) graphing with the CALC feature; (2) quadratic formula program; (3) table; and (4) solver. Includes a worksheet for a lab activity on factoring quadratic equations. (KHR)

Taylor, Sharon E.; Mittag, Kathleen Cage

2001-01-01

171

Non-Gaussian bias: insights from discrete density peaks  

SciTech Connect

Corrections induced by primordial non-Gaussianity to the linear halo bias can be computed from a peak-background split or the widespread local bias model. However, numerical simulations clearly support the prediction of the former, in which the non-Gaussian amplitude is proportional to the linear halo bias. To understand better the reasons behind the failure of standard Lagrangian local bias, in which the halo overdensity is a function of the local mass overdensity only, we explore the effect of a primordial bispectrum on the 2-point correlation of discrete density peaks. We show that the effective local bias expansion to peak clustering vastly simplifies the calculation. We generalize this approach to excursion set peaks and demonstrate that the resulting non-Gaussian amplitude, which is a weighted sum of quadratic bias factors, precisely agrees with the peak-background split expectation, which is a logarithmic derivative of the halo mass function with respect to the normalisation amplitude. We point out that statistics of thresholded regions can be computed using the same formalism. Our results suggest that halo clustering statistics can be modelled consistently (in the sense that the Gaussian and non-Gaussian bias factors agree with peak-background split expectations) from a Lagrangian bias relation only if the latter is specified as a set of constraints imposed on the linear density field. This is clearly not the case of standard Lagrangian local bias. Therefore, one is led to consider additional variables beyond the local mass overdensity.

Desjacques, Vincent; Riotto, Antonio [Département de Physique Théorique and Center for Astroparticle Physics, Université de Genève, CH-1211 Genève (Switzerland); Gong, Jinn-Ouk, E-mail: Vincent.Desjacques@unige.ch, E-mail: jinn-ouk.gong@apctp.org, E-mail: Antonio.Riotto@unige.ch [Theory Division, CERN, CH-1211 Genève 23 (Switzerland)

2013-09-01

172

Quantum information with Gaussian states  

E-print Network

Quantum optical Gaussian states are a type of important robust quantum states which are manipulatable by the existing technologies. So far, most of the important quantum information experiments are done with such states, including bright Gaussian light and weak Gaussian light. Extending the existing results of quantum information with discrete quantum states to the case of continuous variable quantum states is an interesting theoretical job. The quantum Gaussian states play a central role in such a case. We review the properties and applications of Gaussian states in quantum information with emphasis on the fundamental concepts, the calculation techniques and the effects of imperfections of the real-life experimental setups. Topics here include the elementary properties of Gaussian states and relevant quantum information device, entanglement-based quantum tasks such as quantum teleportation, quantum cryptography with weak and strong Gaussian states and the quantum channel capacity, mathematical theory of quantum entanglement and state estimation for Gaussian states.

X. -B. Wang; T. Hiroshima; A. Tomita; M. Hayashi

2008-01-30

173

Design of Linear Quadratic Regulators and Kalman Filters  

NASA Technical Reports Server (NTRS)

AESOP solves problems associated with design of controls and state estimators for linear time-invariant systems. Systems considered are modeled in state-variable form by set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are linear quadratic regulator (LQR) design problem and steady-state Kalman filter design problem. AESOP is interactive. User solves design problems and analyzes solutions in single interactive session. Both numerical and graphical information available to user during the session.

Lehtinen, B.; Geyser, L.

1986-01-01

174

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

175

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

176

RELIABLE SOLUTION OF CONVEX QUADRATIC PROGRAMS ...  

E-print Network

lems in Sequential Quadratic Programming (SQP), a state-of-the-art method for ...... Support by the German Federal Ministry of Education and Research (BMBF) under ... sults has received funding from the European Union Seventh Framework ...

2011-01-28

177

Improved semidefinite programming bounds for quadratic ...  

E-print Network

Sep 15, 2009 ... gramming Relaxations for the Quadratic Assignment Problem. Journal ... a partial assignment of facilities to locations leads to a smaller QAP problem ...... Society for Industrial and Applied Mathematics, 12(1): 131–135, 1964.

2009-09-15

178

BLOCK STRUCTURED QUADRATIC PROGRAMMING FOR THE ...  

E-print Network

brid null–space range–space approach to exploit the block sparse structure of the quadratic ... ment of the theoretical run time complexity reveals significant advantages of the proposed ... complementary condensing, based on work by [35

2009-09-11

179

Remarks on Quadratic Hamiltonians in Spaceflight Mechanics  

E-print Network

Remarks on Quadratic Hamiltonians in Spaceflight Mechanics Bernard Bonnard1 , Jean-Baptiste Caillau in spaceflight mechanics when the averaged system of energy minimizing trajectories of the Kepler equation

Caillau, Jean-Baptiste

180

sensitivity analysis in convex quadratic optimization: simultaneous ...  

E-print Network

of using optimal bases in parametric LO showing by an example that different ...... maximization game correspond to optimal solutions of the following quadratic minimization .... mization, Springer Science+Business Media, New York, USA.

2007-08-30

181

Weight of quadratic forms and graph states  

E-print Network

We prove a connection between Schmidt-rank and weight of quadratic forms. This provides a new tool for the classification of graph states based on entanglement. Our main tool arises from a reformulation of previously known results concerning the weight of quadratic forms in terms of graph states properties. As a byproduct, we obtain a straightforward characterization of the weight of functions associated with pivot-minor of bipartite graphs.

Alessandro Cosentino; Simone Severini

2009-06-13

182

Linear and quadratic programming neural network analysis  

Microsoft Academic Search

Neural networks for linear and quadratic programming are analyzed. The network proposed by M.P. Kennedy and L.O. Chua (IEEE Trans. Circuits Syst., vol.35, pp.554-562, May 1988) is justified from the viewpoint of optimization theory and the technique is extended to solve optimization problems, such as the least-squares problem. For quadratic programming, the network converges either to an equilibrium or to

Chia-Yiu Maa; Michael A. Shanblatt

1992-01-01

183

Gaussian Quantum Marginal Problem  

Microsoft Academic Search

The quantum marginal problem asks what local spectra are consistent with a given spectrum of a joint state of a composite\\u000a quantum system. This setting, also referred to as the question of the compatibility of local spectra, has several applications\\u000a in quantum information theory. Here, we introduce the analogue of this statement for Gaussian states for any number of modes,

Jens Eisert; Tomás Tyc; Terry Rudolph; Barry C. Sanders

2008-01-01

184

A Solvable Mean Field Model of a Gaussian Spin Glass  

E-print Network

We introduce a mean field spin glass model with gaussian distribuited spins and pairwise interactions, whose couplings are drawn randomly from a normal gaussian distribution too. We completely control the main thermodynamical properties of the model (free energy, phase diagram, fluctuations theory) in the whole phase space. In particular we prove that in thermodynamic limit the free energy equals its replica symmetric expression.

Adriano Barra; Giuseppe Genovese; Francesco Guerra; Daniele Tantari

2011-09-19

185

Gaussian interferometric power  

NASA Astrophysics Data System (ADS)

The interferometric power of a bipartite quantum state quantifies the precision, measured by quantum Fisher information, that such a state enables for the estimation of a parameter embedded in a unitary dynamics applied to one subsystem only, in the worst-case scenario where a full knowledge of the generator of the dynamics is not available a priori. For finite-dimensional systems, this quantity was proven to be a faithful measure of quantum correlations beyond entanglement. Here we extend the notion of interferometric power to the technologically relevant setting of optical interferometry with continuous-variable probes. By restricting to Gaussian local dynamics, we obtain a closed formula for the interferometric power of all two-mode Gaussian states. We identify separable and entangled Gaussian states which maximize the interferometric power at fixed mean photon number of the probes and discuss the associated metrological scaling. At fixed entanglement of the probes, highly thermalized states can guarantee considerably larger precision than pure two-mode squeezed states.

Adesso, Gerardo

2014-08-01

186

Resonant non-gaussianity  

SciTech Connect

We provide a derivation from first principles of the primordial bispectrum of scalar perturbations produced during inflation driven by a canonically normalized scalar field whose potential exhibits small sinusoidal modulations. A potential of this type has been derived in a class of string theory models of inflation based on axion monodromy. We use this model as a concrete example, but we present our derivations and results for a general slow-roll potential with superimposed modulations. We show analytically that a resonance between the oscillations of the background and the oscillations of the fluctuations is responsible for the production of an observably large non-Gaussian signal. We provide an explicit expression for the shape of this resonant non-Gaussianity. We show that there is essentially no overlap between this shape and the local, equilateral, and orthogonal shapes, and we stress that resonant non-Gaussianity is not captured by the simplest version of the effective field theory of inflation. We hope our analytic expression will be useful to further observationally constrain this class of models.

Flauger, Raphael [Department of Physics, Yale University, New Haven, CT 06520 (United States); Pajer, Enrico, E-mail: raphael.flauger@yale.edu, E-mail: ep295@cornell.edu [Department of Physics, Cornell University, Ithaca, NY 14853 (United States)

2011-01-01

187

Quadratic constrained mixed discrete optimization with an adiabatic quantum optimizer  

E-print Network

We extend the family of problems that may be implemented on an adiabatic quantum optimizer (AQO). When a quadratic optimization problem has at least one set of discrete controls and the constraints are linear, we call this a quadratic constrained mixed discrete optimization (QCMDO) problem. QCMDO problems are NP-hard, and no efficient classical algorithm for their solution is known. Included in the class of QCMDO problems are combinatorial optimization problems constrained by a linear partial differential equation (PDE) or system of linear PDEs. An essential complication commonly encountered in solving this type of problem is that the linear constraint may introduce many intermediate continuous variables into the optimization while the computational cost grows exponentially with problem size. We resolve this difficulty by developing a constructive mapping from QCMDO to quadratic unconstrained binary optimization (QUBO) such that the size of the QUBO problem depends only on the number of discrete control variables. With a suitable embedding, taking into account the physical constraints of the realizable coupling graph, the resulting QUBO problem can be implemented on an existing AQO. The mapping itself is efficient, scaling cubically with the number of continuous variables in the general case and linearly in the PDE case if an efficient preconditioner is available.

Rishabh Chandra; N. Tobias Jacobson; Jonathan E. Moussa; Steven H. Frankel; Sabre Kais

2013-10-07

188

Ensemble Kalman filter method for Gaussian and non-Gaussian priors  

NASA Astrophysics Data System (ADS)

The objective of this work is to find an efficient and robust way to implement the ensemble Kalman filter (EnKF) to assimilate production and seismic data for both Gaussian and truncated pluri-Gaussian geological models. Truncated pluri-Gaussian models have proven to be useful for generating realistic geological models of facies distributions. In this work, we will specifically test a new idea for modeling of a channelized reservoir (fluvial system with two fades, channel facies and non-channel facies). EnKF is used to adjust the facies distribution (e.g. channel and non-channel fades) as well as the porosity and permeability of each fades to match production data and seismic data. For two and three-dimensional pluri-Gaussian models, we present a new procedure to ensure that facies observations at wells are honored at each data assimilation step. As the erroneous saturation distribution obtained with EnKF may result from nonlinearity or the failure of the assumption that the ensemble of predictions is approximately Gaussian, we investigate the application of a global and local normal score transform to transform water saturation to a Gaussian variables before applying the EnKF analysis step. We also apply an iterative EnKF scheme to obtain more plausible saturations distributions. To improve water cut data matches, we consider matching breakthrough times directly before matching watercut data. The integration of seismic data poses problems because of the large number of data that are assimilated. With a global assimilation procedure based on subspace projection, filter divergence becomes severe. On the other hand, our implementation of a local updating method to reduce filter divergence results in an unrealistic rough facies map. We introduce a projection method to obtain a more realistic map of the facies distribution, which retains the inherent smoothness of the underlying geological model. The characterization of measurement error is important if one uses a Bayesian approach to condition reservoir models to dynamic data. We use Savitzky-Golay smoother and wavelet smoother to estimate the measurement error in the production data, and use a modified EM (Expectation-Maximization) algorithm combined with a quadratic fitting to estimate the measurement error in the 4-D seismic data.

Zhao, Yong

189

The Factorability of Quadratics: Motivation for More Techniques  

ERIC Educational Resources Information Center

Typically, secondary and college algebra students attempt to utilize either completing the square or the quadratic formula as techniques to solve a quadratic equation only after frustration with factoring has arisen. While both completing the square and the quadratic formula are techniques which can determine solutions for all quadratic equations,…

Bosse, Michael J.; Nandakumar, N. R.

2005-01-01

190

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

191

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

192

Quadratic Integrate-and-Fire Model  

NSDL National Science Digital Library

The Quadratic Integrate-and-Fire model is a slight modification of the integrate-and-fire model. This slight modification has some drastic changes on the dynamics, although the equation is still solvable analytically in order to determine the period of a continuously-spiking neuron. Because of its simplicity, the Quadratic Integrate-and-Fire model and its variations are favorites for mathematical treatments of neural networks. The Quadratic Integrate-and-Fire 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.

2012-11-06

193

Non-Gaussian Isocurvature Models  

Microsoft Academic Search

The distribution of primordial density fluctuations is a potential discriminator between inhomogeneities caused by inflation, and those created by topological defects. We discuss statistical methods for detecting primordial non-Gaussian fields using redshift surveys. In particular, we examine the effect of non-Gaussian initial conditions on the clustering of galaxies, comparing the non-linear evolution of the power spectrum in non-Gaussian models with

A. J. Stirling; J. A. Peacock

1999-01-01

194

Scintillations of Laguerre Gaussian beams  

Microsoft Academic Search

By using the Rytov method, we formulate and numerically evaluate the scintillations of Laguerre Gaussian beams in weak atmospheric\\u000a turbulence. Our results indicate that at on-axis positions, Laguerre Gaussian beams with zero angular mode number will have\\u000a less scintillations than fundamental Gaussian beams, where the amount of scintillations will further decrease with rising\\u000a radial mode number. When off-axis positions are

H. T. Eyyubo?lu; Y. Baykal; X. Ji

2010-01-01

195

Optical power flow with sequential quadratic programming  

NASA Astrophysics Data System (ADS)

Newton's method as an approach to solve the optimal power flow problem in electric power plants is presented. A general formulation of the optimal flow problem is given. Newton's method is applied to solve the nonlinear Kuhn-Tucker conditions by iteration. Every Newton step is calculated by solving a quadratic programming problem. Variations of the sequential quadratic programming method are presented. Byproducts of the optimization, namely the Lagrange multipliers and their interpretation as marginal costs and shadow prices, are outlined. The most important computer programs are enclosed.

Vanamerongen, R. A. M.

1985-01-01

196

Optical implementation and entanglement distribution in Gaussian valence bond states  

NASA Astrophysics Data System (ADS)

We study Gaussian valence bond states of continuous variable systems obtained as the outputs of projection operations from an ancillary space of M infinitely entangled bonds connecting neighboring sites applied at each ofN sites of a harmonic chain. The entanglement distribution in Gaussian valence bond states can be controlled by varying the input amount of entanglement engineered in a (2M+ 1)-mode Gaussian state known as the building block, which is isomorphic to the projector applied at a given site. We show how this mechanism can be interpreted in terms of multiple entanglement swapping from the chain of ancillary bonds, through the building blocks. We provide optical schemes to produce bisymmetric three-mode Gaussian building blocks (which correspond to a single bond, M = 1), and study the entanglement structure in the output Gaussian valence bond states. Finally, the usefulness of such states for quantum communication protocols with continuous variables, like telecloning and teleportation networks, is discussed.

Adesso, G.; Ericsson, M.

2007-08-01

197

Non-Gaussian fingerprints of self-interacting curvaton  

SciTech Connect

We investigate non-Gaussianities in self-interacting curvaton models treating both renormalizable and non-renormalizable polynomial interactions. We scan the parameter space systematically and compute numerically the non-linearity parameters f{sub NL} and g{sub NL}. We find that even in the interaction dominated regime there are large regions consistent with current observable bounds. Whenever the interactions dominate, we discover significant deviations from the relations f{sub NL} ? r{sub dec}{sup ?1} and g{sub NL} ? r{sub dec}{sup ?1} valid for quadratic curvaton potentials, where r{sub dec} measures the curvaton contribution to the total energy density at the time of its decay. Even if r{sub dec} || 1, there always exists regions with f{sub NL} ? 0 since the sign of f{sub NL} oscillates as a function of the parameters. While g{sub NL} can also change sign, typically g{sub NL} is non-zero in the low-f{sub NL} regions. Hence, for some parameters the non-Gaussian statistics is dominated by g{sub NL} rather than by f{sub NL}. Due to self-interactions, both the relative signs of f{sub NL} and g{sub NL} and the functional relation between them is typically modified from the quadratic case, offering a possible experimental test of the curvaton interactions.

Enqvist, Kari; Taanila, Olli [Physics Department, University of Helsinki, FIN-00014 (Finland); Nurmi, Sami [Institute for Theoretical Physics, University of Heidelberg, 69120 Heidelberg (Germany); Takahashi, Tomo, E-mail: kari.enqvist@helsinki.fi, E-mail: s.nurmi@thphys.uni-heidelberg.de, E-mail: olli.taanila@iki.fi, E-mail: tomot@cc.saga-u.ac.jp [Department of Physics, Saga University, Saga 840-8502 (Japan)

2010-04-01

198

Local ensemble transform Kalman filter, a fast non-stationary control law for adaptive optics on ELTs: theoretical aspects and first simulation results.  

PubMed

We propose a new algorithm for an adaptive optics system control law, based on the Linear Quadratic Gaussian approach and a Kalman Filter adaptation with localizations. It allows to handle non-stationary behaviors, to obtain performance close to the optimality defined with the residual phase variance minimization criterion, and to reduce the computational burden with an intrinsically parallel implementation on the Extremely Large Telescopes (ELTs). PMID:25321291

Gray, Morgan; Petit, Cyril; Rodionov, Sergey; Bocquet, Marc; Bertino, Laurent; Ferrari, Marc; Fusco, Thierry

2014-08-25

199

Local ensemble transform Kalman filter, a fast non-stationary control law for adaptive optics on ELTs: theoretical aspects and first simulation results  

E-print Network

We propose a new algorithm for an adaptive optics system control law, based on the Linear Quadratic Gaussian approach and a Kalman Filter adaptation with localizations. It allows to handle non-stationary behaviors, to obtain performance close to the optimality defined with the residual phase variance minimization criterion, and to reduce the computational burden with an intrinsically parallel implementation on the Extremely Large Telescopes (ELTs).

Gray, Morgan; Rodionov, Sergey; Bocquet, Marc; Bertino, Laurent; Ferrari, Marc; Fusco, Thierry

2014-01-01

200

Quadratic and Hilbert Reciprocity Timothy Curry  

E-print Network

. . . . . . . . . . . . . . . . . . . . . 17 3.5 Hilbert Reciprocity Law on Q . . . . . . . . . . . . . . . . . . . . . . 24 Ch. 4. The Hilbert vi #12;Chapter 1 Introduction The law of quadratic reciprocity provides conditions that tell whether . The Hilbert symbol satisfies the Hilbert reciprocity law, which we will show is equivalent to the law

Lozano-Robledo, Alvaro

201

SELMER GROUPS AND QUADRATIC RECIPROCITY FRANZ LEMMERMEYER  

E-print Network

typical for early class field theory, and were used for proving explicit reciprocity laws. Hecke, on the other hand, first proved (a large part of) the quadratic reciprocity law in number fields using his essentially is just the calculation of the order of a certain Selmer group) from the reciprocity law

Lemmermeyer, Franz

202

Uncertain Conic Quadratic and Semidefinite Optimization  

E-print Network

Uncertain Conic Quadratic and Semidefinite Optimization "Canonical" Conic problem: min x cT xI KI (CP) Uncertain canonical conic problem P: a collec- tion of canonical conic programsI) : Z Robust Counterpart of uncertain canonical conic problem P: the problem min t,x t : t - c[]T x

Nemirovski, Arkadi

203

Robust Conic Quadratic and Semidefinite Optimization  

E-print Network

Lecture 3 Robust Conic Quadratic and Semidefinite Optimization In this lecture, we extend the RO methodology onto non-linear convex optimization problems, specifically, conic ones. 3.1 Uncertain Conic Optimization: Preliminaries 3.1.1 Conic Programs A conic optimization (CO) problem (also called conic program

Nemirovski, Arkadi

204

Global quadratic optimization via conic relaxation  

Microsoft Academic Search

We present a convex conic relaxation for a problem of maximizing an indefinite quadratic form over a set of convex constraints on the squared variables. We show that for all these problems we get at least 12\\/37-relative accuracy of the approximation. In the second part of the paper we derive the conic relaxation by another approach based on the second

Yurii NESTEROV

1998-01-01

205

A Practical Approach to Quadratic Equations.  

ERIC Educational Resources Information Center

The usual methods for solving quadratic equations are noted to require either the use of numerical formula or curve plotting on graph paper. The method described here enables pupils to solve equations using only a 45 degree setsquare, graph paper, and a pencil for those which have both real roots and real coefficients. (Author/MP)

Light, Peter

1983-01-01

206

Theory of the Quadratic Zeeman Effect  

Microsoft Academic Search

The experiments of Jenkins and Segrè, reported in the accompanying paper, are considered theoretically. The quadratic Zeeman effect observed in absorption to large orbits in strong magnetic fields is due to the diamagnetic term in the Hamiltonian, which is proportional to the square of the vector potential and hence to the square of the magnetic field. For the alkalis, the

L. I. Schiff; H. Snyder

1939-01-01

207

Inhomogeneous quadratic forms and triangular numbers  

Microsoft Academic Search

We prove an explicit formula for the number of representations of an integer as the sum of n triangular numbers for each n in the range 2 ? n ? 8 as special cases of a more general formula applicable to an inhomogeneous quadratic form over a totally real number field. The formula can be derived by calculating explicitly the

Goro Shimura

2004-01-01

208

Globally Solving Nonconvex Quadratic Programming Problems via ...  

E-print Network

Mar 7, 2011 ... the new algorithm with existing codes on a diverse set of test instances, ... We consider the problem of optimizing a general quadratic function ... in Matlab's Optimization Toolbox (MathWorks, 2010) is a widely ..... Quadprogbb does, we were unsuccessful due to CPLEX run-time errors that we could not fix.

2011-08-15

209

ESTIMATION OF QUADRATIC FUNCTIONS: NONINFORMATIVE PRIORS FOR  

E-print Network

ESTIMATION OF QUADRATIC FUNCTIONS: NONINFORMATIVE PRIORS FOR NON­CENTRALITY PARAMETERS by James O­Centrality Parameters \\Lambda James O. Berger 1 , Anne Philippe 2 and Christian P. Robert 2;3 1 ISDS, Duke University 2 sets arising from these reference priors. Starting with Welch and Peers (1963) and Peers (1965

Berger, Jim

210

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

211

Machine Learning srihari Gaussian Distribution  

E-print Network

maximizes entropy (for given mean and variance) ­ Sum of set of random variables becomes increasingly) Proportional to Identity matrix (concentric circles) #12;6 Machine Learning srihari Joint, Marginal densities and the two marginals are also Gaussian · Given joint Gaussian N(x|µ,) with =-1 and x = [xa

212

Rocket ascent trajectory optimization via recursive quadratic programming  

NASA Astrophysics Data System (ADS)

An algorithm for solving parameterized optimal control problems such as the ascent trajectory optimization problem of a multistage launch vehicle is developed. The implementation of this algorithm, designated as the Recursive Quadratic Programming Approach, for the pitch and yaw optimization of a multistage launch vehicle is discussed, and results are given for injection into a polar orbit from the Indian launch site where in order to satisfy safety conditions curved ascent trajectories are necessary. It is concluded that the algorithm provides relatively fast optimization, is easy to implement, and has a large convergence region.

Well, K. H.; Tandon, S. R.

1982-06-01

213

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

214

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

215

A Coordinate System for Gaussian Networks  

E-print Network

This paper investigates network information theory problems where the external noise is Gaussian distributed. In particular, the Gaussian broadcast channel with coherent fading and the Gaussian interference channel are ...

Zheng, Lizhong

216

Optimal Quantum Feedback Control for Canonical Observables  

E-print Network

We show that the stochastic Schrodinger equation for the filtered state of a system, with linear free dynamics, undergoing continual non-demolition measurement or either position or momentum, or both together, can be solved explicitly within a class of Gaussian states which we call extended coherent states. The asymptotic limit yields a class of relaxed states which we describe explicitly. Bellman's principle is then applied directly to optimal feedback control of such dynamical systems and the Hamilton Jacobi Bellman equation for the minimum cost is derived. The situation of quadratic performance criteria is treated as the important special case and solved exactly for the class of relaxed states.

John Gough

2005-04-13

217

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

218

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

219

THE EFFECTIVENESS OF QUADRATS FOR MEASURING VASCULAR PLANT DIVERSITY  

EPA Science Inventory

Quadrats are widely used for measuring characteristics of vascular plant communities. It is well recognized that quadrat size affects measurements of frequency and cover. The ability of quadrats of varying sizes to adequately measure diversity has not been established. An exha...

220

QUADRATIC RECIPROCITY VIA LINEAR ALGEBRA M. RAM MURTY  

E-print Network

from this, the law of quadratic reciprocity. 1.Introduction Let p to determine trA when n is an odd number and this allows us to deduce the law of quadratic reciprocity QUADRATIC RECIPROCITY VIA LINEAR ALGEBRA M. RAM MURTY

Murty, Ram

221

Applications: Quadratic Formulas Up to NCTM's Curriculum Standards.  

ERIC Educational Resources Information Center

Discusses an alternative form of the quadratic formula to solve quadratic equations. Presents an application to chemistry to illustrate the need for quadratic formulas better suited to approximations obtained using hand-held calculators. Addresses the problems of rounding errors, accuracy of solutions, and factoring as a method of solution. (MDH)

Nievergelt, Yves

1992-01-01

222

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

223

Some results on Gaussian mixtures  

NASA Astrophysics Data System (ADS)

We investigate Gaussian mixtures with independent components, whose parameters are numerically estimated. A decomposition of a Gaussian mixture is presented when the components have a common variance. We introduce a shifted and scaled t-Student distribution as an approximation for the distribution of Gaussian mixtures when their components have a common mean and develop a hypothesis test for testing the equality of the components means. Finally, we analyse the fitness of the approximate model to the logarithmic daily returns of the Portuguese stock index PSI-20.

Felgueiras, Miguel; Santos, Rui; Martins, João Paulo

2014-10-01

224

A Mechanical Proof of Quadratic Reciprocity  

Microsoft Academic Search

We describe the use of the Boyer-Moore theorem prover in mechanically generating a proof of the Law of Quadratic Reciprocity: for distinct odd primes p and q, the congruences x2=q (mod p) and x2=p (mod q) are either both solvable or both unsolvable, unless p=q=3 (mod 4). The proof is a formalization of an argument due to Eisenstein, based on

David M. Russinoff

1992-01-01

225

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

226

Optimal Approximation of Quadratic Interval Functions  

NASA Technical Reports Server (NTRS)

Measurements are never absolutely accurate, as a result, after each measurement, we do not get the exact value of the measured quantity; at best, we get an interval of its possible values, For dynamically changing quantities x, the additional problem is that we cannot measure them continuously; we can only measure them at certain discrete moments of time t(sub 1), t(sub 2), ... If we know that the value x(t(sub j)) at a moment t(sub j) of the last measurement was in the interval [x-(t(sub j)), x + (t(sub j))], and if we know the upper bound D on the rate with which x changes, then, for any given moment of time t, we can conclude that x(t) belongs to the interval [x-(t(sub j)) - D (t - t(sub j)), x + (t(sub j)) + D (t - t(sub j))]. This interval changes linearly with time, an is, therefore, called a linear interval function. When we process these intervals, we get an expression that is quadratic and higher order w.r.t. time t, Such "quadratic" intervals are difficult to process and therefore, it is necessary to approximate them by linear ones. In this paper, we describe an algorithm that gives the optimal approximation of quadratic interval functions by linear ones.

Koshelev, Misha; Taillibert, Patrick

1997-01-01

227

How many eigenvalues of a Gaussian random matrix are positive?  

PubMed

We study the probability distribution of the index N(+), i.e., the number of positive eigenvalues of an N×N Gaussian random matrix. We show analytically that, for large N and large N(+) with the fraction 0?c=N(+)/N?1 of positive eigenvalues fixed, the index distribution P(N(+)=cN,N)~exp[-?N(2)?(c)] where ? is the Dyson index characterizing the Gaussian ensemble. The associated large deviation rate function ?(c) is computed explicitly for all 0?c?1. It is independent of ? 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 ?(N) of index fluctuations growing as ?(N)~lnN/??(2) for large N. For ?=2, this result is independently confirmed against an exact finite-N formula, yielding ?(N)=lnN/2?(2)+C+O(N(-1)) for large N, where the constant C for even N has the nontrivial value C=(?+1+3ln2)/2?(2)?0.185 248… and ?=0.5772… is the Euler constant. We also determine for large N the probability that the interval [?(1),?(2)] is free of eigenvalues. Some of these results have been announced in a recent letter [Phys. Rev. Lett. 103, 220603 (2009)]. PMID:21599113

Majumdar, Satya N; Nadal, Céline; Scardicchio, Antonello; Vivo, Pierpaolo

2011-04-01

228

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

NASA Technical Reports Server (NTRS)

The use of well-known root-locus techniques for sequentially finding the weighting matrices and the linear quadratic state regulators of multivariable control systems in the frequency domain is considered. This sequential design method permits the retention of some stable open-loop poles and the associated eigenvectors in the closed-loop system; it also allows some optimal closed-loop poles to be placed in a specific region of the complex plane. In addition, it provides a design procedure for determining the weighting matrices and linear quadratic state regulators for the optimal control of multivariable systems in the frequency domain.

Shieh, L. S.; Dib, H. M.; Yates, R. E.

1988-01-01

229

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

230

A closed-loop control scheme for steering steady states of glycolysis and glycogenolysis pathway.  

PubMed

Biochemical networks normally operate in the neighborhood of one of its multiple steady states. It may reach from one steady state to other within a finite time span. In this paper, a closed-loop control scheme is proposed to steer states of the glycolysis and glycogenolysis (GG) pathway from one of its steady states to other. The GG pathway is modeled in the synergism and saturation system formalism, known as S-system. This S-system model is linearized into the controllable Brunovsky canonical form using a feedback linearization technique. For closed-loop control, the linear-quadratic regulator (LQR) and the linear-quadratic gaussian (LQG) regulator are invoked to design a controller for tracking prespecified steady states. In the feedback linearization technique, a global diffeomorphism function is proposed that facilitates in achieving the regulation requirement. The robustness of the regulated GG pathway is studied considering input perturbation and with measurement noise. PMID:24334381

Panja, Surajit; Patra, Sourav; Mukherjee, Anirban; Basu, Madhumita; Sengupta, Sanghamitra; Dutta, Pranab K

2013-01-01

231

Robust linear quadratic designs with respect to parameter uncertainty  

NASA Technical Reports Server (NTRS)

The authors derive a linear quadratic regulator (LQR) which is robust to parametric uncertainty by using the overbounding method of I. R. Petersen and C. V. Hollot (1986). The resulting controller is determined from the solution of a single modified Riccati equation. It is shown that, when applied to a structural system, the controller gains add robustness by minimizing the potential energy of uncertain stiffness elements, and minimizing the rate of dissipation of energy through uncertain damping elements. A worst-case disturbance in the direction of the uncertainty is also considered. It is proved that performance robustness has been increased with the robust LQR when compared to a mismatched LQR design where the controller is designed on the nominal system, but applied to the actual uncertain system.

Douglas, Joel; Athans, Michael

1992-01-01

232

Smoothed analysis of Gaussian elimination  

E-print Network

We present a smoothed analysis of Gaussian elimination, both with partial pivoting and without pivoting. Let A be any matrix and let A be a slight random perturbation of A. We prove that it is unlikely that A has large ...

Sankar, Arvind, 1976-

2004-01-01

233

Quantification of Gaussian quantum steering  

E-print Network

Einstein-Podolsky-Rosen steering incarnates a useful nonclassical correlation which sits in-between entanglement and Bell nonlocality. While a number of qualitative steering criteria exist, very little has been achieved for what concerns quantifying steerability. We introduce a computable measure of steering for arbitrary bipartite Gaussian states of continuous variable systems. For two-mode Gaussian states, the measure reduces to a form of coherent information, which is proven never to exceed entanglement, and to reduce to it on pure states. We provide an operational connection between our measure and the key rate in one-sided device-independent quantum key distribution. We further prove that steering bound entangled Gaussian states by Gaussian measurements is impossible.

Ioannis Kogias; Antony R. Lee; Sammy Ragy; Gerardo Adesso

2014-10-07

234

Quantification of Gaussian quantum steering  

E-print Network

Einstein-Podolsky-Rosen steering incarnates a useful nonclassical correlation which sits in-between entanglement and Bell nonlocality. While a number of qualitative steering criteria exist, very little has been achieved for what concerns quantifying steerability. We introduce a computable measure of steering for arbitrary bipartite Gaussian states of continuous variable systems. For two-mode Gaussian states, the measure reduces to a form of coherent information, which is proven never to exceed entanglement, and to reduce to it on pure states. We provide an operational connection between our measure and the key rate in one-sided device-independent quantum key distribution. We further prove that steering bound entangled Gaussian states by Gaussian measurements is impossible.

Kogias, Ioannis; Ragy, Sammy; Adesso, Gerardo

2014-01-01

235

Learning mixtures of arbitrary gaussians  

Microsoft Academic Search

Mixtures of gaussian (or normal) distributions arise in a variety of application areas. Many techniques have been proposed for the task of finding the component gaussians given samples from the mixture, such as the EM algorithm, a local-search heuristic from Dempster, Laird and Rubin~(1977). However, such heuristics are known to require time exponential in the dimension (i.e., number of variables)

Arora Sanjeev; Ravi Kannan

2001-01-01

236

Gaussian local unitary equivalence of $n$-mode Gaussian states and Gaussian transformations by local operations with classical communication  

E-print Network

We derive necessary and sufficient conditions for arbitrary multi--mode (pure or mixed) Gaussian states to be equivalent under Gaussian local unitary operations. To do so, we introduce a standard form for Gaussian states, which has the properties that (i) every state can be transformed into its standard form via Gaussian local unitaries and (ii) it is unique and (iii) it can be easily computed. Thus, two states are equivalent under Gaussian local unitaries iff their standard form coincides. We explicitly derive the standard form for two-- and three--mode Gaussian pure states. We then investigate transformations between these classes by means of Gaussian local operations assisted by classical communication. For three-mode pure states, we identify a global property that cannot be created but only destroyed by local operations. This implies that the highly entangled family of symmetric three--mode Gaussian states is not sufficient to generated all three-mode Gaussian states by local Gaussian operations.

Géza Giedke; Barbara Kraus

2013-11-03

237

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

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 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

239

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

240

Approximately optimum detection of deterministic signals in Gaussian and compound Poisson noise  

NASA Astrophysics Data System (ADS)

An approximate but explicit likelihood ratio is derived for detecting deterministic signals in Gaussian and compound Poisson noise. The approximation in the derivation is based on the assumption that the localized noise elements rarely overlap each other. The derived log-likelihood ratio consists of two distinct parts. One is the conventional correlation detector for detecting deterministic signals in Gaussian noise. The other is a nonlinear processor which compensates for the degradation of the correlation detector caused by the localized noise, and is activated only by the presence of the localized noise. As such, it involves covariance operators of both the Gaussian and the localized noise, and is obtained by using the simultaneous diagonalization and orthogonalization of quadratic forms in function space involving eigenfunctions of certain composite operators.

Kadota, T. T.

1988-11-01

241

Using a Mixed Integer Quadratic Programming Solver for the Unconstrained Quadratic 0-1 Problem  

Microsoft Academic Search

In this paper, we consider problem (P) of minimizing a quadratic function q(x)=x\\u000a \\u000a t\\u000a \\u000a Qx+c\\u000a \\u000a t\\u000a \\u000a x of binary variables. Our main idea is to use the recent Mixed Integer Quadratic Programming (MIQP) solvers. But, for this,\\u000a we have to first convexify the objective function q(x). A classical trick is to raise up the diagonal entries of Q by a

Alain Billionnet; Sourour Elloumi

2007-01-01

242

Discrete wave propagation in quadratically nonlinear media  

NASA Astrophysics Data System (ADS)

Discrete models are used in describing various microscopic phenomena in many branches of science, ranging from biology through chemistry to physics. Arrays of evanescently coupled, equally spaced, identical waveguides are prime examples of optical structures in which discrete dynamics can be easily observed and investigated. As a result of discretization, these structures exhibit unique diffraction properties with no analogy in continuous systems. Recently nonlinear discrete optics has attracted a growing interest, triggered by the observation of discrete solitons in AlGaAs waveguide arrays reported by Eisenberg et al. in 1998. So far, the following experiments involved systems with third order nonlinearities. In this work, an experimental investigation of discrete nonlinear wave propagation in a second order nonlinear medium is presented. This system deserves particular attention because the nonlinear process involves two or three components at different frequencies mutually locked by a quadratic nonlinearity, and new degrees of freedom enter the dynamical process. In the first part of dissertation, observation of the discrete Talbot effect is reported. In contrast to continuous systems, where Talbot self-imaging effect occurs irrespective of the pattern period, in discrete configurations this process is only possible for a specific set of periodicities. The major part of the dissertation is devoted to the investigation of soliton formation in lithium niobate waveguide arrays with a tunable cascaded quadratic nonlinearity. Soliton species with different topology (unstaggered---all channels in-phase, and staggered---neighboring channels with a pi relative phase difference) are identified in the same array. The stability of the discrete solitons and plane waves (modulational instability) are experimentally investigated. In the last part of the dissertation, a phase-insensitive, ultrafast, all-optical spatial switching and frequency conversion device based on quadratic waveguide array is demonstrated. Spatial routing and wavelength conversion of milliwatt signals is achieved without pulse distortions.

Iwanow, Robert

243

On the Approximation of Correlated NonGaussian Noise Pdfs using Gaussian Mixture Models  

E-print Network

On the Approximation of Correlated Non­Gaussian Noise Pdfs using Gaussian Mixture Models R. S. Blum & Y. Zhang \\Lambda B. M. Sadler y R. J. Kozick z Abstract Gaussian mixture probability density of Gaussian mixture pdfs to model correlated non­Gaussian noise processes. In this paper, we initiate

Blum, Rick

244

Complex modes in unstable quadratic bosonic forms  

E-print Network

We discuss the necessity of using non-standard boson operators for diagonalizing quadratic bosonic forms which are not positive definite and its convenience for describing the temporal evolution of the system. Such operators correspond to non-hermitian coordinates and momenta and are associated with complex frequencies. As application, we examine a bosonic version of a BCS-like pairing Hamiltonian, which, in contrast with the fermionic case, is stable just for limited values of the gap parameter and requires the use of the present extended treatment for a general diagonal representation. The dynamical stability of such forms and the occurrence of non-diagonalizable cases are also discussed.

R. Rossignoli; A. M. Kowalski

2014-04-17

245

Complex modes in unstable quadratic bosonic forms  

SciTech Connect

We discuss the necessity of using nonstandard boson operators for diagonalizing quadratic bosonic forms which are not positive definite and its convenience for describing the temporal evolution of the system. Such operators correspond to non-Hermitian coordinates and momenta and are associated with complex frequencies. As application, we examine a bosonic version of a BCS-like pairing Hamiltonian, which, in contrast with the fermionic case, is stable just for limited values of the gap parameter and requires the use of the present extended treatment for a general diagonal representation. The dynamical stability of such forms and the occurrence of nondiagonalizable cases are also discussed.

Rossignoli, R.; Kowalski, A.M. [Departamento de Fisica, Universidad Nacional de La Plata, C.C.67, La Plata (1900) (Argentina)

2005-09-15

246

Transformations of symmetric multipartite Gaussian states by Gaussian LOCC  

E-print Network

Multipartite quantum correlations, in spite of years of intensive research, still leave many questions unanswered. While bipartite entanglement is relatively well understood for Gaussian states, the complexity of mere qualitative characterization grows rapidly with increasing number of parties. Here, we present two schemes for transformations of multipartite permutation invariant Gaussian states by Gaussian local operations and classical communication. To this end, we use a scheme for possible experimental realization, making use of the fact, that in this picture, the whole N - partite state can be described using two separable modes. Numerically, we study entanglement transformations of tripartite states. Finally, we look at the effect our protocols have on fidelity of assisted quantum teleportation and find that while adding correlated noise does not affect the fidelity at all, there is strong evidence that partial non-demolition measurement leads to a drop in teleportation fidelity.

Ond?ej ?ernotík; Jaromír Fiurášek

2014-03-04

247

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. PMID:24473281

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

2014-01-01

248

Generation of Knot Net for Calculation of Quadratic Triangular B-spline Surface of Human Head  

NASA Astrophysics Data System (ADS)

This paper deals with calculation of the quadratic triangular B-spline surface of the human head for the purpose of its modeling in the standard videocodec MPEG-4 SNHC. In connection with this we propose an algorithm of generation of the knot net and present the results of its application for triangulation of the 3D polygonal model Candide. Then for the model and generated knot net as well as an established distribution of control points we show the results of the calculated quadratic triangular B-spline surface of the human head including its textured version for the texture of the selected avatar.

Mihalík, Ján

2011-09-01

249

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

250

Quadratic Scaling Local Canonical Transformation Method.  

NASA Astrophysics Data System (ADS)

Canonical transformation theory [1] can be used to describe the detailed dynamic correlation in bonding situations where there is significant non-dynamic, i.e. multireference character. This theory uses an exponential ansatz and is size-consistent. The computational cost of this method scales as N^6 which is about the same as in a single reference coupled cluster theory. We have devised a local Canonical transformation method for large systems. For large systems, we have been able to obtain quadratic scaling with the size of the system. Reduced and linear scaling algorithms for methods like MP2 and coupled cluster are well known. However, all these reduced scaling algorithms have been primarily developed for single reference correlation calculations. By combining the local canonical transformation method with, e.g. the quadratic scaling ab-initio Density Matrix Renormalization Group theory, we can now obtain a reduced-scaling description of dynamical and non-dynamical correlation in large multireference problems. [1] Takeshi Yanai, Garnet K.L. Chan, J. Chem. Phys. 124, 194106, 2006.

Ghosh, Debashree; Yanai, Takeshi; Kin-Lic Chan, Garnet

2007-03-01

251

A quadratic pulse height analyzer for space applications.  

NASA Technical Reports Server (NTRS)

A flight-worthy pulse height analyzer that has a quadratic transfer function is described. This quadratic function permits optimum usage of the entire PHA dynamic range due to the quadratic nature of the gamma ray spectrometer's resolution vs energy. After the theoretical design discussion, the implementation of the design is examined and test results described. The analyzer is part of the University of New Hampshire gamma ray monitor for OSO-H.

Burtis, D. W.; Aalami, D.; Evelyn-Veere, R. H.; Sarkady, A. A.

1972-01-01

252

Face detection by quadratic Gabor filter on feature inertia surface and its verification by modified retinal model  

NASA Astrophysics Data System (ADS)

This paper presents s new scheme for face localization in a complex background. A Difference Offset of Gaussian filter is first introduced to calculate a feature inertia surface of an image. Then skeletonization on the inertia surface is carried out by a combination of fast construction of Euclidean Distance Maps and morphological operations. After that, face regions in this resulting skeleton image are detected by a quadratic Gabor filter, and its face trueness of each located area is verified by a modified retinal model. Experiments in practical applications have shown its feasibility.

Ma, Lihong; Zhang, Yu

2001-09-01

253

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

254

ChemXSeer Digital Library Gaussian Search  

E-print Network

We report on the Gaussian file search system designed as part of the ChemXSeer digital library. Gaussian files are produced by the Gaussian software [4], a software package used for calculating molecular electronic structure and properties. The output files are semi-structured, allowing relatively easy access to the Gaussian attributes and metadata. Our system is currently capable of searching Gaussian documents using a boolean combination of atoms (chemical elements) and attributes. We have also implemented a faceted browsing feature on three important Gaussian attribute types - Basis Set, Job Type and Method Used. The faceted browsing feature enables a user to view and process a smaller, filtered subset of documents.

Lahiri, Shibamouli; Nangia, Shikha; Mitra, Prasenjit; Giles, C Lee; Mueller, Karl T

2011-01-01

255

Analysis of bipolar junction transistors with a Gaussian base-dopant impurity-concentration profile  

Microsoft Academic Search

A method for a quantitative charge-control analysis of bipolar base-junction transistors with a Gaussian dopant impurity-concentration profile is demonstrated. Analytical expressions for the base transit time are given for two different Gaussian impurity-concentration profiles with the peak concentration at the edge, and within the quasi-neutral base layer. It is also shown that approximating the Gaussian profile by a simple exponential

Guoxin Li; A. Neugroschel; Chih-Tang Sah; D. Hemmenway; T. Rivoli; J. Maddux

2001-01-01

256

Estimation of kernel function of non-linear system by gaussian non-white noise  

Microsoft Academic Search

The kernel function of a non-linear system characterizes the properties of that system. The kernel function is well developed in the case of gaussian white noise. However in practice it is often necessary to apply an input of gaussian non-white noise in the control of biological systems. Although some methods have been developed that use gaussian non-white noise they do

KATSUMI YOSHINE; NAOHIRO ISHII

1991-01-01

257

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

258

Gaussian processes for machine learning.  

PubMed

Gaussian processes (GPs) are natural generalisations of multivariate Gaussian random variables to infinite (countably or continuous) index sets. GPs have been applied in a large number of fields to a diverse range of ends, and very many deep theoretical analyses of various properties are available. This paper gives an introduction to Gaussian processes on a fairly elementary level with special emphasis on characteristics relevant in machine learning. It draws explicit connections to branches such as spline smoothing models and support vector machines in which similar ideas have been investigated. Gaussian process models are routinely used to solve hard machine learning problems. They are attractive because of their flexible non-parametric nature and computational simplicity. Treated within a Bayesian framework, very powerful statistical methods can be implemented which offer valid estimates of uncertainties in our predictions and generic model selection procedures cast as nonlinear optimization problems. Their main drawback of heavy computational scaling has recently been alleviated by the introduction of generic sparse approximations.13,78,31 The mathematical literature on GPs is large and often uses deep concepts which are not required to fully understand most machine learning applications. In this tutorial paper, we aim to present characteristics of GPs relevant to machine learning and to show up precise connections to other "kernel machines" popular in the community. Our focus is on a simple presentation, but references to more detailed sources are provided. PMID:15112367

Seeger, Matthias

2004-04-01

259

Elliptic Laguerre-Gaussian beams  

Microsoft Academic Search

An analytical expression for the diffraction of an elliptic Laguerre-Gaussian (LG) beam is derived and analyzed. We show that a beam with even singularity order has nonzero axial intensity for any degree of ellipticity and at any finite distance z from the initial plane, whereas at z=0 and z=? the axial intensity is zero. We show that for a beam

Victor V. Kotlyar; Svetlana N. Khonina; Anton A. Almazov; Victor A. Soifer; Konstantins Jefimovs; Jari Turunen

2006-01-01

260

Quadratic dynamical decoupling with nonuniform error suppression  

SciTech Connect

We analyze numerically the performance of the near-optimal quadratic dynamical decoupling (QDD) single-qubit decoherence errors suppression method [J. West et al., Phys. Rev. Lett. 104, 130501 (2010)]. The QDD sequence is formed by nesting two optimal Uhrig dynamical decoupling sequences for two orthogonal axes, comprising N{sub 1} and N{sub 2} pulses, respectively. Varying these numbers, we study the decoherence suppression properties of QDD directly by isolating the errors associated with each system basis operator present in the system-bath interaction Hamiltonian. Each individual error scales with the lowest order of the Dyson series, therefore immediately yielding the order of decoherence suppression. We show that the error suppression properties of QDD are dependent upon the parities of N{sub 1} and N{sub 2}, and near-optimal performance is achieved for general single-qubit interactions when N{sub 1}=N{sub 2}.

Quiroz, Gregory; Lidar, Daniel A. [Department of Physics and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089 (United States); Departments of Electrical Engineering, Chemistry, and Physics, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089 (United States)

2011-10-15

261

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

262

Constraining running non-gaussianity  

SciTech Connect

The primordial non-Gaussian parameter f{sub NL} has been shown to be scale-dependent in several models of inflation with a variable speed of sound, such as Dirac-Born-Infeld (DBI) models. We perform a Fisher matrix analysis of the bispectra of the temperature and polarization of the Cosmic Microwave Background (CMB) radiation and derive the expected constraints on the parameter n{sub NG} that quantifies the running of f{sub NL}(k) for current and future CMB missions. We find that CMB information alone, in the event of a significant detection of the non-Gaussian component, corresponding to f{sub NL} = 50 for the local model and f{sub NL} = 100 for the equilateral model of non-Gaussianity, is able to determine n{sub NG} with a 1-? uncertainty of n{sub NG} ? 0.1 and ?n{sub NG} ? 0.3, respectively, for the Planck mission and a factor of two better for CMBPol. In addition, we show how future large-scale structure observations should achieve results comparable to or even better than those from the CMB, while showing some complementarity due to the different distribution of the non-Gaussian signal over the relevant range of scales. Finally, we compare our findings to the predictions on the amplitude and running of non-Gaussianity of DBI inflation, showing how the constraints on a scale-dependent f{sub NL}(k) translate into constraints on the parameter space of the theory.

Sefusatti, Emiliano [Institut de Physique Théorique, CEA, IPhT, F-91191 Gif-sur-Yvette (France); Liguori, Michele [DAMTP, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA (United Kingdom); Yadav, Amit P.S. [Center for Astrophysics, Harvard University, Cambridge, MA 02138 (United States); Jackson, Mark G. [Center for Particle Astrophysics, Fermilab, Batavia, IL 60510 (United States); Pajer, Enrico, E-mail: emiliano.sefusatti@cea.fr, E-mail: M.Liguori@damtp.cam.ac.uk, E-mail: ayadav@cfa.harvard.edu, E-mail: markj@fnal.gov, E-mail: e.pajer@sns.it [Laboratory for Elementary Particle Physics, Cornell University, Ithaca, NY 14853 (United States)

2009-12-01

263

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

264

Gaussian Velocity Distributions in Avalanches  

NASA Astrophysics Data System (ADS)

Imagine a world where gravity is so strong that if an ice cube is tilted the shear forces melt the surface and water avalanches down. Further imagine that the ambient temperature is so low that the water re-freezes almost immediately. This is the world of granular flows. As a granular solid is tilted the surface undergoes a sublimation phase transition and a granular gas avalanches down the surface, but the inelastic collisions rapidly remove energy from the flow lowering the granular temperature (kinetic energy per particle) until the gas solidifies again. It is under these extreme conditions that we attempt to uncover continuum granular flow properties. Typical continuum theories like Navier-Stokes equation for fluids follow the space-time evolution of the first few moments of the velocity distribution. We study continuously avalanching flow in a rotating two-dimensional granular drum using high-speed video imaging and extract the position and velocities of the particles. We find a universal near Gaussian velocity distribution throughout the flowing regions, which are characterized by a liquid-like radial distribution function. In the remaining regions, in which the radial distribution function develops sharp crystalline peaks, the velocity distribution has a Gaussian peak but is much broader in the tails. In a companion experiment on a vibrated two-dimensional granular fluid under constant pressure, we find a clear gas-solid phase transition in which both the temperature and density change discontinuously. This suggests that a low temperature crystal and a high temperature gas can coexist in steady state. This coexistence could result in a narrower, cooler, Gaussian peak and a broader, warmer, Gaussian tail like the non-Gaussian behavior seen in the crystalline portions of the rotating drum.

Shattuck, Mark

2004-03-01

265

Profile-Following Entry Guidance Using Linear Quadratic Regulator Theory  

NASA Technical Reports Server (NTRS)

This paper describes one of the entry guidance concepts that is currently being tested as part of Marshall Space Flight Center's Advance Guidance and Control Project. The algorithm is of the reference profile tracking type. The reference profile consists of the reference states, range-to-go, altitude, and flight path angle, and reference controls, bank angle and angle of attack, versus energy. A linear control law using state feedback is used with energy-scheduled gains. The gains are obtained offline using Matlab's steady state linear quadratic regulator function. Lateral trajectory control is effected by performing periodic bank sign reversals based on a heading error corridor. A description and results of the AG&C test cases on which it has been tested are given. Although it is not anticipated that the algorithm will be quite as robust as algorithms with onboard trajectory re-generation capability, the results nevertheless show it to be very robust with respect to varying initial conditions and works satisfactorily even for entries from widely different orbits than that of the reference profile. Moreover, the commanded bank and angle of attack histories are very smooth, making it easier for the attitude control system to implement the guidance commands. Finally, results indicate that the guidance gains are more or less trajectory-independent which is a potentially useful property.

Dukeman, Greg A.; Fogle, Frank (Technical Monitor)

2002-01-01

266

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

267

A Public Key Block Cipher Based on Multivariate Quadratic Quasigroups  

E-print Network

- formations using a specific class of quasigroups called multivariate quadratic quasigroups (MQQ). Our public key algorithm is a bijective mapping, it does not perform message expansions and can be used both for encryption and signatures. The public key consist of n quadratic polynomials with n variables where n = 140

268

High order approximation of conic sections by quadratic splines  

E-print Network

High order approximation of conic sections by quadratic splines Michael Floater SINTEF P.O. Box 124, Blindern 0314 Oslo Norway December 1993. Revised, October 1994 Abstract. Given a segment of a conic section and cylinder. Keywords. approximation, conic sections, quadratic splines §1. Introduction The approximate

Floater, Michael S.

269

Sketching the General Quadratic Equation Using Dynamic Geometry Software  

ERIC Educational Resources Information Center

This paper explores a geometrical way to sketch graphs of the general quadratic in two variables with Geometer's Sketchpad. To do this, a geometric procedure as described by De Temple is used, bearing in mind that this general quadratic equation (1) represents all the possible conics (conics sections), and the fact that five points (no three of…

Stols, G. H.

2005-01-01

270

Some Paradoxical Results for the Quadratically Weighted Kappa  

ERIC Educational Resources Information Center

The quadratically weighted kappa is the most commonly used weighted kappa statistic for summarizing interrater agreement on an ordinal scale. The paper presents several properties of the quadratically weighted kappa that are paradoxical. For agreement tables with an odd number of categories "n" it is shown that if one of the raters uses the same…

Warrens, Matthijs J.

2012-01-01

271

Quadratic elongation: A quantitative measure of distortion in coordination polyhedra  

USGS Publications Warehouse

Quadratic elongation and the variance of bond angles are linearly correlated for distorted octahedral and tetrahedral coordination complexes, both of which show variations in bond length and bond angle. The quadratic elonga tion is dimensionless, giving a quantitative measure of polyhedral distortion which is independent of the effective size of the polyhedron.

Robinson, K.; Gibbs, G.V.; Ribbe, P.H.

1971-01-01

272

Analytical placement: A linear or a quadratic objective function?  

Microsoft Academic Search

This paper addresses the problem of cell placement which is considered crucial for layout quality. Based on the combined analytical and partitioning strategy successfully applied in the GORDIAN placement tool, we discuss the consequences of using linear or quadratic ob- jective functions. By joining the linear objective with an efficient quadratic programming approach, and by applying a refined iterative partitioning

Georg Sigl; Konrad Doll; Frank M. Johannes

1991-01-01

273

Clock Distribution Network Optimization by Sequential Quadratic Programing  

E-print Network

. Quasi-Newton Approximation of Hessian . . . . . . . 18 III SENSITIVITY ANALYSIS : : : : : : : : : : : : : : : : : : : : : 20 IV RESULTS AND CONCLUSIONS : : : : : : : : : : : : : : : : : 24 A. Experimental Setup... of quadratic approximations. We use the Karush-Kuhn-Tucker (KKT) conditions to improve the computational e ciency. A quadratic delay formula used in our problem improves the accuracy compared to a linear delay approximation used in [6]. So, we use the quasi-newton...

Mekala, Venkata

2010-07-14

274

Shaping super-Gaussian beam through digital micro-mirror device  

NASA Astrophysics Data System (ADS)

We have set up a novel system for shaping the Gaussian laser beams into super-Gaussian beams. The digital micro-mirror device (DMD) is able to modulate the laser light spatially through binary-amplitude modulation mechanism. With DMD, the irradiance of the laser beam can be redistributed flexibly and various beams with different intensity distribution can be produced. A super-Gaussian beam has been successfully shaped from the Gaussian beam with the use of DMD. This technique will be widely applied in lithography, quantum emulation and holographic optical tweezers which require precise control of beam profile.

Ding, XiangYu; Ren, YuXuan; Lu, RongDe

2014-08-01

275

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

276

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

277

Gaussian Process Change Point Models Yunus Saatci  

E-print Network

Gaussian Process Change Point Models Yunus Saat¸ci Haifa, Israel June 24, 2010 Joint work with Ryan Turner and Carl Edward Rasmussen Saat¸ci (Engineering, Cambridge) Gaussian Process Change Point Models 1 to nonstationarity. Saat¸ci (Engineering, Cambridge) Gaussian Process Change Point Models 2 #12;Aims A time series

Edinburgh, University of

278

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

279

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

280

Limited variance control in statistical low thrust guidance analysis. [stochastic algorithm for SEP comet Encke flyby mission  

NASA Technical Reports Server (NTRS)

Difficulties arise in guiding a solar electric propulsion spacecraft due to nongravitational accelerations caused by random fluctuations in the magnitude and direction of the thrust vector. These difficulties may be handled by using a low thrust guidance law based on the linear-quadratic-Gaussian problem of stochastic control theory with a minimum terminal miss performance criterion. Explicit constraints are imposed on the variances of the control parameters, and an algorithm based on the Hilbert space extension of a parameter optimization method is presented for calculation of gains in the guidance law. The terminal navigation of a 1980 flyby mission to the comet Encke is used as an example.

Jacobson, R. A.

1975-01-01

281

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

282

On the generation of a non-gaussian curvature perturbation during preheating  

SciTech Connect

The perturbation of a light field might affect preheating and hence generate a contribution to the spectrum and non-gaussianity of the curvature perturbation ?. The field might appear directly in the preheating model (curvaton-type preheating) or indirectly through its effect on a mass or coupling (modulated preheating). We give general expressions for ? based on the ?N formula, and apply them to the cases of quadratic and quartic chaotic inflation. For the quadratic case, curvaton-type preheating is ineffective in contributing to ?, but modulated preheating can be effective. For quartic inflation, curvaton-type preheating may be effective but the usual ?N formalism has to be modified. We see under what circumstances the recent numerical simulation of Bond et al. [0903.3407] may be enough to provide a rough estimate for this case.

Kohri, Kazunori; Lyth, David H. [Department of Physics, Lancaster University, Lancaster LA1 4YB (United Kingdom); Valenzuela-Toledo, Cesar A., E-mail: k.kohri@lancaster.ac.uk, E-mail: d.lyth@lancaster.ac.uk, E-mail: cavalto@ciencias.uis.edu.co [Escuela de Física, Universidad Industrial de Santander, Ciudad Universitaria, Bucaramanga (Colombia)

2010-02-01

283

Entangled Bessel-Gaussian beams.  

PubMed

Orbital angular momentum (OAM) entanglement is investigated in the Bessel-Gaussian (BG) basis. Having a readily adjustable radial scale, BG modes provide an alternative basis for OAM entanglement over Laguerre-Gaussian modes. We show that the OAM bandwidth in terms of BG modes can be increased by selection of particular radial wavevectors and leads to a flattening of the spectrum, which allows for higher dimensionality in the entangled state. We demonstrate entanglement in terms of BG modes by performing a Bell-type experiment and showing a violation of the Clauser-Horne-Shimony-Holt inequality for the ? = ±1 subspace. In addition, we use quantum state tomography to indicate higher-dimensional entanglement in terms of BG modes. PMID:23188323

McLaren, Melanie; Agnew, Megan; Leach, Jonathan; Roux, Filippus S; Padgett, Miles J; Boyd, Robert W; Forbes, Andrew

2012-10-01

284

Coding along hermite polynomials for gaussian noise channels  

E-print Network

This paper shows that the capacity achieving input distribution for a fading Gaussian broadcast channel is not Gaussian in general. The construction of non-Gaussian distributions that strictly outperform Gaussian ones, for ...

Abbe, Emmanuel A.

285

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

286

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

287

Quadratic Model for Reservoir Management: Application to the Central Valley Project  

NASA Astrophysics Data System (ADS)

A quadratic optimization model is applied to a large-scale reservoir system to obtain operation schedules. The model has the minimum possible dimensionality, treats spillage and penstock releases as decision variables and takes advantage of system-dependent features to reduce the size of the decision space. An efficient and stable quadratic programming active set algorithm is used to solve for the optimal release policies. The stability and convergence of the solution algorithm are ensured by the factorization of the reduced Hessian matrix and the accurate computation of the Lagrange multipliers. The quadratic model is compared with a simplified linear model and it is found that optimal release schedules are robust to the choice of model, both yielding an increase of nearly 27% in the total annual energy production with respect to conventional operation procedures, although the quadratic model is more flexible and of general applicability. The adequate fulfillment of other system functions such as flood control and water supply is guaranteed via constraints on storage and spillage variables.

MariñO, Miguel A.; Loaiciga, Hugo A.

1985-05-01

288

Local classifier weighting by quadratic programming.  

PubMed

It has been widely accepted that the classification accuracy can be improved by combining outputs of multiple classifiers. However, how to combine multiple classifiers with various (potentially conflicting) decisions is still an open problem. A rich collection of classifier combination procedures -- many of which are heuristic in nature -- have been developed for this goal. In this brief, we describe a dynamic approach to combine classifiers that have expertise in different regions of the input space. To this end, we use local classifier accuracy estimates to weight classifier outputs. Specifically, we estimate local recognition accuracies of classifiers near a query sample by utilizing its nearest neighbors, and then use these estimates to find the best weights of classifiers to label the query. The problem is formulated as a convex quadratic optimization problem, which returns optimal nonnegative classifier weights with respect to the chosen objective function, and the weights ensure that locally most accurate classifiers are weighted more heavily for labeling the query sample. Experimental results on several data sets indicate that the proposed weighting scheme outperforms other popular classifier combination schemes, particularly on problems with complex decision boundaries. Hence, the results indicate that local classification-accuracy-based combination techniques are well suited for decision making when the classifiers are trained by focusing on different regions of the input space. PMID:18842488

Cevikalp, Hakan; Polikar, Robi

2008-10-01

289

Are ghost surfaces quadratic-flux-minimizing?  

E-print Network

Two candidates for "almost-invariant" toroidal surfaces passing through magnetic islands, namely quadratic-flux-minimizing (QFMin) surfaces and ghost surfaces, use families of periodic pseudo-orbits (i.e. paths for which the action is not exactly extremal). QFMin pseudo-orbits, which are coordinate-dependent, are field lines obtained from a modified magnetic field, and ghost-surface pseudo-orbits are obtained by displacing closed field lines in the direction of steepest descent of magnetic action, $\\oint \\vec{A}\\cdot\\mathbf{dl}$. A generalized Hamiltonian definition of ghost surfaces is given and specialized to the usual Lagrangian definition. A modified Hamilton's Principle is introduced that allows the use of Lagrangian integration for calculation of the QFMin pseudo-orbits. Numerical calculations show QFMin and Lagrangian ghost surfaces give very similar results for a chaotic magnetic field perturbed from an integrable case, and this is explained using a perturbative construction of an auxiliary poloidal angle for which QFMin and Lagrangian ghost surfaces are the same up to second order. While presented in the context of 3-dimensional magnetic field line systems, the concepts are applicable to defining almost-invariant tori in other $1{1/2}$ degree-of-freedom nonintegrable Lagrangian/Hamiltonian systems.

S. R. Hudson; R. L. Dewar

2009-09-11

290

Non Gaussian models for hyperspectral algorithm design and assessment  

Microsoft Academic Search

In this paper, we explore the use of elliptically contoured distributions (ECDs) to model the statistical variability of hyperspectral imaging (HSI) data. ECDs have the elliptical symmetry of the multivariate Gaussian distribution and therefore share most of its properties. However, the presence of additional parameters, allows to control the behavior of their tails to match the distribution of the data

Dimitris Manolakis; David Marden

2002-01-01

291

Smooth Conditional Transition Paths in Dynamical Gaussian Networks  

E-print Network

be generated by mixing existing ones. One of the available methods is an interpolation of motion data, which­Wentzell action functionals in Gaussian networks set-up. We use our method to construct a system controlling be applied to spacecrafts in a deep space or in the Earth orbit, see survey papers [20

Miekisz, Jacek

292

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

293

A general formulation for the efficient evaluation of n-electron integrals over products of Gaussian charge distributions with Gaussian geminal functions.  

PubMed

In this work, we present a general formulation for the evaluation of many-electron integrals which arise when traditional one particle expansions are augmented with explicitly correlated Gaussian geminal functions. The integrand is expressed as a product of charge distributions, one for each electron, multiplied by one or more Gaussian geminal factors. Our formulation begins by focusing on the quadratic form that arises in the general n-electron integral. Using the Rys polynomial method for the evaluation of potential energy integrals, we derive a general formula for the evaluation of any n-electron integral. This general expression contains four parameters ?, ?, v, and h, which can be evaluated by an examination of the general quadratic form. Our analysis contains general expressions for any n-electron integral over s-type functions as well as the recursion needed to build up arbitrary angular momentum. The general recursion relation requires at most n + 1 terms for any n-electron integral. To illustrate the general method, we develop explicit expressions for the evaluation of two, three, and four particle electron repulsion integrals as well as two and three particle overlap and nuclear attraction integrals. We conclude our exposition with a discussion of a preliminary computational implementation as well as general computational requirements. Implementation on parallel computers is briefly discussed. PMID:21721620

Komornicki, Andrew; King, Harry F

2011-06-28

294

Iterative LQG Controller Design Through Closed-Loop Identification  

NASA Technical Reports Server (NTRS)

This paper presents an iterative Linear Quadratic Gaussian (LQG) controller design approach for a linear stochastic system with an uncertain open-loop model and unknown noise statistics. This approach consists of closed-loop identification and controller redesign cycles. In each cycle, the closed-loop identification method is used to identify an open-loop model and a steady-state Kalman filter gain from closed-loop input/output test data obtained by using a feedback LQG controller designed from the previous cycle. Then the identified open-loop model is used to redesign the state feedback. The state feedback and the identified Kalman filter gain are used to form an updated LQC controller for the next cycle. This iterative process continues until the updated controller converges. The proposed controller design is demonstrated by numerical simulations and experiments on a highly unstable large-gap magnetic suspension system.

Hsiao, Min-Hung; Huang, Jen-Kuang; Cox, David E.

1996-01-01

295

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

296

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

297

Gaussian Decomposition of Laser Altimeter Waveforms  

NASA Technical Reports Server (NTRS)

We develop a method to decompose a laser altimeter return waveform into its Gaussian components assuming that the position of each Gaussian within the waveform can be used to calculate the mean elevation of a specific reflecting surface within the laser footprint. We estimate the number of Gaussian components from the number of inflection points of a smoothed copy of the laser waveform, and obtain initial estimates of the Gaussian half-widths and positions from the positions of its consecutive inflection points. Initial amplitude estimates are obtained using a non-negative least-squares method. To reduce the likelihood of fitting the background noise within the waveform and to minimize the number of Gaussians needed in the approximation, we rank the "importance" of each Gaussian in the decomposition using its initial half-width and amplitude estimates. The initial parameter estimates of all Gaussians ranked "important" are optimized using the Levenburg-Marquardt method. If the sum of the Gaussians does not approximate the return waveform to a prescribed accuracy, then additional Gaussians are included in the optimization procedure. The Gaussian decomposition method is demonstrated on data collected by the airborne Laser Vegetation Imaging Sensor (LVIS) in October 1997 over the Sequoia National Forest, California.

Hofton, Michelle A.; Minster, J. Bernard; Blair, J. Bryan

1999-01-01

298

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

299

Closed-form solutions for a class of optimal quadratic regulator problems with terminal constraints  

NASA Technical Reports Server (NTRS)

Closed-form solutions are derived for coupled Riccati-like matrix differential equations describing the solution of a class of optimal finite time quadratic regulator problems with terminal constraints. Analytical solutions are obtained for the feedback gains and the closed-loop response trajectory. A computational procedure is presented which introduces new variables for efficient computation of the terminal control law. Two examples are given to illustrate the validity and usefulness of the theory.

Juang, J.-N.; Turner, J. D.; Chun, H. M.

1984-01-01

300

On the Convergence of Successive Linear-Quadratic Programming Algorithms  

E-print Network

. M. Gould Jorge Nocedal Richard A. Waltz April 12, 2005 (revised) Abstract The global convergence-quadratic programming approach presented by Byrd, Gould, Nocedal and Waltz (Math. Programming 100(1):27­48, 2004). Every

Waltz, Richard A.

301

Quadratic discrete Fourier transform and mutually unbiased bases  

E-print Network

The present chapter [submitted for publication in "Fourier Transforms, Theory and Applications", G. Nikolic (Ed.), InTech (Open Access Publisher), Vienna, 2011] is concerned with the introduction and study of a quadratic discrete Fourier transform. This Fourier transform can be considered as a two-parameter extension, with a quadratic term, of the usual discrete Fourier transform. In the case where the two parameters are taken to be equal to zero, the quadratic discrete Fourier transform is nothing but the usual discrete Fourier transform. The quantum quadratic discrete Fourier transform plays an important role in the field of quantum information. In particular, such a transformation in prime dimension can be used for obtaining a complete set of mutually unbiased bases.

Maurice Robert Kibler

2010-10-28

302

Geometric Procedures for Graphing the General Quadratic Equation.  

ERIC Educational Resources Information Center

How tedious algebraic manipulations for simplifying general quadratic equations can be supplemented with simple geometric procedures is discussed. These procedures help students determine the type of conic and its axes and allow a graph to be sketched quickly. (MNS)

DeTemple, Duane W.

1984-01-01

303

Good Numerical Technique in Chemistry: The Quadratic Equation.  

ERIC Educational Resources Information Center

Discusses the loss of precision that normally results in solving equilibrium problems, particularly as presented through the use of quadratic formulas in most introductory college chemistry textbooks. Provides examples of demonstrations. (TW)

Thompson, H. Bradford

1987-01-01

304

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

305

A Sequential Quadratic Optimization Algorithm with Rapid Infeasibility Detection  

E-print Network

, Frank E. Curtis, and Hao Wang Lehigh Industrial and Systems Engineering COR@L Technical Report 2012T-12, FRANK E. CURTIS, AND HAO WANG Abstract. We present a sequential quadratic optimization (SQO) algorithm

Snyder, Larry

306

Contingency Simulation Using Single Phase Quadratized Power Flow  

E-print Network

Contingency Simulation Using Single Phase Quadratized Power Flow Fang Yang, Student Member, IEEE, A, Student Member, IEEE Abstract -- Contingency simulation is an essential but computationally demanding procedure for power system security assessment, reliability evaluation, and real time operation. Simulation

307

A method of Weil sum in multivariate quadratic cryptosystem  

E-print Network

A new cryptanalytic application is proposed for a number theoretic tool Weil sum to the birthday attack against multivariate quadratic trapdoor function. This new customization of the birthday attack is developed by evaluating the explicit Weil sum...

Harayama, Tomohiro

2007-09-17

308

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. PMID:19907539

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

2010-01-01

309

Control-structure interaction  

NASA Technical Reports Server (NTRS)

The feasibility of using conventional proportional-integral-derivative (PID) control and an alternative optimal control to perform the pointing and tracking functions of the Space Station solar dynamic power module is investigated. A very large state model of 6 rigid body modes and 272 flexible modes is used in conjunction with classical linear-quadratic-Gaussian (LQG) optimal control to produce a full-order controller that satisfies the requirements. The results are compared with a classically designed PID controller that was implemented for a much smaller (6 rigid body, 40 flexible modes) model. The conventional control design approach is shown to be very much influenced by the order reduction of the plant model, i.e., the number of retained elastic modes from the full-order model, suggesting that for a complex, large space structure, such as the Space Station Freedom solar dynamic module, application of conventional control system design methods may not be adequate. The use of LQG control is recommended, and method for solving the large matrix. Riccati equation that arises from the optimal formulation is provided.

Cheng, Joseph K.; Ianculescu, George D.; Kenney, Charles S.; Laub, Alan J.; Ly, Jason H. Q.; Papadopoulos, Philip M.

1992-01-01

310

Estimation of wildlife populations using the quadrat method of sampling  

E-print Network

ESTIMATION OF WILDLIFE POPULATIONS USING THE QUADRAT METHOD OF SAMPLING A Thesis by JOHN RICHARD HRIBAR Submitted to the Graduate College of Texas A&M University in partial fulfillment of the requirement for the degree of MASTER OF SCIENCE... May 1970 Major Subject: Statistics ESTIMATION OF WILDLIFE POPUIATIONS USING THE QUADRAT METHOD OF SAMPLING A Thesis by JOHN RICHARD HRZBAR Approved as to style and content by: ( airman of Committee (Member Head of Departme t Member, May 1970...

Hribar, John Richard

2012-06-07

311

On the Convergence of Successive Linear-Quadratic Programming Algorithms  

Microsoft Academic Search

The global convergence properties of a class of penalty methods for nonlinear pro- gramming are analyzed. These methods include successive linear programming ap- proaches, and more specically , the successive linear-quadratic programming approach presented by Byrd, Gould, Nocedal and Waltz (Math. Programming 100(1):27{48, 2004). Every iteration requires the solution of two trust-region subproblems involving piecewise linear and quadratic models, respectively.

Richard H. ByrdNicholas; I. M. Gould; Jorge Nocedalz; Richard A. Waltz

312

The classical bi-Poisson process: An invertible quadratic harness  

Microsoft Academic Search

We give an elementary construction of a time-invertible Markov process which is discrete except at one instance. The process is one of the quadratic harnesses studied in Bryc and Weso?owski [2005. Conditional moments of q-Meixner processes. Probab. Theory Related Fields 131, 415–441 ?arxiv.org\\/abs\\/math.PR\\/0403016?], Bryc et al. [2005b. Quadratic harnesses, q-commutations, and orthogonal martingale polynomials. Trans. Amer. Math. Soc. ?arxiv.org\\/abs\\/math.PR\\/0504194?, to

W?odzimierz Bryc; Jacek Weso?owski

2006-01-01

313

Bipartite and Multipartite Entanglement of Gaussian States  

E-print Network

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 to a given bipartition, we show how the multimode block entanglement can be completely and reversibly localized onto a single pair of modes by local, unitary operations. We then analyze the distribution of entanglement among multiple parties in multimode Gaussian states. We introduce the continuous-variable tangle to quantify entanglement sharing in Gaussian states and we prove that it satisfies the Coffman-Kundu-Wootters monogamy inequality. Nevertheless, we show that pure, symmetric three-mode Gaussian states, at variance with their discrete-variable counterparts, allow a promiscuous sharing of ...

Adesso, G; Adesso, Gerardo; Illuminati, Fabrizio

2005-01-01

314

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

315

Monogamy inequality for distributed Gaussian entanglement  

E-print Network

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.

Tohya Hiroshima; Gerardo Adesso; Fabrizio Illuminati

2006-05-02

316

Running Non-Gaussianities in DBI Inflation  

Microsoft Academic Search

We study the non-Gaussianity in the simplest infrared (IR) model of the DBI\\u000ainflation. We show that the non-Gaussianity in such a model is compatible with\\u000athe current observational bound, and is within the sensitivity of future\\u000aexperiments. We also discuss the scale dependence of the non-Gaussianity. In\\u000athe DBI inflation, such a feature can be used as a probe

Xingang Chen

2005-01-01

317

Non-Gaussianity After BICEP2.  

PubMed

We analyze primordial non-Gaussianity in single-field inflationary models when the tensor-to-scalar ratio is large. Our results show that detectable levels of non-Gaussianity f_{NL}?50 are still possible in the simplest class of models described by the effective theory of inflation. However, the shape is very tightly constrained, making a sharp prediction that could be confirmed or falsified by a future detection of non-Gaussianity. PMID:25192084

D'Amico, Guido; Kleban, Matthew

2014-08-22

318

Optical limiting using Laguerre-Gaussian beams  

E-print Network

We demonstrate optical limiting using the self-lensing effect of a higher-order Laguerre-Gaussian beam in a thin dye-doped polymer sample, which we find is consistent with our model using Gaussian decomposition. The limiting threshold is found to be smaller than for a fundamental gaussian beam when the nonlinear medium is placed either in front of or behind the beam focus.

Zhang, Weiya

2007-01-01

319

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

E-print Network

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 are derived by acting with differential operators on this fundamental solution. Even special beam modes as the recently introduced Bessel beams are easily described within that framework.

Pampaloni, F; Pampaloni, Francesco; Enderlein, Joerg

2004-01-01

320

Super-Gaussian conical refraction beam  

NASA Astrophysics Data System (ADS)

We demonstrate the transformation of Gaussian input beams into super-Gaussian beams with a quasi flat-top transverse profile by means of the conical refraction phenomenon by adjusting the ratio between the ring radius and the waist radius of the input beam to 0.445. We discuss the beam propagation of the super-Gaussian beam and show that it has a confocal parameter three times larger than the one that would be obtained from a Gaussian beam. The experiments performed with a KGd(WO4)2 biaxial crystal are in good agreement with the theoretical predictions.

Turpin, A.; Loiko, Yu. V.; Kalkandkiev, T. K.; Tomizawa, H.; Mompart, J.

2014-08-01

321

Gaussian measures of entanglement versus negativities and the ordering of two-mode Gaussian states  

E-print Network

In this work we focus on entanglement of two--mode Gaussian states of continuous variable systems. We introduce the formalism of Gaussian entanglement measures, adopting the framework developed in [M. M. Wolf {\\em et al.}, Phys. Rev. A {\\bf 69}, 052320 (2004)], where the Gaussian entanglement of formation was defined. We compute Gaussian measures explicitely for two important families of nonsymmetric two--mode Gaussian states, namely the states of extremal (maximal and minimal) negativities at fixed global and local purities, introduced in [G. Adesso {\\em et al.}, Phys. Rev. Lett. {\\bf 92}, 087901 (2004)]. This allows us to compare the {\\em orderings} induced on the set of entangled two--mode Gaussian states by the negativities and by the Gaussian entanglement measures. We find that in a certain range of global and local purities (characterizing the covariance matrix of the corresponding extremal states), states of minimum negativity can have more Gaussian entanglement than states of maximum negativity. Thus ...

Adesso, G; Adesso, Gerardo; Illuminati, Fabrizio

2005-01-01

322

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

323

A Comparison of Methods for Estimating Quadratic Effects in Nonlinear Structural Equation Models  

PubMed Central

Two Monte Carlo simulations were performed to compare methods for estimating and testing hypotheses of quadratic effects in latent variable regression models. The methods considered in the current study were (a) a 2-stage moderated regression approach using latent variable scores, (b) an unconstrained product indicator approach, (c) a latent moderated structural equation method, (d) a fully Bayesian approach, and (e) marginal maximum likelihood estimation. Of the 5 estimation methods, it was found that overall the methods based on maximum likelihood estimation and the Bayesian approach performed best in terms of bias, root-mean-square error, standard error ratios, power, and Type I error control, although key differences were observed. Similarities as well as disparities among methods are highlight and general recommendations articulated. As a point of comparison, all 5 approaches were fit to a reparameterized version of the latent quadratic model to educational reading data. PMID:22429193

Harring, Jeffrey R.; Weiss, Brandi A.; Hsu, Jui-Chen

2012-01-01

324

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

325

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

326

Quadratic 0-1 programming: Geometric methods and duality analysis  

NASA Astrophysics Data System (ADS)

The unconstraint quadratic binary problem (UBQP), as a classical combinatorial problem, finds wide applications in broad field and human activities including engineering, science, finance, etc. The NP-hardness of the combinatorial problems makes a great challenge to solve the ( UBQP). The main purpose of this research is to develop high performance solution method for solving (UBQP) via the geometric properties of the objective ellipse contour and the optimal solution. This research makes several contributions to advance the state-of-the-art of geometric approach of (UBQP). These contributions include both theoretical and numerical aspects as stated below. In part I of this dissertation, certain rich geometric properties hidden behind quadratic 0-1 programming are investigated. Especially, we derive new lower bounding methods and variable fixation techniques for quadratic 0-1 optimization problems by investigating geometric features of the ellipse contour of a (perturbed) convex quadratic function. These findings further lead to some new optimality conditions for quadratic 0-1 programming. Integrating these novel solution schemes into a proposed solution algorithm of a branch-and-bound type, we obtain promising preliminary computational results. In part II of this dissertation, we present new results of the duality gap between the binary quadratic optimization problem and its Lagrangian dual. We first derive a necessary and sufficient condition for the zero duality gap and discuss its relationship with the polynomial solvability of the problem. We then characterize the zeroness of duality gap by the distance, delta, between the binary set and certain affine space C. Finally, we discuss a computational procedure of the distance delta. These results provide new insights into the duality gap and polynomial solvability of binary quadratic optimization problems.

Liu, Chunli

327

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

328

On implementing a primal-dual interior-point method for conic quadratic optimization  

Microsoft Academic Search

Conic quadratic optimization is the problem of minimizing a linear function subject to the intersection of an ane set and the product of quadratic cones. The problem is a convex optimization problem and has numerous applications in engineering, economics, and other areas of science. Indeed, linear and convex quadratic optimization is a special case. Conic quadratic optimization problems can in

Erling D. Andersen; Cornelis Roos; Tamás Terlaky

2003-01-01

329

Matching optics for Gaussian beams  

NASA Technical Reports Server (NTRS)

A system of matching optics for Gaussian beams is described. The matching optics system is positioned between a light beam emitter (such as a laser) and the input optics of a second optics system whereby the output from the light beam emitter is converted into an optimum input for the succeeding parts of the second optical system. The matching optics arrangement includes the combination of a light beam emitter, such as a laser with a movable afocal lens pair (telescope) and a single movable lens placed in the laser's output beam. The single movable lens serves as an input to the telescope. If desired, a second lens, which may be fixed, is positioned in the beam before the adjustable lens to serve as an input processor to the movable lens. The system provides the ability to choose waist diameter and position independently and achieve the desired values with two simple adjustments not requiring iteration.

Gunter, William D. (inventor)

1991-01-01

330

Quadratic interior-point methods in statistical disclosure control  

E-print Network

cal relation (e.g., zip code and city). ... from some microfiles (e.g., a population census). ... To avoid the above lacks of rounding, we suggest a new perturbation .... when the size of the instances increases. ..... 155 (Springer, New York 2000).

2003-05-09

331

Optimal PHP production of multiple part-types on a failure-prone machine with quadratic buffer costs  

Microsoft Academic Search

We consider a single, failure-prone machine, producing multiple part-types The objective is to minimize the expected sum of quadratic buffer costs. In general, the optimal solution to this problem is unknown. However, by restricting the allowable set of control policies to the class of prioritized hedging point (PHP) policies, we are able to determine simple, analytical expressions for the optimal

Chang Shu; James R. Perkins

2001-01-01

332

Ballistic Phonon Transport Through Gaussian Acoustic Nanocavities  

Microsoft Academic Search

We investigate ballistic phonon transport through Gaussian acoustic nanocavities in a semiconductor nanowire at low temperatures. When the transverse widths of acoustic nanocavities takes a Gaussian function, it is found that wide band gap and resonant peaks appear in transmission spectra. The phonon-cavity confined modes exist as the number of the nanocavities is large. The phonon transmission and thermal conductance

Shu-Juan Li; Gui-Fang Huang; Yuan Chen; Wei-Qing Huang; Wangyu Hu; Ling-Ling Wang; Anlian Pan

2011-01-01

333

Distillability Criterion for all Bipartite Gaussian States  

E-print Network

We prove that all inseparable Gaussian states of two modes can be distilled into maximally entangled pure states by local operations. Using this result we show that a bipartite Gaussian state of arbitrarily many modes can be distilled if and only if its partial transpose is not positive.

G. Giedke; L. -M. Duan; J. I. Cirac; P. Zoller

2001-04-13

334

On Gaussian Beams Described by Jacobi's Equation  

E-print Network

Gaussian beams describe the amplitude and phase of rays and are widely used to model acoustic propagation. This paper describes four new results in the theory of Gaussian beams. (1) A new version of the \\v{C}erven\\'y equations for the amplitude and phase of Gaussian beams is developed by applying the equivalence of Hamilton-Jacobi theory with Jacobi's equation that connects Riemannian curvature to geodesic flow. Thus the paper makes a fundamental connection between Gaussian beams and an acoustic channel's so-called intrinsic Gaussian curvature from differential geometry. (2) A new formula $\\pi(c/c")^{1/2}$ for the distance between convergence zones is derived and applied to several well-known profiles. (3) A class of "model spaces" are introduced that connect the acoustics of ducting/divergence zones with the channel's Gaussian curvature $K=cc"-(c')^2$. The "model" SSPs yield constant Gaussian curvature in which the geometry of ducts corresponds to great circles on a sphere and convergence zones correspond to antipodes. The distance between caustics $\\pi(c/c")^{1/2}$ is equated with an ideal hyperbolic cosine SSP duct. (4) An "intrinsic" version of \\v{C}erven\\'y's formulae for the amplitude and phase of Gaussian beams is derived that does not depend on an "extrinsic" arbitrary choice of coordinates such as range and depth. Direct comparisons are made between the computational frameworks used by the three different approaches to Gaussian beams: Snell's law, the extrinsic Frenet-Serret formulae, and the intrinsic Jacobi methods presented here. The relationship of Gaussian beams to Riemannian curvature is explained with an overview of the modern covariant geometric methods that provide a general framework for application to other special cases.

Steven Thomas Smith

2013-04-06

335

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

336

Active Cancellation of Noise in a CAR Cabin Using the Zero Spillover Controller  

NASA Astrophysics Data System (ADS)

In active noise control problems, spillover will occur because of the Bode integral constraint if the performance sensors and measurement sensors are collocated, or if the control speakers and the noise sources are collocate. This paper is focused on the implementation of a multiple-channel zero-spillover ANC controller using a spatially feedforward structure for a car cabin. The plant model is realized by using a frequency-domain procedure. The linear-quadratic-Gaussian algorithm is used in controller design. Experiments are carried out to verify the proposed technique, where random noise and engine noise are chosen as the primary noise. The results indicate that the proposed controller yields a broadband attenuation for the random noise. The proposed method is also effective in attenuating the engine noise if an assumed model of the noise is incorporated into controller design.

Bai, Mingsian R.; Chen, Hsiuhong

2000-08-01

337

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

338

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

339

Quadratically consistent nodal integration for second order meshfree Galerkin methods  

NASA Astrophysics Data System (ADS)

Robust and efficient integration of the Galerkin weak form only at the approximation nodes for second order meshfree Galerkin methods is proposed. The starting point of the method is the Hu-Washizu variational principle. The orthogonality condition between stress and strain difference is satisfied by correcting nodal derivatives. The corrected nodal derivatives are essentially linear functions which can exactly reproduce linear strain fields. With the known area moments, the stiffness matrix resulting from these corrected nodal derivatives can be exactly evaluated using only the nodes as quadrature points. The proposed method can exactly pass the quadratic patch test and therefore is named as quadratically consistent nodal integration. In contrast, the stabilized conforming nodal integration (SCNI) which prevails in the nodal integrations for meshfree Galerkin methods fails to pass the quadratic patch test. Better accuracy, convergence, efficiency and stability than SCNI are demonstrated by several elastostatic and elastodynamic examples.

Duan, Qinglin; Wang, Bingbing; Gao, Xin; Li, Xikui

2014-08-01

340

On the use of the OCM's quadratic objective function as a pilot rating metric  

NASA Technical Reports Server (NTRS)

A correlation between the magnitude of the quadratic objective function from an optimal control pilot model and the subjective rating of the vehicle and task provides a valuable tool for handling qualities research and flight control synthesis. An analysis of simulation results for fourteen aircraft configurations flight tested earlier was conducted. A fixed set of pilot model parameters, are found for all cases in modeling the simulated regulation task. The agreement obtained between performance statistics is shown and a strong correlation was obtained between the cost function and rating.

Schmidt, D. K.

1981-01-01

341

Inverse modelling of atmospheric tracers: non-Gaussian methods and second-order sensitivity analysis  

NASA Astrophysics Data System (ADS)

For a start, recent techniques devoted to the reconstruction of sources of an atmospheric tracer at continental scale are introduced. A first method is based on the principle of maximum entropy on the mean and is briefly reviewed here. A second approach, which has not been applied in this field yet, is based on an exact Bayesian approach, through a maximum a posteriori estimator. The methods share common grounds, and both perform equally well in practice. When specific prior hypotheses on the sources are taken into account such as positivity, or boundedness, both methods lead to purposefully devised cost-functions. These cost-functions are not necessarily quadratic because the underlying assumptions are not Gaussian. As a consequence, several mathematical tools developed in data assimilation on the basis of quadratic cost-functions in order to establish a posteriori analysis, need to be extended to this non-Gaussian framework. Concomitantly, the second-order sensitivity analysis needs to be adapted, as well as the computations of the averaging kernels of the source and the errors obtained in the reconstruction. All of these developments are applied to a real case of tracer dispersion: the European Tracer Experiment [ETEX]. Comparisons are made between a least squares cost function (similar to the so-called 4D-Var) approach and a cost-function which is not based on Gaussian hypotheses. Besides, the information content of the observations which is used in the reconstruction is computed and studied on the application case. A connection with the degrees of freedom for signal is also established. As a by-product of these methodological developments, conclusions are drawn on the information content of the ETEX dataset as seen from the inverse modelling point of view.

Bocquet, M.

2008-02-01

342

On volumes of hyperbolic Coxeter polytopes and quadratic forms  

E-print Network

In this paper, we compute the covolume of the group of units of the quadratic form f_d^n(x) = x_1^2 + x_2^2 + . . . + x_n^2 - d x_{n+1}^2 with d an odd, positive, square-free integer. Mcleod has determined the hyperbolic Coxeter fundamental domain of the reflection subgroup of the group of units of the quadratic form f_3^n. We apply our covolume formula to compute the volumes of these hyperbolic Coxeter polytopes.

Ratcliffe, John G

2012-01-01

343

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

344

Laguerre Gaussian beam multiplexing through turbulence  

NASA Astrophysics Data System (ADS)

We analyze the effect of atmospheric turbulence on the propagation of multiplexed Laguerre Gaussian modes. We present a method to multiplex Laguerre Gaussian modes using digital holograms and decompose the resulting field after encountering a laboratory simulated atmospheric turbulence. The proposed technique makes use of a single spatial light modulator for the generation of superimposed beam and a second spatial light modulator and a CCD camera for the modal decomposition. The obtained results demonstrate how sensitive the Laguerre Gaussian beams are to atmospheric distortions.

Trichili, Abderrahmen; Mhlanga, Thandeka; Naidoo, Darryl; Dudley, Angela; Zghal, Mourad; Forbes, Andrew

2014-10-01

345

Gaussian coordinate systems for the Kerr metric  

E-print Network

We present the whole class of Gaussian coordinate systems for the Kerr metric. This is achieved through the uses of the relationship between Gaussian observers and the relativistic Hamilton-Jacobi equation. We analyze the completeness of this coordinate system. In the appendix we present the equivalent JEK formulation of General Relativity -- the so-called quasi-Maxwellian equations -- which acquires a simpler form in the Gaussian coordinate system. We show how this set of equations can be used to obtain the internal metric of the Schwazschild solution, as a simple example. We suggest that this path can be followed to the search of the internal Kerr metric.

M. Novello; E. Bittencourt

2010-04-22

346

Quark and Lepton Masses from Gaussian Landscapes  

SciTech Connect

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.

Hall, Lawrence J. [Department of Physics and Lawrence Berkeley National Laboratory, University of California, Berkeley, California 94720 (United States); Salem, Michael P. [California Institute of Technology, Pasadena, California 91125 (United States); Watari, Taizan [Department of Physics, University of Tokyo, Tokyo, 113-0033 (Japan)

2008-04-11

347

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

348

Energy management of a power-split plug-in hybrid electric vehicle based on genetic algorithm and quadratic programming  

NASA Astrophysics Data System (ADS)

This paper introduces an online and intelligent energy management controller to improve the fuel economy of a power-split plug-in hybrid electric vehicle (PHEV). Based on analytic analysis between fuel-rate and battery current at different driveline power and vehicle speed, quadratic equations are applied to simulate the relationship between battery current and vehicle fuel-rate. The power threshold at which engine is turned on is optimized by genetic algorithm (GA) based on vehicle fuel-rate, battery state of charge (SOC) and driveline power demand. The optimal battery current when the engine is on is calculated using quadratic programming (QP) method. The proposed algorithm can control the battery current effectively, which makes the engine work more efficiently and thus reduce the fuel-consumption. Moreover, the controller is still applicable when the battery is unhealthy. Numerical simulations validated the feasibility of the proposed controller.

Chen, Zheng; Mi, Chris Chunting; Xiong, Rui; Xu, Jun; You, Chenwen

2014-02-01

349

Quadratic algebra contractions and 2nd order superintegrable systems  

E-print Network

Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. For constant curvature spaces we show that the free quadratic algebras generated by the 1st and 2nd order elements in the enveloping algebras of their Euclidean and orthogonal symmetry algebras correspond one-to-one with the possible superintegrable systems with potential defined on these spaces. We describe a contraction theory for quadratic algebras and show that for constant curvature superintegrable systems, ordinary Lie algebra contractions induce contractions of the quadratic algebras of the superintegrable systems that correspond to geometrical pointwise limits of the physical systems. One consequence is that by contracting function space realizations of representations of the generic superintegrable quantum system on the 2-sphere (which give the structure equations for Racah/Wilson polynomials) to the other superintegrable systems one obtains the full Askey scheme of orthogonal hypergeometric polynomials.

Ernest G. Kalnins; Willard Miller Jr

2014-01-04

350

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

351

Finding the Best Quadratic Approximation of a Function  

ERIC Educational Resources Information Center

This article examines the question of finding the best quadratic function to approximate a given function on an interval. The prototypical function considered is f(x) = e[superscript x]. Two approaches are considered, one based on Taylor polynomial approximations at various points in the interval under consideration, the other based on the fact…

Yang, Yajun; Gordon, Sheldon P.

2011-01-01

352

Information-Theoretic Learning Using Renyi's Quadratic Entropy  

E-print Network

to offer to learning theory since it is a deep mathematical theory concerned with the very essenceInformation-Theoretic Learning Using Renyi's Quadratic Entropy Jose C. Principe, Dongxin Xu of Florida, Gainesville, FL 32611, USA ABSTRACT Learning from examples has been traditionally based

Slatton, Clint

353

Near-optimal placement using a quadratic objective function  

Microsoft Academic Search

Placement algorithms for IC layout which are optimal are known to be NP-complete 5. As a result, heuristics such as pairwise-interchange techniques must be employed to generate satisfactory placements. Unfortunately, with these algorithms, there is generally no way of knowing just how far away the result is from optimum. With the quadratic metric used in this study, however, a useful

John P. Blanks

1985-01-01

354

On Quadratic g-Evaluations/Expectations and Related Analysis  

E-print Network

On Quadratic g-Evaluations/Expectations and Related Analysis Jin Ma, Song Yao Abstract In this paper we extend the notion of g-evaluation, in particular g-expectation, of Peng [9, 10] to the case of the g-expectations, including a representation theorem between the generator and the corresponding g-expectation

Zhang, Jianfeng

355

Solving the quadratic assignment problem by means of general ...  

E-print Network

The Quadratic Assignment Problem (QAP) can be solved by linearization, where one ... locations j and l, and cij denotes the cost of locating facility i at location j. xij = 1 if facility ...... Journal of the Society for Industrial and Applied Mathematices, ...

2010-04-19

356

ON THE GEOMETRY OF BIFURCATION CURRENTS FOR QUADRATIC RATIONAL MAPS.  

E-print Network

ON THE GEOMETRY OF BIFURCATION CURRENTS FOR QUADRATIC RATIONAL MAPS. FRANÃ?OIS BERTELOOT AND THOMAS current. 1. Introduction. For any holomorphic family (f)M of degree d rational maps on P1, the bifurcation GAUTHIER Abstract. We describe the behaviour at infinity of the bifurcation current in the mod- uli space

Paris-Sud XI, Université de

357

A Greedy Genetic Algorithm for the Quadratic Assignment Problem  

Microsoft Academic Search

The Quadratic Assignment Problem (QAP) is one of the classical combinatorial optimizationproblems and is known for its diverse applications. In this paper, we suggest a genetic algorithm for theQAP and report its computational behavior. The genetic algorithm incorporates many greedyprinciples in its design and, hence, is called the greedy genetic algorithm. The ideas we incorporate inthe greedy genetic algorithm include

Ravindra K. Ahuja; James B. Orlin

1997-01-01

358

A greedy genetic algorithm for the quadratic assignment problem  

Microsoft Academic Search

The Quadratic Assignment Problem (QAP) is one of the classical combinatorial optimization problems and is known for its diverse applications. In this paper, we suggest a genetic algorithm for the QAP and report its computational behavior. The genetic algorithm incorporates many greedy principles in its design and, hence, we refer to it as a greedy genetic algorithm. The ideas we

Ravindra K. Ahuja; James B. Orlin; Ashish Tiwari

2000-01-01

359

Solving the Quadratic Capacitated Facilities Location Problem by Computer.  

ERIC Educational Resources Information Center

Several computer programs were developed to solve various versions of the quadratic capacitated facilities location problem. Matrices, which represent various business costs, are defined for the factors of sites, facilities, customers, commodities, and production units. The objective of the program is to find an optimization matrix for the lowest…

Cote, Leon C.; Smith, Wayland P.

360

Quadratic Approximation-Based Coordinate Change in Genetic Algorithms  

Microsoft Academic Search

This paper proposes a procedure for space coordinate change, inside genetic algorithms, based on convex quadratic approximations of the general nonlinear objective function. It is shown that in the transformed coordinates the genetic algorithm is able to And the problem optimum in less iterations and with greater proportion of successful attempts. The proposed procedure employs only the objective function samples

Elizabeth F. Wanner; Frederico G. Guimaraes; Ricardo H. C. Takahashi; Peter J. Fleming

2006-01-01

361

Analysis of Quadratic Diophantine Equations with Fibonacci Number Solutions  

ERIC Educational Resources Information Center

An analysis is made of the role of Fibonacci numbers in some quadratic Diophantine equations. A general solution is obtained for finding factors in sums of Fibonacci numbers. Interpretation of the results is facilitated by the use of a modular ring which also permits extension of the analysis.

Leyendekkers, J. V.; Shannon, A. G.

2004-01-01

362

Delay Robustness of Interconnected Passive Systems: An Integral Quadratic Constraint  

E-print Network

consider networks of passive systems with time delays in the interconnections, and present a stability1 Delay Robustness of Interconnected Passive Systems: An Integral Quadratic Constraint Approach that depend on the duration of delay. Since the effect of delay depends on its duration relative to the time

Arcak, Murat

363

Confidence set interference with a prior quadratic bound. [in geophysics  

NASA Technical Reports Server (NTRS)

Neyman's (1937) theory of confidence sets is developed as a replacement for Bayesian interference (BI) and stochastic inversion (SI) when the prior information is a hard quadratic bound. It is recommended that BI and SI be replaced by confidence set interference (CSI) only in certain circumstances. The geomagnetic problem is used to illustrate the general theory of CSI.

Backus, George E.

1989-01-01

364

Confidence set interference with a prior quadratic bound  

Microsoft Academic Search

Neyman's (1937) theory of confidence sets is developed as a replacement for Bayesian interference (BI) and stochastic inversion (SI) when the prior information is a hard quadratic bound. It is recommended that BI and SI be replaced by confidence set interference (CSI) only in certain circumstances. The geomagnetic problem is used to illustrate the general theory of CSI.

George E. Backus

1989-01-01

365

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

366

Word Alignment via Quadratic Assignment Simon Lacoste-Julien  

E-print Network

in various dic- tionaries, the similarity of the frequency of its two words, choices made by other alignmentWord Alignment via Quadratic Assignment Simon Lacoste-Julien UC Berkeley, Berkeley, CA 94720@cs.berkeley.edu Abstract Recently, discriminative word alignment methods have achieved state-of-the-art accuracies

Plotkin, Joshua B.

367

An Attempt to Remove Quadratic Divergences in the Standard Theory  

E-print Network

The quadratic divergences caused by Yukawa interactions in the standard theory of elementary particle physics is shown to be removed by introducing finite-mass complex-ghost regulator fields. In this modification of the standard theory, its manifest covariance, renormalizability, gauge invariance and unitarity are retained, and no new observable particles are introduced.

Noboru Nakanishi

2007-11-29

368

On Interpolation Errors over Quadratic Nodal Triangular Finite Elements  

E-print Network

On Interpolation Errors over Quadratic Nodal Triangular Finite Elements Shankar P. Sastry to interpolate a solution (within an element) of a partial differential equation obtained by the finite element the bounds on the error of the interpolated solution. For linear elements, the error bounds at a point have

Kirby, Mike

369

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

370

Propagation of Laguerre-Bessel-Gaussian beams.  

PubMed

New exact solutions to the paraxial wave equation are obtained in the form of a product of Laguerre polynomials, Bessel functions, and Gaussian functions. In the limit of large Laguerre-Gaussian beam size, the Bessel factor dominates and the solution sets reduce to the modes of closed resonators, hollow metal waveguides, and dielectric waveguides. In the opposite limit the solutions reduce to Laguerre-Gaussian modes of open resonators and graded-index waveguides. These solutions are valid for electromagnetic waves traveling through free space, and they are valid for propagation through circularly symmetric optical systems representable by ABCD matrices as well. An interesting feature of the new solution set is the existence of three mode indices, where only two are required for an orthogonal expansion. As an example, Laguerre-Gaussian beam propagation through an optical system that contains a Bessel-like amplitude filter is discussed. PMID:11059596

Tovar, A A

2000-11-01

371

Optimal unitary dilation for bosonic Gaussian channels  

SciTech Connect

A general quantum channel can be represented in terms of a unitary interaction between the information-carrying system and a noisy environment. In this paper the minimal number of quantum Gaussian environmental modes required to provide a unitary dilation of a multimode bosonic Gaussian channel is analyzed for both pure and mixed environments. We compute this quantity in the case of pure environment corresponding to the Stinespring representation and give an improved estimate in the case of mixed environment. The computations rely, on one hand, on the properties of the generalized Choi-Jamiolkowski state and, on the other hand, on an explicit construction of the minimal dilation for arbitrary bosonic Gaussian channel. These results introduce a new quantity reflecting ''noisiness'' of bosonic Gaussian channels and can be applied to address some issues concerning transmission of information in continuous variables systems.

Caruso, Filippo [Institut fuer Theoretische Physik, Universitaet Ulm, Albert-Einstein-Allee 11, D-89069 Ulm (Germany); Eisert, Jens [Dahlem Center for Complex Quantum Systems, Freie Universitaet Berlin, D-14195 Berlin (Germany); Giovannetti, Vittorio [NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, Piazza dei Cavalieri 7, I-56126 Pisa (Italy); Holevo, Alexander S. [Steklov Mathematical Institute, Gubkina 8, RU-119991 Moscow (Russian Federation)

2011-08-15

372

String Gas Cosmology and Non-Gaussianities  

E-print Network

Recently it has been shown that string gas cosmology, an alternative model of the very early universe which does not involve a period of cosmological inflation, can give rise to an almost scale invariant spectrum of metric perturbations. Here we calculate the non-Gaussianities of the spectrum of cosmological fluctuations in string gas cosmology, and find that these non-Gaussianities depend linearly on the wave number and that their amplitude depends sensitively on the string scale. If the string scale is at the TeV scale, string gas cosmology could lead to observable non-Gaussianities, if it is close to the Planck scale, then the non-Gaussianities on current cosmological scales are negligible.

Bin Chen; Yi Wang; Wei Xue; Robert Brandenberger

2007-12-14

373

Gaussian functions optimized for molecules  

NASA Astrophysics Data System (ADS)

We consider floating Gaussian basis sets in which all parameters (positions, exponents and contraction coefficients) are optimised together with geometrical parameters of molecules. Exact results for H2+ are analysed. Test calculations are presented for the alkane series with basis sets of double zeta quality. Results for uncontracted basis sets using Hartree-Fock and perturbation theory are shown to be transferable to propane. Geometrical parameters as well as the electric field at the nuclei are in most cases significantly improved. Results for contracted basis sets at the HF level show similar improvements and transferability properties. At the CI level, the advantages over the corresponding atomic basis sets with polarisation functions appear even more clearly when CPU times are compared. Cet article s'intéresse à des bases d'orbitales gaussiennes flottantes pour lesquelles tous les paramètres (positions, exposants, coefficients de contraction) sont optimisés simultanément avec les paramètres géométriques de molécules. Des résultats exacts pour H2+ sont analysés. Des calculs tests sont présentés pour la série des alcanes avec une base de qualité double zêta. Les résultats au niveau HF et MP2 pour les bases non contractées s'avèrent transférables au propane. Les paramètres géométriques ainsi que le champs électrique aux noyaux sont améliorés de façon significative dans la plupart des cas. Les résultats aux niveaux HF pour les bases contractées montrent des améliorations et des propriétés de transférabilité similaires. Au niveau IC l'intérêt de ces bases par rapport aux bases atomiques correspondantes augmentées de fonctions de polarisation apparaît encore plus clairement lorsque les temps CPU sont comparés.

Cassam-Chenaï, P.; Jayatilaka, D.; Chandler, G. S.

1998-11-01

374

Speaker Verification Using Adapted Gaussian Mixture Models  

Microsoft Academic Search

Reynolds, Douglas A., Quatieri, Thomas F., and Dunn, Robert B., Speaker Verification Using Adapted Gaussian Mixture Models, Digital Signal Processing10(2000), 19–41.In this paper we describe the major elements of MIT Lincoln Laboratory's Gaussian mixture model (GMM)-based speaker verification system used successfully in several NIST Speaker Recognition Evaluations (SREs). The system is built around the likelihood ratio test for verification, using

Douglas A. Reynolds; Thomas F. Quatieri; Robert B. Dunn

2000-01-01

375

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

376

Propagation of Hermite-Gaussian and Laguerre-Gaussian beams beyond the paraxial approximation  

Microsoft Academic Search

On the basis of the vectorial Rayleigh-Sommerfeld formulas and by means of the relation between Hermite and Laguerre polynomials, the analytical expressions for the propagation of the Hermite-Gaussian (HG) and Laguerre-Gaussian (LG) beams beyond the paraxial approximation are derived, with the corresponding far-field propagation expressions and that for the Gaussian beams being given as special cases of the results. Some

Kailiang Duan; Beizhan Wang; Baida Lü

2005-01-01

377

Unified operator approach for deriving Hermite-Gaussian and Laguerre-Gaussian laser modes  

Microsoft Academic Search

A unified operator approach is described for deriving Hermite-Gaussian and Laguerre-Gaussian laser beams by using as a starting point a plane-wave-spectrum representation of the electromagnetic field. We show that by using the plane-wave representation of the fundamental Gaussian mode as a seed function, all higher-order beam modes can be derived by acting with differential operators on this fundamental solution. The

Jörg Enderlein; Francesco Pampaloni

2004-01-01

378

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

379

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

380

Engineering extremal two-qubit entangled states with maximally entangled Gaussian light  

E-print Network

We study state engineering induced by bilinear interactions between two remote qubits and light fields prepared in two-mode Gaussian states. The attainable two-qubit states span the entire physically allowed region in the entanglement-vs-global-purity plane. We show that two-mode Gaussian states with maximal entanglement at fixed global and marginal entropies produce maximally entangled two-qubit states in the corresponding entropic diagram. The target two-qubit entanglement is determined quantitatively only by the purities of the two-mode Gaussian resource. Thus, a small set of parameters characterizing extremally entangled two-mode Gaussian states is sufficient to control completely the engineering of extremally entangled two-qubit states, which can be realized in realistic scenarios of cavity and circuit quantum electrodynamics.

Adesso, G; Illuminati, F; Paternostro, M

2010-01-01

381

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

382

FIBER OPTIC POINT QUADRAT SYSTEM FOR IMPROVED ACCURACY IN VEGETATION SAMPLING  

EPA Science Inventory

An automated, fiber optic point quadrat system for vegetation sampling is described. Because the effective point diameter of the system never exceeds 25um it minimizes the substantial errors which can arise with conventional point quadrats. Automatic contact detection eliminates ...

383

GONII: UNIVERSAL QUATERNARY QUADRATIC FORMS PETE L. CLARK, JACOB HICKS, KATHERINE THOMPSON, AND NATHAN WALTERS  

E-print Network

, AND NATHAN WALTERS Contents 1. Introduction 1 2. Review of Quadratic Forms 2 2.1. Quadratic forms over a ring;2 PETE L. CLARK, JACOB HICKS, KATHERINE THOMPSON, AND NATHAN WALTERS and include a link to the C++ code

Smith, Roy

384

On the time-weighted quadratic sum of linear discrete systems  

NASA Technical Reports Server (NTRS)

A method is proposed for obtaining the time-weighted quadratic sum for linear discrete systems. The formula of the weighted quadratic sum is obtained from matrix z-transform formulation. In addition, it is shown that this quadratic sum can be derived in a recursive form for several useful weighted functions. The discussion presented parallels that of MacFarlane (1963) for weighted quadratic integral for linear continuous systems.

Jury, E. I.; Gutman, S.

1975-01-01

385

Z-scan analysis for near-Gaussian beams through Hermite-Gaussian decomposition  

Microsoft Academic Search

Gaussian decomposition is used as a theoretical infrastructure with which Z-scan experiments are analyzed. This procedure is extended here to the interesting, from a practical point of view, case in which the laser beam used is not perfectly Gaussian. We follow a perturbative approach to obtain the far-field pattern of the beam after the beam passes through a nonlinear sample.

G. Tsigaridas; M. Fakis; I. Polyzos; M. Tsibouri; P. Persephonis; V. Giannetas

2003-01-01

386

SPATIAL PREDICTION OF NONLINEAR RANDOM OCEAN WAVES: IDENTIFICATION OF GAUSSIAN AND NON-GAUSSIAN CONTRIBUTIONS  

E-print Network

SPATIAL PREDICTION OF NONLINEAR RANDOM OCEAN WAVES: IDENTIFICATION OF GAUSSIAN AND NON-Gaussian (second-order random) ocean waves are re- viewed here. A new method is introduced to address the "inverse in cases where wave histories must be ex- trapolated spatially--e.g., for spatially distributed ocean

Sweetman, Bert

387

Using Absolute Non-Gaussian Non-White Observations in Gaussian SLAM  

Microsoft Academic Search

In the navigation context it is typical the presence of sensors that introduce uncertainties that cannot be modeled as white Gaussian noise. Such measures cannot be directly used in gaussian estimators. This paper presents a technique that allows the consistent processing of this type of measurements in combination with a standard EKF estimator. The method can be applied in an

José E. Guivant; Favio R. Masson

2005-01-01

388

Gauss Sums and Quadratic Reciprocity c W W L Chen, 1981, 2013.  

E-print Network

, where q = 1, if q 1 mod 4, i, if q -1 mod 4. To deduce the Law of quadratic reciprocity, note the proof of the Law of quadratic reciprocity, it remains to establish Theorem 7.3, which we do in Section 7CHAPTER 7 Gauss Sums and Quadratic Reciprocity c W W L Chen, 1981, 2013. This chapter originates

Chen, William

389

On Approximate Robust Counterparts of Uncertain Semidefinite and Conic Quadratic Programs  

E-print Network

On Approximate Robust Counterparts of Uncertain Semidefinite and Conic Quadratic Programs Aharon conditions for the validity of specific NP-hard semi-infinite systems of semidefinite and conic quadratic as robust counterparts of uncertain conic quadratic and semidefinite problems. We start with specifying

Nemirovski, Arkadi

390

A Lifted Linear Programming Branch-and-Bound Algorithm for Mixed Integer Conic Quadratic Programs  

E-print Network

A Lifted Linear Programming Branch-and-Bound Algorithm for Mixed Integer Conic Quadratic Programs develops a linear programming based branch-and-bound algorithm for mixed in- teger conic quadratic programs. The algorithm is based on a higher dimensional or lifted polyhedral relaxation of conic quadratic constraints

Ahmed, Shabbir

391

An Attribute Weight Setting Method for k-NN Based Binary Classification using Quadratic Programming  

E-print Network

An Attribute Weight Setting Method for k-NN Based Binary Classification using Quadratic Programming. In this paper, we propose a new attribute weight setting method for k-NN based classifiers using quadratic the attribute weight setting problem as a quadratic programming problem and exploits commercial software

Coenen, Frans

392

Genetic\\/quadratic search algorithm for plant economic optimizations using a process simulator  

Microsoft Academic Search

The genetic\\/quadratic search algorithm (GQSA) is a hybrid genetic algorithms (GA) for optimizing plant economics when a process simulator models the plant. By coupling a regular GA with an algorithm based upon a quadratic search, the required number of objective function evaluations for obtaining an acceptable solution decreases significantly in most cases. The GQSA combines advantages of GA and quadratic

Won-hyouk Jang; Juergen Hahn; Kenneth R. Hall

2005-01-01

393

QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES  

PubMed Central

We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called ‘serendipity’ elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed.

RAND, ALEXANDER; GILLETTE, ANDREW; BAJAJ, CHANDRAJIT

2013-01-01

394

The averaged characteristic polynomial for the Gaussian and chiral Gaussian ensembles with a source  

NASA Astrophysics Data System (ADS)

In classical random matrix theory the Gaussian and chiral Gaussian random matrix models with a source are realized as shifted mean Gaussian, and chiral Gaussian, random matrices with real (? = 1), complex (? = 2) and real quaternion (? = 4) elements. We use the Dyson Brownian motion model to give a meaning for general ? > 0. In the Gaussian case a further construction valid for ? > 0 is given, as the eigenvalue PDF of a recursively defined random matrix ensemble. In the case of real or complex elements, a combinatorial argument is used to compute the averaged characteristic polynomial. The resulting functional forms are shown to be special cases of duality formulas due to Desrosiers. New derivations of the general case of Desrosiers' dualities are given. A soft edge scaling limit of the averaged characteristic polynomial is identified, and an explicit evaluation in terms of so-called incomplete Airy functions is obtained.

Forrester, Peter J.

2013-08-01

395

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

396

Graphical calculus for Gaussian pure states  

E-print Network

We provide a unified graphical calculus for all Gaussian pure states, including graph transformation rules for all local and semi-local 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 new 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.

Nicolas C. Menicucci; Steven T. Flammia; Peter van Loock

2010-07-05

397

Temperature modes for nonlinear Gaussian beams.  

PubMed

In assessing the influence of nonlinear acoustic propagation on thermal bioeffects, approximate methods for quickly estimating the temperature rise as operational parameters are varied can be very useful. This paper provides a formula for the transient temperature rise associated with nonlinear propagation of Gaussian beams. The pressure amplitudes for the Gaussian modes can be obtained rapidly using a method previously published for simulating nonlinear propagation of Gaussian beams. The temperature-mode series shows that the nth temperature mode generated by nonlinear propagation, when normalized by the fundamental, is weaker than the nth heat-rate mode (also normalized by the fundamental in the heat-rate series) by a factor of log(n)/n, where n is the mode number. Predictions of temperature rise and thermal dose were found to be in close agreement with full, finite-difference calculations of the pressure fields, temperature rise, and thermal dose. Applications to non-Gaussian beams were made by fitting the main lobe of the significant modes to Gaussian functions. PMID:19603899

Myers, Matthew R; Soneson, Joshua E

2009-07-01

398

Hydraulic Conductivity Fields: Gaussian or Not?  

PubMed Central

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. PMID:24415806

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

2013-01-01

399

Iterative Gaussianization: from ICA to random rotations.  

PubMed

Most signal processing problems involve the challenging task of multidimensional probability density function (PDF) estimation. In this paper, we propose a solution to this problem by using a family of rotation-based iterative Gaussianization (RBIG) transforms. The general framework consists of the sequential application of a univariate marginal Gaussianization transform followed by an orthonormal transform. The proposed procedure looks for differentiable transforms to a known PDF so that the unknown PDF can be estimated at any point of the original domain. In particular, we aim at a zero-mean unit-covariance Gaussian for convenience. RBIG is formally similar to classical iterative projection pursuit algorithms. However, we show that, unlike in PP methods, the particular class of rotations used has no special qualitative relevance in this context, since looking for interestingness is not a critical issue for PDF estimation. The key difference is that our approach focuses on the univariate part (marginal Gaussianization) of the problem rather than on the multivariate part (rotation). This difference implies that one may select the most convenient rotation suited to each practical application. The differentiability, invertibility, and convergence of RBIG are theoretically and experimentally analyzed. Relation to other methods, such as radial Gaussianization, one-class support vector domain description, and deep neural networks is also pointed out. The practical performance of RBIG is successfully illustrated in a number of multidimensional problems such as image synthesis, classification, denoising, and multi-information estimation. PMID:21349790

Laparra, Valero; Camps-Valls, Gustavo; Malo, Jesús

2011-04-01

400

Symmetry-breaking instability of quadratic soliton bound states  

SciTech Connect

We study both numerically and experimentally two-dimensional soliton bound states in quadratic media and demonstrate their symmetry-breaking instability. The experiment is performed in a potassium titanyl phosphate crystal in a type-II configuration. The bound state is generated by the copropagation of the antisymmetric fundamental beam locked in phase with the symmetrical second harmonic one. Experimental results are in good agreement with numerical simulations of the nonlinear wave equations.

Delque, Michaeel [Service OPERA-photonique, CP194/5, Universite Libre de Bruxelles U.L.B. Avenue F.D. Roosevelt, B-1050 Bruxelles (Belgium); Departement d'Optique P.M. Duffieux, Institut FEMTO-ST, Universite de Franche-Comte, CNRS UMR 6174, F-25030 Besancon (France); Fanjoux, Gil; Maillotte, Herve; Kockaert, Pascal; Sylvestre, Thibaut; Haelterman, Marc [Departement d'Optique P.M. Duffieux, Institut FEMTO-ST, Universite de Franche-Comte, CNRS UMR 6174, F-25030 Besancon (France)

2011-01-15

401

Quadratic Reciprocity and the Group Orders of Particle States  

Microsoft Academic Search

The construction of inverse states in a finite field F{sub P{sub Pα}} enables the organization of the mass scale by associating particle states with residue class designations. With the assumption of perfect flatness (Ωtotal = 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

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

2001-01-01

402

High-order approximation of conic sections by quadratic splines  

Microsoft Academic Search

Given a segment of a conic section in the form of a rational Bezier curve, a quadratic spline approximation is constructed and an explicit error bound is derived. The convergence order of the error bound is shown to be O(h4) which is optimal, and the spline curve is both C1 and G2. The approximation method is very efficient as it

Michael Floater

1995-01-01

403

Quadratic thermal terms in the deconfined phase from holography  

E-print Network

Recent lattice simulation has uncovered many interesting properties of SU(N) gauge theory at finite temperature. Especially, above the deconfinement phase transition all the thermodynamics quantities acquire significant quadratic contributions in inverse temperature. Such a term is also found to dominate the logarithmic of the renormalized Polyakov loop. Using the Hawking-Page transition in Anti-de Sitter space as an example, we show how such contributions can be naturally generated in the holographic approach.

Zuo, Fen

2014-01-01

404

Quadratic thermal terms in the deconfined phase from holography  

E-print Network

Recent lattice simulation has uncovered many interesting properties of SU(N) gauge theory at finite temperature. Especially, above the deconfinement phase transition all the thermodynamics quantities acquire significant quadratic contributions in inverse temperature. Such a term is also found to dominate the logarithmic of the renormalized Polyakov loop. Using the Hawking-Page transition in Anti-de Sitter space as an example, we show how such contributions can be naturally generated in the holographic approach.

Fen Zuo; Yi-Hong Gao

2014-03-10

405

Quadratic Volume-Preserving Maps: Invariant Circles and Bifurcations  

E-print Network

We study the dynamics of the five-parameter quadratic family of volume-preserving diffeomorphisms of R^3. This family is the unfolded normal form for a bifurcation of a fixed point with a triple-one multiplier and also is the general form of a quadratic three-dimensional map with a quadratic inverse. Much of the nontrivial dynamics of this map occurs when its two fixed points are saddle-foci with intersecting two-dimensional stable and unstable manifolds that bound a spherical ``vortex-bubble''. We show that this occurs near a saddle-center-Neimark-Sacker (SCNS) bifurcation that also creates, at least in its normal form, an elliptic invariant circle. We develop a simple algorithm to accurately compute these elliptic invariant circles and their longitudinal and transverse rotation numbers and use it to study their bifurcations, classifying them by the resonances between the rotation numbers. In particular, rational values of the longitudinal rotation number are shown to give rise to a string of pearls that creates multiple copies of the original spherical structure for an iterate of the map.

Holger R. Dullin; James D. Meiss

2008-07-04

406

Revisiting the naturalness problem: Who is afraid of quadratic divergences?  

NASA Astrophysics Data System (ADS)

It is widely believed that quadratic divergences severely restrict natural constructions of particle physics models beyond the standard model (SM). Supersymmetry provides a beautiful solution, but the recent LHC experiments have excluded large parameter regions of supersymmetric extensions of the SM. It will now be important to reconsider whether we have been misinterpreting the quadratic divergences in field theories. In this paper, we revisit the problem from the viewpoint of the Wilsonian renormalization group and argue that quadratic divergences—which can always be absorbed into a position of the critical surface—should be simply subtracted in model constructions. Such a picture gives another justification to the argument [W. A. Bardeen, Report No. FERMILAB-CONF-95-391-T] that the scale invariance of the SM, except for the soft-breaking terms, is an alternative solution to the naturalness problem. It also largely broadens possibilities of model constructions beyond the SM since we just need to take care of logarithmic divergences, which cause mixings of various physical scales and runnings of couplings.

Aoki, Hajime; Iso, Satoshi

2012-07-01

407

Quantum entropic characterization of Gaussian optical transformations using the replica method  

E-print Network

In spite of their very simple description in terms of rotations or symplectic transformations in phase space, quadratic Hamiltonians such as those modelling the most common Gaussian operations in quantum optics remain poorly understood in terms of entropies. For instance, determining the von Neumann entropy produced by an optical beam splitter or a two-mode squeezer is notably a hard problem, with generally no known analytical solution. Here, we overcome this difficulty by using the replica method, a tool borrowed from statistical physics and quantum field theory. We find a first application of this method to the field of quantum optics, where it enables accessing the entropic characteristics of the Bogoliubov transformation effected by a two-mode squeezer or optical amplifier. In particular, we determine the entropy produced by amplifying a binary superposition of the vacuum and an arbitrary Fock state, which yields a surprisingly simple analytical expression.

C. N. Gagatsos; A. I. Karanikas; G. Kordas; N. J. Cerf

2014-08-21

408

Gaussian states and geometrically uniform symmetry  

NASA Astrophysics Data System (ADS)

Quantum Gaussian states can be considered as the majority of the practical quantum states used in quantum communications and more generally in quantum information. Here we consider their properties in relation to the geometrically uniform symmetry, a property of quantum states that greatly simplifies the derivation of the optimal decision by means of the square root measurements. In a general framework of the N-mode Gaussian states we show the general properties of this symmetry and the application of the optimal quantum measurements. An application example is presented to quantum communication systems employing pulse position modulation. We prove that the geometrically uniform symmetry can be applied to the general class of multimode Gaussian states.

Cariolaro, Gianfranco; Corvaja, Roberto; Pierobon, Gianfranco

2014-10-01

409

Black holes as bosonic Gaussian channels  

E-print Network

We identify the quantum channels corresponding to the interaction of a Gaussian quantum state with an already formed Schwarzschild black hole. Using recent advances in the classification of one-mode bosonic Gaussian channels we find that (with one exception) the black hole Gaussian channels lie in the non-entanglement breaking subset of the lossy channels C(loss), amplifying channels C(amp) and classical-noise channels B_2. We show that the channel parameters depend on the black hole mass and the properties of the potential barrier surrounding it. This classification enables us to calculate the classical and quantum capacity of the black hole and to estimate the quantum capacity where no tractable quantum capacity expression exists today. We discuss these findings in the light of the black hole quantum information loss problem.

Kamil Bradler; Christoph Adami

2014-05-05

410

Non-Gaussianity from Lifshitz Scalar  

E-print Network

A Lifshitz scalar with the dynamical critical exponent z = 3 obtains scale-invariant, super-horizon field fluctuations without the need of an inflationary era. Since this mechanism is due to the special scaling of the Lifshitz scalar and persists in the presence of unsuppressed self-couplings, the resulting fluctuation spectrum can deviate from a Gaussian distribution. We study the non-Gaussian nature of the Lifshitz scalar's intrinsic field fluctuations, and show that primordial curvature perturbations sourced from such field fluctuations can have large non-Gaussianity of order f_NL = O(100), which will be detected by upcoming CMB observations. We compute the bispectrum and trispectrum of the fluctuations, and discuss their configurations in momentum space. In particular, the bispectrum is found to take various shapes, including the local, equilateral, and orthogonal shapes. Intriguingly, all integrals in the in-in formalism can be performed analytically.

Keisuke Izumi; Takeshi Kobayashi; Shinji Mukohyama

2010-08-08

411

Gaussian states and geometrically uniform symmetry  

E-print Network

Quantum Gaussian states can be considered as the majority of the practical quantum states used in quantum communications and more generally in quantum information. Here we consider their properties in relation with the geometrically uniform symmetry, a property of quantum states that greatly simplifies the derivation of the optimal decision by means of the square root measurements. In a general framework of the $N$-mode Gaussian states we show the general properties of this symmetry and the application of the optimal quantum measurements. An application example is presented, to quantum communication systems employing pulse position modulation. We prove that the geometrically uniform symmetry can be applied to the general class of multimode Gaussian states.

Gianfranco Cariolaro; Roberto Corvaja; Gianfranco Pierobon

2014-10-20

412

N-body simulations with generic non-Gaussian initial conditions II: halo bias  

NASA Astrophysics Data System (ADS)

We present N-body simulations for generic non-Gaussian initial conditions with the aim of exploring and modelling the scale-dependent halo bias. This effect is evident on very large scales requiring large simulation boxes. In addition, the previously available prescription to implement generic non-Gaussian initial conditions has been improved to keep under control higher-order terms which were spoiling the power spectrum on large scales. We pay particular attention to the differences between physical, inflation-motivated primordial bispectra and their factorizable templates, and to the operational definition of the non-Gaussian halo bias (which has both a scale-dependent and an approximately scale-independent contributions). We find that analytic predictions for both the non-Gaussian halo mass function and halo bias work well once a fudge factor (which was introduced before but still lacks convincing physical explanation) is calibrated on simulations. The halo bias remains therefore an extremely promising tool to probe primordial non-Gaussianity and thus to give insights into the physical mechanism that generated the primordial perturbations. The simulation outputs and tables of the analytic predictions will be made publicly available via the non-Gaussian comparison project web site http://icc.ub.edu/~liciaverde/NGSCP.html.

Wagner, Christian; Verde, Licia

2012-03-01

413

Primordial non-Gaussianity and Dark Energy constraints from Cluster Surveys  

SciTech Connect

Galaxy cluster surveys will be a powerful probe of dark energy. At the same time, cluster abundances is sensitive to any non-Gaussianity of the primordial density field. It is therefore possible that non-Gaussian initial conditions might be misinterpreted as a sign of dark energy or at least degrade the expected constraints on dark energy parameters. To address this issue, we perform a likelihood analysis of an ideal cluster survey similar in size and depth to the upcoming South Pole Telescope/Dark Energy Survey (SPT-DES).We analyze a model in which the strength of the non-Gaussianity is parameterized by the constant f{sub NL}; this model has been used extensively to derive Cosmic Microwave Background (CMB) anisotropy constraints on non-Gaussianity, allowing us to make contact with those works. We find that the constraining power of the cluster survey on dark energy observables is not significantly diminished by non-Gaussianity provided that cluster redshift information is included in the analysis. We also find that even an ideal cluster survey is unlikely to improve significantly current and future CMB constraints on non-Gaussianity. However, when all systematics are under control, it could constitute a valuable cross check to CMB observations.

Sefusatti, Emiliano; Vale, Chris; /Fermilab; Kadota, Kenji; /Fermilab /Minnesota U., Theor. Phys. Inst.; Frieman, Joshua; /Fermilab /KICP, Chicago /Chicago U., Astron.

2006-09-01

414

Fresnel filtering of Gaussian beams in microcavities.  

PubMed

We study the output from the modes described by the superposition of Gaussian beams confined in the quasi-stadium microcavities. We experimentally observe the deviation from Snell's law in the output when the incident angle of the Gaussian beam at the cavity interface is near the critical angle for total internal reflection, providing direct experimental evidence on the Fresnel filtering. The theory of the Fresnel filtering for a planar interface qualitatively reproduces experimental data, and a discussion is given on small deviation between the measured data and the theory. PMID:21403763

Shinohara, Susumu; Harayama, Takahisa; Fukushima, Takehiro

2011-03-15

415

Achievable rates for the Gaussian quantum channel  

E-print Network

We study the properties of quantum stabilizer codes that embed a finite-dimensional protected code space in an infinite-dimensional Hilbert space. The stabilizer group of such a code is associated with a symplectically integral lattice in the phase space of 2N canonical variables. From the existence of symplectically integral lattices with suitable properties, we infer a lower bound on the quantum capacity of the Gaussian quantum channel that matches the one-shot coherent information optimized over Gaussian input states.

Jim Harrington; John Preskill

2001-05-13

416

Entropic characterization of separability in Gaussian states  

SciTech Connect

We explore separability of bipartite divisions of mixed Gaussian states based on the positivity of the Abe-Rajagopal (AR) q-conditional entropy. The AR q-conditional entropic characterization provide more stringent restrictions on separability (in the limit q{yields}{infinity}) than that obtained from the corresponding von Neumann conditional entropy (q=1 case)--similar to the situation in finite dimensional states. Effectiveness of this approach, in relation to the results obtained by partial transpose criterion, is explicitly analyzed in three illustrative examples of two-mode Gaussian states of physical significance.

Sudha [Department of Physics, Kuvempu University, Shankaraghatta, Shimoga 577-451 (India); Devi, A. R. Usha [Department of Physics, Bangalore University, Bangalore 560-056 (India); Inspire Institute Inc., McLean, Virginia 22101 (United States); Rajagopal, A. K. [Inspire Institute Inc., McLean, Virginia 22101 (United States)

2010-02-15

417

Entropic characterization of Separability in Gaussian states  

E-print Network

We explore separability of bipartite divisions of mixed Gaussian states based on the positivity of the Abe-Rajagopal (AR) q-conditional entropy. The AR q-conditional entropic characterization provide more stringent restrictions on separability (in the limit q tending to infinity) than that obtained from the corresponding von Neumann conditional entropy (q = 1 case)--similar to the situation in finite dimensional states. Effectiveness of this approach, in relation to the results obtained by partial transpose criterion, is explicitly analyzed in three illustrative examples of two-mode Gaussian states of physical significance.

Sudha Shenoy; A. R. Usha Devi; A. K. Rajagopal

2009-09-06

418

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

419

Novel coordinate system for Gaussian beam reflection.  

PubMed

A novel coordinate system for Gaussian beam reflection has been proposed in this Letter. Reflection from a spherical mirror is used to describe the novel coordinate system. One single segment of a general resonator is chosen to describe coordinate rotation in detail. Nonplanar ring resonators are chosen to show the application of the novel coordinate system. This novel coordinate system has been proved by two simple experiments and the problem existing in using the traditional coordinate system has been pointed out. This novel coordinate system is valuable for not only the designing of laser resonators but also Gaussian beam propagation analysis. PMID:22660128

Yuan, Jie; Chen, Meixiong; Kang, Zhenglong; Long, Xingwu

2012-06-01

420

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

421

Electromagnetically induced transparency with Laguerre-Gaussian modes in ultracold rubidium  

E-print Network

We demonstrate electromagnetically induced transparency with the control laser in a Laguerre-Gaussian mode. The transmission spectrum is studied in an ultracold gas for the D2 line in both $^{85}$Rb and $^{87}$Rb, where the decoherence due to diffusion of the atomic medium is negligible. We compare these results to a similar configuration, but with the control laser in the fundamental laser mode. We model the transmission of a probe laser under both configurations, and we find good agreement with the experiment. We conclude that the use of Laguerre-Gaussian modes in electromagnetically induced transparency results in narrower resonance linewidths as compared to uniform control laser intensity. The narrowing of the linewidth is caused by the spatial distribution of the Laguerre-Gaussian intensity profile.

Akin, T G; Marino, A M; Abraham, E R I

2014-01-01

422

Spacecraft Formation Flying Maneuvers Using Linear Quadratic Regulation With No Radial Axis Inputs  

NASA Technical Reports Server (NTRS)

Regarding multiple spacecraft formation flying, the observation has been made that control thrust need only be applied coplanar to the local horizon to achieve complete controllability of a two-satellite (leader-follower) formation. A formulation of orbital dynamics using the state of one satellite relative to another is used. Without the need for thrust along the radial (zenith-nadir) axis of the relative reference frame, propulsion system simplifications and weight reduction may be accomplished. This work focuses on the validation of this control system on its own merits, and in comparison to a related system which does provide thrust along the radial axis of the relative frame. Maneuver simulations are performed using commercial ODE solvers to propagate the Keplerian dynamics of a controlled satellite relative to an uncontrolled leader. These short maneuver simulations demonstrate the capacity of the controller to perform changes from one formation geometry to another. Control algorithm performance is evaluated based on measures such as the fuel required to complete a maneuver and the maximum acceleration required by the controller. Based on this evaluation, the exclusion of the radial axis of control still allows enough control authority to use Linear Quadratic Regulator (LQR) techniques to design a gain matrix of adequate performance over finite maneuvers. Additional simulations are conducted including perturbations and using no radial control inputs. A major conclusion presented is that control inputs along the three axes have significantly different relationships to the governing orbital dynamics that may be exploited using LQR.

Starin, Scott R.; Yedavalli, R. K.; Sparks, Andrew G.; Bauer, Frank H. (Technical Monitor)

2001-01-01

423

Secondary diffraction of diffracted Gaussian beam of laser radiation  

NASA Astrophysics Data System (ADS)

The diffraction of a narrow Gaussian beam of laser radiation on mutually perpendicular edges of crossed, superimposed sharp wedge-shaped blades (safety razors) has been studied. The diffraction pattern observed on a flat screen behind the blades comprises a very bright central spot, which exhibits the structure of a "light network" with rectangular cells, and four groups of narrow bright bands that expand from the central spot toward the periphery and form a rectangular cross. The spatial frequency of light-field modulation on the screen can be controlled by varying the distance from the blades to screen.

Vasil'Ev, Yu. V.; Kozar', A. V.; Matyunin, A. V.

2011-10-01

424

Large-scale bias and efficient generation of initial conditions for nonlocal primordial non-Gaussianity  

NASA Astrophysics Data System (ADS)

We study the scale dependence of halo bias in generic (nonlocal) primordial non-Gaussian (PNG) initial conditions of the type motivated by inflation, parametrized by an arbitrary quadratic kernel. We first show how to generate nonlocal PNG initial conditions with minimal overhead compared to local PNG models for a general class of primordial bispectra that can be written as linear combinations of separable templates. We run cosmological simulations for the local, and nonlocal equilateral and orthogonal models and present results on the scale dependence of halo bias. We also derive a general formula for the Fourier-space bias using the peak-background split in the context of the excursion-set approach to halos and discuss the difference and similarities with the known corresponding result from local bias models. Our peak-background split bias formula generalizes previous results in the literature to include non-Markovian effects and nonuniversality of the mass function and are in better agreement with measurements in numerical simulations than previous results for a variety of halo masses, redshifts and halo definitions. We also derive for the first time quadratic bias results for arbitrary nonlocal PNG, and show that nonlinear bias loops give small corrections at large scales. The resulting well-behaved perturbation theory paves the way to constrain nonlocal PNG from measurements of the power spectrum and bispectrum in galaxy redshift surveys.

Scoccimarro, Román; Hui, Lam; Manera, Marc; Chan, Kwan Chuen

2012-04-01

425

First on-sky SCAO validation of full LQG control with vibration mitigation on the CANARY pathfinder.  

PubMed

Adaptive optics provides real time correction of wavefront disturbances on ground based telescopes. Optimizing control and performance is a key issue for ever more demanding instruments on ever larger telescopes affected not only by atmospheric turbulence, but also by vibrations, windshake and tracking errors. Linear Quadratic Gaussian control achieves optimal correction when provided with a temporal model of the disturbance. We present in this paper the first on-sky results of a Kalman filter based LQG control with vibration mitigation on the CANARY instrument at the Nasmyth platform of the 4.2-m William Herschel Telescope. The results demonstrate a clear improvement of performance for full LQG compared with standard integrator control, and assess the additional improvement brought by vibration filtering with a tip-tilt model identified from on-sky data, thus validating the strategy retained on the instrument SPHERE at the VLT. PMID:25321824

Sivo, Gaetano; Kulcsár, Caroline; Conan, Jean-Marc; Raynaud, Henri-François; Gendron, Eric; Basden, Alastair; Vidal, Fabrice; Morris, Tim; Meimon, Serge; Petit, Cyril; Gratadour, Damien; Martin, Olivier; Hubert, Zoltan; Sevin, Arnaud; Perret, Denis; Chemla, Fanny; Rousset, Gérard; Dipper, Nigel; Talbot, Gordon; Younger, Eddy; Myers, Richard; Henry, David; Todd, Stephen; Atkinson, David; Dickson, Colin; Longmore, Andy

2014-09-22

426

Scalable Hyper-parameter Estimation for Gaussian Process Based Time Series Analysis  

SciTech Connect

Gaussian process (GP) is increasingly becoming popular as a kernel machine learning tool for non-parametric data analysis. Recently, GP has been applied to model non-linear dependencies in time series data. GP based analysis can be used to solve problems of time series prediction, forecasting, missing data imputation, change point detection, anomaly detection, etc. But the use of GP to handle massive scientific time series data sets has been limited, owing to its expensive computational complexity. The primary bottleneck is the handling of the covariance matrix whose size is quadratic in the length of the time series. In this paper we propose a scalable method that exploit the special structure of the covariance matrix for hyper-parameter estimation in GP based learning. The proposed method allows estimation of hyper parameters associated with GP in quadratic time, which is an order of magnitude improvement over standard methods with cubic complexity. Moreover, the proposed method does not require explicit computation of the covariance matrix and hence has memory requirement linear to the length of the time series as opposed to the quadratic memory requirement of standard methods. To further improve the computational complexity of the proposed method, we provide a parallel version to concurrently estimate the log likelihood for a set of time series which is the key step in the hyper-parameter estimation. Performance results on a multi-core system show that our proposed method provides significant speedups as high as 1000, even when running in serial mode, while maintaining a small memory footprint. The parallel version exploits the natural parallelization potential of the serial algorithm and is shown to perform significantly better than the serial faster algorithm, with speedups as high as 10.

Chandola, Varun [ORNL; Vatsavai, Raju [ORNL

2010-01-01

427

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

428

Dominos and the Gaussian free field  

E-print Network

We define a scaling limit of the height function on the domino tiling model (dimer model) on simply-connected regions in Z^2 and show that it is the ``massless free field'', a Gaussian process with independent coefficients when expanded in the eigenbasis of the Laplacian.

R. Kenyon

2000-02-09

429

Tilted Gaussian beam propagation in inhomogeneous media  

E-print Network

- dependent pulsed beams, in dispersive media [11­15]. The need for these solutions arises from beam-type exTilted Gaussian beam propagation in inhomogeneous media Yakir Hadad and Timor Melamed* Department-type spectral expansions of aperture fields in 2D inhomogeneous media that are characterized by a generic wave

Melamed, Timor

430

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

431

Rockburst Prediction Using Gaussian Process Machine Learning  

Microsoft Academic Search

Rockburst is a geological disaster occurred usually in deep mines. Because of poor understanding of the mechanism and influence factors of rockburst, it is very difficult to give accurate prediction using conventional methods. A new model based on Gaussian process (GP), which is a probabilistic kernel machine leaning and has become a power tool for solving highly nonlinear problems, therefore,

Guo-Shao Su; Ke-Shi Zhang; Zhi Chen

2009-01-01

432

Phase Space Tranformations of Gaussian Diffusions.  

National Technical Information Service (NTIS)

It is shown that for Gaussian diffusions, the transformation back to Brownian motion, via the Girsanov (or Feynman-Kac) formula and time-shaft, can be accomplished through a classical canonical, i.e. symplectic, transformation in phase space. The method i...

A. Brandao, T. Kolsrud

1996-01-01

433

Gaussian process modulated renewal processes Vinayak Rao  

E-print Network

of nonstationarity. In this work, we take a nonparametric Bayesian approach, modelling this nonstationarity Introduction Renewal processes are stochastic point processes on the real line where intervals between succes to recharge stresses released after an earthquake and an inverse Gaussian distribution is used to model

Rattray, Magnus

434

Relations between Hermite and Laguerre Gaussian modes  

Microsoft Academic Search

Relations between Hermite (HG) and Laguerre (LG) Gaussian modes are derived. With these, a LG mode is written as a sum of HG modes, and vice versa. These mode relations are derived from addition identities between a Laguerre polynomial and a pair of Hermite polynomials. The addition relations are derived in two appendices. One figure illustrates the contents of a

Isidoro Kimel; Luis R. Elias

1993-01-01

435

Diffusion of Super-Gaussian Profiles  

ERIC Educational Resources Information Center

The present analysis describes an analytically simple and systematic approximation procedure for modelling the free diffusive spreading of initially super-Gaussian profiles. The approach is based on a self-similar ansatz for the evolution of the diffusion profile, and the parameter functions involved in the modelling are determined by suitable…

Rosenberg, C.-J.; Anderson, D.; Desaix, M.; Johannisson, P.; Lisak, M.

2007-01-01

436

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

437

Tests of Gaussianity of CMB Maps  

Microsoft Academic Search

We study two different methods to test Gaussianity in CMB maps. One of them is based on the partition function and the other on the morphology of hot and cold spots. The partition function contains information on all the moments and scales, being a useful quantity to compress the large data sets expected from future space missions like Planck. In

E. Martínez-González; R. Belén Barreiro; J. M. Diego; J. L. Sanz; L. Cayón; J. Silk; S. Mollerach; V. J. Martínez

2000-01-01

438

Linear and quadratic models of point process systems: contributions of patterned input to output.  

PubMed

In the 1880's Volterra characterised a nonlinear system using a functional series connecting continuous input and continuous output. Norbert Wiener, in the 1940's, circumvented problems associated with the application of Volterra series to physical problems by deriving from it a new series of terms that are mutually uncorrelated with respect to Gaussian processes. Subsequently, Brillinger, in the 1970's, introduced a point-process analogue of Volterra's series connecting point-process inputs to the instantaneous rate of point-process output. We derive here a new series from this analogue in which its terms are mutually uncorrelated with respect to Poisson processes. This new series expresses how patterned input in a spike train, represented by third-order cross-cumulants, is converted into the instantaneous rate of an output point-process. Given experimental records of suitable duration, the contribution of arbitrary patterned input to an output process can, in principle, be determined. Solutions for linear and quadratic point-process models with one and two inputs and a single output are investigated. Our theoretical results are applied to isolated muscle spindle data in which the spike trains from the primary and secondary endings from the same muscle spindle are recorded in response to stimulation of one and then two static fusimotor axons in the absence and presence of a random length change imposed on the parent muscle. For a fixed mean rate of input spikes, the analysis of the experimental data makes explicit which patterns of two input spikes contribute to an output spike. PMID:22721703

Lindsay, K A; Rosenberg, J R

2012-08-01

439

Quantifying non-Gaussianity for quantum information  

NASA Astrophysics Data System (ADS)

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.

2010-11-01

440

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

441

Creepers: Real quadratic orders with large class number  

NASA Astrophysics Data System (ADS)

Shanks's sequence of quadratic fields Q(sqrt{S_{n}}) where S_{n}=(2^n+1)^2 + 2^{n+2} instances a class of quadratic fields for which the class number is large and, therefore, the continued fraction period is relatively short. Indeed, that period length increases linearly with n, that is: in arithmetic progression. The fields have regulator O(n^2). In the late nineties, these matters intrigued Irving Kaplansky, and led him to compute period length of the square root of sequences a^2x^{2n}+bx^{n}+c for integers a, b, c, and x. In brief, Kap found unsurprisingly that, generically, triples (a,b,c) are `leapers': they yield sequences with period length increasing at exponential rate. But there are triples yielding sequences with constant period length, Kap's `sleepers'. Finally, there are triples, as exemplified by the Shanks's sequence, for which the period lengths increase in arithmetic progression. Felicitously, Kaplansky called these `creepers'. It seems that the sleepers and creepers are precisely those for which one is able to detail the explicit continued fraction expansion for all n. Inter alia, this thesis noticeably extends the known classes of creepers and finds that not all are `kreepers' (of the shape identified by Kaplansky) and therefore not of the shape of examples studied by earlier authors looking for families of quadratic number fields with explicitly computable unit and of relatively large regulator. The work of this thesis includes the discovery of old and new families of hyperelliptic curves of increasing genus g and torsion divisor of order O(g^2). It follows that the apparent trichotomy leaper/sleeper/creeper coincides with the folk belief that the just-mentioned torsion is maximum possible.

Patterson, Roger

2007-03-01

442

Adaptive Laguerre-Gaussian variant of the Gaussian beam expansion method.  

PubMed

A variant of the Gaussian beam expansion method consists in expanding the Bessel function J0 appearing in the Fresnel-Kirchhoff integral into a finite sum of complex Gaussian functions to derive an analytical expression for a Laguerre-Gaussian beam diffracted through a hard-edge aperture. However, the validity range of the approximation depends on the number of expansion coefficients that are obtained by optimization-computation directly. We propose another solution consisting in expanding J0 onto a set of collimated Laguerre-Gaussian functions whose waist depends on their number and then, depending on its argument, predicting the suitable number of expansion functions to calculate the integral recursively. PMID:19884935

Cagniot, Emmanuel; Fromager, Michael; Ait-Ameur, Kamel

2009-11-01

443

Neural network for solving convex quadratic bilevel programming problems.  

PubMed

In this paper, using the idea of successive approximation, we propose a neural network to solve convex quadratic bilevel programming problems (CQBPPs), which is modeled by a nonautonomous differential inclusion. Different from the existing neural network for CQBPP, the model has the least number of state variables and simple structure. Based on the theory of nonsmooth analysis, differential inclusions and Lyapunov-like method, the limit equilibrium points sequence of the proposed neural networks can approximately converge to an optimal solution of CQBPP under certain conditions. Finally, simulation results on two numerical examples and the portfolio selection problem show the effectiveness and performance of the proposed neural network. PMID:24333480

He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie

2014-03-01

444

Deterministic macroscopic quantum superpositions of motion via quadratic optomechanical coupling  

E-print Network

We propose a scheme to prepare macroscopic quantum superpositions of motion in optomachanical nano- or micromechanical oscillators quadratically coupled to an intracavity field. The nonlinear optomechanical coupling leads to an effective degenerate three-wave mixing interaction between the mechanical and cavity modes. The quantum superpositions result from the combined effects of the interaction and cavity dissipation. We show analytically and confirm numerically that various deterministic quantum superpositions can be achieved, depending on initial mechanical state. The effect of mechanical damping is also studied in detail via the negativity of the Wigner function. The present scheme can be realized in various optomechanical systems with current technology.

Huatang Tan; F. Bariani; Gaoxiang Li; P. Meystre

2013-02-28

445

Negative-frequency dispersive wave generation in quadratic media  

NASA Astrophysics Data System (ADS)

We show that the extremely blueshifted dispersive wave emitted in Kerr media owing to the coupling with the negative-frequency branch [E. Rubino , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.108.253901 108, 253901 (2012)] can be observed in quadratic media via second-harmonic generation. Not only is such a phenomenon thus independent of the specific nonlinear mechanism, but it is shown to occur regardless of the fact that the process is pumped by a pulse which exhibits soliton-like features or vice versa undergoes wave breaking. A simple unified formula gives the frequencies of the emitted dispersive waves in both cases.

Conforti, Matteo; Westerberg, Niclas; Baronio, Fabio; Trillo, Stefano; Faccio, Daniele

2013-07-01

446

Strange Quark Star Model with Quadratic Equation of State  

E-print Network

In this paper, we studied the behaviour of compact relativistic objects with anisotropic matter distribution considering quadratic equation of state of Feroze and Siddiqui (2011). We specify the gravitational potential Z(x) in order to integrate the fields equations and there has been calculated the energy density, the radial pressure, the anisotropy and the mass function. The new solutions to the Einstein-Maxwell system of equations are found in term of elementary functions. For n=2, we have obtained the expressions for mass function, energy density, radius and metric functions of the model of Thirukkanesh and Ragel (2012) with polytropic equation of state.

Manuel Malaver

2014-07-03

447

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

448

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

449

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...

450

The quadratic phase factor of tightly focused wavefronts  

NASA Astrophysics Data System (ADS)

The phase structure is investigated at the focal plane of an aplanatic, high numerical aperture focusing optical system. The tightly focused field is numerically evaluated using combination of the Richards-Wolf approach and the Stratton-Chu diffraction integral. An investigation is performed for both 2D and 3D geometries for a number of different illumination structures, having piecewise quasi-constant phase at the entrance pupil and different polarization states. For the investigated illumination structures, the quadratic phase term of the focused field was found to depend on the structure of the incident illumination contrary to the paraxial case where it depends solely on the optical system parameters.

Normatov, Alexander; Spektor, Boris; Shamir, Joseph

2010-10-01

451

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

452

New deconvolution method for microscopic images based on the continuous Gaussian radial basis function interpolation model.  

PubMed

A deconvolution method based on the Gaussian radial basis function (GRBF) interpolation is proposed. Both the original image and Gaussian point spread function are expressed as the same continuous GRBF model, thus image degradation is simplified as convolution of two continuous Gaussian functions, and image deconvolution is converted to calculate the weighted coefficients of two-dimensional control points. Compared with Wiener filter and Lucy-Richardson algorithm, the GRBF method has an obvious advantage in the quality of restored images. In order to overcome such a defect of long-time computing, the method of graphic processing unit multithreading or increasing space interval of control points is adopted, respectively, to speed up the implementation of GRBF method. The experiments show that based on the continuous GRBF model, the image deconvolution can be efficiently implemented by the method, which also has a considerable reference value for the study of three-dimensional microscopic image deconvolution. PMID:25014659

Chen, Zhaoxue; Chen, Hao

2014-07-01

453

New deconvolution method for microscopic images based on the continuous Gaussian radial basis function interpolation model  

NASA Astrophysics Data System (ADS)

A deconvolution method based on the Gaussian radial basis function (GRBF) interpolation is proposed. Both the original image and Gaussian point spread function are expressed as the same continuous GRBF model, thus image degradation is simplified as convolution of two continuous Gaussian functions, and image deconvolution is converted to calculate the weighted coefficients of two-dimensional control points. Compared with Wiener filter and Lucy-Richardson algorithm, the GRBF method has an obvious advantage in the quality of restored images. In order to overcome such a defect of long-time computing, the method of graphic processing unit multithreading or increasing space interval of control points is adopted, respectively, to speed up the implementation of GRBF method. The experiments show that based on the continuous GRBF model, the image deconvolution can be efficiently implemented by the method, which also has a considerable reference value for the study of three-dimensional microscopic image deconvolution.

Chen, Zhaoxue; Chen, Hao

2014-07-01

454

Simplified algebraic description of weak measurements with Hermite-Gaussian and Laguerre-Gaussian pointer states  

NASA Astrophysics Data System (ADS)

Weak measurements are recognized as a very powerful tool in measuring tiny effects that are perpendicular to the propagation direction of a light beam. In this paper, we develop a simple algebraic description of the weak measurement protocol for both Laguerre-Gaussian and Hermite-Gaussian pointer states in the Schrödinger representation. Since a novel class of position and momentum expectation values could be derived, the present scenario appeared to be very efficient and insightful when compared to analytical methods.

de Lima Bernardo, Bertúlio; Azevedo, Sérgio; Rosas, Alexandre

2014-11-01

455

Hermite–Gaussian and Laguerre–Gaussian beams beyond the paraxial approximation  

Microsoft Academic Search

The exact electric field vectors of the higher-order Hermite–Gaussian and Laguerre–Gaussian beams are derived from the transverse component of the electric field given at the z=0 plane by use of the angular spectrum method and the electric field divergence theorem. The total beam powers are proved to be conserved along the beam propagation direction. The power-series solutions are also obtained

Hyo-Chang Kim; Yeon H. Lee

1999-01-01

456

Daily spatiotemporal precipitation simulation using latent and transformed Gaussian processes  

E-print Network

Daily spatiotemporal precipitation simulation using latent and transformed Gaussian processes is described. The methodology relies on a latent Gaussian process to drive precipitation occurrence precipitation generator that yields spatially consistent gridded quantitative precipitation realizations

Katz, Richard

457

Convolution of a Doppler line by a Gaussian instrument function  

NASA Technical Reports Server (NTRS)

A simple and direct method is obtained for assessing the distortion of a Doppler line by a Gaussian instrument function. It is suggested that a close approximation to the width of a Gaussian instrument function, or an almost Gaussian function, may be obtained by measuring a line with a Doppler absorption coefficient. The method is applicable to diode laser measurements, and may be used whenever a Gaussian instrument function is a reasonable approximation to real conditions

Fridovich, B.; Devi, V. M.; Das, P. P.

1980-01-01

458

Optical Angular Momentum Laguerre-Gaussian Modes of Laser Light  

E-print Network

Optical Angular Momentum Laguerre-Gaussian Modes of Laser Light Dimitri Dounas-Frazer drdf;Overview Beth's 1936 experiment phy250 ­ p.2/14 #12;Overview Beth's 1936 experiment Laguerre-Gaussian (LGp ) modes phy250 ­ p.2/14 #12;Overview Beth's 1936 experiment Laguerre-Gaussian (LGp ) modes Production

Budker, Dmitry

459

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

460

Confidence set inference with a prior quadratic bound  

NASA Technical Reports Server (NTRS)

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

Backus, George E.

1989-01-01

461

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

462

Practical robustness measures in multivariable control system analysis. Ph.D. Thesis  

NASA Technical Reports Server (NTRS)

The robustness of the stability of multivariable linear time invariant feedback control systems with respect to model uncertainty is considered using frequency domain criteria. Available robustness tests are unified under a common framework based on the nature and structure of model errors. These results are derived using a multivariable version of Nyquist's stability theorem in which the minimum singular value of the return difference transfer matrix is shown to be the multivariable generalization of the distance to the critical point on a single input, single output Nyquist diagram. Using the return difference transfer matrix, a very general robustness theorem is presented from which all of the robustness tests dealing with specific model errors may be derived. The robustness tests that explicitly utilized model error structure are able to guarantee feedback system stability in the face of model errors of larger magnitude than those robustness tests that do not. The robustness of linear quadratic Gaussian control systems are analyzed.

Lehtomaki, N. A.

1981-01-01

463

Frequency-doubled Hermite–Gaussian beam and the mode conversion to the Laguerre–Gaussian beam  

Microsoft Academic Search

Frequency-doubled beam of the higher-order Laguerre–Gaussian mode is obtained with a high power (2 mW) aiming at an investigation of the interaction between the Laguerre–Gaussian beam and ions in a radio-frequency ion trap. For a sufficient beam power, the Hermite–Gaussian beam is obtained at first, frequency-doubled, and then mode-converted to the Laguerre–Gaussian mode. The beam profile is analyzed theoretically.

Taro Hasegawa; Tadao Shimizu

1999-01-01

464

Non-gaussianities from perturbing recombination  

NASA Astrophysics Data System (ADS)

We approximately compute the bispectrum induced on the CMB temperature by fluctuations in the standard recombination epoch. Of all the second order sources that can induce non-Gaussianity during recombination, we concentrate on those proportional to the perturbation in the free electron density, which is about a factor of 5 larger than the other first order perturbations. This term induces some non-Gaussianity by delaying the time of recombination and by changing the photon diffusion scale. We find that the signal is not scale invariant, peaked on squeezed triangles with the smaller multipole around the scale of the first acoustic peak, and that its size corresponds to an effective fNL simeq -3.5, which could be marginally detected by Planck if both temperature and polarization are measured.

Senatore, Leonardo; Tassev, Svetlin; Zaldarriaga, Matias

2009-09-01

465

Spatial properties of rectified cosine Gaussian beams  

NASA Astrophysics Data System (ADS)

The cosine Gaussian beam (CGB) resulting from the coherent coaxial superposition of two Gaussian beams having the same width W and opposite radii of curvature R and - R is a ringed beam characterized by an M2 factor which can be very high, and adjustable by changing R. According to the paper by Hasnaoui et al(2011 Opt. Commun.284 1331-4) we expect that the CGB after ‘rectification’ by a binary diffractive optical element could be a good candidate for focal volume reduction, so useful to many laser applications. Unfortunately, this is not the case, and the physical factors responsible for this unexpected behaviour have been analysed. In particular, we have demonstrated that the three features (M2 factor, divergence and on-axis intensity) do not hold the same information about the spatial characteristics of rectified or unrectified CGBs.

Boubaha, B.; Bencheikh, A.; Aït-Ameur, K.

2014-02-01

466

Large Non-Gaussianity in Axion Inflation  

SciTech Connect

The inflationary paradigm has enjoyed phenomenological success; however, a compelling particle physics realization is still lacking. Axions are among the best-motivated inflaton candidates, since the flatness of their potential is naturally protected by a shift symmetry. We reconsider the cosmological perturbations in axion inflation, consistently accounting for the coupling to gauge fields c{phi}FF-tilde, which is generically present in these models. This coupling leads to production of gauge quanta, which provide a new source of inflaton fluctuations, {delta}{phi}. For c > or approx. 10{sup 2}M{sub p}{sup -1}, these dominate over the vacuum fluctuations, and non-Gaussianity exceeds the current observational bound. This regime is typical for concrete realizations that admit a UV completion; hence, large non-Gaussianity is easily obtained in minimal and natural realizations of inflation.

Barnaby, Neil; Peloso, Marco [School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455 (United States)

2011-05-06

467

Further Notes on the Gaussian Beam Expansion  

NASA Astrophysics Data System (ADS)

We provide alternatively a simple way of computing the Fresnel field integral, a further extension to the Gaussian-beam expansion. With a known result that the circ function is approximately decomposed into a sum of Gaussian functions, the zero-order Bessel function of the first kind is similarly expanded by the Bessel—Fourior transform. Two expansions are together inserted in this integral, which is then expressible in terms of the simple algebraic functions. The approach is useful in treatment of the field radiation problem for a large and important group of piston sources in acoustics. As examples, the calculation results for the uniform and the simply supported piston sources are presented, in a good agreement with those evaluated by numerical integration.

Dai, Yu-Rong; Ding, De-Sheng

2012-02-01

468

Model selection for Gaussian kernel PCA denoising.  

PubMed

We propose kernel parallel analysis (kPA) for automatic kernel scale and model order selection in Gaussian kernel principal component analysis (KPCA). Parallel analysis is based on a permutation test for covariance and has previously been applied for model order selection in linear PCA, we here augment the procedure to also tune the Gaussian kernel scale of radial basis function based KPCA. We evaluate kPA for denoising of simulated data and the U.S. postal data set of handwritten digits. We find that kPA outperforms other heuristics to choose the model order and kernel scale in terms of signal-to-noise ratio of the denoised data. PMID:24808465

Jørgensen, Kasper Winther; Hansen, Lars Kai

2012-01-01

469

Primordial non-Gaussianity in the forest: 3D bispectrum of Lyman-? flux spectra along multiple lines of sight.  

PubMed

We investigate the possibility of constraining primordial non-Gaussianity using the 3D bispectrum of the Lyman (Ly)-? forest. The strength of the quadratic non-Gaussian correction to an otherwise Gaussian primordial gravitational field is assumed to be dictated by a single parameter f(NL). We present the first prediction for bounds on f(NL) using Ly-? flux spectra along multiple lines of sight. The 3D Ly-? transmitted flux field is modeled as a biased tracer of the underlying matter distribution sampled along 1D skewers corresponding to quasar sight lines. The precision to which f(NL) can be constrained depends on the survey volume, pixel noise, and aliasing noise (arising from discrete sampling of the density field). We consider various combinations of these factors to predict bounds on f(NL). We find that in an idealized situation of full sky survey and negligible Poisson noise one may constrain f(NL)?23 in the equilateral limit. Assuming a Ly-? survey covering large parts of the sky (k(min) = 8 × 10(-4) Mpc(-1)) and with a quasar density of n = 5 × 10(-3) Mpc(-2), it is possible to constrain f(NL)?100 for equilateral configurations. The possibility of measuring f(NL) at a precision comparable to large scale structure studies maybe useful for joint constraining of inflationary scenarios using different data sets. PMID:23005934

Hazra, Dhiraj Kumar; Guha Sarkar, Tapomoy

2012-09-21

470

Computational aspects of Gaussian beam migration  

SciTech Connect

The computational efficiency of Gaussian beam migration depends on the solution of two problems: (1) computation of complex-valued beam times and amplitudes in Cartesian (x,z) coordinates, and (2) limiting computations to only those (x,z) coordinates within a region where beam amplitudes are significant. The first problem can be reduced to a particular instance of a class of closest-point problems in computational geometry, for which efficient solutions, such as the Delaunay triangulation, are well known. Delaunay triangulation of sampled points along a ray enables the efficient location of that point on the raypath that is closest to any point (x,z) at which beam times and amplitudes are required. Although Delaunay triangulation provides an efficient solution to this closest point problem, a simpler solution, also presented in this paper, may be sufficient and more easily extended for use in 3-D Gaussian beam migration. The second problem is easily solved by decomposing the subsurface image into a coarse grid of square cells. Within each cell, simple and efficient loops over (x,z) coordinates may be used. Because the region in which beam amplitudes are significant may be difficult to represent with simple loops over (x,z) coordinates, I use recursion to move from cell to cell, until entire region defined by the beam has been covered. Benchmark tests of a computer program implementing these solutions suggest that the cost of Gaussian hewn migration is comparable to that of migration via explicit depth extrapolation in the frequency-space domain. For the data sizes and computer programs tested here, the explicit method was faster. However, as data size was increased, the computation time for Gaussian beam migration grew more slowly than that for the explicit method.

Hale, D.

1992-08-01

471

Computational aspects of Gaussian beam migration  

SciTech Connect

The computational efficiency of Gaussian beam migration depends on the solution of two problems: (1) computation of complex-valued beam times and amplitudes in Cartesian (x,z) coordinates, and (2) limiting computations to only those (x,z) coordinates within a region where beam amplitudes are significant. The first problem can be reduced to a particular instance of a class of closest-point problems in computational geometry, for which efficient solutions, such as the Delaunay triangulation, are well known. Delaunay triangulation of sampled points along a ray enables the efficient location of that point on the raypath that is closest to any point (x,z) at which beam times and amplitudes are required. Although Delaunay triangulation provides an efficient solution to this closest point problem, a simpler solution, also presented in this paper, may be sufficient and more easily extended for use in 3-D Gaussian beam migration. The second problem is easily solved by decomposing the subsurface image into a coarse grid of square cells. Within each cell, simple and efficient loops over (x,z) coordinates may be used. Because the region in which beam amplitudes are significant may be difficult to represent with simple loops over (x,z) coordinates, I use recursion to move from cell to cell, until entire region defined by the beam has been covered. Benchmark tests of a computer program implementing these solutions suggest that the cost of Gaussian hewn migration is comparable to that of migration via explicit depth extrapolation in the frequency-space domain. For the data sizes and computer programs tested here, the explicit method was faster. However, as data size was increased, the computation time for Gaussian beam migration grew more slowly than that for the explicit method.

Hale, D.

1992-01-01

472

Talbot effect in Gaussian optical systems  

SciTech Connect

It is shown that the diffraction reproduction of a periodically modulated wave field takes place when light propagates through Gaussian optical systems. Generally, such a reproduction is accompanied by image scaling. Equations are derived that relate the reproducton distance and scaling factor to the ABCD matrix elements of the optical system. The Talbot effect in a convergent (divergent) wave is considered. (laser applications and other topics in quantum electronics)

Kandidov, V P [Department of Physics, M.V. Lomonosov Moscow State University, Moscow (Russian Federation); Kondrat'ev, Andrei V [International Laser Center, M. V. Lomonosov Moscow State University, Moscow (Russian Federation)

2001-11-30

473

On Gaussian Marginals of Uniformly Convex Bodies  

Microsoft Academic Search

Recently, Bo’az Klartag showed that arbitrary convex bodies have Gaussian marginals in most directions. We show that Klartag’s\\u000a quantitative estimates may be improved for many uniformly convex bodies. These include uniformly convex bodies with power\\u000a type 2, and power type p>2 with some additional type condition. In particular, our results apply to all unit-balls of subspaces of quotients of L

Emanuel Milman

2009-01-01

474

Observations on Gaussian bases for Schrodinger's equation  

Microsoft Academic Search

One of the few methods for generating efficient function spaces for multi-D Schrodinger eigenproblems is given by Garashchuk and Light in J.Chem.Phys. 114 (2001) 3929. Their Gaussian basis functions are wider and sparser in high potential regions, and narrower and denser in low ones. We suggest a modification of their approach based on the following observation: In very steep potential

Ilan Degani

2007-01-01

475

Scaling Laws for the Multidimensional Burgers Equation with Quadratic External Potential  

Microsoft Academic Search

The reordering of the multidimensional exponential quadratic operator in coordinate-momentum space (see X. Wang, C.H. Oh and L.C. Kwek (1998). J. Phys. A.: Math. Gen.\\u000a 31:4329–4336) is applied to derive an explicit formulation of the solution to the multidimensional heat equation with quadratic external potential and random initial conditions. The solution to the multidimensional Burgers equation with quadratic external potential

N. N. Leonenko; M. D. Ruiz-Medina

2006-01-01

476

Unitarily localizable entanglement of Gaussian states  

SciTech Connect

We consider generic (mxn)-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 uncorrelated single-mode states. The entanglement between the m-mode and the n-mode blocks can then be completely concentrated on a single pair of modes by means of local unitary operations alone. This result allows us to prove that the PPT (positivity of the partial transpose) condition is necessary and sufficient for the separability of (m+n)-mode bisymmetric Gaussian states. We determine exactly their negativity and identify a subset of bisymmetric states whose multimode entanglement of formation can be computed analytically. We consider explicit examples of pure and mixed bisymmetric states and study their entanglement scaling with the number of modes.

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

2005-03-01

477

Annular Gaussian beams in turbulent media  

NASA Astrophysics Data System (ADS)

A laser beam with a different irradiance profile may have favorable scintillation and diffraction characteristics, which are important qualities in the area of optical wireless communication. The propagation in random media (atmosphere) of a laser beam with an annular, donut-shaped, irradiance cross section was examined. Annular beams are created by unstable optical resonators, which are used as resonant cavities in high power lasers, and by beam expanders that consist of telescopes where the second mirror obstruct the central portion of the circular aperture. The annular beam was modeled as the difference of two collimated Gaussian beams, with different spot sizes. Diffraction and scintillation characteristics of the annular beam, for horizontal near ground propagation (i.e. constant refractive-index structure parameter Cn2), were compared to one collimated and one focused Gaussian beam. The Rytov approximation was used to calculate the on-axis scintillation index in weak atmospheric turbulence for both the annular and the Gaussian beams. The extended Huygens-Fresnel integral was solved to obtain the mean irradiance, from which the fraction of power in half aperture diameter was calculated.

Stromqvist Vetelino, Frida E.; Andrews, Larry C.

2004-01-01

478

Resonant non-Gaussianity with equilateral properties  

SciTech Connect

We discuss the effect of superimposing multiple sources of resonant non-Gaussianity, which arise for instance in models of axion inflation. The resulting sum of oscillating shape contributions can be used to ''Fourier synthesize'' different non-oscillating shapes in the bispectrum. As an example we reproduce an approximately equilateral shape from the superposition of O(10) oscillatory contributions with resonant shape. This implies a possible degeneracy between the equilateral-type non-Gaussianity typical of models with non-canonical kinetic terms, such as DBI inflation, and an equilateral-type shape arising from a superposition of resonant-type contributions in theories with canonical kinetic terms. The absence of oscillations in the 2-point function together with the structure of resonant N-point functions give a constraint of f{sub NL}?Gaussianity with resonant origin, but this constraint can be avoided when additional U(1)s are involved in the breaking of the shift symmetry. We comment on the questions arising from possible embeddings of this idea in a string theory setting.

Gwyn, Rhiannon [AEI Max-Planck-Institut für Gravitationsphysik, D-14476 Potsdam (Germany); Rummel, Markus [II. Institut für Theoretische Physik der Universität Hamburg, D-22761 Hamburg (Germany); Westphal, Alexander, E-mail: rhiannon.gwyn@aei.mpg.de, E-mail: markus.rummel@desy.de, E-mail: alexander.westphal@desy.de [Deutsches Elektronen-Synchrotron DESY, Theory Group, D-22603 Hamburg (Germany)

2013-04-01

479

Improved Discrete Approximation of Laplacian of Gaussian  

NASA Technical Reports Server (NTRS)

An improved method of computing a discrete approximation of the Laplacian of a Gaussian convolution of an image has been devised. The primary advantage of the method is that without substantially degrading the accuracy of the end result, it reduces the amount of information that must be processed and thus reduces the amount of circuitry needed to perform the Laplacian-of- Gaussian (LOG) operation. Some background information is necessary to place the method in context. The method is intended for application to the LOG part of a process of real-time digital filtering of digitized video data that represent brightnesses in pixels in a square array. The particular filtering process of interest is one that converts pixel brightnesses to binary form, thereby reducing the amount of information that must be performed in subsequent correlation processing (e.g., correlations between images in a stereoscopic pair for determining distances or correlations between successive frames of the same image for detecting motions). The Laplacian is often included in the filtering process because it emphasizes edges and textures, while the Gaussian is often included because it smooths out noise that might not be consistent between left and right images or between successive frames of the same image.

Shuler, Robert L., Jr.

2004-01-01

480

Fixing convergence of Gaussian belief propagation  

SciTech Connect

Gaussian belief propagation (GaBP) is an iterative message-passing algorithm for inference in Gaussian graphical models. It is known that when GaBP converges it converges to the correct MAP estimate of the Gaussian random vector and simple sufficient conditions for its convergence have been established. In this paper we develop a double-loop algorithm for forcing convergence of GaBP. Our method computes the correct MAP estimate even in cases where standard GaBP would not have converged. We further extend this construction to compute least-squares solutions of over-constrained linear systems. We believe that our construction has numerous applications, since the GaBP algorithm is linked to solution of linear systems of equations, which is a fundamental problem in computer science and engineering. As a case study, we discuss the linear detection problem. We show that using our new construction, we are able to force convergence of Montanari's linear detection algorithm, in cases where it would originally fail. As a consequence, we are able to increase significantly the number of users that can transmit concurrently.

Johnson, Jason K [Los Alamos National Laboratory; Bickson, Danny [IBM RESEARCH LAB; Dolev, Danny [HEBREW UNIV

2009-01-01