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.
Steering of Frequency Standards by the Use of Linear Quadratic Gaussian Control Theory
NASA Technical Reports Server (NTRS)
Koppang, Paul; Leland, Robert
1996-01-01
Linear quadratic Gaussian control is a technique that uses Kalman filtering to estimate a state vector used for input into a control calculation. A control correction is calculated by minimizing a quadratic cost function that is dependent on both the state vector and the control amount. Different penalties, chosen by the designer, are assessed by the controller as the state vector and control amount vary from given optimal values. With this feature controllers can be designed to force the phase and frequency differences between two standards to zero either more or less aggressively depending on the application. Data will be used to show how using different parameters in the cost function analysis affects the steering and the stability of the frequency standards.
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.
Linear quadratic Gaussian and feedforward controllers for the DSS-13 antenna
NASA Technical Reports Server (NTRS)
Gawronski, W. K.; Racho, C. S.; Mellstrom, J. A.
1994-01-01
The controller development and the tracking performance evaluation for the DSS-13 antenna are presented. A trajectory preprocessor, linear quadratic Gaussian (LQG) controller, feedforward controller, and their combination were designed, built, analyzed, and tested. The antenna exhibits nonlinear behavior when the input to the antenna and/or the derivative of this input exceeds the imposed limits; for slewing and acquisition commands, these limits are typically violated. A trajectory preprocessor was designed to ensure that the antenna behaves linearly, just to prevent nonlinear limit cycling. The estimator model for the LQG controller was identified from the data obtained from the field test. Based on an LQG balanced representation, a reduced-order LQG controller was obtained. The feedforward controller and the combination of the LQG and feedforward controller were also investigated. The performance of the controllers was evaluated with the tracking errors (due to following a trajectory) and the disturbance errors (due to the disturbances acting on the antenna). The LQG controller has good disturbance rejection properties and satisfactory tracking errors. The feedforward controller has small tracking errors but poor disturbance rejection properties. The combined LQG and feedforward controller exhibits small tracking errors as well as good disturbance rejection properties. However, the cost for this performance is the complexity of the controller.
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)
Gangsaas, D.; Ly, U.; Norman, D. C.
1981-01-01
A modified linear quadratic Gaussian (LQG) synthesis procedure has been used to design low-order robust multiloop controllers for a flexible airplane. The introduction of properly constructed fictitious Gauss-Markov processes in the control loops allowed meeting classical frequency-domain stability criteria using the direct synthesis procedures of modern time-domain control theory. Model reduction was used to simplify the control laws to the point where they could be easily implemented on onboard flight computers. These control laws provided excellent gust load and flutter mode control with good stability margins and compared very favorably to other control laws synthesized by the classical root-locus technique.
NASA Astrophysics Data System (ADS)
Clement, M. D.; Navratil, G. A.; Hanson, J. M.; Bialek, J.; Piglowski, D. A.; Penaflor, B. G.
2015-11-01
A Graphics Processing Unit (GPU) based control system has been installed on the DIII-D tokamak for Resistive Wall Mode (RWM) control similar to one implemented at the HBT-EP tokamak. DIII-D can excite RWMs, which are strong, locked or nearly locked kink modes whose rotation frequencies do not evolve quickly and are slow compared to their growth rates. Simulations have predicted that modern control techniques like Linear Quadratic Gaussian (LQG) control will perform better than classical control techniques when using control coils external to the vacuum vessel. An LQG control algorithm based on the VALEN model for the RWM has been developed and tested on this system. Early tests have shown the algorithm is able to track and suppress with external control coils the plasma response of an n=1 perturbation driven by internal control coils. An overview of the control hardware, VALEN model, control algorithm and initial results will be presented. Supported by the US DOE under DE-FG02-04ER54761 and DE-FC02-04ER54698.
NASA Technical Reports Server (NTRS)
Joshi, S. M.; Groom, N. J.
1979-01-01
The paper presents several approaches for the design of reduced order controllers for large space structures. These approaches are shown to be based on LQG control theory and include truncation, modified truncation regulators and estimators, use of higher order estimators, selective modal suppression, and use of polynomial estimators. Further, the use of direct sensor feedback, as opposed to a state estimator, is investigated for some of these approaches. Finally, numerical results are given for a long free beam.
Habibullah, H. Pota, H. R. Petersen, I. R.
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.
NASA Astrophysics Data System (ADS)
Habibullah, H.; Pota, H. R.; Petersen, I. R.
2014-03-01
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.
Linear-Quadratic-Gaussian Regulator Developed for a Magnetic Bearing
NASA Technical Reports Server (NTRS)
Choi, Benjamin B.
2002-01-01
Linear-Quadratic-Gaussian (LQG) control is a modern state-space technique for designing optimal dynamic regulators. It enables us to trade off regulation performance and control effort, and to take into account process and measurement noise. The Structural Mechanics and Dynamics Branch at the NASA Glenn Research Center has developed an LQG control for a fault-tolerant magnetic bearing suspension rig to optimize system performance and to reduce the sensor and processing noise. The LQG regulator consists of an optimal state-feedback gain and a Kalman state estimator. The first design step is to seek a state-feedback law that minimizes the cost function of regulation performance, which is measured by a quadratic performance criterion with user-specified weighting matrices, and to define the tradeoff between regulation performance and control effort. The next design step is to derive a state estimator using a Kalman filter because the optimal state feedback cannot be implemented without full state measurement. Since the Kalman filter is an optimal estimator when dealing with Gaussian white noise, it minimizes the asymptotic covariance of the estimation error.
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
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.
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.
Non-Gaussianity and gravitational waves from a quadratic and self-interacting curvaton
Fonseca, Jose; Wands, David
2011-03-15
In this paper we consider how non-Gaussianity of the primordial density perturbation and the amplitude of gravitational waves from inflation can be used to determine parameters of the curvaton scenario for the origin of structure. We show that in the simplest quadratic model, where the curvaton evolves as a free scalar field, measurement of the bispectrum relative to the power spectrum, f{sub NL}, and the tensor-to-scalar ratio can determine both the expectation value of the curvaton field during inflation and its dimensionless decay rate relative to the curvaton mass. We show how these predictions are altered by the introduction of self-interactions, in models where higher-order corrections are determined by a characteristic mass scale and discuss how additional information about primordial non-Gaussianity and scale dependence may constrain curvaton interactions.
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.
Linear quadratic stochastic control of atomic hydrogen masers.
Koppang, P; Leland, R
1999-01-01
Data are given showing the results of using the linear quadratic Gaussian (LQG) technique to steer remote hydrogen masers to Coordinated Universal Time (UTC) as given by the United States Naval Observatory (USNO) via two-way satellite time transfer and the Global Positioning System (GPS). Data also are shown from the results of steering a hydrogen maser to the real-time USNO mean. A general overview of the theory behind the LQG technique also is given. The LQG control is a technique that uses Kalman filtering to estimate time and frequency errors used as input into a control calculation. A discrete frequency steer is calculated by minimizing a quadratic cost function that is dependent on both the time and frequency errors and the control effort. Different penalties, chosen by the designer, are assessed by the controller as the time and frequency errors and control effort vary from zero. With this feature, controllers can be designed to force the time and frequency differences between two standards to zero, either more or less aggressively depending on the application.
S., Juan Manuel Franco; Cywiak, Moises; Cywiak, David; Mourad, Idir
2015-06-24
A homodyne profiler is used for recording the intensity distribution of focused non-truncated Gaussian beams. The spatial distributions are obtained at planes in the vicinity of the back-focal plane of a focusing lens placed at different distances from a He–Ne laser beam with a Gaussian intensity profile. Comparisons of the experimental data with those obtained from the analytical equations for an ideal focusing lens allow us to propose formulae to fine-tune the quadratic term in the Fresnel Gaussian shape invariant at each interface of the propagated field. Furthermore, we give analytical expressions to calculate adequately the propagation of the field through an optical system.
Reaction Wheel Control Design Using Linear Quadratic Controller
NASA Astrophysics Data System (ADS)
Nubli Muhamad, Nur; Susanto, Erwin; Syihabuddin, Budi; Prasetya Dwi Wibawa, Ig.
2016-01-01
This paper studies the design of active attitude control system of a nanosatellite in a single axis. In this paper, we consider dc motor based reaction wheel as an actuator, because of its pointing accuracy. However, the power consumption of the dc motor is often relatively large and needed to be optimized. Linear quadratic controller is supposed to have an ability to minimize power consumption and able to enhance the system performance. To show the advantage of this method, simulation result of attitude response, state trajectory, and trajectory of DC motor voltage are presented.
Tuning a fuzzy controller using quadratic response surfaces
NASA Technical Reports Server (NTRS)
Schott, Brian; Whalen, Thomas
1992-01-01
Response surface methodology, an alternative method to traditional tuning of a fuzzy controller, is described. An example based on a simulated inverted pendulum 'plant' shows that with (only) 15 trial runs, the controller can be calibrated using a quadratic form to approximate the response surface.
A Riccati approach for constrained linear quadratic optimal control
NASA Astrophysics Data System (ADS)
Sideris, Athanasios; Rodriguez, Luis A.
2011-02-01
An active-set method is proposed for solving linear quadratic optimal control problems subject to general linear inequality path constraints including mixed state-control and state-only constraints. A Riccati-based approach is developed for efficiently solving the equality constrained optimal control subproblems generated during the procedure. The solution of each subproblem requires computations that scale linearly with the horizon length. The algorithm is illustrated with numerical examples.
Control charts for non-Gaussian distributions
NASA Astrophysics Data System (ADS)
Babus, Florina; Kobi, Abdessamad; Tiplica, Th.; Bacivarov, Ioan; Bacivarov, Angelica
2007-05-01
Traditional statistical process control (SPC) techniques applied in the industrial processes field consider often that the distribution ofdata is Gaussian. The estimation ofparameters, the detection ofthe out oforder situations and the control of the followed characteristics are easy to achieve for the normal populations. In reality, whatever the origin of a characteristic (large series productions for components, mechanical parts of OE communication systems, etc. ) the curve of distributions of the measured values is generally far from being normal. The simple approximation to the Gauss distribution and the use of the classical control methods sometimes induces serious errors. In this paper, a study on the statistical control of non Gaussian populations is presented. Particularly we discuss the Rayleigh and the Weibull distribution as being representatives in (SPC for some category of data. The X control charts with variable limits are tested. Experimental simulations are presented for different parameters of the two distributions. The results confirm the methodology and encourage the research in the field of non Gaussian processes.
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.
Dynamics and linear quadratic optimal control of flexible multibody systems
NASA Astrophysics Data System (ADS)
Tung, Chin-Wei
1994-12-01
An efficient algorithm for the modeling, dynamic analysis, and optimal control of flexible multibody systems (FMBS) is presented. The cantilevered Bernoulli-Euler beam model and the assumed mode method are used to represent flexibility of elastic bodies in 3D vibration problems. Centrifugal stiffening effects are introduced to correctly represent the dynamic response. The governing equations of motion are based on Kane's equations, adopting a recursive formulation and strategic positioning of the generalized coordinates. The linear quadratic optimization scheme is employed to formulate the vibration control problem. The solutions to the Riccati equation and the use of Kalman gain as optimal control feedbacks to the control of flexibility are also introduced. Based on the optimal control theory and the property of the built-in redundancy for flexible multibody systems, the performance index measure in the optimization control of such systems can be classified into two manifolds: (1) using the extra degrees of freedom resulting from redundancy as control inputs and choosing an integral-type performance index which results in a global optimization scheme and (2) using the joint forces and torques as control inputs and allowing the system output state to keep close track to a reference state while the performance index is kept minimum. Several numerical examples are presented to demonstrate the effectiveness of the methodologies developed.
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
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).
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.
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.
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
Optimal Control Using Pontryagin's Maximum Principle in a Linear Quadratic Differential Game
NASA Astrophysics Data System (ADS)
Khakestari, Marzieh; Ibragimov, Gafurjan; Suleiman, Mohamed
This paper deals with a class of two person zero-sum linear quadratic differential games, where the control functions for both players subject to integral constraints. Also the necessary conditions of the Maximum Principle are studied. Main objective in this work is to obtain optimal control by using method of Pontryagin's Maximum Principle. This method for a time-varying linear quadratic differential game is described. Finally, we discuss about an example.
Controllably accelerating and decelerating Airy–Bessel–Gaussian wave packets
NASA Astrophysics Data System (ADS)
Deng, Fu; Yu, Weihao; Deng, Dongmei
2016-11-01
By solving the (3 + 1)D free-space Schrödinger equation in polar coordinates analytically, we have investigated the propagation of 3D controllably accelerating and decelerating Airy–Bessel–Gaussian (CAiBG) wave packets, even CAiBG wave packets, odd CAiBG wave packets and the superposition of several CAiBG wave packets in free space. The CAiBG wave packets are constructed with the Airy pulses with initial velocity in temporal domain and the Bessel–Gaussian beams in space domain. Due to the initial velocity on Airy pulses, we can obtain decelerating and accelerating Airy–Bessel–Gaussian wave packets by selecting different initial velocities. Moreover, by superposing several CAiBG wave packets, we can obtain the rotating wave packets.
NASA Astrophysics Data System (ADS)
Popescu, Mihai; Dumitrache, Alexandru
2011-05-01
This study refers to minimization of quadratic functionals in infinite time. The coefficients of the quadratic form are quadratic matrix, function of the state variable. Dynamic constraints are represented by bilinear differential systems of the form x˙=A(x)x+B(x)u,x(0)=x0. One selects an adequate factorization of A( x) such that the analyzed system should be controllable. Employing the Hamilton-Jacobi equation it results the matrix algebraic equation of Riccati associated to the optimum problem. The necessary extremum conditions determine the adjoint variables λ and the control variables u as functions of state variable, as well as the adjoint system corresponding to those functions. Thus one obtains a matrix differential equation where the solution representing the positive defined symmetric matrix P( x), verifies the Riccati algebraic equation. The stability analysis for the autonomous systems solution resulting for the determined feedback control is performed using the Liapunov function method. Finally we present certain significant cases.
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.
Linear quadratic servo control of a reusable rocket engine
NASA Technical Reports Server (NTRS)
Musgrave, Jeffrey L.
1991-01-01
A design method for a servo compensator is developed in the frequency domain using singular values. The method is applied to a reusable rocket engine. An intelligent control system for reusable rocket engines was proposed which includes a diagnostic system, a control system, and an intelligent coordinator which determines engine control strategies based on the identified failure modes. The method provides a means of generating various linear multivariable controllers capable of meeting performance and robustness specifications and accommodating failure modes identified by the diagnostic system. Command following with set point control is necessary for engine operation. A Kalman filter reconstructs the state while loop transfer recovery recovers the required degree of robustness while maintaining satisfactory rejection of sensor noise from the command error. The approach is applied to the design of a controller for a rocket engine satisfying performance constraints in the frequency domain. Simulation results demonstrate the performance of the linear design on a nonlinear engine model over all power levels during mainstage operation.
Multivariable design of improved linear quadratic regulation control for MIMO industrial processes.
Zhang, Ridong; Lu, Renquan; Jin, Qibing
2015-07-01
In this study, a multivariable linear quadratic control system using a new state space structure was developed for the chamber pressure in the industrial coke furnace. Such processes typically have complex and nonlinear dynamic behavior, which causes the performance of controllers using conventional design and tuning to be poor or to require significant effort in practice. The process model is first treated into a new state space form and the implementation of linear quadratic control is designed using this new model structure. Performance in terms of regulatory/servo, disturbance rejection and measurement noise problems were all compared with the recent model predictive control strategy. Results revealed that the control system showed more robustness and improved the closed-loop process performance under model/process mismatches.
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.
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.
A new linear quadratic optimal controller for the 34-meter high efficiency antenna position loop
NASA Technical Reports Server (NTRS)
Nickerson, J. A.
1987-01-01
The design of a new position loop controller for the 34-meter High Efficiency Deep Space antennas using linear quadratic (LQ) optimal control techniques is discussed. The LQ optimal control theory is reviewed, and model development and verification are discussed. Families of optimal gain vectors are generated by varying weight parameters. Performance specifications were used to select a final gain vector. Estimator dynamics were selected and the corresponding gain vectors were computed. Final estimator selection was based on position, commanded rate, and estimator error responses.
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)
Frost, Susan A.; Bodson, Marc; Acosta, Diana M.
2009-01-01
The Next Generation (NextGen) transport aircraft configurations being investigated as part of the NASA Aeronautics Subsonic Fixed Wing Project have more control surfaces, or control effectors, than existing transport aircraft configurations. Conventional flight control is achieved through two symmetric elevators, two antisymmetric ailerons, and a rudder. The five effectors, reduced to three command variables, produce moments along the three main axes of the aircraft and enable the pilot to control the attitude and flight path of the aircraft. The NextGen aircraft will have additional redundant control effectors to control the three moments, creating a situation where the aircraft is over-actuated and where a simple relationship does not exist anymore between the required effector deflections and the desired moments. NextGen flight controllers will incorporate control allocation algorithms to determine the optimal effector commands and attain the desired moments, taking into account the effector limits. Approaches to solving the problem using linear programming and quadratic programming algorithms have been proposed and tested. It is of great interest to understand their relative advantages and disadvantages and how design parameters may affect their properties. In this paper, we investigate the sensitivity of the effector commands with respect to the desired moments and show on some examples that the solutions provided using the l2 norm of quadratic programming are less sensitive than those using the l1 norm of linear programming.
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.
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.
Singular linear-quadratic control problem for systems with linear delay
Sesekin, A. N.
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.
Anderson, Charles W; Young, Peter Michael; Buehner, Michael R; Knight, James N; Bush, Keith A; Hittle, Douglas C
2007-07-01
The applicability of machine learning techniques for feedback control systems is limited by a lack of stability guarantees. Robust control theory offers a framework for analyzing the stability of feedback control loops, but for the integral quadratic constraint (IQC) framework used here, all components are required to be represented as linear, time-invariant systems plus uncertainties with, for IQCs used here, bounded gain. In this paper, the stability of a control loop including a recurrent neural network (NN) is analyzed by replacing the nonlinear and time-varying components of the NN with IQCs on their gain. As a result, a range of the NN's weights is found within which stability is guaranteed. An algorithm is demonstrated for training the recurrent NN using reinforcement learning and guaranteeing stability while learning.
Irrigation Control in the Presence of Salinity: Extended Linear Quadratic Approach
NASA Astrophysics Data System (ADS)
Bras, Rafael L.; Seo, Dong-Jun
1987-07-01
An intraseasonal irrigation scheduling problem is dealt with via extended linear quadratic (ELQ) control. The ELQ control is well-suited for constrained multidimensional problems and provides openloop feedback control rules over the control horizon. A conceptual model is developed to describe the dynamics of water allocation and salt movement in the root zone of a crop. Moisture stress and osmotic stress are combined to obtain the integrated inhibitory effect of salinity on transpiration. For the intraseasonal model to be effective against perennial salt accumulation in the root zone, it should be able to yield control laws which will lead to favorable root zone conditions at the end of an irrigation season, thus avoiding any significant leaching prior to the next growing season. This long-term aspect of salinity control is handled via probabilistic state constraints which impose desired salinity and moisture levels with desired confidence level. The ELQ control is employed in a case study of expected net benefit maximization over an irrigation season of corn in Fort Morgan, Colorado. The results, in general, correspond well with expected irrigation schedules under different conditions and provide valuable information on both short- and long-term aspects of irrigation control under saline conditions. The ELQ control, being an analytic iterative solution scheme with theoretically guaranteed fast convergence, has a distinct computational advantage over state-of-the-art procedures.
Linear-quadratic-regulator pointing control system design for a high-altitude balloon payload
White, J.E.; Etter, J.R.
1987-11-01
A pointing control system design for the science package of a NASA high-altitude research balloon is described. The balloon assembly consists of a single helium balloon connected to a payload recovery parachute, payload gondola, and ballast hopper. Pointing of the scientific payload is accomplished via an arrangement of drive motors and a flywheel. Linear quadratic regulator (LQR) synthesis techniques are employed to produce the azimuth and elevation controller designs. The use of LQR synthesis is motivated by the azimuthal dynamic coupling encountered between the balloon and gondola. Two control devices are employed in azimuth, one of which is a decoupler motor and the other a flywheel. The decoupler motor is intended to isolate the gondola from the balloon such that the flywheel can be accelerated or decelerated about a steady-state angular velocity to provide precise azimuthal pointing. The multiple-input/multiple-output nature of the azimuth pointing problem is best handled in a matrix synthesis procedure such as LQR. The controller design methodology is explained, and a combination of time responses and singular value analyses are used to analytically evaluate the performance of the control system. 11 refs., 17 figs.
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…
NASA Astrophysics Data System (ADS)
Arimoto, Suguru
An optimal regulator problem for endpoint position control of a robot arm with (or without) redundancy in its total degrees-of-freedom (DOF) is solved by combining Riemannian geometry with nonlinear control theory. Given a target point, within the task-space, that the arm endpoint should reach, a task-space position feedback with joint damping is shown to asymptotically stabilize reaching movements even if the number of DOF of the arm is greater than the dimension of the task space and thereby the inverse kinematics is ill-posed. Usually the speed of convergence of the endpoint trajectory is unsatisfactory, depending on the choice of feedback gains for joint damping. Hence, to speed up the convergence without incurring further energy consumption, an optimal control design for minimizing a performance index composed of an integral of joint dissipation energy plus a linear quadratic form of the task-space control input and output is introduced. It is then shown that the Hamilton-Jacobi-Bellman equation derived from the principle of optimality is solvable in control variables and the Hamilton-Jacobi equation itself has an explicit solution. Although the state of the original dynamics (the Euler-Lagrange equation) with DOF-redundancy contains uncontrollable and unobservable manifolds, the dynamics satisfies a nonlinear version of the Kalman-Yakubovich-Popov lemma and the task-space input-output passivity. An inverse problem of optimal regulator design for robotic arms under the effect of gravity is also tackled by combining Riemannian geometry with passivity-based control theory.
Ayvaz, Muzaffer; Demiralp, Metin
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.
A feedback control strategy for the airfoil system under non-Gaussian colored noise excitation.
Huang, Yong; Tao, Gang
2014-09-01
The stability of a binary airfoil with feedback control under stochastic disturbances, a non-Gaussian colored noise, is studied in this paper. First, based on some approximated theories and methods the non-Gaussian colored noise is simplified to an Ornstein-Uhlenbeck process. Furthermore, via the stochastic averaging method and the logarithmic polar transformation, one dimensional diffusion process can be obtained. At last by applying the boundary conditions, the largest Lyapunov exponent which can determine the almost-sure stability of the system and the effective region of control parameters is calculated.
A feedback control strategy for the airfoil system under non-Gaussian colored noise excitation
Huang, Yong E-mail: taogang@njust.edu.cn; Tao, Gang E-mail: taogang@njust.edu.cn
2014-09-01
The stability of a binary airfoil with feedback control under stochastic disturbances, a non-Gaussian colored noise, is studied in this paper. First, based on some approximated theories and methods the non-Gaussian colored noise is simplified to an Ornstein-Uhlenbeck process. Furthermore, via the stochastic averaging method and the logarithmic polar transformation, one dimensional diffusion process can be obtained. At last by applying the boundary conditions, the largest Lyapunov exponent which can determine the almost-sure stability of the system and the effective region of control parameters is calculated.
Kim, Dae Seok; Cha, Yun Jeong; Kim, Mun Ho; Lavrentovich, Oleg D; Yoon, Dong Ki
2016-01-01
Soft materials with layered structure such as membranes, block copolymers and smectics exhibit intriguing morphologies with nontrivial curvatures. Here, we report restructuring the Gaussian and mean curvatures of smectic A films with free surface in the process of sintering, that is, reshaping at elevated temperatures. The pattern of alternating patches of negative, zero and positive mean curvature of the air-smectic interface has a profound effect on the rate of sublimation. As a result of sublimation, condensation and restructuring, initially equilibrium smectic films with negative and zero Gaussian curvature are transformed into structures with pronounced positive Gaussian curvature of layers packing, which are rare in the samples obtained by cooling from the isotropic melt. The observed relationship between the curvatures, bulk elastic behaviour and interfacial geometries in sintering of smectic liquid crystals might pave the way for new approaches to control soft morphologies at micron and submicron scales. PMID:26725975
Kim, Dae Seok; Cha, Yun Jeong; Kim, Mun Ho; Lavrentovich, Oleg D; Yoon, Dong Ki
2016-01-04
Soft materials with layered structure such as membranes, block copolymers and smectics exhibit intriguing morphologies with nontrivial curvatures. Here, we report restructuring the Gaussian and mean curvatures of smectic A films with free surface in the process of sintering, that is, reshaping at elevated temperatures. The pattern of alternating patches of negative, zero and positive mean curvature of the air-smectic interface has a profound effect on the rate of sublimation. As a result of sublimation, condensation and restructuring, initially equilibrium smectic films with negative and zero Gaussian curvature are transformed into structures with pronounced positive Gaussian curvature of layers packing, which are rare in the samples obtained by cooling from the isotropic melt. The observed relationship between the curvatures, bulk elastic behaviour and interfacial geometries in sintering of smectic liquid crystals might pave the way for new approaches to control soft morphologies at micron and submicron scales.
Kim, Dae Seok; Cha, Yun Jeong; Kim, Mun Ho; Lavrentovich, Oleg D.; Yoon, Dong Ki
2016-01-01
Soft materials with layered structure such as membranes, block copolymers and smectics exhibit intriguing morphologies with nontrivial curvatures. Here, we report restructuring the Gaussian and mean curvatures of smectic A films with free surface in the process of sintering, that is, reshaping at elevated temperatures. The pattern of alternating patches of negative, zero and positive mean curvature of the air–smectic interface has a profound effect on the rate of sublimation. As a result of sublimation, condensation and restructuring, initially equilibrium smectic films with negative and zero Gaussian curvature are transformed into structures with pronounced positive Gaussian curvature of layers packing, which are rare in the samples obtained by cooling from the isotropic melt. The observed relationship between the curvatures, bulk elastic behaviour and interfacial geometries in sintering of smectic liquid crystals might pave the way for new approaches to control soft morphologies at micron and submicron scales. PMID:26725975
NASA Astrophysics Data System (ADS)
Chen, Shinn-Horng; Chou, Jyh-Horng; Zheng, Liang-An; Lin, Sheng-Kai
2010-08-01
This paper presents a design method for designing the robust-stable and quadratic-finite-horizon-optimal controllers of uncertain active suspension systems. The method integrates a robust stabilisability condition, the orthogonal functions approach (OFA) and the hybrid Taguchi-genetic algorithm (HTGA). Using the integrative computational method, a robust-stable and quadratic-finite-horizon-optimal controller with low-trajectory sensitivity can be obtained such that (i) the active suspension system with elemental parametric uncertainties is stabilised and (ii) a quadratic-finite-horizon-integral performance index including a quadratic trajectory sensitivity term for the nominal active suspension system is minimised. The robust stabilisability condition is proposed in terms of linear matrix inequalities (LMIs). Based on the OFA, an algebraic algorithm only involving the algebraic computation is derived for solving the nominal active suspension feedback dynamic equations. By using the OFA and the LMI-based robust stabilisability condition, the dynamic optimisation problem for the robust-stable and quadratic-finite-horizon-optimal controller design of the linear uncertain active suspension system is transformed into a static-constrained-optimisation problem represented by the algebraic equations with constraint of LMI-based robust stabilisability condition; thus greatly simplifies the design problem. Then, for the static-constrained-optimisation problem, the HTGA is employed to find the robust-stable and quadratic-finite-horizon-optimal controllers of the linear uncertain active suspension systems. A design example is given to demonstrate the applicability of the proposed integrative computational approach.
NASA Astrophysics Data System (ADS)
Na, Xiaoxiang; Cole, David J.
2013-02-01
This paper is concerned with the modelling of strategic interactions between the human driver and the vehicle active front steering (AFS) controller in a path-following task where the two controllers hold different target paths. The work is aimed at extending the use of mathematical models in representing driver steering behaviour in complicated driving situations. Two game theoretic approaches, namely linear quadratic game and non-cooperative model predictive control (non-cooperative MPC), are used for developing the driver-AFS interactive steering control model. For each approach, the open-loop Nash steering control solution is derived; the influences of the path-following weights, preview and control horizons, driver time delay and arm neuromuscular system (NMS) dynamics are investigated, and the CPU time consumed is recorded. It is found that the two approaches give identical time histories as well as control gains, while the non-cooperative MPC method uses much less CPU time. Specifically, it is observed that the introduction of weight on the integral of vehicle lateral displacement error helps to eliminate the steady-state path-following error; the increase in preview horizon and NMS natural frequency and the decline in time delay and NMS damping ratio improve the path-following accuracy.
Spin-controlled orbital motion in tightly focused high-order Laguerre-Gaussian beams.
Cao, Yongyin; Zhu, Tongtong; Lv, Haiyi; Ding, Weiqiang
2016-02-22
Spin angular momentum can contribute to both optical force and torque exerted on spheres. Orbit rate of spheres located in tightly focused LG beams with the same azimuthal mode index l is spin-controlled due to spin-orbit coupling. Laguerre-Gaussian beams with high-order azimuthal mode are used here to study the orbit rate of dielectric spheres. Orbit rates of spheres with varying sizes and refravtive indices are investigated as well as optical forces acting on spheres in LG beams with different azimuthal modes. These results would be much helpful to investigation on optical rotation and transfer of spin and orbital angular momentum. PMID:26906996
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.
NASA Astrophysics Data System (ADS)
Yi, Yang; Sun, ChangYin; Guo, Lei
2013-07-01
A new generalised iterative learning algorithm is presented for complex dynamic non-Gaussian stochastic processes. After designed neural networks are used to approximate the output probability density function (PDF) of the stochastic system in the repetitive processes or the batch processes, the complex probabilistic tracking control to the output PDF is simplified into a parameter tuning problem between two adjacent repetitive processes. Under this framework, this article studies a novel model free iterative learning control problem and proposes a convex optimisation algorithm based on a set of designed linear matrix inequalities and L 1 optimisation index. It is noted that such an algorithm can improve the tracking performance and robustness for the closed-loop PDF control. A simulated example is given, which effectively demonstrates the use of the proposed control algorithm.
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…
Gaussian Processes for Data-Efficient Learning in Robotics and Control.
Deisenroth, Marc Peter; Fox, Dieter; Rasmussen, Carl Edward
2015-02-01
Autonomous learning has been a promising direction in control and robotics for more than a decade since data-driven learning allows to reduce the amount of engineering knowledge, which is otherwise required. However, autonomous reinforcement learning (RL) approaches typically require many interactions with the system to learn controllers, which is a practical limitation in real systems, such as robots, where many interactions can be impractical and time consuming. To address this problem, current learning approaches typically require task-specific knowledge in form of expert demonstrations, realistic simulators, pre-shaped policies, or specific knowledge about the underlying dynamics. In this paper, we follow a different approach and speed up learning by extracting more information from data. In particular, we learn a probabilistic, non-parametric Gaussian process transition model of the system. By explicitly incorporating model uncertainty into long-term planning and controller learning our approach reduces the effects of model errors, a key problem in model-based learning. Compared to state-of-the art RL our model-based policy search method achieves an unprecedented speed of learning. We demonstrate its applicability to autonomous learning in real robot and control tasks. PMID:26353251
Qubit Noise Spectroscopy for Non-Gaussian Dephasing Environments.
Norris, Leigh M; Paz-Silva, Gerardo A; Viola, Lorenza
2016-04-15
We introduce open-loop quantum control protocols for characterizing the spectral properties of non-Gaussian noise, applicable to both classical and quantum dephasing environments. By engineering a multidimensional frequency comb via repetition of suitably designed pulse sequences, the desired high-order spectra may be related to observable properties of the qubit probe. We prove that access to a high time resolution is key to achieving spectral reconstruction over an extended bandwidth, overcoming the limitations of existing schemes. Non-Gaussian spectroscopy is demonstrated for a classical noise model describing quadratic dephasing at an optimal point, as well as a quantum spin-boson model out of equilibrium. In both cases, we obtain spectral reconstructions that accurately predict the qubit dynamics in the non-Gaussian regime.
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.
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.
NASA Astrophysics Data System (ADS)
Withers, Christopher S.; Nadarajah, Saralees
2012-06-01
We show that there are exactly four quadratic polynomials, Q(x) = x 2 + ax + b, such that
Ellis, John; Fairbairn, Malcolm; Sueiro, Maria E-mail: malcolm.fairbairn@kcl.ac.uk
2014-02-01
Inflationary models based on a single scalar field φ with a quadratic potential V = ½m{sup 2}φ{sup 2} are disfavoured by the recent Planck constraints on the scalar index, n{sub s}, and the tensor-to-scalar ratio for cosmological density perturbations, r{sub T}. In this paper we study how such a quadratic inflationary model can be rescued by postulating additional fields with quadratic potentials, such as might occur in sneutrino models, which might serve as either curvatons or supplementary inflatons. Introducing a second scalar field reduces but does not remove the pressure on quadratic inflation, but we find a sample of three-field models that are highly compatible with the Planck data on n{sub s} and r{sub T}. We exhibit a specific three-sneutrino example that is also compatible with the data on neutrino mass difference and mixing angles.
NASA Astrophysics Data System (ADS)
Al Hamidi, Yasser; Rakotondrabe, Micky
2016-05-01
This paper deals with the control of a two degrees of freedom (2-DOF) piezoelectric cantilever actuator which is characterized by badly damped oscillations, hysteresis nonlinearity and cross-couplings. First, a feedforward control scheme based on the zero placement technique is introduced to annihilate the oscillations. Then a disturbance observer and a disturbance compensator are introduced to reduce the effects of low frequencies phenomena (hysteresis and creep) which were approximated by a fictive disturbance. Finally an output feedback scheme based on the linear quadratic regulator is added in order to reduce the cross-couplings effects to improve the tracking performances, and eventually to add robustness. Experiments were carried out and confirm the predicted performances.
The Mystical "Quadratic Formula."
ERIC Educational Resources Information Center
March, Robert H.
1993-01-01
Uses projectile motion to explain the two roots found when using the quadratic formula. An example is provided for finding the time of flight for a projectile which has a negative root implying a negative time of flight. This negative time of flight also has a useful physical meaning. (MVL)
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]…
A line-of-sight performance criterion for controller design of a proposed laboratory model
NASA Technical Reports Server (NTRS)
Lim, Kyong B.; Horta, Lucas G.
1990-01-01
A line-of-sight performance criterion is derived for a proposed Controls Structures Interaction model, and its many uses in the control design process for fine pointing control are illustrated. A linearized line-of-sight (LOS) criterion is used for direct controller design and as a performance measure to judge different control methodologies. Numerical simulation results are shown where the three approaches: linear quadratic Gaussian theory, robust eigensystem assignment, and local velocity feedback are used for vibration control. Results indicate that the linear quadratic Gaussian controller, which incorporates a linearized LOS weighting matrix directly, yields good performance without wasting energy to control motions that have no influence on the LOS.
NASA Astrophysics Data System (ADS)
Storto, Andrea
2016-08-01
Quality control procedures aiming at identifying observations suspected of gross errors are an important component of modern ocean data assimilation systems. On the one hand, assimilating observations whose departures from the background state are large may result in detrimental analyses and compromise the stability of the ocean analysis system. On the other hand, the rejection of these observations may prevent the analysis from ingesting useful information, especially in areas of large variability. In this work, we investigate the quality control of in-situ hydrographic profiles through modifying the probability density function (PDF) of the observational errors and relaxing the assumption of Gaussian PDF. The new PDF is heavier-tailed than Gaussian, thus accommodating the assimilation of observations with large misfits, albeit with smaller weight given to them in the analysis. This implies a different observational term in the analysis equation, and an adaptive quality control procedure based on the innovation statistics themselves. Implemented in a global ocean variational data assimilation system at moderate horizontal resolution, the scheme proves robust and successful in assimilating more observations with respect to the simpler background quality check scheme. This leads to better skill scores against both conventional and satellite observing systems. This approach proves superior also to the case where no quality control is considered. Furthermore, the implementation considers switching on the modified cost function at the 10th iteration of the minimization so that innovation statistics are based on a good approximation of the analysis. Neglecting this strategy and turning on the variational quality control since the beginning of the minimization exhibits worse scores, qualitatively similar to those of the experiment without quality control, suggesting that in this case quality control procedures are too gentle. A specific study investigating the upper
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
NASA Technical Reports Server (NTRS)
Bensoussan, A.; Delfour, M. C.; Mitter, S. K.
1976-01-01
Available published results are surveyed for a special class of infinite-dimensional control systems whose evolution is characterized by a semigroup of operators of class C subscript zero. Emphasis is placed on an approach that clarifies the system-theoretic relationship among controllability, stabilizability, stability, and the existence of a solution to an associated operator equation of the Riccati type. Formulation of the optimal control problem is reviewed along with the asymptotic behavior of solutions to a general system of equations and several theorems concerning L2 stability. Examples are briefly discussed which involve second-order parabolic systems, first-order hyperbolic systems, and distributed boundary control.
NASA Astrophysics Data System (ADS)
Colin, M.; Di Menza, L.; Saut, J. C.
2016-03-01
In this paper, we investigate the properties of solitonic structures arising in quadratic media. First, we recall the derivation of systems governing the interaction process for waves propagating in such media and we check the local and global well-posedness of the corresponding Cauchy problem. Then, we look for stationary states in the context of normal or anomalous dispersion regimes, that lead us to either elliptic or non-elliptic systems and we address the problem of orbital stability. Finally, some numerical experiments are carried out in order to compute localized states for several regimes and to study dynamic stability as well as long-time asymptotics.
Guises and disguises of quadratic divergences
Cherchiglia, A.L.; Vieira, A.R.; Hiller, Brigitte; Baêta Scarpelli, A.P.; Sampaio, Marcos
2014-12-15
In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.
Quadratic spatial soliton interactions
NASA Astrophysics Data System (ADS)
Jankovic, Ladislav
Quadratic spatial soliton interactions were investigated in this Dissertation. The first part deals with characterizing the principal features of multi-soliton generation and soliton self-reflection. The second deals with two beam processes leading to soliton interactions and collisions. These subjects were investigated both theoretically and experimentally. The experiments were performed by using potassium niobate (KNBO 3) and periodically poled potassium titanyl phosphate (KTP) crystals. These particular crystals were desirable for these experiments because of their large nonlinear coefficients and, more importantly, because the experiments could be performed under non-critical-phase-matching (NCPM) conditions. The single soliton generation measurements, performed on KNBO3 by launching the fundamental component only, showed a broad angular acceptance bandwidth which was important for the soliton collisions performed later. Furthermore, at high input intensities multi-soliton generation was observed for the first time. The influence on the multi-soliton patterns generated of the input intensity and beam symmetry was investigated. The combined experimental and theoretical efforts indicated that spatial and temporal noise on the input laser beam induced multi-soliton patterns. Another research direction pursued was intensity dependent soliton routing by using of a specially engineered quadratically nonlinear interface within a periodically poled KTP sample. This was the first time demonstration of the self-reflection phenomenon in a system with a quadratic nonlinearity. The feature investigated is believed to have a great potential for soliton routing and manipulation by engineered structures. A detailed investigation was conducted on two soliton interaction and collision processes. Birth of an additional soliton resulting from a two soliton collision was observed and characterized for the special case of a non-planar geometry. A small amount of spiraling, up to 30
Quadratic soliton self-reflection at a quadratically nonlinear interface
NASA Astrophysics Data System (ADS)
Jankovic, Ladislav; Kim, Hongki; Stegeman, George; Carrasco, Silvia; Torner, Lluis; Katz, Mordechai
2003-11-01
The reflection of bulk quadratic solutions incident onto a quadratically nonlinear interface in periodically poled potassium titanyl phosphate was observed. The interface consisted of the boundary between two quasi-phase-matched regions displaced from each other by a half-period. At high intensities and small angles of incidence the soliton is reflected.
2006-01-01
Statistical image reconstruction methods based on maximum a posteriori (MAP) principle have been developed for emission tomography. The prior distribution of the unknown image plays an important role in MAP reconstruction. The most commonly used prior are Gaussian priors, whose logarithm has a quadratic form. Gaussian priors are relatively easy to analyze. It has been shown that the effect of a Gaussian prior can be approximated by linear filtering a maximum likelihood (ML) reconstruction. As a result, sharp edges in reconstructed images are not preserved. To preserve sharp transitions, non-Gaussian priors have been proposed. However, their effect on clinical tasks is less obvious. In this paper, we compare MAP reconstruction with Gaussian and non-Gaussian priors for lesion detection and region of interest quantification using computer simulation. We evaluate three representative priors: Gaussian prior, Huber prior, and Geman-McClure prior. We simulate imaging a prostate tumor using positron emission tomography (PET). The detectability of a known tumor in either a fixed background or a random background is measured using a channelized Hotelling observer. The bias-variance tradeoff curves are calculated for quantification of the total tumor activity. The results show that for the detection and quantification tasks, the Gaussian prior is as effective as non-Gaussian priors. PMID:23165056
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.
Gaussian quantum operator representation for bosons
Corney, Joel F.; Drummond, Peter D.
2003-12-01
We introduce a Gaussian quantum operator representation, using the most general possible multimode Gaussian operator basis. The representation unifies and substantially extends existing phase-space representations of density matrices for Bose systems and also includes generalized squeezed-state and thermal bases. It enables first-principles dynamical or equilibrium calculations in quantum many-body systems, with quantum uncertainties appearing as dynamical objects. Any quadratic Liouville equation for the density operator results in a purely deterministic time evolution. Any cubic or quartic master equation can be treated using stochastic methods.
Statistical process control for AR(1) or non-Gaussian processes using wavelets coefficients
NASA Astrophysics Data System (ADS)
Cohen, A.; Tiplica, T.; Kobi, A.
2015-11-01
Autocorrelation and non-normality of process characteristic variables are two main difficulties that industrial engineers must face when they should implement control charting techniques. This paper presents new issues regarding the probability distribution of wavelets coefficients. Firstly, we highlight that wavelets coefficients have capacities to strongly decrease autocorrelation degree of original data and are normally-like distributed, especially in the case of Haar wavelet. We used AR(1) model with positive autoregressive parameters to simulate autocorrelated data. Illustrative examples are presented to show wavelets coefficients properties. Secondly, the distributional parameters of wavelets coefficients are derived, it shows that wavelets coefficients reflect an interesting statistical properties for SPC purposes.
Students' Understanding of Quadratic Equations
ERIC Educational Resources Information Center
López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael
2016-01-01
Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…
An application of modern control theory to an elastic spacecraft
NASA Technical Reports Server (NTRS)
Larson, V.; Likins, P. W.
1976-01-01
Results are presented to illustrate the application of established procedures of linear, quadratic, Gaussian optimal estimation and control to a spacecraft with dynamically significant elastic appendages. Interpretations are provided in both time domain and frequency domain, and conclusions are drawn for a wide class of problems of flexible spacecraft attitude control.
Effective potential and quadratic divergences
Einhorn, M.B. ); Jones, D.R.T. )
1992-12-01
We use the effective potential to give a simple derivation of Veltman's formula for the quadratic divergence in the Higgs self-energy. We also comment on the effect of going beyond the one-loop approximation.
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.
Communications circuit including a linear quadratic estimator
Ferguson, Dennis D.
2015-07-07
A circuit includes a linear quadratic estimator (LQE) configured to receive a plurality of measurements a signal. The LQE is configured to weight the measurements based on their respective uncertainties to produce weighted averages. The circuit further includes a controller coupled to the LQE and configured to selectively adjust at least one data link parameter associated with a communication channel in response to receiving the weighted averages.
Shape Control of Plates with Piezo Actuators and Collocated Position/Rate Sensors
NASA Technical Reports Server (NTRS)
Balakrishnan, A. V.
1994-01-01
This paper treats the control problem of shaping the surface deformation of a circular plate using embedded piezo-electric actuators and collocated rate sensors. An explicit Linear Quadratic Gaussian (LQG) optimizer stability augmentation compensator is derived as well as the optimal feed-forward control. Corresponding performance evaluation formulas are also derived.
Shape Control of Plates with Piezo Actuators and Collocated Position/Rate Sensors
NASA Technical Reports Server (NTRS)
Balakrishnan, A. V.
1994-01-01
This paper treats the control problem of shaping the surface deformation of a circular plate using embedded piezo-electric actuator and collocated rate sensors. An explicit Linear Quadratic Gaussian (LQG) optimizer stability augmentation compensator is derived as well as the optimal feed-forward control. Corresponding performance evaluation formulas are also derived.
Students' understanding of quadratic equations
NASA Astrophysics Data System (ADS)
López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael
2016-05-01
Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help students achieve an understanding of quadratic equations with improved interrelation of ideas and more flexible application of solution methods. Semi-structured interviews with eight beginning undergraduate students explored which of the mental constructions conjectured in the genetic decomposition students could do, and which they had difficulty doing. Two of the mental constructions that form part of the genetic decomposition are highlighted and corresponding further data were obtained from the written work of 121 undergraduate science and engineering students taking a multivariable calculus course. The results suggest the importance of explicitly considering these two highlighted mental constructions.
Gaussian cloning of coherent states with known phases
Alexanian, Moorad
2006-04-15
The fidelity for cloning coherent states is improved over that provided by optimal Gaussian and non-Gaussian cloners for the subset of coherent states that are prepared with known phases. Gaussian quantum cloning duplicates all coherent states with an optimal fidelity of 2/3. Non-Gaussian cloners give optimal single-clone fidelity for a symmetric 1-to-2 cloner of 0.6826. Coherent states that have known phases can be cloned with a fidelity of 4/5. The latter is realized by a combination of two beam splitters and a four-wave mixer operated in the nonlinear regime, all of which are realized by interaction Hamiltonians that are quadratic in the photon operators. Therefore, the known Gaussian devices for cloning coherent states are extended when cloning coherent states with known phases by considering a nonbalanced beam splitter at the input side of the amplifier.
Optimal channels for channelized quadratic estimators.
Kupinski, Meredith K; Clarkson, Eric
2016-06-01
We present a new method for computing optimized channels for estimation tasks that is feasible for high-dimensional image data. Maximum-likelihood (ML) parameter estimates are challenging to compute from high-dimensional likelihoods. The dimensionality reduction from M measurements to L channels is a critical advantage of channelized quadratic estimators (CQEs), since estimating likelihood moments from channelized data requires smaller sample sizes and inverting a smaller covariance matrix is easier. The channelized likelihood is then used to form ML estimates of the parameter(s). In this work we choose an imaging example in which the second-order statistics of the image data depend upon the parameter of interest: the correlation length. Correlation lengths are used to approximate background textures in many imaging applications, and in these cases an estimate of the correlation length is useful for pre-whitening. In a simulation study we compare the estimation performance, as measured by the root-mean-squared error (RMSE), of correlation length estimates from CQE and power spectral density (PSD) distribution fitting. To abide by the assumptions of the PSD method we simulate an ergodic, isotropic, stationary, and zero-mean random process. These assumptions are not part of the CQE formalism. The CQE method assumes a Gaussian channelized likelihood that can be a valid for non-Gaussian image data, since the channel outputs are formed from weighted sums of the image elements. We have shown that, for three or more channels, the RMSE of CQE estimates of correlation length is lower than conventional PSD estimates. We also show that computing CQE by using a standard nonlinear optimization method produces channels that yield RMSE within 2% of the analytic optimum. CQE estimates of anisotropic correlation length estimation are reported to demonstrate this technique on a two-parameter estimation problem. PMID:27409452
Metin, Baris; Wiersema, Jan R; Verguts, Tom; Gasthuys, Roos; van Der Meere, Jacob J; Roeyers, Herbert; Sonuga-Barke, Edmund
2016-01-01
According to the state regulation deficit (SRD) account, ADHD is associated with a problem using effort to maintain an optimal activation state under demanding task settings such as very fast or very slow event rates. This leads to a prediction of disrupted performance at event rate extremes reflected in higher Gaussian response variability that is a putative marker of activation during motor preparation. In the current study, we tested this hypothesis using ex-Gaussian modeling, which distinguishes Gaussian from non-Gaussian variability. Twenty-five children with ADHD and 29 typically developing controls performed a simple Go/No-Go task under four different event-rate conditions. There was an accentuated quadratic relationship between event rate and Gaussian variability in the ADHD group compared to the controls. The children with ADHD had greater Gaussian variability at very fast and very slow event rates but not at moderate event rates. The results provide evidence for the SRD account of ADHD. However, given that this effect did not explain all group differences (some of which were independent of event rate) other cognitive and/or motivational processes are also likely implicated in ADHD performance deficits. PMID:26835532
Metin, Baris; Wiersema, Jan R; Verguts, Tom; Gasthuys, Roos; van Der Meere, Jacob J; Roeyers, Herbert; Sonuga-Barke, Edmund
2016-01-01
According to the state regulation deficit (SRD) account, ADHD is associated with a problem using effort to maintain an optimal activation state under demanding task settings such as very fast or very slow event rates. This leads to a prediction of disrupted performance at event rate extremes reflected in higher Gaussian response variability that is a putative marker of activation during motor preparation. In the current study, we tested this hypothesis using ex-Gaussian modeling, which distinguishes Gaussian from non-Gaussian variability. Twenty-five children with ADHD and 29 typically developing controls performed a simple Go/No-Go task under four different event-rate conditions. There was an accentuated quadratic relationship between event rate and Gaussian variability in the ADHD group compared to the controls. The children with ADHD had greater Gaussian variability at very fast and very slow event rates but not at moderate event rates. The results provide evidence for the SRD account of ADHD. However, given that this effect did not explain all group differences (some of which were independent of event rate) other cognitive and/or motivational processes are also likely implicated in ADHD performance deficits.
Metin, Baris; Wiersema, Jan R; Verguts, Tom; Gasthuys, Roos; van Der Meere, Jacob J; Roeyers, Herbert; Sonuga-Barke, Edmund
2014-12-01
According to the state regulation deficit (SRD) account, ADHD is associated with a problem using effort to maintain an optimal activation state under demanding task settings such as very fast or very slow event rates. This leads to a prediction of disrupted performance at event rate extremes reflected in higher Gaussian response variability that is a putative marker of activation during motor preparation. In the current study, we tested this hypothesis using ex-Gaussian modeling, which distinguishes Gaussian from non-Gaussian variability. Twenty-five children with ADHD and 29 typically developing controls performed a simple Go/No-Go task under four different event-rate conditions. There was an accentuated quadratic relationship between event rate and Gaussian variability in the ADHD group compared to the controls. The children with ADHD had greater Gaussian variability at very fast and very slow event rates but not at moderate event rates. The results provide evidence for the SRD account of ADHD. However, given that this effect did not explain all group differences (some of which were independent of event rate) other cognitive and/or motivational processes are also likely implicated in ADHD performance deficits.
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.
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.
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.
Computer-aided design of flight control systems
NASA Technical Reports Server (NTRS)
Stengel, Robert F.; Sircar, Subrata
1991-01-01
A computer program is presented for facilitating the development and assessment of flight control systems, and application to a control design is discussed. The program is a computer-aided control-system design program based on direct digital synthesis of a proportional-integral-filter controller with scheduled linear-quadratic-Gaussian gains and command generator tracking of pilot inputs. The FlightCAD system concentrates on aircraft dynamics, flight-control systems, stability and performance, and has practical engineering applications.
Consensus-ADMM for General Quadratically Constrained Quadratic Programming
NASA Astrophysics Data System (ADS)
Huang, Kejun; Sidiropoulos, Nicholas D.
2016-10-01
Non-convex quadratically constrained quadratic programming (QCQP) problems have numerous applications in signal processing, machine learning, and wireless communications, albeit the general QCQP is NP-hard, and several interesting special cases are NP-hard as well. This paper proposes a new algorithm for general QCQP. The problem is first reformulated in consensus optimization form, to which the alternating direction method of multipliers (ADMM) can be applied. The reformulation is done in such a way that each of the sub-problems is a QCQP with only one constraint (QCQP-1), which is efficiently solvable irrespective of (non-)convexity. The core components are carefully designed to make the overall algorithm more scalable, including efficient methods for solving QCQP-1, memory efficient implementation, parallel/distributed implementation, and smart initialization. The proposed algorithm is then tested in two applications: multicast beamforming and phase retrieval. The results indicate superior performance over prior state-of-the-art methods.
Binary Inspiral in Quadratic Gravity
NASA Astrophysics Data System (ADS)
Yagi, Kent
2015-01-01
Quadratic gravity is a general class of quantum-gravity-inspired theories, where the Einstein-Hilbert action is extended through the addition of all terms quadratic in the curvature tensor coupled to a scalar field. In this article, we focus on the scalar Gauss- Bonnet (sGB) theory and consider the black hole binary inspiral in this theory. By applying the post-Newtonian (PN) formalism, we found that there is a scalar dipole radiation which leads to -1PN correction in the energy flux relative to gravitational radiation in general relativity. From the orbital decay rate of a low-mass X-ray binary A0600-20, we obtain the bound that is six orders of magnitude stronger than the current solar system bound. Furthermore, we show that the excess in the orbital decay rate of XTE J1118+480 can be explained by the scalar radiation in sGB theory.
Quantum bouncer with quadratic dissipation
NASA Astrophysics Data System (ADS)
González, G.
2008-02-01
The energy loss due to a quadratic velocity dependent force on a quantum particle bouncing on a perfectly reflecting surface is obtained for a full cycle of motion. We approach this problem by means of a new effective phenomenological Hamiltonian which corresponds to the actual energy of the system and obtained the correction to the eigenvalues of the energy in first order quantum perturbation theory for the case of weak dissipation.
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)
Orthogonality preserving infinite dimensional quadratic stochastic operators
Akın, Hasan; Mukhamedov, Farrukh
2015-09-18
In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.
Control law design to meet constraints using SYNPAC-synthesis package for active controls
NASA Technical Reports Server (NTRS)
Adams, W. M., Jr.; Tiffany, S. H.
1982-01-01
Major features of SYNPAC (Synthesis Package for Active Controls) are described. SYNPAC employs constrained optimization techniques which allow explicit inclusion of design criteria (constraints) in the control law design process. Interrelationships are indicated between this constrained optimization approach, classical and linear quadratic Gaussian design techniques. Results are presented that were obtained by applying SYNPAC to the design of a combined stability augmentation/gust load alleviation control law for the DAST ARW-2.
Gaussian entanglement of formation
Wolf, M.M.; Giedke, G.; Krueger, O.; Werner, R. F.; Cirac, J.I.
2004-05-01
We introduce a Gaussian version of the entanglement of formation adapted to bipartite Gaussian states by considering decompositions into pure Gaussian states only. We show that this quantity is an entanglement monotone under Gaussian operations and provide a simplified computation for states of arbitrary many modes. For the case of one mode per site the remaining variational problem can be solved analytically. If the considered state is in addition symmetric with respect to interchanging the two modes, we prove additivity of the considered entanglement measure. Moreover, in this case and considering only a single copy, our entanglement measure coincides with the true entanglement of formation.
Evolution of massive haloes in non-Gaussian scenarios
NASA Astrophysics Data System (ADS)
Grossi, M.; Dolag, K.; Branchini, E.; Matarrese, S.; Moscardini, L.
2007-12-01
We have performed high-resolution cosmological N-body simulations of a concordance ΛCDM model to study the evolution of virialized, dark matter haloes in the presence of primordial non-Gaussianity. Following a standard procedure, departures from Gaussianity are modelled through a quadratic Gaussian term in the primordial gravitational potential, characterized by a dimensionless non-linearity strength parameter fNL. We find that the halo mass function and its redshift evolution closely follow the analytic predictions of Matarrese, Verde & Jimenez. The existence of precise analytic predictions makes the observation of rare, massive objects at large redshift an even more attractive test to detect primordial non-Gaussian features in the large-scale structure of the Universe.
Primordial bubbles from quadratic gravity
NASA Astrophysics Data System (ADS)
Occhionero, Franco; Amendola, Luca
1994-10-01
A toy model of inflation with a first order phase transition built on a nonminimal generalization of quadratic gravity effectively implements a two field inflation and copiously spurs bubbles before the end of the slow roll. In particular, the phase transition may be brought to completion quickly enough to leave an observable signature at the large scales. We identify analytically and numerically the parameter space region capable of fitting the observed galaxy correlation function, while passing the microwave background constraints. Thus, astronomical observations can yield information upon the parameters of fundamental physics.
NASA Astrophysics Data System (ADS)
Dong, Jun; He, Yu; Bai, Sheng-Chuang; Ueda, Ken-ichi; Kaminskii, Alexander A.
2016-09-01
A nanosecond, high peak power, passively Q-switched laser for controllable Hermite–Gaussian (HG) modes has been achieved by manipulating the saturated inversion population inside the gain medium. The stable HG modes are generated in a Cr4+:YAG passively Q-switched Nd:YVO4 microchip laser by applying a tilted pump beam. The asymmetrical saturated inversion population distribution inside the Nd:YVO4 crystal for desirable HG modes is manipulated by choosing the proper pump beam diameter and varying pump power. A HG9,8 mode passively Q-switched Nd:YVO4 microchip laser with average output power of 265 mW has been obtained. Laser pulses with a pulse width of 7.3 ns and peak power of over 1.7 kW working at 21 kHz have been generated in the passively Q-switched Nd:YVO4 microchip laser.
NASA Astrophysics Data System (ADS)
Dong, Jun; He, Yu; Bai, Sheng-Chuang; Ueda, Ken-ichi; Kaminskii, Alexander A.
2016-09-01
A nanosecond, high peak power, passively Q-switched laser for controllable Hermite-Gaussian (HG) modes has been achieved by manipulating the saturated inversion population inside the gain medium. The stable HG modes are generated in a Cr4+:YAG passively Q-switched Nd:YVO4 microchip laser by applying a tilted pump beam. The asymmetrical saturated inversion population distribution inside the Nd:YVO4 crystal for desirable HG modes is manipulated by choosing the proper pump beam diameter and varying pump power. A HG9,8 mode passively Q-switched Nd:YVO4 microchip laser with average output power of 265 mW has been obtained. Laser pulses with a pulse width of 7.3 ns and peak power of over 1.7 kW working at 21 kHz have been generated in the passively Q-switched Nd:YVO4 microchip laser.
Robust controller synthesis for large flexible space structures
NASA Technical Reports Server (NTRS)
Joshi, S. M.; Rowell, L. F.; Armstrong, E. S.
1988-01-01
The application of a multivariable frequency domain method for the attitude control and vibration suppression of large flexible space structures is discussed. Results of application of the linear-quadratic-Gaussian/loop transfer recovery method to the cases of a hop/column antenna, a wrap-rib antenna, and the Spacecraft Control Laboratory Experiment are presented. Controller order reduction is implemented using the balanced realization method, a Hankel-norm-based method, and a method based on stable factorization.
Asymmetric Laguerre-Gaussian beams
NASA Astrophysics Data System (ADS)
Kovalev, A. A.; Kotlyar, V. V.; Porfirev, A. P.
2016-06-01
We introduce a family of asymmetric Laguerre-Gaussian (aLG) laser beams. The beams have been derived via a complex-valued shift of conventional LG beams in the Cartesian plane. While propagating in a uniform medium, the first bright ring of the aLG beam becomes less asymmetric and the energy is redistributed toward peripheral diffraction rings. The projection of the orbital angular momentum (OAM) onto the optical axis is calculated. The OAM is shown to grow quadratically with increasing asymmetry parameter of the aLG beam, which equals the ratio of the shift to the waist radius. Conditions for the OAM becoming equal to the topological charge have been derived. For aLG beams with zero radial index, we have deduced an expression to define the intensity maximum coordinates and shown the crescent-shaped intensity pattern to rotate during propagation. Results of the experimental generation and rotation of aLG beams agree well with theoretical predictions.
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.
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
Anatomy of an experimental two-link flexible manipulator under end-point control
NASA Technical Reports Server (NTRS)
Oakley, Celia M.; Cannon, Robert H., Jr.
1990-01-01
The design and experimental implementation of an end-point controller for two-link flexible manipulators are presented. The end-point controller is based on linear quadratic Gaussian (LQG) theory and is shown to exhibit significant improvements in trajectory tracking over a conventional controller design. To understand the behavior of the manipulator structure under end-point control, a strobe sequence illustrating the link deflections during a typical slew maneuver is included.
Optimizing Electromagnetically Induced Transparency Signals with Laguerre-Gaussian Beams
NASA Astrophysics Data System (ADS)
Holtfrerich, Matthew; Akin, Tom; Krzyzewski, Sean; Marino, Alberto; Abraham, Eric
2016-05-01
We have performed electromagnetically induced transparency in ultracold Rubidium atoms using a Laguerre-Gaussian laser mode as the control beam. Laguerre-Gaussian modes are characterized by a ring type transverse intensity profile and carry intrinsic orbital angular momentum. This angular momentum carried by the control beam can be utilized in optical computing applications which is unavailable to the more common Gaussian laser field. Specifically, we use a Laguerre-Gaussian control beam with a Gaussian probe to show that the linewidth of the transmission spectrum can be narrowed when compared to a Gaussian control beam that has the same peak intensity. We present data extending this work to compare control fields in both the Gaussian and Laguerre-Gaussian modes with constant total power. We have made efforts to find the optical overlap that best minimizes the transmission linewidth while also maintaining signal contrast. This was done by changing the waist size of the control beam with respect to the probe. The best results were obtained when the waist of a Laguerre-Gaussian control beam is equal to the waist of the Gaussian probe resulting in narrow linewidth features.
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…
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…
Factorising a Quadratic Expression with Geometric Insights
ERIC Educational Resources Information Center
Joarder, Anwar H.
2015-01-01
An algorithm is presented for factorising a quadratic expression to facilitate instruction and learning. It appeals to elementary geometry which may provide better insights to some students or teachers. There have been many methods for factorising a quadratic expression described in school text books. However, students often seem to struggle with…
Faraday rotation due to quadratic gravitation
NASA Astrophysics Data System (ADS)
Chen, Yihan; Liu, Liping; Tian, Wen-Xiu
2011-01-01
The linearized field equations of quadratic gravitation in stationary space-time are written in quasi-Maxwell form. The rotation of the polarization plane for an electromagnetic wave propagating in the gravito-electromagnetic field caused by a rotating gravitational lens is discussed. The influences of the Yukawa potential in quadratic gravitation on the gravitational Faraday rotation are investigated.
Byrnes, Christian T.; Nurmi, Sami; Tasinato, Gianmassimo; Wands, David E-mail: s.nurmi@thphys.uni-heidelberg.de E-mail: david.wands@port.ac.uk
2012-03-01
We propose a method to probe higher-order correlators of the primordial density field through the inhomogeneity of local non-Gaussian parameters, such as f{sub NL}, measured within smaller patches of the sky. Correlators between n-point functions measured in one patch of the sky and k-point functions measured in another patch depend upon the (n+k)-point functions over the entire sky. The inhomogeneity of non-Gaussian parameters may be a feasible way to detect or constrain higher- order correlators in local models of non-Gaussianity, as well as to distinguish between single and multiple-source scenarios for generating the primordial density perturbation, and more generally to probe the details of inflationary physics.
Quantum steering of Gaussian states via non-Gaussian measurements
NASA Astrophysics Data System (ADS)
Ji, Se-Wan; Lee, Jaehak; Park, Jiyong; Nha, Hyunchul
2016-07-01
Quantum steering—a strong correlation to be verified even when one party or its measuring device is fully untrusted—not only provides a profound insight into quantum physics but also offers a crucial basis for practical applications. For continuous-variable (CV) systems, Gaussian states among others have been extensively studied, however, mostly confined to Gaussian measurements. While the fulfilment of Gaussian criterion is sufficient to detect CV steering, whether it is also necessary for Gaussian states is a question of fundamental importance in many contexts. This critically questions the validity of characterizations established only under Gaussian measurements like the quantification of steering and the monogamy relations. Here, we introduce a formalism based on local uncertainty relations of non-Gaussian measurements, which is shown to manifest quantum steering of some Gaussian states that Gaussian criterion fails to detect. To this aim, we look into Gaussian states of practical relevance, i.e. two-mode squeezed states under a lossy and an amplifying Gaussian channel. Our finding significantly modifies the characteristics of Gaussian-state steering so far established such as monogamy relations and one-way steering under Gaussian measurements, thus opening a new direction for critical studies beyond Gaussian regime.
Quantum steering of Gaussian states via non-Gaussian measurements
Ji, Se-Wan; Lee, Jaehak; Park, Jiyong; Nha, Hyunchul
2016-01-01
Quantum steering—a strong correlation to be verified even when one party or its measuring device is fully untrusted—not only provides a profound insight into quantum physics but also offers a crucial basis for practical applications. For continuous-variable (CV) systems, Gaussian states among others have been extensively studied, however, mostly confined to Gaussian measurements. While the fulfilment of Gaussian criterion is sufficient to detect CV steering, whether it is also necessary for Gaussian states is a question of fundamental importance in many contexts. This critically questions the validity of characterizations established only under Gaussian measurements like the quantification of steering and the monogamy relations. Here, we introduce a formalism based on local uncertainty relations of non-Gaussian measurements, which is shown to manifest quantum steering of some Gaussian states that Gaussian criterion fails to detect. To this aim, we look into Gaussian states of practical relevance, i.e. two-mode squeezed states under a lossy and an amplifying Gaussian channel. Our finding significantly modifies the characteristics of Gaussian-state steering so far established such as monogamy relations and one-way steering under Gaussian measurements, thus opening a new direction for critical studies beyond Gaussian regime. PMID:27411853
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)
State space control of frequency standards
NASA Astrophysics Data System (ADS)
Koppang, Paul A.
2016-06-01
Discrete time control systems are widely used in time and frequency applications. Control systems can be designed to reduce phase and frequency offsets to a given reference either more or less aggressively depending on overall system needs. There are many methods available to aid in designing control systems, including techniques based on state space system models. Several state space control design methods will be shown. The control concepts covered in this paper are pole placement, minimum control effort, and linear quadratic Gaussian. The effects of steering limits on system performance will also be discussed.
Autonomous Gaussian Decomposition
NASA Astrophysics Data System (ADS)
Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirović, 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.
AUTONOMOUS GAUSSIAN DECOMPOSITION
Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirović, Snežana; Babler, Brian; Heiles, Carl; Hennebelle, Patrick; Dickey, John
2015-04-15
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.
Quantum integrability of quadratic Killing tensors
Duval, C.; Valent, G.
2005-05-01
Quantum integrability of classical integrable systems given by quadratic Killing tensors on curved configuration spaces is investigated. It is proven that, using a 'minimal' quantization scheme, quantum integrability is ensured for a large class of classic examples.
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.)
The explicit dependence of quadrat variance on the ratio of clump size to quadrat size.
Ferrandino, Francis J
2005-05-01
ABSTRACT In the past decade, it has become common practice to pool mapped binary epidemic data into quadrats. The resultant "quadrat counts" can then be analyzed by fitting them to a probability distribution (i.e., betabinomial). Often a binary form of Taylor's power law is used to relate the quadrat variance to the quadrat mean. The fact that there is an intrinsic dependence of such analyses on quadrat size and shape is well known. However, a clear-cut exposition of the direct connection between the spatial properties of the two-dimensional pattern of infected plants in terms of the geometry of the quadrat and the results of quadrat-based analyses is lacking. This problem was examined both empirically and analytically. The empirical approach is based on a set of stochastically generated "mock epidemics" using a Neyman-Scott cluster process. The resultant spatial point-patterns of infected plants have a fixed number of disease foci characterized by a known length scale (monodisperse) and saturated to a known disease level. When quadrat samples of these epidemics are fit to a beta-binomial distribution, the resulting measures of aggregation are totally independent of disease incidence and most strongly dependent on the ratio of the length scale of the quadrat to the length scale of spatial aggregation and to a lesser degree on disease saturation within individual foci. For the analytical approach, the mathematical form for the variation in the sum of random variates is coupled to the geometry of a quadrat through an assumed exponential autocorrelation function. The net result is an explicit equation expressing the intraquadrat correlation, quadrat variance, and the index of dispersion in terms of the ratio of the quadrat length scale to the correlative length scale.
Large Non-Gaussianity from Multi-Brid Inflation
NASA Astrophysics Data System (ADS)
Naruko, A.; Sasaki, M.
2009-01-01
A model of multi-component hybrid inflation, dubbed multi-brid inflation, in which various observable quantities including the non-Gaussianity parameter f_{NL} can be analytically calculated was proposed recently. In particular, for a two-brid inflation model with an exponential potential and the condition that the end of inflation is an ellipse in the field space, it was found that, while keeping the other observational quantities within the range consistent with observations, large non-Gaussianity is possible for certain inflationary trajectories, provided that the ratio of the two masses is large. One might question whether the resulting large non-Gaussianity is specific to this particular form of the potential and the condition for the end of inflation. In this paper, we consider a model of multi-brid inflation with a potential given by an exponential function of terms quadratic in the scalar field components. We also consider a more general class of ellipses for the end of inflation than those studied previously. Then, focusing on the case of two-brid inflation, we find that large non-Gaussianity is possible in the present model even for the equal-mass case. Then by tuning the model parameters, we find that there exist models for which both the non-Gaussianity and the tensor-to-scalar ratio are large enough to be detected in the very near future.
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.
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.
Gaussian discriminating strength
NASA Astrophysics Data System (ADS)
Rigovacca, L.; Farace, A.; De Pasquale, A.; Giovannetti, V.
2015-10-01
We present a quantifier of nonclassical correlations for bipartite, multimode Gaussian states. It is derived from the Discriminating Strength measure, introduced for finite dimensional systems in Farace et al., [New J. Phys. 16, 073010 (2014), 10.1088/1367-2630/16/7/073010]. As the latter the new measure exploits the quantum Chernoff bound to gauge the susceptibility of the composite system with respect to local perturbations induced by unitary gates extracted from a suitable set of allowed transformations (the latter being identified by posing some general requirements). Closed expressions are provided for the case of two-mode Gaussian states obtained by squeezing or by linearly mixing via a beam splitter a factorized two-mode thermal state. For these density matrices, we study how nonclassical correlations are related with the entanglement present in the system and with its total photon number.
NASA Astrophysics Data System (ADS)
Trofimov, M. Yu.; Zakharenko, A. D.; Kozitskiy, S. B.
2016-10-01
A mode parabolic equation in the ray centered coordinates for 3D underwater sound propagation is developed. The Gaussian beam tracing in this case is constructed. The test calculations are carried out for the ASA wedge benchmark and proved an excellent agreement with the source images method in the case of cross-slope propagation. But in the cases of wave propagation at some angles to the cross-slope direction an account of mode interaction becomes necessary.
Flauger, Raphael; Pajer, Enrico E-mail: ep295@cornell.edu
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.
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,…
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
Quadratic forms of projective spaces over rings
NASA Astrophysics Data System (ADS)
Levchuk, V. M.; Starikova, O. A.
2006-06-01
In the passage from fields to rings of coefficients quadratic forms with invertible matrices lose their decisive role. It turns out that if all quadratic forms over a ring are diagonalizable, then in effect this is always a local principal ideal ring R with 2\\in R^*. The problem of the construction of a `normal' diagonal form of a quadratic form over a ring R faces obstacles in the case of indices \\vert R^*:R^{*2}\\vert greater than 1. In the case of index 2 this problem has a solution given in Theorem 2.1 for 1+R^{*2}\\subseteq R^{*2} (an extension of the law of inertia for real quadratic forms) and in Theorem 2.2 for 1+R^2 containing an invertible non-square. Under the same conditions on a ring R with nilpotent maximal ideal the number of classes of projectively congruent quadratic forms of the projective space associated with a free R-module of rank n is explicitly calculated (Proposition 3.2). Up to projectivities, the list of forms is presented for the projective plane over R and also (Theorem 3.3) over the local ring F\\lbrack\\lbrack x,y\\rbrack\\rbrack/\\langle x^{2},xy,y^{2}\\rangle with non-principal maximal ideal, where F=2F is a field with an invertible non-square in 1+F^{2} and \\vert F^{*}:F^{*2}\\vert=2. In the latter case the number of classes of non-diagonalizable quadratic forms of rank 0 depends on one's choice of the field F and is not even always finite; all the other forms make up 21 classes.
Quadratic-Like Dynamics of Cubic Polynomials
NASA Astrophysics Data System (ADS)
Blokh, Alexander; Oversteegen, Lex; Ptacek, Ross; Timorin, Vladlen
2016-02-01
A small perturbation of a quadratic polynomial f with a non-repelling fixed point gives a polynomial g with an attracting fixed point and a Jordan curve Julia set, on which g acts like angle doubling. However, there are cubic polynomials with a non-repelling fixed point, for which no perturbation results into a polynomial with Jordan curve Julia set. Motivated by the study of the closure of the Cubic Principal Hyperbolic Domain, we describe such polynomials in terms of their quadratic-like restrictions.
On orthogonality preserving quadratic stochastic operators
NASA Astrophysics Data System (ADS)
Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd
2015-05-01
A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.
Quintessence with quadratic coupling to dark matter
Boehmer, Christian G.; Chan, Nyein; Caldera-Cabral, Gabriela; Lazkoz, Ruth; Maartens, Roy
2010-04-15
We introduce a new form of coupling between dark energy and dark matter that is quadratic in their energy densities. Then we investigate the background dynamics when dark energy is in the form of exponential quintessence. The three types of quadratic coupling all admit late-time accelerating critical points, but these are not scaling solutions. We also show that two types of coupling allow for a suitable matter era at early times and acceleration at late times, while the third type of coupling does not admit a suitable matter era.
On orthogonality preserving quadratic stochastic operators
Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd
2015-05-15
A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.
Mean-field fluid behavior of the Gaussian core model
NASA Astrophysics Data System (ADS)
Louis, A. A.; Bolhuis, P. G.; Hansen, J. P.
2000-12-01
We show that the Gaussian core model of particles interacting via a penetrable repulsive Gaussian potential, first considered by Stillinger [J. Chem. Phys. 65, 3968 (1976)], behaves as a weakly correlated ``mean-field fluid'' over a surprisingly wide density and temperature range. In the bulk, the structure of the fluid phase is accurately described by the random phase approximation for the direct correlation function, and by the more sophisticated hypernetted chain integral equation. The resulting pressure deviates very little from a simple mean-field-like quadratic form in the density, while the low density virial expansion turns out to have an extremely small radius of convergence. Density profiles near a hard wall are also very accurately described by the corresponding mean-field free-energy functional. The binary version of the model exhibits a spinodal instability against demixing at high densities. Possible implications for semidilute polymer solutions are discussed.
Robust Control of Uncertain Systems via Dissipative LQG-Type Controllers
NASA Technical Reports Server (NTRS)
Joshi, Suresh M.
2000-01-01
Optimal controller design is addressed for a class of linear, time-invariant systems which are dissipative with respect to a quadratic power function. The system matrices are assumed to be affine functions of uncertain parameters confined to a convex polytopic region in the parameter space. For such systems, a method is developed for designing a controller which is dissipative with respect to a given power function, and is simultaneously optimal in the linear-quadratic-Gaussian (LQG) sense. The resulting controller provides robust stability as well as optimal performance. Three important special cases, namely, passive, norm-bounded, and sector-bounded controllers, which are also LQG-optimal, are presented. The results give new methods for robust controller design in the presence of parametric uncertainties.
Lee, E.P.
1982-11-03
The growth rate of the hose instability is derived for a beam with Gaussian radial profile, using the spread mass model of phase mix damping. It is found that the maximum growth rate of a convecting wave packet is 49% larger than that derived for a beam with the Bennett profile, and the inverse group velocity (dz/d tau) is also increased by about this amount. A general discussion of spread mass models is presented along with an explanation of the regurgitation phenomena seen in their numerical treatment.
Large Non-Gaussianity from Multi-Brid Inflation
NASA Astrophysics Data System (ADS)
Naruko, Atsushi; Sasaki, Misao
A model of multi-component hybrid inflation, dubbed multi-brid inflation, which may yield a large non-Gaussian paramter fNL, was proposed recently. In particular, for a two-brid inflation model with an exponential potential and the condition that the end of inflation is an ellipse in the field space, it was found that, while keeping the other observational quantities within the range consistent with observations, large non-Gaussianity is possible for certain inflationary trajectories. In this talk, in order to see if this result is a general feature of multi-brid inflation, we consider a model with a potential with an exponent quadratic in the scalar field components. We also consider a more general class of ellipses for the end of inflation. Focusing on the case of two-brid inflation, we find that large non-Gaussianity is also possible in the present model. Then by tuning the model parameters, we find that there exist models for which both the non-Gaussianity and the tensor-to-scalar ratio are large enough to be detected in the very near future.
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.
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…
Inverse problem of quadratic time-dependent Hamiltonians
NASA Astrophysics Data System (ADS)
Guo, Guang-Jie; Meng, Yan; Chang, Hong; Duan, Hui-Zeng; Di, Bing
2015-08-01
Using an algebraic approach, it is possible to obtain the temporal evolution wave function for a Gaussian wave-packet obeying the quadratic time-dependent Hamiltonian (QTDH). However, in general, most of the practical cases are not exactly solvable, for we need general solutions of the Riccatti equations which are not generally known. We therefore bypass directly solving for the temporal evolution wave function, and study its inverse problem. We start with a particular evolution of the wave-packet, and get the required Hamiltonian by using the inverse method. The inverse approach opens up a new way to find new exact solutions to the QTDH. Some typical examples are studied in detail. For a specific time-dependent periodic harmonic oscillator, the Berry phase is obtained exactly. Project supported by the National Natural Science Foundation of China (Grant No. 11347171), the Natural Science Foundation of Hebei Province of China (Grant No. A2012108003), and the Key Project of Educational Commission of Hebei Province of China (Grant No. ZD2014052).
Gaussian matrix-product states for coding in bosonic communication channels
NASA Astrophysics Data System (ADS)
Schäfer, Joachim; Karpov, Evgueni; Cerf, Nicolas J.
2012-01-01
The communication capacity of Gaussian bosonic channels with memory has recently attracted much interest. Here, we investigate a method to prepare the multimode entangled input symbol states for encoding classical information into these channels. In particular, we study the usefulness of a Gaussian matrix-product state (GMPS) as an input symbol state, which can be sequentially generated although it remains heavily entangled for an arbitrary number of modes. We show that the GMPS can achieve more than 99.9% of the Gaussian capacity for Gaussian bosonic memory channels with a Markovian or non-Markovian correlated noise model in a large range of noise correlation strengths. Furthermore, we present a noise class for which the GMPS is the exact optimal input symbol state of the corresponding channel. Since GMPS are ground states of particular quadratic Hamiltonians, our results suggest a possible link between the theory of quantum communication channels and quantum many-body physics.
Non-Gaussian fingerprints of self-interacting curvaton
Enqvist, Kari; Taanila, Olli; Nurmi, Sami; Takahashi, Tomo E-mail: s.nurmi@thphys.uni-heidelberg.de E-mail: tomot@cc.saga-u.ac.jp
2010-04-01
We investigate non-Gaussianities in self-interacting curvaton models treating both renormalizable and non-renormalizable polynomial interactions. We scan the parameter space systematically and compute numerically the non-linearity parameters f{sub NL} and g{sub NL}. We find that even in the interaction dominated regime there are large regions consistent with current observable bounds. Whenever the interactions dominate, we discover significant deviations from the relations f{sub NL} ∼ r{sub dec}{sup −1} and g{sub NL} ∼ r{sub dec}{sup −1} valid for quadratic curvaton potentials, where r{sub dec} measures the curvaton contribution to the total energy density at the time of its decay. Even if r{sub dec} || 1, there always exists regions with f{sub NL} ∼ 0 since the sign of f{sub NL} oscillates as a function of the parameters. While g{sub NL} can also change sign, typically g{sub NL} is non-zero in the low-f{sub NL} regions. Hence, for some parameters the non-Gaussian statistics is dominated by g{sub NL} rather than by f{sub NL}. Due to self-interactions, both the relative signs of f{sub NL} and g{sub NL} and the functional relation between them is typically modified from the quadratic case, offering a possible experimental test of the curvaton interactions.
Stochastic Control of Energy Efficient Buildings: A Semidefinite Programming Approach
Ma, Xiao; Dong, Jin; Djouadi, Seddik M; Nutaro, James J; Kuruganti, Teja
2015-01-01
The key goal in energy efficient buildings is to reduce energy consumption of Heating, Ventilation, and Air- Conditioning (HVAC) systems while maintaining a comfortable temperature and humidity in the building. This paper proposes a novel stochastic control approach for achieving joint performance and power control of HVAC. We employ a constrained Stochastic Linear Quadratic Control (cSLQC) by minimizing a quadratic cost function with a disturbance assumed to be Gaussian. The problem is formulated to minimize the expected cost subject to a linear constraint and a probabilistic constraint. By using cSLQC, the problem is reduced to a semidefinite optimization problem, where the optimal control can be computed efficiently by Semidefinite programming (SDP). Simulation results are provided to demonstrate the effectiveness and power efficiency by utilizing the proposed control approach.
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)
Wind turbine power tracking using an improved multimodel quadratic approach.
Khezami, Nadhira; Benhadj Braiek, Naceur; Guillaud, Xavier
2010-07-01
In this paper, an improved multimodel optimal quadratic control structure for variable speed, pitch regulated wind turbines (operating at high wind speeds) is proposed in order to integrate high levels of wind power to actively provide a primary reserve for frequency control. On the basis of the nonlinear model of the studied plant, and taking into account the wind speed fluctuations, and the electrical power variation, a multimodel linear description is derived for the wind turbine, and is used for the synthesis of an optimal control law involving a state feedback, an integral action and an output reference model. This new control structure allows a rapid transition of the wind turbine generated power between different desired set values. This electrical power tracking is ensured with a high-performance behavior for all other state variables: turbine and generator rotational speeds and mechanical shaft torque; and smooth and adequate evolution of the control variables.
Normal form decomposition for Gaussian-to-Gaussian superoperators
De Palma, Giacomo; Mari, Andrea; Giovannetti, Vittorio; Holevo, Alexander S.
2015-05-15
In this paper, we explore the set of linear maps sending the set of quantum Gaussian states into itself. These maps are in general not positive, a feature which can be exploited as a test to check whether a given quantum state belongs to the convex hull of Gaussian states (if one of the considered maps sends it into a non-positive operator, the above state is certified not to belong to the set). Generalizing a result known to be valid under the assumption of complete positivity, we provide a characterization of these Gaussian-to-Gaussian (not necessarily positive) superoperators in terms of their action on the characteristic function of the inputs. For the special case of one-mode mappings, we also show that any Gaussian-to-Gaussian superoperator can be expressed as a concatenation of a phase-space dilatation, followed by the action of a completely positive Gaussian channel, possibly composed with a transposition. While a similar decomposition is shown to fail in the multi-mode scenario, we prove that it still holds at least under the further hypothesis of homogeneous action on the covariance matrix.
Factorization using the quadratic sieve algorithm
Davis, J.A.; Holdridge, D.B.
1983-12-01
Since the cryptosecurity of the RSA two key cryptoalgorithm is no greater than the difficulty of factoring the modulus (product of two secret primes), a code that implements the Quadratic Sieve factorization algorithm on the CRAY I computer has been developed at the Sandia National Laboratories to determine as sharply as possible the current state-of-the-art in factoring. Because all viable attacks on RSA thus far proposed are equivalent to factorization of the modulus, sharper bounds on the computational difficulty of factoring permit improved estimates for the size of RSA parameters needed for given levels of cryptosecurity. Analysis of the Quadratic Sieve indicates that it may be faster than any previously published general purpose algorithm for factoring large integers. The high speed of the CRAY I coupled with the capability of the CRAY to pipeline certain vectorized operations make this algorithm (and code) the front runner in current factoring techniques.
Factorization using the quadratic sieve algorithm
Davis, J.A.; Holdridge, D.B.
1983-01-01
Since the cryptosecurity of the RSA two key cryptoalgorithm is no greater than the difficulty of factoring the modulus (product of two secret primes), a code that implements the Quadratic Sieve factorization algorithm on the CRAY I computer has been developed at the Sandia National Laboratories to determine as sharply as possible the current state-of-the-art in factoring. Because all viable attacks on RSA thus far proposed are equivalent to factorization of the modulus, sharper bounds on the computational difficulty of factoring permit improved estimates for the size of RSA parameters needed for given levels of cryptosecurity. Analysis of the Quadratic Sieve indicates that it may be faster than any previously published general purpose algorithm for factoring large integers. The high speed of the CRAY I coupled with the capability of the CRAY to pipeline certain vectorized operations make this algorithm (and code) the front runner in current factoring techniques.
Convex quadratic optimization on artificial neural networks
Adler, I.; Verma, S.
1994-12-31
We present continuous-valued Hopfield recurrent neural networks on which we map convex quadratic optimization problems. We consider two different convex quadratic programs, each of which is mapped to a different neural network. Activation functions are shown to play a key role in the mapping under each model. The class of activation functions which can be used in this mapping is characterized in terms of the properties needed. It is shown that the first derivatives of penalty as well as barrier functions belong to this class. The trajectories of dynamics under the first model are shown to be closely related to affine-scaling trajectories of interior-point methods. On the other hand, the trajectories of dynamics under the second model correspond to projected steepest descent pathways.
Use of quadratic components for buckling calculations
Dohrmann, C.R.; Segalman, D.J.
1996-12-31
A buckling calculation procedure based on the method of quadratic components is presented. Recently developed for simulating the motion of rotating flexible structures, the method of quadratic components is shown to be applicable to buckling problems with either conservative or nonconservative loads. For conservative loads, stability follows from the positive definiteness of the system`s stiffness matrix. For nonconservative loads, stability is determined by solving a nonsymmetric eigenvalue problem, which depends on both the stiffness and mass distribution of the system. Buckling calculations presented for a cantilevered beam are shown to compare favorably with classical results. Although the example problem is fairly simple and well-understood, the procedure can be used in conjunction with a general-purpose finite element code for buckling calculations of more complex systems.
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.
Efficient entanglement criteria beyond Gaussian limits using Gaussian measurements.
Nha, Hyunchul; Lee, Su-Yong; Ji, Se-Wan; Kim, M S
2012-01-20
We present a formalism to derive entanglement criteria beyond the Gaussian regime that can be readily tested by only homodyne detection. The measured observable is the Einstein-Podolsky-Rosen (EPR) correlation. Its arbitrary functional form enables us to detect non-Gaussian entanglement even when an entanglement test based on second-order moments fails. We illustrate the power of our experimentally friendly criteria for a broad class of non-Gaussian states under realistic conditions. We also show rigorously that quantum teleportation for continuous variables employs a specific functional form of EPR correlation. PMID:22400723
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...
Graphical Solution of the Monic Quadratic Equation with Complex Coefficients
ERIC Educational Resources Information Center
Laine, A. D.
2015-01-01
There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…
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).
Non-Gaussian eccentricity fluctuations
NASA Astrophysics Data System (ADS)
Grönqvist, Hanna; Blaizot, Jean-Paul; Ollitrault, Jean-Yves
2016-09-01
We study the fluctuations of the anisotropy of the energy density profile created in a high-energy collision at the LHC. We show that the anisotropy in harmonic n has generic non-Gaussian fluctuations. We argue that these non-Gaussianities have a universal character for small systems such as p+Pb collisions, but not for large systems such as Pb+Pb collisions where they depend on the underlying non-Gaussian statistics of the initial density profile. We generalize expressions for the eccentricity cumulants ɛ2{4 } and ɛ3{4 } previously obtained within the independent-source model to a general fluctuating initial density profile.
Gaussian-Based Hue Descriptors.
Mirzaei, Hamidreza; Funt, Brian
2015-12-01
A robust and accurate hue descriptor that is useful in modeling human color perception and for computer vision applications is explored. The hue descriptor is based on the peak wavelength of a Gaussian-like function (called a wraparound Gaussian) and is shown to correlate as well as CIECAM02 hue to the hue designators of papers from the Munsell and Natural Color System color atlases and to the hue names found in Moroney's Color Thesaurus. The new hue descriptor is also shown to be significantly more stable under a variety of illuminants than CIECAM02. The use of wraparound Gaussians as a hue model is similar in spirit to the use of subtractive Gaussians proposed by Mizokami et al., but overcomes many of their limitations. PMID:26539849
Reliable design of H-2 optimal reduced-order controllers via a homotopy algorithm
NASA Technical Reports Server (NTRS)
Collins, Emmanuel G.; Richter, Stephen; Davis, Larry D.
1992-01-01
Due to control processor limitations, the design of reduced-order controllers is an active area of research. Suboptimal methods based on truncating the order of the corresponding linear-quadratic-Gaussian (LQG) compensator tend to fail if the requested controller dimension is sufficiently small and/or the requested controller authority is sufficiently high. Also, traditional parameter optimization approaches have only local convergence properties. This paper discusses a homotopy algorithm for optimal reduced-order control that has global convergence properties. The exposition is for discrete-time systems. The algorithm has been implemented in MATLAB and is applied to a benchmark problem.
Holographic entropy increases in quadratic curvature gravity
NASA Astrophysics Data System (ADS)
Bhattacharjee, Srijit; Sarkar, Sudipta; Wall, Aron C.
2015-09-01
Standard methods for calculating the black hole entropy beyond general relativity are ambiguous when the horizon is nonstationary. We fix these ambiguities in all quadratic curvature gravity theories, by demanding that the entropy be increasing at every time, for linear perturbations to a stationary black hole. Our result matches with the entropy formula found previously in holographic entanglement entropy calculations. We explicitly calculate the entropy increase for Vaidya-like solutions in Ricci-tensor gravity to show that (unlike the Wald entropy) the holographic entropy obeys a second law.
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 (γH = 2) and eight (γ1st = 8) Gaussians on hydrogen and first-row atoms, respectively, with exponents greater than a given threshold (α _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
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 (γ(H) = 2) and eight (γ(1st) = 8) Gaussians on hydrogen and first-row atoms, respectively, with exponents greater than a given threshold (αmin (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
Contact symmetries of constrained quadratic Lagrangians
NASA Astrophysics Data System (ADS)
Dimakis, N.; Terzis, Petros A.; Christodoulakis, T.
2016-01-01
The conditions for the existence of (polynomial in the velocities) contact symmetries of constrained systems that are described by quadratic Lagrangians is presented. These Lagrangians mainly appear in mini-superspace reductions of gravitational plus matter actions. In the literature, one usually adopts a gauge condition (mostly for the lapse N) prior to searching for symmetries. This, however, is an unnecessary restriction which may lead to a loss of symmetries and consequently to the respective integrals of motion. A generalization of the usual procedure rests in the identification of the lapse function N as an equivalent degree of freedom and the according extension of the infinitesimal generator. As a result, conformal Killing tensors (with appropriate conformal factors) can define integrals of motion (instead of just Killing tensors used in the regular gauge fixed case). Additionally, rheonomic integrals of motion - whose existence is unique in this type of singular systems - of various orders in the momenta can be constructed. An example of a relativistic particle in a pp-wave space-time and under the influence of a quadratic potential is illustrated.
Quantum correlations in Gaussian states via Gaussian channels: steering, entanglement, and discord
NASA Astrophysics Data System (ADS)
Wang, Zhong-Xiao; Wang, Shuhao; Li, Qiting; Wang, Tie-Jun; Wang, Chuan
2016-06-01
Here we study the quantum steering, quantum entanglement, and quantum discord for Gaussian Einstein-Podolsky-Rosen states via Gaussian channels. And the sudden death phenomena for Gaussian steering and Gaussian entanglement are theoretically observed. We find that some Gaussian states have only one-way steering, which confirms the asymmetry of quantum steering. Also we investigate that the entangled Gaussian states without Gaussian steering and correlated Gaussian states own no Gaussian entanglement. Meanwhile, our results support the assumption that quantum entanglement is intermediate between quantum discord and quantum steering. Furthermore, we give experimental recipes for preparing quantum states with desired types of quantum correlations.
Reduced-order model based feedback control of the modified Hasegawa-Wakatani model
Goumiri, I. R.; Rowley, C. W.; Ma, Z.; Gates, D. A.; Krommes, J. A.; Parker, J. B.
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.
Reduced-Order Model Based Feedback Control For Modified Hasegawa-Wakatani Model
Goumiri, I. R.; Rowley, C. W.; Ma, Z.; Gates, D. A.; Krommes, J. A.; Parker, J. B.
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
NASA Astrophysics Data System (ADS)
Goumiri, I. R.; Rowley, C. W.; Ma, Z.; Gates, D. A.; Krommes, J. A.; Parker, J. B.
2013-04-01
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.
Reduced-order-model based feedback control of the Modified Hasegawa-Wakatani equations
NASA Astrophysics Data System (ADS)
Goumiri, Imene; Rowley, Clarence; Ma, Zhanhua; Gates, David; Parker, Jeffrey; Krommes, John
2012-10-01
In this study, we demonstrate the development of model-based feedback control for stabilization of an unstable equilibrium obtained in the Modified Hasegawa-Wakatani (MHW) equations, a classic model in plasma turbulence. First, a balanced truncation is applied; a model reduction technique that has been proved successful in flow control design problems, to obtain a low dimensional model of the linearized MHW equation. A model-based feedback controller is then designed for the reduced order model using linear quadratic regulators (LQR) then a linear quadratic gaussian (LQG) control. The controllers are then applied on the original linearized and nonlinear MHW equations to stabilize the equilibrium and suppress the transition to drift-wave induced turbulences.
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
Information geometry of Gaussian channels
Monras, Alex; Illuminati, Fabrizio
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).
NASA Technical Reports Server (NTRS)
Moore, Douglas B.; Miller, Gerald D.; Klepl, Martin J.
1991-01-01
Three designs for controlling loads while rolling for the Active Flexible Wing (AFW) are discussed. The goal is to provide good roll control while simultaneously limiting the torsion and bending loads experienced by the wing. The first design uses Linear Quadratic Gaussian/Loop Transfer Recovery (LQG/LTR) modern control methods to control roll rate and torsional loads at four different wing locations. The second design uses a nonlinear surface command function to produce surface position commands as a function of current roll rate and commanded roll rate. The final design is a flutter suppression control system. This system stabilizes both symmetric and axisymmetric flutter modes of the AFW.
Design of a Cascade Controller for a Flexible Spray Boom
NASA Astrophysics Data System (ADS)
Ramon, H.; De Baerdemaeker, J.; van Brussel, H.
1996-03-01
Longitudinal accelerations and yawning angular accelerations of a tractor induce horizontal flexible spray boom deformations which cannot be reduced sufficiently by simple structural adaptations. An electro-hydraulic control system has therefore been developed in order to attenuate the negative effect of longitudinal tractor accelerations on a spray boom. The linear quadratic Gaussian theory with loop transfer recovery has been used to design the compensator. Four different variants of the compensator are implemented in an experimental set-up to test the performance and the robustness of the feedback system and to investigate the applicability of the electro-hydraulic devices in active vibration control.
Gaussian entanglement distribution via satellite
NASA Astrophysics Data System (ADS)
Hosseinidehaj, Nedasadat; Malaney, Robert
2015-02-01
In this work we analyze 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 tradeoff between space-based engineering complexity and the rate of ground-station entanglement generation.
Quadratic dynamical decoupling with nonuniform error suppression
Quiroz, Gregory; Lidar, Daniel A.
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}.
Quadratic quantum cosmology with Schutz' perfect fluid
NASA Astrophysics Data System (ADS)
Vakili, Babak
2010-01-01
We study the classical and quantum models of a Friedmann-Robertson-Walker (FRW) cosmology, coupled to a perfect fluid, in the context of the f(R) gravity. Using Schutz' representation for the perfect fluid, we show that, under a particular gauge choice, it may lead to the identification of a time parameter for the corresponding dynamical system. Moreover, this formalism gives rise to a Schrödinger-Wheeler-DeWitt (SWD) equation for the quantum-mechanical description of the model under consideration, the eigenfunctions of which can be used to construct the wavefunction of the universe. In the case of f(R) = R2 (pure quadratic model), for some particular choices of the perfect fluid source, exact solutions to the SWD equation can be obtained and the corresponding results are compared to the usual f(R) = R model.
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.
Large-size Gaussian mode in unstable resonators using Gaussian mirrors.
McCarthy, N; Lavigne, P
1985-11-01
Gaussian modes with large sections have been experimentally produced in Cassegrain resonators using Gaussian reflectivity convex couplers. The far field of the beam, which was coupled through a Gaussian coupler, was found to be free from secondary rings. PMID:19730482
Tachyon mediated non-Gaussianity
Dutta, Bhaskar; Leblond, Louis; Kumar, Jason
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 closed-loop control scheme for steering steady states of glycolysis and glycogenolysis pathway.
Panja, Surajit; Patra, Sourav; Mukherjee, Anirban; Basu, Madhumita; Sengupta, Sanghamitra; Dutta, Pranab K
2013-01-01
Biochemical networks normally operate in the neighborhood of one of its multiple steady states. It may reach from one steady state to other within a finite time span. In this paper, a closed-loop control scheme is proposed to steer states of the glycolysis and glycogenolysis (GG) pathway from one of its steady states to other. The GG pathway is modeled in the synergism and saturation system formalism, known as S-system. This S-system model is linearized into the controllable Brunovsky canonical form using a feedback linearization technique. For closed-loop control, the linear-quadratic regulator (LQR) and the linear-quadratic gaussian (LQG) regulator are invoked to design a controller for tracking prespecified steady states. In the feedback linearization technique, a global diffeomorphism function is proposed that facilitates in achieving the regulation requirement. The robustness of the regulated GG pathway is studied considering input perturbation and with measurement noise.
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.
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.
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.)
Visualising the Roots of Quadratic Equations with Complex Coefficients
ERIC Educational Resources Information Center
Bardell, Nicholas S.
2014-01-01
This paper is a natural extension of the root visualisation techniques first presented by Bardell (2012) for quadratic equations with real coefficients. Consideration is now given to the familiar quadratic equation "y = ax[superscript 2] + bx + c" in which the coefficients "a," "b," "c" are generally…
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…
Analysis of Students' Error in Learning of Quadratic Equations
ERIC Educational Resources Information Center
Zakaria, Effandi; Ibrahim; Maat, Siti Mistima
2010-01-01
The purpose of the study was to determine the students' error in learning quadratic equation. The samples were 30 form three students from a secondary school in Jambi, Indonesia. Diagnostic test was used as the instrument of this study that included three components: factorization, completing the square and quadratic formula. Diagnostic interview…
Convexity preserving C2 rational quadratic trigonometric spline
NASA Astrophysics Data System (ADS)
Dube, Mridula; Tiwari, Preeti
2012-09-01
A C2 rational quadratic trigonometric spline interpolation has been studied using two kind of rational quadratic trigonometric splines. It is shown that under some natural conditions the solution of the problem exits and is unique. The necessary and sufficient condition that constrain the interpolation curves to be convex in the interpolating interval or subinterval are derived.
Geometric quadratic stochastic operator on countable infinite set
Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar
2015-02-03
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.
Quadratic elongation: A quantitative measure of distortion in coordination polyhedra
Robinson, Kelly F.; 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.
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…
GAUSSIAN BEAM LASER RESONATOR PROGRAM
NASA Technical Reports Server (NTRS)
Cross, P. L.
1994-01-01
In designing a laser cavity, the laser engineer is frequently concerned with more than the stability of the resonator. Other considerations include the size of the beam at various optical surfaces within the resonator or the performance of intracavity line-narrowing or other optical elements. Laser resonators obey the laws of Gaussian beam propagation, not geometric optics. The Gaussian Beam Laser Resonator Program models laser resonators using Gaussian ray trace techniques. It can be used to determine the propagation of radiation through laser resonators. The algorithm used in the Gaussian Beam Resonator program has three major components. First, the ray transfer matrix for the laser resonator must be calculated. Next calculations of the initial beam parameters, specifically, the beam stability, the beam waist size and location for the resonator input element, and the wavefront curvature and beam radius at the input surface to the first resonator element are performed. Finally the propagation of the beam through the optical elements is computed. The optical elements can be modeled as parallel plates, lenses, mirrors, dummy surfaces, or Gradient Index (GRIN) lenses. A Gradient Index lens is a good approximation of a laser rod operating under a thermal load. The optical system may contain up to 50 elements. In addition to the internal beam elements the optical system may contain elements external to the resonator. The Gaussian Beam Resonator program was written in Microsoft FORTRAN (Version 4.01). It was developed for the IBM PS/2 80-071 microcomputer and has been implemented on an IBM PC compatible under MS DOS 3.21. The program was developed in 1988 and requires approximately 95K bytes to operate.
Gaussian Velocity Distributions in Avalanches
NASA Astrophysics Data System (ADS)
Shattuck, Mark
2004-03-01
Imagine a world where gravity is so strong that if an ice cube is tilted the shear forces melt the surface and water avalanches down. Further imagine that the ambient temperature is so low that the water re-freezes almost immediately. This is the world of granular flows. As a granular solid is tilted the surface undergoes a sublimation phase transition and a granular gas avalanches down the surface, but the inelastic collisions rapidly remove energy from the flow lowering the granular temperature (kinetic energy per particle) until the gas solidifies again. It is under these extreme conditions that we attempt to uncover continuum granular flow properties. Typical continuum theories like Navier-Stokes equation for fluids follow the space-time evolution of the first few moments of the velocity distribution. We study continuously avalanching flow in a rotating two-dimensional granular drum using high-speed video imaging and extract the position and velocities of the particles. We find a universal near Gaussian velocity distribution throughout the flowing regions, which are characterized by a liquid-like radial distribution function. In the remaining regions, in which the radial distribution function develops sharp crystalline peaks, the velocity distribution has a Gaussian peak but is much broader in the tails. In a companion experiment on a vibrated two-dimensional granular fluid under constant pressure, we find a clear gas-solid phase transition in which both the temperature and density change discontinuously. This suggests that a low temperature crystal and a high temperature gas can coexist in steady state. This coexistence could result in a narrower, cooler, Gaussian peak and a broader, warmer, Gaussian tail like the non-Gaussian behavior seen in the crystalline portions of the rotating drum.
Sensitivity Analysis of Parameters in Linear-Quadratic Radiobiologic Modeling
Fowler, Jack F.
2009-04-01
Purpose: Radiobiologic modeling is increasingly used to estimate the effects of altered treatment plans, especially for dose escalation. The present article shows how much the linear-quadratic (LQ) (calculated biologically equivalent dose [BED] varies when individual parameters of the LQ formula are varied by {+-}20% and by 1%. Methods: Equivalent total doses (EQD2 = normalized total doses (NTD) in 2-Gy fractions for tumor control, acute mucosal reactions, and late complications were calculated using the linear- quadratic formula with overall time: BED = nd (1 + d/ [{alpha}/{beta}]) - log{sub e}2 (T - Tk) / {alpha}Tp, where BED is BED = total dose x relative effectiveness (RE = nd (1 + d/ [{alpha}/{beta}]). Each of the five biologic parameters in turn was altered by {+-}10%, and the altered EQD2s tabulated; the difference was finally divided by 20. EQD2 or NTD is obtained by dividing BED by the RE for 2-Gy fractions, using the appropriate {alpha}/{beta} ratio. Results: Variations in tumor and acute mucosal EQD ranged from 0.1% to 0.45% per 1% change in each parameter for conventional schedules, the largest variation being caused by overall time. Variations in 'late' EQD were 0.4% to 0.6% per 1% change in the only biologic parameter, the {alpha}/{beta} ratio. For stereotactic body radiotherapy schedules, variations were larger, up to 0.6 to 0.9 for tumor and 1.6% to 1.9% for late, per 1% change in parameter. Conclusions: Robustness occurs similar to that of equivalent uniform dose (EUD), for the same reasons. Total dose, dose per fraction, and dose-rate cause their major effects, as well known.
Quadratic algebras for three-dimensional superintegrable systems
Daskaloyannis, C. Tanoudis, Y.
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.
Inseparability of photon-added Gaussian states
Li Hongrong; Li Fuli; Zhu Shiyao
2007-06-15
The inseparability of photon-added Gaussian states which are generated from two-mode Gaussian states by adding photons is investigated. According to the established inseparability conditions [New J. Phys. 7, 211 (2005); Phys. Rev. Lett. 96, 050503 (2006)], we find that even if a two-mode Gaussian state is separable, the photon-added Gaussian state becomes entangled when the purity of the Gaussian state is larger than a certain value. The lower bound of entanglement of symmetric photon-added Gaussian states is derived. The result shows that entanglement of the photon-added Gaussian states is involved with high-order moment correlations. We find that fidelity of teleporting coherent states cannot be raised by employing the photon-added Gaussian states as a quantum channel of teleportation.
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.
Gaussian statistics for palaeomagnetic vectors
Love, J.J.; Constable, C.G.
2003-01-01
With the aim of treating the statistics of palaeomagnetic directions and intensities jointly and consistently, we represent the mean and the variance of palaeomagnetic vectors, at a particular site and of a particular polarity, by a probability density function in a Cartesian three-space of orthogonal magnetic-field components consisting of a single (unimoda) non-zero mean, spherically-symmetrical (isotropic) Gaussian function. For palaeomagnetic data of mixed polarities, we consider a bimodal distribution consisting of a pair of such symmetrical Gaussian functions, with equal, but opposite, means and equal variances. For both the Gaussian and bi-Gaussian distributions, and in the spherical three-space of intensity, inclination, and declination, we obtain analytical expressions for the marginal density functions, the cumulative distributions, and the expected values and variances for each spherical coordinate (including the angle with respect to the axis of symmetry of the distributions). The mathematical expressions for the intensity and off-axis angle are closed-form and especially manageable, with the intensity distribution being Rayleigh-Rician. In the limit of small relative vectorial dispersion, the Gaussian (bi-Gaussian) directional distribution approaches a Fisher (Bingham) distribution and the intensity distribution approaches a normal distribution. In the opposite limit of large relative vectorial dispersion, the directional distributions approach a spherically-uniform distribution and the intensity distribution approaches a Maxwell distribution. We quantify biases in estimating the properties of the vector field resulting from the use of simple arithmetic averages, such as estimates of the intensity or the inclination of the mean vector, or the variances of these quantities. With the statistical framework developed here and using the maximum-likelihood method, which gives unbiased estimates in the limit of large data numbers, we demonstrate how to
How many eigenvalues of a Gaussian random matrix are positive?
Majumdar, Satya N.; Nadal, Celine; Scardicchio, Antonello; Vivo, Pierpaolo
2011-04-15
We study the probability distribution of the index N{sub +}, i.e., the number of positive eigenvalues of an NxN Gaussian random matrix. We show analytically that, for large N and large N{sub +} with the fraction 0{<=}c=N{sub +}/N{<=}1 of positive eigenvalues fixed, the index distribution P(N{sub +}=cN,N){approx}exp[-{beta}N{sup 2}{Phi}(c)] where {beta} is the Dyson index characterizing the Gaussian ensemble. The associated large deviation rate function {Phi}(c) is computed explicitly for all 0{<=}c{<=}1. It is independent of {beta} and displays a quadratic form modulated by a logarithmic singularity around c=1/2. As a consequence, the distribution of the index has a Gaussian form near the peak, but with a variance {Delta}(N) of index fluctuations growing as {Delta}(N){approx}lnN/{beta}{pi}{sup 2} for large N. For {beta}=2, this result is independently confirmed against an exact finite-N formula, yielding {Delta}(N)=lnN/2{pi}{sup 2}+C+O(N{sup -1}) for large N, where the constant C for even N has the nontrivial value C=({gamma}+1+3ln2)/2{pi}{sup 2}{approx_equal}0.185 248... and {gamma}=0.5772... is the Euler constant. We also determine for large N the probability that the interval [{zeta}{sub 1},{zeta}{sub 2}] is free of eigenvalues. Some of these results have been announced in a recent letter [Phys. Rev. Lett. 103, 220603 (2009)].
On the design of the dissipative LQG-type controllers
NASA Technical Reports Server (NTRS)
Lozano-Leal, R.; Joshi, S. M.
1988-01-01
The design of dissipative linear-quadratic-Gaussian-type compensators for positive real plants is considered. It is shown that if the noise covariance matrices (used as weighting matrices) satisfy certain conditions, the compensator has a strictly positive real transfer function matrix. The stability of the resulting closed-loop system is guaranteed regardless of modeling errors as long as the plant remains positive real. In view of this property, the controller is expected to be useful for vibration suppression in large, flexible space structures.
Achromatic doublets for Gaussian beams
NASA Astrophysics Data System (ADS)
Biraud, F.; Daigne, G.
1991-04-01
The properties of doublets of thin lenses in the Gaussian optics approximation were investigated. Two different ways for such a doublet to give strictly achromatic images of the input beam waist were found. Both solutions may be useful in a variety of applications, one being the possibility of shaping asymmetrical beams for fan beam antennas illumination. Using modes higher than the fundamental mode will allow the design of more realistic focal systems.
Quadratic stabilisability of multi-agent systems under switching topologies
NASA Astrophysics Data System (ADS)
Guan, Yongqiang; Ji, Zhijian; Zhang, Lin; Wang, Long
2014-12-01
This paper addresses the stabilisability of multi-agent systems (MASs) under switching topologies. Necessary and/or sufficient conditions are presented in terms of graph topology. These conditions explicitly reveal how the intrinsic dynamics of the agents, the communication topology and the external control input affect stabilisability jointly. With the appropriate selection of some agents to which the external inputs are applied and the suitable design of neighbour-interaction rules via a switching topology, an MAS is proved to be stabilisable even if so is not for each of uncertain subsystem. In addition, a method is proposed to constructively design a switching rule for MASs with norm-bounded time-varying uncertainties. The switching rules designed via this method do not rely on uncertainties, and the switched MAS is quadratically stabilisable via decentralised external self-feedback for all uncertainties. With respect to applications of the stabilisability results, the formation control and the cooperative tracking control are addressed. Numerical simulations are presented to demonstrate the effectiveness of the proposed results.
Nurmi, Sami; Byrnes, Christian T.; Tasinato, Gianmassimo E-mail: ctb22@sussex.ac.uk
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.
Variational viewpoint of the quadratic Markov measure field models: theory and algorithms.
Rivera, Mariano; Dalmau, Oscar
2012-03-01
We present a framework for image segmentation based on quadratic programming, i.e., by minimization of a quadratic regularized energy linearly constrained. In particular, we present a new variational derivation of the quadratic Markov measure field (QMMF) models, which can be understood as a procedure for regularizing model preferences (memberships or likelihoods). We also present efficient optimization algorithms. In the QMMFs, the uncertainty in the computed regularized probability measure field is controlled by penalizing Gini's coefficient, and hence, it affects the convexity of the quadratic programming problem. The convex case is reduced to the solution of a positive definite linear system, and for that case, an efficient Gauss-Seidel (GS) scheme is presented. On the other hand, we present an efficient projected GS with subspace minimization for optimizing the nonconvex case. We demonstrate the proposal capabilities by experiments and numerical comparisons with interactive two-class segmentation, as well as the simultaneous estimation of segmentation and (parametric and nonparametric) generative models. We present extensions to the original formulation for including color and texture clues, as well as imprecise user scribbles in an interactive framework.
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.
Purification of Gaussian maximally mixed states
NASA Astrophysics Data System (ADS)
Jeong, Kabgyun; Lim, Youngrong
2016-10-01
We find that the purifications of several Gaussian maximally mixed states (GMMSs) correspond to some Gaussian maximally entangled states (GMESs) in the continuous-variable regime. Here, we consider a two-mode squeezed vacuum (TMSV) state as a purification of the thermal state and construct a general formalism of the Gaussian purification process. Moreover, we introduce other kind of GMESs via the process. All of our purified states of the GMMSs exhibit Gaussian profiles; thus, the states show maximal quantum entanglement in the Gaussian regime.
NASA Technical Reports Server (NTRS)
Schiller, Noah H.; Cabell, Randolph H.; Fuller, Chris R.
2008-01-01
This paper describes a combined control strategy designed to reduce sound radiation from stiffened aircraft-style panels. The control architecture uses robust active damping in addition to high-authority linear quadratic Gaussian (LQG) control. Active damping is achieved using direct velocity feedback with triangularly shaped anisotropic actuators and point velocity sensors. While active damping is simple and robust, stability is guaranteed at the expense of performance. Therefore the approach is often referred to as low-authority control. In contrast, LQG control strategies can achieve substantial reductions in sound radiation. Unfortunately, the unmodeled interaction between neighboring control units can destabilize decentralized control systems. Numerical simulations show that combining active damping and decentralized LQG control can be beneficial. In particular, augmenting the in-bandwidth damping supplements the performance of the LQG control strategy and reduces the destabilizing interaction between neighboring control units.
Degenerate nonlinear programming with a quadratic growth condition.
Anitescu, M.; Mathematics and Computer Science
2000-01-01
We show that the quadratic growth condition and the Mangasarian-Fromovitz constraint qualification (MFCQ) imply that local minima of nonlinear programs are isolated stationary points. As a result, when started sufficiently close to such points, an L1 exact penalty sequential quadratic programming algorithm will induce at least R-linear convergence of the iterates to such a local minimum. We construct an example of a degenerate nonlinear program with a unique local minimum satisfying the quadratic growth and the MFCQ but for which no positive semidefinite augmented Lagrangian exists. We present numerical results obtained using several nonlinear programming packages on this example and discuss its implications for some algorithms.
On a 'Mysterious' Case of a Quadratic Hamiltonian
NASA Astrophysics Data System (ADS)
Sakovich, Sergei
2006-07-01
We show that one of the five cases of a quadratic Hamiltonian, which were recently selected by Sokolov and Wolf who used the Kovalevskaya-Lyapunov test, fails to pass the Painlevé test for integrability.
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.
AdS waves as exact solutions to quadratic gravity
Guellue, Ibrahim; Sisman, Tahsin Cagri; Tekin, Bayram; Guerses, Metin
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.
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
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.
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.
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.
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.
Generation of singular optical beams from fundamental Gaussian beam using Sagnac interferometer
NASA Astrophysics Data System (ADS)
Naik, Dinesh N.; Viswanathan, Nirmal K.
2016-09-01
We propose a simple free-space optics recipe for the controlled generation of optical vortex beams with a vortex dipole or a single charge vortex, using an inherently stable Sagnac interferometer. We investigate the role played by the amplitude and phase differences in generating higher-order Gaussian beams from the fundamental Gaussian mode. Our simulation results reveal how important the control of both the amplitude and the phase difference between superposing beams is to achieving optical vortex beams. The creation of a vortex dipole from null interference is unveiled through the introduction of a lateral shear and a radial phase difference between two out-of-phase Gaussian beams. A stable and high quality optical vortex beam, equivalent to the first-order Laguerre–Gaussian beam, is synthesized by coupling lateral shear with linear phase difference, introduced orthogonal to the shear between two out-of-phase Gaussian beams.
Generation of singular optical beams from fundamental Gaussian beam using Sagnac interferometer
NASA Astrophysics Data System (ADS)
Naik, Dinesh N.; Viswanathan, Nirmal K.
2016-09-01
We propose a simple free-space optics recipe for the controlled generation of optical vortex beams with a vortex dipole or a single charge vortex, using an inherently stable Sagnac interferometer. We investigate the role played by the amplitude and phase differences in generating higher-order Gaussian beams from the fundamental Gaussian mode. Our simulation results reveal how important the control of both the amplitude and the phase difference between superposing beams is to achieving optical vortex beams. The creation of a vortex dipole from null interference is unveiled through the introduction of a lateral shear and a radial phase difference between two out-of-phase Gaussian beams. A stable and high quality optical vortex beam, equivalent to the first-order Laguerre-Gaussian beam, is synthesized by coupling lateral shear with linear phase difference, introduced orthogonal to the shear between two out-of-phase Gaussian beams.
An LQG based PSS design for controlling the SSR in power systems with series-compensated lines
Seo, J.C.; Kim, T.H.; Park, J.K.; Moon, S.I.
1996-06-01
This paper presents a linear quadratic Gaussian (LQG) based power system stabilizer (PSS) to control the subsynchronous resonance (SSR) that may occur in a series capacitor compensated power system. This paper investigates the dominant parameters on the SSR using the critical compensation level (CCL), and selects the design parameters to confirm the stability robustness. The complete SSR simulation system based on the IEEE first benchmark is employed in this study. Eigenvalue analysis and time domain simulations using a nonlinear system model show that the proposed PSS can control the SSR efficiently.
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.
Strongly scale-dependent non-Gaussianity
Riotto, Antonio; Sloth, Martin S.
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.
D'Amico, Guido; Kleban, Matthew
2014-08-22
We analyze primordial non-Gaussianity in single-field inflationary models when the tensor-to-scalar ratio is large. Our results show that detectable levels of non-Gaussianity f(NL) ∼ 50 are still possible in the simplest class of models described by the effective theory of inflation. However, the shape is very tightly constrained, making a sharp prediction that could be confirmed or falsified by a future detection of non-Gaussianity. PMID:25192084
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
A transient, quadratic nodal method for triangular-Z geometry
DeLorey, T.F.
1993-06-01
Many systematically-derived nodal methods have been developed for Cartesian geometry due to the extensive interest in Light Water Reactors. These methods typically model the transverse-integrated flux as either an analytic or low order polynomial function of position within the node. Recently, quadratic nodal methods have been developed for R-Z and hexagonal geometry. A static and transient quadratic nodal method is developed for triangular-Z geometry. This development is particularly challenging because the quadratic expansion in each node must be performed between the node faces and the triangular points. As a consequence, in the 2-D plane, the flux and current at the points of the triangles must be treated. Quadratic nodal equations are solved using a non-linear iteration scheme, which utilizes the corrected, mesh-centered finite difference equations, and forces these equations to match the quadratic equations by computing discontinuity factors during the solution. Transient nodal equations are solved using the improved quasi-static method, which has been shown to be a very efficient solution method for transient problems. Several static problems are used to compare the quadratic nodal method to the Coarse Mesh Finite Difference (CMFD) method. The quadratic method is shown to give more accurate node-averaged fluxes. However, it appears that the method has difficulty predicting node leakages near reactor boundaries and severe material interfaces. The consequence is that the eigenvalue may be poorly predicted for certain reactor configurations. The transient methods are tested using a simple analytic test problem, a heterogeneous heavy water reactor benchmark problem, and three thermal hydraulic test problems. Results indicate that the transient methods have been implemented correctly.
Elegant Gaussian beams for enhanced optical manipulation
Alpmann, Christina Schöler, Christoph; Denz, Cornelia
2015-06-15
Generation of micro- and nanostructured complex light beams attains increasing impact in photonics and laser applications. In this contribution, we demonstrate the implementation and experimental realization of the relatively unknown, but highly versatile class of complex-valued Elegant Hermite- and Laguerre-Gaussian beams. These beams create higher trapping forces compared to standard Gaussian light fields due to their propagation changing properties. We demonstrate optical trapping and alignment of complex functional particles as nanocontainers with standard and Elegant Gaussian light beams. Elegant Gaussian beams will inspire manifold applications in optical manipulation, direct laser writing, or microscopy, where the design of the point-spread function is relevant.
Breaking Gaussian incompatibility on continuous variable quantum systems
Heinosaari, Teiko; Kiukas, Jukka; Schultz, Jussi
2015-08-15
We characterise Gaussian quantum channels that are Gaussian incompatibility breaking, that is, transform every set of Gaussian measurements into a set obtainable from a joint Gaussian observable via Gaussian postprocessing. Such channels represent local noise which renders measurements useless for Gaussian EPR-steering, providing the appropriate generalisation of entanglement breaking channels for this scenario. Understanding the structure of Gaussian incompatibility breaking channels contributes to the resource theory of noisy continuous variable quantum information protocols.
Combined control-structure optimization
NASA Technical Reports Server (NTRS)
Salama, M.; Milman, M.; Bruno, R.; Scheid, R.; Gibson, S.
1989-01-01
An approach for combined control-structure optimization keyed to enhancing early design trade-offs is outlined and illustrated by numerical examples. The approach employs a homotopic strategy and appears to be effective for generating families of designs that can be used in these early trade studies. Analytical results were obtained for classes of structure/control objectives with linear quadratic Gaussian (LQG) and linear quadratic regulator (LQR) costs. For these, researchers demonstrated that global optima can be computed for small values of the homotopy parameter. Conditions for local optima along the homotopy path were also given. Details of two numerical examples employing the LQR control cost were given showing variations of the optimal design variables along the homotopy path. The results of the second example suggest that introducing a second homotopy parameter relating the two parts of the control index in the LQG/LQR formulation might serve to enlarge the family of Pareto optima, but its effect on modifying the optimal structural shapes may be analogous to the original parameter lambda.
A Comparison of Methods for Estimating Quadratic Effects in Nonlinear Structural Equation Models
Harring, Jeffrey R.; Weiss, Brandi A.; Hsu, Jui-Chen
2012-01-01
Two Monte Carlo simulations were performed to compare methods for estimating and testing hypotheses of quadratic effects in latent variable regression models. The methods considered in the current study were (a) a 2-stage moderated regression approach using latent variable scores, (b) an unconstrained product indicator approach, (c) a latent moderated structural equation method, (d) a fully Bayesian approach, and (e) marginal maximum likelihood estimation. Of the 5 estimation methods, it was found that overall the methods based on maximum likelihood estimation and the Bayesian approach performed best in terms of bias, root-mean-square error, standard error ratios, power, and Type I error control, although key differences were observed. Similarities as well as disparities among methods are highlight and general recommendations articulated. As a point of comparison, all 5 approaches were fit to a reparameterized version of the latent quadratic model to educational reading data. PMID:22429193
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.
Applying the J-optimal channelized quadratic observer to SPECT myocardial perfusion defect detection
NASA Astrophysics Data System (ADS)
Kupinski, Meredith K.; Clarkson, Eric; Ghaly, Michael; Frey, Eric C.
2016-03-01
To evaluate performance on a perfusion defect detection task from 540 image pairs of myocardial perfusion SPECT image data we apply the J-optimal channelized quadratic observer (J-CQO). We compare AUC values of the linear Hotelling observer and J-CQO when the defect location is fixed and when it occurs in one of two locations. As expected, when the location is fixed a single channels maximizes AUC; location variability requires multiple channels to maximize the AUC. The AUC is estimated from both the projection data and reconstructed images. J-CQO is quadratic since it uses the first- and second- order statistics of the image data from both classes. The linear data reduction by the channels is described by an L x M channel matrix and in prior work we introduced an iterative gradient-based method for calculating the channel matrix. The dimensionality reduction from M measurements to L channels yields better estimates of these sample statistics from smaller sample sizes, and since the channelized covariance matrix is L x L instead of M x M, the matrix inverse is easier to compute. The novelty of our approach is the use of Jeffrey's divergence (J) as the figure of merit (FOM) for optimizing the channel matrix. We previously showed that the J-optimal channels are also the optimum channels for the AUC and the Bhattacharyya distance when the channel outputs are Gaussian distributed with equal means. This work evaluates the use of J as a surrogate FOM (SFOM) for AUC when these statistical conditions are not satisfied.
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.
Sequential quadratic programming with step control using the Lagrange function
Danilin, Yu.M.
1995-01-01
This article examines some methods of solving the problem min f (x), x {epsilon} S {contained_in} E{sup n}, S = (x:g{sub j}(x) = O,j = 1,...,t). These methods construct the iterative sequence x{sub k}+1 = x{sub k} + {alpha}{sub k}p{sub k}, k = 0, 1,..., where the vector p{sub k} is the solution of the problem min [
NASA Technical Reports Server (NTRS)
Fleming, P.
1985-01-01
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 non-linear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer-aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer.
On Volterra quadratic stochastic operators with continual state space
Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar
2015-05-15
Let (X,F) be a measurable space, and S(X,F) be the set of all probability measures on (X,F) where X is a state space and F is σ - algebraon X. We consider a nonlinear transformation (quadratic stochastic operator) defined by (Vλ)(A) = ∫{sub X}∫{sub X}P(x,y,A)dλ(x)dλ(y), where P(x, y, A) is regarded as a function of two variables x and y with fixed A ∈ F . A quadratic stochastic operator V is called a regular, if for any initial measure the strong limit lim{sub n→∞} V{sup n }(λ) is exists. In this paper, we construct a family of quadratic stochastic operators defined on the segment X = [0,1] with Borel σ - algebra F on X , prove their regularity and show that the limit measure is a Dirac measure.
A Projection Neural Network for Constrained Quadratic Minimax Optimization.
Liu, Qingshan; Wang, Jun
2015-11-01
This paper presents a projection neural network described by a dynamic system for solving constrained quadratic minimax programming problems. Sufficient conditions based on a linear matrix inequality are provided for global convergence of the proposed neural network. Compared with some of the existing neural networks for quadratic minimax optimization, the proposed neural network in this paper is capable of solving more general constrained quadratic minimax optimization problems, and the designed neural network does not include any parameter. Moreover, the neural network has lower model complexities, the number of state variables of which is equal to that of the dimension of the optimization problems. The simulation results on numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural network.
Conditional and unconditional Gaussian quantum dynamics
NASA Astrophysics Data System (ADS)
Genoni, Marco G.; Lami, Ludovico; Serafini, Alessio
2016-07-01
This article focuses on the general theory of open quantum systems in the Gaussian regime and explores a number of diverse ramifications and consequences of the theory. We shall first introduce the Gaussian framework in its full generality, including a classification of Gaussian (also known as 'general-dyne') quantum measurements. In doing so, we will give a compact proof for the parametrisation of the most general Gaussian completely positive map, which we believe to be missing in the existing literature. We will then move on to consider the linear coupling with a white noise bath, and derive the diffusion equations that describe the evolution of Gaussian states under such circumstances. Starting from these equations, we outline a constructive method to derive general master equations that apply outside the Gaussian regime. Next, we include the general-dyne monitoring of the environmental degrees of freedom and recover the Riccati equation for the conditional evolution of Gaussian states. Our derivation relies exclusively on the standard quantum mechanical update of the system state, through the evaluation of Gaussian overlaps. The parametrisation of the conditional dynamics we obtain is novel and, at variance with existing alternatives, directly ties in to physical detection schemes. We conclude our study with two examples of conditional dynamics that can be dealt with conveniently through our formalism, demonstrating how monitoring can suppress the noise in optical parametric processes as well as stabilise systems subject to diffusive scattering.
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.
NASA Astrophysics Data System (ADS)
Troncossi, M.; Di Sante, R.; Rivola, A.
2016-10-01
In the field of vibration qualification testing, random excitations are typically imposed on the tested system in terms of a power spectral density (PSD) profile. This is the one of the most popular ways to control the shaker or slip table for durability tests. However, these excitations (and the corresponding system responses) exhibit a Gaussian probability distribution, whereas not all real-life excitations are Gaussian, causing the response to be also non-Gaussian. In order to introduce non-Gaussian peaks, a further parameter, i.e., kurtosis, has to be controlled in addition to the PSD. However, depending on the specimen behaviour and input signal characteristics, the use of non-Gaussian excitations with high kurtosis and a given PSD does not automatically imply a non-Gaussian stress response. For an experimental investigation of these coupled features, suitable measurement methods need to be developed in order to estimate the stress amplitude response at critical failure locations and consequently evaluate the input signals most representative for real-life, non-Gaussian excitations. 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 burst non-Gaussian excitation signals. The laser Doppler vibrometry technique was used in this type of test for the first time, in order to estimate the specimen stress amplitude response as proportional to the differential displacement measured at the notch section ends. A method based on the use of measurements using accelerometers to correct for the occasional signal dropouts occurring during the experiment is described. The results demonstrate the ability of the test procedure to evaluate the output signal features and therefore to select the most appropriate input signal for the fatigue test.
Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation
NASA Astrophysics Data System (ADS)
Fernández, Francisco M.
2016-06-01
We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit.
Quadratic α‧-corrections to heterotic double field theory
NASA Astrophysics Data System (ADS)
Lee, Kanghoon
2015-10-01
We investigate α‧-corrections of heterotic double field theory up to quadratic order in the language of supersymmetric O (D, D + dim G) gauged double field theory. After introducing double-vielbein formalism with a parametrization which reproduces heterotic supergravity, we show that supersymmetry for heterotic double field theory up to leading order α‧-correction is obtained from supersymmetric gauged double field theory. We discuss the necessary modifications of the symmetries defined in supersymmetric gauged double field theory. Further, we construct supersymmetric completion at quadratic order in α‧.
NASA Astrophysics Data System (ADS)
Bai, Zheng-Jian; Datta, Biswa Nath; Wang, Jinwei
2010-04-01
The partial quadratic eigenvalue assignment problem (PQEVAP) concerns reassigning a few undesired eigenvalues of a quadratic matrix pencil to suitably chosen locations and keeping the other large number of eigenvalues and eigenvectors unchanged (no spill-over). The problem naturally arises in controlling dangerous vibrations in structures by means of active feedback control design. For practical viability, the design must be robust, which requires that the norms of the feedback matrices and the condition number of the closed-loop eigenvectors are as small as possible. The problem of computing feedback matrices that satisfy the above two practical requirements is known as the Robust Partial Quadratic Eigenvalue Assignment Problem (RPQEVAP). In this paper, we formulate the RPQEVAP as an unconstrained minimization problem with the cost function involving the condition number of the closed-loop eigenvector matrix and two feedback norms. Since only a small number of eigenvalues of the open-loop quadratic pencil are computable using the state-of-the-art matrix computational techniques and/or measurable in a vibration laboratory, it is imperative that the problem is solved using these small number of eigenvalues and the corresponding eigenvectors. To this end, a class of the feedback matrices are obtained in parametric form, parameterized by a single parametric matrix, and the cost function and the required gradient formulas for the optimization problem are developed in terms of the small number of eigenvalues that are reassigned and their corresponding eigenvectors. The problem is solved directly in quadratic setting without transforming it to a standard first-order control problem and most importantly, the significant "no spill-over property" of the closed-loop eigenvalues and eigenvectors is established by means of a mathematical result. These features make the proposed method practically applicable even for very large structures. Results on numerical experiments show
Emotion suppression moderates the quadratic association between RSA and executive function
Spangler, Derek P.; Bell, Martha Ann; Deater-Deckard, Kirby
2016-01-01
There is uncertainty about whether respiratory sinus arrhythmia (RSA), a cardiac marker of adaptive emotion regulation, is involved in relatively low or high executive function performance. In the present study, we investigated: (1) whether RSA during rest and tasks predict both relatively low and high executive function within a larger quadratic association among the two variables, and (2) the extent to which this quadratic trend was moderated by individual differences in emotion regulation. To achieve these aims, a sample of ethnically and socioeconomically diverse women self-reported reappraisal and emotion suppression. They next experienced a two-minute resting period during which ECG was continually assessed. In the next phase, the women completed an array of executive function and non-executive cognitive tasks while ECG was measured throughout. As anticipated, resting RSA showed a quadratic association with executive function that was strongest for high suppression. These results suggest that relatively high resting RSA may predict poor executive function ability when emotion regulation consumes executive control resources needed for ongoing cognitive performance. PMID:26018941
NASA Astrophysics Data System (ADS)
Wu, Yu Mao; Teng, Si Jia
2016-11-01
In this work, we develop the numerical steepest descent path (NSDP) method to calculate the physical optics (PO) radiations with the quadratic concave phase variations. With the surface integral equation method, the physical optics (PO) scattered fields are formulated and further reduced to the surface integrals. The high frequency physical critical points contributions, including the stationary phase points, the boundary resonance points and the vertex points are comprehensively studied via the proposed NSDP method. The key contributions of this work are twofold. One is that together with the PO integrals taking the quadratic parabolic and hyperbolic phase terms, this work makes the NSDP theory be complete for treating the PO integrals with quadratic phase variations. Another is that, in order to illustrate the transition effect of the high frequency physical critical points, in this work, we consider and further extend the NSDP method to calculate the PO integrals with the coalescence of the high frequency critical points. Numerical results for the highly oscillatory PO integral with the coalescence of the critical points are given to verify the efficiency of the proposed NSDP method. The NSDP method could achieve the frequency independent computational workload and error controllable accuracy in all the numerical experiments, especially for the case of the coalescence of the high frequency critical points.
Measurement-induced disturbances and nonclassical correlations of Gaussian states
Mista, Ladislav Jr.; Tatham, Richard; Korolkova, Natalia; Girolami, Davide; Adesso, Gerardo
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.
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.
NASA Astrophysics Data System (ADS)
Zhang, De-Long; Wu, Bo
2002-02-01
Starting with two dimensional, scalar wave equation, a variational equation was established for the fundamental TE and TM modes guided in Ti : LiNbO 3 waveguides on the basis of assuming a symmetric Gaussian mode field function in the width direction and two-half Gaussian trial functions in the depth direction. The controllable waveguide fabrication parameters, including channel width, diffusion temperature, initial Ti-strip thickness and diffusion time, dependent of fundamental mode size, effective pump area, coupling efficiency between pump and laser modes, and the coupling loss between a Ti : LiNbO 3 waveguide and a fiber were numerically calculated for Z-cut Er : Ti : LiNbO 3 channel waveguide lasers at three possible emission wavelengths 1532,1563 and 1576 nm and two possible pump wavelengths 1480 and 980 nm. The calculated results were compared with those of Gaussian/Hermite-Gaussian mode field distribution in detail.
Gaussian translation operator in a multilevel scheme
NASA Astrophysics Data System (ADS)
Hansen, Thorkild B.; Borries, Oscar
2015-08-01
A multilevel computation scheme for time-harmonic fields in three dimensions will be formulated with a new Gaussian translation operator that decays exponentially outside a circular cone centered on the line connecting the source and observation groups. This Gaussian translation operator is directional and diagonal with its sharpness determined by a beam parameter. When the beam parameter is set to zero, the Gaussian translation operator reduces to the standard fast multipole method translation operator. The directionality of the Gaussian translation operator makes it possible to reduce the number of plane waves required to achieve a given accuracy. The sampling rate can be determined straightforwardly to achieve any desired accuracy. The use of the computation scheme will be illustrated through a near-field scanning problem where the far-field pattern of a source is determined from near-field measurements with a known probe. Here the Gaussian translation operator improves the condition number of the matrix equation that determines the far-field pattern. The Gaussian translation operator can also be used when the probe pattern is known only in one hemisphere, as is common in practice. Also, the Gaussian translation operator will be used to solve the scattering problem of the perfectly conducting sphere.
Radar Rainfall Estimation using a Quadratic Z-R equation
NASA Astrophysics Data System (ADS)
Hall, Will; Rico-Ramirez, Miguel Angel; Kramer, Stefan
2016-04-01
The aim of this work is to test a method that enables the input of event based drop size distributions to alter a quadratic reflectivity (Z) to rainfall (R) equation that is limited by fixed upper and lower points. Results will be compared to the Marshall-Palmer Z-R relation outputs and validated by a network of gauges and a single polarisation weather radar located close to Essen, Germany. The time window over which the drop size distribution measurements will be collected is varied to note any effect on the generated quadratic Z-R relation. The new quadratic algorithm shows some distinct improvement over the Marshall-Palmer relationship through multiple events. The inclusion of a minimum number of Z-R points helped to decrease the associated error by defaulting back to the Marshall-Palmer equation if the limit was not reached. More research will be done to discover why the quadratic performs poorly in some events as there appears to be little correlation between number of drops or mean rainfall amount and the associated error. In some cases it seems the spatial distribution of the disdrometers has a significant effect as a large percentage of the rain bands pass to the north of two of the three disdrometers, frequently in a slightly north-easterly direction. However during widespread precipitation events the new algorithm works very well with reductions compared to the Marshall-Palmer relation.
A Unified Approach to Teaching Quadratic and Cubic Equations.
ERIC Educational Resources Information Center
Ward, A. J. B.
2003-01-01
Presents a simple method for teaching the algebraic solution of cubic equations via completion of the cube. Shows that this method is readily accepted by students already familiar with completion of the square as a method for quadratic equations. (Author/KHR)
Canonical realization of Bondi-Metzner-Sachs symmetry: Quadratic Casimir
NASA Astrophysics Data System (ADS)
Gomis, Joaquim; Longhi, Giorgio
2016-01-01
We study the canonical realization of Bondi-Metzner-Sacks symmetry for a massive scalar field introduced by Longhi and Materassi [J. Math. Phys. 40, 480 (1999)]. We construct an invariant scalar product for the generalized momenta. As a consequence we introduce a quadratic Casimir with the supertranslations.
Finding the Best Quadratic Approximation of a Function
ERIC Educational Resources Information Center
Yang, Yajun; Gordon, Sheldon P.
2011-01-01
This article examines the question of finding the best quadratic function to approximate a given function on an interval. The prototypical function considered is f(x) = e[superscript x]. Two approaches are considered, one based on Taylor polynomial approximations at various points in the interval under consideration, the other based on the fact…
Visualising the Complex Roots of Quadratic Equations with Real Coefficients
ERIC Educational Resources Information Center
Bardell, Nicholas S.
2012-01-01
The roots of the general quadratic equation y = ax[superscript 2] + bx + c (real a, b, c) are known to occur in the following sets: (i) real and distinct; (ii) real and coincident; and (iii) a complex conjugate pair. Case (iii), which provides the focus for this investigation, can only occur when the values of the real coefficients a, b, and c are…
Analyzing Quadratic Unconstrained Binary Optimization Problems Via Multicommodity Flows
Wang, Di; Kleinberg, Robert D.
2009-01-01
Quadratic Unconstrained Binary Optimization (QUBO) problems concern the minimization of quadratic polynomials in n {0, 1}-valued variables. These problems are NP-complete, but prior work has identified a sequence of polynomial-time computable lower bounds on the minimum value, denoted by C2, C3, C4,…. It is known that C2 can be computed by solving a maximum-flow problem, whereas the only previously known algorithms for computing Ck (k > 2) require solving a linear program. In this paper we prove that C3 can be computed by solving a maximum multicommodity flow problem in a graph constructed from the quadratic function. In addition to providing a lower bound on the minimum value of the quadratic function on {0, 1}n, this multicommodity flow problem also provides some information about the coordinates of the point where this minimum is achieved. By looking at the edges that are never saturated in any maximum multicommodity flow, we can identify relational persistencies: pairs of variables that must have the same or different values in any minimizing assignment. We furthermore show that all of these persistencies can be detected by solving single-commodity flow problems in the same network. PMID:20161596
Solving quadratic programming problems by delayed projection neural network.
Yang, Yongqing; Cao, Jinde
2006-11-01
In this letter, the delayed projection neural network for solving convex quadratic programming problems is proposed. The neural network is proved to be globally exponentially stable and can converge to an optimal solution of the optimization problem. Three examples show the effectiveness of the proposed network.
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.
Quadratic invariants for discrete clusters of weakly interacting waves
NASA Astrophysics Data System (ADS)
Harper, Katie L.; Bustamante, Miguel D.; Nazarenko, Sergey V.
2013-06-01
We consider discrete clusters of quasi-resonant triads arising from a Hamiltonian three-wave equation. A cluster consists of N modes forming a total of M connected triads. We investigate the problem of constructing a functionally independent set of quadratic constants of motion. We show that this problem is equivalent to an underlying basic linear problem, consisting of finding the null space of a rectangular M × N matrix {A} with entries 1, -1 and 0. In particular, we prove that the number of independent quadratic invariants is equal to J ≡ N - M* ⩾ N - M, where M* is the number of linearly independent rows in {A}. Thus, the problem of finding all independent quadratic invariants is reduced to a linear algebra problem in the Hamiltonian case. We establish that the properties of the quadratic invariants (e.g., locality) are related to the topological properties of the clusters (e.g., types of linkage). To do so, we formulate an algorithm for decomposing large clusters into smaller ones and show how various invariants are related to certain parts of a cluster, including the basic structures leading to M* < M. We illustrate our findings by presenting examples from the Charney-Hasegawa-Mima wave model, and by showing a classification of small (up to three-triad) clusters.
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…
Confidence set interference with a prior quadratic bound. [in geophysics
NASA Technical Reports Server (NTRS)
Backus, George E.
1989-01-01
Neyman's (1937) theory of confidence sets is developed as a replacement for Bayesian interference (BI) and stochastic inversion (SI) when the prior information is a hard quadratic bound. It is recommended that BI and SI be replaced by confidence set interference (CSI) only in certain circumstances. The geomagnetic problem is used to illustrate the general theory of CSI.
Cloning of Gaussian states by linear optics
Olivares, Stefano; Paris, Matteo G. A.; Andersen, Ulrik L.
2006-06-15
We analyze in details a scheme for cloning of Gaussian states based on linear optical components and homodyne detection recently demonstrated by Andersen et al. [Phys. Rev. Lett. 94, 240503 (2005)]. The input-output fidelity is evaluated for a generic (pure or mixed) Gaussian state taking into account the effect of nonunit quantum efficiency and unbalanced mode mixing. In addition, since in most quantum information protocols the covariance matrix of the set of input states is not perfectly known, we evaluate the average cloning fidelity for classes of Gaussian states with the degree of squeezing and the number of thermal photons being only partially known.
Quark and Lepton Masses from Gaussian Landscapes
Hall, Lawrence J.; Salem, Michael P.; Watari, Taizan
2008-04-11
The flavor structure of the standard model (SM) might arise from random selection on a landscape. We propose a class of simple models, 'Gaussian landscapes', where Yukawa couplings derive from overlap integrals of Gaussian wave functions on extra-dimensions. Statistics of vacua are generated by scanning the peak positions of these zero-modes, giving probability distributions for all flavor observables. Gaussian landscapes can account for all observed flavor patterns with few free parameters. Although they give broad probability distributions, the predictions are correlated and accounting for measured parameters sharpens the distributions of future neutrino measurements.
Quantum bit commitment under Gaussian constraints
NASA Astrophysics Data System (ADS)
Mandilara, Aikaterini; Cerf, Nicolas J.
2012-06-01
Quantum bit commitment has long been known to be impossible. Nevertheless, just as in the classical case, imposing certain constraints on the power of the parties may enable the construction of asymptotically secure protocols. Here, we introduce a quantum bit commitment protocol and prove that it is asymptotically secure if cheating is restricted to Gaussian operations. This protocol exploits continuous-variable quantum optical carriers, for which such a Gaussian constraint is experimentally relevant as the high optical nonlinearity needed to effect deterministic non-Gaussian cheating is inaccessible.
Gaussian measures of entanglement versus negativities: Ordering of two-mode Gaussian states
Adesso, Gerardo; Illuminati, Fabrizio
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
Sepke, Scott M; Umstadter, Donald P
2006-05-15
The exact vector integral solution for all the electromagnetic field components of a general flattened Gaussian laser mode is derived by using the angular spectrum method. This solution includes the pure and annular Gaussian modes as special cases. The integrals are of the form of Gegenbauer's finite integral and are computed analytically for each case, yielding fields satisfying the Maxwell equations exactly in the form of quickly converging Fourier-Gegenbauer series. PMID:16642134
Ruban, V. P.
2015-05-15
The nonlinear dynamics of an obliquely oriented wave packet on a sea surface is analyzed analytically and numerically for various initial parameters of the packet in relation to the problem of the so-called rogue waves. Within the Gaussian variational ansatz applied to the corresponding (1+2)-dimensional hyperbolic nonlinear Schrödinger equation (NLSE), a simplified Lagrangian system of differential equations is derived that describes the evolution of the coefficients of the real and imaginary quadratic forms appearing in the Gaussian. This model provides a semi-quantitative description of the process of nonlinear spatiotemporal focusing, which is one of the most probable mechanisms of rogue wave formation in random wave fields. The system of equations is integrated in quadratures, which allows one to better understand the qualitative differences between linear and nonlinear focusing regimes of a wave packet. Predictions of the Gaussian model are compared with the results of direct numerical simulation of fully nonlinear long-crested waves.
Optimal cloning of mixed Gaussian states
Guta, Madalin; Matsumoto, Keiji
2006-09-15
We construct the optimal one to two cloning transformation for the family of displaced thermal equilibrium states of a harmonic oscillator, with a fixed and known temperature. The transformation is Gaussian and it is optimal with respect to the figure of merit based on the joint output state and norm distance. The proof of the result is based on the equivalence between the optimal cloning problem and that of optimal amplification of Gaussian states which is then reduced to an optimization problem for diagonal states of a quantum oscillator. A key concept in finding the optimum is that of stochastic ordering which plays a similar role in the purely classical problem of Gaussian cloning. The result is then extended to the case of n to m cloning of mixed Gaussian states.
Why Should We Pivot in Gaussian Elimination?
ERIC Educational Resources Information Center
Rozema, Edward
1988-01-01
The article discusses the use of computers to teacher college level mathematics. In particular, the Gaussian elimination procedure for solving a system of n linear equations in n unknowns, using a computer, is examined. (PK)
Improved Gaussian Beam-Scattering Algorithm
NASA Technical Reports Server (NTRS)
Lock, James A.
1995-01-01
The localized model of the beam-shape coefficients for Gaussian beam-scattering theory by a spherical particle provides a great simplification in the numerical implementation of the theory. We derive an alternative form for the localized coefficients that is more convenient for computer computations and that provides physical insight into the details of the scattering process. We construct a FORTRAN program for Gaussian beam scattering with the localized model and compare its computer run time on a personal computer with that of a traditional Mie scattering program and with three other published methods for computing Gaussian beam scattering. We show that the analytical form of the beam-shape coefficients makes evident the fact that the excitation rate of morphology-dependent resonances is greatly enhanced for far off-axis incidence of the Gaussian beam.
Non-Gaussianities in New Ekpyrotic Cosmology.
Buchbinder, Evgeny I; Khoury, Justin; Ovrut, Burt A
2008-05-01
The new ekpyrotic model is an alternative scenario of the early Universe which relies on a phase of slow contraction before the big bang. We calculate the 3-point and 4-point correlation functions of primordial density perturbations and find a generically large non-Gaussian signal, just below the current sensitivity level of cosmic microwave background experiments. This is in contrast with slow-roll inflation, which predicts negligible non-Gaussianity. The model is also distinguishable from alternative inflationary scenarios that can yield large non-Gaussianity, such as Dirac-Born-Infeld inflation and the simplest curvatonlike models, through the shape dependence of the correlation functions. Non-Gaussianity therefore provides a distinguishing and testable prediction of New Ekpyrotic Cosmology.
Gaussian-Beam Laser-Resonator Program
NASA Technical Reports Server (NTRS)
Cross, Patricia L.; Bair, Clayton H.; Barnes, Norman
1989-01-01
Gaussian Beam Laser Resonator Program models laser resonators by use of Gaussian-beam-propagation techniques. Used to determine radii of beams as functions of position in laser resonators. Algorithm used in program has three major components. First, ray-transfer matrix for laser resonator must be calculated. Next, initial parameters of beam calculated. Finally, propagation of beam through optical elements computed. Written in Microsoft FORTRAN (Version 4.01).
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.
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.
Eyyuboğlu, Halil T
2014-06-10
Using the random phase screen approach, we carry out a simulation analysis of the probability of error performance of Gaussian, annular Gaussian, cos Gaussian, and cosh Gaussian beams. In our scenario, these beams are intensity-modulated by the randomly generated binary symbols of an electrical message signal and then launched from the transmitter plane in equal powers. They propagate through a turbulent atmosphere modeled by a series of random phase screens. Upon arriving at the receiver plane, detection is performed in a circuitry consisting of a pin photodiode and a matched filter. The symbols detected are compared with the transmitted ones, errors are counted, and from there the probability of error is evaluated numerically. Within the range of source and propagation parameters tested, the lowest probability of error is obtained for the annular Gaussian beam. Our investigation reveals that there is hardly any difference between the aperture-averaged scintillations of the beams used, and the distinctive advantage of the annular Gaussian beam lies in the fact that the receiver aperture captures the maximum amount of power when this particular beam is launched from the transmitter plane.
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.
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.
Tableau-based protein substructure search using quadratic programming
Stivala, Alex; Wirth, Anthony; Stuckey, Peter J
2009-01-01
Background Searching for proteins that contain similar substructures is an important task in structural biology. The exact solution of most formulations of this problem, including a recently published method based on tableaux, is too slow for practical use in scanning a large database. Results We developed an improved method for detecting substructural similarities in proteins using tableaux. Tableaux are compared efficiently by solving the quadratic program (QP) corresponding to the quadratic integer program (QIP) formulation of the extraction of maximally-similar tableaux. We compare the accuracy of the method in classifying protein folds with some existing techniques. Conclusion We find that including constraints based on the separation of secondary structure elements increases the accuracy of protein structure search using maximally-similar subtableau extraction, to a level where it has comparable or superior accuracy to existing techniques. We demonstrate that our implementation is able to search a structural database in a matter of hours on a standard PC. PMID:19450287
Gravitomagnetic effects in quadratic gravity with a scalar field
NASA Astrophysics Data System (ADS)
Finch, Andrew; Said, Jackson Levi
2016-10-01
The two gravitomagnetic effects which influence bodies orbiting around a gravitational source are the geodetic effect and the Lense-Thirring effect. The former describes the precession angle of the axis of a spinning gyroscope while in orbit around a nonrotating gravitational source whereas the latter provides a correction for this angle in the case of a spinning source. In this paper we derive the relevant equations in quadratic gravity and relate them to their equivalents in general relativity. Starting with an investigation into Kepler's third law in quadratic gravity with a scalar field, the effects of an axisymmetric and rotating gravitational source on an orbiting body in a circular, equatorial orbit are introduced.
Nonlocal quadratic Poisson algebras, monodromy map, and Bogoyavlensky lattices
NASA Astrophysics Data System (ADS)
Suris, Yuri B.
1997-08-01
A new Lax representation for the Bogoyavlensky lattice is found and its r-matrix interpretation is elaborated. The r-matrix structure turns out to be related to a highly nonlocal quadratic Poisson structure on a direct sum of associative algebras. The theory of such nonlocal structures is developed and the Poisson property of the monodromy map is worked out in the most general situation. Some problems concerning the duality of Lax representations are raised.
Quantum integrals of motion for variable quadratic Hamiltonians
Cordero-Soto, Ricardo; Suazo, Erwin; Suslov, Sergei K.
2010-09-15
We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic Hamiltonians. An extension of the Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy-related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application.
Discrete quadratic solitons with competing second-harmonic components
Setzpfandt, Frank; Pertsch, Thomas; Sukhorukov, Andrey A.
2011-11-15
We describe families of discrete solitons in quadratic waveguide arrays supported by competing cascaded nonlinear interactions between one fundamental and two second-harmonic modes. We characterize the existence, stability, and excitation dynamics of these solitons and show that their features may resemble those of solitons in saturable media. Our results also demonstrate that a power threshold may appear for soliton formation, leading to a suppression of beam self-focusing which explains recent experimental observations.
Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality
NASA Technical Reports Server (NTRS)
Acikmese, Ahmet Behcet; Corless, Martin
2004-01-01
We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.
Gaussian vs non-Gaussian turbulence: impact on wind turbine loads
NASA Astrophysics Data System (ADS)
Berg, J.; Mann, J.; Natarajan, A.; Patton, E. G.
2014-12-01
In wind energy applications the turbulent velocity field of the Atmospheric Boundary Layer (ABL) is often characterised by Gaussian probability density functions. When estimating the dynamical loads on wind turbines this has been the rule more than anything else. From numerous studies in the laboratory, in Direct Numerical Simulations, and from in-situ measurements of the ABL we know, however, that turbulence is not purely Gaussian: the smallest and fastest scales often exhibit extreme behaviour characterised by strong non-Gaussian statistics. In this contribution we want to investigate whether these non-Gaussian effects are important when determining wind turbine loads, and hence of utmost importance to the design criteria and lifetime of a wind turbine. We devise a method based on Principal Orthogonal Decomposition where non-Gaussian velocity fields generated by high-resolution pseudo-spectral Large-Eddy Simulation (LES) of the ABL are transformed so that they maintain the exact same second-order statistics including variations of the statistics with height, but are otherwise Gaussian. In that way we can investigate in isolation the question whether it is important for wind turbine loads to include non-Gaussian properties of atmospheric turbulence. As an illustration the Figure show both a non-Gaussian velocity field (left) from our LES, and its transformed Gaussian Counterpart (right). Whereas the horizontal velocity components (top) look close to identical, the vertical components (bottom) are not: the non-Gaussian case is much more fluid-like (like in a sketch by Michelangelo). The question is then: Does the wind turbine see this? Using the load simulation software HAWC2 with both the non-Gaussian and newly constructed Gaussian fields, respectively, we show that the Fatigue loads and most of the Extreme loads are unaltered when using non-Gaussian velocity fields. The turbine thus acts like a low-pass filter which average out the non-Gaussian behaviour on time
Measurement of quadratic electrogyration effect in castor oil
NASA Astrophysics Data System (ADS)
Izdebski, Marek; Ledzion, Rafał; Górski, Piotr
2015-07-01
This work presents a detailed analysis of electrogyration measurement in liquids with the usage of an optical polarimetric technique. Theoretical analysis of the optical response to an applied electric field is illustrated by experimental data for castor oil which exhibits natural optical activity, quadratic electro-optic effect and quadratic electrogyration effect. Moreover, the experimental data show that interaction of the oil with a pair of flat electrodes induces a significant dichroism and natural linear birefringence. The combination of these effects occurring at the same time complicates the procedure of measurements. It has been found that a single measurement is insufficient to separate the contribution of the electrogyration effect, but it is possible on the basis of several measurements performed with various orientations of the polarizer and the analyser. The obtained average values of the quadratic electrogyration coefficient β13 in castor oil at room temperature are from - 0.92 ×10-22 to - 1.44 ×10-22m2V-2 depending on the origin of the oil. Although this study is focused on measurements in castor oil, the presented analysis is much more general.
Revisiting the naturalness problem: Who is afraid of quadratic divergences?
NASA Astrophysics Data System (ADS)
Aoki, Hajime; Iso, Satoshi
2012-07-01
It is widely believed that quadratic divergences severely restrict natural constructions of particle physics models beyond the standard model (SM). Supersymmetry provides a beautiful solution, but the recent LHC experiments have excluded large parameter regions of supersymmetric extensions of the SM. It will now be important to reconsider whether we have been misinterpreting the quadratic divergences in field theories. In this paper, we revisit the problem from the viewpoint of the Wilsonian renormalization group and argue that quadratic divergences—which can always be absorbed into a position of the critical surface—should be simply subtracted in model constructions. Such a picture gives another justification to the argument [W. A. Bardeen, Report No. FERMILAB-CONF-95-391-T] that the scale invariance of the SM, except for the soft-breaking terms, is an alternative solution to the naturalness problem. It also largely broadens possibilities of model constructions beyond the SM since we just need to take care of logarithmic divergences, which cause mixings of various physical scales and runnings of couplings.
From particle counting to Gaussian tomography
NASA Astrophysics Data System (ADS)
Parthasarathy, K. R.; Sengupta, Ritabrata
2015-12-01
The momentum and position observables in an n-mode boson Fock space Γ(ℂn) have the whole real line ℝ as their spectrum. But the total number operator N has a discrete spectrum ℤ+ = {0, 1, 2,…}. An n-mode Gaussian state in Γ(ℂn) is completely determined by the mean values of momentum and position observables and their covariance matrix which together constitute a family of n(2n + 3) real parameters. Starting with N and its unitary conjugates by the Weyl displacement operators and operators from a representation of the symplectic group Sp(2n) in Γ(ℂn), we construct n(2n + 3) observables with spectrum ℤ+ but whose expectation values in a Gaussian state determine all its mean and covariance parameters. Thus measurements of discrete-valued observables enable the tomography of the underlying Gaussian state and it can be done by using five one-mode and four two-mode Gaussian symplectic gates in single and pair mode wires of Γ(ℂn) = Γ(ℂ)⊗n. Thus the tomography protocol admits a simple description in a language similar to circuits in quantum computation theory. Such a Gaussian tomography applied to outputs of a Gaussian channel with coherent input states permit a tomography of the channel parameters. However, in our procedure the number of counting measurements exceeds the number of channel parameters slightly. Presently, it is not clear whether a more efficient method exists for reducing this tomographic complexity. As a byproduct of our approach an elementary derivation of the probability generating function of N in a Gaussian state is given. In many cases the distribution turns out to be infinitely divisible and its underlying Lévy measure can be obtained. However, we are unable to derive the exact distribution in all cases. Whether this property of infinite divisibility holds in general is left as an open problem.
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.
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.
A formal approach to the design of multibunch feedback systems: LQG controllers
Hindi, H.; Fox, J.; Prabhaker, S.; Sapozhnikov, L.; Oxoby, G.; Linscott, I.; Teytelman, D.
1994-06-01
We formulate the multibunch feedback problem as a standard control-systems design problem and solve it using Linear Quadratic Gaussian (LQG) regulator theory. Use of a specific optimality criterion allows quantitative evaluation of different controllers and leads to the design of optimal LQG controllers. Computer simulations are used to show that, as compared to the existing Finite Impulse Response (FIR) control, LQG control can provide the same closed-loop damping for less peak power, thus making more effective use of limited kicker power. Furthermore, LQG control enables us to use more power to provide better damping without the problem of driving instabilities with higher loop gains. The code for the LQG filters described has been written for the Quick prototype installed at ALS.
Modeling and control of flow-induced vibrations of a flexible hydrofoil in viscous flow
NASA Astrophysics Data System (ADS)
Caverly, Ryan James; Li, Chenyang; Chae, Eun Jung; Forbes, James Richard; Young, Yin Lu
2016-06-01
In this paper, a reduced-order model (ROM) of the flow-induced vibrations of a flexible cantilevered hydrofoil is developed and used to design an active feedback controller. The ROM is developed using data from high-fidelity viscous fluid-structure interaction (FSI) simulations and includes nonlinear terms to accurately capture the effect of lock-in. An active linear quadratic Gaussian (LQG) controller is designed based on a linearization of the ROM and is implemented in simulation with the ROM and the high-fidelity viscous FSI model. A controller saturation method is also presented that ensures that the control force applied to the system remains within a prescribed range. Simulation results demonstrate that the LQG controller successfully suppresses vibrations in both the ROM and viscous FSI simulations using a reasonable amount of control force.
Error probabilities in optical PPM receivers with Gaussian mixture densities
NASA Technical Reports Server (NTRS)
Gagliardi, R. M.
1982-01-01
A Gaussian mixture density arises when a discrete variable (e.g., a photodetector count variable) is added to a continuous Gaussian variable (e.g., thermal noise). Making use of some properties of photomultiplier Gaussian mixture distributions, some approximate error probability formulas can be derived. These appear as averages of M-ary orthogonal Gaussian error probabilities. The use of a pure Gaussian assumption is considered, and when properly defined, appears as an accurate upper bound to performance.
Mechanisms of particle clustering in Gaussian and non-Gaussian synthetic turbulence.
Nilsen, Christopher; Andersson, Helge I
2014-10-01
We use synthetic turbulence simulations to study how inertial particles cluster in a turbulent flow, for a wide range of Stokes numbers. Two different types of synthetic turbulence are used: one Gaussian, where the time evolution of the velocity field is a simple phase shift, and one non-Gaussian, where convection is used to evolve the velocity field in time. In both flow types we observe significant particle clustering over a wide range of scales and Stokes numbers. The clustering found at low Stokes numbers can be attributed to the vortex centrifuge effect, where heavy particles are expelled from regions dominated by vorticity. This mechanism is much more effective in the non-Gaussian turbulence, because local flow structures are convected with the particles. The preferential sampling of regions with low vorticity is almost negligible in the Gaussian turbulence. At higher Stokes numbers, caustics are formed in a very similar manner in both Gaussian and non-Gaussian synthetic turbulence. In non-Gaussian turbulence, heavy particles cluster in regions of low fluid kinetic energy, while the opposite is true in Gaussian turbulence. Our results show that synthetic simulations cannot correctly predict how the particle clustering correlates with local fluid flow properties, without including convection.
Non-Gaussian structure of B-mode polarization after delensing
NASA Astrophysics Data System (ADS)
Namikawa, Toshiya; Nagata, Ryo
2015-10-01
The B-mode polarization of the cosmic microwave background on large scales has been considered as a probe of gravitational waves from the cosmic inflation. Ongoing and future experiments will, however, suffer from contamination due to the B-modes of non-primordial origins, one of which is the lensing induced B-mode polarization. Subtraction of the lensing B-modes, usually referred to as delensing, will be required for further improvement of detection sensitivity of the gravitational waves. In such experiments, knowledge of statistical properties of the B-modes after delensing is indispensable to likelihood analysis particularly because the lensing B-modes are known to be non-Gaussian. In this paper, we study non-Gaussian structure of the delensed B-modes on large scales, comparing it with that of the lensing B-modes. In particular, we investigate the power spectrum correlation matrix and the probability distribution function (PDF) of the power spectrum amplitude. Assuming an experiment in which the quadratic delensing is an almost optimal method, we find that delensing reduces correlations of the lensing B-mode power spectra between different multipoles, and that the PDF of the power spectrum amplitude is well described as a normal distribution function with a variance larger than that in the case of a Gaussian field. These features are well captured by an analytic model based on the 4th order Edgeworth expansion. As a consequence of the non-Gaussianity, the constraint on the tensor-to-scalar ratio after delensing is degraded within approximately a few percent, which depends on the multipole range included in the analysis.
Non-Gaussian structure of B-mode polarization after delensing
Namikawa, Toshiya; Nagata, Ryo
2015-10-01
The B-mode polarization of the cosmic microwave background on large scales has been considered as a probe of gravitational waves from the cosmic inflation. Ongoing and future experiments will, however, suffer from contamination due to the B-modes of non-primordial origins, one of which is the lensing induced B-mode polarization. Subtraction of the lensing B-modes, usually referred to as delensing, will be required for further improvement of detection sensitivity of the gravitational waves. In such experiments, knowledge of statistical properties of the B-modes after delensing is indispensable to likelihood analysis particularly because the lensing B-modes are known to be non-Gaussian. Inmore » this paper, we study non-Gaussian structure of the delensed B-modes on large scales, comparing it with that of the lensing B-modes. In particular, we investigate the power spectrum correlation matrix and the probability distribution function (PDF) of the power spectrum amplitude. Assuming an experiment in which the quadratic delensing is an almost optimal method, we find that delensing reduces correlations of the lensing B-mode power spectra between different multipoles, and that the PDF of the power spectrum amplitude is well described as a normal distribution function with a variance larger than that in the case of a Gaussian field. These features are well captured by an analytic model based on the 4th order Edgeworth expansion. Furthermore, as a consequence of the non-Gaussianity, the constraint on the tensor-to-scalar ratio after delensing is degraded within approximately a few percent, which depends on the multipole range included in the analysis.« less
Non-Gaussian structure of B-mode polarization after delensing
Namikawa, Toshiya; Nagata, Ryo
2015-10-01
The B-mode polarization of the cosmic microwave background on large scales has been considered as a probe of gravitational waves from the cosmic inflation. Ongoing and future experiments will, however, suffer from contamination due to the B-modes of non-primordial origins, one of which is the lensing induced B-mode polarization. Subtraction of the lensing B-modes, usually referred to as delensing, will be required for further improvement of detection sensitivity of the gravitational waves. In such experiments, knowledge of statistical properties of the B-modes after delensing is indispensable to likelihood analysis particularly because the lensing B-modes are known to be non-Gaussian. In this paper, we study non-Gaussian structure of the delensed B-modes on large scales, comparing it with that of the lensing B-modes. In particular, we investigate the power spectrum correlation matrix and the probability distribution function (PDF) of the power spectrum amplitude. Assuming an experiment in which the quadratic delensing is an almost optimal method, we find that delensing reduces correlations of the lensing B-mode power spectra between different multipoles, and that the PDF of the power spectrum amplitude is well described as a normal distribution function with a variance larger than that in the case of a Gaussian field. These features are well captured by an analytic model based on the 4th order Edgeworth expansion. Furthermore, as a consequence of the non-Gaussianity, the constraint on the tensor-to-scalar ratio after delensing is degraded within approximately a few percent, which depends on the multipole range included in the analysis.
On the non-Gaussian errors in high-z supernovae type Ia data
NASA Astrophysics Data System (ADS)
Singh, Meghendra; Pandey, Ashwini; Sharma, Amit; Gupta, Shashikant; Sharma, Satendra
2016-11-01
The nature of random errors in any data set is Gaussian, which is a well established fact according to the Central Limit Theorem. Supernovae type Ia data have played a crucial role in major discoveries in cosmology. Unlike in laboratory experiments, astronomical measurements cannot be performed in controlled situations. Thus, errors in astronomical data can be more severe in terms of systematics and non-Gaussianity compared to those of laboratory experiments. In this paper, we use the Kolmogorov-Smirnov statistic to test non-Gaussianity in high-z supernovae data. We apply this statistic to four data sets, i.e., Gold data (2004), Gold data (2007), the Union2 catalog and the Union2.1 data set for our analysis. Our results show that in all four data sets the errors are consistent with a Gaussian distribution.
Iterative Gaussianization: from ICA to random rotations.
Laparra, Valero; Camps-Valls, Gustavo; Malo, Jesús
2011-04-01
Most signal processing problems involve the challenging task of multidimensional probability density function (PDF) estimation. In this paper, we propose a solution to this problem by using a family of rotation-based iterative Gaussianization (RBIG) transforms. The general framework consists of the sequential application of a univariate marginal Gaussianization transform followed by an orthonormal transform. The proposed procedure looks for differentiable transforms to a known PDF so that the unknown PDF can be estimated at any point of the original domain. In particular, we aim at a zero-mean unit-covariance Gaussian for convenience. RBIG is formally similar to classical iterative projection pursuit algorithms. However, we show that, unlike in PP methods, the particular class of rotations used has no special qualitative relevance in this context, since looking for interestingness is not a critical issue for PDF estimation. The key difference is that our approach focuses on the univariate part (marginal Gaussianization) of the problem rather than on the multivariate part (rotation). This difference implies that one may select the most convenient rotation suited to each practical application. The differentiability, invertibility, and convergence of RBIG are theoretically and experimentally analyzed. Relation to other methods, such as radial Gaussianization, one-class support vector domain description, and deep neural networks is also pointed out. The practical performance of RBIG is successfully illustrated in a number of multidimensional problems such as image synthesis, classification, denoising, and multi-information estimation. PMID:21349790
Propagation properties of cylindrical sinc Gaussian beam
NASA Astrophysics Data System (ADS)
Eyyuboğlu, Halil T.; Bayraktar, Mert
2016-09-01
We investigate the propagation properties of cylindrical sinc Gaussian beam in turbulent atmosphere. Since an analytic solution is hardly derivable, the study is carried out with the aid of random phase screens. Evolutions of the beam intensity profile, beam size and kurtosis parameter are analysed. It is found that on the source plane, cylindrical sinc Gaussian beam has a dark hollow appearance, where the side lobes also start to emerge with increase in width parameter and Gaussian source size. During propagation, beams with small width and Gaussian source size exhibit off-axis behaviour, losing the dark hollow shape, accumulating the intensity asymmetrically on one side, whereas those with large width and Gaussian source size retain dark hollow appearance even at long propagation distances. It is seen that the beams with large widths expand more in beam size than the ones with small widths. The structure constant values chosen do not seem to alter this situation. The kurtosis parameters of the beams having small widths are seen to be larger than the ones with the small widths. Again the choice of the structure constant does not change this trend.
Optimal estimation of non-Gaussianity
Babich, Daniel
2005-08-15
We systematically analyze the primordial non-Gaussianity estimator used by the Wilkinson Microwave Anisotropy Probe (WMAP) science team with the basic ideas of estimation theory in order to see if the limited cosmic microwave background (CMB) data is being optimally utilized. The WMAP estimator is based on the implicit assumption that the CMB bispectrum, the harmonic transform of the three-point correlation function, contains all of the primordial non-Gaussianity information in a CMB map. We first demonstrate that the signal-to-noise (S/N) of an estimator based on CMB three-point correlation functions is significantly larger than the S/N of any estimator based on higher-order correlation functions; justifying our choice to focus on the three-point correlation function. We then conclude that the estimator based on the three-point correlation function, which was used by WMAP, is optimal, meaning it saturates the Cramer-Rao inequality when the underlying CMB map is nearly Gaussian. We quantify this restriction by demonstrating that the suboptimal character of our estimator is proportional to the square of the fiducial non-Gaussianity, which is already constrained to be extremely small, so we can consider the WMAP estimator to be optimal in practice. Our conclusions do not depend on the form of the primordial bispectrum, only on the observationally established weak levels of primordial non-Gaussianity.
Hydraulic Conductivity Fields: Gaussian or Not?
Meerschaert, Mark M.; Dogan, Mine; Van Dam, Remke L.; Hyndman, David W.; Benson, David A.
2013-01-01
Hydraulic conductivity (K) fields are used to parameterize groundwater flow and transport models. Numerical simulations require a detailed representation of the K field, synthesized to interpolate between available data. Several recent studies introduced high resolution K data (HRK) at the Macro Dispersion Experiment (MADE) site, and used ground-penetrating radar (GPR) to delineate the main structural features of the aquifer. This paper describes a statistical analysis of these data, and the implications for K field modeling in alluvial aquifers. Two striking observations have emerged from this analysis. The first is that a simple fractional difference filter can have a profound effect on data histograms, organizing non-Gaussian ln K data into a coherent distribution. The second is that using GPR facies allows us to reproduce the significantly non-Gaussian shape seen in real HRK data profiles, using a simulated Gaussian ln K field in each facies. This illuminates a current controversy in the literature, between those who favor Gaussian ln K models, and those who observe non-Gaussian ln K fields. Both camps are correct, but at different scales. PMID:24415806
Graphical calculus for Gaussian pure states
Menicucci, Nicolas C.; Flammia, Steven T.; Loock, Peter van
2011-04-15
We provide a unified graphical calculus for all Gaussian pure states, including graph transformation rules for all local and semilocal Gaussian unitary operations, as well as local quadrature measurements. We then use this graphical calculus to analyze continuous-variable (CV) cluster states, the essential resource for one-way quantum computing with CV systems. Current graphical approaches to CV cluster states are only valid in the unphysical limit of infinite squeezing, and the associated graph transformation rules only apply when the initial and final states are of this form. Our formalism applies to all Gaussian pure states and subsumes these rules in a natural way. In addition, the term 'CV graph state' currently has several inequivalent definitions in use. Using this formalism we provide a single unifying definition that encompasses all of them. We provide many examples of how the formalism may be used in the context of CV cluster states: defining the 'closest' CV cluster state to a given Gaussian pure state and quantifying the error in the approximation due to finite squeezing; analyzing the optimality of certain methods of generating CV cluster states; drawing connections between this graphical formalism and bosonic Hamiltonians with Gaussian ground states, including those useful for CV one-way quantum computing; and deriving a graphical measure of bipartite entanglement for certain classes of CV cluster states. We mention other possible applications of this formalism and conclude with a brief note on fault tolerance in CV one-way quantum computing.
Paulitz, T C; Dutilleul, P; Yamasaki, S H; Fernando, W G; Seaman, W L
1999-01-01
ABSTRACT A generalized two-dimensional Gaussian model is proposed to describe disease foci of head blight of wheat in plots (100 to 2,500 m(2)) originating from small areas (1 to 16 m(2)) inoculated with Gibberella zeae-colonized corn kernels. These anisotropic, asymmetrical foci arose from ascospores produced in perithecia. The model is Z = exp[-(AX(2) + BY(2) + CXY + DX + EY + F)], in which Z = the incidence of seed or spikelet infection at point (X,Y) located in the plot, exp = the exponential function, X = the abscissa or spatial coordinate of the point along a given axis (approximately parallel to the average wind vector during the period of spore release in these experiments), Y = the ordinate or spatial coordinate of the point along the axis perpendicular to the X axis (approximately perpendicular to the wind direction in these experiments), A and B = the quadratic coefficients of the second-order polynomial AX(2) + BY(2) + CXY + DX + EY + F, C = the bilinear coefficient, D and E = the linear coefficients, and exp(-F) = the incidence of seed or spikelet infection at the focus peak in which X = 0 and Y = 0. The generalized two-dimensional Gaussian model was tested on data from a circular or isotropic focus, an elliptical or anisotropic focus with two axes of symmetry, and two anisotropic foci with one and zero axis of symmetry. Its goodness-of-fit (r(2) and adjusted r(2)) was compared with the inverse power, modified inverse power, exponential, and classical Gaussian models. Submodels using only the linear terms, only the quadratic terms, or combinations selected from stepwise regression procedures using various probabilities to enter and to stay and a procedure maximizing the adjusted r (2) were also considered. Spatial analysis of the residuals was performed using Geary's c coefficient at the first distance class. For the circular and elliptical foci, our model provided a fit similar to the modified inverse power and exponential models. However, for
Paulitz, T C; Dutilleul, P; Yamasaki, S H; Fernando, W G; Seaman, W L
1999-01-01
ABSTRACT A generalized two-dimensional Gaussian model is proposed to describe disease foci of head blight of wheat in plots (100 to 2,500 m(2)) originating from small areas (1 to 16 m(2)) inoculated with Gibberella zeae-colonized corn kernels. These anisotropic, asymmetrical foci arose from ascospores produced in perithecia. The model is Z = exp[-(AX(2) + BY(2) + CXY + DX + EY + F)], in which Z = the incidence of seed or spikelet infection at point (X,Y) located in the plot, exp = the exponential function, X = the abscissa or spatial coordinate of the point along a given axis (approximately parallel to the average wind vector during the period of spore release in these experiments), Y = the ordinate or spatial coordinate of the point along the axis perpendicular to the X axis (approximately perpendicular to the wind direction in these experiments), A and B = the quadratic coefficients of the second-order polynomial AX(2) + BY(2) + CXY + DX + EY + F, C = the bilinear coefficient, D and E = the linear coefficients, and exp(-F) = the incidence of seed or spikelet infection at the focus peak in which X = 0 and Y = 0. The generalized two-dimensional Gaussian model was tested on data from a circular or isotropic focus, an elliptical or anisotropic focus with two axes of symmetry, and two anisotropic foci with one and zero axis of symmetry. Its goodness-of-fit (r(2) and adjusted r(2)) was compared with the inverse power, modified inverse power, exponential, and classical Gaussian models. Submodels using only the linear terms, only the quadratic terms, or combinations selected from stepwise regression procedures using various probabilities to enter and to stay and a procedure maximizing the adjusted r (2) were also considered. Spatial analysis of the residuals was performed using Geary's c coefficient at the first distance class. For the circular and elliptical foci, our model provided a fit similar to the modified inverse power and exponential models. However, for
Index Distribution of Gaussian Random Matrices
Majumdar, Satya N.; Nadal, Celine; Scardicchio, Antonello; Vivo, Pierpaolo
2009-11-27
We compute analytically, for large N, the probability distribution of the number of positive eigenvalues (the index N{sub +}) of a random NxN matrix belonging to Gaussian orthogonal (beta=1), unitary (beta=2) or symplectic (beta=4) ensembles. The distribution of the fraction of positive eigenvalues c=N{sub +}/N scales, for large N, as P(c,N){approx_equal}exp[-betaN{sup 2}PHI(c)] where the rate function PHI(c), symmetric around c=1/2 and universal (independent of beta), is calculated exactly. The distribution has non-Gaussian tails, but even near its peak at c=1/2 it is not strictly Gaussian due to an unusual logarithmic singularity in the rate function.
CMB non-gaussianity from vector fields
Peloso, Marco
2014-01-01
The Planck satellite has recently measured the CMB temperature anisotropies with unprecedented accuracy, and it has provided strong bounds on primordial non-gaussianity. Such bounds constrain models of inflation, and mechanisms that produce the primordial perturbations. We discuss the non-gaussian signatures from the interactions of the inflation φ with spin-1 fields. We study the two different cases in which the inflaton is (i) a pseudo-scalar field with a (φ)/(fa) F·F interaction with a vector field, and (ii) a scalar field with a f (φ)F² interaction. In the first case we obtain the strong limit f{sub a} ≥ 10¹⁶GeV on the decay constant. In the second case, specific choices of the function f (φ) can lead to a non-gaussianity with a characteristic shape not encountered in standard models of scalar field inflation, and which has also been constrained by Planck.
Majorization preservation of Gaussian bosonic channels
NASA Astrophysics Data System (ADS)
Jabbour, Michael G.; García-Patrón, Raúl; Cerf, Nicolas J.
2016-07-01
It is shown that phase-insensitive Gaussian bosonic channels are majorization-preserving over the set of passive states of the harmonic oscillator. This means that comparable passive states under majorization are transformed into equally comparable passive states by any phase-insensitive Gaussian bosonic channel. Our proof relies on a new preorder relation called Fock-majorization, which coincides with regular majorization for passive states but also induces another order relation in terms of mean boson number, thereby connecting the concepts of energy and disorder of a quantum state. The consequences of majorization preservation are discussed in the context of the broadcast communication capacity of Gaussian bosonic channels. Because most of our results are independent of the specific nature of the system under investigation, they could be generalized to other quantum systems and Hamiltonians, providing a new tool that may prove useful in quantum information theory and especially quantum thermodynamics.
Gaussian entanglement in the turbulent atmosphere
NASA Astrophysics Data System (ADS)
Bohmann, M.; Semenov, A. A.; Sperling, J.; Vogel, W.
2016-07-01
We provide a rigorous treatment of the entanglement properties of two-mode Gaussian states in atmospheric channels by deriving and analyzing the input-output relations for the corresponding entanglement test. A key feature of such turbulent channels is a nontrivial dependence of the transmitted continuous-variable entanglement on coherent displacements of the quantum state of the input field. Remarkably, this allows one to optimize the entanglement certification by modifying local coherent amplitudes using a finite, but optimal amount of squeezing. In addition, we propose a protocol which, in principle, renders it possible to transfer the Gaussian entanglement through any turbulent channel over arbitrary distances. Therefore, our approach provides the theoretical foundation for advanced applications of Gaussian entanglement in free-space quantum communication.
Quadrotor UAV Control for Vision-based Moving Target Tracking Task
NASA Astrophysics Data System (ADS)
Bohdanov, Denys
The problem of stand-off tracking of a moving target using a quadrotor unmanned aerial vehicle (UAV) based on vision-sensing is investigated. A PID (Proportional-Integral-Derivative) controller is implemented for attitude stabilization of the quadrotor. An LQG-based (Linear-Quadratic-Gaussian) control law is designed and implemented for position control of the quadrotor for a moving target tracking task. A novel vision-based estimation algorithm is developed, enabling estimation of quadrotor's position, altitude and yaw relative to the target based on limited information about the target. Two image processing algorithms are implemented and compared for the task of feature detection and feature tracking in a series of images. Image processing algorithms are integrated with quadrotor control and experiments are performed to validate proposed control and estimation approaches.
Inflationary prediction for primordial non-gaussianity.
Lyth, David H; Rodríguez, Yeinzon
2005-09-16
We extend the deltaN formalism so that it gives all of the stochastic properties of the primordial curvature perturbation zeta if the initial field perturbations are Gaussian. The calculation requires only the knowledge of some family of unperturbed universes. A formula is given for the normalization f(NL) of the bispectrum of zeta, which is the main signal of non-Gaussianity. Examples of the use of the formula are given, and its relation to cosmological perturbation theory is explained. PMID:16197063
Invariant measures on multimode quantum Gaussian states
Lupo, C.; Mancini, S.; De Pasquale, A.; Facchi, P.; Florio, G.; Pascazio, S.
2012-12-15
We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom-the symplectic eigenvalues-which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.
A Gaussian-product stochastic Gent-McWilliams parameterization
NASA Astrophysics Data System (ADS)
Grooms, Ian
2016-10-01
The locally-averaged horizontal buoyancy flux by mesoscale eddies is computed from eddy-resolving quasigeostrophic simulations of ocean-mesoscale eddy dynamics. This flux has a very non-Gaussian distribution peaked at zero, not at the mean value. This non-Gaussian flux distribution arises because the flux is a product of zero-mean random variables: the eddy velocity and buoyancy. A framework for stochastic Gent-McWilliams (GM) parameterization is presented. Gaussian random field models for subgrid-scale velocity and buoyancy are developed. The product of these Gaussian random fields is used to construct a non-Gaussian stochastic parameterization of the horizontal subgrid-scale density flux, which leads to a non-Gaussian stochastic GM parameterization. This new non-Gaussian stochastic GM parameterization is tested in an idealized box ocean model, and compared to a Gaussian approach that simply multiplies the deterministic GM parameterization by a Gaussian random field. The non-Gaussian approach has a significant impact on both the mean and variability of the simulations, more so than the Gaussian approach; for example, the non-Gaussian simulation has a much larger net kinetic energy and a stronger overturning circulation than a comparable Gaussian simulation. Future directions for development of the stochastic GM parameterization and extensions of the Gaussian-product approach are discussed.
NASA Astrophysics Data System (ADS)
Ji, Se-Wan; Kim, M. S.; Nha, Hyunchul
2015-04-01
It is a topic of fundamental and practical importance how a quantum correlated state can be reliably distributed through a noisy channel for quantum information processing. The concept of quantum steering recently defined in a rigorous manner is relevant to study it under certain circumstances and here we address quantum steerability of Gaussian states to this aim. In particular, we attempt to reformulate the criterion for Gaussian steering in terms of local and global purities and show that it is sufficient and necessary for the case of steering a 1-mode system by an N-mode system. It subsequently enables us to reinforce a strong monogamy relation under which only one party can steer a local system of 1-mode. Moreover, we show that only a negative partial-transpose state can manifest quantum steerability by Gaussian measurements in relation to the Peres conjecture. We also discuss our formulation for the case of distributing a two-mode squeezed state via one-way quantum channels making dissipation and amplification effects, respectively. Finally, we extend our approach to include non-Gaussian measurements, more precisely, all orders of higher-order squeezing measurements, and find that this broad set of non-Gaussian measurements is not useful to demonstrate steering for Gaussian states beyond Gaussian measurements.
Linear and quadratic models of point process systems: contributions of patterned input to output.
Lindsay, K A; Rosenberg, J R
2012-08-01
In the 1880's Volterra characterised a nonlinear system using a functional series connecting continuous input and continuous output. Norbert Wiener, in the 1940's, circumvented problems associated with the application of Volterra series to physical problems by deriving from it a new series of terms that are mutually uncorrelated with respect to Gaussian processes. Subsequently, Brillinger, in the 1970's, introduced a point-process analogue of Volterra's series connecting point-process inputs to the instantaneous rate of point-process output. We derive here a new series from this analogue in which its terms are mutually uncorrelated with respect to Poisson processes. This new series expresses how patterned input in a spike train, represented by third-order cross-cumulants, is converted into the instantaneous rate of an output point-process. Given experimental records of suitable duration, the contribution of arbitrary patterned input to an output process can, in principle, be determined. Solutions for linear and quadratic point-process models with one and two inputs and a single output are investigated. Our theoretical results are applied to isolated muscle spindle data in which the spike trains from the primary and secondary endings from the same muscle spindle are recorded in response to stimulation of one and then two static fusimotor axons in the absence and presence of a random length change imposed on the parent muscle. For a fixed mean rate of input spikes, the analysis of the experimental data makes explicit which patterns of two input spikes contribute to an output spike.
Calculation of eigenfunctions of bounded waveguide with quadratic refractive index
NASA Astrophysics Data System (ADS)
Kirilenko, M. S.; Zubtsov, R. O.; Khonina, S. N.
2016-08-01
In this work, the one-dimensional finite fractional Fourier transform has been considered in application to gradient optical waveguides. The eigenfunctions of it has been discussed. The relation between obtained functions, Hermite-Gaussian modes and spheroidal functions has been shown. The dependence of input domain width and number of nonzero eigenfunctions of transformation has been demonstrated. The functions which recover its form at given distance from the front plane have been calculated.
Control of Separated Boundary Layers
NASA Astrophysics Data System (ADS)
Huang, Shao-Ching; Kim, John
2003-11-01
The control of separated boundary layers are numerically investigated. Two types of flow geometry are considered. The first case is flow separation on a flat plate caused by an imposed adverse pressure gradient. The second case is flow separation downstream of a curved leading edge. These cases represent laminar separation with turbulent reattachment with and without curvature effects. Open-loop control, with distributed surface blowing and suction as control input, is first applied to establish base-line cases. We then use a system identification approach to construct approximate system models for design of closed-loop control. The models are based on the input-output relationship obtained from numerical simulations. The linear quadratic Gaussian (LQG) control synthesis is applied to the models to produce feedback control laws. The distributed sensors and actuators are confined to the walls. The efficacy of the controllers are quantified by pressure distribution, separation bubble size and Reynolds stresses. Visualization of the controlled and uncontrolled flow fields will also be presented.
Compact stellar models obeying quadratic equation of state
NASA Astrophysics Data System (ADS)
Bhar, Piyali; Singh, Ksh. Newton; Pant, Neeraj
2016-10-01
In present paper we obtain a new model of compact star by considering quadratic equation of state for the matter distribution and assuming a physically reasonable choice for metric coefficient g_{rr}. The solution is singularity free and well behaved inside the stellar interior. Several features are described analytically as well as graphically. From our analysis we have shown that our model is compatible with the observational data of the compact stars. We have discussed a detail analysis of neutron star PSR J1614-2230 via different graphs after determining all the constant parameters from boundary conditions.
Rigorous performance bounds for quadratic and nested dynamical decoupling
Xia, Yuhou; Uhrig, Goetz S.; Lidar, Daniel A.
2011-12-15
We present rigorous performance bounds for the quadratic dynamical decoupling pulse sequence which protects a qubit from general decoherence, and for its nested generalization to an arbitrary number of qubits. Our bounds apply under the assumptions of instantaneous pulses and of bounded perturbing environment and qubit-environment Hamiltonians such as those realized by baths of nuclear spins in quantum dots. We prove that if the total sequence time is fixed then the trace-norm distance between the unperturbed and protected system states can be made arbitrarily small by increasing the number of applied pulses.
Frontogenesis driven by horizontally quadratic distributions of density
NASA Technical Reports Server (NTRS)
Jacqmin, David
1991-01-01
Attention is given to the quadratic density distribution in a channel, which has been established by Simpson and Linden to be the simplest case of the horizontally nonlinear distribution of fluid density required for the production of frontogenesis. The porous-media and Boussinesq flow models are examined, and their evolution equations are reduced to one-dimensional systems. While both the porous-media and the inviscid/nondiffusive Boussinesq systems exhibit classic frontogenesis behavior, the viscous Boussinesq system exhibits a more complex behavior: boundary-layer effects force frontogenesis away from the lower boundary, and at late times the steepest density gradients are close to mid-channel.
Restart-Based Genetic Algorithm for the Quadratic Assignment Problem
NASA Astrophysics Data System (ADS)
Misevicius, Alfonsas
The power of genetic algorithms (GAs) has been demonstrated for various domains of the computer science, including combinatorial optimization. In this paper, we propose a new conceptual modification of the genetic algorithm entitled a "restart-based genetic algorithm" (RGA). An effective implementation of RGA for a well-known combinatorial optimization problem, the quadratic assignment problem (QAP), is discussed. The results obtained from the computational experiments on the QAP instances from the publicly available library QAPLIB show excellent performance of RGA. This is especially true for the real-life like QAPs.
Quantum mechanical study of a generic quadratically coupled optomechanical system
NASA Astrophysics Data System (ADS)
Shi, H.; Bhattacharya, M.
2013-04-01
Typical optomechanical systems involving optical cavities and mechanical oscillators rely on a coupling that varies linearly with the oscillator displacement. However, recently a coupling varying instead as the square of the mechanical displacement has been realized, presenting new possibilities for nondemolition measurements and mechanical squeezing. In this article we present a quantum mechanical study of a generic quadratic-coupling optomechanical Hamiltonian. First, neglecting dissipation, we provide analytical results for the dressed states, spectrum, phonon statistics and entanglement. Subsequently, accounting for dissipation, we supply a numerical treatment using a master equation approach. We expect our results to be of use to optomechanical spectroscopy, state transfer, wave-function engineering, and entanglement generation.
Neural network for solving convex quadratic bilevel programming problems.
He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie
2014-03-01
In this paper, using the idea of successive approximation, we propose a neural network to solve convex quadratic bilevel programming problems (CQBPPs), which is modeled by a nonautonomous differential inclusion. Different from the existing neural network for CQBPP, the model has the least number of state variables and simple structure. Based on the theory of nonsmooth analysis, differential inclusions and Lyapunov-like method, the limit equilibrium points sequence of the proposed neural networks can approximately converge to an optimal solution of CQBPP under certain conditions. Finally, simulation results on two numerical examples and the portfolio selection problem show the effectiveness and performance of the proposed neural network.
Nios II hardware acceleration of the epsilon quadratic sieve algorithm
NASA Astrophysics Data System (ADS)
Meyer-Bäse, Uwe; Botella, Guillermo; Castillo, Encarnacion; García, Antonio
2010-04-01
The quadratic sieve (QS) algorithm is one of the most powerful algorithms to factor large composite primes used to break RSA cryptographic systems. The hardware structure of the QS algorithm seems to be a good fit for FPGA acceleration. Our new ɛ-QS algorithm further simplifies the hardware architecture making it an even better candidate for C2H acceleration. This paper shows our design results in FPGA resource and performance when implementing very long arithmetic on the Nios microprocessor platform with C2H acceleration for different libraries (GMP, LIP, FLINT, NRMP) and QS architecture choices for factoring 32-2048 bit RSA numbers.
On a quadratic transformation due to Kummer and its generalizations
NASA Astrophysics Data System (ADS)
Shekhawat, Nidhi; Rathie, Arjun K.; Prakash, Om
2016-05-01
The aim of this paper is to obtain explicit expressions of (1-x ) -a2F1[a ,b 2 b +j ; -2/x 1 -x ] for j = 0, ±1,…, ±9. For j = 0, we have a well-known quadratic transformations formula of Kummer. The results are obtained by using the known hypergeometric identities available in the literature. Several known results obtained earlier by Kim, et al. follow special cases of our main findings. The results derived in this paper are simple, interesting and potentially useful in the applicable sciences.
Quadratic integrand double-hybrid made spin-component-scaled
NASA Astrophysics Data System (ADS)
Brémond, Éric; Savarese, Marika; Sancho-García, Juan C.; Pérez-Jiménez, Ángel J.; Adamo, Carlo
2016-03-01
We propose two analytical expressions aiming to rationalize the spin-component-scaled (SCS) and spin-opposite-scaled (SOS) schemes for double-hybrid exchange-correlation density-functionals. Their performances are extensively tested within the framework of the nonempirical quadratic integrand double-hybrid (QIDH) model on energetic properties included into the very large GMTKN30 benchmark database, and on structural properties of semirigid medium-sized organic compounds. The SOS variant is revealed as a less computationally demanding alternative to reach the accuracy of the original QIDH model without losing any theoretical background.
Nonlinear interaction of intense hypergeometric Gaussian subfamily laser beams in plasma
NASA Astrophysics Data System (ADS)
Sobhani, H.; Vaziri (Khamedi), M.; Rooholamininejad, H.; Bahrampour, A. R.
2016-07-01
Propagation of Hypergeometric-Gaussian laser beam in a nonlinear plasma medium is investigated by considering the Source Dependent Expansion method. A subfamily of Hypergeometric-Gaussian beams with a non-negative, even and integer radial index, can be expressed as the linear superposition of finite number of Laguerre-Gaussian functions. Propagation of Hypergeometric-Gaussian beams in a nonlinear plasma medium depends on the value of radial index. The bright rings' number of these beams is changed during the propagation in plasma medium. The effect of beam vortex charge number l and initial (input) beam intensity on the self-focusing of Hypergeometric-Gaussian beams is explored. Also, by choosing the suitable initial conditions, Hypergeometric-Gaussian subfamily beams can be converted to one or more mode components that a typical of mode conversion may be occurred. The self-focusing of these winding beams can be used to control the focusing force and improve the electron bunch quality in laser plasma accelerators.
N-body simulations with generic non-Gaussian initial conditions II: halo bias
NASA Astrophysics Data System (ADS)
Wagner, Christian; Verde, Licia
2012-03-01
We present N-body simulations for generic non-Gaussian initial conditions with the aim of exploring and modelling the scale-dependent halo bias. This effect is evident on very large scales requiring large simulation boxes. In addition, the previously available prescription to implement generic non-Gaussian initial conditions has been improved to keep under control higher-order terms which were spoiling the power spectrum on large scales. We pay particular attention to the differences between physical, inflation-motivated primordial bispectra and their factorizable templates, and to the operational definition of the non-Gaussian halo bias (which has both a scale-dependent and an approximately scale-independent contributions). We find that analytic predictions for both the non-Gaussian halo mass function and halo bias work well once a fudge factor (which was introduced before but still lacks convincing physical explanation) is calibrated on simulations. The halo bias remains therefore an extremely promising tool to probe primordial non-Gaussianity and thus to give insights into the physical mechanism that generated the primordial perturbations. The simulation outputs and tables of the analytic predictions will be made publicly available via the non-Gaussian comparison project web site http://icc.ub.edu/~liciaverde/NGSCP.html.
Primordial non-Gaussianity and Dark Energy constraints from Cluster Surveys
Sefusatti, Emiliano; Vale, Chris; Kadota, Kenji; Frieman, Joshua; /Fermilab /KICP, Chicago /Chicago U., Astron. Astrophys. Ctr.
2006-09-01
Galaxy cluster surveys will be a powerful probe of dark energy. At the same time, cluster abundances is sensitive to any non-Gaussianity of the primordial density field. It is therefore possible that non-Gaussian initial conditions might be misinterpreted as a sign of dark energy or at least degrade the expected constraints on dark energy parameters. To address this issue, we perform a likelihood analysis of an ideal cluster survey similar in size and depth to the upcoming South Pole Telescope/Dark Energy Survey (SPT-DES).We analyze a model in which the strength of the non-Gaussianity is parameterized by the constant f{sub NL}; this model has been used extensively to derive Cosmic Microwave Background (CMB) anisotropy constraints on non-Gaussianity, allowing us to make contact with those works. We find that the constraining power of the cluster survey on dark energy observables is not significantly diminished by non-Gaussianity provided that cluster redshift information is included in the analysis. We also find that even an ideal cluster survey is unlikely to improve significantly current and future CMB constraints on non-Gaussianity. However, when all systematics are under control, it could constitute a valuable cross check to CMB observations.
Unified operator approach for deriving Hermite-Gaussian and Laguerre-Gaussian laser modes.
Enderlein, Jörg; Pampaloni, Francesco
2004-08-01
A unified operator approach is described for deriving Hermite-Gaussian and Laguerre-Gaussian laser beams by using as a starting point a plane-wave-spectrum representation of the electromagnetic field. We show that by using the plane-wave representation of the fundamental Gaussian mode as a seed function, all higher-order beam modes can be derived by acting with differential operators on this fundamental solution. The approach presented can be easily generalized to nonparaxial situations and to include vector effects of the electromagnetic field.
Unified operator approach for deriving Hermite-Gaussian and Laguerre-Gaussian laser modes
NASA Astrophysics Data System (ADS)
Enderlein, Jörg; Pampaloni, Francesco
2004-08-01
A unified operator approach is described for deriving Hermite-Gaussian and Laguerre-Gaussian laser beams by using as a starting point a plane-wave-spectrum representation of the electromagnetic field. We show that by using the plane-wave representation of the fundamental Gaussian mode as a seed function, all higher-order beam modes can be derived by acting with differential operators on this fundamental solution. The approach presented can be easily generalized to nonparaxial situations and to include vector effects of the electromagnetic field.
Spacecraft Formation Flying Maneuvers Using Linear Quadratic Regulation With No Radial Axis Inputs
NASA Technical Reports Server (NTRS)
Starin, Scott R.; Yedavalli, R. K.; Sparks, Andrew G.; Bauer, Frank H. (Technical Monitor)
2001-01-01
Regarding multiple spacecraft formation flying, the observation has been made that control thrust need only be applied coplanar to the local horizon to achieve complete controllability of a two-satellite (leader-follower) formation. A formulation of orbital dynamics using the state of one satellite relative to another is used. Without the need for thrust along the radial (zenith-nadir) axis of the relative reference frame, propulsion system simplifications and weight reduction may be accomplished. This work focuses on the validation of this control system on its own merits, and in comparison to a related system which does provide thrust along the radial axis of the relative frame. Maneuver simulations are performed using commercial ODE solvers to propagate the Keplerian dynamics of a controlled satellite relative to an uncontrolled leader. These short maneuver simulations demonstrate the capacity of the controller to perform changes from one formation geometry to another. Control algorithm performance is evaluated based on measures such as the fuel required to complete a maneuver and the maximum acceleration required by the controller. Based on this evaluation, the exclusion of the radial axis of control still allows enough control authority to use Linear Quadratic Regulator (LQR) techniques to design a gain matrix of adequate performance over finite maneuvers. Additional simulations are conducted including perturbations and using no radial control inputs. A major conclusion presented is that control inputs along the three axes have significantly different relationships to the governing orbital dynamics that may be exploited using LQR.
NASA Astrophysics Data System (ADS)
Scoccimarro, Román; Hui, Lam; Manera, Marc; Chan, Kwan Chuen
2012-04-01
We study the scale dependence of halo bias in generic (nonlocal) primordial non-Gaussian (PNG) initial conditions of the type motivated by inflation, parametrized by an arbitrary quadratic kernel. We first show how to generate nonlocal PNG initial conditions with minimal overhead compared to local PNG models for a general class of primordial bispectra that can be written as linear combinations of separable templates. We run cosmological simulations for the local, and nonlocal equilateral and orthogonal models and present results on the scale dependence of halo bias. We also derive a general formula for the Fourier-space bias using the peak-background split in the context of the excursion-set approach to halos and discuss the difference and similarities with the known corresponding result from local bias models. Our peak-background split bias formula generalizes previous results in the literature to include non-Markovian effects and nonuniversality of the mass function and are in better agreement with measurements in numerical simulations than previous results for a variety of halo masses, redshifts and halo definitions. We also derive for the first time quadratic bias results for arbitrary nonlocal PNG, and show that nonlinear bias loops give small corrections at large scales. The resulting well-behaved perturbation theory paves the way to constrain nonlocal PNG from measurements of the power spectrum and bispectrum in galaxy redshift surveys.
NASA Astrophysics Data System (ADS)
Kuyuk, H. S.; Yildirim, E.; Dogan, E.; Horasan, G.
2012-08-01
Two unsupervised pattern recognition algorithms, k-means, and Gaussian mixture model (GMM) analyses have been applied to classify seismic events in the vicinity of Istanbul. Earthquakes, which are occurring at different seismicity rates and extensions of the Thrace-Eskisehir Fault Zone and the North Anatolian Fault (NAF), Turkey, are being contaminated by quarries operated around Istanbul. We have used two time variant parameters, complexity, the ratio of integrated powers of the velocity seismogram, and S/P amplitude ratio as classifiers by using waveforms of 179 events (1.8 < M < 3.0). We have compared two algorithms with classical multivariate linear/quadratic discriminant analyses. The total accuracies of the models for GMM, k-means, linear discriminant function (LDF), and quadratic discriminant function (QDF) are 96.1%, 95.0%, 96.1%, 96.6%, respectively. The performances of models are discussed for earthquakes and quarry blasts separately. All methods clustered the seismic events acceptably where QDF slightly gave better improvements compared to others. We have found that unsupervised clustering algorithms, for which no a-prior target information is available, display a similar discriminatory power as supervised methods of discriminant analysis.
NASA Astrophysics Data System (ADS)
Zhang, Lin; Kong, Hong-Yan
2014-02-01
Many works are based on the steady-state analysis of mean-value dynamics in electro- or optomechanical systems to explore vibration cooling, squeezing, and quantum-state controlling of massive objects. These studies are always conducted in a red-detuned pumping field under a lower power to maintain a stable situation. In this paper we consider self-sustained oscillations of a cavity-field-driven oscillator combined with quadratic coupling in a blue-detuned regime above a pumping threshold. Our study finds that the oscillator will be far away from its steady-state behavior by conducting a self-sustained oscillation with a discrete amplitude locking effect producing a rich energy-balanced structure. The dynamical backaction of this self-oscillation on the field mode induces a multipeak field spectrum, which implies an efficient harmonic generation with its intensity modified not only by the displacement x0 but also by the amplitude A of the mechanical oscillation. The corresponding nonlinear field spectrum and its magnitude are analytically analyzed with quadratic coupling when the mechanical oscillator is dynamically locked to a self-sustained oscillation.
Cluster size distribution in Gaussian glasses
NASA Astrophysics Data System (ADS)
Novikov, S. V.
2011-03-01
A simple method for the estimation of the asymptotics of the cluster numbers in Gaussian glasses is described. Validity of the method was tested by the comparison with the exact analytic result for the non-correlated field and simulation data for the distribution of random energies in strongly spatially correlated dipolar glass model.
Diffusion of Super-Gaussian Profiles
ERIC Educational Resources Information Center
Rosenberg, C.-J.; Anderson, D.; Desaix, M.; Johannisson, P.; Lisak, M.
2007-01-01
The present analysis describes an analytically simple and systematic approximation procedure for modelling the free diffusive spreading of initially super-Gaussian profiles. The approach is based on a self-similar ansatz for the evolution of the diffusion profile, and the parameter functions involved in the modelling are determined by suitable…
Scalable Hyper-parameter Estimation for Gaussian Process Based Time Series Analysis
Chandola, Varun; Vatsavai, Raju
2010-01-01
Gaussian process (GP) is increasingly becoming popular as a kernel machine learning tool for non-parametric data analysis. Recently, GP has been applied to model non-linear dependencies in time series data. GP based analysis can be used to solve problems of time series prediction, forecasting, missing data imputation, change point detection, anomaly detection, etc. But the use of GP to handle massive scientific time series data sets has been limited, owing to its expensive computational complexity. The primary bottleneck is the handling of the covariance matrix whose size is quadratic in the length of the time series. In this paper we propose a scalable method that exploit the special structure of the covariance matrix for hyper-parameter estimation in GP based learning. The proposed method allows estimation of hyper parameters associated with GP in quadratic time, which is an order of magnitude improvement over standard methods with cubic complexity. Moreover, the proposed method does not require explicit computation of the covariance matrix and hence has memory requirement linear to the length of the time series as opposed to the quadratic memory requirement of standard methods. To further improve the computational complexity of the proposed method, we provide a parallel version to concurrently estimate the log likelihood for a set of time series which is the key step in the hyper-parameter estimation. Performance results on a multi-core system show that our proposed method provides significant speedups as high as 1000, even when running in serial mode, while maintaining a small memory footprint. The parallel version exploits the natural parallelization potential of the serial algorithm and is shown to perform significantly better than the serial faster algorithm, with speedups as high as 10.
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.
Electroweak vacuum stability and finite quadratic radiative corrections
NASA Astrophysics Data System (ADS)
Masina, Isabella; Nardini, Germano; Quiros, Mariano
2015-08-01
If the Standard Model (SM) is an effective theory, as currently believed, it is valid up to some energy scale Λ to which the Higgs vacuum expectation value is sensitive throughout radiative quadratic terms. The latter ones destabilize the electroweak vacuum and generate the SM hierarchy problem. For a given perturbative ultraviolet (UV) completion, the SM cutoff can be computed in terms of fundamental parameters. If the UV mass spectrum involves several scales, the cutoff is not unique and each SM sector has its own UV cutoff Λi. We have performed this calculation assuming the minimal supersymmetric standard model (MSSM) is the SM UV completion. As a result, from the SM point of view, the quadratic corrections to the Higgs mass are equivalent to finite threshold contributions. For the measured values of the top quark and Higgs masses, and depending on the values of the different cutoffs Λi, these contributions can cancel even at renormalization scales as low as multi-TeV, unlike the case of a single cutoff where the cancellation only occurs at Planckian energies, a result originally obtained by Veltman. From the MSSM point of view, the requirement of stability of the electroweak minimum under radiative corrections is incorporated into the matching conditions and provides an extra constraint on the focus point solution to the little hierarchy problem in the MSSM. These matching conditions can be employed for precise calculations of the Higgs sector in scenarios with heavy supersymmetric fields.
Wave propagation in elastic medium with heterogeneous quadratic nonlinearity
Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin
2011-06-23
This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter {beta} when the nonlinearity distribution in the layer is a stochastic process.
Confidence set inference with a prior quadratic bound
NASA Technical Reports Server (NTRS)
Backus, George E.
1989-01-01
In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z=(z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y (sup 0) = (y (sub 1) (sup 0), ..., y (sub D (sup 0)), using full or partial knowledge of the statistical distribution of the random errors in y (sup 0). The data space Y containing y(sup 0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x, Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. Confidence set inference is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface.
Quadratic Reciprocity and the Group Orders of Particle States
DAI,YANG; BORISOV,ALEXEY B.; LONGWORTH,JAMES W.; BOYER,KEITH; RHODES,CHARLES K.
2001-06-01
The construction of inverse states in a finite field F{sub P{sub P{alpha}}} enables the organization of the mass scale by associating particle states with residue class designations. With the assumption of perfect flatness ({Omega}total = 1.0), this approach leads to the derivation of a cosmic seesaw congruence which unifies the concepts of space and mass. The law of quadratic reciprocity profoundly constrains the subgroup structure of the multiplicative group of units F{sub P{sub {alpha}}}* defined by the field. Four specific outcomes of this organization are (1) a reduction in the computational complexity of the mass state distribution by a factor of {approximately}10{sup 30}, (2) the extension of the genetic divisor concept to the classification of subgroup orders, (3) the derivation of a simple numerical test for any prospective mass number based on the order of the integer, and (4) the identification of direct biological analogies to taxonomy and regulatory networks characteristic of cellular metabolism, tumor suppression, immunology, and evolution. It is generally concluded that the organizing principle legislated by the alliance of quadratic reciprocity with the cosmic seesaw creates a universal optimized structure that functions in the regulation of a broad range of complex phenomena.
QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.
Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit
2014-01-01
We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called 'serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed. PMID:25301974
An Instability Index Theory for Quadratic Pencils and Applications
NASA Astrophysics Data System (ADS)
Bronski, Jared; Johnson, Mathew A.; Kapitula, Todd
2014-04-01
Primarily motivated by the stability analysis of nonlinear waves in second-order in time Hamiltonian systems, in this paper we develop an instability index theory for quadratic operator pencils acting on a Hilbert space. In an extension of the known theory for linear pencils, explicit connections are made between the number of eigenvalues of a given quadratic operator pencil with positive real parts to spectral information about the individual operators comprising the coefficients of the spectral parameter in the pencil. As an application, we apply the general theory developed here to yield spectral and nonlinear stability/instability results for abstract second-order in time wave equations. More specifically, we consider the problem of the existence and stability of spatially periodic waves for the "good" Boussinesq equation. In the analysis our instability index theory provides an explicit, and somewhat surprising, connection between the stability of a given periodic traveling wave solution of the "good" Boussinesq equation and the stability of the same periodic profile, but with different wavespeed, in the nonlinear dynamics of a related generalized Korteweg-de Vries equation.
Implementation of Multivariate Quadratic Quasigroup for Wireless Sensor Network
NASA Astrophysics Data System (ADS)
Maia, Ricardo José Menezes; Barreto, Paulo Sérgio Licciardi Messeder; de Oliveira, Bruno Trevizan
Wireless sensor networks (WSN) consists of sensor nodes with limited energy, processing, communication and memory. Security in WSN is becoming critical with the emergence of applications that require mechanisms for authenticity, integrity and confidentiality. Due to resource constraints in WSN, matching public key cryptosystems (PKC) for these networks is an open research problem. Recently a new PKC based on quasigroups multivariate quadratic. Experiments performed show that MQQ performed in less time than existing major PKC, so that some articles claim that has MQQ speed of a typical symmetric block cipher. Considering features promising to take a new path in the difficult task of providing wireless sensor networks in public key cryptosystems. This paper implements in nesC a new class of public key algorithm called Multivariate Quadratic Quasigroup. This implementation focuses on modules for encryption and decryption of 160-bit MQQ, the modules have been implemented on platforms TelosB and MICAz. We measured execution time and space occupied in the ROM and RAM of the sensors.
Half-quadratic-based iterative minimization for robust sparse representation.
He, Ran; Zheng, Wei-Shi; Tan, Tieniu; Sun, Zhenan
2014-02-01
Robust sparse representation has shown significant potential in solving challenging problems in computer vision such as biometrics and visual surveillance. Although several robust sparse models have been proposed and promising results have been obtained, they are either for error correction or for error detection, and learning a general framework that systematically unifies these two aspects and explores their relation is still an open problem. In this paper, we develop a half-quadratic (HQ) framework to solve the robust sparse representation problem. By defining different kinds of half-quadratic functions, the proposed HQ framework is applicable to performing both error correction and error detection. More specifically, by using the additive form of HQ, we propose an ℓ1-regularized error correction method by iteratively recovering corrupted data from errors incurred by noises and outliers; by using the multiplicative form of HQ, we propose an ℓ1-regularized error detection method by learning from uncorrupted data iteratively. We also show that the ℓ1-regularization solved by soft-thresholding function has a dual relationship to Huber M-estimator, which theoretically guarantees the performance of robust sparse representation in terms of M-estimation. Experiments on robust face recognition under severe occlusion and corruption validate our framework and findings.
a Distributed Gaussian Discrete Variable Representation
NASA Astrophysics Data System (ADS)
Karabulut, Hasan
In this work a discrete variable representation (DVR) is constructed from a distributed Gaussian basis (DGB). A DGB is a finite or infinite chain of uniformly distributed Gaussians g_{n}(x) = e^{-c^2(x/d-n)^2} where n takes integer values. There are three main parts of this thesis. In the first part (Chapter III) the finite chain distributed Gaussian DVR (Finite Chain DG-DVR) is derived. In order to accomplish this, the distributed Gaussian orthogonal polynomials are introduced. The connection of these polynomials to Stieltjes-Wigert polynomials is shown. The recurrence relation for these orthogonal polynomials is derived. Tested recipes are given to calculate the quadrature points and weights and to construct the corresponding Lagrange functions which are analogs of Lagrange interpolation polynomials. The symmetries of quadrature points, weights, and Lagrange functions are derived. Limit cases ctoinfty and cto 0 are studied. In the second part (Chapter IV)the infinite chain limit DG-DVR is derived from a limit of the finite chain DG-DVR. The quadrature points and weights and the Lagrange functions are found in this limit and kinetic energy operator is constructed. It is shown that in the limit c to 0 the infinite chain DG-DVR reduces to Colbert and Miller's DVR. A discussion of ability of a distributed Gaussian basis to represent an arbitrary function is given. The results of this treatment yield a possible explanation of surprising accuracy of Colbert-Miller DVR. In the third part construction of the DG-DVR is given when one point is chosen arbitrarily. Some interesting identities and integral representations for the b _{n} and sigma_ {n} coefficients that are introduced in the second part are found.
NASA Astrophysics Data System (ADS)
Das, S.; Goswami, K.; Datta, B. N.
2016-05-01
Failure of structural systems under dynamic loading can be prevented via active vibration control which shifts the damped natural frequencies of the systems away from the dominant range of a loading spectrum. The damped natural frequencies and the dynamic load typically show significant variations in practice. A computationally efficient methodology based on quadratic partial eigenvalue assignment technique and optimization under uncertainty has been formulated in the present work that will rigorously account for these variations and result in economic and resilient design of structures. A novel scheme based on hierarchical clustering and importance sampling is also developed in this work for accurate and efficient estimation of probability of failure to guarantee the desired resilience level of the designed system. Finally the most robust set of feedback matrices is selected from the set of probabilistically characterized optimal closed-loop system to implement the new methodology for design of active controlled structures. Numerical examples are presented to illustrate the proposed methodology.
On the optimum ride control of a stochastic model of a tractor-semitrailer vehicle
NASA Astrophysics Data System (ADS)
ElMadany, M. M.; Samaha, M. E.
1992-07-01
A systematic approach based on stochastic optimal control and estimation theories for the optimal design of active suspension systems for a tractor-semitrailer vehicle is presented. The vehicle-road system dynamics combined with the human perception of random vibrations are cast in the standard linear quadratic Gaussian format. The time delays of the stochastic excitation process of the multi-axled vehicle are represented by a first order Padé approximation. The optimal controller/observer is derived which minimizes the mean-squared values of performance variables reflecting the human comfort, cargo safety, suspension working space, roadholding ability and control forces. The advantages of optimally controlled suspension systems over their passive counterparts are indicated.
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.
Chao, R.M.; Ko, S.H.; Lin, I.H.; Pai, F.S.; Chang, C.C.
2009-12-15
The historically high cost of crude oil price is stimulating research into solar (green) energy as an alternative energy source. In general, applications with large solar energy output require a maximum power point tracking (MPPT) algorithm to optimize the power generated by the photovoltaic effect. This work aims to provide a stand-alone solution for solar energy applications by integrating a DC/DC buck converter to a newly developed quadratic MPPT algorithm along with its appropriate software and hardware. The quadratic MPPT method utilizes three previously used duty cycles with their corresponding power outputs. It approaches the maximum value by using a second order polynomial formula, which converges faster than the existing MPPT algorithm. The hardware implementation takes advantage of the real-time controller system from National Instruments, USA. Experimental results have shown that the proposed solar mechatronics system can correctly and effectively track the maximum power point without any difficulties. (author)
Linear Quadratic Tracking Design for a Generic Transport Aircraft with Structural Load Constraints
NASA Technical Reports Server (NTRS)
Burken, John J.; Frost, Susan A.; Taylor, Brian R.
2011-01-01
When designing control laws for systems with constraints added to the tracking performance, control allocation methods can be utilized. Control allocations methods are used when there are more command inputs than controlled variables. Constraints that require allocators are such task as; surface saturation limits, structural load limits, drag reduction constraints or actuator failures. Most transport aircraft have many actuated surfaces compared to the three controlled variables (such as angle of attack, roll rate & angle of side slip). To distribute the control effort among the redundant set of actuators a fixed mixer approach can be utilized or online control allocation techniques. The benefit of an online allocator is that constraints can be considered in the design whereas the fixed mixer cannot. However, an online control allocator mixer has a disadvantage of not guaranteeing a surface schedule, which can then produce ill defined loads on the aircraft. The load uncertainty and complexity has prevented some controller designs from using advanced allocation techniques. This paper considers actuator redundancy management for a class of over actuated systems with real-time structural load limits using linear quadratic tracking applied to the generic transport model. A roll maneuver example of an artificial load limit constraint is shown and compared to the same no load limitation maneuver.
Approximating Gaussian mixture model or radial basis function network with multilayer perceptron.
Patrikar, Ajay M
2013-07-01
Gaussian mixture models (GMMs) and multilayer perceptron (MLP) are both popular pattern classification techniques. This brief shows that a multilayer perceptron with quadratic inputs (MLPQ) can accurately approximate GMMs with diagonal covariance matrices. The mapping equations between the parameters of GMM and the weights of MLPQ are presented. A similar approach is applied to radial basis function networks (RBFNs) to show that RBFNs with Gaussian basis functions and Euclidean norm can be approximated accurately with MLPQ. The mapping equations between RBFN and MLPQ weights are presented. There are well-established training procedures for GMMs, such as the expectation maximization (EM) algorithm. The GMM parameters obtained by the EM algorithm can be used to generate a set of initial weights of MLPQ. Similarly, a trained RBFN can be used to generate a set of initial weights of MLPQ. MLPQ training can be continued further with gradient-descent based methods, which can lead to improvement in performance compared to the GMM or RBFN from which it is initialized. Thus, the MLPQ can always perform as well as or better than the GMM or RBFN.
Repopulation Kinetics and the Linear-Quadratic Model
NASA Astrophysics Data System (ADS)
O'Rourke, S. F. C.; McAneney, H.; Starrett, C.; O'Sullivan, J. M.
2009-08-01
The standard Linear-Quadratic (LQ) survival model for radiotherapy is used to investigate different schedules of radiation treatment planning for advanced head and neck cancer. We explore how these treament protocols may be affected by different tumour repopulation kinetics between treatments. The laws for tumour cell repopulation include the logistic and Gompertz models and this extends the work of Wheldon et al. [1], which was concerned with the case of exponential repopulation between treatments. Treatment schedules investigated include standarized and accelerated fractionation. Calculations based on the present work show, that even with growth laws scaled to ensure that the repopulation kinetics for advanced head and neck cancer are comparable, considerable variation in the survival fraction to orders of magnitude emerged. Calculations show that application of the Gompertz model results in a significantly poorer prognosis for tumour eradication. Gaps in treatment also highlight the differences in the LQ model with the effect of repopulation kinetics included.
Renormalisation of correlations in a barrier billiard: Quadratic irrational trajectories
NASA Astrophysics Data System (ADS)
Adamson, L. N. C.; Osbaldestin, A. H.
2014-03-01
We present an analysis of autocorrelation functions in symmetric barrier billiards using a renormalisation approach for quadratic irrational trajectories. Depending on the nature of the barrier, this leads to either self-similar or chaotic behaviour. In the self-similar case we give an analysis of the half barrier and present a detailed calculation of the locations, asymptotic heights and signs of the main peaks in the autocorrelation function. Then we consider arbitrary barriers, illustrating that typically these give rise to chaotic correlations of the autocorrelation function which we further represent by showing the invariant sets associated with these correlations. Our main ingredient here is a functional recurrence which has been previously derived and used in work on the Harper equation, strange non-chaotic attractors and a quasi-periodically forced two-level system.
Quadratic Finite Element Method for 1D Deterministic Transport
Tolar, Jr., D R; Ferguson, J M
2004-01-06
In the discrete ordinates, or SN, numerical solution of the transport equation, both the spatial ({und r}) and angular ({und {Omega}}) dependences on the angular flux {psi}{und r},{und {Omega}}are modeled discretely. While significant effort has been devoted toward improving the spatial discretization of the angular flux, we focus on improving the angular discretization of {psi}{und r},{und {Omega}}. Specifically, we employ a Petrov-Galerkin quadratic finite element approximation for the differencing of the angular variable ({mu}) in developing the one-dimensional (1D) spherical geometry S{sub N} equations. We develop an algorithm that shows faster convergence with angular resolution than conventional S{sub N} algorithms.
Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions.
Alase, Abhijeet; Cobanera, Emilio; Ortiz, Gerardo; Viola, Lorenza
2016-08-12
We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D-1. The key is a Hamiltonian-dependent separation of the bulk from the boundary. By combining information from the two, we identify a matrix function that fully characterizes the solutions, and may be used to construct an efficiently computable indicator of bulk-boundary correspondence. As an illustration, we show how our approach correctly describes the zero-energy Majorana modes of a time-reversal-invariant s-wave two-band superconductor in a Josephson ring configuration, and predicts that a fractional 4π-periodic Josephson effect can only be observed in phases hosting an odd number of Majorana pairs per boundary. PMID:27563986
Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions
NASA Astrophysics Data System (ADS)
Alase, Abhijeet; Cobanera, Emilio; Ortiz, Gerardo; Viola, Lorenza
2016-08-01
We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D -1 . The key is a Hamiltonian-dependent separation of the bulk from the boundary. By combining information from the two, we identify a matrix function that fully characterizes the solutions, and may be used to construct an efficiently computable indicator of bulk-boundary correspondence. As an illustration, we show how our approach correctly describes the zero-energy Majorana modes of a time-reversal-invariant s -wave two-band superconductor in a Josephson ring configuration, and predicts that a fractional 4 π -periodic Josephson effect can only be observed in phases hosting an odd number of Majorana pairs per boundary.
Recognition of Graphs with Convex Quadratic Stability Number
NASA Astrophysics Data System (ADS)
Pacheco, Maria F.; Cardoso, Domingos M.
2009-09-01
A stable set of a graph is a set of mutually non-adjacent vertices. The determination of a maximum size stable set, which is called maximum stable set, and the determination of its size, which is called stability number, are central combinatorial optimization problems. However, given a nonnegative integer k, to determine if a graph G has a stable set of size k is NP-complete. In this paper we deal with graphs for which the stability number can be determined by solving a convex quadratic programming problem. Such graphs were introduced in [13] and are called graphs with convex-QP stability number. A few algorithmic techniques for the recognition of this type of graphs in particular families are presented.
Schwarz and multilevel methods for quadratic spline collocation
Christara, C.C.; Smith, B.
1994-12-31
Smooth spline collocation methods offer an alternative to Galerkin finite element methods, as well as to Hermite spline collocation methods, for the solution of linear elliptic Partial Differential Equations (PDEs). Recently, optimal order of convergence spline collocation methods have been developed for certain degree splines. Convergence proofs for smooth spline collocation methods are generally more difficult than for Galerkin finite elements or Hermite spline collocation, and they require stronger assumptions and more restrictions. However, numerical tests indicate that spline collocation methods are applicable to a wider class of problems, than the analysis requires, and are very competitive to finite element methods, with respect to efficiency. The authors will discuss Schwarz and multilevel methods for the solution of elliptic PDEs using quadratic spline collocation, and compare these with domain decomposition methods using substructuring. Numerical tests on a variety of parallel machines will also be presented. In addition, preliminary convergence analysis using Schwarz and/or maximum principle techniques will be presented.
Cosmology for quadratic gravity in generalized Weyl geometry
NASA Astrophysics Data System (ADS)
Beltrán Jiménez, Jose; Heisenberg, Lavinia; Koivisto, Tomi S.
2016-04-01
A class of vector-tensor theories arises naturally in the framework of quadratic gravity in spacetimes with linear vector distortion. Requiring the absence of ghosts for the vector field imposes an interesting condition on the allowed connections with vector distortion: the resulting one-parameter family of connections generalises the usual Weyl geometry with polar torsion. The cosmology of this class of theories is studied, focusing on isotropic solutions wherein the vector field is dominated by the temporal component. De Sitter attractors are found and inhomogeneous perturbations around such backgrounds are analysed. In particular, further constraints on the models are imposed by excluding pathologies in the scalar, vector and tensor fluctuations. Various exact background solutions are presented, describing a constant and an evolving dark energy, a bounce and a self-tuning de Sitter phase. However, the latter two scenarios are not viable under a closer scrutiny.
Large non-gaussianity in axion inflation.
Barnaby, Neil; Peloso, Marco
2011-05-01
The inflationary paradigm has enjoyed phenomenological success; however, a compelling particle physics realization is still lacking. Axions are among the best-motivated inflaton candidates, since the flatness of their potential is naturally protected by a shift symmetry. We reconsider the cosmological perturbations in axion inflation, consistently accounting for the coupling to gauge fields cΦFF, which is generically present in these models. This coupling leads to production of gauge quanta, which provide a new source of inflaton fluctuations, δΦ. For c≥10(2)M(p)(-1), these dominate over the vacuum fluctuations, and non-Gaussianity exceeds the current observational bound. This regime is typical for concrete realizations that admit a UV completion; hence, large non-Gaussianity is easily obtained in minimal and natural realizations of inflation.
Quantum Fidelity for Arbitrary Gaussian States
NASA Astrophysics Data System (ADS)
Banchi, Leonardo; Braunstein, Samuel L.; Pirandola, Stefano
2015-12-01
We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can be written in terms of symplectic invariants and used to derive closed forms for a variety of basic quantities and tools, such as the Bures metric, the quantum Fisher information, and various fidelity-based bounds. Our result can be used to extend the study of continuous-variable protocols, such as quantum teleportation and cloning, beyond the current one-mode or two-mode analyses, and paves the way to solve general problems in quantum metrology and quantum hypothesis testing with arbitrary multimode Gaussian resources.
Fock expansion of multimode pure Gaussian states
Cariolaro, Gianfranco; Pierobon, Gianfranco
2015-12-15
The Fock expansion of multimode pure Gaussian states is derived starting from their representation as displaced and squeezed multimode vacuum states. The approach is new and appears to be simpler and more general than previous ones starting from the phase-space representation given by the characteristic or Wigner function. Fock expansion is performed in terms of easily evaluable two-variable Hermite–Kampé de Fériet polynomials. A relatively simple and compact expression for the joint statistical distribution of the photon numbers in the different modes is obtained. In particular, this result enables one to give a simple characterization of separable and entangled states, as shown for two-mode and three-mode Gaussian states.
A Fast Incremental Gaussian Mixture Model
Pinto, Rafael Coimbra; Engel, Paulo Martins
2015-01-01
This work builds upon previous efforts in online incremental learning, namely the Incremental Gaussian Mixture Network (IGMN). The IGMN is capable of learning from data streams in a single-pass by improving its model after analyzing each data point and discarding it thereafter. Nevertheless, it suffers from the scalability point-of-view, due to its asymptotic time complexity of O(NKD3) for N data points, K Gaussian components and D dimensions, rendering it inadequate for high-dimensional data. In this work, we manage to reduce this complexity to O(NKD2) by deriving formulas for working directly with precision matrices instead of covariance matrices. The final result is a much faster and scalable algorithm which can be applied to high dimensional tasks. This is confirmed by applying the modified algorithm to high-dimensional classification datasets. PMID:26444880
Gaussian quadrature for multiple orthogonal polynomials
NASA Astrophysics Data System (ADS)
Coussement, Jonathan; van Assche, Walter
2005-06-01
We study multiple orthogonal polynomials of type I and type II, which have orthogonality conditions with respect to r measures. These polynomials are connected by their recurrence relation of order r+1. First we show a relation with the eigenvalue problem of a banded lower Hessenberg matrix Ln, containing the recurrence coefficients. As a consequence, we easily find that the multiple orthogonal polynomials of type I and type II satisfy a generalized Christoffel-Darboux identity. Furthermore, we explain the notion of multiple Gaussian quadrature (for proper multi-indices), which is an extension of the theory of Gaussian quadrature for orthogonal polynomials and was introduced by Borges. In particular, we show that the quadrature points and quadrature weights can be expressed in terms of the eigenvalue problem of Ln.
Quantum Fidelity for Arbitrary Gaussian States.
Banchi, Leonardo; Braunstein, Samuel L; Pirandola, Stefano
2015-12-31
We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can be written in terms of symplectic invariants and used to derive closed forms for a variety of basic quantities and tools, such as the Bures metric, the quantum Fisher information, and various fidelity-based bounds. Our result can be used to extend the study of continuous-variable protocols, such as quantum teleportation and cloning, beyond the current one-mode or two-mode analyses, and paves the way to solve general problems in quantum metrology and quantum hypothesis testing with arbitrary multimode Gaussian resources. PMID:26764978
Edge Detection By Differences Of Gaussians
NASA Astrophysics Data System (ADS)
Marthon, Ph.; Thiesse, B.; Bruel, A.
1986-06-01
The Differences of Gaussians (DOGs) are of fundamental importance in edge detection. They belong to the human vision system as shown by Enroth-Cugell and Robson [ENR66]. The zero-crossings of their outputs mark the loci of the intensity changes. The set of descriptions from different operator sizes forms the input for later visual processes, such as stereopsis and motion analysis. We show that DOGs uniformly converge to the Laplacian of a Gaussian (ΔG2,σ) when both the inhibitory and excitatory variables converge to σ. Spatial and spectral properties of DOGs and ΔGs are compared: width and height of their central positive regions, bandiwidths... Finally, DOGs' responses to some features such as ideal edge, right angle corner, general corner..., are presented and magnitudes of error on edge position are given.
Confidence set inference with a prior quadratic bound
NASA Technical Reports Server (NTRS)
Backus, George E.
1988-01-01
In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z = (z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y(0)=(y sub 1(0),...,y sub D(0)) knowledge of the statistical distribution of the random errors in y(0). The data space Y containing y(0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x (e.g., energy or dissipation rate), Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. CSI is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface. Neither the heat flow nor the energy bound is strong enough to permit estimation of B(r) at single points on the CMB, but the heat flow bound permits estimation of uniform averages of B(r) over discs on the CMB, and both bounds permit weighted disc-averages with continous weighting kernels. Both bounds also permit estimation of low-degree Gauss coefficients at the CMB. The heat flow bound resolves them up to degree 8 if the crustal field at satellite altitudes must be treated as a systematic error, but can resolve to degree 11 under the most favorable statistical treatment of the crust. These two limits produce circles of confusion on the CMB with diameters of 25 deg and 19 deg respectively.
Spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity
Golubkov, A A; Makarov, Vladimir A
2011-11-30
We present a brief review of the results of fifty years of development efforts in spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity. The recent original results obtained by the authors show the fundamental possibility of determining, from experimental data, the coordinate dependences of complex quadratic susceptibility tensor components of a onedimensionally inhomogeneous (along the z axis) medium with an arbitrary frequency dispersion, if the linear dielectric properties of the medium also vary along the z axis and are described by a diagonal tensor of the linear dielectric constant. It is assumed that the medium in question has the form of a plane-parallel plate, whose surfaces are perpendicular to the direction of the inhomogeneity. Using the example of several components of the tensors X{sup (2)}(z, {omega}{sub 1} {+-} {omega}{sub 2}; {omega}{sub 1}, {+-} {omega}{sub 2}), we describe two methods for finding their spatial profiles, which differ in the interaction geometry of plane monochromatic fundamental waves with frequencies {omega}{sub 1} and {omega}{sub 2}. The both methods are based on assessing the intensity of the waves propagating from the plate at the sum or difference frequency and require measurements over a range of angles of incidence of the fundamental waves. Such measurements include two series of additional estimates of the intensities of the waves generated under special conditions by using the test and additional reference plates, which eliminates the need for complicated phase measurements of the complex amplitudes of the waves at the sum (difference) frequency.
Non-Markovianity of Gaussian Channels.
Torre, G; Roga, W; Illuminati, F
2015-08-14
We introduce a necessary and sufficient criterion for the non-Markovianity of Gaussian quantum dynamical maps based on the violation of divisibility. The criterion is derived by defining a general vectorial representation of the covariance matrix which is then exploited to determine the condition for the complete positivity of partial maps associated with arbitrary time intervals. Such construction does not rely on the Choi-Jamiolkowski representation and does not require optimization over states.
Microwave Realization of the Gaussian Symplectic Ensemble
NASA Astrophysics Data System (ADS)
Rehemanjiang, A.; Allgaier, M.; Joyner, C. H.; Müller, S.; Sieber, M.; Kuhl, U.; Stöckmann, H.-J.
2016-08-01
Following an idea by Joyner et al. [Europhys. Lett. 107, 50004 (2014)], a microwave graph with an antiunitary symmetry T obeying T2=-1 is realized. The Kramers doublets expected for such systems are clearly identified and can be lifted by a perturbation which breaks the antiunitary symmetry. The observed spectral level spacings distribution of the Kramers doublets is in agreement with the predictions from the Gaussian symplectic ensemble expected for chaotic systems with such a symmetry.
Consistency relations for non-Gaussianity
NASA Astrophysics Data System (ADS)
Li, Miao; Wang, Yi
2008-09-01
We investigate consistency relations for non-Gaussianity. We provide a model-independent dynamical proof for the consistency relation for three-point correlation functions from the Hamiltonian and field redefinition. This relation can be applied to single-field inflation, multi-field inflation and the curvaton scenario. This relation can also be generalized to n-point correlation functions up to arbitrary order in perturbation theory and with arbitrary number of loops.
Computational aspects of Gaussian beam migration
Hale, D.
1992-01-01
The computational efficiency of Gaussian beam migration depends on the solution of two problems: (1) computation of complex-valued beam times and amplitudes in Cartesian (x,z) coordinates, and (2) limiting computations to only those (x,z) coordinates within a region where beam amplitudes are significant. The first problem can be reduced to a particular instance of a class of closest-point problems in computational geometry, for which efficient solutions, such as the Delaunay triangulation, are well known. Delaunay triangulation of sampled points along a ray enables the efficient location of that point on the raypath that is closest to any point (x,z) at which beam times and amplitudes are required. Although Delaunay triangulation provides an efficient solution to this closest point problem, a simpler solution, also presented in this paper, may be sufficient and more easily extended for use in 3-D Gaussian beam migration. The second problem is easily solved by decomposing the subsurface image into a coarse grid of square cells. Within each cell, simple and efficient loops over (x,z) coordinates may be used. Because the region in which beam amplitudes are significant may be difficult to represent with simple loops over (x,z) coordinates, I use recursion to move from cell to cell, until entire region defined by the beam has been covered. Benchmark tests of a computer program implementing these solutions suggest that the cost of Gaussian hewn migration is comparable to that of migration via explicit depth extrapolation in the frequency-space domain. For the data sizes and computer programs tested here, the explicit method was faster. However, as data size was increased, the computation time for Gaussian beam migration grew more slowly than that for the explicit method.
Computational aspects of Gaussian beam migration
Hale, D.
1992-08-01
The computational efficiency of Gaussian beam migration depends on the solution of two problems: (1) computation of complex-valued beam times and amplitudes in Cartesian (x,z) coordinates, and (2) limiting computations to only those (x,z) coordinates within a region where beam amplitudes are significant. The first problem can be reduced to a particular instance of a class of closest-point problems in computational geometry, for which efficient solutions, such as the Delaunay triangulation, are well known. Delaunay triangulation of sampled points along a ray enables the efficient location of that point on the raypath that is closest to any point (x,z) at which beam times and amplitudes are required. Although Delaunay triangulation provides an efficient solution to this closest point problem, a simpler solution, also presented in this paper, may be sufficient and more easily extended for use in 3-D Gaussian beam migration. The second problem is easily solved by decomposing the subsurface image into a coarse grid of square cells. Within each cell, simple and efficient loops over (x,z) coordinates may be used. Because the region in which beam amplitudes are significant may be difficult to represent with simple loops over (x,z) coordinates, I use recursion to move from cell to cell, until entire region defined by the beam has been covered. Benchmark tests of a computer program implementing these solutions suggest that the cost of Gaussian hewn migration is comparable to that of migration via explicit depth extrapolation in the frequency-space domain. For the data sizes and computer programs tested here, the explicit method was faster. However, as data size was increased, the computation time for Gaussian beam migration grew more slowly than that for the explicit method.
Entropic Fluctuations in Gaussian Dynamical Systems
NASA Astrophysics Data System (ADS)
Jakšić, V.; Pillet, C.-A.; Shirikyan, A.
2016-06-01
We study nonequilibrium statistical mechanics of a Gaussian dynamical system and compute in closed form the large deviation functionals describing the fluctuations of the entropy production observable with respect to the reference state and the nonequilibrium steady state. The entropy production observable of this model is an unbounded function on the phase space, and its large deviation functionals have a surprisingly rich structure. We explore this structure in some detail.
Gaussian Confinement in a Jkj Decay Model
NASA Astrophysics Data System (ADS)
da Silva, Mario L. L.; Hadjimichef, Dimiter; Vasconcellos, Cesar A. Z.
In microscopic decay models, one attempts to describe hadron strong decays in terms of quark and gluon degrees of freedom. We begin by assuming that strong decays are driven by the same interquark Hamiltonian which determines the spectrum, and that it incorporates gaussian confinement. An A → BC decay matrix element of the JKJ Hamiltonian involves a pair-production current matrix elements times a scatering matrix element. Diagrammatically this corresponds to an interaction between an initial line and produced pair.
Non-Markovianity of Gaussian Channels.
Torre, G; Roga, W; Illuminati, F
2015-08-14
We introduce a necessary and sufficient criterion for the non-Markovianity of Gaussian quantum dynamical maps based on the violation of divisibility. The criterion is derived by defining a general vectorial representation of the covariance matrix which is then exploited to determine the condition for the complete positivity of partial maps associated with arbitrary time intervals. Such construction does not rely on the Choi-Jamiolkowski representation and does not require optimization over states. PMID:26317700
Microwave Realization of the Gaussian Symplectic Ensemble.
Rehemanjiang, A; Allgaier, M; Joyner, C H; Müller, S; Sieber, M; Kuhl, U; Stöckmann, H-J
2016-08-01
Following an idea by Joyner et al. [Europhys. Lett. 107, 50004 (2014)], a microwave graph with an antiunitary symmetry T obeying T^{2}=-1 is realized. The Kramers doublets expected for such systems are clearly identified and can be lifted by a perturbation which breaks the antiunitary symmetry. The observed spectral level spacings distribution of the Kramers doublets is in agreement with the predictions from the Gaussian symplectic ensemble expected for chaotic systems with such a symmetry. PMID:27541466
Reliable fusion of control and sensing in intelligent machines. Thesis
NASA Technical Reports Server (NTRS)
Mcinroy, John E.
1991-01-01
Although robotics research has produced a wealth of sophisticated control and sensing algorithms, very little research has been aimed at reliably combining these control and sensing strategies so that a specific task can be executed. To improve the reliability of robotic systems, analytic techniques are developed for calculating the probability that a particular combination of control and sensing algorithms will satisfy the required specifications. The probability can then be used to assess the reliability of the design. An entropy formulation is first used to quickly eliminate designs not capable of meeting the specifications. Next, a framework for analyzing reliability based on the first order second moment methods of structural engineering is proposed. To ensure performance over an interval of time, lower bounds on the reliability of meeting a set of quadratic specifications with a Gaussian discrete time invariant control system are derived. A case study analyzing visual positioning in robotic system is considered. The reliability of meeting timing and positioning specifications in the presence of camera pixel truncation, forward and inverse kinematic errors, and Gaussian joint measurement noise is determined. This information is used to select a visual sensing strategy, a kinematic algorithm, and a discrete compensator capable of accomplishing the desired task. Simulation results using PUMA 560 kinematic and dynamic characteristics are presented.
Non-Gaussianity from axionic curvaton
Kawasaki, Masahiro; Kobayashi, Takeshi; Takahashi, Fuminobu E-mail: takeshi@cita.utoronto.ca
2013-03-01
We study non-Gaussianity of density perturbations generated by an axionic curvaton, focusing on the case that the curvaton sits near the hilltop of the potential during inflation. Such hilltop curvatons can generate a red-tilted density perturbation spectrum without invoking large-field inflation. We show that, even when the curvaton dominates the Universe, the non-Gaussianity parameter f{sub NL} is positive and mildly increases towards the hilltop of the curvaton potential, and that f{sub NL} = O(10) is a general and robust prediction of such hilltop axionic curvatons. In particular, we find that the non-Gaussianity parameter is bounded as f{sub NL}∼<30–40 for a range of the scalar spectral index, n{sub s} = 0.94–0.99, and that f{sub NL} = 20–40 is realized for the curvaton mass m{sub σ} = 10–10{sup 6} GeV and the decay constant f = 10{sup 12}–10{sup 17} GeV. One of the plausible candidates for the axionic curvaton is an imaginary component of a modulus field with mass of order 10–100 TeV and decay constant of 10{sup 16–17}GeV. We also discuss extreme cases where the curvaton drives a second inflation and find that f{sub NL} is typically smaller compared to non-inflating cases.
Unitarily localizable entanglement of Gaussian states
Serafini, Alessio; Adesso, Gerardo; Illuminati, Fabrizio
2005-03-01
We consider generic (mxn)-mode bipartitions of continuous-variable systems, and study the associated bisymmetric multimode Gaussian states. They are defined as (m+n)-mode Gaussian states invariant under local mode permutations on the m-mode and n-mode subsystems. We prove that such states are equivalent, under local unitary transformations, to the tensor product of a two-mode state and of m+n-2 uncorrelated single-mode states. The entanglement between the m-mode and the n-mode blocks can then be completely concentrated on a single pair of modes by means of local unitary operations alone. This result allows us to prove that the PPT (positivity of the partial transpose) condition is necessary and sufficient for the separability of (m+n)-mode bisymmetric Gaussian states. We determine exactly their negativity and identify a subset of bisymmetric states whose multimode entanglement of formation can be computed analytically. We consider explicit examples of pure and mixed bisymmetric states and study their entanglement scaling with the number of modes.
Exact Results for `Bouncing' Gaussian Wave Packets
NASA Astrophysics Data System (ADS)
Belloni, M.; Doncheski, M. A.; Robinett, R. W.
2005-01-01
We consider time-dependent Gaussian wave packet solutions of the Schrödinger equation, with arbitrary initial central position, x0, and momentum, p0, for an otherwise free particle, but with an infinite wall at x = 0, so-called bouncing wave packets. We show how difference or mirror solutions of the form ψ(x,t) - ψ(-x,t) can, in this case, be normalized exactly, allowing for the evaluation of a number of time-dependent expectation values and other quantities in closed form. For example, we calculate langp2rangt explicitly which illustrates how the free-particle kinetic (and hence total energy) is affected by the presence of the distant boundary. We also discuss the time dependence of the expectation values of position, langxrangt, and momentum, langprangt, and their relation to the impulsive force during the `collision' with the wall. Finally, the x0, p0 → 0 limit is shown to reduce a special case of a non-standard free-particle Gaussian solution. The addition of this example to the literature then expands of the relatively small number of Gaussian solutions to quantum mechanical problems with familiar classical analogs (free particle, uniform acceleration, harmonic oscillator, unstable oscillator, and uniform magnetic field) available in closed form.
Resonant non-Gaussianity with equilateral properties
Gwyn, Rhiannon; Rummel, Markus; Westphal, Alexander E-mail: markus.rummel@desy.de
2013-04-01
We discuss the effect of superimposing multiple sources of resonant non-Gaussianity, which arise for instance in models of axion inflation. The resulting sum of oscillating shape contributions can be used to ''Fourier synthesize'' different non-oscillating shapes in the bispectrum. As an example we reproduce an approximately equilateral shape from the superposition of O(10) oscillatory contributions with resonant shape. This implies a possible degeneracy between the equilateral-type non-Gaussianity typical of models with non-canonical kinetic terms, such as DBI inflation, and an equilateral-type shape arising from a superposition of resonant-type contributions in theories with canonical kinetic terms. The absence of oscillations in the 2-point function together with the structure of resonant N-point functions give a constraint of f{sub NL}∼
NASA Astrophysics Data System (ADS)
Aras, Mohd Shahrieel Mohd; Abdullah, Shahrum Shah; Kamarudin, Muhammad Nizam; Rahman, Ahmad Fadzli Nizam Abdul; Azis, Fadilah Abd; Jaafar, Hazriq Izzuan
2015-05-01
This paper describes the effectiveness of observer-based output feedback for Unmanned Underwater Vehicle (UUV) with Linear Quadratic Regulation (LQR) performance. Tuning of observer parameters is crucial for tracking purpose. Prior to tuning facility, the ranges of observer and LQR parameters are obtained via system output cum error. The validation of this technique using unmanned underwater vehicles called Remotely Operated Vehicle (ROV) modelling helps to improve steady state performance of system response. The ROV modeling is focused for depth control using ROV 1 developed by the Underwater Technology Research Group (UTeRG). The results are showing that this technique improves steady state performances in term of overshoot and settling time of the system response.
Das, Sonjoy; Goswami, Kundan; Datta, Biswa N.
2014-12-10
Failure of structural systems under dynamic loading can be prevented via active vibration control which shifts the damped natural frequencies of the systems away from the dominant range of loading spectrum. The damped natural frequencies and the dynamic load typically show significant variations in practice. A computationally efficient methodology based on quadratic partial eigenvalue assignment technique and optimization under uncertainty has been formulated in the present work that will rigorously account for these variations and result in an economic and resilient design of structures. A novel scheme based on hierarchical clustering and importance sampling is also developed in this work for accurate and efficient estimation of probability of failure to guarantee the desired resilience level of the designed system. Numerical examples are presented to illustrate the proposed methodology.
NASA Astrophysics Data System (ADS)
Das, Sonjoy; Goswami, Kundan; Datta, Biswa N.
2014-12-01
Failure of structural systems under dynamic loading can be prevented via active vibration control which shifts the damped natural frequencies of the systems away from the dominant range of loading spectrum. The damped natural frequencies and the dynamic load typically show significant variations in practice. A computationally efficient methodology based on quadratic partial eigenvalue assignment technique and optimization under uncertainty has been formulated in the present work that will rigorously account for these variations and result in an economic and resilient design of structures. A novel scheme based on hierarchical clustering and importance sampling is also developed in this work for accurate and efficient estimation of probability of failure to guarantee the desired resilience level of the designed system. Numerical examples are presented to illustrate the proposed methodology.
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.
Angle hybrid control for a two-axis piezo-positioning system and its application
NASA Astrophysics Data System (ADS)
Zhu, Wei; Zhou, Qinbo; Rui, Xiaoting
2016-09-01
The hysteresis characteristics of piezoelectric actuators and the residual vibration in the rapid positioning process will greatly affect the positioning accuracy and speed of a piezo-driven positioning system (PPS). In order to improve the positioning accuracy and to restrain the residual vibration of a two-axis PPS, a hybrid controller is proposed and explored based on a comprehensive model by combining the proposed feedforward linearization, the zero vibration and derivative shaping, and the linear-quadratic Gaussian feedback control for the PPS. The experimental results show that the proposed hybrid control significantly improves the positioning accuracy and suppresses the residual vibration of the PPS. Its application shows that the PPS proposed herein can effectively enhance the astronomical telescope’s star tracking and pointing performance.
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.
Local Gaussian operations can enhance continuous-variable entanglement distillation
Zhang Shengli; Loock, Peter van
2011-12-15
Entanglement distillation is a fundamental building block in long-distance quantum communication. Though known to be useless on their own for distilling Gaussian entangled states, local Gaussian operations may still help to improve non-Gaussian entanglement distillation schemes. Here we show that by applying local squeezing operations both the performance and the efficiency of existing distillation protocols can be enhanced. We find that such an enhancement through local Gaussian unitaries can be obtained even when the initially shared Gaussian entangled states are mixed, as, for instance, after their distribution through a lossy-fiber communication channel.
First on-sky SCAO validation of full LQG control with vibration mitigation on the CANARY pathfinder.
Sivo, Gaetano; Kulcsár, Caroline; Conan, Jean-Marc; Raynaud, Henri-François; Gendron, Eric; Basden, Alastair; Vidal, Fabrice; Morris, Tim; Meimon, Serge; Petit, Cyril; Gratadour, Damien; Martin, Olivier; Hubert, Zoltan; Sevin, Arnaud; Perret, Denis; Chemla, Fanny; Rousset, Gérard; Dipper, Nigel; Talbot, Gordon; Younger, Eddy; Myers, Richard; Henry, David; Todd, Stephen; Atkinson, David; Dickson, Colin; Longmore, Andy
2014-09-22
Adaptive optics provides real time correction of wavefront disturbances on ground based telescopes. Optimizing control and performance is a key issue for ever more demanding instruments on ever larger telescopes affected not only by atmospheric turbulence, but also by vibrations, windshake and tracking errors. Linear Quadratic Gaussian control achieves optimal correction when provided with a temporal model of the disturbance. We present in this paper the first on-sky results of a Kalman filter based LQG control with vibration mitigation on the CANARY instrument at the Nasmyth platform of the 4.2-m William Herschel Telescope. The results demonstrate a clear improvement of performance for full LQG compared with standard integrator control, and assess the additional improvement brought by vibration filtering with a tip-tilt model identified from on-sky data, thus validating the strategy retained on the instrument SPHERE at the VLT. PMID:25321824
First on-sky SCAO validation of full LQG control with vibration mitigation on the CANARY pathfinder.
Sivo, Gaetano; Kulcsár, Caroline; Conan, Jean-Marc; Raynaud, Henri-François; Gendron, Eric; Basden, Alastair; Vidal, Fabrice; Morris, Tim; Meimon, Serge; Petit, Cyril; Gratadour, Damien; Martin, Olivier; Hubert, Zoltan; Sevin, Arnaud; Perret, Denis; Chemla, Fanny; Rousset, Gérard; Dipper, Nigel; Talbot, Gordon; Younger, Eddy; Myers, Richard; Henry, David; Todd, Stephen; Atkinson, David; Dickson, Colin; Longmore, Andy
2014-09-22
Adaptive optics provides real time correction of wavefront disturbances on ground based telescopes. Optimizing control and performance is a key issue for ever more demanding instruments on ever larger telescopes affected not only by atmospheric turbulence, but also by vibrations, windshake and tracking errors. Linear Quadratic Gaussian control achieves optimal correction when provided with a temporal model of the disturbance. We present in this paper the first on-sky results of a Kalman filter based LQG control with vibration mitigation on the CANARY instrument at the Nasmyth platform of the 4.2-m William Herschel Telescope. The results demonstrate a clear improvement of performance for full LQG compared with standard integrator control, and assess the additional improvement brought by vibration filtering with a tip-tilt model identified from on-sky data, thus validating the strategy retained on the instrument SPHERE at the VLT.
Stochastic geometry and topology of non-Gaussian fields
Beuman, Thomas H.; Turner, Ari M.; Vitelli, Vincenzo
2012-01-01
Gaussian random fields pervade all areas of science. However, it is often the departures from Gaussianity that carry the crucial signature of the nonlinear mechanisms at the heart of diverse phenomena, ranging from structure formation in condensed matter and cosmology to biomedical imaging. The standard test of non-Gaussianity is to measure higher-order correlation functions. In the present work, we take a different route. We show how geometric and topological properties of Gaussian fields, such as the statistics of extrema, are modified by the presence of a non-Gaussian perturbation. The resulting discrepancies give an independent way to detect and quantify non-Gaussianities. In our treatment, we consider both local and nonlocal mechanisms that generate non-Gaussian fields, both statically and dynamically through nonlinear diffusion. PMID:23169625
Ita, B. I.
2014-11-12
By using the Nikiforov-Uvarov (NU) method, the Schrödinger equation has been solved for the interaction of inversely quadratic Hellmann (IQHP) and inversely quadratic potential (IQP) for any angular momentum quantum number, l. The energy eigenvalues and their corresponding eigenfunctions have been obtained in terms of Laguerre polynomials. Special cases of the sum of these potentials have been considered and their energy eigenvalues also obtained.
A new adaptive control approach for aerospace vehicles with parameter uncertainties
NASA Technical Reports Server (NTRS)
Hahn, Yungsun; Speyer, Jason L.
1989-01-01
A new stochastic adaptive control structure is developed for the problem of combined parameter estimation and control of aerospace vehicles with changing parameters. Parameter uncertainties are modeled as first-order Gauss-Markov processes, and are introduced to the system dynamics through a small parameter. It is assumed that an accurate inertial measurement unit gives perfect measurements of the state variables. Since the stochastic system is assumed to be Gauss-Markov, the density function of the parameters given these measurements is conditionally Gaussian. Based on this conditionally Gaussian density, the problem of minimizing a quadratic cost over an infinite time horizon can be set up within the framework of stochastic optimal control theory. The optimal feedback control law is derived from a straightforward expansion of the Hamilton-Jacobi-Bellman equation, based on the LQG solution. The resulting nonlinear controller is applied to the pitch axis control of a space platform with uncertain moments of inertia and is shown to produce marked improvement over a fixed controller.
A multiloop, digital flutter suppression control law synthesis case study
NASA Technical Reports Server (NTRS)
Mukhopadhyay, Vivek; Perry, Boyd, III; Noll, Thomas E.
1989-01-01
A methodology for obtaining a digital low-order, multiloop, robust control law for aeroelastic application from a full-state Linear Quadratic Gaussian design is presented. As part of the design methodology, the multivariable system robustness at the plant input and output is evaluated using singular value properties and improved using constrained optimization procedures. To validate the methodology, a digital flutter suppression system has been designed for the full-span Active Flexible Wing (AFW) wind-tunnel model as part of a collaborative effort between the NASA Langley Research Center and Rockwell International. Preliminary results for a low-order discrete, symmetric flutter suppression system design that significantly improved the AFW model stability are provided and the experiences gained during the design process are discussed.
Variational Bayesian localization of EEG sources with generalized Gaussian priors
NASA Astrophysics Data System (ADS)
Cortes, J. M.; Lopez, A.; Molina, R.; Katsaggelos, A. K.
2012-11-01
Although in the last decades the use of Magnetic Resonance Imaging has grown in popularity as a tool for the structural analysis of the brain, including MRI, fMRI and recently DTI, the ElectroEncephaloGraphy (EEG) is, still today, an interesting technique for the understanding of brain organization and function. The main reason for this is that the EEG is a direct measure of brain bioelectrical activity, and such activity can be monitorized in the millisecond time window. For some situations and cognitive scenarios, such fine temporal resolution might suffice for some aspects of brain function; however, the EEG spatial resolution is very poor since it is based on a small number of scalp recordings, thus turning the source localization problem into an ill-posed one in which infinite possibilities exist for the localization of the neuronal generators. This is an old problem in computational neuroimaging; indeed, many methods have been proposed to overcome this localization. Here, by performing a Variational Bayesian Inference procedure with a generalized Gaussian prior, we come out with an algorithm that performs simultaneously the estimation of both sources and model parameters. The novelty for the inclusion of the generalized Gaussian prior allows to control the smoothness degree of the estimated sources. Finally, the suggested algorithm is validated on simulated data.
Evaluation of the gaussian beam model for prediction of LDV fringe fields
Miles, P.C.; Witze, P.O.
1996-12-31
A simple model is developed to estimate the fringe field geometry at the intersection of two Gaussian laser beams. Comparison of the model results to experimentally measured fringe spacing demonstrates that while the model predicts the fringe geometry well when the beam waists are far from the intersection volume, it performs poorly under nominally ideal conditions- when the beam waists are located at the intersection. Data obtained with two different laser sources indicate that the discrepancies between the theory and experiment are likely due to deviations of the laser beam from an ideal Gaussian beam. With a high quality laser, the details of the fringe field geometry are still not well duplicated by the Gaussian beam model, although the magnitude of the variation in fringe spacing and the effect of the controlling system parameters are correctly predicted.
ERIC Educational Resources Information Center
Ellis, Amy B.; Grinstead, Paul
2008-01-01
This article presents secondary students' generalizations about the connections between algebraic and graphical representations of quadratic functions, focusing specifically on the roles of the parameters a, b, and c in the general form of a quadratic function, y = ax[superscript 2] + bx + c. Students' generalizations about these connections led…
ERIC Educational Resources Information Center
Man, Yiu-Kwong
2012-01-01
In this note, a new method for computing the partial fraction decomposition of rational functions with irreducible quadratic factors in the denominators is presented. This method involves polynomial divisions and substitutions only, without having to solve for the complex roots of the irreducible quadratic polynomial or to solve a system of linear…
Pseudo-continuous-time quadratic regulators with pole placement in a specific region
NASA Technical Reports Server (NTRS)
Shieh, L. S.; Zhang, J. L.; Ganesan, S.
1990-01-01
The paper comments on the pseudo-continuous-time quadratic regulator developed in an earlier paper. It also presents a new digital redesign technique, based on matching all the states at all the sampling instants, for finding the pseudo-continuous-time quadratic regulator.
Geometrical Solutions of Some Quadratic Equations with Non-Real Roots
ERIC Educational Resources Information Center
Pathak, H. K.; Grewal, A. S.
2002-01-01
This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the…
ERIC Educational Resources Information Center
Strickland, Tricia K.; Maccini, Paula
2013-01-01
The current study focuses on the effects of incorporating multiple visual representations on students' conceptual understanding of quadratic expressions embedded within area word problems and students' procedural fluency of transforming quadratic expressions in standard form to factored-form and vice versa. The intervention included the…
The cyclicity of period annulus of a quadratic reversible Lotka-Volterra system
NASA Astrophysics Data System (ADS)
Li, Chengzhi; Llibre, Jaume
2009-12-01
We prove that by perturbing the periodic annulus of the quadratic polynomial reversible Lotka-Volterra differential system \\dot x=y+\\case{3}{2}(x^2-y^2) , \\dot y=-x(1-y) , inside the class of all quadratic polynomial differential systems we can obtain at most two limit cycles.
Spacecraft Formation Flying Maneuvers Using Linear-Quadratic Regulation with No Radial Axis Inputs
NASA Technical Reports Server (NTRS)
Starin, Scott R.; Yedavalli, R. K.; Sparks, Andrew G.; Bauer, Frank H. (Technical Monitor)
2001-01-01
Regarding multiple spacecraft formation flying, the observation has been made that control thrust need only be applied coplanar to the local horizon to achieve complete controllability of a two-satellite (leader-follower) formation. A formulation of orbital dynamics using the state of one satellite relative to another is used. Without the need for thrust along the radial (zenith-nadir) axis of the relative reference frame ' propulsion system simplifications and weight reduction may be accomplished. Several linear-quadratic regulators (LQR) are explored and compared based on performance measures likely to be important to many missions, but not directly optimized in the LQR designs. Maneuver simulations are performed using commercial ODE solvers to propagate the Keplerian dynamics of a controlled satellite relative to an uncontrolled leader. These short maneuver simulations demonstrate the capacity of the controller to perform changes from one formation geometry to another. This work focusses on formations in which the controlled satellite has a relative trajectory which projects onto the local horizon of the uncontrolled satellite as a circle. This formation has potential uses for distributed remote sensing systems.
Non-Gaussian Photon Probability Distribution
NASA Astrophysics Data System (ADS)
Solomon, Benjamin T.
2010-01-01
This paper investigates the axiom that the photon's probability distribution is a Gaussian distribution. The Airy disc empirical evidence shows that the best fit, if not exact, distribution is a modified Gamma mΓ distribution (whose parameters are α = r, βr/√u ) in the plane orthogonal to the motion of the photon. This modified Gamma distribution is then used to reconstruct the probability distributions along the hypotenuse from the pinhole, arc from the pinhole, and a line parallel to photon motion. This reconstruction shows that the photon's probability distribution is not a Gaussian function. However, under certain conditions, the distribution can appear to be Normal, thereby accounting for the success of quantum mechanics. This modified Gamma distribution changes with the shape of objects around it and thus explains how the observer alters the observation. This property therefore places additional constraints to quantum entanglement experiments. This paper shows that photon interaction is a multi-phenomena effect consisting of the probability to interact Pi, the probabilistic function and the ability to interact Ai, the electromagnetic function. Splitting the probability function Pi from the electromagnetic function Ai enables the investigation of the photon behavior from a purely probabilistic Pi perspective. The Probabilistic Interaction Hypothesis is proposed as a consistent method for handling the two different phenomena, the probability function Pi and the ability to interact Ai, thus redefining radiation shielding, stealth or cloaking, and invisibility as different effects of a single phenomenon Pi of the photon probability distribution. Sub wavelength photon behavior is successfully modeled as a multi-phenomena behavior. The Probabilistic Interaction Hypothesis provides a good fit to Otoshi's (1972) microwave shielding, Schurig et al. (2006) microwave cloaking, and Oulton et al. (2008) sub wavelength confinement; thereby providing a strong case that
Monthly streamflow forecasting using Gaussian Process Regression
NASA Astrophysics Data System (ADS)
Sun, Alexander Y.; Wang, Dingbao; Xu, Xianli
2014-04-01
Streamflow forecasting plays a critical role in nearly all aspects of water resources planning and management. In this work, Gaussian Process Regression (GPR), an effective kernel-based machine learning algorithm, is applied to probabilistic streamflow forecasting. GPR is built on Gaussian process, which is a stochastic process that generalizes multivariate Gaussian distribution to infinite-dimensional space such that distributions over function values can be defined. The GPR algorithm provides a tractable and flexible hierarchical Bayesian framework for inferring the posterior distribution of streamflows. The prediction skill of the algorithm is tested for one-month-ahead prediction using the MOPEX database, which includes long-term hydrometeorological time series collected from 438 basins across the U.S. from 1948 to 2003. Comparisons with linear regression and artificial neural network models indicate that GPR outperforms both regression methods in most cases. The GPR prediction of MOPEX basins is further examined using the Budyko framework, which helps to reveal the close relationships among water-energy partitions, hydrologic similarity, and predictability. Flow regime modification and the resulting loss of predictability have been a major concern in recent years because of climate change and anthropogenic activities. The persistence of streamflow predictability is thus examined by extending the original MOPEX data records to 2012. Results indicate relatively strong persistence of streamflow predictability in the extended period, although the low-predictability basins tend to show more variations. Because many low-predictability basins are located in regions experiencing fast growth of human activities, the significance of sustainable development and water resources management can be even greater for those regions.
Boson sampling from a Gaussian state.
Lund, A P; Laing, A; Rahimi-Keshari, S; Rudolph, T; O'Brien, J L; Ralph, T C
2014-09-01
We pose a randomized boson-sampling problem. Strong evidence exists that such a problem becomes intractable on a classical computer as a function of the number of bosons. We describe a quantum optical processor that can solve this problem efficiently based on a Gaussian input state, a linear optical network, and nonadaptive photon counting measurements. All the elements required to build such a processor currently exist. The demonstration of such a device would provide empirical evidence that quantum computers can, indeed, outperform classical computers and could lead to applications. PMID:25238340
Non-gaussianity from broken symmetries
Kolb, Edward W.; Riotto, Antonio; Vallinotto, Alberto; /Chicago U. /Fermilab
2005-11-01
Recently we studied inflation models in which the inflation potential is characterized by an underlying approximate global symmetry. In the first work we pointed out that in such a model curvature perturbations are generated after the end of the slow-roll phase of inflation. In this work we develop further the observational implications of the model and compute the degree of non-Gaussianity predicted in the scenario. We find that the corresponding nonlinearity parameter, F{sub NL}, can be as large as 10{sup 2}.
A Gaussian measure of quantum phase noise
NASA Technical Reports Server (NTRS)
Schleich, Wolfgang P.; Dowling, Jonathan P.
1992-01-01
We study the width of the semiclassical phase distribution of a quantum state in its dependence on the average number of photons (m) in this state. As a measure of phase noise, we choose the width, delta phi, of the best Gaussian approximation to the dominant peak of this probability curve. For a coherent state, this width decreases with the square root of (m), whereas for a truncated phase state it decreases linearly with increasing (m). For an optimal phase state, delta phi decreases exponentially but so does the area caught underneath the peak: all the probability is stored in the broad wings of the distribution.
Negative Gaussian curvature from induced metric changes
NASA Astrophysics Data System (ADS)
Modes, Carl D.; Warner, Mark
2015-07-01
We revisit the light or heat-induced changes in topography of initially flat sheets of a solid that elongate or contract along patterned in-plane director fields. For radial or azimuthal directors, negative Gaussian curvature is generated—so-called "anticones." We show that azimuthal material displacements are required for the distorted state to be stretch free and bend minimizing. The resultant shapes are smooth and asterlike and can become reentrant in the azimuthal coordinate for large deformations. We show that care is needed when considering elastomers rather than glasses, although the former offer huge deformations.
Video compressive sensing using Gaussian mixture models.
Yang, Jianbo; Yuan, Xin; Liao, Xuejun; Llull, Patrick; Brady, David J; Sapiro, Guillermo; Carin, Lawrence
2014-11-01
A Gaussian mixture model (GMM)-based algorithm is proposed for video reconstruction from temporally compressed video measurements. The GMM is used to model spatio-temporal video patches, and the reconstruction can be efficiently computed based on analytic expressions. The GMM-based inversion method benefits from online adaptive learning and parallel computation. We demonstrate the efficacy of the proposed inversion method with videos reconstructed from simulated compressive video measurements, and from a real compressive video camera. We also use the GMM as a tool to investigate adaptive video compressive sensing, i.e., adaptive rate of temporal compression.
Quadratic Fermi node in a 3D strongly correlated semimetal.
Kondo, Takeshi; Nakayama, M; Chen, R; Ishikawa, J J; Moon, E-G; Yamamoto, T; Ota, Y; Malaeb, W; Kanai, H; Nakashima, Y; Ishida, Y; Yoshida, R; Yamamoto, H; Matsunami, M; Kimura, S; Inami, N; Ono, K; Kumigashira, H; Nakatsuji, S; Balents, L; Shin, S
2015-12-07
Strong spin-orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin-orbit and strong electron-electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour is predicted, for which we observe some evidence. Our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states.
Monitoring bioeroding sponges: using rubble, Quadrat, or intercept surveys?
Schönberg, C H L
2015-04-01
Relating to recent environmental changes, bioerosion rates of calcium carbonate materials appear to be increasing worldwide, often driven by sponges that cause bioerosion and are recognized bioindicators for coral reef health. Various field methods were compared to encourage more vigorous research on bioeroding sponges and their inclusion in major monitoring projects. The rubble technique developed by Holmes et al. (2000) had drawbacks often due to small specimen sizes: it was time-costly, generated large variation, and created a biased impression about dominant species. Quadrat surveys were most rapid but overestimated cover of small specimens. Line intercepts are recommended as easiest, least spatially biased, and most accurate, especially when comparing results from different observers. Intercepts required fewer samples and provided the best statistical efficiency, evidenced by better significances and test power. Bioeroding sponge abundances and biodiversities are influenced by water depth, sediment quality, and most importantly by availability of suitable attached substrate. Any related data should thus be standardized to amount of suitable substrate to allow comparison between different environments, concentrating on dominant, easily recognized species to avoid bias due to experience of observers.
Junction conditions in quadratic gravity: thin shells and double layers
NASA Astrophysics Data System (ADS)
Reina, Borja; Senovilla, José M. M.; Vera, Raül
2016-05-01
The junction conditions for the most general gravitational theory with a Lagrangian containing terms quadratic in the curvature are derived. We include the cases with a possible concentration of matter on the joining hypersurface—termed as thin shells, domain walls or braneworlds in the literature—as well as the proper matching conditions where only finite jumps of the energy-momentum tensor are allowed. In the latter case we prove that the matching conditions are more demanding than in general relativity. In the former case, we show that generically the shells/domain walls are of a new kind because they possess, in addition to the standard energy-momentum tensor, a double layer energy-momentum contribution which actually induces an external energy flux vector and an external scalar pressure/tension on the shell. We prove that all these contributions are necessary to make the entire energy-momentum tensor divergence-free, and we present the field equations satisfied by these energy-momentum quantities. The consequences of all these results are briefly analyzed.
Elastic Model Transitions Using Quadratic Inequality Constrained Least Squares
NASA Technical Reports Server (NTRS)
Orr, Jeb S.
2012-01-01
A technique is presented for initializing multiple discrete finite element model (FEM) mode sets for certain types of flight dynamics formulations that rely on superposition of orthogonal modes for modeling the elastic response. Such approaches are commonly used for modeling launch vehicle dynamics, and challenges arise due to the rapidly time-varying nature of the rigid-body and elastic characteristics. By way of an energy argument, a quadratic inequality constrained least squares (LSQI) algorithm is employed to e ect a smooth transition from one set of FEM eigenvectors to another with no requirement that the models be of similar dimension or that the eigenvectors be correlated in any particular way. The physically unrealistic and controversial method of eigenvector interpolation is completely avoided, and the discrete solution approximates that of the continuously varying system. The real-time computational burden is shown to be negligible due to convenient features of the solution method. Simulation results are presented, and applications to staging and other discontinuous mass changes are discussed
Quadratic isothermal amplification for the detection of microRNA.
Duan, Ruixue; Zuo, Xiaolei; Wang, Shutao; Quan, Xiyun; Chen, Dongliang; Chen, Zhifei; Jiang, Lei; Fan, Chunhai; Xia, Fan
2014-03-01
This protocol describes an isothermal amplification approach for ultrasensitive detection of specific microRNAs (miRNAs). It achieves this level of sensitivity through quadratic amplification of the target oligonucleotide by using a Bst DNA polymerase-induced strand-displacement reaction and a lambda exonuclease-aided recycling reaction. First, the target miRNA binds to a specifically designed molecular beacon, causing it to become a fluorescence emitter. A primer then binds to the activated beacon, and Bst polymerase initiates the synthesis of a double-stranded DNA segment templated on the molecular beacon. This causes the concomitant release of the target miRNA from the beacon--the first round of 'recycling'. Second, the duplex beacon thus produced is a suitable substrate for a nicking enzyme present in solution. After the duplex beacon is nicked, the lambda exonuclease digests the beacon and releases the DNA single strand just synthesized, which is complementary to the molecular beacon, inducing the second round of recycling. The miRNA detection limit of this protocol is 10 fmol at 37 °C and 1 amol at 4 °C. This approach also affords high selectivity when applied to miRNA extracted from MCF-7 and PC3 cell lines and even from breast cancer tissue samples. Upon isolation of miRNA, the detection process can be completed in ∼2 h.
Quadratic Fermi node in a 3D strongly correlated semimetal
Kondo, Takeshi; Nakayama, M.; Chen, R.; Ishikawa, J. J.; Moon, E. -G.; Yamamoto, T.; Ota, Y.; Malaeb, W.; Kanai, H.; Nakashima, Y.; et al
2015-12-07
We report that strong spin–orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin–orbit and strong electron–electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour ismore » predicted, for which we observe some evidence. Lastly, our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states.« less
Linear versus quadratic portfolio optimization model with transaction cost
NASA Astrophysics Data System (ADS)
Razak, Norhidayah Bt Ab; Kamil, Karmila Hanim; Elias, Siti Masitah
2014-06-01
Optimization model is introduced to become one of the decision making tools in investment. Hence, it is always a big challenge for investors to select the best model that could fulfill their goal in investment with respect to risk and return. In this paper we aims to discuss and compare the portfolio allocation and performance generated by quadratic and linear portfolio optimization models namely of Markowitz and Maximin model respectively. The application of these models has been proven to be significant and popular among others. However transaction cost has been debated as one of the important aspects that should be considered for portfolio reallocation as portfolio return could be significantly reduced when transaction cost is taken into consideration. Therefore, recognizing the importance to consider transaction cost value when calculating portfolio' return, we formulate this paper by using data from Shariah compliant securities listed in Bursa Malaysia. It is expected that, results from this paper will effectively justify the advantage of one model to another and shed some lights in quest to find the best decision making tools in investment for individual investors.
GR angular momentum in the quadratic spinor Lagrangian formulation
NASA Astrophysics Data System (ADS)
Li, Siao-Jing
2016-08-01
We inquire into the question of whether the quadratic spinor Lagrangian (QSL) formulation can describe the angular momentum for a general-relativistic system. The QSL Hamiltonian has previously been shown to be able to yield an energy-momentum quasilocalization which brings a proof of the positive gravitational energy when the spinor satisfies the conformal Witten equation. After inspection, we find that, under the constraint that the spinor on the asymptotic boundary is a constant, the QSL Hamiltonian is successful in giving an angular momentum quasilocalization. We also make certain the spinor in the Hamiltonian plays the role of a gauge field, a warrant of our permission to impose constraints on the spinor. Then, by some adjustment of the QSL Hamiltonian, we gain a covariant center-of-mass moment quasilocalization only under the condition that the displacement on the asymptotic boundary is a Killing boost vector. We expect the spinor expression will bring a proof of some connection between the gravitational energy and angular momentum.
Quadratic Fermi node in a 3D strongly correlated semimetal
Kondo, Takeshi; Nakayama, M.; Chen, R.; Ishikawa, J. J.; Moon, E. -G.; Yamamoto, T.; Ota, Y.; Malaeb, W.; Kanai, H.; Nakashima, Y.; Ishida, Y.; Yoshida, R.; Yamamoto, H.; Matsunami, M.; Kimura, S.; Inami, N.; Ono, K.; Kumigashira, H.; Nakatsuji, S.; Balents, L.; Shin, S.
2015-12-07
We report that strong spin–orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin–orbit and strong electron–electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr_{2}Ir_{2}O_{7}, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour is predicted, for which we observe some evidence. Lastly, our discovery implies that Pr_{2}Ir_{2}O_{7} is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states.
Quadratic Fermi node in a 3D strongly correlated semimetal
Kondo, Takeshi; Nakayama, M.; Chen, R.; Ishikawa, J. J.; Moon, E.-G.; Yamamoto, T.; Ota, Y.; Malaeb, W.; Kanai, H.; Nakashima, Y.; Ishida, Y.; Yoshida, R.; Yamamoto, H.; Matsunami, M.; Kimura, S.; Inami, N.; Ono, K.; Kumigashira, H.; Nakatsuji, S.; Balents, L.; Shin, S.
2015-01-01
Strong spin–orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin–orbit and strong electron–electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour is predicted, for which we observe some evidence. Our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states. PMID:26640114
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.
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.
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
Gaussian and non-Gaussian inverse modeling of groundwater flow using copulas and random mixing
NASA Astrophysics Data System (ADS)
Bárdossy, András.; Hörning, Sebastian
2016-06-01
This paper presents a new copula-based methodology for Gaussian and non-Gaussian inverse modeling of groundwater flow. The presented approach is embedded in a Monte Carlo framework and it is based on the concept of mixing spatial random fields where a spatial copula serves as spatial dependence function. The target conditional spatial distribution of hydraulic transmissivities is obtained as a linear combination of unconditional spatial fields. The corresponding weights of this linear combination are chosen such that the combined field has the prescribed spatial variability, and honors all the observations of hydraulic transmissivities. The constraints related to hydraulic head observations are nonlinear. In order to fulfill these constraints, a connected domain in the weight space, inside which all linear constraints are fulfilled, is identified. This domain is defined analytically and includes an infinite number of conditional fields (i.e., conditioned on the observed hydraulic transmissivities), and the nonlinear constraints can be fulfilled via minimization of the deviation of the modeled and the observed hydraulic heads. This procedure enables the simulation of a great number of solutions for the inverse problem, allowing a reasonable quantification of the associated uncertainties. The methodology can be used for fields with Gaussian copula dependence, and fields with specific non-Gaussian copula dependence. Further, arbitrary marginal distributions can be considered.
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.
Hierarchical similarity transformations between Gaussian mixtures.
Rigas, George; Nikou, Christophoros; Goletsis, Yorgos; Fotiadis, Dimitrios I
2013-11-01
In this paper, we propose a method to estimate the density of a data space represented by a geometric transformation of an initial Gaussian mixture model. The geometric transformation is hierarchical, and it is decomposed into two steps. At first, the initial model is assumed to undergo a global similarity transformation modeled by translation, rotation, and scaling of the model components. Then, to increase the degrees of freedom of the model and allow it to capture fine data structures, each individual mixture component may be transformed by another, local similarity transformation, whose parameters are distinct for each component of the mixture. In addition, to constrain the order of magnitude of the local transformation (LT) with respect to the global transformation (GT), zero-mean Gaussian priors are imposed onto the local parameters. The estimation of both GT and LT parameters is obtained through the expectation maximization framework. Experiments on artificial data are conducted to evaluate the proposed model, with varying data dimensionality, number of model components, and transformation parameters. In addition, the method is evaluated using real data from a speech recognition task. The obtained results show a high model accuracy and demonstrate the potential application of the proposed method to similar classification problems. PMID:24808615
Rogue Waves in Near Gaussian Sea States
NASA Astrophysics Data System (ADS)
Osborne, Alfred R.
2015-04-01
The field of nonlinear waves often emphasizes the importance of small amplitude modulations in the nonlinear Schroedinger equation (NLS). The Akhmediev and Peregrine breather trains are examples which manifest themselves from the usual linear instability analyses of NLS. In reality, however, oceanic sea states generated by wind waves are very nearly Gaussian processes and so the modulus of the Hilbert transform envelope is approximately Rayleigh distributed (with of course the possibility of a large amplitude tail) and is therefore never a small amplitude modulation. How can we then reconcile our usual perceptions with this fact? What are indeed the solutions of the nonlinear Schroedinger equation non Gaussianity have on the actual types of solutions that are likely to occur in the real ocean? I discuss how finite gap theory for NLS allows us to answer these and many more questions about rogue sea states. I analyze data from various laboratory and oceanic experiments to illustrate the method. Finally, I discuss whether breather trains such as Akhmediev, Peregrine and Ma-Kuznetsov can actually occur in ocean wave data.
Scaling Multidimensional Inference for Structured Gaussian Processes.
Gilboa, Elad; Saatçi, Yunus; Cunningham, John P
2013-09-30
Exact Gaussian process (GP) regression has O(N^3) runtime for data size N, making it intractable for large N. Many algorithms for improving GP scaling approximate the covariance with lower rank matrices. Other work has exploited structure inherent in particular covariance functions, including GPs with implied Markov structure, and inputs on a lattice (both enable O(N) or O(N log N) runtime). However, these GP advances have not been well extended to the multidimensional input setting, despite the preponderance of multidimensional applications. This paper introduces and tests three novel extensions of structured GPs to multidimensional inputs, for models with additive and multiplicative kernels. First we present a new method for inference in additive GPs, showing a novel connection between the classic backfitting method and the Bayesian framework. We extend this model using two advances: a variant of projection pursuit regression, and a Laplace approximation for non-Gaussian observations. Lastly, for multiplicative kernel structure, we present a novel method for GPs with inputs on a multidimensional grid. We illustrate the power of these three advances on several datasets, achieving performance equal to or very close to the naive GP at orders of magnitude less cost.
Scaling Multidimensional Inference for Structured Gaussian Processes.
Gilboa, Elad; Saatçi, Yunus; Cunningham, John P
2015-02-01
Exact Gaussian process (GP) regression has O(N(3)) runtime for data size N, making it intractable for large N . Many algorithms for improving GP scaling approximate the covariance with lower rank matrices. Other work has exploited structure inherent in particular covariance functions, including GPs with implied Markov structure, and inputs on a lattice (both enable O(N) or O(N log N) runtime). However, these GP advances have not been well extended to the multidimensional input setting, despite the preponderance of multidimensional applications. This paper introduces and tests three novel extensions of structured GPs to multidimensional inputs, for models with additive and multiplicative kernels. First we present a new method for inference in additive GPs, showing a novel connection between the classic backfitting method and the Bayesian framework. We extend this model using two advances: a variant of projection pursuit regression, and a Laplace approximation for non-Gaussian observations. Lastly, for multiplicative kernel structure, we present a novel method for GPs with inputs on a multidimensional grid. We illustrate the power of these three advances on several data sets, achieving performance equal to or very close to the naive GP at orders of magnitude less cost.
Harmonic Pinnacles in the Discrete Gaussian Model
NASA Astrophysics Data System (ADS)
Lubetzky, Eyal; Martinelli, Fabio; Sly, Allan
2016-06-01
The 2 D Discrete Gaussian model gives each height function {η : {mathbb{Z}^2tomathbb{Z}}} a probability proportional to {exp(-β mathcal{H}(η))}, where {β} is the inverse-temperature and {mathcal{H}(η) = sum_{x˜ y}(η_x-η_y)^2} sums over nearest-neighbor bonds. We consider the model at large fixed {β}, where it is flat unlike its continuous analog (the Discrete Gaussian Free Field). We first establish that the maximum height in an {L× L} box with 0 boundary conditions concentrates on two integers M, M + 1 with {M˜ √{(1/2πβ)log Lloglog L}}. The key is a large deviation estimate for the height at the origin in {mathbb{Z}2}, dominated by "harmonic pinnacles", integer approximations of a harmonic variational problem. Second, in this model conditioned on {η≥ 0} (a floor), the average height rises, and in fact the height of almost all sites concentrates on levels H, H + 1 where {H˜ M/√{2}}. This in particular pins down the asymptotics, and corrects the order, in results of Bricmont et al. (J. Stat. Phys. 42(5-6):743-798, 1986), where it was argued that the maximum and the height of the surface above a floor are both of order {√{log L}}. Finally, our methods extend to other classical surface models (e.g., restricted SOS), featuring connections to p-harmonic analysis and alternating sign matrices.
Relaxation oscillations in a laser with a Gaussian mirror.
Mossakowska-Wyszyńska, Agnieszka; Witoński, Piotr; Szczepański, Paweł
2002-03-20
We present an analysis of the relaxation oscillations in a laser with a Gaussian mirror by taking into account the three-dimensional spatial field distribution of the laser modes and the spatial hole burning effect. In particular, we discuss the influence of the Gaussian mirror peak reflectivity and a Gaussian parameter on the damping rate and frequency of the relaxation oscillation for two different laser structures, i.e., with a classically unstable resonator and a classically stable resonator. PMID:11921794
The properties of the anti-tumor model with coupling non-Gaussian noise and Gaussian colored noise
NASA Astrophysics Data System (ADS)
Guo, Qin; Sun, Zhongkui; Xu, Wei
2016-05-01
The anti-tumor model with correlation between multiplicative non-Gaussian noise and additive Gaussian-colored noise has been investigated in this paper. The behaviors of the stationary probability distribution demonstrate that the multiplicative non-Gaussian noise plays a dual role in the development of tumor and an appropriate additive Gaussian colored noise can lead to a minimum of the mean value of tumor cell population. The mean first passage time is calculated to quantify the effects of noises on the transition time of tumors between the stable states. An increase in both the non-Gaussian noise intensity and the departure from the Gaussian noise can accelerate the transition from the disease state to the healthy state. On the contrary, an increase in cross-correlated degree will slow down the transition. Moreover, the correlation time can enhance the stability of the disease state.
New type of Weyl semimetal with quadratic double Weyl fermions
Huang, Shin-Ming; Xu, Su-Yang; Belopolski, Ilya; Lee, Chi-Cheng; Chang, Guoqing; Chang, Tay-Rong; Wang, BaoKai; Alidoust, Nasser; Bian, Guang; Neupane, Madhab; Sanchez, Daniel; Zheng, Hao; Jeng, Horng-Tay; Bansil, Arun; Neupert, Titus; Lin, Hsin; Hasan, M. Zahid
2016-01-01
Weyl semimetals have attracted worldwide attention due to their wide range of exotic properties predicted in theories. The experimental realization had remained elusive for a long time despite much effort. Very recently, the first Weyl semimetal has been discovered in an inversion-breaking, stoichiometric solid TaAs. So far, the TaAs class remains the only Weyl semimetal available in real materials. To facilitate the transition of Weyl semimetals from the realm of purely theoretical interest to the realm of experimental studies and device applications, it is of crucial importance to identify other robust candidates that are experimentally feasible to be realized. In this paper, we propose such a Weyl semimetal candidate in an inversion-breaking, stoichiometric compound strontium silicide, SrSi2, with many new and novel properties that are distinct from TaAs. We show that SrSi2 is a Weyl semimetal even without spin–orbit coupling and that, after the inclusion of spin–orbit coupling, two Weyl fermions stick together forming an exotic double Weyl fermion with quadratic dispersions and a higher chiral charge of ±2. Moreover, we find that the Weyl nodes with opposite charges are located at different energies due to the absence of mirror symmetry in SrSi2, paving the way for the realization of the chiral magnetic effect. Our systematic results not only identify a much-needed robust Weyl semimetal candidate but also open the door to new topological Weyl physics that is not possible in TaAs. PMID:26787914
New type of Weyl semimetal with quadratic double Weyl fermions.
Huang, Shin-Ming; Xu, Su-Yang; Belopolski, Ilya; Lee, Chi-Cheng; Chang, Guoqing; Chang, Tay-Rong; Wang, BaoKai; Alidoust, Nasser; Bian, Guang; Neupane, Madhab; Sanchez, Daniel; Zheng, Hao; Jeng, Horng-Tay; Bansil, Arun; Neupert, Titus; Lin, Hsin; Hasan, M Zahid
2016-02-01
Weyl semimetals have attracted worldwide attention due to their wide range of exotic properties predicted in theories. The experimental realization had remained elusive for a long time despite much effort. Very recently, the first Weyl semimetal has been discovered in an inversion-breaking, stoichiometric solid TaAs. So far, the TaAs class remains the only Weyl semimetal available in real materials. To facilitate the transition of Weyl semimetals from the realm of purely theoretical interest to the realm of experimental studies and device applications, it is of crucial importance to identify other robust candidates that are experimentally feasible to be realized. In this paper, we propose such a Weyl semimetal candidate in an inversion-breaking, stoichiometric compound strontium silicide, SrSi2, with many new and novel properties that are distinct from TaAs. We show that SrSi2 is a Weyl semimetal even without spin-orbit coupling and that, after the inclusion of spin-orbit coupling, two Weyl fermions stick together forming an exotic double Weyl fermion with quadratic dispersions and a higher chiral charge of ±2. Moreover, we find that the Weyl nodes with opposite charges are located at different energies due to the absence of mirror symmetry in SrSi2, paving the way for the realization of the chiral magnetic effect. Our systematic results not only identify a much-needed robust Weyl semimetal candidate but also open the door to new topological Weyl physics that is not possible in TaAs. PMID:26787914
New type of Weyl semimetal with quadratic double Weyl fermions.
Huang, Shin-Ming; Xu, Su-Yang; Belopolski, Ilya; Lee, Chi-Cheng; Chang, Guoqing; Chang, Tay-Rong; Wang, BaoKai; Alidoust, Nasser; Bian, Guang; Neupane, Madhab; Sanchez, Daniel; Zheng, Hao; Jeng, Horng-Tay; Bansil, Arun; Neupert, Titus; Lin, Hsin; Hasan, M Zahid
2016-02-01
Weyl semimetals have attracted worldwide attention due to their wide range of exotic properties predicted in theories. The experimental realization had remained elusive for a long time despite much effort. Very recently, the first Weyl semimetal has been discovered in an inversion-breaking, stoichiometric solid TaAs. So far, the TaAs class remains the only Weyl semimetal available in real materials. To facilitate the transition of Weyl semimetals from the realm of purely theoretical interest to the realm of experimental studies and device applications, it is of crucial importance to identify other robust candidates that are experimentally feasible to be realized. In this paper, we propose such a Weyl semimetal candidate in an inversion-breaking, stoichiometric compound strontium silicide, SrSi2, with many new and novel properties that are distinct from TaAs. We show that SrSi2 is a Weyl semimetal even without spin-orbit coupling and that, after the inclusion of spin-orbit coupling, two Weyl fermions stick together forming an exotic double Weyl fermion with quadratic dispersions and a higher chiral charge of ±2. Moreover, we find that the Weyl nodes with opposite charges are located at different energies due to the absence of mirror symmetry in SrSi2, paving the way for the realization of the chiral magnetic effect. Our systematic results not only identify a much-needed robust Weyl semimetal candidate but also open the door to new topological Weyl physics that is not possible in TaAs.
Gravity waves from non-minimal quadratic inflation
Pallis, Constantinos; Shafi, Qaisar
2015-03-12
We discuss non-minimal quadratic inflation in supersymmetric (SUSY) and non-SUSY models which entails a linear coupling of the inflaton to gravity. Imposing a lower bound on the parameter c{sub R}, involved in the coupling between the inflaton and the Ricci scalar curvature, inflation can be attained even for subplanckian values of the inflaton while the corresponding effective theory respects the perturbative unitarity up to the Planck scale. Working in the non-SUSY context we also consider radiative corrections to the inflationary potential due to a possible coupling of the inflaton to bosons or fermions. We find ranges of the parameters, depending mildly on the renormalization scale, with adjustable values of the spectral index n{sub s}, tensor-to-scalar ratio r≃(2−4)⋅10{sup −3}, and an inflaton mass close to 3⋅10{sup 13} GeV. In the SUSY framework we employ two gauge singlet chiral superfields, a logarithmic Kähler potential including all the allowed terms up to fourth order in powers of the various fields, and determine uniquely the superpotential by applying a continuous R and a global U(1) symmetry. When the Kähler manifold exhibits a no-scale-type symmetry, the model predicts n{sub s}≃0.963 and r≃0.004. Beyond no-scale SUGRA, n{sub s} and r depend crucially on the coefficient involved in the fourth order term, which mixes the inflaton with the accompanying non-inflaton field in the Kähler potential, and the prefactor encountered in it. Increasing slightly the latter above (−3), an efficient enhancement of the resulting r can be achieved putting it in the observable range. The inflaton mass in the last case is confined in the range (5−9)⋅10{sup 13} GeV.
Quadratic adaptive algorithm for solving cardiac action potential models.
Chen, Min-Hung; Chen, Po-Yuan; Luo, Ching-Hsing
2016-10-01
An adaptive integration method is proposed for computing cardiac action potential models accurately and efficiently. Time steps are adaptively chosen by solving a quadratic formula involving the first and second derivatives of the membrane action potential. To improve the numerical accuracy, we devise an extremum-locator (el) function to predict the local extremum when approaching the peak amplitude of the action potential. In addition, the time step restriction (tsr) technique is designed to limit the increase in time steps, and thus prevent the membrane potential from changing abruptly. The performance of the proposed method is tested using the Luo-Rudy phase 1 (LR1), dynamic (LR2), and human O'Hara-Rudy dynamic (ORd) ventricular action potential models, and the Courtemanche atrial model incorporating a Markov sodium channel model. Numerical experiments demonstrate that the action potential generated using the proposed method is more accurate than that using the traditional Hybrid method, especially near the peak region. The traditional Hybrid method may choose large time steps near to the peak region, and sometimes causes the action potential to become distorted. In contrast, the proposed new method chooses very fine time steps in the peak region, but large time steps in the smooth region, and the profiles are smoother and closer to the reference solution. In the test on the stiff Markov ionic channel model, the Hybrid blows up if the allowable time step is set to be greater than 0.1ms. In contrast, our method can adjust the time step size automatically, and is stable. Overall, the proposed method is more accurate than and as efficient as the traditional Hybrid method, especially for the human ORd model. The proposed method shows improvement for action potentials with a non-smooth morphology, and it needs further investigation to determine whether the method is helpful during propagation of the action potential. PMID:27639239
Convergence properties of a quadratic approach to the inverse-scattering problem
NASA Astrophysics Data System (ADS)
Persico, Raffaele; Soldovieri, Francesco; Pierri, Rocco
2002-12-01
The local-minima question that arises in the framework of a quadratic approach to inverse-scattering problems is investigated. In particular, a sufficient condition for the absence of local minima is given, and some guidelines to ensure the reliability of the algorithm are outlined for the case of data not belonging to the range of the relevant quadratic operator. This is relevant also when an iterated solution procedure based on a quadratic approximation of the electromagnetic scattering at each step is considered.
Non-Gaussian Photon Probability Distribution
Solomon, Benjamin T.
2010-01-28
This paper investigates the axiom that the photon's probability distribution is a Gaussian distribution. The Airy disc empirical evidence shows that the best fit, if not exact, distribution is a modified Gamma mGAMMA distribution (whose parameters are alpha = r, betar/sq root(u)) in the plane orthogonal to the motion of the photon. This modified Gamma distribution is then used to reconstruct the probability distributions along the hypotenuse from the pinhole, arc from the pinhole, and a line parallel to photon motion. This reconstruction shows that the photon's probability distribution is not a Gaussian function. However, under certain conditions, the distribution can appear to be Normal, thereby accounting for the success of quantum mechanics. This modified Gamma distribution changes with the shape of objects around it and thus explains how the observer alters the observation. This property therefore places additional constraints to quantum entanglement experiments. This paper shows that photon interaction is a multi-phenomena effect consisting of the probability to interact P{sub i}, the probabilistic function and the ability to interact A{sub i}, the electromagnetic function. Splitting the probability function P{sub i} from the electromagnetic function A{sub i} enables the investigation of the photon behavior from a purely probabilistic P{sub i} perspective. The Probabilistic Interaction Hypothesis is proposed as a consistent method for handling the two different phenomena, the probability function P{sub i} and the ability to interact A{sub i}, thus redefining radiation shielding, stealth or cloaking, and invisibility as different effects of a single phenomenon P{sub i} of the photon probability distribution. Sub wavelength photon behavior is successfully modeled as a multi-phenomena behavior. The Probabilistic Interaction Hypothesis provides a good fit to Otoshi's (1972) microwave shielding, Schurig et al.(2006) microwave cloaking, and Oulton et al.(2008) sub
NASA Astrophysics Data System (ADS)
Cheng, Z.; Chen, Y.; Liu, Y.; Liu, W.; Zhang, G.
2015-12-01
Among those hydrocarbon reservoir detection techniques, the time-frequency analysis based approach is one of the most widely used approaches because of its straightforward indication of low-frequency anomalies from the time-frequency maps, that is to say, the low-frequency bright spots usually indicate the potential hydrocarbon reservoirs. The time-frequency analysis based approach is easy to implement, and more importantly, is usually of high fidelity in reservoir prediction, compared with the state-of-the-art approaches, and thus is of great interest to petroleum geologists, geophysicists, and reservoir engineers. The S transform has been frequently used in obtaining the time-frequency maps because of its better performance in controlling the compromise between the time and frequency resolutions than the alternatives, such as the short-time Fourier transform, Gabor transform, and continuous wavelet transform. The window function used in the majority of previous S transform applications is the symmetric Gaussian window. However, one problem with the symmetric Gaussian window is the degradation of time resolution in the time-frequency map due to the long front taper. In our study, a bi-Gaussian S transform that substitutes the symmetric Gaussian window with an asymmetry bi-Gaussian window is proposed to analyze the multi-channel seismic data in order to predict hydrocarbon reservoirs. The bi-Gaussian window introduces asymmetry in the resultant time-frequency spectrum, with time resolution better in the front direction, as compared with the back direction. It is the first time that the bi-Gaussian S transform is used for analyzing multi-channel post-stack seismic data in order to predict hydrocarbon reservoirs since its invention in 2003. The superiority of the bi-Gaussian S transform over traditional S transform is tested on a real land seismic data example. The performance shows that the enhanced temporal resolution can help us depict more clearly the edge of the
Fractional Gaussian noise, functional MRI and Alzheimer's disease.
Maxim, Voichiţa; Sendur, Levent; Fadili, Jalal; Suckling, John; Gould, Rebecca; Howard, Rob; Bullmore, Ed
2005-03-01
Fractional Gaussian noise (fGn) provides a parsimonious model for stationary increments of a self-similar process parameterised by the Hurst exponent, H, and variance, sigma2. Fractional Gaussian noise with H < 0.5 demonstrates negatively autocorrelated or antipersistent behaviour; fGn with H > 0.5 demonstrates 1/f, long memory or persistent behaviour; and the special case of fGn with H = 0.5 corresponds to classical Gaussian white noise. We comparatively evaluate four possible estimators of fGn parameters, one method implemented in the time domain and three in the wavelet domain. We show that a wavelet-based maximum likelihood (ML) estimator yields the most efficient estimates of H and sigma2 in simulated fGn with 0 < H < 1. Applying this estimator to fMRI data acquired in the "resting" state from healthy young and older volunteers, we show empirically that fGn provides an accommodating model for diverse species of fMRI noise, assuming adequate preprocessing to correct effects of head movement, and that voxels with H > 0.5 tend to be concentrated in cortex whereas voxels with H < 0.5 are more frequently located in ventricles and sulcal CSF. The wavelet-ML estimator can be generalised to estimate the parameter vector beta for general linear modelling (GLM) of a physiological response to experimental stimulation and we demonstrate nominal type I error control in multiple testing of beta, divided by its standard error, in simulated and biological data under the null hypothesis beta = 0. We illustrate these methods principally by showing that there are significant differences between patients with early Alzheimer's disease (AD) and age-matched comparison subjects in the persistence of fGn in the medial and lateral temporal lobes, insula, dorsal cingulate/medial premotor cortex, and left pre- and postcentral gyrus: patients with AD had greater persistence of resting fMRI noise (larger H) in these regions. Comparable abnormalities in the AD patients were also identified
Distributed static linear Gaussian models using consensus.
Belanovic, Pavle; Valcarcel Macua, Sergio; Zazo, Santiago
2012-10-01
Algorithms for distributed agreement are a powerful means for formulating distributed versions of existing centralized algorithms. We present a toolkit for this task and show how it can be used systematically to design fully distributed algorithms for static linear Gaussian models, including principal component analysis, factor analysis, and probabilistic principal component analysis. These algorithms do not rely on a fusion center, require only low-volume local (1-hop neighborhood) communications, and are thus efficient, scalable, and robust. We show how they are also guaranteed to asymptotically converge to the same solution as the corresponding existing centralized algorithms. Finally, we illustrate the functioning of our algorithms on two examples, and examine the inherent cost-performance trade-off.
Bimetric structure formation: Non-Gaussian predictions
Magueijo, Joao; Noller, Johannes; Piazza, Federico
2010-08-15
The minimal bimetric theory employing a disformal transformation between matter and gravity metrics is known to produce exactly scale-invariant fluctuations. It has a purely equilateral non-Gaussian signal, with an amplitude smaller than that of Dirac Born Infeld inflation (with opposite sign) but larger than standard inflation. We consider nonminimal bimetric models, where the coupling B appearing in the disformal transformation g-circumflex{sub {mu}{nu}}=g{sub {mu}{nu}}-B{partial_derivative}{sub {mu}{phi}{partial_derivative}{nu}{phi}} can run with {phi}. For power-law B({phi}) these models predict tilted spectra. For each value of the spectral index, a distinctive distortion to the equilateral property can be found. The constraint between this distortion and the spectral index can be seen as a 'consistency relation' for nonminimal bimetric models.
Bimetric structure formation: Non-Gaussian predictions
NASA Astrophysics Data System (ADS)
Magueijo, João; Noller, Johannes; Piazza, Federico
2010-08-01
The minimal bimetric theory employing a disformal transformation between matter and gravity metrics is known to produce exactly scale-invariant fluctuations. It has a purely equilateral non-Gaussian signal, with an amplitude smaller than that of Dirac Born Infeld inflation (with opposite sign) but larger than standard inflation. We consider nonminimal bimetric models, where the coupling B appearing in the disformal transformation g^μν=gμν-B∂μϕ∂νϕ can run with ϕ. For power-law B(ϕ) these models predict tilted spectra. For each value of the spectral index, a distinctive distortion to the equilateral property can be found. The constraint between this distortion and the spectral index can be seen as a “consistency relation” for nonminimal bimetric models.
IBS for non-gaussian distributions
Fedotov, A.; Sidorin, A.O.; Smirnov, A.V.
2010-09-27
In many situations distribution can significantly deviate from Gaussian which requires accurate treatment of IBS. Our original interest in this problem was motivated by the need to have an accurate description of beam evolution due to IBS while distribution is strongly affected by the external electron cooling force. A variety of models with various degrees of approximation were developed and implemented in BETACOOL in the past to address this topic. A more complete treatment based on the friction coefficient and full 3-D diffusion tensor was introduced in BETACOOL at the end of 2007 under the name 'local IBS model'. Such a model allowed us calculation of IBS for an arbitrary beam distribution. The numerical benchmarking of this local IBS algorithm and its comparison with other models was reported before. In this paper, after briefly describing the model and its limitations, they present its comparison with available experimental data.
Non-Gaussian Berkson errors in bioassay.
Althubaiti, Alaa; Donev, Alexander
2016-02-01
The experimental design plays an important role in every experimental study. However, if errors in the settings of the studied factors cannot be avoided, i.e. Berkson errors occur, the estimates of the model parameters may be biased and the variability in the study increased. Correction methods for the effect of Berkson errors are compared. The emphasis is on the study of correlated Berkson errors which follow non-Gaussian distribution as this appears to have been a neglected, yet important, area. It is shown that the regression calibration approach bias correction methods are useful when the Berkson errors are independent. However, when these errors are dependent, the newly proposed method B-SIMEX clearly outperforms the other methods.
Absolute instability of the Gaussian wake profile
NASA Technical Reports Server (NTRS)
Hultgren, Lennart S.; Aggarwal, Arun K.
1987-01-01
Linear parallel-flow stability theory has been used to investigate the effect of viscosity on the local absolute instability of a family of wake profiles with a Gaussian velocity distribution. The type of local instability, i.e., convective or absolute, is determined by the location of a branch-point singularity with zero group velocity of the complex dispersion relation for the instability waves. The effects of viscosity were found to be weak for values of the wake Reynolds number, based on the center-line velocity defect and the wake half-width, larger than about 400. Absolute instability occurs only for sufficiently large values of the center-line wake defect. The critical value of this parameter increases with decreasing wake Reynolds number, thereby indicating a shrinking region of absolute instability with decreasing wake Reynolds number. If backflow is not allowed, absolute instability does not occur for wake Reynolds numbers smaller than about 38.
Exploring scalar field dynamics with Gaussian processes
Nair, Remya; Jhingan, Sanjay; Jain, Deepak E-mail: sanjay.jhingan@gmail.com
2014-01-01
The origin of the accelerated expansion of the Universe remains an unsolved mystery in Cosmology. In this work we consider a spatially flat Friedmann-Robertson-Walker (FRW) Universe with non-relativistic matter and a single scalar field contributing to the energy density of the Universe. Properties of this scalar field, like potential, kinetic energy, equation of state etc. are reconstructed from Supernovae and BAO data using Gaussian processes. We also reconstruct energy conditions and kinematic variables of expansion, such as the jerk and the slow roll parameter. We find that the reconstructed scalar field variables and the kinematic quantities are consistent with a flat ΛCDM Universe. Further, we find that the null energy condition is satisfied for the redshift range of the Supernovae data considered in the paper, but the strong energy condition is violated.
Scintillations of partially coherent Laguerre Gaussian beams
NASA Astrophysics Data System (ADS)
Yüceer, M.; Eyyuboğlu, H. T.; Lukin, I. P.
2010-12-01
Scintillations of Laguerre-Gaussian (LG) beams for weak atmospheric turbulence conditions are derived for on-axis receiver positions by using Huygens-Fresnel (HF) method in semi-analytic fashion. Numerical evaluations indicate that at the fully coherent limit, higher values of radial mode numbers will give rise to more scintillations, at medium and low partial coherence levels, particularly at longer propagation distances, scintillations will fall against rises in radial mode numbers. At small source sizes, the scintillations of LG beams having full coherence will initially rise, reaching saturation at large source sizes. For LG beams with low partial coherence levels, a steady fall toward the larger source sizes is observed. Partially coherent beams of medium levels generally exhibit a rising trend toward the large source sizes, also changing the respective positions of the related curves. Beams of low coherence levels will be less affected by the variations in the refractive index structure constant.
Gaussian polarizable-ion tight binding
NASA Astrophysics Data System (ADS)
Boleininger, Max; Guilbert, Anne AY; Horsfield, Andrew P.
2016-10-01
To interpret ultrafast dynamics experiments on large molecules, computer simulation is required due to the complex response to the laser field. We present a method capable of efficiently computing the static electronic response of large systems to external electric fields. This is achieved by extending the density-functional tight binding method to include larger basis sets and by multipole expansion of the charge density into electrostatically interacting Gaussian distributions. Polarizabilities for a range of hydrocarbon molecules are computed for a multipole expansion up to quadrupole order, giving excellent agreement with experimental values, with average errors similar to those from density functional theory, but at a small fraction of the cost. We apply the model in conjunction with the polarizable-point-dipoles model to estimate the internal fields in amorphous poly(3-hexylthiophene-2,5-diyl).
Turbo Equalization Using Partial Gaussian Approximation
NASA Astrophysics Data System (ADS)
Zhang, Chuanzong; Wang, Zhongyong; Manchon, Carles Navarro; Sun, Peng; Guo, Qinghua; Fleury, Bernard Henri
2016-09-01
This paper deals with turbo-equalization for coded data transmission over intersymbol interference (ISI) channels. We propose a message-passing algorithm that uses the expectation-propagation rule to convert messages passed from the demodulator-decoder to the equalizer and computes messages returned by the equalizer by using a partial Gaussian approximation (PGA). Results from Monte Carlo simulations show that this approach leads to a significant performance improvement compared to state-of-the-art turbo-equalizers and allows for trading performance with complexity. We exploit the specific structure of the ISI channel model to significantly reduce the complexity of the PGA compared to that considered in the initial paper proposing the method.
Semiconductor band gap localization via Gaussian function
NASA Astrophysics Data System (ADS)
Ullrich, B.; Brown, G. J.; Xi, H.
2012-10-01
To determine the band gap of bulk semiconductors with transmission spectroscopy alone is considered as an extremely difficult task because in the higher energy range, approaching and exceeding the band gap energy, the material is opaque yielding no useful data to be recorded. In this paper, by investigating the transmission of industrial GaSb wafers with a thickness of 500 µm, we demonstrate how these obstacles of transmission spectroscopy can be overcome. The key is the transmission spectrums’ derivative, which coincides with the Gaussian function. This understanding can be used to transfer Beers’ law in an integral form opening the pathway of band gap determinations based on mathematical parameters only. The work also emphasizes the correlation between the thermal band gap variation and Debye temperature.
NASA Astrophysics Data System (ADS)
Chiou, J.-S.; Liu, M.-T.
2008-02-01
As a powerful machine-learning approach to pattern recognition problems, the support vector machine (SVM) is known to easily allow generalization. More importantly, it works very well in a high-dimensional feature space. This paper presents a nonlinear active suspension controller which achieves a high level performance by compensating for actuator dynamics. We use a linear quadratic regulator (LQR) to ensure optimal control of nonlinear systems. An LQR is used to solve the problem of state feedback and an SVM is used to address the question of the estimation and examination of the state. These two are then combined and designed in a way that outputs feedback control. The real-time simulation demonstrates that an active suspension using the combined SVM-LQR controller provides passengers with a much more comfortable ride and better road handling.
NASA Technical Reports Server (NTRS)
Lehtinen, B.; Geyser, L. C.
1984-01-01
AESOP is a computer program for use in designing feedback controls and state estimators for linear multivariable systems. AESOP is meant to be used in an interactive manner. Each design task that the program performs is assigned a "function" number. The user accesses these functions either (1) by inputting a list of desired function numbers or (2) by inputting a single function number. In the latter case the choice of the function will in general depend on the results obtained by the previously executed function. The most important of the AESOP functions are those that design,linear quadratic regulators and Kalman filters. The user interacts with the program when using these design functions by inputting design weighting parameters and by viewing graphic displays of designed system responses. Supporting functions are provided that obtain system transient and frequency responses, transfer functions, and covariance matrices. The program can also compute open-loop system information such as stability (eigenvalues), eigenvectors, controllability, and observability. The program is written in ANSI-66 FORTRAN for use on an IBM 3033 using TSS 370. Descriptions of all subroutines and results of two test cases are included in the appendixes.
The Existence of Periodic Orbits and Invariant Tori for Some 3-Dimensional Quadratic Systems
Jiang, Yanan; Han, Maoan; Xiao, Dongmei
2014-01-01
We use the normal form theory, averaging method, and integral manifold theorem to study the existence of limit cycles in Lotka-Volterra systems and the existence of invariant tori in quadratic systems in ℝ3. PMID:24982980
The existence of periodic orbits and invariant tori for some 3-dimensional quadratic systems.
Jiang, Yanan; Han, Maoan; Xiao, Dongmei
2014-01-01
We use the normal form theory, averaging method, and integral manifold theorem to study the existence of limit cycles in Lotka-Volterra systems and the existence of invariant tori in quadratic systems in ℝ(3).
Stability of the equilibrium positions of an engine with nonlinear quadratic springs
NASA Astrophysics Data System (ADS)
Stănescu, Nicolae-Doru; Popa, Dinel
2014-06-01
Our paper realizes a study of the equilibrium positions for an engine supported by four identical nonlinear springs of quadratic characteristic. The systems with quadratic characteristic are generally avoided because they lead to mathematical complications. Our goal is to realize such a study for an engine supported on quadratic springs. For the model purposed, we established the equations of motion and we discussed the possibilities for the equilibrium positions. Because of the quadratic characteristic of the springs and of the approximations made for the small rotations, the equations obtained for the equilibrium lead us to a paradox, which consists in the existence of an open neighborhood in which there exists an infinity of positions of indifferent equilibrium, or a curve where the equilibrium positions are situated. Moreover, the study of the stability shows that the stability is assured for the position at which the springs are not compressed. Finally, a numerical example is presented and completely solved.
The existence of periodic orbits and invariant tori for some 3-dimensional quadratic systems.
Jiang, Yanan; Han, Maoan; Xiao, Dongmei
2014-01-01
We use the normal form theory, averaging method, and integral manifold theorem to study the existence of limit cycles in Lotka-Volterra systems and the existence of invariant tori in quadratic systems in ℝ(3). PMID:24982980
Observers for a class of systems with nonlinearities satisfying an incremental quadratic inequality
NASA Technical Reports Server (NTRS)
Acikmese, Ahmet Behcet; Martin, Corless
2004-01-01
We consider the problem of state estimation from nonlinear time-varying system whose nonlinearities satisfy an incremental quadratic inequality. Observers are presented which guarantee that the state estimation error exponentially converges to zero.
On ideal structure in quadratic DDS in R{sup 2}
Kutnjak, Milan
2008-11-13
We consider the dynamics in a special case of two-dimensional quadratic homogeneous discrete dynamical systems. It is well known (c.f. [1, 2]) that homogeneous quadratic maps are in one to one correspondence with two-dimensional commutative (nonassociative) algebras. Algebraic concepts (such as the structure of algebra and existence of special elements like idempotents and nilpotents) help us to study the dynamics of the corresponding discrete homogeneous quadratic maps. It is well-known that such systems can exhibit chaotic behavior [3], In this article we consider the influence of the existence of an algebra ideal on the dynamics of the corresponding discrete homogeneous quadratic system. We also present some examples in the plane.
Using Simple Quadratic Equations to Estimate Equilibrium Concentrations of an Acid
ERIC Educational Resources Information Center
Brilleslyper, Michael A.
2004-01-01
Application of quadratic equations to standard problem in chemistry like finding equilibrium concentrations of ions in an acid solution is explained. This clearly shows that pure mathematical analysis has meaningful applications in other areas as well.
Optimality of Gaussian attacks in continuous-variable quantum cryptography.
Navascués, Miguel; Grosshans, Frédéric; Acín, Antonio
2006-11-10
We analyze the asymptotic security of the family of Gaussian modulated quantum key distribution protocols for continuous-variables systems. We prove that the Gaussian unitary attack is optimal for all the considered bounds on the key rate when the first and second momenta of the canonical variables involved are known by the honest parties.
Degeneracy of energy levels of pseudo-Gaussian oscillators
Iacob, Theodor-Felix; Iacob, Felix; Lute, Marina
2015-12-07
We study the main features of the isotropic radial pseudo-Gaussian oscillators spectral properties. This study is made upon the energy levels degeneracy with respect to orbital angular momentum quantum number. In a previous work [6] we have shown that the pseudo-Gaussian oscillators belong to the class of quasi-exactly solvable models and an exact solution has been found.
A Paper-and-Pencil gcd Algorithm for Gaussian Integers
ERIC Educational Resources Information Center
Szabo, Sandor
2005-01-01
As with natural numbers, a greatest common divisor of two Gaussian (complex) integers "a" and "b" is a Gaussian integer "d" that is a common divisor of both "a" and "b". This article explores an algorithm for such gcds that is easy to do by hand.
A note on the wide-band Gaussian broadcast channel
NASA Technical Reports Server (NTRS)
Mceliece, Robert J.; Swanson, Laif
1987-01-01
The observations of Posner (1983) that on a wideband Gaussian broadcast channel ordinary time-shared coding performs almost as well as broadcast coding are investigated. A quantitative version of Posner's results is derived. A numerical example comparing the performance of broadcast coding and time-shared coding for a Gaussian broadcast channel model is presented.
Limitations of quantum computing with Gaussian cluster states
Ohliger, M.; Kieling, K.; Eisert, J.
2010-10-15
We discuss the potential and limitations of Gaussian cluster states for measurement-based quantum computing. Using a framework of Gaussian-projected entangled pair states, we show that no matter what Gaussian local measurements are performed on systems distributed on a general graph, transport and processing of quantum information are not possible beyond a certain influence region, except for exponentially suppressed corrections. We also demonstrate that even under arbitrary non-Gaussian local measurements, slabs of Gaussian cluster states of a finite width cannot carry logical quantum information, even if sophisticated encodings of qubits in continuous-variable systems are allowed for. This is proven by suitably contracting tensor networks representing infinite-dimensional quantum systems. The result can be seen as sharpening the requirements for quantum error correction and fault tolerance for Gaussian cluster states and points toward the necessity of non-Gaussian resource states for measurement-based quantum computing. The results can equally be viewed as referring to Gaussian quantum repeater networks.
Weakly anomalous diffusion with non-Gaussian propagators
NASA Astrophysics Data System (ADS)
Cressoni, J. C.; Viswanathan, G. M.; Ferreira, A. S.; da Silva, M. A. A.
2012-08-01
A poorly understood phenomenon seen in complex systems is diffusion characterized by Hurst exponent H≈1/2 but with non-Gaussian statistics. Motivated by such empirical findings, we report an exact analytical solution for a non-Markovian random walk model that gives rise to weakly anomalous diffusion with H=1/2 but with a non-Gaussian propagator.
Bingi, Jayachandra; Murukeshan, Vadakke Matham
2015-01-01
Laser speckle pattern is a granular structure formed due to random coherent wavelet interference and generally considered as noise in optical systems including photolithography. Contrary to this, in this paper, we use the speckle pattern to generate predictable and controlled Gaussian random structures and quasi-random structures photo-lithographically. The random structures made using this proposed speckle lithography technique are quantified based on speckle statistics, radial distribution function (RDF) and fast Fourier transform (FFT). The control over the speckle size, density and speckle clustering facilitates the successful fabrication of black silicon with different surface structures. The controllability and tunability of randomness makes this technique a robust method for fabricating predictable 2D Gaussian random structures and black silicon structures. These structures can enhance the light trapping significantly in solar cells and hence enable improved energy harvesting. Further, this technique can enable efficient fabrication of disordered photonic structures and random media based devices.
Bingi, Jayachandra; Murukeshan, Vadakke Matham
2015-01-01
Laser speckle pattern is a granular structure formed due to random coherent wavelet interference and generally considered as noise in optical systems including photolithography. Contrary to this, in this paper, we use the speckle pattern to generate predictable and controlled Gaussian random structures and quasi-random structures photo-lithographically. The random structures made using this proposed speckle lithography technique are quantified based on speckle statistics, radial distribution function (RDF) and fast Fourier transform (FFT). The control over the speckle size, density and speckle clustering facilitates the successful fabrication of black silicon with different surface structures. The controllability and tunability of randomness makes this technique a robust method for fabricating predictable 2D Gaussian random structures and black silicon structures. These structures can enhance the light trapping significantly in solar cells and hence enable improved energy harvesting. Further, this technique can enable efficient fabrication of disordered photonic structures and random media based devices. PMID:26679513
Dynamics and control of multibody tethered systems
NASA Astrophysics Data System (ADS)
Kalantzis, S.; Modi, V. J.; Pradhan, S.; Misra, A. K.
The equations of motion for a multibody tethered satellite system in a three dimensional Keplerian orbit are derived. The model considers a multi-satellite system connected in series by flexible tethers. Both tethers and subsatellites are free to undergo three dimensional attitude motion, together with longitudinal and transverse vibration for the tether. The elastic deformations of the tethers are discretized using the assumed-mode method. In addition, the tether attachment points to the subsatellites are kept arbitrary and time varying, with deployment and retrieval degrees of freedom. The governing equations of motion are derived using an Order ( N) Lagrangian formulation. Next, two independent controllers, i.e. an attitude and vibration controller, are designed to regulate the rigid and flexible motion present in the system, excited from various maneuvres performed during the course of a mission. The former controller utilizes the thrusters and momentum-wheels located on the rigid satellites with a control algorithm based on the feedback linearization technique. On the other hand, the latter is designed using the robust linear quadratic Gaussian-loop transfer recovery method actuating the variable tether attachment point, or offset position. Both controllers are successful in suppressing unwanted disturbances in the system in a acceptable amount of time.
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.
Models of quadratic quantum algebras and their relation to classical superintegrable systems
Kalnins, E. G.; Miller, W.; Post, S.
2009-05-15
We show how to construct realizations (models) of quadratic algebras for 2D second order superintegrable systems in terms of differential or difference operators in one variable. We demonstrate how various models of the quantum algebras arise naturally from models of the Poisson algebras for the corresponding classical superintegrable system. These techniques extend to quadratic algebras related to superintegrable systems in n dimensions and are intimately related to multivariable orthogonal polynomials.
Distillation and purification of symmetric entangled Gaussian states
Fiurasek, Jaromir
2010-10-15
We propose an entanglement distillation and purification scheme for symmetric two-mode entangled Gaussian states that allows to asymptotically extract a pure entangled Gaussian state from any input entangled symmetric Gaussian state. The proposed scheme is a modified and extended version of the entanglement distillation protocol originally developed by Browne et al. [Phys. Rev. A 67, 062320 (2003)]. A key feature of the present protocol is that it utilizes a two-copy degaussification procedure that involves a Mach-Zehnder interferometer with single-mode non-Gaussian filters inserted in its two arms. The required non-Gaussian filtering operations can be implemented by coherently combining two sequences of single-photon addition and subtraction operations.
Non-ideal boson system in the Gaussian approximation
Tommasini, P.R.; de Toledo Piza, A.F.
1997-01-01
We investigate ground-state and thermal properties of a system of non-relativistic bosons interacting through repulsive, two-body interactions in a self-consistent Gaussian mean-field approximation which consists in writing the variationally determined density operator as the most general Gaussian functional of the quantized field operators. Finite temperature results are obtained in a grand canonical framework. Contact is made with the results of Lee, Yang, and Huang in terms of particular truncations of the Gaussian approximation. The full Gaussian approximation supports a free phase or a thermodynamically unstable phase when contact forces and a standard renormalization scheme are used. When applied to a Hamiltonian with zero range forces interpreted as an effective theory with a high momentum cutoff, the full Gaussian approximation generates a quasi-particle spectrum having an energy gap, in conflict with perturbation theory results. {copyright} 1997 Academic Press, Inc.
REJUVENATING POWER SPECTRA. II. THE GAUSSIANIZED GALAXY DENSITY FIELD
Neyrinck, Mark C.; Szalay, Alexander S.; Szapudi, Istvan
2011-04-20
We find that, even in the presence of discreteness noise, a Gaussianizing transform (producing a more Gaussian one-point distribution) reduces nonlinearities in the power spectra of cosmological matter and galaxy density fields, in many cases drastically. Although Gaussianization does increase the effective shot noise, it also increases the power spectrum's fidelity to the linear power spectrum on scales where the shot noise is negligible. Gaussianizing also increases the Fisher information in the power spectrum in all cases and resolutions, although the gains are smaller in redshift space than in real space. We also find that the gain in cumulative Fisher information from Gaussianizing peaks at a particular grid resolution depends on the sampling level.
Jitter Reduces Response-Time Variability in ADHD: An Ex-Gaussian Analysis
Lee, Ryan W. Y.; Jacobson, Lisa A.; Pritchard, Alison E.; Ryan, Matthew S.; Yu, Qilu; Denckla, Martha B.; Mostofsky, Stewart; Mahone, E. Mark
2012-01-01
Objective “Jitter” involves randomization of intervals between stimulus events. Compared with controls, individuals with ADHD demonstrate greater intrasubject variability (ISV) performing tasks with fixed interstimulus intervals (ISIs). Because Gaussian curves mask the effect of extremely slow or fast response times (RTs), ex-Gaussian approaches have been applied to study ISV. Method This study applied ex-Gaussian analysis to examine the effects of jitter on RT variability in children with and without ADHD. A total of 75 children, aged 9 to 14 years (44 ADHD, 31 controls), completed a go/no-go test with two conditions: fixed ISI and jittered ISI. Results ADHD children showed greater variability, driven by elevations in exponential (tau), but not normal (sigma) components of the RT distribution. Jitter decreased tau in ADHD to levels not statistically different than controls, reducing lapses in performance characteristic of impaired response control. Conclusion Jitter may provide a nonpharmacologic mechanism to facilitate readiness to respond and reduce lapses from sustained (controlled) performance. PMID:23190614
Use of digital control theory state space formalism for feedback at SLC
Himel, T.; Hendrickson, L.; Rouse, F.; Shoaee, H.
1991-05-01
The algorithms used in the database-driven SLC fast-feedback system are based on the state space formalism of digital control theory. These are implemented as a set of matrix equations which use a Kalman filter to estimate a vector of states from a vector of measurements, and then apply a gain matrix to determine the actuator settings from the state vector. The matrices used in the calculation are derived offline using Linear Quadratic Gaussian minimization. For a given noise spectrum, this procedure minimizes the rms of the states (e.g., the position or energy of the beam). The offline program also allows simulation of the loop's response to arbitrary inputs, and calculates its frequency response. 3 refs., 3 figs.
Decay rates of Gaussian-type I-balls and Bose-enhancement effects in 3+1 dimensions
Kawasaki, Masahiro; Yamada, Masaki
2014-02-03
I-balls/oscillons are long-lived spatially localized lumps of a scalar field which may be formed after inflation. In the scalar field theory with monomial potential nearly and shallower than quadratic, which is motivated by chaotic inflationary models and supersymmetric theories, the scalar field configuration of I-balls is approximately Gaussian. If the I-ball interacts with another scalar field, the I-ball eventually decays into radiation. Recently, it was pointed out that the decay rate of I-balls increases exponentially by the effects of Bose enhancement under some conditions and a non-perturbative method to compute the exponential growth rate has been derived. In this paper, we apply the method to the Gaussian-type I-ball in 3+1 dimensions assuming spherical symmetry, and calculate the partial decay rates into partial waves, labelled by the angular momentum of daughter particles. We reveal the conditions that the I-ball decays exponentially, which are found to depend on the mass and angular momentum of daughter particles and also be affected by the quantum uncertainty in the momentum of daughter particles.
Decay rates of Gaussian-type I-balls and Bose-enhancement effects in 3+1 dimensions
Kawasaki, Masahiro; Yamada, Masaki E-mail: yamadam@icrr.u-tokyo.ac.jp
2014-02-01
I-balls/oscillons are long-lived spatially localized lumps of a scalar field which may be formed after inflation. In the scalar field theory with monomial potential nearly and shallower than quadratic, which is motivated by chaotic inflationary models and supersymmetric theories, the scalar field configuration of I-balls is approximately Gaussian. If the I-ball interacts with another scalar field, the I-ball eventually decays into radiation. Recently, it was pointed out that the decay rate of I-balls increases exponentially by the effects of Bose enhancement under some conditions and a non-perturbative method to compute the exponential growth rate has been derived. In this paper, we apply the method to the Gaussian-type I-ball in 3+1 dimensions assuming spherical symmetry, and calculate the partial decay rates into partial waves, labelled by the angular momentum of daughter particles. We reveal the conditions that the I-ball decays exponentially, which are found to depend on the mass and angular momentum of daughter particles and also be affected by the quantum uncertainty in the momentum of daughter particles.
NASA Astrophysics Data System (ADS)
Jimaa, Shihab A.; Jadah, Mohamed E.
2005-10-01
This paper investigates the performance of using various non-quadratic adaptive algorithms in the adaptation of a non-linear receiver, coupled with a second-order phase tracking subsystem, for asynchronous DS-CDMA communication system impaired by double-spread multipath channel and Gaussian mixture impulsive noise. These algorithms are the lower order (where the power of the cost function is lower than 2), the least-mean mixed norm (where a mixed-norm function is introduced, which combines the LMS and the LMF functions), and the least mean square-fourth switching (where this algorithm switches between LMS and LMF depending on the value of the error). The non-linear receiver comprises feed-forward filter (FFF), feedback filter (FBF), and an equalizer/second order phase locked loop (PLL). The investigations study the effect of using the proposed algorithms on the performance of the non-linear receiver in terms of the mean-square error (MSE) and bit-error-rate (BER). Computer simulation results indicate that the least-mean mixed proposed receiver's algorithm gives the fastest convergence rate and similar BER performance, in comparison with the NLMS adaptive receiver. Furthermore, extensive computer simulation tests have been carried out to determine the optimum values of the step-size, the power of the cost function, and the adaptation parameter of the proposed algorithms. Results show that the optimum values of the step-size for the lower-order, least-mean square fourth, least-mean mixed norm, and the NLMS algorithms are 5x10 -4, 10 -6, 5x10 -4, and 0.01, respectively. The optimum value of the power of the lower-order algorithm is 1.9 and the optimum value of the adaptation parameter of the least-mean mixed algorithm is 0.9.
Total decoupling of general quadratic pencils, Part II: Structure preserving isospectral flows
NASA Astrophysics Data System (ADS)
Chu, Moody T.; Del Buono, Nicoletta
2008-01-01
Quadratic pencils, λ2M+λC+K, where M, C, and K are n×n real matrices with or without some additional properties such as symmetry, connectivity, bandedness, or positive definiteness, arise in many important applications. Recently an existence theory has been established, showing that almost all n-degree-of-freedom second-order systems can be reduced to n totally independent single-degree-of-freedom second-order subsystems by real-valued isospectral transformations. In contrast to the common knowledge that generally no three matrices can be diagonalized simultaneously by equivalence transformations, these isospectral transformations endeavor to maintain a special linearization form called the Lancaster structure and do break down M, C and K into diagonal matrices simultaneously. However, these transformations depend on the matrices in a rather complicated way and, hence, are difficult to construct directly. In this paper, a second part of a continuing study, a closed-loop control system that preserves both the Lancaster structure and the isospectrality is proposed as a means to achieve the diagonal reduction. Consequently, these transformations are acquired.
NASA Astrophysics Data System (ADS)
Chun, Tae Yoon; Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho
2016-03-01
In this paper, we analyse the convergence and stability properties of generalised policy iteration (GPI) applied to discrete-time linear quadratic regulation problems. GPI is one kind of the generalised adaptive dynamic programming methods used for solving optimal control problems, and is composed of policy evaluation and policy improvement steps. To analyse the convergence and stability of GPI, the dynamic programming (DP) operator is defined. Then, GPI and its equivalent formulas are presented based on the notation of DP operator. The convergence of the approximate value function to the exact one in policy evaluation is proven based on the equivalent formulas. Furthermore, the positive semi-definiteness, stability, and the monotone convergence (PI-mode and VI-mode convergence) of GPI are presented under certain conditions on the initial value function. The online least square method is also presented for the implementation of GPI. Finally, some numerical simulations are carried out to verify the effectiveness of GPI as well as to further investigate the convergence and stability properties.
Design and test of three active flutter suppression controllers
NASA Technical Reports Server (NTRS)
Christhilf, David M.; Waszak, Martin R.; Adams, William M.; Srinathkumar, S.; Mukhopadhyay, Vivek
1991-01-01
Three flutter suppression control law design techniques are presented. Each uses multiple control surfaces and/or sensors. The first uses linear combinations of several accelerometer signals together with dynamic compensation to synthesize the modal rate of the critical mode for feedback to distributed control surfaces. The second uses traditional tools (pole/zero loci and Nyquist diagrams) to develop a good understanding of the flutter mechanism and produce a controller with minimal complexity and good robustness to plant uncertainty. The third starts with a minimum energy Linear Quadratic Gaussian controller, applies controller order reduction, and then modifies weight and noise covariance matrices to improve multi-variable robustness. The resulting designs were implemented digitally and tested subsonically on the Active Flexible Wing (AFW) wind tunnel model. Test results presented here include plant characteristics, maximum attained closed-loop dynamic pressure, and Root Mean Square control surface activity. A key result is that simultaneous symmetric and antisymmetric flutter suppression was achieved by the second control law, with a 24 percent increase in attainable dynamic pressure.
Digital robust control law synthesis using constrained optimization
NASA Technical Reports Server (NTRS)
Mukhopadhyay, Vivekananda
1989-01-01
Development of digital robust control laws for active control of high performance flexible aircraft and large space structures is a research area of significant practical importance. The flexible system is typically modeled by a large order state space system of equations in order to accurately represent the dynamics. The active control law must satisy multiple conflicting design requirements and maintain certain stability margins, yet should be simple enough to be implementable on an onboard digital computer. Described here is an application of a generic digital control law synthesis procedure for such a system, using optimal control theory and constrained optimization technique. A linear quadratic Gaussian type cost function is minimized by updating the free parameters of the digital control law, while trying to satisfy a set of constraints on the design loads, responses and stability margins. Analytical expressions for the gradients of the cost function and the constraints with respect to the control law design variables are used to facilitate rapid numerical convergence. These gradients can be used for sensitivity study and may be integrated into a simultaneous structure and control optimization scheme.
Constraint optimized weight adaptation for Gaussian mixture reduction
NASA Astrophysics Data System (ADS)
Chen, H. D.; Chang, K. C.; Smith, Chris
2010-04-01
Gaussian mixture model (GMM) has been used in many applications for dynamic state estimation such as target tracking or distributed fusion. However, the number of components in the mixture distribution tends to grow rapidly when multiple GMMs are combined. In order to keep the computational complexity bounded, it is necessary to approximate a Gaussian mixture by one with reduced number of components. Gaussian mixture reduction is traditionally conducted by recursively selecting two components that appear to be most similar to each other and merging them. Different definitions on similarity measure have been used in literature. For the case of one-dimensional Gaussian mixtures, Kmeans algorithms and some variations are recently proposed to cluster Gaussian mixture components in groups, use a center component to represent all in each group, readjust parameters in the center components, and finally perform weight optimization. In this paper, we focus on multi-dimensional Gaussian mixture models. With a variety of reduction algorithms and possible combinations, we developed a hybrid algorithm with constraint optimized weight adaptation to minimize the integrated squared error (ISE). In additions, with extensive simulations, we showed that the proposed algorithm provides an efficient and effective Gaussian mixture reduction performance in various random scenarios.
Axial acoustic radiation force on a sphere in Gaussian field
Wu, Rongrong; Liu, Xiaozhou Gong, Xiufen
2015-10-28
Based on the finite series method, the acoustical radiation force resulting from a Gaussian beam incident on a spherical object is investigated analytically. When the position of the particles deviating from the center of the beam, the Gaussian beam is expanded as a spherical function at the center of the particles and the expanded coefficients of the Gaussian beam is calculated. The analytical expression of the acoustic radiation force on spherical particles deviating from the Gaussian beam center is deduced. The acoustic radiation force affected by the acoustic frequency and the offset distance from the Gaussian beam center is investigated. Results have been presented for Gaussian beams with different wavelengths and it has been shown that the interaction of a Gaussian beam with a sphere can result in attractive axial force under specific operational conditions. Results indicate the capability of manipulating and separating spherical spheres based on their mechanical and acoustical properties, the results provided here may provide a theoretical basis for development of single-beam acoustical tweezers.
Probing Non-Gaussianity in Confined Diffusion of Nanoparticles.
Xue, Chundong; Zheng, Xu; Chen, Kaikai; Tian, Yu; Hu, Guoqing
2016-02-01
Confined diffusion is ubiquitous in nature. Ever since the "anomalous yet Brownian" motion was observed, the non-Gaussianity in confined diffusion has been unveiled as an important issue. In this Letter, we experimentally investigate the characteristics and source of non-Gaussian behavior in confined diffusion of nanoparticles suspended in polymer solutions. A time-varied and size-dependent non-Gaussianity is reported based on the non-Gaussian parameter and displacement probability distribution, especially when the nanoparticle's size is smaller than the typical polymer mesh size. This non-Gaussianity does not vanish even at the long-time Brownian stage. By inspecting the displacement autocorrelation, we observe that the nanoparticle-structure interaction, indicated by the anticorrelation, is limited in the short-time stage and makes little contribution to the non-Gaussianity in the long-time stage. The main source of the non-Gaussianity can therefore be attributed to hopping diffusion that results in an exponential probability distribution with the large displacements, which may also explain certain processes dominated by rare events in the biological environment. PMID:26784864
Recovering dark-matter clustering from galaxies with Gaussianization
NASA Astrophysics Data System (ADS)
McCullagh, Nuala; Neyrinck, Mark; Norberg, Peder; Cole, Shaun
2016-04-01
The Gaussianization transform has been proposed as a method to remove the issues of scale-dependent galaxy bias and non-linearity from galaxy clustering statistics, but these benefits have yet to be thoroughly tested for realistic galaxy samples. In this paper, we test the effectiveness of the Gaussianization transform for different galaxy types by applying it to realistic simulated blue and red galaxy samples. We show that in real space, the shapes of the Gaussianized power spectra of both red and blue galaxies agree with that of the underlying dark matter, with the initial power spectrum, and with each other to smaller scales than do the statistics of the usual (untransformed) density field. However, we find that the agreement in the Gaussianized statistics breaks down in redshift space. We attribute this to the fact that red and blue galaxies exhibit very different fingers of god in redshift space. After applying a finger-of-god compression, the agreement on small scales between the Gaussianized power spectra is restored. We also compare the Gaussianization transform to the clipped galaxy density field and find that while both methods are effective in real space, they have more complicated behaviour in redshift space. Overall, we find that Gaussianization can be useful in recovering the shape of the underlying dark-matter power spectrum to k ˜ 0.5 h Mpc-1 and of the initial power spectrum to k ˜ 0.4 h Mpc-1 in certain cases at z = 0.
Spatial entanglement of nonvacuum Gaussian states
NASA Astrophysics Data System (ADS)
Kiałka, Filip; Ahmadi, Mehdi; Dragan, Andrzej
2016-06-01
The vacuum state of a relativistic quantum field contains entanglement between regions separated by spacelike intervals. Such spatial entanglement can be revealed using an operational method introduced in [M. Rodriguez-Vazquez, M. del Rey, H. Westman, and J. Leon, Ann. Phys. (N.Y.) 351, 112 (2014), E. G. Brown, M. del Rey, H. Westman, J. Leon, and A. Dragan, Phys. Rev. D 91, 016005 (2015)]. In this approach, a cavity is instantaneously divided into halves by an introduction of an extra perfect mirror. Causal separation of the two regions of the cavity reveals nonlocal spatial correlations present in the field, which can be quantified by measuring particles generated in the process. We use this method to study spatial entanglement properties of nonvacuum Gaussian field states. In particular, we show how to enhance the amount of harvested spatial entanglement by an appropriate choice of the initial state of the field in the cavity. We find a counterintuitive influence of the initial entanglement between cavity modes on the spatial entanglement which is revealed by dividing the cavity in half.
Anomalous dimensions and non-gaussianity
Green, Daniel; Lewandowski, Matthew; Senatore, Leonardo; Silverstein, Eva; Zaldarriaga, Matias
2013-10-01
We analyze the signatures of inflationary models that are coupled to interacting field theories, a basic class of multifield models also motivated by their role in providing dynamically small scales. Near the squeezed limit of the bispectrum, we find a simple scaling behavior determined by operator dimensions, which are constrained by the appropriate unitarity bounds. Specifically, we analyze two simple and calculable classes of examples: conformal field theories (CFTs), and large-N CFTs deformed by relevant time-dependent double-trace operators. Together these two classes of examples exhibit a wide range of scalings and shapes of the bispectrum, including nearly equilateral, orthogonal and local non-Gaussianity in different regimes. Along the way, we compare and contrast the shape and amplitude with previous results on weakly coupled fields coupled to inflation. This signature provides a precision test for strongly coupled sectors coupled to inflation via irrelevant operators suppressed by a high mass scale up to ~ 103 times the inflationary Hubble scale.