Extended Decentralized Linear-Quadratic-Gaussian Control
NASA Technical Reports Server (NTRS)
Carpenter, J. Russell
2000-01-01
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.
Adaptive continuous-time linear quadratic Gaussian control
Duncan, Tyrone E.; Guo, L.; Pasik-Duncan, Bozenna
1999-09-01
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, ...
CREATED ON MAY 31, 2013 1 Linear Quadratic Gaussian (LQG) Control of Wind
Lavaei, Javad
navigation control systems, medical porocesses controllers and even nuclear power plants. It combines both A(state ma- trix), B(control input gain matrix), G(plant noise gain matrix), C(measured state matrixCREATED ON MAY 31, 2013 1 Linear Quadratic Gaussian (LQG) Control of Wind Turbines Abdulrahman
Neural network-based nonlinear model predictive control vs. linear quadratic gaussian control
Cho, C.; Vance, R.; Mardi, N.; Qian, Z.; Prisbrey, K.
1997-01-01
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.
Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures
NASA Technical Reports Server (NTRS)
Gibson, J. S.; Adamian, A.
1988-01-01
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.
Feasibility of Decentralized Linear-Quadratic-Gaussian Control of Autonomous Distributed Spacecraft
NASA Technical Reports Server (NTRS)
Carpenter, J. Russell
1999-01-01
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.
NASA Technical Reports Server (NTRS)
Gawronski, W.
2004-01-01
Wind gusts are the main disturbances that depreciate tracking precision of microwave antennas and radiotelescopes. The linear-quadratic-Gaussian (LQG) controllers - as compared with the proportional-and-integral (PI) controllers significantly improve the tracking precision in wind disturbances. However, their properties have not been satisfactorily understood; consequently, their tuning is a trial-and-error process. A control engineer has two tools to tune an LQG controller: the choice of coordinate system of the controller model and the selection of weights of the LQG performance index. This article analyzes properties of an open- and closed-loop antenna. It shows that the proper choice of coordinates of the open-loop model simplifies the shaping of the closed-loop performance. The closed-loop properties are influenced by the LQG weights. The article shows the impact of the weights on the antenna closed-loop bandwidth, disturbance rejection properties, and antenna acceleration. The bandwidth and the disturbance rejection characterize the antenna performance, while the acceleration represents the performance limit set by the antenna hardware (motors). The article presents the controller tuning procedure, based on the coordinate selection and the weight properties. The procedure rationally shapes the closed-loop performance, as an alternative to the trial-and-error approach.
ORACLS: A system for linear-quadratic-Gaussian control law design
NASA Technical Reports Server (NTRS)
Armstrong, E. S.
1978-01-01
A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.
NASA Technical Reports Server (NTRS)
Jacobson, R. A.
1978-01-01
The formulation of the classical Linear-Quadratic-Gaussian stochastic control problem as employed in low thrust navigation analysis is reviewed. A reformulation is then presented which eliminates a potentially unreliable matrix subtraction in the control calculations, improves the computational efficiency, and provides for a cleaner computational interface between the estimation and control processes. Lastly, the application of the U-D factorization method to the reformulated equations is examined with the objective of achieving a complete set of factored equations for the joint estimation and control problem.
Habibullah, H., E-mail: h.habib@student.adfa.edu.au; Pota, H. R., E-mail: h.pota@adfa.edu.au; Petersen, I. R., E-mail: i.petersen@adfa.edu.au [School of Engineering and Information Technology, University of New South Wales, Canberra, Australian Capital Territory 2612 (Australia)
2014-03-15
This paper demonstrates a high-speed spiral imaging technique for an atomic force microscope (AFM). As an alternative to traditional raster scanning, an approach of gradient pulsing using a spiral line is implemented and spirals are generated by applying single-frequency cosine and sine waves of slowly varying amplitudes to the X and Y-axes of the AFM’s piezoelectric tube scanner (PTS). Due to these single-frequency sinusoidal input signals, the scanning process can be faster than that of conventional raster scanning. A linear quadratic Gaussian controller is designed to track the reference sinusoid and a vibration compensator is combined to damp the resonant mode of the PTS. An internal model of the reference sinusoidal signal is included in the plant model and an integrator for the system error is introduced in the proposed control scheme. As a result, the phase error between the input and output sinusoids from the X and Y-PTSs is reduced. The spirals produced have particularly narrow-band frequency measures which change slowly over time, thereby making it possible for the scanner to achieve improved tracking and continuous high-speed scanning rather than being restricted to the back and forth motion of raster scanning. As part of the post-processing of the experimental data, a fifth-order Butterworth filter is used to filter noises in the signals emanating from the position sensors and a Gaussian image filter is used to filter the images. A comparison of images scanned using the proposed controller (spiral) and the AFM PI controller (raster) shows improvement in the scanning rate using the proposed method.
J. Speyer
1979-01-01
A decentralized control problem involvingKnodes is formulated At each node are sensors and controls. The object is to share the information of each sensor, processed with a local Kalman estimator, with all the other nodes so that the controllers can be computed using the best estimate of the state of the system given the information from all the sensors. The
Submersible control using the Linear Quadratic Gaussian with Loop Transfer Recovery (LQG/LTR) method
Juul, Douglas Lawton
1993-01-01
in the ANSI C programming language because of portability between platforms and the modularity of the language. As with any control system design, the first step is the generation of equations of motion. The general submarine equations of motion were... automatic control of submarines have appeared in the open literature. Lively', Harris', Milliken', Mette', and Martin' used the LQG/LTR methodology to control submarines. In each of these cases, the vehicles were equipped with stern planes, bow planes...
Endusa Billy Muhando; T. Senjyu; O. Zachary Siagi; T. Funabashi
2007-01-01
As wind turbines continue to grow in size and flexibility and are deployed in more hostile environments, the need to develop advanced control schemes will be essential to deliver the lowest possible energy costs. A sophisticated control strategy is presented to compensate for the complicated effects of a stochastic operating environment and nonlinearities inherent in wind turbine generator (WTG) dynamics
Optimal and suboptimal quadratic forms for noncentered Gaussian processes.
Grebenkov, Denis S
2013-09-01
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
Optimal and suboptimal quadratic forms for noncentered Gaussian processes
NASA Astrophysics Data System (ADS)
Grebenkov, Denis S.
2013-09-01
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.
NASA Technical Reports Server (NTRS)
Folta, David C.; Carpenter, J. Russell
1999-01-01
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.
A tutorial on the LQG/LTR method. [Linear Quadratic Gaussian/Loop Transfer Recovery
NASA Technical Reports Server (NTRS)
Athans, M.
1986-01-01
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.
Quadratic Optimization of Impedance Control
Rolf Johansson; Mark W. Spong
1994-01-01
This paper presents algorithms for continuous-time quadratic optimization of impedance control. Explicit solutions to the Hamilton-Jacobi equation for optimal control of rigid-body motion are found by solving an algebraic matrix equation. System stability is investigated according to Lyapunov function theory, and it is shown that global asymptotic stability holds. The solution results in design parameters in the form of square
A user oriented microcomputer facility for designing linear quadratic Gaussian feedback compensators
NASA Technical Reports Server (NTRS)
Houpt, P. K.; Wahid, J.; Johnson, T. L.; Ward, S. A.
1979-01-01
The paper describes a laboratory design facility for digital microprocessor implementation of Linear-Quadratic-Gaussian feedback compensators. Outputs from user interactive programs for solving infinite time horizon LQ regulator and Kalman filter problems are conditioned for implementation on a laboratory microcomputer system. The software consists of two parts: (1) an off-line high-level program for solving the LQ Ricatti equations and generating associated feedback and filter gains, and (2) a cross compiler/macro assembler which generates object code for the target microprocessor system. Application to the control of a two dimensional inverted pendulum and expanding the design/prototyping system to other target machine architectures are discussed.
Xijia Miao
2007-10-12
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 position and/or momentum of an atomic Gaussian wave-packet motional state. A Gaussian wave-packet state is one of the simplest wave-packet states that can be easily manipulated and controlled in time and space. The paper also investigates how to manipulate in time and space an atomic Gaussian wave-packet motional state by a generalized quadratic potential field. A general quadratic Hamiltonian can affect not only the center-of-mass position and momentum but also the complex linewidth of a Gaussian wave-packet motional state while keep Gaussian shape of the motional state unchanged. It is shown that generally quadratic terms of a quadratic Hamiltonian can control directly the complex linewidth, while linear terms of a quadratic Hamiltonian can affect only the center-of-mass position and momentum of a Gaussian wave-packet motional state.
A user oriented microcomputer facility for designing linear quadratic Gaussian feedback compensators
NASA Technical Reports Server (NTRS)
Houpt, P. K.; Wahid, J.; Johnson, T. L.; Ward, S. A.
1978-01-01
A laboratory design facility for digital microprocessor implementation of linear-quadratic-Gaussian feedback compensators is described. Outputs from user interactive programs for solving infinite time horizon LQ regulator and Kalman filter problems were conditioned for implementation on the laboratory microcomputer system. The software consisted of two parts: an offline high-level program for solving the LQ Ricatti equations and generating associated feedback and filter gains and a cross compiler/macro assembler which generates object code for the target microprocessor system. A PDP 11/70 with a UNIX operating system was used for all high level program and data management, and the target microprocessor system is an Intel MDS (8080-based processor). Application to the control of a two dimensional inverted pendulum is presented and issues in expanding the design/prototyping system to other target machine architectures are discussed.
Asymptotic expansion and central limit theorem for quadratic variations of Gaussian processes
Arnaud Begyn; Lycee Pierre de Fermat
2007-01-01
Cohen, Guyon, Perrin and Pontier have given assumptions under which the second-order quadratic variations of a Gaussian process converge almost surely to a deterministic limit. In this paper we present two new convergence results about these variations: the first is a deterministic asymptotic expansion; the second is a central limit theorem. Next we apply these results to identify two-parameter fractional
Linear-quadratic fractional Gaussian control
Duncan, Tyrone E.; Pasik-Duncan, Bozenna
2013-01-01
real-valued standard fractional Brownian motion with Hurst parameter H ? (0, 1) and let c ? L2H . Then E [ ? t s cdB | B(r), r ? [0, s] ] = ? s 0 u 1 2?H ( I?(H?1/2)s? ( I(H?1/2)t? uH?1/2c )) dB, (2.7) where ua(s) = sa for a > 0, s > 0 and I? is a... that is given by J(U) = 1 2 E [ ? T 0 ?QX(s), X(s)?+ ?RU(s), U(s)?ds ] + 1 2 E?MX(T ), X(T )?,(3.4) where Q ? L(Rn,Rn), R ? L(Rm,Rm),M ? L(Rn,Rn), Q > 0, R > 0, and M ? 0 are symmetric linear transformations and ?·, ·? denotes the canonical Euclidean inner...
Quadratic Programming for Allocating Control Effort
NASA Technical Reports Server (NTRS)
Singh, Gurkirpal
2005-01-01
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.
Achieving the Quadratic Gaussian Rate-Distortion Function for Source Uncorrelated Distortions
Milan S. Derpich; Jan Østergaard; Daniel E. Quevedo
2008-01-01
We prove achievability of the recently characterized quadratic Gaussian\\u000arate-distortion function (RDF) subject to the constraint that the distortion is\\u000auncorrelated to the source. This result is based on shaped dithered lattice\\u000aquantization in the limit as the lattice dimension tends to infinity and holds\\u000afor all positive distortions. It turns out that this uncorrelated distortion\\u000aRDF can be realized
LINEAR-QUADRATIC CONTROL OF BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS
Lim, Andrew
LINEAR-QUADRATIC CONTROL OF BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS ANDREW E. B. LIM AND XUN YU differential equations (BSDEs) with a quadratic cost criteria, or backward linear-quadratic (BLQ) control, an uncontrolled BSDE, and an uncontrolled forward stochastic differential equation (SDE), while the second
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.
Jointly Optimal LQG Quantization and Control Policies for Multi-Dimensional Linear Gaussian Sources
YÃ¼ksel, Serdar
. Definition 1.1: Let M = {1, 2, . . ., M} with M = |M|. Let A be a topological space. A quantizer Q(A; MJointly Optimal LQG Quantization and Control Policies for Multi-Dimensional Linear Gaussian Sources quadratic cost criteria, we investigate the existence and the structure of optimal quantization and control
NASA Technical Reports Server (NTRS)
Chen, George T.
1987-01-01
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.
A game theoretic controller and its relationship to H? and linear-exponential-Gaussian synthesis
Ihnseok Rhee; Jason L. Speyer
1989-01-01
A simple derivation of a controller whose structure is identical to that of both the linear-exponential-Gaussian and H? controllers is presented. The controller is determined by a game-theoretic approach, in which the control plays against adversaries consisting of the process and measurement disturbances and the initial state. The game formulation considers a quadratic performance index subject to linear time-varying dynamics
Finding Optimal Gains In Linear-Quadratic Control Problems
NASA Technical Reports Server (NTRS)
Milman, Mark H.; Scheid, Robert E., Jr.
1990-01-01
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.
Multivariable linear quadratic generalized predictive control
Michael J. Grimble
1995-01-01
The multivariable generalized predictive control (GPC) law is derived in a stochastic setting which closely follows the usual polynomial solution of the LQG problem. The assumptions which must be made to ensure a GPC type of control law emerges are clear from the analysis which provides insights into the relationship between LQG and GPC control. The form of the single
Design of a linear Gaussian control law for an adaptive optics system
NASA Astrophysics Data System (ADS)
Vonbokern, Mark A.
1990-12-01
This thesis considers the design of a linear quadratic Gaussian (LQG) controller for a ground-based adaptive-optics telescopes. The incoming aberrated image is reflected from a 97-element piezoelectric mirror, then measured with a Hartmann-type wavefront sensor. A Kalman filter processes the outputs of the wavefront sensor and obtains estimates of system states. A linear quadratic regulator processes these state estimates and determines an appropriate set of commands for the deformable mirror. Atmospheric distortion is modeled as a set of fourteen Zernike coefficients whose dynamic behavior is produced by excitation of a set of shaping filters by zero-mean Gaussian white noise. The response of the mirror to control voltages is modeled as a set of Zernike coefficients whose dynamics are modeled as deterministic first-order systems. The entire control system is simulated using the multimode simulation for optimal filter evaluation (MSOFE) software.
Gain and phase margin for multiloop LQG regulators. [Linear-Quadratic-Gaussian theory
NASA Technical Reports Server (NTRS)
Safonov, M. G.; Athans, M.
1977-01-01
Multiloop linear-quadratic state-feedback (LQSF) regulators are shown to be robust against a variety of large dynamical linear time-invariant and memoryless nonlinear time-varying variations in open-loop dynamics. The results are interpreted in terms of the classical concepts of gain and phase margin, thus strengthening the link between classical and modern feedback theory.
Discrete-time Markovian-jump linear quadratic optimal control
NASA Technical Reports Server (NTRS)
Chizeck, H. J.; Willsky, A. S.; Castanon, D.
1986-01-01
This paper is concerned with the optimal control of discrete-time linear systems that possess randomly jumping parameters described by finite-state Markov processes. For problems having quadratic costs and perfect observations, the optimal control laws and expected costs-to-go can be precomputed from a set of coupled Riccati-like matrix difference equations. Necessary and sufficient conditions are derived for the existence of optimal constant control laws which stabilize the controlled system as the time horizon becomes infinite, with finite optimal expected cost.
A decentralized linear quadratic control design method for flexible structures
NASA Technical Reports Server (NTRS)
Su, Tzu-Jeng; Craig, Roy R., Jr.
1990-01-01
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.
ADAPTIVE, CAUTIOUS, PREDICTIVE CONTROL WITH GAUSSIAN PROCESS PRIORS
Williamson, John
ADAPTIVE, CAUTIOUS, PREDICTIVE CONTROL WITH GAUSSIAN PROCESS PRIORS Roderick Murray-Smith Daniel the variance of the model predictions. The general method and its main features are illustrated on a simulation, nonlinear model-based predictive control, propagation of uncertainty. 1. INTRODUCTION Gaussian process
Antenna Linear-Quadratic-Gaussian (LQG) Ccontrollers: Properties, Limits of Performance, and Tuning
NASA Technical Reports Server (NTRS)
Gawronski, Wodek K.
2004-01-01
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.
Bayesian nonparametric adaptive control using gaussian processes.
Chowdhary, Girish; Kingravi, Hassan A; How, Jonathan P; Vela, Patricio A
2015-03-01
Most current model reference adaptive control (MRAC) methods rely on parametric adaptive elements, in which the number of parameters of the adaptive element are fixed a priori, often through expert judgment. An example of such an adaptive element is radial basis function networks (RBFNs), with RBF centers preallocated based on the expected operating domain. If the system operates outside of the expected operating domain, this adaptive element can become noneffective in capturing and canceling the uncertainty, thus rendering the adaptive controller only semiglobal in nature. This paper investigates a Gaussian process-based Bayesian MRAC architecture (GP-MRAC), which leverages the power and flexibility of GP Bayesian nonparametric models of uncertainty. The GP-MRAC does not require the centers to be preallocated, can inherently handle measurement noise, and enables MRAC to handle a broader set of uncertainties, including those that are defined as distributions over functions. We use stochastic stability arguments to show that GP-MRAC guarantees good closed-loop performance with no prior domain knowledge of the uncertainty. Online implementable GP inference methods are compared in numerical simulations against RBFN-MRAC with preallocated centers and are shown to provide better tracking and improved long-term learning. PMID:25720009
J. V. L. Longstaff; K. Singer
1960-01-01
The results reported in this paper constitute a first examination of the use of Gaussian wave functions with correlation as approximations to electronic wave functions. Functions of the form sumk=nk=1 C_k exp (-Q_k), where C_k is a constant and Q_k is a quadratic form corresponding to orbitals with cylindrical symmetry, variable centres and with correlation, are used for the hydrogen
Human-Inspired Control of Bipedal Robots via Control Lyapunov Functions and Quadratic Programs
Ames, Aaron
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
Quadratic Optimization in the Problems of Active Control of Sound
NASA Technical Reports Server (NTRS)
Loncaric, J.; Tsynkov, S. V.; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulations of the problem. We have also obtained optimal solutions that minimize the overall absolute acoustic source strength of active control sources. These optimal solutions happen to be particular layers of monopoles on the perimeter of the protected region. Mathematically, minimization of acoustic source strength is equivalent to minimization in the sense of L(sub 1). By contrast. in the current paper we formulate and study optimization problems that involve quadratic functions of merit. Specifically, we minimize the L(sub 2) norm of the control sources, and we consider both the unconstrained and constrained minimization. The unconstrained L(sub 2) minimization is certainly the easiest problem to address numerically. On the other hand, the constrained approach allows one to analyze sophisticated geometries. In a special case, we call compare our finite-difference optimal solutions to the continuous optimal solutions obtained previously using a semi-analytic technique. We also show that the optima obtained in the sense of L(sub 2) differ drastically from those obtained in the sense of L(sub 1).
Approaches to quadratic stability conditions and H? control designs for TS fuzzy systems
Xiaodong Liu; Qingling Zhang
2003-01-01
In this paper, the problems of quadratic stability conditions and H? control designs for Takagi-Sugeno (T-S) fuzzy systems have been studied. First, a new quadratic stability condition, which is more simple than that in a previous paper, has been proposed. Second, two new sufficient conditions in the terms of linear matrix inequalities (LMIs) which guarantee the existence of the state
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.
Controllable gaussian-qubit interface for extremal quantum state engineering.
Adesso, Gerardo; Campbell, Steve; Illuminati, Fabrizio; Paternostro, Mauro
2010-06-18
We study state engineering through bilinear interactions between two remote qubits and two-mode gaussian light fields. The attainable two-qubit states span the entire physically allowed region in the entanglement-versus-global-purity plane. Two-mode gaussian states with maximal entanglement at fixed global and marginal entropies produce maximally entangled two-qubit states in the corresponding entropic diagram. We show that a small set of parameters characterizing extremally entangled two-mode gaussian states is sufficient to control the engineering of extremally entangled two-qubit states, which can be realized in realistic matter-light scenarios. PMID:20867288
ADAPTIVE BEAMPATTERN CONTROL USING QUADRATIC CONSTRAINTS FOR CIRCULAR ARRAY STAP
George Mason University
Space-Time Adaptive Processing (STAP) used in airborne radar systems combines signals from N antenna for adaptive and non-adaptive space- time beampattern synthesis using quadratic beampattern constraints on the weighted mean-square error between the adaptive pattern and a desired beampattern over a set of angle-Doppler
Quadratic interior-point methods in statistical disclosure control
2003-05-09
(they change the cell values) or nonperturbative (no change is performed). The most widely .... Therefore, in principle, that seems to be the best choice. To confirm the ... The second one is similar to the first generator of [11]. Cell values are ..... A thorough study of the behaviour of the spectral radius for quadratic problems is ...
L. Faybusovich; T. Mouktonglang; T. Tsuchiya
2006-01-01
We describe an implementation of an infinite-dimensional primal–dual algorithm based on the Nesterov–Todd direction. Several applications to both continuous and discrete-time multi-criteria linear-quadratic control problems and linear-quadratic control problem with quadratic constraints are described. Numerical results show a very fast convergence (typically, within 3–4 iterations) to optimal solutions.
Central Control, Sewers and (0,1) quadratic programming
NASA Astrophysics Data System (ADS)
Kolechkina, Alla; van Nooijen, Ronald
2013-04-01
We consider small sewer systems that combine foul water and storm water sewer functions in flat terrain. These systems are a combination of local gravity flow networks connected by pumps. The pumps are usually fixed speed, so they are on or off. We formulate a (0,1) quadratic programming problem, provide an overview of known solution methods and examine the relative speed of different solution methods.
Linear-quadratic model predictive control for urban traffic , Hai L. Vu a
Nazarathy, Yoni
traffic networks. This paper presents a general model predictive control framework for both centralizedLinear-quadratic model predictive control for urban traffic networks q Tung Le a, , Hai L. Vu Accepted 30 June 2013 Keywords: Model predictive control Intelligent transport system Congestion control
Nonlinear Predictive Control with a Gaussian Process Model
Williamson, John
algorithms are based on neural network models e.g. [17], fuzzy models e.g. [8] or local model networks eNonlinear Predictive Control with a Gaussian Process Model Jus Kocijan1,2 and Roderick Murray a probabilistic non-para- metric modelling approach for black-box identification of nonlinear dy- namic systems
Nonlinear system control based on Gaussian potential function network
Sukhan Lee; R. M. Kil
1991-01-01
A new approach for the neural network-based control of a nonlinear system subject to input saturation, is presented. The approach is based on: 1) the training of a Gaussian potential function network (GPFN) to model nonlinear system dynamics based on the hierarchically self-organizing learning (HSOL) algorithm; and 2) the planning of a path from the initial state to the goal
A linear quadratic tracker for Control Moment Gyro based attitude control of the Space Station
NASA Technical Reports Server (NTRS)
Kaidy, J. T.
1986-01-01
The paper discusses a design for an attitude control system for the Space Station which produces fast response, with minimal overshoot and cross-coupling with the use of Control Moment Gyros (CMG). The rigid body equations of motion are linearized and discretized and a Linear Quadratic Regulator (LQR) design and analysis study is performed. The resulting design is then modified such that integral and differential terms are added to the state equations to enhance response characteristics. Methods for reduction of computation time through channelization are discussed as well as the reduction of initial torque requirements.
NASA Technical Reports Server (NTRS)
Milman, Mark H.
1988-01-01
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.
NASA Technical Reports Server (NTRS)
Milman, Mark H.
1987-01-01
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.
Gaussian Networks for Direct Adaptive Control
Robert M. Sanner; Jean-Jacques E. Slotine
1991-01-01
A direct adaptive tracking control architecture is proposed and evaluated for a class of continuous-time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible. The architecture employs a network of gausian radial basis functions to adaptively compensate for the plant nonlinearities. Under mild assumptions about the degree of smoothness
Cost-effective management of invasive species using linear-quadratic control
Julie Blackwood; Alan Hastings; Christopher Costello
2010-01-01
The removal of invasive species is the first step toward restoring an ecosystem following invasion. We develop spatially-explicit, dynamic optimal control strategies for a large class of invasion problems using linear-quadratic control. This approach allows us to produce new insights that help guide policy that could not have emerged from existing models. We assume adults are sedentary, and heterogeneous patches
Nazarathy, Yoni
2013-01-01
traffic networks. This paper presents a general model predictive control framework for both centralized-Quadratic Model Predictive Control for Urban Traffic Networks Tung Lea , Hai L. Vua Yoni Nazarathyb , Bao Voa generally tractable with quadratic costs. The end result is a central control scheme that may be realized
NASA Astrophysics Data System (ADS)
Yamada, Katsuhiko; Jikuya, Ichiro
2014-09-01
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.
Quadratic Programming and Impedance Control for Transfemoral Prosthesis
Ames, Aaron
and therefore form a suitable substitute to human subjects on which a prosthetic control can be tested. Based. INTRODUCTION As one of the most important applications of bipedal robotic research, the development of lower-limb prosthetic devices and controllers for these devices has garnered the attention of the control and robotics
On some dynamical and geometrical properties of the Maxwell-Bloch equations with a quadratic control
Tudor Binzar; Cristian Lazureanu
2014-02-24
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.
Control of free space propagation of Airy beams generated by quadratic nonlinear photonic crystals
Arie, Ady
space propagation of an Airy beam. This beam is generated by a nonlinear wave mixing process waves. The Y com- ponent of the nonlinear coefficient modulation imposes a cu- bic phaseControl of free space propagation of Airy beams generated by quadratic nonlinear photonic crystals
M. Hinze; S. Volkwein
2008-01-01
In this paper we investigate POD discretizations of abstract linear–quadratic optimal control problems with control constraints.\\u000a We apply the discrete technique developed by Hinze (Comput. Optim. Appl. 30:45–61, 2005) and prove error estimates for the corresponding discrete controls, where we combine error estimates for the state and the\\u000a adjoint system from Kunisch and Volkwein (Numer. Math. 90:117–148, 2001; SIAM J.
Optimal impulse control for cash management¶with quadratic holding-penalty costs
Stefano Baccarin
2002-01-01
. 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
Ames, Aaron
Quadratic Program based Control of Fully-Actuated Transfemoral Prosthesis for Flat-Ground and Up to achieve flat-ground and up-slope walking on a fully-actuated above-knee prosthesis. CLF based quadratic--implemented as a feed-forward term--the end result is a prosthesis controller that utilizes only local information while
Learning control for minimizing a quadratic cost during repetitions of a task
NASA Technical Reports Server (NTRS)
Longman, Richard W.; Chang, Chi-Kuang
1990-01-01
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.
The application of quadratic optimal cooperative control synthesis to a CH-47 helicopter
NASA Technical Reports Server (NTRS)
Townsend, Barbara K.
1986-01-01
A control-system design method, Quadratic Optimal Cooperative Control Synthesis (CCS), is applied to the design of a Stability and Control Augmentation Systems (SCAS). The CCS design method is different from other design methods in that it does not require detailed a priori design criteria, but instead relies on an explicit optimal pilot-model to create desired performance. The design model, which was developed previously for fixed-wing aircraft, is simplified and modified for application to a Boeing Vertol CH-47 helicopter. Two SCAS designs are developed using the CCS design methodology. The resulting CCS designs are then compared with designs obtained using classical/frequency-domain methods and Linear Quadratic Regulator (LQR) theory in a piloted fixed-base simulation. Results indicate that the CCS method, with slight modifications, can be used to produce controller designs which compare favorably with the frequency-domain approach.
Heinkenschloss, Matthias (Rice University, Houston, TX); Bartlett, Roscoe Ainsworth; Van Bloeman Waanders, Paul; Ridzal, Denis (Rice University, Houston, TX)
2005-04-01
We present an optimization-level domain decomposition (DD) preconditioner for the solution of advection dominated elliptic linear-quadratic optimal control problems. The DD preconditioner is based on a decomposition of the optimality conditions for the elliptic linear-quadratic optimal control problem into smaller subdomain optimality conditions with Dirichlet boundary conditions for the states and the adjoints on the subdomain interfaces. These subdomain optimality conditions are coupled through Robin transmission conditions for the states and the adjoints. The parameters in the Robin transmission condition depend on the advection. This decomposition leads to a Schur complement system in which the unknowns are the state and adjoint variables on the subdomain interfaces. The Schur complement operator is the sum of subdomain Schur complement operators, the application of which is shown to correspond to the solution of subdomain optimal control problems, which are essentially smaller copies of the original optimal control problem. We show that, under suitable conditions, the application of the inverse of the subdomain Schur complement operators requires the solution of a subdomain elliptic linear-quadratic optimal control problem with Robin boundary conditions for the state. Numerical tests for problems with distributed and with boundary control show that the dependence of the preconditioners on mesh size and subdomain size is comparable to its counterpart applied to a single advection dominated equation. These tests also show that the preconditioners are insensitive to the size of the control regularization parameter.
Vojislav Kecman; Stanoje P. Bingulac; Zoran Gajic
1999-01-01
In this paper we show how to decompose the singularly perturbed algebraic Riccati equation and the corresponding linear-quadratic optimal control problem at steady state in terms of reduced-order pure-slow and pure-fast problems by using the eigenvector approach. The eigenvector approach should be used for decomposition of singularly perturbed control systems in the cases when the singular perturbation parameter is not
Group-velocity control by quadratic nonlinear interactions.
Marangoni, Marco; Manzoni, Cristian; Ramponi, Roberta; Cerullo, Giulio; Baronio, Fabio; De Angelis, Costantino; Kitamura, Kenji
2006-02-15
We give direct experimental evidence that the group velocity of ultrashort pulses can be controlled through chi(2)-cascaded interactions, under the condition of large group-velocity mismatch. The group velocity can be finely tuned by acting on pulse intensity and phase mismatch. Group-delay shifts up to 50 fs are achieved by propagating 40 fs pulses around 1400 nm in a 25 mm long periodically poled stoichiometric lithium tantalate crystal. PMID:16496911
Group-velocity control by quadratic nonlinear interactions
NASA Astrophysics Data System (ADS)
Marangoni, Marco; Manzoni, Cristian; Ramponi, Roberta; Cerullo, Giulio; Baronio, Fabio; de Angelis, Costantino; Kitamura, Kenji
2006-02-01
We give direct experimental evidence that the group velocity of ultrashort pulses can be controlled through chi(2)-cascaded interactions, under the condition of large group-velocity mismatch. The group velocity can be finely tuned by acting on pulse intensity and phase mismatch. Group-delay shifts up to 50 fs are achieved by propagating 40 fs pulses around 1400 nm in a 25 mm long periodically poled stoichiometric lithium tantalate crystal.
Controlling the disorder properties of quadratic nonlinear photonic crystals.
Varon, Idith; Porat, Gil; Arie, Ady
2011-10-15
We experimentally 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, whereby each block is followed by a short section of random length. We use this scheme to achieve broadband second harmonic generation in KTiOPO4 nonlinear crystals while independently controlling the bandwidth and the center of the converted wavelengths as well as the efficiency of conversion. The trade-off between bandwidth and efficiency is improved in comparison with periodically poled crystals. PMID:22002358
Searchless tuning of linear controllers for the minimum of quadratic criterion
NASA Astrophysics Data System (ADS)
Pikina, G. A.; Burtseva, Yu. S.
2014-03-01
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.
NASA Technical Reports Server (NTRS)
Ito, Kazufumi; Teglas, Russell
1987-01-01
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.
NASA Technical Reports Server (NTRS)
Ito, K.; Teglas, R.
1984-01-01
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.
NASA Technical Reports Server (NTRS)
Young, J. W.; Hamer, H. A.; Johnson, K. G.
1984-01-01
A decoupled-control analysis was performed for a large flexible space antenna. Control involved commanding changes in the rigid-body modes or nulling disturbances in the flexible modes. The study provides parametric-type data which could be useful in the final design of a large space antenna control system. Results are presented to illustrate the effect on control requirements of (1) the number of modes controlled; (2) the number, type, and location of control actuators; and (3) variations in the closed-loop dynamics of the control system. Comparisons are given between the decoupled-control results and those obtained by using a linear quadratic regulator approach. Time history responses are presented to illustrate the effects of the control procedures.
NASA Technical Reports Server (NTRS)
Milman, M. H.
1985-01-01
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.
Space shuttle active-pogo-suppressor control design using linear quadratic regulator techniques
NASA Technical Reports Server (NTRS)
Lehtinen, B.; Lorenz, C. F.
1979-01-01
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.
Singular linear-quadratic control problem for systems with linear delay
Sesekin, A. N. [Ural Federal University, 19 S. Mira, Ekaterinburg, 620002 (Russian Federation); Institute of Mathematics and Mechanics, Ural Division of Russian Academy of Sciences, 16 S. Kovalevskaya, Ekaterinburg, 620990 (Russian Federation)
2013-12-18
A singular linear-quadratic optimization problem on the trajectories of non-autonomous linear differential equations with linear delay is considered. The peculiarity of this problem is the fact that this problem has no solution in the class of integrable controls. To ensure the existence of solutions is required to expand the class of controls including controls with impulse components. Dynamical systems with linear delay are used to describe the motion of pantograph from the current collector with electric traction, biology, etc. It should be noted that for practical problems fact singularity criterion of quality is quite commonly occurring, and therefore the study of these problems is surely important. For the problem under discussion optimal programming control contained impulse components at the initial and final moments of time is constructed under certain assumptions on the functional and the right side of the control system.
NASA Technical Reports Server (NTRS)
Turso, James A.; Litt, Jonathan S.
2004-01-01
A method for accommodating engine deterioration via a scheduled Linear Parameter Varying Quadratic Lyapunov Function (LPVQLF)-Based controller is presented. The LPVQLF design methodology provides a means for developing unconditionally stable, robust control of Linear Parameter Varying (LPV) systems. The controller is scheduled on the Engine Deterioration Index, a function of estimated parameters that relate to engine health, and is computed using a multilayer feedforward neural network. Acceptable thrust response and tight control of exhaust gas temperature (EGT) is accomplished by adjusting the performance weights on these parameters for different levels of engine degradation. Nonlinear simulations demonstrate that the controller achieves specified performance objectives while being robust to engine deterioration as well as engine-to-engine variations.
CAD of control systems: Application of nonlinear programming to a linear quadratic formulation
NASA Technical Reports Server (NTRS)
Fleming, P.
1983-01-01
The familiar suboptimal regulator design approach is recast as a constrained optimization problem and incorporated in a Computer Aided Design (CAD) package where both design objective and constraints are quadratic cost functions. This formulation permits the separate consideration of, for example, model following errors, sensitivity measures and control energy as objectives to be minimized or limits to be observed. Efficient techniques for computing the interrelated cost functions and their gradients are utilized in conjunction with a nonlinear programming algorithm. The effectiveness of the approach and the degree of insight into the problem which it affords is illustrated in a helicopter regulation design example.
NASA Technical Reports Server (NTRS)
Byrnes, C. I.
1980-01-01
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.
Paris-Sud XI, UniversitÃ© de
Characterization of local quadratic growth for strong minima in the optimal control of semi-linear elliptic equations TÂ´erence Bayen J. FrÂ´edÂ´eric Bonnans Francisco J. SilvaÂ§ September 11, 2013 Abstract In this article we consider an optimal control problem of a semi-linear elliptic equation, with bound constraints
Laflamme, Simon
This paper proposes an adaptive neural network composed of Gaussian radial functions for mapping the behavior of civil structures controlled with magnetorheological dampers. The online adaptation takes into account the ...
Soliton transmission control by super-Gaussian filters
NASA Astrophysics Data System (ADS)
Peral, E.; Capmany, J.; Marti, J.
1996-12-01
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.
Bullo, Francesco
Voltage Stabilization in Microgrids via Quadratic Droop Control John W. Simpson-Porco, Florian D microgrid, we present a concise and closed-form condition for the existence of an exponentially stable high and social factors, and the rapidly expanding integration of low voltage small-scale renewable energy sources
Lyapunov functions for quadratic differential equations with applications to adaptive control
G. Luders; K. Narendra
1972-01-01
Conditions are derived for the existence of quadratic Lyapunov functions for vector differential equations with quadratic terms. These conditions are used to establish a set of nonlinear equations for which the null solution is asymptotically stable in the whole. Many of the recent results in the stability of model reference adaptive systems are particular cases of these general conditions.
NASA Astrophysics Data System (ADS)
Badreddine, Hassan; Vandewalle, Stefan; Meyers, Johan
2014-01-01
The current work focuses on the development and application of an efficient algorithm for optimization of three-dimensional turbulent flows, simulated using Direct Numerical Simulation (DNS) or Large-Eddy Simulations, and further characterized by large-dimensional optimization-parameter spaces. The optimization algorithm is based on Sequential Quadratic Programming (SQP) in combination with a damped formulation of the limited-memory BFGS method. The latter is suitable for solving large-scale constrained optimization problems whose Hessian matrices cannot be computed and stored at a reasonable cost. We combine the algorithm with a line-search merit function based on an L1-norm to enforce the convergence from any remote point. It is first shown that the proposed form of the damped L-BFGS algorithm is suitable for solving equality constrained Rosenbrock type functions. Then, we apply the algorithm to an optimal-control test problem that consists of finding the optimal initial perturbations to a turbulent temporal mixing layer such that mixing is improved at the end of a simulation time horizon T. The controls are further subject to a non-linear equality constraint on the total control energy. DNSs are used to resolve all turbulent scales of motion, and a continuous adjoint formulation is employed to calculate the gradient of the cost functionals. We compare the convergence speed of the SQP L-BFGS algorithm to a conventional non-linear conjugate-gradient method (i.e. the current standard in DNS-based optimal control), and find that the SQP algorithm is more than an order of magnitude faster than the conjugate-gradient method.
Ayvaz, Muzaffer; Demiralp, Metin [Istanbul Technical University, Informatics Institute, Maslak, 34469, Istanbul (Turkey)
2011-09-14
In this study, the optimal control equations for one dimensional quantum harmonic oscillator under the quadratic control operators together with linear dipole polarizability effects are constructed in the sense of Heisenberg equation of motion. A numerical technique based on the approximation to the non-commuting quantum mechanical operators from the fluctuation free expectation value dynamics perspective in the classical limit is also proposed for the solution of optimal control equations which are ODEs with accompanying boundary conditions. The dipole interaction of the system is considered to be linear, and the observable whose expectation value will be suppressed during the control process is considered to be quadratic in terms of position operator x. The objective term operator is also assumed to be quadratic.
NSDL National Science Digital Library
2013-06-21
The quadratic formula is easy to solve, yet sufficiently sophisticated that it provides insight into oscillations of masses connected by springs, as well as insight into chemical bonds between atoms. The purpose of this video is to illustrate what it means to find the "zeros" or "roots" of the quadratic equation, both using a graphical description, as well as by analytically completing the square to obtain the famous quadratic formula.
ERIC Educational Resources Information Center
Fay, Temple H.
2012-01-01
Quadratic friction involves a discontinuous damping term in equations of motion in order that the frictional force always opposes the direction of the motion. Perhaps for this reason this topic is usually omitted from beginning texts in differential equations and physics. However, quadratic damping is more realistic than viscous damping in many…
Nonlinear system identification using a Bayesian-Gaussian neural network for predictive control
Haiwen Ye; Weidou Ni
1999-01-01
A Bayesian–Gaussian neural network (BGNN) is presented for nonlinear system identification, as well as for model predictive control. The topology and connection weights of this network can be set immediately when the training samples are available, and the output of it is a fusion of multiple pieces of information. The training of this network is a minimization process to optimize
ACCEPTED TO IEEE TRANS. IMAGE PROCESSING. AUGUST 2007 1 EntropyControlled Quadratic Markov Measure
Rivera, Mariano
of directly computing a label map, our method computes the probability that the observed data at each pixel is generated by a particular intensity model. Prior information about segmentation smoothness and low entropy of the probability distribution maps is codified in the form of a MRF with quadratic potentials, so that the optimal
Zhang, Jianhua; Jiang, Man; Ren, Mifeng; Hou, Guolian; Xu, Jinliang
2013-11-01
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
NASA Astrophysics Data System (ADS)
Ranjita Chanu, Sapam; Natarajan, Vasant
2013-05-01
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.
Control of nonlinear system with input saturation based on Gaussian potential function network
Sukhan Lee; R. M. Kil
1991-01-01
The authors present a novel approach to the neural-network-based control of a nonlinear system, or in particular for the neural-network-based regulation of a nonlinear system subject to input saturation. This approach is based on (1) the training of a Gaussian potential function network (GPFN) to model nonlinear system dynamics based on the hierarchically self-organizing learning (HSOL) algorithm, and (2) the
Quadratic synthesis of integrated active controls for an aeroelastic forward-swept-wing-aircraft
NASA Technical Reports Server (NTRS)
Gilbert, M. G.; Schmidt, D. K.; Weisshaar, T. A.
1982-01-01
State variable representations of flexible aircraft are obtained using a modeling approach which first defines a mean-reference axis coordinate system. The active system design approach for forward-swept-wing aircraft also expresses structural deformations of the wing in terms of free normal vibration modes relative to this mean reference axis. Calculations which assume quasi-steady incompressible aerodynamics are performed to obtain generalized force expressions for flight conditions. The use of this quadratic synthesis technique shows that increased performance and redundancy over decentralized approaches can be achieved using integrated active longitudinal stability augmentation and aeroelastic stabilization.
Duncan, Tyrone E.; Maslowski, B.; Pasik-Duncan, B.
2012-01-01
2 (Ru(s) + B?P (s)X(s) +B??(s))|2U ? |R ?1B??(s)|2U } ds + lim ??? lim n?? N?,n, and by Lemma 4.5 ( E?(0) = 0) the following equality is obtained: J(x, u)? 1 2 ?P (0)x, x? H (4.51) = 1 2 E ? T 0 { |R 1 2 (u(s) +R?1B?P (s)X(s) +R?1B??(s))|2U ? |R ?1B...(t? r)CdBH (r), t ? [0, T ], is a well-defined Gaussian process with sample paths in C([0, T ],H ) (cf. [5]). (b) It easily follows (e.g., [5]) that the condition (A3) is satisfied if the mapping t #8;? t??StC ˜Q1/2 belongs to L 1 H (0, T ;L 2 (V...
A Quadratic Programming Bibliography - Optimization Online
2001-02-27
Feb 27, 2001 ... quadratic programming methods for nonlinear programming, nor to those on ... system of the quadratic programming problem by an approximate system of smaller rank. ..... predictive control via multiparametric quadratic programming. ...... This paper presents a neural-network computational scheme with ...
NASA Technical Reports Server (NTRS)
Hamer, H. A.; Johnson, K. G.
1986-01-01
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.
Solving quadratic Introduction
Vickers, James
Solving quadratic equations 3.2 Introduction A quadratic equation is one which can be written. In this section we describe several ways in which quadratic equations can be solved. ' & $ % Prerequisites Before completing this Section you should be able to . . . recognise a quadratic equation solve a quadratic
POD a-posteriori error estimates for linear-quadratic optimal control problems
F. Tröltzsch; S. Volkwein
2009-01-01
The main focus of this paper is on an a-posteriori analysis for the method of proper orthogonal decomposition (POD) applied\\u000a to optimal control problems governed by parabolic and elliptic PDEs. Based on a perturbation method it is deduced how far\\u000a the suboptimal control, computed on the basis of the POD model, is from the (unknown) exact one. Numerical examples illustrate
Time-varying sliding mode control for spacecraft attitude tracking maneuvers with a quadratic cost
Binglong Cong; LIU Xiangdongl; Zhen Chen; Yongjiang Xia
2011-01-01
com Abstract: In this paper, the problem of spacecraft attitude tracking maneuvers in the presence of parametric uncertainty and external disturbance is addressed. A time-varying sliding mode controller with an exponential time-varying sliding surface is presented. The attitude of spacecraft is represented by modified Rodrigues parameters for the non-redundancy. The proposed control algorithm eliminates the reaching phase of conventional time-invariant
Application of optimal control theory to the design of the NASA/JPL 70-meter antenna servos
NASA Technical Reports Server (NTRS)
Alvarez, L. S.; Nickerson, J.
1989-01-01
The application of Linear Quadratic Gaussian (LQG) techniques to the design of the 70-m axis servos is described. Linear quadratic optimal control and Kalman filter theory are reviewed, and model development and verification are discussed. Families of optimal controller and Kalman filter gain vectors were generated by varying weight parameters. Performance specifications were used to select final gain vectors.
Quadratic rollback: A technique to model ambient concentrations due to undefined emission controls
Duff, M.; Horst, R.L. Jr. [Mathtech, Inc. (United States); Johnson, T.R. [TRJ Environmental, Inc. (United States)
1998-12-31
Rollback methods are often employed to assess the impact of emission controls when actual emission controls are not defined or can not be modeled. Two rollback methods are commonly used, proportional rollback and peak shaving. Proportional rollback assumes that if manmade emissions from all sources in an area are reduced by one percent, then anthropogenic pollutant concentrations are also reduced by one percent. Proportional rollback assumes modeled concentrations are first-order linear functions in terms of the level of emission controls that limit peak emissions. Peak shaving assumes that no change in concentrations occurs except for the specific hours that an ambient standard is exceeded, and then the concentrations are instantly adjusted such that the ambient standard is just met. Analyses of air quality standards often use proportional rollback to assess the impact of control strategies crafted to meet these standards. By design, proportional rollback attains ambient standards yet often underpredicts concentrations outside of peak concentration periods. Peak shaving is also unrealistic because neither emission sources nor atmospheric responses to emissions can instantly adjust pollution concentrations so as to avoid violation of a concentration-based standard. Assuming compliance with a standard, these two techniques generally bound the expected level of off-peak concentrations. This paper presents a new methodology that simulates concentrations resulting from emission controls required to meet a concentration-based standard. The model is based on the assumption that post-control concentration over time is a smooth mathematical function of uncontrolled concentrations and the level of control required for compliance. The model uses historical monitored data and produces simulations that do not appear as overcontrolled as proportional rollback methods and yet not as undercontrolled as peak shaving methods.
Vibration control of large linear quadratic symmetric systems. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Jeon, G. J.
1983-01-01
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.
Multirate LQG controller applied to self-location and path-tracking in mobile robots
Josep Tornero; R. Piza; Pedro Albertos; Julian Salt
2001-01-01
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
Centralized and decentralized solutions of the linear-exponential-Gaussian problem
Chih-Hai Fan; Jason L. Speyer; Christian R. Jaensch
1994-01-01
A particular class of stochastic control problems constrained to different information patterns is considered. This class consists of minimizing the expectation of an exponential cost criterion with quadratic argument subject to a discrete-time Gauss-Markov dynamic system, i.e., the linear-exponential-Gaussian (LEG) control problem. Besides the one-step delayed information pattern previously considered, the classical and the one-step delayed information-sharing (OSDIS) patterns are
Optimal Linear LQG Control Over Lossy Networks Without Packet Acknowledgment
Bruno Sinopoli; Luca Schenato; Massimo Franceschetti; Kameshwar Poolla; Shankar Sastry
2006-01-01
This paper is concerned with control applications over lossy data networks. Sensor data is transmitted to an estimation-control unit over a network, and control commands are issued to subsystems over the same network. Sensor and control packets may be randomly lost according to a Bernoulli process. In this context, the discrete-time linear quadratic Gaussian (LQG) optimal control problem is considered.
Estimation and Control over Lossy Networks
Bruno Sinopoli; Luca Schenato; Massimo Franceschetti; Kameshwar Poolla; Shankar Sastry
Motivated by control applications over lossy packet networks, this paper considers the Linear Quadratic Gaussian (LQG) optimal control problem in the discrete time setting and when packet losses may occur between the sensors and the estimation-control unit and between the latter and the actuation points. Previous work (1) shows that, for protocols where packets are acknowledged at the receiver (e.g.
Application of Soft Computing Techniques to a LQG Controller Design
S. G. Khan; W. Naeem; R. Sutton; S. Sharma
Optimal control with a linear quadratic Gaussian (LQG) controller is a very popular and a modern control methodology. However,\\u000a the optimization of design matrices of a linear quadratic regulator (LQR) and Kalman filter is a time consuming process and\\u000a needs a significant amount of effort. Herein, soft computing techniques are proposed to automate this process. The noise covariance\\u000a matrix V
Acceleration-Augmented LQG Control of an Active Magnetic Bearing
NASA Technical Reports Server (NTRS)
Feeley, Joseph J.
1993-01-01
A linear-quadratic-gaussian (LQG) regulator controller design for an acceleration-augmented active magnetic bearing (AMB) is outlined. Acceleration augmentation is a key feature in providing improved dynamic performance of the controller. The optimal control formulation provides a convenient method of trading-off fast transient response and force attenuation as control objectives.
Optimal linear LQG control over lossy networks without packet acknowledgment
Bruno Sinopoli; Luca Schenato; Massimo Franceschetti; Kameshwar Poolla; Shankar Sastry
2008-01-01
This paper is concerned with control applications over lossy data net- works. Sensor data is transmitted to an estimation-control unit over a network, and control commands are issued to subsystems over the same network. Sensor and control packets may be randomly lost according to a Bernoulli process. In this context, the discrete-time linear quadratic Gaussian (LQG) optimal con- trol problem
Improved temperature control of a PWR nuclear reactor using an LQG\\/LTR based controller
Hussein Arab-Alibeik; Saeed Setayeshi
2003-01-01
State feedback assisted classical (SFAC) control has been developed to improve the temperature response performance of nuclear reactors via modifying the embedded classical controller reference signal. This is done by means of an outermost state feedback controller. A linear quadratic Gaussian with loop transfer recovery (LQG\\/LTR) at the plant output seems a good candidate for the state feedback loop of
An LQG Optimal Linear Controller for Control Systems with Packet Losses
Bruno Sinopoli; Luca Schenato; Massimo Franceschetti; Kameshwar Poolla; Shankar Sastry
2005-01-01
Motivated by control applications over lossy packet networks, this paper considers the Linear Quadratic Gaussian (LQG) optimal control problem in the discrete time setting and when packet losses may occur between the sensors and the estimation-control unit and between the latter and the actuation points. Previous work [1] shows that, for protocols where packets are acknowledged at the receiver (e.g.
?p-norms of codewords from capacity- and dispersion-achieveing Gaussian codes
Polyanskiy, Yury
It is demonstrated that codewords of good codes for the additive white Gaussian noise (AWGN) channel become more and more isotropically distributed (in the sense of evaluating quadratic forms) and resemble white Gaussian ...
ERIC Educational Resources Information Center
Withers, Christopher S.; Nadarajah, Saralees
2012-01-01
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…
NSDL National Science Digital Library
2011-01-01
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.
LQG control over lossy TCP-like networks with probabilistic packet acknowledgements
Emanuele Garone; Bruno Sinopoli; Alessandro Casavola
2008-01-01
This paper is concerned with control applica- tions over lossy data networks. Sensor data is transmitted to an estimation-control unit over a network, and control commands are issued to subsystems over the same network. Sensor, control and acknowledgement packets may be randomly lost according to a Bernoulli process. In this context, the discrete-time Linear Quadratic Gaussian (LQG) optimal control problem
NSDL National Science Digital Library
Loy, Jim
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.
Power control for the additive white Gaussian noise channel under channel estimation errors
Thierry E. Klein; Robert G. Gallager
2001-01-01
We investigate the time-varying additive white Gaussian noise channel with imperfect side-information. In practical systems, the channel gain may be estimated from a probing signal and estimation errors cannot be avoided. The goal of this paper is to determine a power allocation that a priori incorporates statistical knowledge of the estimation error. This is in contrast to prior work which
Homotopy approach to optimal, linear quadratic, fixed architecture compensation
NASA Technical Reports Server (NTRS)
Mercadal, Mathieu
1991-01-01
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.
Non-Gaussian control of continuous variables with photon counting and filtering
NASA Astrophysics Data System (ADS)
Sasaki, M.; Wakui, K.; Takahashi, H.; Takeoka, M.; Suzuki, S.
2007-09-01
We study various non-Gaussian states generated by photon subtrastion from a squeezed light source. The source is a cw beam generated by optical parametric oscillator. The photon subtraction is made by tapping a small fraction of the squeezed light source and by guiding it into two Si-APDs, which enable the subtraction of one to two photons. Trigger photon clicks specify a certain temporally localized mode in the remaining squeezed beam. By filtering the remaining squeezed beam through an appropriate mode function, one can generate a variety of non-Gaussian states. This includes single and two photon states, the NOON state (N = 2), Schrödinger kitten states of both odd and even parities, and their arbitrarily desired superposition.
A new eddy current model for magnetic bearing control system design
NASA Technical Reports Server (NTRS)
Feeley, Joseph J.; Ahlstrom, Daniel J.
1992-01-01
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.
Design of a candidate flutter suppression control law for DAST ARW-2
NASA Technical Reports Server (NTRS)
Adams, W. M., Jr.; Tiffany, S. H.
1984-01-01
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.
Gain scheduling control of variable speed WTG under widely varying turbulence loading
Endusa Billy Muhando; Tomonobu Senjyu; Naomitsu Urasaki; Atsushi Yona; Hiroshi Kinjo; Toshihisa Funabashi
2007-01-01
Probabilistic paradigms for wind turbine controller design have been gaining attention. Motivation derives from the need to replace outdated empirical-based designs with more physically relevant models. This paper proposes an adaptive controller in the form of a linear quadratic Gaussian (LQG) for control of a stall-regulated, variable speed wind turbine generator (WTG). In the control scheme, the strategy is twofold:
NASA Technical Reports Server (NTRS)
Patel, R. V.; Toda, M.; Sridhar, B.
1977-01-01
The paper deals with the problem of expressing the robustness (stability) property of a linear quadratic state feedback (LQSF) design quantitatively in terms of bounds on the perturbations (modeling errors or parameter variations) in the system matrices so that the closed-loop system remains stable. Nonlinear time-varying and linear time-invariant perturbations are considered. The only computation required in obtaining a measure of the robustness of an LQSF design is to determine the eigenvalues of two symmetric matrices determined when solving the algebraic Riccati equation corresponding to the LQSF design problem. Results are applied to a complex dynamic system consisting of the flare control of a STOL aircraft. The design of the flare control is formulated as an LQSF tracking problem.
Statistical Cosmology with Quadratic Density Fields
Peter Watts; Peter Coles
2002-08-15
Primordial fluctuations in the cosmic density are usually assumed to take the form of a Gaussian random field that evolves under the action of gravitational instability. In the early stages, while they have low amplitude, the fluctuations grow linearly. During this phase the Gaussian character of the fluctuations is preserved. Later on, when the fluctuations have amplitude of order the mean density or larger, non-linear effects cause departures from Gaussianity. In Fourier space, non-linearity is responsible for coupling Fourier modes and altering the initially random distribution of phases that characterizes Gaussian initial conditions. In this paper we investigate some of the effects of quadratic non-linearity on basic statistical properties of cosmological fluctuations. We demonstrate how this form of non-linearity can affect asymptotic properties of density fields such as homogeneity, ergodicity, and behaviour under smoothing. We also show how quadratic density fluctuations give rise to a particular relationship between the phases of different Fourier modes which, in turn, leads to the generation of a non-vanishing bispectrum. We thus elucidate the relationship between higher-order power spectra and phase distributions.
A quantum mechanical version of Price's theorem for Gaussian states
Igor G. Vladimirov
2014-09-15
This paper is concerned with integro-differential identities which are known in statistical signal processing as Price's theorem for expectations of nonlinear functions of jointly Gaussian random variables. We revisit these relations for classical variables by using the Frechet differentiation with respect to covariance matrices, and then show that Price's theorem carries over to a quantum mechanical setting. The quantum counterpart of the theorem is established for Gaussian quantum states in the framework of the Weyl functional calculus for quantum variables satisfying the Heisenberg canonical commutation relations. The quantum mechanical version of Price's theorem relates the Frechet derivative of the generalized moment of such variables with respect to the real part of their quantum covariance matrix with other moments. As an illustrative example, we consider these relations for quadratic-exponential moments which are relevant to risk-sensitive quantum control.
Han, Min; Fan, Jianchao; Wang, Jun
2011-09-01
A dynamic feedforward neural network (DFNN) is proposed for predictive control, whose adaptive parameters are adjusted by using Gaussian particle swarm optimization (GPSO) in the training process. Adaptive time-delay operators are added in the DFNN to improve its generalization for poorly known nonlinear dynamic systems with long time delays. Furthermore, GPSO adopts a chaotic map with Gaussian function to balance the exploration and exploitation capabilities of particles, which improves the computational efficiency without compromising the performance of the DFNN. The stability of the particle dynamics is analyzed, based on the robust stability theory, without any restrictive assumption. A stability condition for the GPSO+DFNN model is derived, which ensures a satisfactory global search and quick convergence, without the need for gradients. The particle velocity ranges could change adaptively during the optimization process. The results of a comparative study show that the performance of the proposed algorithm can compete with selected algorithms on benchmark problems. Additional simulation results demonstrate the effectiveness and accuracy of the proposed combination algorithm in identifying and controlling nonlinear systems with long time delays. PMID:21803682
Quadratic eigenvalue problems.
Walsh, Timothy Francis; Day, David Minot
2007-04-01
In this report we will describe some nonlinear eigenvalue problems that arise in the areas of solid mechanics, acoustics, and coupled structural acoustics. We will focus mostly on quadratic eigenvalue problems, which are a special case of nonlinear eigenvalue problems. Algorithms for solving the quadratic eigenvalue problem will be presented, along with some example calculations.
Direct adaptive control of wind energy conversion systems using Gaussian networks
Miguel Angel Mayosky; Gustavo I. E. Cancelo
1999-01-01
Grid connected wind energy conversion systems (WECS) present interesting control demands, due to the intrinsic nonlinear characteristics of windmills and electric generators. In this paper a direct adaptive control strategy for WECS control is proposed. It is based on the combination of two control actions: a radial basis function network-based adaptive controller, which drives the tracking error to zero with
Quadratic Functions: Workshop 4
NSDL National Science Digital Library
Annenberg Media, Insights into Algebra, Teaching for Learning
2009-12-23
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.
NASA Technical Reports Server (NTRS)
Adams, W. M., Jr.; Tiffany, S. H.
1983-01-01
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.
Quadratic Liénard Equations with Quadratic Damping
Freddy Dumortier; Chengzhi Li
1997-01-01
In this paper we study the generalized Liénard equations x+f(x)x+g(x)=0 with quadratic polynomialsfandg. We prove that these kind of equations can have at most one limit cycle, and we give the complete bifurcation diagram and classification of the phase portraits. The paper also contains a shorter proof for the result in A. Lins, W. de Melo, and C. C. Pugh,
Precise revolution control in three-dimensional off-axis trapping with single Laguerre-Gaussian beam
NASA Astrophysics Data System (ADS)
Otsu, Tomoko; Ando, Taro; Takiguchi, Yu; Ohtake, Yoshiyuki; Toyoda, Haruyoshi; Itoh, Hiroyasu
2015-02-01
We report the precise study of orbital angular momentum transfer from Laguerre-Gaussian (LG) beams to submicrometer-sized dielectric spheres. Stable three-dimensional off-axis trapping of the spheres was achieved and confirmed by the constant behavior of the sphere's revolution radius against the trapping LG-beam power. By measuring the revolutions of the sphere that was trapped and revolved in mid-water, we confirmed excellent linearity between the revolution rate and the trapping light free from the hydrodynamic coupling with walls of a sample chamber. This result suggests a torque source of precise controllability, which will contribute to the study of biological molecules, nonequilibrium statistical physics, and micromachines.
Main graphs: Quadratic equation
Utrecht, Universiteit
a>0 OR OR OR x x x xxx x x x y y y Quadratic equation: The general solution of a quadratic equation equations: Equation dN dt = kN has the solution: N(t) = N0ekt; N0 is an (arbitrary) initial value of N. Systems of linear differential equations: For system dx dt = ax+by dy dt = cx+dy , the characteristic
Frequency weighted LQG control of spacecraft attitude
M. E. Pittelkau
1992-01-01
A frequency-weighted linear-quadratic-Gaussian (LQG) approach to control of pitch attitude and pitch wheel momentum of an Earth-orbiting spacecraft is presented. Attitude is measured by an Earth horizon sensor, and control torque is produced by magnetic torquer bars and a pitch momentum or reaction wheel. Environmental disturbances are estimated for disturbance rejection. The design features control weighting so that low-frequency control
A Control Methodology for DFIG Type Wind Turbines Connected to Distribution Networks
Pota, Himanshu Roy
A Control Methodology for DFIG Type Wind Turbines Connected to Distribution Networks N. K. Roy, H.roy.h.pota.md.mahmud)@adfa.edu.au Ahstract-This paper proposes a decentralised controller design for doubly-fed induction generators (DFIGs in operating conditions. Index Terms-distributed generation (DG), DFIG, H= norm, linear quadratic Gaussian (LQG
LQG controller design using GUI: Application to antennas and radio-telescopes
Erin Maneri; Wodek Gawronski
2000-01-01
The Linear Quadratic Gaussian (LQG) algorithm has been used to control the JPL's beam wave-guide, and 70-m antennas. This algorithm significantly improves tracking precision in a wind disturbed environment. Based on this algorithm and the implementation experience a Matlab based Graphical User Interface (GUI) was developed to design the LQG controllers applicable to antennas and radiotelescopes. The GUI is described
An efficiently solvable quadratic program for stabilizing dynamic locomotion
Kuindersma, Scott
We describe a whole-body dynamic walking controller implemented as a convex quadratic program. The controller solves an optimal control problem using an approximate value function derived from a simple walking model while ...
NASA Astrophysics Data System (ADS)
Accardi, Luigi; Dhahri, Ameur
2010-02-01
We construct the quadratic analog of the boson Fock functor. While in the first order (linear) case all contractions on the 1-particle space can be second quantized, the semigroup of contractions that admit a quadratic second quantization is much smaller due to the nonlinearity. The encouraging fact is that it contains, as proper subgroups (i.e., the contractions), all the gauge transformations of second kind and all the a.e. invertible maps of Rd into itself leaving the Lebesgue measure quasi-invariant (in particular, all diffeomorphism of Rd). This allows quadratic two-dimensional quantization of gauge theories, of representations of the Witt group (in fact it continuous analog), of the Zamolodchikov hierarchy, and much more. Within this semigroup we characterize the unitary and the isometric elements and we single out a class of natural contractions.
Quadratic spline subroutine package
Rasmussen, L.A.
1982-01-01
A continuous piecewise quadratic function with continuous first derivative is devised for approximating a single-valued, but unknown, function represented by a set of discrete points. The quadratic is proposed as a treatment intermediate between using the angular (but reliable, easily constructed and manipulated) piecewise linear function and using the smoother (but occasionally erratic) cubic spline. Neither iteration nor the solution of a system of simultaneous equations is necessary to determining the coefficients. Several properties of the quadratic function are given. A set of five short FORTRAN subroutines is provided for generating the coefficients (QSC), finding function value and derivatives (QSY), integrating (QSI), finding extrema (QSE), and computing arc length and the curvature-squared integral (QSK). (USGS)
Optical Quadratic Measure Eigenmodes
Michael Mazilu; Joerg Baumgartl; Sebastian Kosmeier; Kishan Dholakia
2010-07-13
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.
Accardi, Luigi; Dhahri, Ameur [Volterra Center, University of Roma Tor Vergata, Via Columbia 2, 00133 Roma (Italy)
2009-12-15
We give a necessary and sufficient condition for the existence of a quadratic exponential vector with test function in L{sup 2}(R{sup d}) intersection L{sup {infinity}}(R{sup d}). We prove the linear independence and totality, in the quadratic Fock space, of these vectors. Using a technique different from the one used by Accardi et al. [Quantum Probability and Infinite Dimensional Analysis, Vol. 25, p. 262, (2009)], we also extend, to a more general class of test functions, the explicit form of the scalar product between two such vectors.
Active flutter control for flexible vehicles, volume 1
NASA Technical Reports Server (NTRS)
Mahesh, J. K.; Garrard, W. L.; Stones, C. R.; Hausman, P. D.
1979-01-01
An active flutter control methodology based on linear quadratic gaussian theory and its application to the control of a super critical wing is presented. Results of control surface and sensor position optimization are discussed. Both frequency response matching and residualization used to obtain practical flutter controllers are examined. The development of algorithms and computer programs for flutter modeling and active control design procedures is reported.
Robert O. Curtis; David D. Marshall
Quadratic mean diameter is the measure of average tree diameter conventionally used in forestry, rather than arithmetic mean diameter. The historical and practical reasons for this convention are reviewed. West. J. Appl. For. 15(3):137-139. Average diameter is a widely used stand statistic that appears in virtually all yield tables, simulator outputs, stand summaries, and much inventory data. To most people,
Generalized quadratic Liénard equations
S. Lynch
1998-01-01
In this article we give explicit formulae for the Liapunov quantities of generalized Liénard systems with either quadratic damping or restoring coefficients. These quantities provide necessary conditions in order for the origin to be a centre. Recent results are also presented for these systems.
J. Killingbeck
1979-01-01
The hydrogen-atom quadratic Zeeman effect is treated by several techniques, and a new perturbation approach is suggested which involves numerical solution of a radial equation based on the s part of the potential. The low-field results appear to be more accurate than those of previous workers.
ERIC Educational Resources Information Center
Fay, Temple H.
2010-01-01
Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…
LQG\\/LTR spacecraft attitude control
T. Lahdhiri; A. T. Alouani
1993-01-01
The control of pitch attitude and pitch momentum of an Earth-orbiting spacecraft using loop-shaping techniques based on the linear-quadratic-Gaussian\\/loop-transfer-recovery (LQG\\/LTR) methodology is considered. Attitude is measured by an Earth horizon sensor, and control torque is produced by magnetic torquer bars and a pitch momentum or reaction wheel. The controller must achieve good tracking, environmental disturbance rejection, and robustness to modeling
Improved perturbation bounds for general quadratic matrix equations
M. M. Konstantinov; P. Hr. Petkov; D. W. Gu
1999-01-01
Perturbation analysis of general algebraic quadratic matrix equations is presented, which include as particular cases the standard and descriptor algebraic matrix Riccati equations, arising in the optimal control and filtering of continuous, time-invariant, linear systems. The perturbation bounds derived are superior to the bounds, already available in the literature. They are applicable to the error analysis of general quadratic matrix
Spinor condensates with a laser-induced quadratic Zeeman effect
L. Santos; M. Fattori; J. Stuhler; T. Pfau
2007-01-01
We show that an effective quadratic Zeeman effect for trapped atoms can be generated by proper laser configurations and, in particular, by the dipole trap itself. The induced quadratic Zeeman effect leads to a rich ground-state phase diagram, e.g., for a degenerate ²Cr gas, can be used to induce topological defects by controllably quenching across transitions between phases of different
The explicit linear quadratic regulator for constrained systems
Alberto Bemporad; Manfred Morari; Vivek Dua; Efstratios N. Pistikopoulos
2002-01-01
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,
Tiltrotor Control Law Design for Rotor Loads Alleviation Using Modern Control Techniques
David G. Miller; Terry M. Black; Mukund Joglekar
1991-01-01
A weighted least-squares eigenstructure assignment technique and a balanced singular value Linear Quadratic Gaussian with Loop Transfer Recovery (LQG\\/LTR) technique are used to develop rotor loads alleviation control laws for the V-22 Osprey aircraft. These techniques were applied to alleviate rotor yoke chord loads as part of a comprehensive Bell-Boeing structural loads limiting control law design effort. The control laws
Main graphs: Quadratic equation
Utrecht, Universiteit
Main graphs: Quadratic equation: Equation A2 +B+C = 0, has solutions given by the following 'abc equations: Equation dN dt = kN has the solution: N(t) = N0ekt; N0 is an (arbitrary) initial value of N. Characteristic time of change is = 1/k. Systems of linear differential equations: For system dx dt = ax+by dy dt
Observation of spectral drift in engineered quadratic nonlinear media
NASA Astrophysics Data System (ADS)
Marangoni, M.; Sanna, G.; Brida, D.; Conforti, M.; Cirmi, G.; Manzoni, C.; Baronio, F.; Bassi, P.; De Angelis, C.; Cerullo, G.
2008-07-01
Spectral blueshifts of femtosecond pulses induced by quadratic cascaded nonlinearities are experimentally studied in an engineered aperiodically poled stoichiometric lithium tantalate crystal with optimized nonlinear pattern and chirp of the input pump pulses. Starting from nearly Gaussian input pulses centered at 1420nm with 70nm spectral width, spectral shifts as high as 40nm were obtained in combination with an almost unaltered spectral shape and a transform-limited pulse duration.
LQG\\/LTR robust control of nuclear reactors with improved temperature performance
Adel Ben-Abdennour; Robert M. Edwards; Kwang Y. Lee
1992-01-01
The authors present the design of a robust controller using the linear quadratic Gaussian with loop transfer recovery (LQG\\/LTR) for nuclear reactors with the objective of maintaining a desirable performance for reactor fuel temperature and the temperature of the coolant leaving the reactor for a wide range of reactor powers. The results obtained are compared to those for an observer-based
Multivariable control of a twin lift helicopter system using the LQG/LTR design methodology
NASA Technical Reports Server (NTRS)
Rodriguez, A. A.; Athans, M.
1986-01-01
Guidelines for developing a multivariable centralized automatic flight control system (AFCS) for a twin lift helicopter system (TLHS) are presented. Singular value ideas are used to formulate performance and stability robustness specifications. A linear Quadratic Gaussian with Loop Transfer Recovery (LQG/LTR) design is obtained and evaluated.
Kazuo Tanaka; T. Ikeda; H. O. Wang
1996-01-01
This paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems, First, a stability condition for Takagi and Sugeno's fuzzy model is given in terms of Lyapunov stability theory. Next, new stability conditions for a generalized class of uncertain systems are derived from robust control
Lesson 17: Quadratic Inequalities
NSDL National Science Digital Library
2011-01-01
The lesson begins with using graphs to solve quadratic inequalities. AN equation modeling the height of a rocket is graphed along with a second equation that represents the minimum height at which the rocket can legally and safely be exploded. The intersections of the graphs provide the solution interval. A second method is then presented where the inequality is put into standard form and then solved for its x-intercepts. Interval notation and union of sets is reviewed before a purely algebraic procedure for solving the inequalities is presented. The lesson concludes with an application problem.
Properties of quadratic equations and their application to power system analysis
Hiskens, Ian A.
Properties of quadratic equations and their application to power system analysis Y.V. Makarova,1 and control can be described by algebraic sets of quadratic equations of the form fx y gx 0 1 where x Rn x as a quadratic equations set with the Jacobian matrix Jx being a linear function of unknown variables. In any
Solving quadratic equations using reduced unimodular quadratic forms
Denis Simon
2005-01-01
Let Q be an n × n symmetric matrix with integral entries and with detQ ?= 0, but not necesarily positive definite. We describe a generalized LLL algorithm to reduce this quadratic form. This algorithm either reduces the quadratic form or stops with some isotropic vector. It is proved to run in polynomial time. We also describe an algorithm for
LQG\\/LTR pitch attitude control of an earth-orbiting spacecraft
T. Lahdhiri; A. T. Alouani
1993-01-01
The control of pitch attitude and pitch momentum of an Earth-orbiting spacecraft is considered in this paper. The control approach uses loop shaping techniques based on the linear quadratic-Gaussian and the loop transfer recovery (LQG\\/LTR) methodology. Attitude is measured by an Earth horizon sensor and control torque is produced by magnetic torquer bars and a pitch momentum. The controller must
NASA Technical Reports Server (NTRS)
Picco, C. E.; Shavers, M. R.; Victor, J. M.; Duron, J. L.; Bowers, W. h.; Gillis, D. B.; VanBaalen, M.
2009-01-01
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.
Semi-Huber Quadratic Function and Comparative Study of Some MRFs for Bayesian Image Restoration
NASA Astrophysics Data System (ADS)
De la Rosa, J. I.; Villa-Hernández, J.; González-Ramírez, E.; De la Rosa, M. E.; Gutiérrez, O.; Olvera-Olvera, C.; Castañeda-Miranda, R.; Fleury, G.
2013-10-01
The present work introduces an alternative method to deal with digital image restoration into a Bayesian framework, particularly, the use of a new half-quadratic function is proposed which performance is satisfactory compared with respect to some other functions in existing literature. The bayesian methodology is based on the prior knowledge of some information that allows an efficient modelling of the image acquisition process. The edge preservation of objects into the image while smoothing noise is necessary in an adequate model. Thus, we use a convexity criteria given by a semi-Huber function to obtain adequate weighting of the cost functions (half-quadratic) to be minimized. The principal objective when using Bayesian methods based on the Markov Random Fields (MRF) in the context of image processing is to eliminate those effects caused by the excessive smoothness on the reconstruction process of image which are rich in contours or edges. A comparison between the new introduced scheme and other three existing schemes, for the cases of noise filtering and image deblurring, is presented. This collection of implemented methods is inspired of course on the use of MRFs such as the semi-Huber, the generalized Gaussian, the Welch, and Tukey potential functions with granularity control. The obtained results showed a satisfactory performance and the effectiveness of the proposed estimator with respect to other three estimators.
Robust reduced-order controller of laminar boundary layer transitions
L. Cortelezzi; J. L. Speyer
1998-01-01
A framework to derive optimal and robust reduced-order controllers of fluid mechanics and plasma physics flows using linear-quadratic-Gaussian design, or, in modern terms, H2 design, is presented. As a test case, two-dimensional channel flow is considered. A reduced model is derived, and a controller is designed based upon this model. Initial conditions creating transient growth of wall-shear stress are constructed.
Testing non-Gaussianity in CMB Maps by Morphological Statistic
Sergei F. Shandarin
2002-05-31
The assumption of Gaussianity of the primordial perturbations plays an important role in modern cosmology. The most direct test of this hypothesis consists in testing Gaussianity of the CMB maps. Counting the pixels with the temperatures in given ranges and thus estimating the one point probability function of the field is the simplest of all the tests. Other usually more complex tests of Gaussianity generally use a great deal of the information already contained in the probability function. However, the most interesting outcome of such a test would be the signal of non-Gaussianity independent of the probability function. It is shown that the independent information has purely morphological character i.e. it depends on the geometry and topology of the level contours only. As an example we discuss in detail the quadratic model $v=u+\\alpha (u^2-1)$ ($u$ is a Gaussian field with $\\bar{u}=0$ and $=1$, $\\alpha$ is a parameter) which may arise in slow-roll or two-field inflation models. We show that in the limit of small amplitude $\\alpha$ the full information about the non-Gaussianity is contained in the probability function. If other tests are performed on this model they simply recycle the same information. A simple procedure allowing to assess the sensitivity of any statistics to the morphological information is suggested. We provide an analytic estimate of the statistical limit for detecting the quadratic non-Gaussianity $\\a_c$ as a function of the map size in the ideal situation when the scale of the field is resolved. This estimate is in a good agreement with the results of the Monte Carlo simulations of $256^2$ and $1024^2$ maps. The effect of resolution on the detection quadratic non-Gaussianity is also briefly discussed.
Skin-friction Drag Reduction Via Robust Reduced-order Linear Feedback Control
L. CORTELEZZI; K. H. LEE; J. KIM; J. L. SPEYER
1998-01-01
A successful application of a linear controller to a two-dimensional channel flow is presented. An optimal and robust reduced-order linear feedback controller is derived by using multi-variable linear-quadratic-Gaussian synthesis, or, in modern term, H2 synthesis, combined with model reduction techniques. This controller based on a reduced-model of the linearized Navier-Stokes equations is applied to suppress finite-amplitude near-wall disturbances in a
Application of reduced-order controller to turbulent flows for drag reduction
Keun H. Lee; Luca Cortelezzi; John Kim; Jason Speyer
2001-01-01
A reduced-order linear feedback controller is designed and applied to turbulent channel flow for drag reduction. From the linearized two-dimensional Navier-Stokes equations a distributed feedback controller, which produces blowing\\/suction at the wall based on the measured turbulent streamwise wall-shear stress, is derived using model reduction techniques and linearquadratic-Gaussian\\/loop-transfer-recovery control synthesis. The quadratic cost criterion used for synthesis is composed of
Spinor condensates with a laser-induced quadratic Zeeman effect
L. Santos; M. Fattori; J. Stuhler; T. Pfau
2007-01-01
We show that an effective quadratic Zeeman effect for trapped atoms can be generated by proper laser configurations and, in particular, by the dipole trap itself. The induced quadratic Zeeman effect leads to a rich ground-state phase diagram, e.g., for a degenerate Cr52 gas, can be used to induce topological defects by controllably quenching across transitions between phases of different
Quadratic optimization in ill-posed problems
NASA Astrophysics Data System (ADS)
Ben Belgacem, F.; Kaber, S.-M.
2008-10-01
Ill-posed quadratic optimization frequently occurs in control and inverse problems and is not covered by the Lax-Milgram-Riesz theory. Typically, small changes in the input data can produce very large oscillations on the output. We investigate the conditions under which the minimum value of the cost function is finite and we explore the 'hidden connection' between the optimization problem and the least-squares method. Eventually, we address some examples coming from optimal control and data completion, showing how relevant our contribution is in the knowledge of what happens for various ill-posed problems. The results we state bring a substantial improvement to the analysis of the regularization methods applied to the ill-posed quadratic optimization problems. Indeed, for the cost quadratic functions bounded from below the Lavrentiev method is just the Tikhonov regularization for the 'hidden least-squares' problem. As a straightforward result, Lavrentiev's regularization exhibits better regularization and convergence results than expected at first glance.
PIECEWISE QUADRATIC APPROXIMATIONS IN CONVEX ...
2010-12-11
For instance, the recent [31] uses a different model ...... Fortunately, increasing ? and/or ? is a reaction to the fact that the ? obtained by ..... Piecewise quadratic approximations in convex numerical optimization. 25 name n function. 1 CB2. 2.
Quadratics, polynomial form in y
NSDL National Science Digital Library
ExploreMath.com
2001-01-01
Explore the graph of a quadratic of the form x = ay2 + by + c. Vary the coefficients of the equation and examine how the graph changes in response. Calculate the location of the vertex and y-intercepts.
An Investigation on Quadratic Equations.
ERIC Educational Resources Information Center
Hirst, Keith
1988-01-01
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)
Gaussian process based recursive system identification
NASA Astrophysics Data System (ADS)
Prüher, Jakub; Šimandl, Miroslav
2014-12-01
This paper is concerned with the problem of recursive system identification using nonparametric Gaussian process model. Non-linear stochastic system in consideration is affine in control and given in the input-output form. The use of recursive Gaussian process algorithm for non-linear system identification is proposed to alleviate the computational burden of full Gaussian process. The problem of an online hyper-parameter estimation is handled using proposed ad-hoc procedure. The approach to system identification using recursive Gaussian process is compared with full Gaussian process in terms of model error and uncertainty as well as computational demands. Using Monte Carlo simulations it is shown, that the use of recursive Gaussian process with an ad-hoc learning procedure offers converging estimates of hyper-parameters and constant computational demands.
Gaussian localizable entanglement
Jaromir Fiurasek; Ladislav Mista Jr
2007-06-19
We investigate localization of entanglement of multimode Gaussian states into a pair of modes by local Gaussian measurements on the remaining modes and classical communication. We find that for pure states and for mixed symmetric states maximum entanglement between two modes can be localized by local homodyne detections, i.e. projections onto infinitely squeezed states. We also show that non-Gaussian measurements allow to localize more entanglement than Gaussian ones.
2014-12-11
ADMM, a quantitative characterization of the impact of the algorithm parameters on ... Institute of Technology, Stockholm, Sweden. ...... played a leading role in several national and international research projects in control and communications.
Entanglement frustration for Gaussian states on symmetric graphs
M. M. Wolf; F. Verstraete; J. I. Cirac
2003-07-08
We investigate the entanglement properties of multi-mode Gaussian states, which have some symmetry with respect to the ordering of the modes. We show how the symmetry constraints the entanglement between two modes of the system. In particular, we determine the maximal entanglement of formation that can be achieved in symmetric graphs like chains, 2d and 3d lattices, mean field models and the platonic solids. The maximal entanglement is always attained for the ground state of a particular quadratic Hamiltonian. The latter thus yields the maximal entanglement among all quadratic Hamiltonians having the considered symmetry.
Optimality of Gaussian Discord
Stefano Pirandola; Gaetana Spedalieri; Samuel L. Braunstein; Nicolas J. Cerf; Seth Lloyd
2014-11-26
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.
A Quadratic Closure for Compressible Turbulence
Futterman, J A
2008-09-16
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.
Solving Quadratic Equations by Factoring
NSDL National Science Digital Library
2012-08-06
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.
Estimation of Clustering Parameters Using Gaussian Process Regression
Rigby, Paul; Pizarro, Oscar; Williams, Stefan B.
2014-01-01
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
Linear state feedback, quadratic weights, and closed loop eigenstructures. M.S. Thesis
NASA Technical Reports Server (NTRS)
Thompson, P. M.
1979-01-01
Results are given on the relationships between closed loop eigenstructures, state feedback gain matrices of the linear state feedback problem, and quadratic weights of the linear quadratic regulator. Equations are derived for the angles of general multivariable root loci and linear quadratic optimal root loci, including angles of departure and approach. The generalized eigenvalue problem is used for the first time to compute angles of approach. Equations are also derived to find the sensitivity of closed loop eigenvalues and the directional derivatives of closed loop eigenvectors (with respect to a scalar multiplying the feedback gain matrix or the quadratic control weight). An equivalence class of quadratic weights that produce the same asymptotic eigenstructure is defined, sufficient conditions to be in it are given, a canonical element is defined, and an algorithm to find it is given. The behavior of the optimal root locus in the nonasymptotic region is shown to be different for quadratic weights with the same asymptotic properties.
Quadratic Optimization Problems Arising in Computer Vision
Gallier, Jean
Quadratic Optimization Problems Arising in Computer Vision Jean Gallier Special Thanks to Jianbo a fundamental problem. Unfortunately, I proved Jean Gallier (Upenn) Quadratic Optimization Problems March 23. Jean Gallier (Upenn) Quadratic Optimization Problems March 23, 2011 2 / 61 #12;Perverse Cohomology
Quadratic Optimization Problems Arising in Computer Vision
Gallier, Jean
Quadratic Optimization Problems Arising in Computer Vision Jean Gallier Special Thanks to Jianbo a fundamental problem. Unfortunately, I proved Jean Gallier (Upenn) Quadratic Optimization Problems March 23. Jean Gallier (Upenn) Quadratic Optimization Problems March 23, 2011 2 / 78 #12;Perverse Cohomology
Quadratic bosonic and free white noises
Piotr Sniady
2003-03-20
We discuss the meaning of renormalization used for deriving quadratic bosonic commutation relations introduced by Accardi and find a representation of these relations on an interacting Fock space. Also, we investigate classical stochastic processes which can be constructed from noncommutative quadratic white noise. We postulate quadratic free white noise commutation relations and find their representation on an interacting Fock space.
Quadratic Residues a is a quadratic residue mod m if x2
Ikenaga, Bruce
if the following equation has a solution: x2 = a (mod m) . Otherwise, a is a quadratic nonresidue mod m. Example. 8 a quadratic equation mod p has at most two solutions (Prove it!), there are exactly two. Example. x2 = 8 (mod6-21-2013 Quadratic Residues Â· a is a quadratic residue mod m if x2 = a (mod m). Otherwise
Attitude and vibration control of a large flexible space-based antenna
NASA Technical Reports Server (NTRS)
Joshi, S. M.
1982-01-01
Control systems synthesis is considered for controlling the rigid body attitude and elastic motion of a large deployable space-based antenna. Two methods for control systems synthesis are considered. The first method utilizes the stability and robustness properties of the controller consisting of torque actuators and collocated attitude and rate sensors. The second method is based on the linear-quadratic-Gaussian control theory. A combination of the two methods, which results in a two level hierarchical control system, is also briefly discussed. The performance of the controllers is analyzed by computing the variances of pointing errors, feed misalignment errors and surface contour errors in the presence of sensor and actuator noise.
OPTICAL SOLITONS: Excitation of two-dimensional soliton matrices by fundamental Gaussian beams
NASA Astrophysics Data System (ADS)
Borovkova, O. V.; Chuprakov, D. A.; Sukhorukov, Anatolii P.
2005-01-01
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.
Geometrical Solutions of Quadratic Equations.
ERIC Educational Resources Information Center
Grewal, A. S.; Godloza, L.
1999-01-01
Demonstrates that the equation of a circle (x-h)2 + (y-k)2 = r2 with center (h; k) and radius r reduces to a quadratic equation x2-2xh + (h2 + k2 -r2) = O at the intersection with the x-axis. Illustrates how to determine the center of a circle as well as a point on a circle. (Author/ASK)
Quadratic Zeeman effect in positronium
G. Feinberg; A. Rich; J. Sucher
1990-01-01
The orbital muL.B and diamagnetic A2 interactions of electrons and positrons with an external magnetic field lead to a small quadratic Zeeman shift in the L=0, mS=+\\/-1 states of positronium, which, unlike the mS=0 states, are not affected by the usual, spin-induced Zeeman shifts. For the n=1 states, this shift would be about 2 kHz in a field of 1000
Gaussian transformations and distillation of entangled Gaussian states
Jaromir Fiurasek
2002-04-19
We prove that it is impossible to distill more entanglement from a single copy of a two-mode bipartite entangled Gaussian state via LOCC Gaussian operations. More generally, we show that any hypothetical distillation protocol for Gaussian states involving only Gaussian operations would be a deterministic protocol. Finally, we argue that the protocol considered by Eisert et al. [quant-ph/0204052] is the optimum Gaussian distillation protocol for two copies of entangled Gaussian states.
Rational quadratic Bézier curve fitting by simulated annealing technique
NASA Astrophysics Data System (ADS)
Mohamed, Najihah; Abd Majid, Ahmad; Mt Piah, Abd Rahni
2013-04-01
A metaheuristic algorithm, which is an approximation method called simulated annealing is implemented in order to have the best rational quadratic Bézier curve from a given data points. This technique is used to minimize sum squared errors in order to improve the middle control point position and the value of weight. As a result, best fitted rational quadratic Bézier curve and its mathematical function that represents all the given data points is obtained. Numerical and graphical examples are also presented to demonstrate the effectiveness and robustness of the proposed method.
Linear quadratic regulators with eigenvalue placement in a horizontal strip
NASA Technical Reports Server (NTRS)
Shieh, Leang S.; Dib, Hani M.; Ganesan, Sekar
1987-01-01
A method for optimally shifting the imaginary parts of the open-loop poles of a multivariable control system to the desirable closed-loop locations is presented. The optimal solution with respect to a quadratic performance index is obtained by solving a linear matrix Liapunov equation.
A Factorization Approach to the Linear Regulator Quadratic Cost Problem
NASA Technical Reports Server (NTRS)
Milman, M. H.
1985-01-01
A factorization approach to the linear regulator quadratic cost problem is developed. This approach makes some new connections between optimal control, factorization, Riccati equations and certain Wiener-Hopf operator equations. Applications of the theory to systems describable by evolution equations in Hilbert space and differential delay equations in Euclidean space are presented.
Wavelets and WMAP non-Gaussianity
Pia Mukherjee; Yun Wang
2004-06-04
We study the statistical properties of the 1st year WMAP data on different scales using the spherical mexican hat wavelet transform. Consistent with the results of Vielva et al. (2003) we find a deviation from Gaussianity in the form of kurtosis of wavelet coefficients on $3-4^\\circ$ scales in the southern Galactic hemisphere. This paper extends the work of Vielva et al. as follows. We find that the non-Gaussian signal shows up more strongly in the form of a larger than expected number of cold pixels and also in the form of scale-scale correlations amongst wavelet coefficients. We establish the robustness of the non-Gaussian signal under more wide-ranging assumptions regarding the Galactic mask applied to the data and the noise statistics. This signal is unlikely to be due to the usual quadratic term parametrized by the non-linearity parameter $f_{NL}$. We use the skewness of the spherical mexican hat wavelet coefficients to constrain $f_{NL}$ with the 1st year WMAP data. Our results constrain $f_{NL}$ to be $50\\pm 80$ at 68% confidence, and less than 280 at 99% confidence.
Gaussian multipartite bound information
Ladislav Mišta, Jr.; Natalia Korolkova
2013-02-07
We demonstrate the existence of Gaussian multipartite bound information which is a classical analog of Gaussian multipartite bound entanglement. We construct a tripartite Gaussian distribution from which no secret key can be distilled, but which cannot be created by local operations and public communication. Further, we show that the presence of bound information is conditional on the presence of a part of the adversary's information creatable only by private communication. Existence of this part of the adversary's information is found to be a more generic feature of classical analogs of quantum phenomena obtained by mapping of non-classically correlated separable quantum states.
NASA Astrophysics Data System (ADS)
Gómez-Hernández, J. Jaime; Xu, Teng
2014-05-01
For many years, hydraulic conductivity was considered to be lognormal. More so, in stochastic hydrogeology it was postulated that the best multivariate model for logconductivity was the multiGaussian one. However, evidence has proven that in many cases, hydraulic conductivity is not normal and that modeling using a multiGaussian distribution can introduce unwanted spatial patterns. This presentation will discuss some algorithms to address the problem of non Gaussianity of logconductivity in the context of inverse modeling. More precisely, the normal-score ensemble Kalman filter (NS-EnKF), and the ensemble pattern matching (EnPAT) will be commented with its advantages and pitfalls.
On the non-Gaussianity from Recombination
Nicola Bartolo; Antonio Riotto
2009-02-10
The non-linear effects operating at the recombination epoch generate a non-Gaussian signal in the CMB anisotropies. Such a contribution is relevant because it represents a major part of the second-order radiation transfer function which must be determined in order to have a complete control of both the primordial and non-primordial part of non-Gaussianity in the CMB anisotropies. We provide an estimate of the level of non-Gaussianity in the CMB arising from the recombination epoch which shows up mainly in the equilateral configuration. We find that it causes a contamination to the possible measurement of the equilateral primordial bispectrum shifting the minimum detectable value of the non-Gaussian parameter f^equil_NL by Delta f^equil_NL= O(10) for an experiment like Planck.
Communicating Correlated Gaussian Sources over Gaussian Z Interference Channels
Wei Liu; Biao Chen
2009-01-01
In this paper, we consider transmission of two correlated Gaussian sources to two receivers through a two-user Gaussian Z interference channel (Z IC). To facilitate our study, we first investigate Gaussian multiple access channels with correlated Gaussian sources and a single distortion constraint at the receiver. Lower bounds on the distortion as well as several achievable schemes are proposed. In
Free-space propagation of second harmonic Laguerre Gaussian beams carrying phase singularity
S. Orlov; K. Regelskis; V. Smilgevicius; A. Stabinis
2004-01-01
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
Nishimichi, Takahiro, E-mail: takahiro.nishimichi@ipmu.jp [Kavli Institute for the Physics and Mathematics of the Universe, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8568 (Japan)
2012-08-01
The large-scale clustering pattern of biased tracers is known to be a powerful probe of the non-Gaussianities in the primordial fluctuations. The so-called scale-dependent bias has been reported in various type of models of primordial non-Gaussianities. We focus on local-type non-Gaussianities, and unify the derivations in the literature of the scale-dependent bias in the presence of multiple Gaussian source fields as well as higher-order coupling to cover the models described by frequently-discussed f{sub NL}, g{sub NL} and t{sub NL} parameterization. We find that the resultant power spectrum is characterized by two parameters responsible for the shape and the amplitude of the scale-dependent bias in addition to the Gaussian bias factor. We show how (a generalized version of) Suyama-Yamaguchi inequality between f{sub NL} and t{sub NL} can directly be accessible from the observed power spectrum through the dependence on our new parameter which controls the shape of the scale-dependent bias. The other parameter for the amplitude of the scale-dependent bias is shown to be useful to distinguish the simplest quadratic non-Gaussianities (i.e., f{sub NL}-type) from higher-order ones (g{sub NL} and higher), if one measures it from multiple species of galaxies or clusters of galaxies. We discuss the validity and limitations of our analytic results by comparison with numerical simulations in an accompanying paper.
Gaussian Multipole Model (GMM)
Elking, Dennis M.; Cisneros, G. Andrés; Piquemal, Jean-Philip; Darden, Thomas A.; Pedersen, Lee G.
2009-01-01
An electrostatic model based on charge density is proposed as a model for future force fields. The model is composed of a nucleus and a single Slater-type contracted Gaussian multipole charge density on each atom. The Gaussian multipoles are fit to the electrostatic potential (ESP) calculated at the B3LYP/6-31G* and HF/aug-cc-pVTZ levels of theory and tested by comparing electrostatic dimer energies, inter-molecular density overlap integrals, and permanent molecular multipole moments with their respective ab initio values. For the case of water, the atomic Gaussian multipole moments Qlm are shown to be a smooth function of internal geometry (bond length and bond angle), which can be approximated by a truncated linear Taylor series. In addition, results are given when the Gaussian multipole charge density is applied to a model for exchange-repulsion energy based on the inter-molecular density overlap. PMID:20209077
Gravitational Energy in Quadratic-Curvature Gravities
S. Deser; Bayram Tekin
2002-01-01
We define energy (E) and compute its values for gravitational systems involving terms quadratic in curvature. There are significant differences, both conceptually and concretely, from Einstein theory. For D=4, all purely quadratic models admit constant curvature vacua with arbitrary Lambda, and E is the ``cosmological'' Abbott-Deser (AD) expression; instead, E always vanishes in flat, Lambda=0, background. For combined Einstein-quadratic curvature
Christian Weedbrook; Stefano Pirandola; Raul Garcia-Patron; Nicolas J. Cerf; Timothy C. Ralph; Jeffrey H. Shapiro; Seth Lloyd
2011-10-14
The science of quantum information has arisen over the last two decades centered on the manipulation of individual quanta of information, known as quantum bits or qubits. Quantum computers, quantum cryptography and quantum teleportation are among the most celebrated ideas that have emerged from this new field. It was realized later on that using continuous-variable quantum information carriers, instead of qubits, constitutes an extremely powerful alternative approach to quantum information processing. This review focuses on continuous-variable quantum information processes that rely on any combination of Gaussian states, Gaussian operations, and Gaussian measurements. Interestingly, such a restriction to the Gaussian realm comes with various benefits, since on the theoretical side, simple analytical tools are available and, on the experimental side, optical components effecting Gaussian processes are readily available in the laboratory. Yet, Gaussian quantum information processing opens the way to a wide variety of tasks and applications, including quantum communication, quantum cryptography, quantum computation, quantum teleportation, and quantum state and channel discrimination. This review reports on the state of the art in this field, ranging from the basic theoretical tools and landmark experimental realizations to the most recent successful developments.
Geometrical and Graphical Solutions of Quadratic Equations.
ERIC Educational Resources Information Center
Hornsby, E. John, Jr.
1990-01-01
Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)
RELIABLE SOLUTION OF CONVEX QUADRATIC PROGRAMS ...
2011-01-28
Key words. active set, convex, homotopy method, parametric quadratic programming ... impluse response design, optimal power flow, economic dispatch, etc. Several ... *Interdisciplinary Center for Scientific Computing, Heidelberg University, ...
Wortman, Kevin
Quadratic Equations and Conics A quadratic equation in two variables is an equation that's equivalent to an equation of the form p(x, y) = 0 where p(x, y) is a quadratic polynomial. Examples. Â· 4x2 - 3xy - 2y2 + x - y + 6 = 0 is a quadratic equation, as are x2 - y2 = 0 and x2 + y2 = 0 and x2 - 1 = 0
NASA Astrophysics Data System (ADS)
Lane, Steven A.; Griffin, Steven; Leo, Don
2003-02-01
This paper investigates active control using single-crystal piezoelectric actuators for reducing the vibration and acoustic loads occurring in payload fairings during launch. These numerical studies imposed reasonable and practical limitations on actuator mass and voltage for the closed-loop control simulations in order to provide a realistic assessment of the control approach. Fully coupled structural-acoustic models were developed with linear quadratic regulator and linear quadratic Gaussian control laws and simulated using realistic disturbance levels. The results are compared to previous studies that used conventional piezoelectric actuators and demonstrate significant improvement. The simulation results indicate that more than 10 dB of reduction in the interior acoustic response can be achieved over the 0-300 Hz bandwidth using full state feedback control. The primary reason for the performance improvement over polycrystalline piezoceramics is the increased strain coefficient, which provides increased control authority. However, performance is significantly reduced by model uncertainty and sensor noise to approximately 3 dB as indicated by linear quadratic Gaussian closed-loop results.
Quadratic Zeeman effect in positronium
Feinberg, G. (Department of Physics, Columbia University, New York, New York 10027 (USA)); Rich, A. (Department of Physics, University of Michigan, Ann Arbor, Michigan 48109 (USA)); Sucher, J. (Department of Physics, University of Maryland, College Park, Maryland 20742 (USA) Astronomy, University of Maryland, College Park, Maryland 20742 (USA))
1990-04-01
The orbital {mu}{sub {ital L}}{center dot}{ital B} and diamagnetic {ital A}{sup 2} interactions of electrons and positrons with an external magnetic field lead to a small quadratic Zeeman shift in the {ital L}=0, {ital m}{sub {ital S}}={plus minus}1 states of positronium, which, unlike the {ital m}{sub {ital S}}=0 states, are not affected by the usual, spin-induced Zeeman shifts. For the {ital n}=1 states, this shift would be about 2 kHz in a field of 1000 G. These additional shifts are the same in all spin states for {ital L}=0 but do depend on {ital n}.
Single-photon quadratic optomechanics
Liao, Jie-Qiao; Nori, Franco
2014-01-01
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
Quadratic Equations: From Factored to Standard Form
NSDL National Science Digital Library
2011-01-01
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
Binary Quadratic Forms: A Historical View
ERIC Educational Resources Information Center
Khosravani, Azar N.; Beintema, Mark B.
2006-01-01
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…
An Unexpected Influence on a Quadratic
ERIC Educational Resources Information Center
Davis, Jon D.
2013-01-01
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…
Existence Theorems for Some Quadratic Integral Equations
Józef Bana?; Millenia Lecko; Wagdy Gomaa El-Sayed
1998-01-01
Using the theory of measures of noncompactness, we prove a few existence theorems for some quadratic integral equations. The class of quadratic integral equations considered below contains as a special case numerous integral equations encountered in the theories of radiative transfer and neutron transport, and in the kinetic theory of gases. In particular, the well-known Chandrasekhar integral equation also belongs
Quadratic stability with real and complex perturbations
A. Packard; J. Doyle
1990-01-01
It is shown that the equivalence between real and complex perturbations in the context of quadratic stability to linear, fractional, unstructured perturbations does not hold when the perturbations are block structured. For a limited class of problems, quadratic stability in the face of structured complex perturbations is equivalent to a particular class of scaled norms, and hence appropriate synthesis techniques,
Gray, Morgan; Petit, Cyril; Rodionov, Sergey; Bocquet, Marc; Bertino, Laurent; Ferrari, Marc; Fusco, Thierry
2014-08-25
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
NASA Astrophysics Data System (ADS)
Gray, Morgan; Petit, Cyril; Rodionov, Sergey; Bocquet, Marc; Bertino, Laurent; Ferrari, Marc; Fusco, Thierry
2014-08-01
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).
Explicit Solution to a Certain Non-ELQG Risk-sensitive Stochastic Control Problem
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
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.
Reduced-Order Model Based Feedback Control For Modified Hasegawa-Wakatani Model
I.R. Goumiri, C.W. Rowley, Z. Ma, D.A. Gates, J.A. Krommes and J.B. Parker
2013-01-28
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.
Reduced-order model based feedback control of the modified Hasegawa-Wakatani model
Goumiri, I. R.; Rowley, C. W.; Ma, Z. [Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544 (United States); Gates, D. A.; Krommes, J. A.; Parker, J. B. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08544 (United States)
2013-04-15
In this work, the development of model-based feedback control that stabilizes an unstable equilibrium is obtained for the Modified Hasegawa-Wakatani (MHW) equations, a classic model in plasma turbulence. First, a balanced truncation (a model reduction technique that has proven successful in flow control design problems) is applied to obtain a low dimensional model of the linearized MHW equation. Then, a model-based feedback controller is designed for the reduced order model using linear quadratic regulators. Finally, a linear quadratic Gaussian 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.
Ikenaga, Bruce
is a root of a quadratic equation with integer coefficients. Â· Quadratic irrationals can be expressed. Definition. A quadratic irrational is an irrational number which is a root of a quadratic equation ax2 + bx)2 = q, r2 x2 - 2rpx + (p2 - q) = 0. This is a quadratic equation with integer coefficients, and r2
Non-Gaussian bias: insights from discrete density peaks
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
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.
Spinor condensates with a laser-induced quadratic Zeeman effect
Santos, L. [Institut fuer Theoretische Physik, Leibniz Universitaet Hannover, Appelstr. 2, D-30167 Hannover (Germany); Fattori, M.; Stuhler, J.; Pfau, T. [5. Physikalisches Institut, Universitaet Stuttgart, Pfaffenwaldring 57 V, D-70550 Stuttgart (Germany)
2007-05-15
We show that an effective quadratic Zeeman effect for trapped atoms can be generated by proper laser configurations and, in particular, by the dipole trap itself. The induced quadratic Zeeman effect leads to a rich ground-state phase diagram, e.g., for a degenerate {sup 52}Cr gas, can be used to induce topological defects by controllably quenching across transitions between phases of different symmetries, allows for the observability of the Einstein-de Haas effect for relatively large magnetic fields, and may be employed to create S=1/2 systems with spinor dynamics. Similar ideas could be explored in other atomic species opening an exciting new control tool in spinor systems.
Seven Wonders of the Ancient and Modern Quadratic World.
ERIC Educational Resources Information Center
Taylor, Sharon E.; Mittag, Kathleen Cage
2001-01-01
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)
Representation of Velocity Gradient Effects in a Gaussian Puff Model
R. I. Sykes; D. S. Henn
1995-01-01
The Gaussian puff model framework is extended to provide a description of velocity shear distortion effects. An efficient splitting-merging algorithm is presented so that a maximum puff size can be specified for a calculation. This localizes the Gaussian puffs so that they represent only a limited region of the flow and the accuracy of the representation is therefore controlled. The
A Solvable Mean Field Model of a Gaussian Spin Glass
Adriano Barra; Giuseppe Genovese; Francesco Guerra; Daniele Tantari
2012-05-17
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.
Design of Linear Quadratic Regulators and Kalman Filters
NASA Technical Reports Server (NTRS)
Lehtinen, B.; Geyser, L.
1986-01-01
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.
Helicopter air resonance modeling and suppression using active control
NASA Technical Reports Server (NTRS)
Takahashi, M. D.; Friedmann, P. P.
1991-01-01
A coupled rotor/fuselage helicopter analysis with the important effects of blade torsional flexibility, unsteady aerodynamics, and forward flight is presented. Using this mathematical model, a nominal configuration is selected with an air resonance instability throughout most of its flight envelope. A multivariable compensator is then designed using two swashplate inputs and a single-body roll rate measurement. The controller design is based on the linear quadratic Gaussian technique and the loop transfer recovery method. The controller is shown to suppress the air resonance instability throughout a wide range of helicopter loading conditions and forward flight speeds.
Optimal Gaussian entanglement swapping
Hoelscher-Obermaier, Jason; Loock, Peter van [Optical Quantum Information Theory Group, Max Planck Institute for the Science of Light, Guenther-Scharowsky-Str. 1/Bau 26, D-91058 Erlangen (Germany) and Institute of Theoretical Physics I, Universitaet Erlangen-Nuernberg, Staudtstr. 7/B2, D-91058 Erlangen (Germany)
2011-01-15
We consider entanglement swapping with general mixed two-mode Gaussian states and calculate the optimal gains for a broad class of such states including those states most relevant in communication scenarios. We show that, for this class of states, entanglement swapping adds no additional mixedness; that is, the ensemble-average output state has the same purity as the input states. This implies that, by using intermediate entanglement swapping steps, it is, in principle, possible to distribute entangled two-mode Gaussian states of higher purity as compared to direct transmission. We then apply the general results on optimal Gaussian swapping to the problem of quantum communication over a lossy fiber and demonstrate that, in contrast to the negative conclusions in the literature, swapping-based schemes in fact often perform better than direct transmission for high input squeezing. However, an effective transmission analysis reveals that the hope for improved performance based on optimal Gaussian entanglement swapping is spurious since the swapping does not lead to an enhancement of the effective transmission. This implies that the same or better results can always be obtained using direct transmission in combination with, in general, less squeezing.
Autonomous Gaussian Decomposition
NASA Astrophysics Data System (ADS)
Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirovi?, Snežana; Babler, Brian; Heiles, Carl; Hennebelle, Patrick; Goss, W. M.; Dickey, John
2015-04-01
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 21 cm absorption spectra from the 21 cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the H i 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 upcoming Square Kilometer Array and pathfinder telescopes.
Sequential design of discrete linear quadratic regulators via optimal root-locus techniques
NASA Technical Reports Server (NTRS)
Shieh, Leang S.; Yates, Robert E.; Ganesan, Sekar
1989-01-01
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.
NASA Technical Reports Server (NTRS)
Halyo, N.; Caglayan, A. K.
1976-01-01
This paper considers the control of a continuous linear plant disturbed by white plant noise when the control is constrained to be a piecewise constant function of time; i.e. a stochastic sampled-data system. The cost function is the integral of quadratic error terms in the state and control, thus penalizing errors at every instant of time while the plant noise disturbs the system continuously. The problem is solved by reducing the constrained continuous problem to an unconstrained discrete one. It is shown that the separation principle for estimation and control still holds for this problem when the plant disturbance and measurement noise are Gaussian.
Quadratic constrained mixed discrete optimization with an adiabatic quantum optimizer
NASA Astrophysics Data System (ADS)
Chandra, Rishabh; Jacobson, N. Tobias; Moussa, Jonathan E.; Frankel, Steven H.; Kais, Sabre
2014-07-01
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.
ESSENTIAL DIMENSION, SPINOR GROUPS, AND QUADRATIC FORMS
. 2.Essential dimension Let k be a field. We will write Fieldskfor the category of field extensions ESSENTIAL DIMENSION, SPINOR GROUPS, AND QUADRATIC FORMS PATRICK BROSNANy, ZINOVY REICHSTEINy, AND ANGELO VISTOLIz Abstract. We prove that the essential
Schur Stability Regions for Complex Quadratic Polynomials
ERIC Educational Resources Information Center
Cheng, Sui Sun; Huang, Shao Yuan
2010-01-01
Given a quadratic polynomial with complex coefficients, necessary and sufficient conditions are found in terms of the coefficients such that all its roots have absolute values less than 1. (Contains 3 figures.)
Quadratic Equations...Origins, Development and Use.
ERIC Educational Resources Information Center
McQualter, J. W.
1988-01-01
There may be a social and an intellectual aspect to the process of development of mathematical knowledge. This paper describes quadratic equations as intellectual mathematics and as colloquial mathematics. Provides some historical data. (YP)
PRIMES AND QUADRATIC RECIPROCITY ANGELICA WONG
May, J. Peter
PRIMES AND QUADRATIC RECIPROCITY ANGELICA WONG Abstract. We discuss number theory with the ultimate xi yp-i . It suffices to show that each term of the expansion Date: August 11, 2008. 1 #12;2 ANGELICA
Flutter suppression digital control law design and testing for the AFW wind tunnel model
NASA Technical Reports Server (NTRS)
Mukhopadhyay, Vivek
1994-01-01
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.
Flutter suppression digital control law design and testing for the AFW wind-tunnel model
NASA Technical Reports Server (NTRS)
Mukhopadhyay, Vivek
1992-01-01
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.
Optimal power flow using sequential quadratic programming
NASA Astrophysics Data System (ADS)
Nejdawi, Imad M.
1999-11-01
Optimal power flow (OPF) is an operational as well as a planning tool used by electric utilities to help them operate their network in the most economic and secure mode of operation. Various algorithms to solve the OPF problem evolved over the past three decades; linear programming (LP) techniques were among the major mathematical programming methods utilized. The linear models of the objective function and the linearization of the constraints are the main features of these techniques. The main advantages of the LP approach are simplicity and speed. Nonlinear programming techniques have been applied to OPF solution. The major drawback is the expensive solution of large sparse systems of equations. This research is concerned with the development of a new OPF solution algorithm using sequential quadratic programming (SQP). In this formulation, a small dense system the size of which is equal to the number of control variables is solved in an inner loop. The Jacobian and Hessian terms are calculated in an outer loop. The total number of outer loop iterations is comparable to those in an ordinary load flow in contrast to 20--30 iterations in other nonlinear methods. In addition, the total number of floating point operations is less than that encountered in direct methods by two orders of magnitude. We also model dispatch over a twenty four-hour time horizon in a transmission constrained power network that includes price-responsive loads where large energy customers can operate their loads in time intervals with lowest spot prices.
Atmospheric Dispersion: Gaussian Models
Mihalis Lazaridis
\\u000a A mathematical description of the concentration profile of different chemical compounds in the atmosphere is one of the applications\\u000a of atmospheric models. The problem which one has to solve is to calculate the spatial and temporal concentration of air pollutants\\u000a under specific emission conditions.In Chap. 6 the dispersion of air pollutants is examined with the analytical Gaussian approach.\\u000a The Euler
The Factorability of Quadratics: Motivation for More Techniques
ERIC Educational Resources Information Center
Bosse, Michael J.; Nandakumar, N. R.
2005-01-01
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,…
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
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.
Interconversion of pure Gaussian states requiring non-Gaussian operations
NASA Astrophysics Data System (ADS)
Jabbour, Michael G.; García-Patrón, Raúl; Cerf, Nicolas J.
2015-01-01
We analyze the conditions under which local operations and classical communication enable entanglement transformations between bipartite pure Gaussian states. A set of necessary and sufficient conditions had been found [G. Giedke et al., Quant. Inf. Comput. 3, 211 (2003)] for the interconversion between such states that is restricted to Gaussian local operations and classical communication. Here, we exploit majorization theory in order to derive more general (sufficient) conditions for the interconversion between bipartite pure Gaussian states that goes beyond Gaussian local operations. While our technique is applicable to an arbitrary number of modes for each party, it allows us to exhibit surprisingly simple examples of 2 ×2 Gaussian states that necessarily require non-Gaussian local operations to be transformed into each other.
Key distillation from Gaussian states by Gaussian operations
M. Navascues; J. Bae; J. I. Cirac; M. Lewenstein; A. Sanpera; A. Acin
2004-05-20
We study the secrecy properties of Gaussian states under Gaussian operations. Although such operations are useless for quantum distillation, we prove that it is possible to distill a secret key secure against any attack from sufficiently entangled Gaussian states with non-positive partial transposition. Moreover, all such states allow for key distillation, when Eve is assumed to perform finite-size coherent attacks before the reconciliation process.
Matsubara, Takahiko [Department of Physics, Nagoya University, Chikusa, Nagoya, 464-8602 (Japan)
2010-04-15
Analytic formulas of Minkowski functionals in two-dimensional random fields are derived, including effects of second-order non-Gaussianity in the presence of both the bispectrum and trispectrum. The set of formulas provides a promising method to constrain the primordial non-Gaussianity of the universe by temperature fluctuations in the cosmic microwave background radiation. In a case of local-type non-Gaussianity, the Minkowski functionals are analytically given by powers of quadratic and cubic parameters, f{sub NL} and g{sub NL} (and {tau}{sub NL}). Our formulas are not restricted to this particular model, and applicable to a wide class of non-Gaussian models. The analytic formulas are compared to numerical evaluations from non-Gaussian realizations of temperature maps, showing very good agreement.
Integrated structure/control law design by multilevel optimization
NASA Technical Reports Server (NTRS)
Gilbert, Michael G.; Schmidt, David K.
1989-01-01
A new approach to integrated structure/control law design based on multilevel optimization is presented. This new approach is applicable to aircraft and spacecraft and allows for the independent design of the structure and control law. Integration of the designs is achieved through use of an upper level coordination problem formulation within the multilevel optimization framework. The method requires the use of structure and control law design sensitivity information. A general multilevel structure/control law design problem formulation is given, and the use of Linear Quadratic Gaussian (LQG) control law design and design sensitivity methods within the formulation is illustrated. Results of three simple integrated structure/control law design examples are presented. These results show the capability of structure and control law design tradeoffs to improve controlled system performance within the multilevel approach.
An optimal projection controller for an experimental truss structure
Peterson, L.D.
1989-01-01
An Optimal Projection reduced order controller is designed and implemented on an experimental controlled structure testbed. Twenty modes of the test structure lie within the controller bandwidth. Four strain sensor signals are fed back through an eighteenth order dynamic controller into four stress actuators (not collocated with the sensors) to reduce the vibration of the structure. Five independent performance measures are simultaneously minimized with an Optimal Projection controller derived from a 58th order state space model. The controller reduces the RMS vibration response by up to 65% without saturating the actuators and without destabilizing high frequency modes. The Optimal Projection controller always performs better than a sub-optimal controller based on ordinary Linear Quadratic Gaussian theory. The homotopy algorithm used to solve the Optimal Projection synthesis equations is described, and both analytical and experimental results are presented. 26 refs., 6 figs., 5 tabs.
Truncated Gaussians as tolerance sets
NASA Technical Reports Server (NTRS)
Cozman, Fabio; Krotkov, Eric
1994-01-01
This work focuses on the use of truncated Gaussian distributions as models for bounded data measurements that are constrained to appear between fixed limits. The authors prove that the truncated Gaussian can be viewed as a maximum entropy distribution for truncated bounded data, when mean and covariance are given. The characteristic function for the truncated Gaussian is presented; from this, algorithms are derived for calculation of mean, variance, summation, application of Bayes rule and filtering with truncated Gaussians. As an example of the power of their methods, a derivation of the disparity constraint (used in computer vision) from their models is described. The authors' approach complements results in Statistics, but their proposal is not only to use the truncated Gaussian as a model for selected data; they propose to model measurements as fundamentally in terms of truncated Gaussians.
Users manual for flight control design programs
NASA Technical Reports Server (NTRS)
Nalbandian, J. Y.
1975-01-01
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.
Martin, Kimball
7 Quadratic forms in n variables In order to understand quadratic forms in n variables over Z, one is let to study quadratic forms over various rings and fields such as Q, Qp, R and Zp. This is consistent equation in Z, it is useful study the equation over other rings. Definition 7.0.8. Let R be a ring
Fast Approximate Quadratic Programming for Graph Matching
Vogelstein, Joshua T.; Conroy, John M.; Lyzinski, Vince; Podrazik, Louis J.; Kratzer, Steven G.; Harley, Eric T.; Fishkind, Donniell E.; Vogelstein, R. Jacob; Priebe, Carey E.
2015-01-01
Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance. PMID:25886624
The Halo Bispectrum in N-body Simulations with non-Gaussian Initial Conditions
Sefusatti, Emiliano; Desjacques, Vincent
2011-01-01
We present measurements of the bispectrum of dark matter halos in numerical simulations with non-Gaussian initial conditions of the local type. We show, in the first place, that the overall effect of primordial non-Gaussianity on the halo bispectrum is larger than on the halo power spectrum when all measurable configurations are taken into account. We then compare our measurements with a tree-level perturbative prediction finding good agreement at large scale when the constant Gaussian bias parameter, both linear and quadratic, and their constant non-Gaussian corrections are fitted for. The best-fit values of the Gaussian bias factors and their non-Gaussian, scale-independent corrections are in qualitative agreement with the peak-background split expectations. In particular, we show that the effect of non-Gaussian initial conditions on squeezed configurations is fairly large (up to 30% for f_NL=100 at redshift z=0.5) and results from contributions of similar amplitude induced by the initial matter bispectrum,...
Instabilities of quadratic band crossing points
NASA Astrophysics Data System (ADS)
Uebelacker, Stefan; Honerkamp, Carsten
2011-03-01
The variation of the orbital composition of bands around band crossing points near the Fermi level can generate interesting effects. In particular, rather simple interactions can give rise to the spontaneous formation of topological insulating phases (S. Raghu et al., Phys. Rev. Lett. 100, 156401 (2008)). In contrast with Dirac points, quadratic band crossing points offer the advantage of a nonzero density of states at the crossing point, and instabilities occur already at small interaction strengths. Here, we present results of functional renormalization group calculations for models with a quadratic band crossing point and discuss the possibilities for nontrivial insulating phases induced by local interactions.
Non-Gaussian quantum states generation and robust quantum non-Gaussianity via squeezing field
NASA Astrophysics Data System (ADS)
Tang, Xu-Bing; Gao, Fang; Wang, Yao-Xiong; Kuang, Sen; Shuang, Feng
2015-03-01
Recent studies show that quantum non-Gaussian states or using non-Gaussian operations can improve entanglement distillation, quantum swapping, teleportation, and cloning. In this work, employing a strategy of non-Gaussian operations (namely subtracting and adding a single photon), we propose a scheme to generate non-Gaussian quantum states named single-photon-added and -subtracted coherent (SPASC) superposition states by implementing Bell measurements, and then investigate the corresponding nonclassical features. By squeezed the input field, we demonstrate that robustness of non-Gaussianity can be improved. Controllable phase space distribution offers the possibility to approximately generate a displaced coherent superposition states (DCSS). The fidelity can reach up to F ? 0.98 and F ? 0.90 for size of amplitude z = 1.53 and 2.36, respectively. Project supported by the National Natural Science Foundation of China (Grant Nos. 61203061 and 61074052), the Outstanding Young Talent Foundation of Anhui Province, China (Grant No. 2012SQRL040), and the Natural Science Foundation of Anhui Province, China (Grant No. KJ2012Z035).
On Exponential Hedging and Related Quadratic Backward Stochastic Differential Equations
Sekine, Jun [Institute of Economic Research, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501 (Japan)], E-mail: sekine@kier.kyoto-u.ac.jp
2006-09-15
The dual optimization problem for the exponential hedging problem is addressed with a cone constraint. Without boundedness conditions on the terminal payoff and the drift of the Ito-type controlled process, the backward stochastic differential equation, which has a quadratic growth term in the drift, is derived as a necessary and sufficient condition for optimality via a variational method and dynamic programming. Further, solvable situations are given, in which the value and the optimizer are expressed in closed forms with the help of the Clark-Haussmann-Ocone formula.
Przybytek, Michal; Helgaker, Trygve
2013-08-01
We analyze the accuracy of the Coulomb energy calculated using the Gaussian-and-finite-element-Coulomb (GFC) method. In this approach, the electrostatic potential associated with the molecular electronic density is obtained by solving the Poisson equation and then used to calculate matrix elements of the Coulomb operator. The molecular electrostatic potential is expanded in a mixed Gaussian-finite-element (GF) basis set consisting of Gaussian functions of s symmetry centered on the nuclei (with exponents obtained from a full optimization of the atomic potentials generated by the atomic densities from symmetry-averaged restricted open-shell Hartree-Fock theory) and shape functions defined on uniform finite elements. The quality of the GF basis is controlled by means of a small set of parameters; for a given width of the finite elements d, the highest accuracy is achieved at smallest computational cost when tricubic (n = 3) elements are used in combination with two (?(H) = 2) and eight (?(1st) = 8) Gaussians on hydrogen and first-row atoms, respectively, with exponents greater than a given threshold (?min (G)=0.5). The error in the calculated Coulomb energy divided by the number of atoms in the system depends on the system type but is independent of the system size or the orbital basis set, vanishing approximately like d(4) with decreasing d. If the boundary conditions for the Poisson equation are calculated in an approximate way, the GFC method may lose its variational character when the finite elements are too small; with larger elements, it is less sensitive to inaccuracies in the boundary values. As it is possible to obtain accurate boundary conditions in linear time, the overall scaling of the GFC method for large systems is governed by another computational step-namely, the generation of the three-center overlap integrals with three Gaussian orbitals. The most unfavorable (nearly quadratic) scaling is observed for compact, truly three-dimensional systems; however, this scaling can be reduced to linear by introducing more effective techniques for recognizing significant three-center overlap distributions. PMID:23927250
NASA Astrophysics Data System (ADS)
Przybytek, Michal; Helgaker, Trygve
2013-08-01
We analyze the accuracy of the Coulomb energy calculated using the Gaussian-and-finite-element-Coulomb (GFC) method. In this approach, the electrostatic potential associated with the molecular electronic density is obtained by solving the Poisson equation and then used to calculate matrix elements of the Coulomb operator. The molecular electrostatic potential is expanded in a mixed Gaussian-finite-element (GF) basis set consisting of Gaussian functions of s symmetry centered on the nuclei (with exponents obtained from a full optimization of the atomic potentials generated by the atomic densities from symmetry-averaged restricted open-shell Hartree-Fock theory) and shape functions defined on uniform finite elements. The quality of the GF basis is controlled by means of a small set of parameters; for a given width of the finite elements d, the highest accuracy is achieved at smallest computational cost when tricubic (n = 3) elements are used in combination with two (?H = 2) and eight (?1st = 8) Gaussians on hydrogen and first-row atoms, respectively, with exponents greater than a given threshold (? _min^G=0.5). The error in the calculated Coulomb energy divided by the number of atoms in the system depends on the system type but is independent of the system size or the orbital basis set, vanishing approximately like 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.
Clustering Based on Gaussian Processes
Hyun-chul Kim; Jaewook Lee
2007-01-01
In this letter, we develop a gaussian process model for clustering. The variances of predictive values in gaussian processes learned from a training data are shown to comprise an estimate of the support of a probability density function. The constructed variance function is then applied to construct a set of contours that enclose the data points, which correspond to cluster
Cyclotomic Matrices over Quadratic Integer Rings
Sheldon, Nathan D.
Cyclotomic Matrices over Quadratic Integer Rings Gary Greaves Thesis submitted to the University's problem is usually stated in terms of a geometric constraint on the zeros of polynomials having integer integer symmetric matrix A we define its associated polynomial as RA(z) := zn A(z + 1/z). A Hermitian
Copositivity and constrained fractional quadratic problems
2011-11-16
The lower bounds based on this technique can be favorably com- pared with bounds ... pendent term, then this problem can be formulated as a fractional quadratic program ...... as a similar rational grid will contain an exponential in n number of points, if, e.g., T .... Furthermore, by Euler's homogeneity theorem,. 0=¯
Integration of the Quadratic Function and Generalization
ERIC Educational Resources Information Center
Mitsuma, Kunio
2011-01-01
We will first recall useful formulas in integration that simplify the calculation of certain definite integrals with the quadratic function. A main formula relies only on the coefficients of the function. We will then explore a geometric proof of one of these formulas. Finally, we will extend the formulas to more general cases. (Contains 3…
Factoring pq2 with Quadratic Forms
Nguyen, Phong Q.
is exactly the case for the so-called NICE family of public-key cryptosystems based on quadratic fields [OU98], Takagi's fast RSA variants [Tak98], and the large family (surveyed in [BTV04 s with s squarefree) is a classical problem in algorithmic number theory (cf. [AM94]), because it is polynomial
Factoring pq2 with Quadratic Forms
Boyer, Edmond
is exactly the case for the so-called NICE family of public-key cryptosystems based on quadratic fields [OU98], Takagi's fast RSA variants [Tak98], and the large family (surveyed in [BTV04 (cf. [AM94]), because it is polynomial-time equivalent to determining the ring of integers of a number
Instabilities of quadratic band crossing points
Stefan Uebelacker; Carsten Honerkamp
2011-01-01
The variation of the orbital composition of bands around band crossing points near the Fermi level can generate interesting effects. In particular, rather simple interactions can give rise to the spontaneous formation of topological insulating phases (S. Raghu et al., Phys. Rev. Lett. 100, 156401 (2008)). In contrast with Dirac points, quadratic band crossing points offer the advantage of a
Fuzzy quadratic minimum spanning tree problem
Lu, Mei
Fuzzy quadratic minimum spanning tree problem Jinwu Gao *, Mei Lu Department of Mathematical the effectiveness of the genetic algorithm. Ã? 2004 Published by Elsevier Inc. Keywords: Minimum spanning tree; Fuzzy programming; Genetic algorithm; Credibility measure 1. Introduction The minimum spanning tree (MST) problem
1 Splitting Patterns of Excellent Quadratic Forms
Rehmann, Ulf
is infinite or a power of 2, an* *d that fields exist having a prescribed power of 2 as its level (cf. 3 that a generic splitting fie* *ld of such an algebra D splits precisely those division algebras which represent * * 2 which occur for the quadratic forms qL := q L with L running through all fie* *ld extensions
ESSENTIAL DIMENSION, SPINOR GROUPS, AND QUADRATIC FORMS
Brosnan, Patrick
. Fakhruddin for helpful correspondence. 2. Essential dimension Let k be a field. We will write Fieldsk write ed G for ed FG and ed(G; p) for ed(FG; p). Essential dimension was originally introducedESSENTIAL DIMENSION, SPINOR GROUPS, AND QUADRATIC FORMS PATRICK BROSNAN , ZINOVY REICHSTEIN
ESSENTIAL DIMENSION, SPINOR GROUPS, AND QUADRATIC FORMS
ESSENTIAL DIMENSION, SPINOR GROUPS, AND QUADRATIC FORMS PATRICK BROSNAN + , ZINOVY REICHSTEIN + , AND ANGELO VISTOLI # Abstract. We prove that the essential dimension of the spinor group Spin n grows of classes of evenÂdimensional forms in W(K); cf. [Lam73]. By abuse of notation, we will write q # I a (K
EFFICIENT AND CHEAP BOUNDS FOR (STANDARD) QUADRATIC ...
2005-07-08
The main tools employed in the conception and analysis of most bounds are ... objective function into a sum of two quadratic functions, each of which is easy to minimize. ...... Now let us take a fresh look at vertex optimality. As before, we start.
A Practical Approach to Quadratic Equations.
ERIC Educational Resources Information Center
Light, Peter
1983-01-01
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)
On quadratic integral equation of fractional orders
Mohamed Abdalla Darwish
2005-01-01
We present an existence theorem for a nonlinear quadratic integral equations of fractional orders, arising in the queuing theory and biology, in the Banach space of real functions defined and continuous on a bounded and closed interval. The concept of measure of noncompactness and a fixed point theorem due to Darbo are the main tool in carrying out our proof.
Block Ciphers and Systems of Quadratic Equations
Alex Biryukov; Christophe De Cannière
2003-01-01
In this paper we compare systems of multivariate poly- nomials, which completely define the block ciphers Khazad, Misty1, Kasumi, Camellia, Rijndael and Serpent in the view of a potential danger of an algebraic re-linearization attack. Keywords: Block ciphers, multivariate quadratic equations, lineariza- tion, Khazad, Misty, Camellia, Rijndael, Serpent.
Quadratic equations and monodromy evolving deformations
Yousuke Ohyama
2007-09-28
We give a basic theory on monodromy evolving deformations. proposed by Chakravarty and Ablowitz in 1996. We show that Halphen's second quadratic system can be described by monodromy evolving deformations. Our result is a generalization of the work on the DH-V system by Chakravarty and Ablowitz.
Solving Underdefined Systems of Multivariate Quadratic Equations
Nicolas Courtois; Louis Goubin; Willi Meier; Jean-daniel Tacier
2002-01-01
The security of several recent digital signature schemes is based on the difficulty of solving large systems of quadratic multivariate polynomial equations over a finite field F. This problem, sometimes called MQ, is known to be NP-hard. When the number m of equations is equal to the number n of variables, and if n< 15, Grobner base algorithms have been
Quadratic trend analysis and heartbeat detection
Stefan Wiens; Stephen N. Palmer
2001-01-01
In heartbeat detection tasks based on the Method of Constant Stimuli (MCS), subjects judge the simultaneity between their heartbeats and stimuli presented at six intervals ranging from 0 to 500 ms after the R-waves on an electrocardiogram. Because research suggests that subjects do not perceive stimuli at 0 or 500 ms as simultaneous, individual performance was indexed with quadratic trend
Decision making with fuzzy quadratic programming
W. Cui; D. I. Blockley
1990-01-01
Decision making in civil engineering systems necessarily involves imprecise data. Fuzzy linear programming (FLP) has been used to deal with imprecision in parameter definitions. In this paper, it is argued that present methods of FLP can be improved upon by using a new method of fuzzy quadratic programming (FQP) which enables the modelling of independent fuzzy parameters. Several numerical examples
Theory of the Quadratic Zeeman Effect
L. I. Schiff; H. Snyder
1939-01-01
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
Semiclassical mechanics of the quadratic Zeeman effect
Kristin D. Krantzman; John A. Milligan; D. Farrelly
1992-01-01
A comprehensive approach to semiclassical quantization of the quadratic Zeeman effect in the hydrogen atom (QZE) is presented which utilizes the connection between the Kepler system and the four-dimensional harmonic oscillator. Past attempts to quantize the QZE have encountered problems associated with singularities arising because of a classical separatrix. Here, a uniform semiclassical quantization scheme that passes smoothly through the
EMBEDDABILITY OF QUADRATIC FORMS IN PFISTER FORMS
Âembeddable over F (resp. over an extension of F ; resp. over a purely transcendental extension of F ). We study transcendental extension of the field F . As an application, we show that for certain ``generic'' quadratic forms transcendental, and anisotropic forms stay anisotropic over purely transcendental extensions, hence W (F (#)/F
Curious Consequences of a Miscopied Quadratic
ERIC Educational Resources Information Center
Poet, Jeffrey L.; Vestal, Donald L., Jr.
2005-01-01
The starting point of this article is a search for pairs of quadratic polynomials x[superscript 2] + bx plus or minus c with the property that they both factor over the integers. The search leads quickly to some number theory in the form of primitive Pythagorean triples, and this paper develops the connection between these two topics.
Class numbers of complex quadratic fields
Ezra Brown
1974-01-01
Congruence conditions on the class numbers of complex quadratic fields have recently been studied by various investigators, including Barrucand and Cohn, Hasse, and the author. In this paper, we study the class number of Q([radical sign] - pq), where p [reverse not equivalent] q (mod 4) are distinct primes.
Energy definition for quadratic curvature gravities
Ahmet Baykal
2012-12-03
A conserved current for generic quadratic curvature gravitational models is defined, and it is shown that, at the linearized level, it corresponds to the Deser-Tekin charges. An explicit expression for the charge for new massive gravity in three dimensions is given. Some implications of the linearized equations are discussed.
Quantification of gaussian quantum steering.
Kogias, Ioannis; Lee, Antony R; Ragy, Sammy; Adesso, Gerardo
2015-02-13
Einstein-Podolsky-Rosen steering incarnates a useful nonclassical correlation which sits 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 Peres' conjecture holds in its stronger form within the fully Gaussian regime: namely, steering bound entangled Gaussian states by Gaussian measurements is impossible. PMID:25723193
Quantification of Gaussian Quantum Steering
NASA Astrophysics Data System (ADS)
Kogias, Ioannis; Lee, Antony R.; Ragy, Sammy; Adesso, Gerardo
2015-02-01
Einstein-Podolsky-Rosen steering incarnates a useful nonclassical correlation which sits 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 Peres' conjecture holds in its stronger form within the fully Gaussian regime: namely, steering bound entangled Gaussian states by Gaussian measurements is impossible.
Geometry of Gaussian quantum states
Valentin Link; Walter T. Strunz
2015-03-09
We study the Hilbert-Schmidt measure on the manifold of mixed Gaussian states in multi mode continuous variable quantum systems. An analytical expression for the Hilbert-Schmidt volume element is derived. Its corresponding probability measure can be used to study typical properties of Gaussian states. It turns out that although the manifold of Gaussian states is unbounded, an ensemble of Gaussian states distributed according to this measure still has a normalizable distribution of symplectic eigenvalues, from which unitarily invariant properties can be obtained. By contrast, we find that for an ensemble of one-mode Gaussian states based on the Bures measure the corresponding distribution cannot be normalized. As important applications, we determine the distribution and the mean value of von Neumann entropy and purity for the Hilbert-Schmidt measure.
Geometric Approaches to Quadratic Equations from Other Times and Places.
ERIC Educational Resources Information Center
Allaire, Patricia R.; Bradley, Robert E.
2001-01-01
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)
Antonio S. de Castro
2003-11-10
The Dirac equation is exactly solved for a pseudoscalar linear plus Coulomb-like potential in a two-dimensional world. This sort of potential gives rise to an effective quadratic plus inversely quadratic potential in a Sturm-Liouville problem, regardless the sign of the parameter of the linear potential, in sharp contrast with the Schroedinger case. The generalized Dirac oscillator already analyzed in a previous work is obtained as a particular case.
Overview of computational control research at UT Austin
NASA Technical Reports Server (NTRS)
Bong, Wie
1989-01-01
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.
Iterative LQG Controller Design Through Closed-Loop Identification
NASA Technical Reports Server (NTRS)
Hsiao, Min-Hung; Huang, Jen-Kuang; Cox, David E.
1996-01-01
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.
Robust linear quadratic designs with respect to parameter uncertainty
NASA Technical Reports Server (NTRS)
Douglas, Joel; Athans, Michael
1992-01-01
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.
Linear and quadratic time-frequency signal representations
F. Hlawatsch; G. F. Boudreaux-Bartels
1992-01-01
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
A Quadratic Gradient Equation for pricing Mortgage-Backed Securities
Monneau, RÃ©gis
A Quadratic Gradient Equation for pricing Mortgage-Backed Securities Marco Papi Institute for Applied Computing - CNR Rome (Italy) A Quadratic Gradient Equation for pricing Mortgage-Backed Securities call option on a corresponding fixed-rate bond. A Quadratic Gradient Equation for pricing Mortgage
THE EFFECTIVENESS OF QUADRATS FOR MEASURING VASCULAR PLANT DIVERSITY
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...
Ruban, V P
2015-01-01
The nonlinear dynamics of an obliquely oriented wave packet at sea surface is studied both analytically and numerically for various initial parameters of the packet, in connection with the problem of oceanic rogue waves. In the framework of Gaussian variational ansatz applied to the corresponding (1+2D) hyperbolic nonlinear Schr\\"odinger equation, a simplified Lagrangian system of differential equations is derived, which determines the evolution of coefficients of the real and imaginary quadratic forms appearing in the Gaussian. This model provides a semi-quantitative description for the process of nonlinear spatio-temporal focusing, which is one of the most probable mechanisms of rogue wave formation in random wave fields. The system is integrated in quadratures, which fact allows us to understand qualitative differences between the linear and nonlinear regimes of the focusing of wave packet. Comparison of the Gaussian model predictions with results of direct numerical simulation of fully nonlinear long-cres...
NASA Technical Reports Server (NTRS)
Cheng, Joseph K.; Ianculescu, George D.; Kenney, Charles S.; Laub, Alan J.; Ly, Jason H. Q.; Papadopoulos, Philip M.
1992-01-01
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.
Some results on Gaussian mixtures
NASA Astrophysics Data System (ADS)
Felgueiras, Miguel; Santos, Rui; Martins, João Paulo
2014-10-01
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.
Higgsed Stueckelberg vector and Higgs quadratic divergence
NASA Astrophysics Data System (ADS)
Demir, Durmu? Ali; Karahan, Canan Nurhan; Korutlu, Beste
2015-01-01
Here we show that, a hidden vector field whose gauge invariance is ensured by a Stueckelberg scalar and whose mass is spontaneously generated by the Standard Model Higgs field contributes to quadratic divergences in the Higgs boson mass squared, and even leads to its cancellation at one-loop when Higgs coupling to gauge field is fine-tuned. In contrast to mechanisms based on hidden scalars where a complete cancellation cannot be achieved, stabilization here is complete in that the hidden vector and the accompanying Stueckelberg scalar are both free from quadratic divergences at one-loop. This stability, deriving from hidden exact gauge invariance, can have important implications for modeling dark phenomena like dark matter, dark energy, dark photon and neutrino masses. The hidden fields can be produced at the LHC.
Stellar objects in the quadratic regime
P. Mafa Takisa; S. D. Maharaj; Subharthi Ray
2014-12-28
We model a charged anisotropic relativistic star with a quadratic equation of state. Physical features of an exact solution of the Einstein-Maxwell system are studied by incorporating the effect of the nonlinear term from the equation of state. It is possible to regain the masses, radii and central densities for a linear equation of state in our analysis. We generate masses for stellar compact objects and perform a detailed study of PSR J1614-2230 in particular. We also show the influence of the nonlinear equation of state on physical features of the matter distribution. We demonstrate that it is possible to incorporate the effects of charge, anisotropy and a quadratic term in the equation of state in modelling a compact relativistic body.
Coherent States of Systems with Quadratic Hamiltonians
NASA Astrophysics Data System (ADS)
Bagrov, V. G.; Gitman, D. M.; Pereira, A. S.
2015-03-01
Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schrödinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency.
Regular models with quadratic equation of state
S. D. Maharaj; P. Mafa Takisa
2013-01-08
We provide new exact solutions to the Einstein-Maxwell system of equations which are physically reasonable. The spacetime is static and spherically symmetric with a charged matter distribution. We utilise an equation of state which is quadratic relating the radial pressure to the energy density. Earlier models, with linear and quadratic equations of state, are shown to be contained in our general class of solutions. The new solutions to the Einstein-Maxwell are found in terms of elementary functions. A physical analysis of the matter and electromagnetic variables indicates that the model is well behaved and regular. In particular there is no singularity in the proper charge density at the stellar centre unlike earlier anisotropic models in the presence of the electromagnetic field.
Stellar objects in the quadratic regime
NASA Astrophysics Data System (ADS)
Mafa Takisa, P.; Maharaj, S. D.; Ray, Subharthi
2014-12-01
We model a charged anisotropic relativistic star with a quadratic equation of state. Physical features of an exact solution of the Einstein-Maxwell system are studied by incorporating the effect of the nonlinear term from the equation of state. It is possible to regain the masses, radii and central densities for a linear equation of state in our analysis. We generate masses for stellar compact objects and perform a detailed study of PSR J1614-2230 in particular. We also show the influence of the nonlinear equation of state on physical features of the matter distribution. We demonstrate that it is possible to incorporate the effects of charge, anisotropy and a quadratic term in the equation of state in modelling a compact relativistic body.
Linear and quadratic sufficiency and commutativity
NASA Astrophysics Data System (ADS)
Ferreira, Sandra S.; Ferreira, Dário; Nunes, Célia
2012-09-01
Given a mixed model let T be the orthogonal projection matrix on the range space spanned by the mean vector. If the model has variance-covariance matrix ?2V we use commutative Jordan algebras to show that Ty is both linear sufficient and linear complete and that Ty, y'V+y with V+ the Moore-Penrose inverse of V is quadratic sufficient whenever T and V commute.
Instabilities of quadratic band crossing points
Stefan Uebelacker; Carsten Honerkamp
2011-01-01
Using a functional renormalization-group approach, we study interaction-driven instabilities in quadratic band crossing point two-orbital models in two dimensions, extending a previous study of Sun [Phys. Rev. Lett.PRLTAO0031-900710.1103\\/PhysRevLett.103.046811 103, 046811 (2009)]. The wave-vector dependence of the Bloch eigenvectors of the free Hamiltonian causes interesting instabilities toward spin-nematic, quantum anomalous Hall, and quantum spin Hall states. In contrast with other known
Numerical analysis of a quadratic matrix equation
NICHOLAS J. HIGHAM; HYUN-MIN KIM
1999-01-01
The quadratic matrix equation AX2+BX +C = 0 in n \\\\Theta n matrices arises inapplications and is of intrinsic interest as one of the simplest nonlinear matrix equations.We give a complete characterization of solutions in terms of the generalizedSchur decomposition and describe and compare various numerical solution techniques.In particular, we give a thorough treatment of functional iteration methodsbased on Bernoulli's
Monotone and convex quadratic spline interpolation
NASA Technical Reports Server (NTRS)
Lam, Maria H.
1990-01-01
A method for producing interpolants that preserve the monotonicity and convexity of discrete data is described. It utilizes the quadratic spline proposed by Schumaker (1983) which was subsequently characterized by De Vore and Yan (1986). The selection of first order derivatives at the given data points is essential to this spline. An observation made by De Vore and Yan is generalized, and an improved method to select these derivatives is proposed. The resulting spline is completely local, efficient, and simple to implement.
Characterization of a Quadratic Function in Rn
ERIC Educational Resources Information Center
Xu, Conway
2010-01-01
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.
NASA Technical Reports Server (NTRS)
Fleming, P.
1983-01-01
A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a nonlinear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer. One concerns helicopter longitudinal dynamics and the other the flight dynamics of an aerodynamically unstable aircraft.
Generation of Knot Net for Calculation of Quadratic Triangular B-spline Surface of Human Head
NASA Astrophysics Data System (ADS)
Mihalík, Ján
2011-09-01
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.
Li, Yong; Wang, Xiufeng; Lin, Jing; Shi, Shengyu
2014-01-01
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
Gaussian modeling of contaminant plumes
Blackwelder, L.S.; Smoot, J.L. [Univ. of Tennessee, Knoxville, TN (United States). Dept. of Civil and Environmental Engineering
1995-11-01
The Gaussian plume model is based on the concept that a groundwater contaminant plume in a homogeneous medium can be modeled by a combination of discrete releases from a point source. Each of the instantaneous releases is represented by a three-dimensional Gaussian distribution modified to reflect processes encountered in groundwater contaminant transport, such as dispersion, retardation and decay. The Gaussian plume model provides the same problem-solving capability provided by analytical solutions but with less mathematical complexity and computational requirements. In addition, the Gaussian plume model offers solutions not readily available through analytical solutions because the basic discrete components are independent of the temporal and spatial characteristics of the source to be modeled.
Constrained quadratic correlation filters for target detection.
Muise, Robert; Mahalanobis, Abhijit; Mohapatra, Ram; Li, Xin; Han, Deguang; Mikhael, Wasfy
2004-01-10
A method for designing and implementing quadratic correlation filters (QCFs) for shift-invariant target detection in imagery is presented. The QCFs are quadratic classifiers that operate directly on the image data without feature extraction or segmentation. In this sense the QCFs retain the main advantages of conventional linear correlation filters while offering significant improvements in other respects. Not only is more processing required for detection of peaks in the outputs of multiple linear filters but choosing the most suitable among them is an error-prone task. All channels in a QCF work together to optimize the same performance metric and to produce a combined output that leads to considerable simplification of the postprocessing scheme. The QCFs that are developed involve hard constraints on the output of the filter. Inasmuch as this design methodology is indicative of the synthetic discriminant function (SDF) approach for linear filters, the filters that we develop here are referred to as quadratic SDFs (QSDFs). Two methods for designing QSDFs are presented, an efficient architecture for achieving them is discussed, and results from the Moving and Stationary Target Acquisition and Recognition synthetic aperture radar data set are presented. PMID:14735950
Quadratic Gabor filters for object detection.
Weber, D M; Casasent, D P
2001-01-01
We present a new class of quadratic filters that are capable of creating spherical, elliptical, hyperbolic and linear decision surfaces which result in better detection and classification capabilities than the linear decision surfaces obtained from correlation filters. Each filter comprises of a number of separately designed linear basis filters. These filters are linearly combined into several macro filters; the output from these macro filters are passed through a magnitude square operation and are then linearly combined using real weights to achieve the quadratic decision surface. For detection, the creation of macro filters (linear combinations of multiple single filters) allows for a substantial computational saving by reducing the number of correlation operations required. In this work, we consider the use of Gabor basis filters; the Gabor filter parameters are separately optimized. The fusion parameters to combine the Gabor filter outputs are optimized using an extended piecewise quadratic neural network (E-PQNN). We demonstrate methods for selecting the number of macro Gabor filters, the filter parameters and the linear and nonlinear combination coefficients. We present preliminary results obtained for an infrared (IR) vehicle detection problem. PMID:18249613
Predicting the Size of Spring Network Swarm in Quadratic Potential Fields
Choset, Howie
of multiple autonomous agents or a swarm of robots have become popular in robotics. Formation control a swarm of robots) have received a lot of attention due to re- cent advances in wireless communicationPredicting the Size of Spring Network Swarm in Quadratic Potential Fields Hyungpil Moon, Howie
Reduced rank space-time adaptive processing with quadratic pattern constraints for airborne radar
Kristine L. Bell; Kathleen E. Wage
2003-01-01
Reduced rank (RR) linearly constrained minimum variance (LCMV) adaptive beamforming with quadratic pattern constraints (QPC) is applied to space-time adaptive processing (STAP) for airborne radar. The problem is formulated for general rank reducing transformations and main beam and sidelobe pattern control is achieved by imposing a set of inequality constraints on the mean-square error between the adaptive pattern and a
Gaussian Filters for Nonlinear Filtering Problems
Kazufumi Ito; Kaiqi Xiong
1999-01-01
In this paper we develop and analyze real-time and accurate filters for nonlinear filtering problems based on the Gaussian distributions. We present the systematic formulation of Gaussian filters and develop efficient and accurate numerical integration of the optimal filter. We also discuss the mixed Gaussian filters in which the conditional probability density is approximated by the sum of Gaussian distributions.
Gaussian Induced Dipole Polarization Model
ELKING, DENNIS; DARDEN, TOM; WOODS, ROBERT J.
2007-01-01
A new induced dipole polarization model based on interacting Gaussian charge densities is presented. In contrast to the original induced point dipole model, the Gaussian polarization model is capable of finite interactions at short distances. Aspects of convergence related to the Gaussian model will be explored. The Gaussian polarization model is compared with the damped Thole-induced dipole model and the point dipole model. It will be shown that the Gaussian polarization model performs slightly better than the Thole model in terms of fitting to molecular polarizability tensors. An advantage of the model based on Gaussian charge distribution is that it can be easily generalized to other multipole moments and provide effective damping for both permanent electrostatic and polarization models. Finally, a method of parameterizing polarizabilities is presented. This method is based on probing a molecule with point charges and fitting polarizabilities to electrostatic potential. In contrast to the generic atom type polarizabilities fit to molecular polarizability tensors, probed polarizabilities are significantly more accurate in terms of reproducing molecular polarizability tensors and electrostatic potential, while retaining conformational transferability. PMID:17299773
G L Esayan; S G Krivoshlykov
1989-01-01
A method of coherent states is used to describe the process of Rayleigh scattering in a multimode graded-index waveguide with a quadratic refractive-index profile. Explicit expressions are obtained for the coefficients representing excitation of Gaussian–Hermite backscattering modes in two cases of practical importance: excitation of a waveguide by an extended noncoherent light source and selective excitation of different modes at
The halo bispectrum in N-body simulations with non-Gaussian initial conditions
NASA Astrophysics Data System (ADS)
Sefusatti, E.; Crocce, M.; Desjacques, V.
2012-10-01
We present measurements of the bispectrum of dark matter haloes in numerical simulations with non-Gaussian initial conditions of local type. We show, in the first place, that the overall effect of primordial non-Gaussianity on the halo bispectrum is larger than on the halo power spectrum when all measurable configurations are taken into account. We then compare our measurements with a tree-level perturbative prediction, finding good agreement at large scales when the constant Gaussian bias parameter, both linear and quadratic, and their constant non-Gaussian corrections are fitted for. The best-fitting values of the Gaussian bias factors and their non-Gaussian, scale-independent corrections are in qualitative agreement with the peak-background split expectations. In particular, we show that the effect of non-Gaussian initial conditions on squeezed configurations is fairly large (up to 30 per cent for fNL = 100 at redshift z = 0.5) and results from contributions of similar amplitude induced by the initial matter bispectrum, scale-dependent bias corrections as well as from non-linear matter bispectrum corrections. We show, in addition, that effects at second order in fNL are irrelevant for the range of values allowed by cosmic microwave background and galaxy power spectrum measurements, at least on the scales probed by our simulations (k > 0.01 h Mpc-1). Finally, we present a Fisher matrix analysis to assess the possibility of constraining primordial non-Gaussianity with future measurements of the galaxy bispectrum. We find that a survey with a volume of about 10 h-3 Gpc3 at mean redshift z ? 1 could provide an error on fNL of the order of a few. This shows the relevance of a joint analysis of galaxy power spectrum and bispectrum in future redshift surveys.
A High-Authority/Low-Authority Control Strategy for Coupled Aircraft-Style Bays
NASA Technical Reports Server (NTRS)
Schiller, N. H.; Fuller, C. R.; Cabell, R. H.
2006-01-01
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.
Discrete wave propagation in quadratically nonlinear media
NASA Astrophysics Data System (ADS)
Iwanow, Robert
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.
Information geometry of Gaussian channels
Monras, Alex [Dipartimento di Matematica e Informatica, Universita degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (Italy); CNR-INFM Coherentia, Napoli (Italy); CNISM Unita di Salerno (Italy) and INFN Sezione di Napoli, Gruppo collegato di Salerno, Baronissi (Italy); Illuminati, Fabrizio [Dipartimento di Matematica e Informatica, Universita degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (Italy); CNR-INFM Coherentia, Napoli (Italy) and CNISM Unita di Salerno; and INFN Sezione di Napoli, Gruppo collegato di Salerno, Baronissi (Italy); ISI Foundation for Scientific Interchange, Villa Gualino, Viale Settimio Severo 65, I-10133 Torino (Italy)
2010-06-15
We define a local Riemannian metric tensor in the manifold of Gaussian channels and the distance that it induces. We adopt an information-geometric approach and define a metric derived from the Bures-Fisher metric for quantum states. The resulting metric inherits several desirable properties from the Bures-Fisher metric and is operationally motivated by distinguishability considerations: It serves as an upper bound to the attainable quantum Fisher information for the channel parameters using Gaussian states, under generic constraints on the physically available resources. Our approach naturally includes the use of entangled Gaussian probe states. We prove that the metric enjoys some desirable properties like stability and covariance. As a by-product, we also obtain some general results in Gaussian channel estimation that are the continuous-variable analogs of previously known results in finite dimensions. We prove that optimal probe states are always pure and bounded in the number of ancillary modes, even in the presence of constraints on the reduced state input in the channel. This has experimental and computational implications. It limits the complexity of optimal experimental setups for channel estimation and reduces the computational requirements for the evaluation of the metric: Indeed, we construct a converging algorithm for its computation. We provide explicit formulas for computing the multiparametric quantum Fisher information for dissipative channels probed with arbitrary Gaussian states and provide the optimal observables for the estimation of the channel parameters (e.g., bath couplings, squeezing, and temperature).
Information geometry of Gaussian channels
Alex Monras; Fabrizio Illuminati
2010-03-22
We define a local Riemannian metric tensor in the manifold of Gaussian channels and the distance that it induces. We adopt an information-geometric approach and define a metric derived from the Bures-Fisher metric for quantum states. The resulting metric inherits several desirable properties from the Bures-Fisher metric and is operationally motivated from distinguishability considerations: It serves as an upper bound to the attainable quantum Fisher information for the channel parameters using Gaussian states, under generic constraints on the physically available resources. Our approach naturally includes the use of entangled Gaussian probe states. We prove that the metric enjoys some desirable properties like stability and covariance. As a byproduct, we also obtain some general results in Gaussian channel estimation that are the continuous-variable analogs of previously known results in finite dimensions. We prove that optimal probe states are always pure and bounded in the number of ancillary modes, even in the presence of constraints on the reduced state input in the channel. This has experimental and computational implications: It limits the complexity of optimal experimental setups for channel estimation and reduces the computational requirements for the evaluation of the metric: Indeed, we construct a converging algorithm for its computation. We provide explicit formulae for computing the multiparametric quantum Fisher information for dissipative channels probed with arbitrary Gaussian states, and provide the optimal observables for the estimation of the channel parameters (e.g. bath couplings, squeezing, and temperature).
Issues in the digital implementation of control compensators. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Moroney, P.
1979-01-01
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.
Plane torsion waves in quadratic gravitational theories
O. V. Babourova; B. N. Frolov; E. A. Klimova
1998-05-03
The definition of the Riemann-Cartan space of the plane wave type is given. The condition under which the torsion plane waves exist is found. It is expressed in the form of the restriction imposed on the coupling constants of the 10-parametric quadratic gravitational Lagrangian. In the mathematical appendix the formula for commutator of the variation operator and Hodge operator is proved. This formula is applied for the variational procedure when the gravitational field equations are obtained in terms of the exterior differential forms.
A quadratic analog-to-digital converter
NASA Technical Reports Server (NTRS)
Harrison, D. C.; Staples, M. H.
1980-01-01
An analog-to-digital converter with a square root transfer function has been developed for use with a pair of CCD imaging detectors in the White Light Coronagraph/X-ray XUV Telescope experiment to be flown as part of the Internal Solar Polar Mission. It is shown that in background-noise-limited instrumentation systems a quadratic analog-to-digital converter will allow a maximum dynamic range with a fixed number of data bits. Low power dissipation, moderately fast conversion time, and reliability are achieved in the proposed design using standard components and avoiding nonlinear elements.
Semiclassical mechanics of the quadratic Zeeman effect
Krantzman, K.D.; Milligan, J.A. (Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90024-1569 (United States)); Farrelly, D. (Department of Chemistry and Biochemistry, Utah State University, Logan, Utah 84322-0300 (United States))
1992-03-01
A comprehensive approach to semiclassical quantization of the quadratic Zeeman effect in the hydrogen atom (QZE) is presented which utilizes the connection between the Kepler system and the four-dimensional harmonic oscillator. Past attempts to quantize the QZE have encountered problems associated with singularities arising because of a classical separatrix. Here, a uniform semiclassical quantization scheme that passes smoothly through the separatrix is developed using classical perturbation theory. This method accounts for the topologically distinct kinds of dynamics that arise in the QZE, and provides good estimates of tunneling splittings. Extension to the quantization of arbitrarily-high-order classical perturbation expansions is straightforward.
Quadratic finite elements and incompressible viscous flows.
Dohrmann, Clark R.; Gartling, David K.
2005-01-01
Pressure stabilization methods are applied to higher-order velocity finite elements for application to viscous incompressible flows. Both a standard pressure stabilizing Petrov-Galerkin (PSPG) method and a new polynomial pressure projection stabilization (PPPS) method have been implemented and tested for various quadratic elements in two dimensions. A preconditioner based on relaxing the incompressibility constraint is also tested for the iterative solution of saddle point problems arising from mixed Galerkin finite element approximations to the Navier-Stokes equations. The preconditioner is demonstrated for BB stable elements with discontinuous pressure approximations in two and three dimensions.
Shaping super-Gaussian beam through digital micro-mirror device
NASA Astrophysics Data System (ADS)
Ding, XiangYu; Ren, YuXuan; Lu, RongDe
2015-03-01
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.
V. V. Kozlov
2005-01-01
We discuss the symplectic geometry of linear Hamiltonian systems with nondegenerate Hamiltonians. These systems can be reduced to linear second-order differential equations characteristic of linear oscillation theory. This reduction is related to the problem on the signatures of restrictions of quadratic forms to Lagrangian planes. We study vortex symplectic planes invariant with respect to linear Hamiltonian systems. These planes are
Gaussian Entanglement Distribution via Satellite
Nedasadat Hosseinidehaj; Robert Malaney
2015-02-05
In this work we analyse three quantum communication schemes for the generation of Gaussian entanglement between two ground stations. Communication occurs via a satellite over two independent atmospheric fading channels dominated by turbulence-induced beam wander. In our first scheme the engineering complexity remains largely on the ground transceivers, with the satellite acting simply as a reflector. Although the channel state information of the two atmospheric channels remains unknown in this scheme, the Gaussian entanglement generation between the ground stations can still be determined. On the ground, distillation and Gaussification procedures can be applied, leading to a refined Gaussian entanglement generation rate between the ground stations. We compare the rates produced by this first scheme with two competing schemes in which quantum complexity is added to the satellite, thereby illustrating the trade-off between space-based engineering complexity and the rate of ground-station entanglement generation.
Profile-Following Entry Guidance Using Linear Quadratic Regulator Theory
NASA Technical Reports Server (NTRS)
Dukeman, Greg A.; Fogle, Frank (Technical Monitor)
2002-01-01
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.
LARGE TIME SOLUTION FOR QUADRATIC SCHRODINGER EQUATIONS IN HANTAEK BAE
Yorke, James
LARGE TIME SOLUTION FOR QUADRATIC SCHRÂ¨ODINGER EQUATIONS IN 2D AND 3D HANTAEK BAE Abstract. The aim of this paper is to establish the large time well-posedness of the quadratic SchrÂ¨odinger equation in 2D and 3D for the solvability of (1.1), see [5]. In this paper, we consider the SchrÂ¨odinger equation with quadratic
Runge-Kutta methods for quadratic ordinary differential equations
Arieh Iserles; Geetha Ramaswami; Mark Sofroniou
1998-01-01
Many systems of ordinary differential equations are quadratic: the derivative can be expressed as a quadratic function of\\u000a the dependent variable. We demonstrate that this feature can be exploited in the numerical solution by Runge-Kutta methods,\\u000a since the quadratic structure serves to decrease the number of order conditions. We discuss issues related to construction\\u000a design and implementation and present a
A Dynamic Programming Approach to Finite-horizon Coherent Quantum LQG Control
Vladimirov, Igor G
2011-01-01
The paper considers the coherent quantum Linear Quadratic Gaussian (CQLQG) control problem for time-varying quantum plants governed by linear quantum stochastic differential equations over a bounded time interval. A controller is sought among quantum linear systems satisfying physical realizability (PR) conditions. The latter describe the dynamic equivalence of the system to an open quantum harmonic oscillator and relate its state-space matrices to the free Hamiltonian, coupling and scattering operators of the oscillator. Using the Hamiltonian parameterization of PR controllers, the CQLQG problem is recast into an optimal control problem for a deterministic system governed by a differential Lyapunov equation. The state of this subsidiary system is the symmetric part of the quantum covariance matrix of the plant-controller state vector. The resulting covariance control problem is treated using dynamic programming and Pontryagin's minimum principle. The associated Hamilton-Jacobi-Bellman equation for the minimu...
Multivariable control of a forward swept wing aircraft. M.S. Thesis
NASA Technical Reports Server (NTRS)
Quinn, W. W.
1986-01-01
The impact of independent canard and flaperon control of the longitudinal axis of a generic forward swept wing aircraft is examined. The Linear Quadratic Gaussian (LQG)/Loop Transfer Recovery (LTR) method is used to design three compensators: two single-input-single-output (SISO) systems, one with angle of attack as output and canard as control, the other with pitch attitude as output and canard as control, and a two-input-two-output system with both canard and flaperon controlling both the pitch attitude and angle of attack. The performances of the three systems are compared showing the addition of flaperon control allows the aircraft to perform in the precision control modes with very little loss of command following accuracy.
Tachyon mediated non-Gaussianity
Dutta, Bhaskar; Leblond, Louis; Kumar, Jason [Department of Physics, Texas A and M University, College Station, Texas 77843 (United States); Department of Physics and Astronomy, University of California, Irvine, California 92697 (United States)
2008-10-15
We describe a general scenario where primordial non-Gaussian curvature perturbations are generated in models with extra scalar fields. The extra scalars communicate to the inflaton sector mainly through the tachyonic (waterfall) field condensing at the end of hybrid inflation. These models can yield significant non-Gaussianity of the local shape, and both signs of the bispectrum can be obtained. These models have cosmic strings and a nearly flat power spectrum, which together have been recently shown to be a good fit to WMAP data. We illustrate with a model of inflation inspired from intersecting brane models.
A Non-Gaussian Factor Analysis Approach To Transcription Network Component Analysis
Xu, Lei
A Non-Gaussian Factor Analysis Approach To Transcription Network Component Analysis Shikui Tu verification. Index Terms--transcription factor activity, network component analysis, non-Gaussian factor@cse.cuhk.edu.hk Abstract--Transcription factor activities (TFAs), rather than expression levels, control gene expression
UNCERTAIN SYSTEMS, BEHAVIOURS AND QUADRATIC DIFFERENTIAL FORMS 1
UNCERTAIN SYSTEMS, BEHAVIOURS AND QUADRATIC DIFFERENTIAL FORMS 1 Ian R. Petersen Jan C. Willems School of Electrical Engineering, Australian Defence Force Academy, Campbell, 2600, Australia, Phone +61
Gaussian process style transfer mapping for historical Chinese character recognition
NASA Astrophysics Data System (ADS)
Feng, Jixiong; Peng, Liangrui; Lebourgeois, Franck
2015-01-01
Historical Chinese character recognition is very important to larger scale historical document digitalization, but is a very challenging problem due to lack of labeled training samples. This paper proposes a novel non-linear transfer learning method, namely Gaussian Process Style Transfer Mapping (GP-STM). The GP-STM extends traditional linear Style Transfer Mapping (STM) by using Gaussian process and kernel methods. With GP-STM, existing printed Chinese character samples are used to help the recognition of historical Chinese characters. To demonstrate this framework, we compare feature extraction methods, train a modified quadratic discriminant function (MQDF) classifier on printed Chinese character samples, and implement the GP-STM model on Dunhuang historical documents. Various kernels and parameters are explored, and the impact of the number of training samples is evaluated. Experimental results show that accuracy increases by nearly 15 percentage points (from 42.8% to 57.5%) using GP-STM, with an improvement of more than 8 percentage points (from 49.2% to 57.5%) compared to the STM approach.
Preliminary structural control results from the Middeck Active Control Experiment (MACE)
NASA Technical Reports Server (NTRS)
Miller, David W.; Saarmaa, Erik; Jacques, Robert N.
1992-01-01
Results are presented of on-going closed-loop ground experiments on the MACE test article, the objective of which is to investigate the extent to which closed-loop behavior of flexible spacecraft in zero gravity can be predicted, as well as to examine orbit system identification and control reconfiguration. The MACE hardware consists of three torque wheels, a two-axis gimballing payload, inertial sensors, and a flexible support structure. With the acquisition of a second payload, this is to represent a multiple payload platform with significant structural flexibility. When linear quadratic Gaussian control is used, payload pointing accuracy is improved by an order of magnitude when disturbed by a broadband torque disturbance. The successes and failures of the design and implementation process are discussed.
Scattering of the polarized Gaussian beam on the metamaterial slab
E. N. Odarenko; A. A. Shmat'ko; A. S. Naklutskiy
2010-01-01
The scattering of Gaussian beam on the metamaterial slab with negative refractive index is considered. Modeling is based on the spectral decomposition of the beam field in plane waves. The effect of different parameters on the polarization characteristics of the electromagnetic field reflected from the metamaterial layer and transmitted through it is investigated. The possibility of control of the beam
Non-gaussian shape recognition
Byun, Joyce; Bean, Rachel, E-mail: byun@astro.cornell.edu, E-mail: rbean@astro.cornell.edu [Department of Astronomy, Cornell University, Ithaca, NY 14853 (United States)
2013-09-01
A detection of primordial non-Gaussianity could transform our understanding of the fundamental theory of inflation. The precision promised by upcoming cosmic microwave background (CMB) and large-scale structure (LSS) surveys raises a natural question: if a detection given a particular template is made, what does this truly tell us about the underlying theory? Even in the case of non-detections and upper bounds on deviations from Gaussianity, what can we then infer about the viable theories that remain? In this paper we present a systematic way to constrain a wide range of non-Gaussian shapes, including general single and multi-field models and models with excited initial states. We present a separable, divergent basis able to recreate many shapes in the literature to high accuracy with between three and seven basis functions. The basis allows shapes to be grouped into broad ''template classes'', satisfying theoretically-relevant priors on their divergence properties in the squeezed limit. We forecast how well a Planck-like CMB survey could not only detect a general non-Gaussian signal but discern more about its shape, using existing templates and new ones we propose. This approach offers an opportunity to tie together minimal theoretical priors with observational constraints on the shape in general, and in the squeezed limit, to gain a deeper insight into what drove inflation.
On Gaussian Beams Described by Jacobi's Equation
Smith, Steven T.
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 ?ervený equations ...
Representation of velocity gradient effects in a Gaussian puff model
Sykes, R.I.; Henn, D.S. [Titan Corp., Princeton, NJ (United States)] [Titan Corp., Princeton, NJ (United States)
1995-12-01
The Gaussian puff model framework is extended to provide a description of velocity shear distortion effects. An efficient splitting-merging algorithm is presented so that a maximum puff size can be specified for a calculation. This localizes the Gaussian puffs so that they represent only a limited region of the flow and the accuracy of the representation is therefore controlled. The model is shown to perform well on the deformational flow of Smolarkiewicz, providing an accurate calculation of the highly distorted solution. The extended puff methodology allows practical applications of an efficient Lagrangian dispersion technique in complex flow fields. 14 refs., 7 figs., 1 tab.
Unfairness caused by quadratic backoff in a packet-radio network
NASA Astrophysics Data System (ADS)
Leib, Melisse
1989-10-01
This note contains the performance analysis of a prototype packet-radio pacing algorithm designed to prevent congestion by throttling traffic sources. In the pacing algorithm, each packet radio measures data-packet forwarding times on a neighbor-by-neighbor basis, and scales them to compute a lower bound on packet inter-transmission times, known as a pacing delay. The scale factor is chosen to prevent packet radios from sending data packets to their neighbors faster than they can forward them. In summary, the pacing algorithm applies flow control to prevent congestion. The prototype algorithm differentiates between packet transmissions at the head of a route and packet transmissions along a route. The pacing delays for the former case are scaled quadratically whereas the pacing delays for the latter case are scaled linearly. The objective is to prevent congestion by metering data packets into the network slower than they can traverse it. This source-throttling technique is called quadratic backoff. A mathematical model was derived for pacing-delay computations in a packet-radio network that demonstrates quadratic backoff introduces unfair stable equilibrium points. In other words, quadratic backoff causes a persistent situation to occur in which some routes get more bandwidth than others.
Instabilities of quadratic band crossing points
NASA Astrophysics Data System (ADS)
Uebelacker, Stefan; Honerkamp, Carsten
2011-11-01
Using a functional renormalization-group approach, we study interaction-driven instabilities in quadratic band crossing point two-orbital models in two dimensions, extending a previous study of Sun [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.103.046811 103, 046811 (2009)]. The wave-vector dependence of the Bloch eigenvectors of the free Hamiltonian causes interesting instabilities toward spin-nematic, quantum anomalous Hall, and quantum spin Hall states. In contrast with other known examples of interaction-driven topological insulators, in the system studied here, the quantum spin Hall state occurs at arbitrarily small interaction strength and for rather simple intraorbital and interorbital repulsions.
Quadratic dynamical decoupling with nonuniform error suppression
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
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}.
Ultrasonic transducer with a two-dimensional Gaussian field profile
NASA Technical Reports Server (NTRS)
Claus, R. O.; Zerwekh, P. S.
1983-01-01
A transducer is described which generates a two-dimensional Gaussian field by controlling both the position of multiple circular electrodes and the voltage applied to each electrode. The transducer is constructed by depositing concentric rings electrodes onto one flat surface of a circular piezoelectric crystal disk and attaching the rings to an impedance matching network which acts as a voltage divider. Geometrical inter-ring separations and electrical inter-ring impedances are designed to minimize the error between the generated acoustic field, modeled as a piecewise linear function, and the desired Gaussian distribution. Total mean squared error between the averaged far-field data and a Gaussian shape is less than two percent.
Bipartite and Multipartite Entanglement of Gaussian States
Gerardo Adesso; Fabrizio Illuminati
2005-01-01
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
Monogamy Inequality for Distributed Gaussian Entanglement
Tohya Hiroshima; Gerardo Adesso; Fabrizio Illuminati
2007-01-01
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
One-mode quantum Gaussian channels
A. S. Holevo
2006-07-16
A classification of one-mode Gaussian channels is given up to canonical unitary equivalence. A complementary to the quantum channel with additive classical Gaussian noise is described providing an example of one-mode Gaussian channel which is neither degradable nor anti-degradable.
Large-scale sequential quadratic programming algorithms
Eldersveld, S.K.
1992-09-01
The problem addressed is the general nonlinear programming problem: finding a local minimizer for a nonlinear function subject to a mixture of nonlinear equality and inequality constraints. The methods studied are in the class of sequential quadratic programming (SQP) algorithms, which have previously proved successful for problems of moderate size. Our goal is to devise an SQP algorithm that is applicable to large-scale optimization problems, using sparse data structures and storing less curvature information but maintaining the property of superlinear convergence. The main features are: 1. The use of a quasi-Newton approximation to the reduced Hessian of the Lagrangian function. Only an estimate of the reduced Hessian matrix is required by our algorithm. The impact of not having available the full Hessian approximation is studied and alternative estimates are constructed. 2. The use of a transformation matrix Q. This allows the QP gradient to be computed easily when only the reduced Hessian approximation is maintained. 3. The use of a reduced-gradient form of the basis for the null space of the working set. This choice of basis is more practical than an orthogonal null-space basis for large-scale problems. The continuity condition for this choice is proven. 4. The use of incomplete solutions of quadratic programming subproblems. Certain iterates generated by an active-set method for the QP subproblem are used in place of the QP minimizer to define the search direction for the nonlinear problem. An implementation of the new algorithm has been obtained by modifying the code MINOS. Results and comparisons with MINOS and NPSOL are given for the new algorithm on a set of 92 test problems.
Controller design and parameter identifiability studies for a large space antenna
NASA Technical Reports Server (NTRS)
Joshi, S. M.
1985-01-01
The problem of control systems synthesis and parameter identifiability are considered for a large, space-based antenna. Two methods are considered for control system synthesis, the first of which uses torque actuators and collocated attitude and rate sensors, and the second method is based on the linear-quadratic-Gaussian (LQG) control theory. The predicted performance obtained by computing variances of pointing, surface and feed misalignment errors in the presence of sensor noise indicates that the LQG-based controller yields superior results. Since controller design requires the knowledge of the system parameters, the identifiability of the structural parameters is investigated by obtaining Cramer-Rao lower bounds. The modal frequencies are found to have the best identifiability, followed by damping ratios, and mode-slopes.
Coding along hermite polynomials for gaussian noise channels
Abbe, Emmanuel A.
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 ...
No-go theorem for Gaussian quantum error correction
Niset, Julien
We prove that Gaussian operations are of no use for protecting Gaussian states against Gaussian errors in quantum communication protocols. Specifically, we introduce a new quantity characterizing any single-mode Gaussian ...
Geometric quadratic stochastic operator on countable infinite set
NASA Astrophysics Data System (ADS)
Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar
2015-02-01
In this paper we construct the family of Geometric quadratic stochastic operators defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. Such operators can be reinterpreted in terms of of evolutionary operator of free population. We show that Geometric quadratic stochastic operators are regular transformations.
A New Adaptive Algorithm for Convex Quadratic Multicriteria Optimization
Fliege, JÃ¶rg
the prob- lem of solving one single-criteria convex-quadratic optimization problem by an interior-point method used for this problem. 1 Introduction Multicriteria optimization problems are a class of difficult The Interior-Point Algorithm 2.1 The Problem Let there be given a primal quadratic optimization problem (PQP
The quadratic interior point method solving power system optimization problems
James A. Momoh; S. X. Guo; E. C. Ogbuobiri; R. Adapa
1994-01-01
Karmarkar's interior point method as a computation method for solving linear programming (LP) has attracted interest in the operation research community, due to its efficiency, reliability, and accuracy. This paper presents an extended quadratic interior point (EQIP) method, based on improvement of initial condition for solving both linear and quadratic programming problems, to solve power system optimization problem (PSOP), such
Rational Quadratic Approximation to Real Plane Algebraic Curves
Xiao-shan Gao; Ming Li
2004-01-01
An algorithm is proposed to give a global approximation of an implicit real plane algebraic curve with rational quadratic B-spline curves. The algorithm consists of f our steps: topol- ogy determination, curve segmentation, segment approximation and curve tracing. Due to the detailed geometric analysis, high accuracy of approximation may be achieved with a small number of quadratic segments. The final
Some Paradoxical Results for the Quadratically Weighted Kappa
ERIC Educational Resources Information Center
Warrens, Matthijs J.
2012-01-01
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…
Quadratic elongation: A quantitative measure of distortion in coordination polyhedra
Robinson, K.; Gibbs, G.V.; Ribbe, P.H.
1971-01-01
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.
Quadratic Elongation: A Quantitative Measure of Distortion in Coordination Polyhedra
Keith Robinson; G. V. Gibbs; P. H. Ribbe
1971-01-01
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 elongation is dimensionless, giving a quantitative measure of polyhedral distortion which is independent of the effective size of the polyhedron.
Design and application of quadratic correlation filters for target detection
ABHIJIT MAHALANOBIS; ROBERT R. MUISE; S. R. Stanfill; A. Van Nevel
2004-01-01
We introduce a method for designing and implementing quadratic correlation filters (QCFs) for shift-invariant target detection in imagery. The QCFs are a quadratic classifier that operates directly on the image data without feature extraction or segmentation. In this sense, the QCFs retain the main advantages of conventional linear correlation filters while offering significant improvements in other respects. Not only is
Weaving a Parabola Web with the Quadratic Transformer
NSDL National Science Digital Library
2012-07-19
Investigate how the graph of a quadratic function and its symbolic expression relate to each other. Start with a set of four graphs, which we?ll call a Parabola Web. Experiment with manipulating them with transformations such as shifting and reflection. Learn about quadratic equations in vertex and root form, and explore how changing these equations affect the graphs.
Frequency-wavenumber spectrum analysis using quadratic estimators
Michael P. Clark; Louis L. Scharj; Wright-Patterson AFB
1992-01-01
A general representation for all non-negative, modulation invariant estimators of the frequency-wavenumber spectrum shows explicitly how the quadratic estimates are constructed from linear transformations of the array data. The windows associated with these transformations are those normally associated with `classical' spectrum estimators. The authors present closed form representations for the moments of quadratic estimators, and show that variance decreases as
Tangent Lines without Derivatives for Quadratic and Cubic Equations
ERIC Educational Resources Information Center
Carroll, William J.
2009-01-01
In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)
Sketching the General Quadratic Equation Using Dynamic Geometry Software
ERIC Educational Resources Information Center
Stols, G. H.
2005-01-01
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…
Effects of Classroom Instruction on Students' Understanding of Quadratic Equations
ERIC Educational Resources Information Center
Vaiyavutjamai, Pongchawee; Clements, M. A.
2006-01-01
Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of…
Problems in Presenting Quadratics as a Unifying Topic.
ERIC Educational Resources Information Center
MacDonald, Theodore H.
1986-01-01
A sequence for teaching quadratic equations is presented. Considered are: multiplying arithmetic binomials, multiplying algebraic polynomials, reversing the process, missing terms, perfect squares, other special forms and diagrams, quadratic equations, completing the square, systematizing the process, the general form, graphing equations, and…
THE EFFECTIVENESS OF QUADRATS FOR MEASURING VASCULAR DIVERSITY: JOURNAL ARTICLE
NRMRL-ADA- 98217 Jorgensen*, E.E., and Tunnell, S.J. The Effectiveness of Quadrats for Measuring Vascular Diversity. The Texas Journal of Science 53 (4):365-368 (2001). EPA/600/J-02/027. Quadrats are widely used for measuring characterist...
Quadratic maps of the plane: Tutorial and Zeraoulia Elhadj1
Sprott, Julien Clinton
Quadratic maps of the plane: Tutorial and review Zeraoulia Elhadj1 , J. C. Sprott2 1 Department quadratic maps, this paper offers an overview of some important issues related to the general case of these mappings, especially predicting the strange attractors and their properties. PACS numbers: 05.45.-a, 05
On Oppenheim-type conjecture for systems of quadratic forms
Gorodnik, Alexander
On Oppenheim-type conjecture for systems of quadratic forms Alexander Gorodnik Abstract Let Qi, i It was conjectured by Oppenheim that if Q(Â¯x) = i,j aijxixj, Â¯x = (x1, . . . , xd), is a real nondegenerate(Â¯x)| Oppenheim conjecture holds for systems of quadratic forms (see
hal00276700, A Quadratic Loss MultiClass SVM
Paris-Sud XI, Université de
hal00276700, version 1 30 Apr 2008 A Quadratic Loss MultiClass SVM Emmanuel Monfrini --- Yann Guermeur April 30, 2008 #12; #12; A Quadratic Loss Multi-Class SVM Emmanuel Monfrini #3; , Yann Guermeur y recognition SVM have been derived. Among those bounds, the most popular one is probably the radius
Development and modification of a Gaussian and non-Gaussian noise exposure system
NASA Astrophysics Data System (ADS)
Schlag, Adam W.
Millions of people across the world currently have noise induced hearing loss, and many are working in conditions with both continuous Gaussian and non-Gaussian noises that could affect their hearing. It was hypothesized that the energy of the noise was the cause of the hearing loss and did not depend on temporal pattern of a noise. This was referred to as the equal energy hypothesis. This hypothesis has been shown to have limitations though. This means that there is a difference in the types of noise a person receives to induce hearing loss and it is necessary to build a system that can easily mimic various conditions to conduct research. This study builds a system that can produce both non-Gaussian impulse/impact noises and continuous Gaussian noise. It was found that the peak sound pressure level of the system could reach well above the needed 120 dB level to represent acoustic trauma and could replicate well above the 85 dB A-weighted sound pressure level to produce conditions of gradual developing hearing loss. The system reached a maximum of 150 dB sound peak pressure level and a maximum of 133 dB A-weighted sound pressure level. Various parameters could easily be adjusted to control the sound, such as the high and low cutoff frequency to center the sound at 4 kHz. The system build can easily be adjusted to create numerous sound conditions and will hopefully be modified and improved in hopes of eventually being used for animal studies to lead to the creation of a method to treat or prevent noise induced hearing loss.
AESOP- INTERACTIVE DESIGN OF LINEAR QUADRATIC REGULATORS AND KALMAN FILTERS
NASA Technical Reports Server (NTRS)
Lehtinen, B.
1994-01-01
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.
NASA Technical Reports Server (NTRS)
Straton, Jack C.
1989-01-01
The four-dimensional Fourier-Feynman transformations previously used in analytically reducing the general class of integrals containing multicenter products of 1s hydrogenic orbitals, Coulomb or Yukawa potentials, and plane waves, are replaced by the one-dimensional Gaussian transformation. This reduces the previously required double-diagonalization of the quadratic form of the multicenter integrals to only one diagonalization, yielding a simpler reduced form of the integral. The present work also extends the result to include all s states and pairs of states with l not equal to zero summed over the m quantum number.
Quadratic algebras for three-dimensional superintegrable systems
Daskaloyannis, C., E-mail: daskalo@math.auth.gr; Tanoudis, Y. [Aristotle University of Thessaloniki, Mathematics Department (Greece)
2010-02-15
The three-dimensional superintegrable systems with quadratic integrals of motion have five functionally independent integrals, one among them is the Hamiltonian. Kalnins, Kress, and Miller have proved that in the case of nondegenerate potentials with quadratic integrals of motion there is a sixth quadratic integral, which is linearly independent of the other integrals. The existence of this sixth integral implies that the integrals of motion form a ternary parafermionic-like quadratic Poisson algebra with five generators. In this contribution we investigate the structure of this algebra. We show that in all the nondegenerate cases there is at least one subalgebra of three integrals having a Poisson quadratic algebra structure, which is similar to the two-dimensional case.
Phase-only shaping algorithm for Gaussian-apodized Bessel beams.
Durfee, Charles G; Gemmer, John; Moloney, Jerome V
2013-07-01
Gaussian-apodized Bessel beams can be used to create a Bessel-like axial line focus at a distance from the focusing lens. For many applications it is desirable to create an axial intensity profile that is uniform along the Bessel zone. In this article, we show that this can be accomplished through phase-only shaping of the wavefront in the far field where the beam has an annular ring structure with a Gaussian cross section. We use a one-dimensional transform to map the radial input field to the axial Bessel field and then optimized the axial intensity with a Gerchberg-Saxton algorithm. By separating out the quadratic portion of the shaping phase the algorithm converges more rapidly. PMID:23842364
A Gradient Descent Approach to Optimal Coherent Quantum LQG Controller Design
Arash Kh. Sichani; Igor G. Vladimirov; Ian R. Petersen
2015-02-01
This paper is concerned with the Coherent Quantum Linear Quadratic Gaussian (CQLQG) control problem of finding a stabilizing measurement-free quantum controller for a quantum plant so as to minimize an infinite-horizon mean square performance index for the fully quantum closed-loop system. In comparison with the observation-actuation structure of classical controllers, the coherent quantum feedback is less invasive to the quantum dynamics and quantum information. Both the plant and the controller are open quantum systems whose dynamic variables satisfy the canonical commutation relations (CCRs) of a quantum harmonic oscillator and are governed by linear quantum stochastic differential equations (QSDEs). In order to correspond to such oscillators, these QSDEs must satisfy physical realizability (PR) conditions, which are organised as quadratic constraints on the controller matrices and reflect the preservation of CCRs in time. The CQLQG problem is a constrained optimization problem for the steady-state quantum covariance matrix of the plant-controller system satisfying an algebraic Lyapunov equation. We propose a gradient descent algorithm equipped with adaptive stepsize selection for the numerical solution of the problem. The algorithm finds a local minimum of the LQG cost over the parameters of the Hamiltonian and coupling operators of a stabilizing PR quantum controller, thus taking the PR constraints into account. A convergence analysis of the proposed algorithm is presented. A numerical example of a locally optimal CQLQG controller design is provided to demonstrate the algorithm performance.
Closed-form solutions for a class of optimal quadratic regulator problems with terminal constraints
NASA Technical Reports Server (NTRS)
Juang, J.-N.; Turner, J. D.; Chun, H. M.
1984-01-01
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.
Spatial superpositions of Gaussian beams
NASA Astrophysics Data System (ADS)
Naidoo, Darryl; Godin, Thomas; Fromager, Michael; Aît-Ameur, Kamel; Forbes, Andrew
2014-02-01
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.
Nurmi, Sami [Department of Physics and Helsinki Institute of Physics, University of Helsinki, P.O. Box 64, FIN-00014 University of Helsinki (Finland); Byrnes, Christian T. [Astronomy Centre, University of Sussex, Brighton, BN1 9QH (United Kingdom); Tasinato, Gianmassimo, E-mail: sami.nurmi@helsinki.fi, E-mail: ctb22@sussex.ac.uk, E-mail: gianmassimo.tasinato@port.ac.uk [Institute of Cosmology and Gravitation, University of Portsmouth, PO1 3FX (United Kingdom)
2013-06-01
Primordial perturbations with wavelengths greater than the observable universe shift the effective background fields in our observable patch from their global averages over the inflating space. This leads to a landscape picture where the properties of our observable patch depend on its location and may significantly differ from the expectation values predicted by the underlying fundamental inflationary model. We show that if multiple fields are present during inflation, this may happen even if our horizon exit would be preceded by only a few e-foldings of inflation. Non-Gaussian statistics are especially affected: for example models of local non-Gaussianity predicting |f{sub NL}{sup 0}| >> 10 over the entire inflating volume can have a probability up to a few tens of percent to generate a non-detectable bispectrum in our observable patch |f{sub NL}{sup obs.}|?<10. In this work we establish systematic connections between the observable local properties of primordial perturbations and the global properties of the inflating space which reflect the underlying high energy physics. We study in detail the implications of both a detection and non-detection of primordial non-Gaussianity by Planck, and discover novel ways of characterising the naturalness of different observational configurations.
Cooling and squeezing via quadratic optomechanical coupling
Nunnenkamp, A.; Boerkje, K.; Harris, J. G. E.; Girvin, S. M. [Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520 (United States)
2010-08-15
We explore the physics of optomechanical systems in which an optical cavity mode is coupled parametrically to the square of the position of a mechanical oscillator. We derive an effective master equation describing two-phonon cooling of the mechanical oscillator. We show that for high temperatures and weak coupling, the steady-state phonon number distribution is nonthermal (Gaussian) and that even for strong cooling the mean phonon number remains finite. Moreover, we demonstrate how to achieve mechanical squeezing by driving the cavity with two beams. Finally, we calculate the optical output and squeezing spectra. Implications for optomechanics experiments with the membrane-in-the-middle geometry or ultracold atoms in optical resonators are discussed.
Non-Gaussianity in the cosmic microwave background induced by dipolar dark matter
Blanchet, Luc; Marsat, Sylvain [GRECO, Institut d'Astrophysique de Paris — UMR 7095 du CNRS, Université Pierre and Marie Curie, 98 bis boulevard Arago, 75014 Paris (France); Langlois, David [Astroparticle and Cosmologie (CNRS-Université Paris 7), 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13 (France); Tiec, Alexandre Le, E-mail: blanchet@iap.fr, E-mail: langlois@iap.fr, E-mail: letiec@umd.edu, E-mail: marsat@iap.fr [Maryland Center for Fundamental Physics and Joint Space-Science Institute, Department of Physics, University of Maryland, College Park, MD 20742 (United States)
2013-02-01
In previous work [L. Blanchet and A. Le Tiec, Phys. Rev. D 80 (2009) 023524], motivated by the phenomenology of dark matter at galactic scales, a model of dipolar dark matter (DDM) was introduced. At linear order in cosmological perturbations, the dynamics of the DDM was shown to be identical to that of standard cold dark matter (CDM). In this paper, the DDM model is investigated at second order in cosmological perturbation theory. We find that the internal energy of the DDM fluid modifies the curvature perturbation generated by CDM with a term quadratic in the dipole field. This correction induces a new type of non-Gaussianity in the bispectrum of the curvature perturbation with respect to standard CDM. Leaving unspecified the primordial amplitude of the dipole field, which could in principle be determined by a more fundamental description of DDM, we find that, in contrast with usual models of primordial non-Gaussianities, the non-Gaussianity induced by DDM increases with time after the radiation-matter equality on super-Hubble scales. This distinctive feature of the DDM model, as compared with standard CDM, could thus provide a specific signature in the CMB and large-scale structure probes of non-Gaussianity.
Gaussianity of LISA's confusion backgrounds
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
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.
LQG controller design using GUI: application to antennas and radio-telescopes
Maneri; Gawronski
2000-01-01
The Linear Quadratic Gaussian (LQG) algorithm has been used to control the JPL's beam wave-guide, and 70-m antennas. This algorithm significantly improves tracking precision in a wind disturbed environment. Based on this algorithm and the implementation experience a Matlab based Graphical User Interface (GUI) was developed to design the LQG controllers applicable to antennas and radiotelescopes. The GUI is described in this paper. It consists of two parts the basic LQG design and the fine-tuning of the basic design using a constrained optimization algorithm. The presented GUI was developed to simplify the design process, to make the design process user-friendly, and to enable design of an LQG controller for one with a limited control engineering background. The user is asked to manipulate the GUI sliders and radio buttons to watch the antenna performance. Simple rules are given at the GUI display. PMID:10871218
NASA Technical Reports Server (NTRS)
Gibson, J. S.; Rosen, I. G.
1986-01-01
An abstract approximation theory and computational methods are developed for the determination of optimal linear-quadratic feedback control, observers and compensators for infinite dimensional discrete-time systems. Particular attention is paid to systems whose open-loop dynamics are described by semigroups of operators on Hilbert spaces. The approach taken is based on the finite dimensional approximation of the infinite dimensional operator Riccati equations which characterize the optimal feedback control and observer gains. Theoretical convergence results are presented and discussed. Numerical results for an example involving a heat equation with boundary control are presented and used to demonstrate the feasibility of the method.
Modern CACSD using the Robust-Control Toolbox
NASA Technical Reports Server (NTRS)
Chiang, Richard Y.; Safonov, Michael G.
1989-01-01
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.
Improving stability margins in discrete-time LQG controllers
NASA Technical Reports Server (NTRS)
Oranc, B. Tarik; Phillips, Charles L.
1987-01-01
Some of the problems are discussed which are encountered in the design of discrete-time stochastic controllers for problems that may adequately be described by the Linear Quadratic Gaussian (LQG) assumptions; namely, the problems of obtaining acceptable relative stability, robustness, and disturbance rejection properties. A dynamic compensator is proposed to replace the optimal full state feedback regulator gains at steady state, provided that all states are measurable. The compensator increases the stability margins at the plant input, which may possibly be inadequate in practical applications. Though the optimal regulator has desirable properties the observer based controller as implemented with a Kalman filter, in a noisy environment, has inadequate stability margins. The proposed compensator is designed to match the return difference matrix at the plant input to that of the optimal regulator while maintaining the optimality of the state estimates as directed by the measurement noise characteristics.
Local classifier weighting by quadratic programming.
Cevikalp, Hakan; Polikar, Robi
2008-10-01
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
Quadratic integer programming for large scale banded matrices
NASA Technical Reports Server (NTRS)
Yan, T. Y.; Tan, H. H.
1982-01-01
This paper is concerned with the integer quadratic program where the variables are constrained to belong to a given set of discrete values. This quadratic integer program is shown to be equivalent to a problem of finding the shortest path in a particular directed graph called a trellis when the matrix is a positive-definite symmetric banded matrix. An efficient procedure for solving this shortest path problem is presented which allows the solution of the integer quadratic program. This method is particularly effective when the half-bandwidth of the matrix is significantly smaller than its dimension.
Models for the 3D singular isotropic oscillator quadratic algebra
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
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.
Gaussian Decomposition of Laser Altimeter Waveforms
NASA Technical Reports Server (NTRS)
Hofton, Michelle A.; Minster, J. Bernard; Blair, J. Bryan
1999-01-01
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.
NASA Astrophysics Data System (ADS)
Troncossi, M.; Di Sante, R.; Rivola, A.
2014-05-01
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.
NASA Astrophysics Data System (ADS)
Athans, M.; Lee, W. H.; Lehtomaki, N. A.; Levy, B. C.; Ng, P. T. P.
1982-05-01
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 and new 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 of a single-input, single-output (SISO) 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 of linear-quadratic-Gaussian control systems are analyzed via this robustness theory and multiloop stability margins are presented; in particular, a new type of margin, a cross-feed margin, is introduced. Other frequency domain analysis and design techniques are also briefly discussed and their relation to the present robustness analysis is examined. In addition a linear-quadratic based design procedure that quarantees a prescribed degree of stability is developed, with special emphasis upon its robustness properties.
A linear quadratic regulator approach to the stabilization of uncertain linear systems
NASA Technical Reports Server (NTRS)
Shieh, L. S.; Sunkel, J. W.; Wang, Y. J.
1990-01-01
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.
Integrated structural control design of large space structures
Allen, J.J.; Lauffer, J.P.
1995-01-01
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.
Constructing Approximations to the Efficient Set of Convex Quadratic ...
quadratic problem with an interior point method, an approach which will be put .... efficient points (i. e. when solving the new optimization problems), we ... of the primal-dual long step algorithm for linear programs by Kojima, Mizuno, and ...
Geometric Procedures for Graphing the General Quadratic Equation.
ERIC Educational Resources Information Center
DeTemple, Duane W.
1984-01-01
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)
The Quadratic Zeeman Effect in Moderately Strong Magnetic Fields
S. L. Coffey; A. Deprit; B. Miller; C. A. Williams
1987-01-01
Contents: 1. Symmetries. 2. The linear Zeeman effect. 3. The quadratic Zeeman effect. 4. The method of secular perturbations. 5. The phase-space as a sphere. 6. Critical inclinations. 7. The circular orbits. 8. Conclusions.
Beyond symmetric Broyden for updating quadratic models in ...
2011-04-12
without derivatives construct changes to the variables by applying trust region methods to quadratic .... causes substantial relative errors in every xk. Furthermore, the property ..... because of the sparsity structure of ?2F. We employ the usual ...
Semidefinite Relaxations for Non-Convex Quadratic Mixed-Integer ...
2011-11-08
Most algorithms and software tools for quadratic mixed-integer optimization ... cutting planes yields a very fast algorithm for solving the maximum cut prob- .... In our evaluation, we are also interested in the dependance of performance on.
Regular zeros of quadratic maps and their application
Arutyunov, Aram V; Karamzin, Dmitry Yu
2011-06-30
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.
Gaussian mass optimization for kernel PCA parameters
NASA Astrophysics Data System (ADS)
Liu, Yong; Wang, Zulin
2011-10-01
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.
Elementary quantum gates with Gaussian states
NASA Astrophysics Data System (ADS)
Podoshvedov, Sergey A.; Kim, Jaewan; Kim, Kisik
2014-08-01
We study the question of converting initially Gaussian states into non-Gaussian ones by two- and three-photon subtraction to improve non-classical properties of the conditional optical fields. We show the photon subtraction may effectively generate non-Gaussian states only in case of small values of the mean values of the position and momentum operators. In particular, the photon-subtracted state can be made arbitrary close to Gaussian state in limiting case of large initial amplitude of displacement. Use of initial displacement in input Gaussian states opens wider prospects to manipulate them. In particular, realization of probabilistic Hadamard gate with input Gaussian states is discussed where photon subtraction is motive force able unevenly to increase measure of non-classicality of the output state. Subtraction of larger number of photons enables to increase fidelity and non-classical measure of the conditional states.
Gaussian effective potential: Quantum mechanics
NASA Astrophysics Data System (ADS)
Stevenson, P. M.
1984-10-01
We advertise the virtues of the Gaussian effective potential (GEP) as a guide to the behavior of quantum field theories. Much superior to the usual one-loop effective potential, the GEP is a natural extension of intuitive notions familiar from quantum mechanics. A variety of quantum-mechanical examples are studied here, with an eye to field-theoretic analogies. Quantum restoration of symmetry, dynamical mass generation, and "quantum-mechanical resuscitation" are among the phenomena discussed. We suggest how the GEP could become the basis of a systematic approximation procedure. A companion paper will deal with scalar field theory.
Generation of Gaussian Density Fields
Hugo Martel
2005-07-15
This document describes analytical and numerical techniques for the generation of Gaussian density fields, which represent cosmological density perturbations. The mathematical techniques involved in the generation of density harmonics in k-space, the filtering of the density fields, and the normalization of the power spectrum to the measured temperature fluctuations of the Cosmic Microwave Background, are presented in details. These techniques are well-known amongst experts, but the current literature lacks a formal description. I hope that this technical report will prove useful to new researchers moving into this field, sparing them the task of reinventing the wheel.
Phase recovery based on quadratic programming
NASA Astrophysics Data System (ADS)
Zhang, Quan Bing; Ge, Xiao Juan; Cheng, Ya Dong; Ni, Na
2014-11-01
Most of the information of optical wavefront is encoded in the phase which includes more details of the object. Conventional optical measuring apparatus is relatively easy to record the intensity of light, but can not measure the phase of light directly. Thus it is important to recovery the phase from the intensity measurements of the object. In recent years, the methods based on quadratic programming such as PhaseLift and PhaseCut can recover the phase of general signal exactly for overdetermined system. To retrieve the phase of sparse signal, the Compressive Phase Retrieval (CPR) algorithm combines the l1-minimization in Compressive Sensing (CS) with low-rank matrix completion problem in PhaseLift, but the result is unsatisfied. This paper focus on the recovery of the phase of sparse signal and propose a new method called the Compressive Phase Cut Retrieval (CPCR) by combining the CPR algorithm with the PhaseCut algorithm. To ensure the sparsity of the recovered signal, we use CPR method to solve a semi-definite programming problem firstly. Then apply linear transformation to the recovered signal, and set the phase of the result as the initial value of the PhaseCut problem. We use TFOCS (a library of Matlab-files) to implement the proposed CPCR algorithm in order to improve the recovered results of the CPR algorithm. Experimental results show that the proposed method can improve the accuracy of the CPR algorithm, and overcome the shortcoming of the PhaseCut method that it can not recover the sparse signal effectively.
G. L. Esayan; S. G. Krivoshlykov
1989-01-01
A method of coherent states is used to describe the process of Rayleigh scattering in a multimode graded-index waveguide with a quadratic refractive-index profile. Explicit expressions are obtained for the coefficients representing excitation of Gaussian-Hermite backscattering modes in two cases of practical importance: excitation of a waveguide by an extended noncoherent light source and selective excitation of different modes at
Quadratic function approaching method for magnetotelluric soundingdata inversion
Liangjun, Yan; Wenbao, Hu; Zhang, Keni
2004-04-05
The quadratic function approaching method (QFAM) is introduced for magnetotelluric sounding (MT) data inversion. The method takes the advantage of that quadratic function has single extreme value, which avoids leading to an inversion solution for local minimum and ensures the solution for global minimization of an objective function. The method does not need calculation of sensitivity matrix and not require a strict initial earth model. Examples for synthetic data and field measurement data indicate that the proposed inversion method is effective.
AdS waves as exact solutions to quadratic gravity
Guellue, Ibrahim; Sisman, Tahsin Cagri; Tekin, Bayram [Department of Physics, Middle East Technical University, 06531 Ankara (Turkey); Guerses, Metin [Department of Mathematics, Faculty of Sciences Bilkent University, 06800 Ankara (Turkey)
2011-04-15
We give an exact solution of the quadratic gravity in D dimensions. The solution is a plane-fronted wave metric with a cosmological constant. This metric solves not only the full quadratic gravity field equations but also the linearized ones which include the linearized equations of the recently found critical gravity. A subset of the solutions change the asymptotic structure of the anti-de Sitter space due to their logarithmic behavior.
Exact solution of the classical mechanical quadratic Zeeman effect
Sambhu N. Datta; Anshu Pandey
2007-01-01
We address the curious problem of quadratic Zeeman effect at the classical mechanical level. The problem has been very well\\u000a understood for decades, but an analytical solution of the equations of motion is still to be found. This state of affairs\\u000a persists because the simultaneous presence of the Coulombic and quadratic terms lowers the dynamical symmetry. Energy and\\u000a orbital angular
Monogamy inequality for distributed Gaussian entanglement
Tohya Hiroshima; Gerardo Adesso; Fabrizio Illuminati
2006-11-08
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.
Monogamy inequality for distributed gaussian entanglement.
Hiroshima, Tohya; Adesso, Gerardo; Illuminati, Fabrizio
2007-02-01
We show that for all n-mode Gaussian states of continuous variable systems, the entanglement shared among n parties exhibits the fundamental monogamy property. The monogamy inequality is proven by introducing the Gaussian tangle, an entanglement monotone under Gaussian local operations and classical communication, which is defined in terms of the squared negativity in complete analogy with the case of n-qubit systems. Our results elucidate the structure of quantum correlations in many-body harmonic lattice systems. PMID:17358836
Strongly scale-dependent non-Gaussianity
Riotto, Antonio [INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padua (Italy); CERN, PH-TH Division, CH-1211, Geneve 23 (Switzerland); Sloth, Martin S. [CERN, PH-TH Division, CH-1211, Geneve 23 (Switzerland)
2011-02-15
We discuss models of primordial density perturbations where the non-Gaussianity is strongly scale dependent. In particular, the non-Gaussianity may have a sharp cutoff and be very suppressed on large cosmological scales, but sizable on small scales. This may have an impact on probes of non-Gaussianity in the large-scale structure and in the cosmic microwave background radiation anisotropies.
Ince Gaussian beams in strongly nonlocal nonlinear media
NASA Astrophysics Data System (ADS)
Deng, Dongmei; Guo, Qi
2008-07-01
Based on the Snyder-Mitchell model that describes the beam propagation in strongly nonlocal nonlinear media, the close forms of Ince-Gaussian (IG) beams have been found. The transverse structures of the IG beams are described by the product of the Ince polynomials and the Gaussian function. Depending on the input power of the beams, the IG beams can be either a soliton state or a breather state. The IG beams constitute the exact and continuous transition modes between Hermite-Gaussian beams and Laguerre-Gaussian beams. The IG vortex beams can be constructed by a linear combination of the even and odd IG beams. The transverse intensity pattern of IG vortex beams consists of elliptic rings, whose number and ellipticity can be controlled, and a phase displaying a number of in-line vortices, each with a unitary topological charge. The analytical solutions of the IG beams are confirmed by the numerical simulations of the nonlocal nonlinear Schr\\rm \\ddot{o} dinger equation.
Operational Gaussian Schmidt-number witnesses
NASA Astrophysics Data System (ADS)
Shahandeh, F.; Sperling, J.; Vogel, W.
2013-12-01
The general class of Gaussian Schmidt-number witness operators for bipartite systems is studied. It is shown that any member of this class is reducible to a convex combination of two types of Gaussian operators using local operations and classical communications. This gives rise to a simple operational method, which is solely based on measurable covariance matrices of quantum states. Our method bridges the gap between theory and experiment of entanglement quantification. In particular, we certify lower bounds of the Schmidt number of squeezed thermal and phase-randomized squeezed vacuum states as examples of Gaussian and non-Gaussian quantum states, respectively.
Searching for non-gaussianity: Statistical tests
O. Forni; N. Aghanim
1999-05-11
Non-gaussianity represents the statistical signature of physical processes such as turbulence. It can also be used as a powerful tool to discriminate between competing cosmological scenarios. A canonical analysis of non-gaussianity is based on the study of the distribution of the signal in the real (or direct) space (e.g. brightness, temperature). This work presents an image processing method in which we propose statistical tests to indicate and quantify the non-gaussian nature of a signal. Our method is based on a wavelet analysis of a signal. Because the temperature or brightness distribution is a rather weak discriminator, the search for the statistical signature of non-gaussianity relies on the study of the coefficient distribution of an image in the wavelet decomposition basis which is much more sensitive. We develop two statistical tests for non-gaussianity. In order to test their reliability, we apply them to sets of test maps representing a combination of gaussian and non-gaussian signals. We deliberately choose a signal with a weak non-gaussian signature and we find that such a non-gaussian signature is easily detected using our statistical discriminators. In a second paper, we apply the tests in a cosmological context.
Time-Inconsistent Stochastic LinearQuadratic Control Hanqing Jin
[1, 14] and Markowitz's continuous-time meanÂvariance portfolio selection model [20, 2] provide two at the initial time); see, e.g., [20] and all the follow-up works to date on the Markowitz problem, as well
Dynamic Network Model of Investment Control for Quadratic Risk Function
E. S. Gerasimov; V. V. Dombrovskii
2002-01-01
For the investment portfolio consisting of the risk investments (ordinary shares) and no-risk investments (bank account, reliable bonds), a method of its structural description in terms of the dynamic stochastic network (with nodes representing the capital invested in the given risk or no-risk financial assets and the arcs, directions and amount of the capital reallocated between the assets in the
NASA Technical Reports Server (NTRS)
Montgomery, Raymond C.; Ghosh, Dave; Scott, Michael A.; Warnaar, Dirk
1991-01-01
A procedure for optimizing the performance of large flexible spacecraft that require active vibration suppression to achieve required performance is presented. The procedure is to conduct on-orbit testing and system identification followed by a control system design. It is applied via simulation to a spacecraft configuration currently being considered for flight test by NASA - the Controls, Astrophysics, and Structures Experiment in Space (CASES). The system simulator is based on a NASTRAN finite element structural model. A finite number of modes is used to represent the structural dynamics. The system simulator also includes models of the electronics, actuators, sensors, the digital controller, and the internal and external disturbances. Nonlinearities caused by quantization are included in the study to examine tolerance of the procedure to modelling errors. Disturbance and sensor noise is modelled as a Gaussian process. For system identification, the system is excited using sinusoidal inputs at the resonant frequencies of the structure using each actuator. Mode shapes, frequencies, and damping ratios are identified from the unforced response sensor data after each excitation. Then, the excitation data is used to identify the actuator influence coefficients. The results of the individual parameter identification analyses are assembled into an aggregate system model. The control design is accomplished based only on the identified model using multi-input/output linear quadratic Gaussian theory. Its performance is evaluated based on time-to-damp as compared with the uncontrolled structure.
Information bounds for Gaussian copulas.
Hoff, Peter D; Niu, Xiaoyue; Wellner, Jon A
2014-01-01
Often of primary interest in the analysis of multivariate data are the copula parameters describing the dependence among the variables, rather than the univariate marginal distributions. Since the ranks of a multivariate dataset are invariant to changes in the univariate marginal distributions, rank-based estimators are natural candidates for semiparametric copula estimation. Asymptotic information bounds for such estimators can be obtained from an asymptotic analysis of the rank likelihood, i.e. the probability of the multivariate ranks. In this article, we obtain limiting normal distributions of the rank likelihood for Gaussian copula models. Our results cover models with structured correlation matrices, such as exchangeable or circular correlation models, as well as unstructured correlation matrices. For all Gaussian copula models, the limiting distribution of the rank likelihood ratio is shown to be equal to that of a parametric likelihood ratio for an appropriately chosen multivariate normal model. This implies that the semiparametric information bounds for rank-based estimators are the same as the information bounds for estimators based on the full data, and that the multivariate normal distributions are least favorable. PMID:25313292
A Comparison of Multivariable Control Design Techniques for a Turbofan Engine Control
NASA Technical Reports Server (NTRS)
Garg, Sanjay; Watts, Stephen R.
1995-01-01
This paper compares two previously published design procedures for two different multivariable control design techniques for application to a linear engine model of a jet engine. The two multivariable control design techniques compared were the Linear Quadratic Gaussian with Loop Transfer Recovery (LQG/LTR) and the H-Infinity synthesis. The two control design techniques were used with specific previously published design procedures to synthesize controls which would provide equivalent closed loop frequency response for the primary control loops while assuring adequate loop decoupling. The resulting controllers were then reduced in order to minimize the programming and data storage requirements for a typical implementation. The reduced order linear controllers designed by each method were combined with the linear model of an advanced turbofan engine and the system performance was evaluated for the continuous linear system. Included in the performance analysis are the resulting frequency and transient responses as well as actuator usage and rate capability for each design method. The controls were also analyzed for robustness with respect to structured uncertainties in the unmodeled system dynamics. The two controls were then compared for performance capability and hardware implementation issues.
On implementing a primal-dual interior-point method for conic quadratic optimization
Erling D. Andersen; Cornelis Roos; Tamás Terlaky
2003-01-01
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
Control Law Synthesis for Vertical Fin Buffeting Alleviation Using Strain Actuation
NASA Technical Reports Server (NTRS)
Nitzsche, F.; Zimcik, D. G.; Ryall, T. G.; Moses, R. W.; Henderson, D. A.
1999-01-01
In the present investigation, the results obtained during the ground test of a closed-loop control system conducted on a full-scale fighter to attenuate vertical fin buffeting response using strain actuation are presented. Two groups of actuators consisting of piezoelectric elements distributed over the structure were designed to achieve authority over the first and second modes of the vertical fin. The control laws were synthesized using the Linear Quadratic Gaussian (LQG) method for a time-invariant control system. Three different pairs of sensors including strain gauges and accelerometers at different locations were used to close the feedback loop. The results demonstrated that measurable reductions in the root-mean-square (RMS) values of the fin dynamic response identified by the strain transducer at the critical point for fatigue at the root were achieved under the most severe buffet condition. For less severe buffet conditions, reductions of up to 58% were achieved.
NASA Technical Reports Server (NTRS)
Banks, H. T.; Silcox, R. J.; Keeling, S. L.; Wang, C.
1989-01-01
A unified treatment of the linear quadratic tracking (LQT) problem, in which a control system's dynamics are modeled by a linear evolution equation with a nonhomogeneous component that is linearly dependent on the control function u, is presented; the treatment proceeds from the theoretical formulation to a numerical approximation framework. Attention is given to two categories of LQT problems in an infinite time interval: the finite energy and the finite average energy. The behavior of the optimal solution for finite time-interval problems as the length of the interval tends to infinity is discussed. Also presented are the formulations and properties of LQT problems in a finite time interval.
Gaussian measures of entanglement versus negativities: the ordering of two-mode Gaussian states
Gerardo Adesso; Fabrizio Illuminati
2005-06-23
In this work we focus on entanglement of two--mode Gaussian states of continuous variable systems. We first review the formalism of Gaussian measures of entanglement, 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 Gaussian measures and negativities are definitely inequivalent on nonsymmetric two--mode Gaussian states (even when restricted to extremal states), while they are completely equivalent on symmetric states, where moreover the Gaussian entanglement of formation coincides with the true one. However, the inequivalence between these two families of continuous-variable entanglement measures is somehow limited. In fact we show rigorously that, at fixed negativities, the Gaussian entanglement measures are bounded from below, and we provide strong evidence that they are also bounded from above.
white Gaussian noises Bidhan Chandra Bag1, * and Chin-Kun Hu1,2, 1 Institute of Physics, Academia Sinica by multiplicative colored Gaussian and additive Gaussian white noises and found resonant activation RA behavior mentioned above driven by multiplicative colored Gaussian and addi- tive Gaussian white noises and found
NASA Astrophysics Data System (ADS)
Chen, Zheng; Mi, Chris Chunting; Xiong, Rui; Xu, Jun; You, Chenwen
2014-02-01
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.
Dispersion of Gaussian Channels Yury Polyanskiy
VerdÃº, Sergio
Dispersion of Gaussian Channels Yury Polyanskiy Dept. of Electrical Engineering Princeton. This paper finds the dispersion of the additive white Gaussian noise (AWGN) channel, the parallel AWGN approximated from two key channel parameters: the capacity and the channel dispersion. The channel dispersion
Distillability Criterion for all Bipartite Gaussian States
G. Giedke; L. -M. Duan; J. I. Cirac; P. Zoller
2001-10-09
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.
Approximate Capacity of Gaussian Relay Networks
Amir Salman Avestimehr; Suhas N. Diggavi; David N. C. Tse
2008-01-01
We present an achievable rate for general Gaussian relay networks. We show that the achievable rate is within a constant number of bits from the information-theoretic cut-set upper bound on the capacity of these networks. This constant depends on the topology of the network, but not the values of the channel gains. Therefore, we uniformly characterize the capacity of Gaussian
Gaussian Mixture Models Introducing Latent Variables
Corso, Jason J.
Sampling from the GMM To sample from the GMM, we can first generate a value for z from the marginal #12;Gaussian Mixture Models Sampling Sampling from the GMM To sample from the GMM, we can first;Gaussian Mixture Models Sampling Sampling from the GMM To sample from the GMM, we can first generate
Poon, Phoenix S. Y.; Law, C. K. [Department of Physics and Institute of Theoretical Physics, Chinese University of Hong Kong, Shatin, Hong Kong (China)
2007-11-15
We show that the negativity of a general two-mode Gaussian state can be explicitly expressed in terms of an optimal uncertainty product in position-momentum space. Such an uncertainty product is shown to have the greatest violation of a separability criterion based on positive partial transposition. Our analytic formula indicates the observables determining the negativity. For asymmetric Gaussian states, we show that the negativity is controlled by an asymmetric parameter which sets an upper bound for the negativity.
Measurement-induced disturbances and nonclassical correlations of Gaussian states
Mista, Ladislav Jr. [Department of Optics, Palacky University, 17. listopadu 12, CZ-771 46 Olomouc (Czech Republic); School of Physics and Astronomy, University of St. Andrews, North Haugh, St. Andrews, Fife, KY16 9SS, Scotland (United Kingdom); Tatham, Richard; Korolkova, Natalia [School of Physics and Astronomy, University of St. Andrews, North Haugh, St. Andrews, Fife, KY16 9SS, Scotland (United Kingdom); Girolami, Davide; Adesso, Gerardo [School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD (United Kingdom)
2011-04-15
We study quantum correlations beyond entanglement in two-mode Gaussian states of continuous-variable systems by means of the measurement-induced disturbance (MID) and its ameliorated version (AMID). In analogy with the recent studies of the Gaussian quantum discord, we define a Gaussian AMID by constraining the optimization to all bi-local Gaussian positive operator valued measurements. We solve the optimization explicitly for relevant families of states, including squeezed thermal states. Remarkably, we find that there is a finite subset of two-mode Gaussian states comprising pure states where non-Gaussian measurements such as photon counting are globally optimal for the AMID and realize a strictly smaller state disturbance compared to the best Gaussian measurements. However, for the majority of two-mode Gaussian states the unoptimized MID provides a loose overestimation of the actual content of quantum correlations, as evidenced by its comparison with Gaussian discord. This feature displays strong similarity with the case of two qubits. Upper and lower bounds for the Gaussian AMID at fixed Gaussian discord are identified. We further present a comparison between Gaussian AMID and Gaussian entanglement of formation, and classify families of two-mode states in terms of their Gaussian AMID, Gaussian discord, and Gaussian entanglement of formation. Our findings provide a further confirmation of the genuinely quantum nature of general Gaussian states, yet they reveal that non-Gaussian measurements can play a crucial role for the optimized extraction and potential exploitation of classical and nonclassical correlations in Gaussian states.
Non-Gaussian Stochastic Gravity
Jason D. Bates
2013-05-16
This paper presents a new, non-Gaussian formulation of stochastic gravity by incorporating the higher moments of the fluctuations of the quantum stress energy tensor for a free quantum scalar field in a consistent way. A scheme is developed for obtaining realizations of these fluctuations in terms of the Wightman function, and the behavior of the fluctuations is investigated. The resulting probability distribution for fluctuations of the energy density in Minkowski spacetime is found to be similar to a shifted Gamma distribution. This distribution features a minimum energy density cutoff at a small negative value, but a sharp peak in the vicinity of this cutoff such that the total probability of observing a negative value is approximately 62%, balanced by correspondingly larger but rarer positive values.
Gaussian packets in smooth isotropic media Lud ek Klime s
Cerveny, Vlastislav
. Introduction Gaussian packets, also called (space{time) Gaussian beams (Ralston, 1983), quasi- photons (Babich for the evolution of a Gaussian packet were derived by Babich & Ulin (1981) and Ralston (1983). Here we brie y
On Gaussian Beams Described by Jacobi's Equation
Steven Thomas Smith
2014-04-18
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.
Primordial black holes as a tool for constraining non-Gaussianity
Christian T. Byrnes; Edmund J. Copeland; Anne M. Green
2013-08-19
Primordial Black Holes (PBH's) can form in the early Universe from the collapse of large density fluctuations. Tight observational limits on their abundance constrain the amplitude of the primordial fluctuations on very small scales which can not otherwise be constrained, with PBH's only forming from the extremely rare large fluctuations. The number of PBH's formed is therefore sensitive to small changes in the shape of the tail of the fluctuation distribution, which itself depends on the amount of non-Gaussianity present. We study, for the first time, how quadratic and cubic local non-Gaussianity of arbitrary size (parameterised by f_nl and g_nl respectively) affects the PBH abundance and the resulting constraints on the amplitude of the fluctuations on very small scales. Intriguingly we find that even non-linearity parameters of order unity have a significant impact on the PBH abundance. The sign of the non-Gaussianity is particularly important, with the constraint on the allowed fluctuation amplitude tightening by an order of magnitude as f_nl changes from just -0.5 to 0.5. We find that if PBH's are observed in the future, then regardless of the amplitude of the fluctuations, non-negligible negative f_nl would be ruled out. Finally we show that g_nl can have an even larger effect on the number of PBH's formed than f_nl.
Nonlinear and non-Gaussian Bayesian based handwriting beautification
NASA Astrophysics Data System (ADS)
Shi, Cao; Xiao, Jianguo; Xu, Canhui; Jia, Wenhua
2013-03-01
A framework is proposed in this paper to effectively and efficiently beautify handwriting by means of a novel nonlinear and non-Gaussian Bayesian algorithm. In the proposed framework, format and size of handwriting image are firstly normalized, and then typeface in computer system is applied to optimize vision effect of handwriting. The Bayesian statistics is exploited to characterize the handwriting beautification process as a Bayesian dynamic model. The model parameters to translate, rotate and scale typeface in computer system are controlled by state equation, and the matching optimization between handwriting and transformed typeface is employed by measurement equation. Finally, the new typeface, which is transformed from the original one and gains the best nonlinear and non-Gaussian optimization, is the beautification result of handwriting. Experimental results demonstrate the proposed framework provides a creative handwriting beautification methodology to improve visual acceptance.
Applications of the Gaussian kinematic formula to CMB data analysis
NASA Astrophysics Data System (ADS)
Fantaye, Yabebal; Marinucci, Domenico; Hansen, Frode; Maino, Davide
2015-03-01
The Gaussian kinematic formula (GKF) [R. J. Adler and J. E. Taylor, Random Fields and Geometry (Springer, New York, 2007).] is an extremely powerful tool allowing for explicit analytic predictions of expected values of Minkowski functionals under realistic experimental conditions for cosmological data collections. In this paper, we implement Minkowski functionals on multipoles and needlet components of CMB fields, thus allowing a better control of cosmic variance and extraction of information on both harmonic and real domains; we then exploit the GKF to provide their expected values on spherical maps, in the presence of arbitrary sky masks, and under non-Gaussian circumstances. All our results are validated by numerical experiments, which show a perfect agreement between theoretical predictions and Monte Carlo simulations.
Quadratically consistent nodal integration for second order meshfree Galerkin methods
NASA Astrophysics Data System (ADS)
Duan, Qinglin; Wang, Bingbing; Gao, Xin; Li, Xikui
2014-08-01
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.
Quadratic algebra approach to relativistic quantum Smorodinsky-Winternitz systems
Marquette, Ian [Department of Mathematics, University of York, Heslington, York YO10 5DD (United Kingdom)
2011-04-15
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.
Mismatch management for optical and matter-wave quadratic solitons
Driben, R.; Oz, Y.; Malomed, B. A.; Gubeskys, A.; Yurovsky, V. A. [Department of Interdisciplinary Studies, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel); School of Chemistry, Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978 (Israel)
2007-02-15
We propose a way to control solitons in {chi}{sup (2)} (quadratically nonlinear) systems by means of periodic modulation imposed on the phase-mismatch parameter ('mismatch management', MM). It may be realized in the cotransmission of fundamental-frequency (FF) and second-harmonic (SH) waves in a planar optical waveguide via a long-period modulation of the usual quasi-phase-matching pattern of ferroelectric domains. In an altogether different physical setting, the MM may also be implemented by dint of the Feshbach resonance in a harmonically modulated magnetic field in a hybrid atomic-molecular Bose-Einstein condensate (BEC), with the atomic and molecular mean fields (MFs) playing the roles of the FF and SH, respectively. Accordingly, the problem is analyzed in two different ways. First, in the optical model, we identify stability regions for spatial solitons in the MM system, in terms of the MM amplitude and period, using the MF equations for spatially inhomogeneous configurations. In particular, an instability enclave is found inside the stability area. The robustness of the solitons is also tested against variation of the shape of the input pulse, and a threshold for the formation of stable solitons is found in terms of the power. Interactions between stable solitons are virtually unaffected by the MM. The second method (parametric approximation), going beyond the MF description, is developed for spatially homogeneous states in the BEC model. It demonstrates that the MF description is valid for large modulation periods, while, at smaller periods, non-MF components acquire gain, which implies destruction of the MF under the action of the high-frequency MM.
Hu, Dawei; Li, Ming; Zhou, Rui; Sun, Yi
2012-01-01
In this paper, a valid kinetic model of photo bioreactor (PBR) used for highly-effective cultivation of blue algae, Spirulina platensis, was developed for fully describing the dynamic characteristics of O(2) concentration, then a closed-loop PBR with Linear-Quadratic Gaussian (LQG) servo controller was established and optimized via digital simulation and dynamic response optimization, and the effectiveness of the closed-loop PBR was further tested and accredited by real-time simulation. The result showed that the closed-loop PBR could regulate and control the O(2) concentration in its gas phase according to the reference with desired dynamic response performance, hence microalgae with unique characteristic could be selected as a powerful tool for O(2) regulation and control whenever O(2) concentration in Bioregenerative Life Support System (BLSS) deviates from the nominal level in emergencies, and greatly enhance safety and reliability of BLSS on space and ground missions. PMID:22153599
H2, fixed architecture, control design for large scale systems. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Mercadal, Mathieu
1990-01-01
The H2, fixed architecture, control problem is a classic linear quadratic Gaussian (LQG) problem whose solution is constrained to be a linear time invariant compensator with a decentralized processing structure. The compensator can be made of p independent subcontrollers, each of which has a fixed order and connects selected sensors to selected actuators. The H2, fixed architecture, control problem allows the design of simplified feedback systems needed to control large scale systems. Its solution becomes more complicated, however, as more constraints are introduced. This work derives the necessary conditions for optimality for the problem and studies their properties. It is found that the filter and control problems couple when the architecture constraints are introduced, and that the different subcontrollers must be coordinated in order to achieve global system performance. The problem requires the simultaneous solution of highly coupled matrix equations. The use of homotopy is investigated as a numerical tool, and its convergence properties studied. It is found that the general constrained problem may have multiple stabilizing solutions, and that these solutions may be local minima or saddle points for the quadratic cost. The nature of the solution is not invariant when the parameters of the system are changed. Bifurcations occur, and a solution may continuously transform into a nonstabilizing compensator. Using a modified homotopy procedure, fixed architecture compensators are derived for models of large flexible structures to help understand the properties of the constrained solutions and compare them to the corresponding unconstrained ones.
Gaussian measures of entanglement versus negativities: Ordering of two-mode Gaussian states
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
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.
On Evgrafov-Fedoryuk's theory and quadratic differentials
NASA Astrophysics Data System (ADS)
Shapiro, Boris
2015-02-01
The purpose of this note is to recall the theory of the (homogenized) spectral problem for Schrödinger equation with a polynomial potential and its relation with quadratic differentials. We derive from results of this theory that the accumulation rays of the eigenvalues of the latter problem are in 1-1 -correspondence with the short geodesics of the singular planar metrics induced by the corresponding quadratic differential. We prove that for a polynomial potential of degree d, the number of such accumulation rays can be any positive integer between (d-1) and d atopwithdelims ()2.
Stability of the Quadratic Equation of Pexider Type
Soon-Mo Jung
2000-01-01
We will investigate the stability problem of the quadratic equation (1) and extend the results of Borelli and Forti, Czerwik,\\u000a and Rassias. By applying this result and an improved theorem of the author, we will also prove the stability of the quadratic\\u000a functional equation of Pexider type,f\\u000a 1 (x +y) + f2(x -y) =f\\u000a 3(x) +f\\u000a 4(y), for a large
Optimal control under spectral constraints: enforcing multi-photon absorption pathways
NASA Astrophysics Data System (ADS)
Reich, Daniel M.; Palao, José P.; Koch, Christiane P.
2014-06-01
Shaped pulses obtained by optimal control theory often possess unphysically broad spectra. In principle, the spectral width of a pulse can be restricted by an additional constraint in the optimization functional. However, it has so far been impossible to impose spectral constraints while strictly guaranteeing monotonic convergence. Here, we show that Krotov's method allows for simultaneously imposing temporal and spectral constraints without perturbing monotonic convergence, provided the constraints can be expressed as positive semi-definite quadratic forms. The optimized field is given by an integral equation which can be solved efficiently using the method of degenerate kernels. We demonstrate that Gaussian filters suppress undesired frequency components in the control of non-resonant two-photon absorption.
Practical robustness measures in multivariable control system analysis. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Lehtomaki, N. A.
1981-01-01
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.
Gaussian Mixture Model of Heart Rate Variability
Costa, Tommaso; Boccignone, Giuseppe; Ferraro, Mario
2012-01-01
Heart rate variability (HRV) is an important measure of sympathetic and parasympathetic functions of the autonomic nervous system and a key indicator of cardiovascular condition. This paper proposes a novel method to investigate HRV, namely by modelling it as a linear combination of Gaussians. Results show that three Gaussians are enough to describe the stationary statistics of heart variability and to provide a straightforward interpretation of the HRV power spectrum. Comparisons have been made also with synthetic data generated from different physiologically based models showing the plausibility of the Gaussian mixture parameters. PMID:22666386
Gaussian coordinate systems for the Kerr metric
M. Novello; E. Bittencourt
2010-04-22
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.
NASA Technical Reports Server (NTRS)
Gibson, J. S.; Rosen, I. G.
1986-01-01
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.
NASA Technical Reports Server (NTRS)
Gibson, J. S.; Rosen, I. G.
1988-01-01
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.
A contribution to matrix quadratic equations
V. Kucera
1972-01-01
The well-known matrix algebraic equation of the optimal control and filtering theory is considered. A necessary and sufficient condition for its solution to yield an optimal as well as asymptotically stable closed-loop system is given. The condition involves the concepts of stabilizability and detectability.
Modeling and control of flexible structures
NASA Technical Reports Server (NTRS)
Gibson, J. S.; Mingori, D. L.
1988-01-01
This monograph presents integrated modeling and controller design methods for flexible structures. The controllers, or compensators, developed are optimal in the linear-quadratic-Gaussian sense. The performance objectives, sensor and actuator locations and external disturbances influence both the construction of the model and the design of the finite dimensional compensator. The modeling and controller design procedures are carried out in parallel to ensure compatibility of these two aspects of the design problem. Model reduction techniques are introduced to keep both the model order and the controller order as small as possible. A linear distributed, or infinite dimensional, model is the theoretical basis for most of the text, but finite dimensional models arising from both lumped-mass and finite element approximations also play an important role. A central purpose of the approach here is to approximate an optimal infinite dimensional controller with an implementable finite dimensional compensator. Both convergence theory and numerical approximation methods are given. Simple examples are used to illustrate the theory.
Nonlinear Inverse Reinforcement Learning with Gaussian Processes
Washington at Seattle, University of
Nonlinear Inverse Reinforcement Learning with Gaussian Processes Sergey Levine Stanford University inverse reinforcement learn- ing. The goal of inverse reinforcement learning is to learn the reward subop- timal stochastic demonstrations, while automatically balancing the simplicity of the learned
Approximate inference in Gaussian graphical models
Malioutov, Dmitry M., 1981-
2008-01-01
The focus of this thesis is approximate inference in Gaussian graphical models. A graphical model is a family of probability distributions in which the structure of interactions among the random variables is captured by a ...
String Gas Cosmology and Non-Gaussianities
Bin Chen; Yi Wang; Wei Xue; Robert Brandenberger
2008-03-05
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.
Linearized Alternating Direction Method with Gaussian Back ...
2011-10-28
Oct 28, 2011 ... Keywords: Alternating direction method, Gaussian back substitution, Linearization, ...... [8] T. F. Chan and R. Glowinski, Finite element approximation and ... Lagrange Methods: Applications to the Solution of Boundary-valued ...
Applications of Gaussian Processes to Supernova Data
NASA Astrophysics Data System (ADS)
Thomas, Rollin; Kim, A. G.; Fakhouri, H. K.; Truong, P.
2012-01-01
We demonstrate the use of Gaussian processes in problems relevant to Type Ia supernova cosmology experiments and the analysis of supernovae in general. Gaussian processes are a powerful statistical approach that generalizes the concept of probability distributions over random variables to functions. Nonlinear regression, smoothing, and machine classification problems are target applications of Gaussian processes. Areas where Gaussian processes may be an interesting solution in Type Ia supernova cosmology are: principled construction of spectroscopic surface templates, robust extraction of spectral feature measurements, and light curve fitting/modeling. We describe our high-performance computer framework that scales to data sets of interest to current and near-term cosmology experiments, describe computational challenges in the implementation (and their resolution), and show example results using data from the Nearby Supernova Factory and simulations from the Dark Energy Survey.
On the Number of Representation of Integers into Quadratic Forms
Nikos Bagis; M. L Glasser
2014-12-18
We give formulas for the number of representations of non negative integers into quadratic forms. We also consider the case cubic and quintic forms. Finally we give a mean value asymptotic formula, for the behavior of the function that counts the number of representations of an integer as sum of two squares, known also as Gauss circle problem.
IMPROVED BOUNDS ON SARKOZY'S THEOREM FOR QUADRATIC POLYNOMIALS
Lyall, Neil
IMPROVED BOUNDS ON SÂ´ARKÂ¨OZY'S THEOREM FOR QUADRATIC POLYNOMIALS MARIAH HAMEL NEIL LYALL ALEX RICE in the late 1970s independently by SÂ´arkÂ¨ozy and Furstenberg. Furstenberg used ergodic theory (see [3]) and obtained a purely qualitative result, proving the conjecture exactly as stated above. SÂ´arkÂ¨ozy, however
IMPROVED BOUNDS ON SARKOZY'S THEOREM FOR QUADRATIC POLYNOMIALS
Lyall, Neil
IMPROVED BOUNDS ON SÂ´ARKÂ¨OZY'S THEOREM FOR QUADRATIC POLYNOMIALS MARIAH HAMEL NEIL LYALL ALEX RICE in the late 1970s independently by SÂ´arkÂ¨ozy and Furstenberg. Furstenberg used ergodic theory in [3] and obtained a purely qualitative result, proving the conjecture exactly as stated above. SÂ´arkÂ¨ozy, however
Iterative Total Variation Regularization with Non-Quadratic Fidelity
Lin He; Martin Burger; Stanley J. Osher
2006-01-01
A generalized iterative regularization procedure based on the total variation penal- ization is introduced for image denoising models with non-quadratic convex fldelity terms. By using a suitable sequence of penalty parameters we solve the issue of solvability of minimization problems arising in each step of the iterative procedure, which has been encountered in a recently developed iterative total variation procedure
Passive harmonic filters design using Fortran Feasible Sequential Quadratic Programming
Mohamed Mamdouh Abdel Aziz; Essam El-Din Abou El-Zahab; Ahmed Faheem Zobaa; Dina Mamdooh Khorshied
2007-01-01
This paper presents an application of Fortran Feasible Sequential Quadratic Programming optimization method for finding the optimum fixed shunt inductive–capacitive compensator for power factor correction of non-linear loads, where source voltage and load current harmonics are considered. Optimization minimizes the transmission line losses, and maximizes the load power factor. The performance of the proposed solution is discussed by means of
Multi-Rank Adaptive Beamforming with Linear and Quadratic Constraints
Pezeshki, Ali
Multi-Rank Adaptive Beamforming with Linear and Quadratic Constraints Henry Cox, Ali Pezeshki the signal is either rank-one of unknown orientation in a subspace or multi-rank. Only signal. The unifying component is the multi-rank MVDR beamformer followed by post processing. Detection statistics
Discriminative learning quadratic discriminant function for handwriting recognition
Cheng-Lin Liu; Hiroshi Sako; Hiromichi Fujisawa
2004-01-01
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
Lower Bounds and Exact Algorithms for the Quadratic Minimum ...
2013-12-16
Dec 16, 2013 ... (QMSTP) is a quadratic 0-1 programming problem that consists of finding a .... incidence vector of a spanning tree of G, in an abuse of language, it will ..... Even in the light of Proposition 4, computing Z(F2) by explicitly solving ..... The process stops when the insertion of every edge not in T is evaluated and.
[On skull recognition of quadratic rational Bezier curve fitting].
Zhao, Wenbin; Xie, Xiaowei; Yang, Fuzeng; Zhang, Yanning
2008-04-01
Skull recognition is a new method of biometrics recognition. A skull recognition algorithm is presented in this paper by Quadratic rational Bezier curve fitting which accurately describes the feature of skull edge; the experiment results based on skull x-ray image show the correctness of this method. PMID:18610606
Quadratic algebra contractions and 2nd order superintegrable systems
Ernest G. Kalnins; Willard Miller Jr
2014-01-04
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.
Holomorphic quantum mechanics with a quadratic Hamiltonian constraint
Jorma Louko
1993-01-01
A finite-dimensional system with a quadratic Hamiltonian constraint is Dirac quantized in holomorphic, antiholomorphic, and mixed representations. A unique inner product is found by imposing Hermitian conjugacy relations on an operator algebra. The different representations yield drastically different Hilbert spaces. In particular, all the spaces obtained in the antiholomorphic representation violate classical expectations for the spectra of certain operators, whereas
Interior-point methods for reduced Hessian successive quadratic programming
David J. Ternet; Lorenz T. Biegler
1999-01-01
Typical chemical process optimization problems have a large number of equations, but relatively few degrees of freedom. A reduced Hessian successive quadratic programming (rSQP) algorithm has been shown to be successful in solving these types of models efficiently. While the rSQP algorithm reduces the dimension of the QP subproblem solved at each iteration, the number of inequality constraints could still
LOQO: AN INTERIOR POINT CODE FOR QUADRATIC PROGRAMMING
ROBERT J. VANDERBEI
1998-01-01
This paper describes a software package, called LOQO, which implements a primal- dual interior-point method for general nonlinear programm ing. We focus in this paper mainly on the algorithm as it applies to linear and quadratic programm ing with only brief mention of the extensions to convex and general nonlinear programming, since a detailed paper describing these extensions were published
Further Development on the Interior Algorithm for Convex Quadratic Programming
Ye, Yinyu
Â tion on interior algorithms for quadratic programming (QP) or linear complementarity problem (LCP. This algorithm creates a sequence of primal and dual interior feasible points converging to the optimal solution, which create a sequence of primal and dual interior feasible points converging to the optimal solution
Efficient Color Histogram Indexing for Quadratic Form Distance Functions
James L. Hafner; Harpreet S. Sawhney; William Equitz; Myron Flickner; Wayne Niblack
1995-01-01
In image retrieval based on color, the weighted distance between color histograms of two images, represented as a quadratic form, may be defined as a match measure. However, this distance measure is computationally expensive and it operates on high dimensional features (O(N)). We propose the use of low-dimensional, simple to compute distance measures between the color distributions, and show that
FUNCTION DIGRAPHS OF QUADRATIC MAPS MODULO p Christie L. Gilbert
Reiter, Clifford A.
FUNCTION DIGRAPHS OF QUADRATIC MAPS MODULO p Christie L. Gilbert 8 Gerome Avenue, Burlington, NJ(u(x)) denote the function digraph which has Zm as vertices and edges of the form (x,u(x)) where x is an element of Zm. This digraph geometrically represents the function u(x) and paths correspond to iteration of u
FUNCTION DIGRAPHS OF QUADRATIC MAPS MODULO p Christie L. Gilbert
Storey, John D.
FUNCTION DIGRAPHS OF QUADRATIC MAPS MODULO p Christie L. Gilbert 8 Gerome Avenue, Burlington, NJ,4]. In particular, let fdm(u(x)) denote the function digraph which has Zm as vertices and edges of the form (x,u(x)) where x is an element of Zm. This digraph geometrically represents the function u(x) and paths
A class of quadratic deformations of Lie superalgebras
NASA Astrophysics Data System (ADS)
Jarvis, P. D.; Rudolph, G.; Yates, L. A.
2011-06-01
We study certain { Z}_2-graded, finite-dimensional polynomial algebras of degree 2 which are a special class of deformations of Lie superalgebras, which we call quadratic Lie superalgebras. Starting from the formal definition, we discuss the generalized Jacobi relations in the context of the Koszul property, and give a proof of the Poincaré-Birkhoff-Witt basis theorem. We give several concrete examples of quadratic Lie superalgebras for low-dimensional cases, and discuss aspects of their structure constants for the 'type I' class. We derive the equivalent of the Kac module construction for typical and atypical modules, and a related direct construction of irreducible modules due to Gould. We investigate in detail one specific case, the quadratic generalization gl2(n/1) of the Lie superalgebra sl(n/1). We formulate the general atypicality conditions at level 1, and present an analysis of zero-and one-step atypical modules for a certain family of Kac modules. Original title: Finite-dimensional quadratic Lie superalgebras (arXiv:1010.3765v1).
QUADRATIC FORMS AND PFISTER NEIGHBORS IN CHARACTERISTIC 2
DETLEV W. HOFFMANN; AHMED LAGHRIBI
We study Pfister neighbors and their characterization over fields of characteristic 2, where we include the case of singular forms. We give a somewhat simplified proof of a theorem of Fitzgerald which provides a criterion for when a nonsingular quadratic form q is similar to a Pfister form in terms of the hyperbolicity of this form over the function field
Cosmological Vorticity in a Gravity with Quadratic Order Curvature Couplings
J. Hwang; H. Noh
1997-10-07
We analyse the evolution of the rotational type cosmological perturbation in a gravity with general quadratic order gravitational coupling terms. The result is expressed independently of the generalized nature of the gravity theory, and is simply interpreted as a conservation of the angular momentum.
Algebraic rules for quadratic regularization of Newton's method
2013-08-06
Aug 6, 2013 ... The use of quadratic regularization dates back to the works of A. N. ... In view of assumption (2), when L is available one can bound the ...... Cholesky factorization fails, the successively more aggressive shifts ... problem name; its dimension (n); the number of performed iterations (#Iter) and function eval-.
A Survey of the Quadratic Assignment Problem, with Applications
CLAYTON WARREN COMMANDER
2003-01-01
The Quadratic Assignment Problem (QAP) is one of the most inter- esting and most challenging combinatorial optimization problems in exis- tence. This paper will be a survey of the QAP. An introduction discussing the origins of the problem will be provided flrst. Next, formal problem descriptions and mathematical formulations will be given. Issues pertain- ing to the computational complexity of
An Identity Based Encryption Scheme Based on Quadratic Residues
Clifford Cocks
2001-01-01
We present a novel public key cryptosystem in which the public key of a subscriber can be chosen to be a publicly known value,\\u000a such as his identity. We discuss the security of the proposed scheme, and show that this is related to the difficulty of solving\\u000a the quadratic residuosity problem
A Linear-Quadratic Game Approach to Estimation and Smoothing
Ravi N. Banavar; Jason L. Speyer
1991-01-01
An estimator and smoother for a linear time varying system, over a finite time interval, are developed from a linear quadratic (LQ) game approach. The exogenous inputs composed of the measurement and process noise, and the initial state, are assumed to be finite energy signals whose statistics are unknown. The measure of performance is in the form of a disturbance
A Model for Quadrat Sampling with “Visibility Bias”
R. Dennis Cook; Frank B. Martin
1974-01-01
In aerial census data “visibility bias” is present because of the failure to observe some animals. A model is presented for quadrat sampling of randomly occurring groups whose size follows a single parameter power series distribution when there is a probability q > 0 of missing single animals. Maximum likelihood estimates of group density, average group size, and the visibility
Lower bounding procedure for the Asymmetric Quadratic Traveling ...
2015-02-04
a lower bound is to linearize the quadratic terms xijxjk for all (i, j),(j, k) ? A ..... Consider any cycle C. Since column Cp is the selected column to enter the basis we ..... some kind of subtour elimination constraint, we restrict the search to find a
Analysis of Quadratic Diophantine Equations with Fibonacci Number Solutions
ERIC Educational Resources Information Center
Leyendekkers, J. V.; Shannon, A. G.
2004-01-01
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.
On a bi-quadratic functional equation and its stability
Won-Gil Park; Jae-Hyeong Bae
2005-01-01
In this paper, we obtain the general solution and the generalized Hyers–Ulam stability of the bi-quadratic functional equation f(x+y,z+w)+f(x+y,z-w)+f(x-y,z+w)+f(x-y,z-w)=4[f(x,z)+f(x,w)+f(y,z)+f(y,w)].
Quadratic Expressions by Means of "Summing All the Matchsticks"
ERIC Educational Resources Information Center
Gierdien, M. Faaiz
2012-01-01
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…
Feasibility testing for systems of real quadratic equations
Alexander I. Barvinok
1992-01-01
We consider the problem of deciding whether a given system of quadratic homogeneous equations over the reals has non-trivial solution. We design an approximative algorithm whose complexity is polynomial in the number of variables and exponential in the number of equations. Some applications to general systems of polynomial equations and inequalities over the reals are discussed.
Feasibility Testing for Systems of Real Quadratic Equations
Alexander I. Barvinok
1993-01-01
We consider the problem of deciding whether a given system of quadratic homogeneous equations over the reals has nontrivial\\u000a solution. We design an algorithm which, for a fixed number of equations, uses a number of arithmetic operations bounded by\\u000a a polynomial in the number of variables only.
Monotonic solutions of a quadratic integral equation of Volterra type
A. Martinon
2004-01-01
We study a nonlinear quadratic integral equation of Volterra type in the Banach space of real functions defined and continuous on a bounded and closed interval. With the help of a suitable measure of noncompactness, we show that the mentioned integral equation has monotonic solutions.
Support set expansion sensitivity analysis in convex quadratic optimization
Kamal Mirnia; Alireza Ghaffari Hadigheh
2007-01-01
In support set expansion sensitivity analysis, one concerns to find the range of parameter variation where the perturbed problem has an optimal solution with the support set that includes the support set of the given optimal solution of the unperturbed problem. In this article, we consider the perturbed convex quadratic optimization problem and present a method to identify the support
Monotonic solutions of a quadratic integral equation of fractional order
Józef Bana?; Beata Rzepka
2007-01-01
In the paper we indicate an error made in the proof of the main result of the paper [M.A. Darwish, On quadratic integral equation of fractional orders, J. Math. Anal. Appl. 311 (2005) 112–119]. Moreover, we provide correct proof of a slightly modified version of the mentioned result. The main tool used in our proof is the technique associated with
Linear and Quadratic Change: A Problem from Japan
ERIC Educational Resources Information Center
Peterson, Blake E.
2006-01-01
In the fall of 2003, the author conducted research on the student teaching process in Japan. The basis for most of the lessons observed was rich mathematics problems. Upon returning to the US, the author used one such problem while teaching an algebra 2 class. This article introduces that problem, which gives rise to both linear and quadratic…