Adaptive continuous-time linear quadratic Gaussian control
Duncan, Tyrone E.; Guo, L.; Pasik-Duncan, Bozenna
1999-09-01
, where Q(1), determines the quadratic form for the state in the integrand of the cost functional, A weighted least squares algorithm is modified by using a random regularization to ensure that the family of estimated models is uniformly controllable...
Soft Computing Design of a Linear Quadratic Gaussian Controller for an Unmanned Surface Vehicle
Wasif Naeem; Robert Sutton; John Chudley
2006-01-01
To develop an unmanned surface vehicle (USV), several issues need to be addressed, however, the most important being the navigation, guidance and control which dictates the performance of the whole system. Herein, the control problem is addressed by designing a fuzzy logic based linear quadratic Gaussian autopilot for the Springer USV being developed at the University of Plymouth, UK. A
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.
Thomas Schuhmann; Wilfried Hofmann; Erik Fleischer
2007-01-01
Magnetic bearings provide an energy-saving and resource-sparing possibility for supporting rotors running at high speed. This paper studies the potential of reducing the energy demand of magnetic levitation systems. Practical investigations show that this is obtainable by combining an optimal state estimator with an optimal state space controller. This configuration is known as Linear Quadratic Gaussian (LQG) regulator. In a
CREATED ON MAY 31, 2013 1 Linear Quadratic Gaussian (LQG) Control of Wind
Lavaei, Javad
concepts of Linear Quadratic Regulators (LQR) for full state feedback and Kalman Filters for state A(state ma- trix), B(control input gain matrix), G(plant noise gain matrix), C(measured state matrix. If these measurements carry enough information about the states of the system, then a state observer using Kalman Filter
The role and use of the stochastic linear-quadratic-Gaussian problem in control system design.
NASA Technical Reports Server (NTRS)
Athans, M.
1971-01-01
The role of the linear-quadratic stochastic control problem in engineering design is reviewed in tutorial fashion. The design approach is motivated by considering the control of a nonlinear uncertain plant about a desired input-output response. It is demonstrated how a design philosophy based on (1) deterministic perturbation control, (2) stochastic state estimation, and (3) linearized stochastic control leads to an overall closed-loop control system. The emphasis of the paper is on the philosophy of the design process, the modeling issue, and the formulation of the problem; the results are given for the sake of completeness, but no proofs are included. The systematic off-line nature of the design process is stressed throughout.
Habibullah, H., E-mail: h.habib@student.adfa.edu.au; Pota, H. R., E-mail: h.pota@adfa.edu.au; Petersen, I. R., E-mail: i.petersen@adfa.edu.au [School of Engineering and Information Technology, University of New South Wales, Canberra, Australian Capital Territory 2612 (Australia)
2014-03-15
This paper demonstrates a high-speed spiral imaging technique for an atomic force microscope (AFM). As an alternative to traditional raster scanning, an approach of gradient pulsing using a spiral line is implemented and spirals are generated by applying single-frequency cosine and sine waves of slowly varying amplitudes to the X and Y-axes of the AFM’s piezoelectric tube scanner (PTS). Due to these single-frequency sinusoidal input signals, the scanning process can be faster than that of conventional raster scanning. A linear quadratic Gaussian controller is designed to track the reference sinusoid and a vibration compensator is combined to damp the resonant mode of the PTS. An internal model of the reference sinusoidal signal is included in the plant model and an integrator for the system error is introduced in the proposed control scheme. As a result, the phase error between the input and output sinusoids from the X and Y-PTSs is reduced. The spirals produced have particularly narrow-band frequency measures which change slowly over time, thereby making it possible for the scanner to achieve improved tracking and continuous high-speed scanning rather than being restricted to the back and forth motion of raster scanning. As part of the post-processing of the experimental data, a fifth-order Butterworth filter is used to filter noises in the signals emanating from the position sensors and a Gaussian image filter is used to filter the images. A comparison of images scanned using the proposed controller (spiral) and the AFM PI controller (raster) shows improvement in the scanning rate using the proposed method.
Alejandro J. Rojas
2009-01-01
The research area of control over networks has attracted great interest in recent years. Inserted in this research area is\\u000a the study of control feedback limitations imposed by the presence of a communication channel. In this paper we analyze the\\u000a fundamental limitations in control feedback stabilizability imposed by a class of Signal-to-Noise Ratio (SNR) constrained\\u000a communication channels. We solve the
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.
Duncan, Tyrone E.; Maslowski, B.; Pasik-Duncan, B.
2012-01-01
A linear-quadratic control problem with a finite time horizon for some infinite-dimensional controlled stochastic differential equations driven by a fractional Gaussian noise is formulated and solved. The feedback form of the optimal control...
Linear Quadratic Gaussian Balancing for Discrete-Time Infinite-Dimensional Linear
Opmeer, Mark
Linear Quadratic Gaussian Balancing for Discrete-Time Infinite-Dimensional Linear Systems Mark R In this paper, we study the existence of linear quadratic Gaussian (LQG)Âbalanced realizations for discrete-time infinite-dimensional sys- tems. LQG-balanced realizations are those for which the smallest nonneg- ative
Gaussian States for Quantum Systems with Linear Constraints and Quadratic Hamiltonians
O. Yu. Shvedov
2008-12-25
Different constructions for Hilbert state space for constrained systems are investigated. Properties of Gaussian states analogous to quantum mechanical Gaussian wave functions are studied. Their evolution for quadratic Hamiltonian case are discussed. A notion of Maslov complex germ is introduced for systems with linear constraints.
Gaussian-Wave-Packet Dynamics in Uniform Magnetic and Quadratic Potential Fields
H. Y. Kim; J. H. Weiner
1973-01-01
For the case of uniform magnetic field and a potential quadratic in its coordinates an electron state originally represented by a Gaussian wave packet remains Gaussian in its subsequent evolution. Under these conditions the state is completely characterized by the first-and second-order quantum means, that is, quantities such as
c WISRL, KAIST, APRIL, 2012 1 A Study on the Series Expansion of Gaussian Quadratic Forms
Sung, Youngchul
c WISRL, KAIST, APRIL, 2012 1 A Study on the Series Expansion of Gaussian Quadratic Forms Technical Report WISRL-2012-APR-1 KAIST Juho Park, Youngchul Sung, Donggun Kim, and H. Vincent Poor All rights reserved c WISRL, KAIST Jan. 14, 2010 DRAFT #12;c WISRL, KAIST, APRIL, 2012 2 This report
LINEAR-QUADRATIC CONTROL OF BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS
Lim, Andrew
LINEAR-QUADRATIC CONTROL OF BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS ANDREW E. B. LIM AND XUN YU differential equations (BSDEs) with a quadratic cost criteria, or backward linear-quadratic (BLQ) control differential equations (BSDEs), linear-quadratic (LQ) optimal control, Riccati equations, completion of squares
Non-gaussianity in axion N-flation models Quadratic and $??^4$ plus axion potentials
Mehran Kamarpour
2012-10-27
In this paper we investigate large non-gaussianity in axion N-flation models, taking account while dynamically a large number of axions begin away from the hilltop region(come down from the hill) and so serve only to be the source of the Hubble rate. Therefore the single field stays closest to the hilltop sources the non-Gaussianity. In this case most of axions can be replaced by a single effective field with a quadratic potential. So our potential will contain two fields. The full cosine is responsible for the axion closest to hilltop and quadratic term which is a source for Hubble rate [4]. We obtain power spectrum, spectral index and non-gaussianity parameter, then we impose conditions from WMAP for power spectrum and spectral index and see how large on non-gaussianity parameter it is possible to achieve with such conditions. Finally we swap quadratic term to {\\lambda}{\\phi}^4 and see whether this makes it harder or easier to achieve large non-gaussianity.We find large non-gaussianity is achievable by imposing data from WMAP conditional on axion decay constant f has reasonable value in connection with Planck mass and by requiring number of e-folds must be bounded between 40-60.When we swap to {\\lambda}{\\phi}^4 we find that it is harder to achieve non-Gaussianity, because we are imposed to investigate only {\\lambda}{\\phi}^4 domination in consistency with WMAP data for spectral index. Although, in this case we find that large non-gaussianity is still achievable. Finally we verify imposing the condition for spectral index to be nearly one and find acceptable and detectable value for non-gaussianity typically of order of 10 and 100 depending on value of decay constant f.Swapping to {\\lambda}{\\phi}^4 in this case does not give us any significant relation. In this paper we consider models which can generate large non-gaussianity. We restrict ourselves to axion N-flation models.
Time evolution of a Gaussian class of quasi-distribution functions under quadratic Hamiltonian
Dimitry Ginzburg; Ady Mann
2014-04-15
A Lie algebraic method for propagation of the Wigner quasi-distribution function under quadratic Hamiltonian was presented by Zoubi and Ben-Aryeh. We show that the same method can be used in order to propagate a rather general class of quasi distribution functions, which we call "Gaussian class". This class contains as special cases the well-known Wigner, Husimi, Glauber and Kirkwood-Rihaczek quasi-distribution functions. We present some examples of the calculation of the time-evolution of those functions.
Quadratic Inverse Eigenvalue Problems, Active Vibration Control and Model Updating
Datta, Biswa
important applications of model updating in damage detection and health monitoring in vibrating structuresQuadratic Inverse Eigenvalue Problems, Active Vibration Control and Model Updating Biswa N. Datta,1 to active vibration control and finite element model updating. 1. Introduction The Quadratic Inverse
Using convex quadratic programming to model random media with Gaussian random fields.
Quintanilla, John A; Jones, W Max
2007-04-01
Excursion sets of Gaussian random fields (GRFs) have been frequently used in the literature to model two-phase random media with measurable phase autocorrelation functions. The goal of successful modeling is finding the optimal field autocorrelation function that best approximates the prescribed phase autocorrelation function. In this paper, we present a technique which uses convex quadratic programming to find the best admissible field autocorrelation function under a prescribed discretization. Unlike previous methods, this technique efficiently optimizes over all admissible field autocorrelation functions, instead of optimizing only over a predetermined parametrized family. The results from using this technique indicate that the GRF model is significantly more versatile than observed in previous studies. An application to modeling a base-catalyzed tetraethoxysilane aerogel system given small-angle neutron scattering data is also presented. PMID:17501018
Using convex quadratic programming to model random media with Gaussian random fields
NASA Astrophysics Data System (ADS)
Quintanilla, John A.; Jones, W. Max
2007-04-01
Excursion sets of Gaussian random fields (GRFs) have been frequently used in the literature to model two-phase random media with measurable phase autocorrelation functions. The goal of successful modeling is finding the optimal field autocorrelation function that best approximates the prescribed phase autocorrelation function. In this paper, we present a technique which uses convex quadratic programming to find the best admissible field autocorrelation function under a prescribed discretization. Unlike previous methods, this technique efficiently optimizes over all admissible field autocorrelation functions, instead of optimizing only over a predetermined parametrized family. The results from using this technique indicate that the GRF model is significantly more versatile than observed in previous studies. An application to modeling a base-catalyzed tetraethoxysilane aerogel system given small-angle neutron scattering data is also presented
NSDL National Science Digital Library
Shows how the roots of a quadratic change as the b term in the equation changes. The equation was chosen to illustrate the fact that only real roots are seen as points where the curve crosses the x-axis. This can lead to a useful discussion of what is meant by a physically meaningful solution.
NASA Technical Reports Server (NTRS)
Chen, George T.
1987-01-01
An automatic control scheme for spacecraft proximity operations is presented. The controller is capable of holding the vehicle at a prescribed location relative to a target, or maneuvering it to a different relative position using straight line-of-sight translations. The autopilot uses a feedforward loop to initiate and terminate maneuvers, and for operations at nonequilibrium set-points. A multivariate feedback loop facilitates precise position and velocity control in the presence of sensor noise. The feedback loop is formulated using the Linear Quadratic Gaussian (LQG) with Loop Transfer Recovery (LTR) design procedure. Linear models of spacecraft dynamics, adapted from Clohessey-Wiltshire Equations, are augmented and loop shaping techniques are applied to design a target feedback loop. The loop transfer recovery procedure is used to recover the frequency domain properties of the target feedback loop. The resulting compensator is integrated into an autopilot which is tested in a high fidelity Space Shuttle Simulator. The autopilot performance is evaluated for a variety of proximity operations tasks envisioned for future Shuttle flights.
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.
Finding Optimal Gains In Linear-Quadratic Control Problems
NASA Technical Reports Server (NTRS)
Milman, Mark H.; Scheid, Robert E., Jr.
1990-01-01
Analytical method based on Volterra factorization leads to new approximations for optimal control gains in finite-time linear-quadratic control problem of system having infinite number of dimensions. Circumvents need to analyze and solve Riccati equations and provides more transparent connection between dynamics of system and optimal gain.
LECTURE NOTES ON LINEAR QUADRATIC CONTROL VERSION OF 02-07-2010
Bonnans, Frédéric
quadratic problems (i.e., with a lin- ear state equation and a quadratic cost). The first section starts with the discussion of critical points of quadratic functionals, the shooting equations, and the associated RiccatiLECTURE NOTES ON LINEAR QUADRATIC CONTROL VERSION OF 02-07-2010 J. FR´ED´ERIC BONNANS Contents 1
Application of quadratic optimization to supersonic inlet control
NASA Technical Reports Server (NTRS)
Lehtinen, B.; Zeller, J. R.
1971-01-01
The application of linear stochastic optimal control theory to the design of the control system for the air intake (inlet) of a supersonic air-breathing propulsion system is discussed. The controls must maintain a stable inlet shock position in the presence of random airflow disturbances and prevent inlet unstart. Two different linear time invariant control systems are developed. One is designed to minimize a nonquadratic index, the expected frequency of inlet unstart, and the other is designed to minimize the mean square value of inlet shock motion. The quadratic equivalence principle is used to obtain the best linear controller that minimizes the nonquadratic performance index. The two systems are compared on the basis of unstart prevention, control effort requirements, and sensitivity to parameter variations.
Constrained Quadratic Programming, Active Control of Rotating Mass Imbalance
NASA Astrophysics Data System (ADS)
Manchala, D. W.; Palazzolo, A. B.; Kascak, A. F.; Montague, G. T.; Brown, G. V.
1997-09-01
Jet engines may experience severe vibration due to the sudden imbalance caused by blade failure. The current research investigates employment of piezoelectric actuators to suppress this using active vibration control. This requires identification of the source of the vibrations via an expert system, determination of the required phase angles and amplitudes for the correction forces, and application of the desired control signals to the piezoelectric actuators. Correction forces may exceed the physical limitations of the actuators; hence results of “constrained force” quadratic programming, least squares and multi-point correction algorithms will be compared. It is demonstrated that simply scaling down the least squares predicted correction forces to satisfy the actuator saturation constraints does not necessarily yield optimal reductions in vibration. In this paper test results are shown for sudden imbalance, and the computational time requirements and balancing effectiveness for the various approaches are compared.
Human-Inspired Control of Bipedal Robots via Control Lyapunov Functions and Quadratic Programs
Ames, Aaron
Human-Inspired Control of Bipedal Robots via Control Lyapunov Functions and Quadratic Programs walking through controller synthesis inspired by human locomotion. Motivated by the hierarchical con- trol present in humans, we begin by viewing the human as a "black box" and describe outputs, or virtual
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.
Larry A. Curtiss; Krishnan Raghavachari; John A. Pople
1995-01-01
The performance of Gaussian-2 theory is investigated when higher level theoretical methods are included for correlation effects, geometries, and zero-point energies. A higher level of correlation treatment is examined using Brueckner doubles [BD(T)] and coupled cluster [CCSD(T)] methods rather than quadratic configuration interaction [QCISD(T)]. The use of geometries optimized at the QCISD level rather than the second-order Moller--Plesset level (MP2)
An active set quadratic programming algorithm for real-time model predictive control
Indraneel Das
2006-01-01
On-board model predictive control of a nonlinear dynamical system often involves linearizing the nonlinear dynamics and posing a quadratic program to stay close to a desired profile of outputs. As on-board control requires computing a reliable solution in a robust manner in real time, the quadratic programming algorithm needs to use linear algebra optimally. This article describes an active set
Robust controller synthesis via shifted parameter-dependent and quadratic cost bounds
Vikram Kapila; Wassim M. Haddad; Richard S. Erwin; Dennis S. Bernstein
1997-01-01
Parametrized Lyapunov bounds and shifted quadratic guaranteed cost bounds are merged to develop shifted parameter-dependent quadratic cost bounds for robust stability and robust performance. Robust fixed-order (i.e., full- and reduced-order) controllers are developed based on new shifted parameter-dependent bounding functions. A numerical example is presented to demonstrate the effectiveness of the proposed approach
Robust controller synthesis via shifted parameter-dependent quadratic cost bounds
Vikram Kapila; Wassim M. Haddad; Richard S. Erwin; Dennis S. Bernstein
1998-01-01
Parameterized Lyapunov bounds and shifted quadratic guaranteed cost bounds are merged to develop shifted parameter-dependent quadratic cost bounds for robust stability and robust performance. Robust fixed-order (i.e., full- and reduced-order) controllers are developed based on new shifted parameter-dependent bounding functions. A numerical example is presented to demonstrate the effectiveness of the proposed approach
Controllable Gaussian-qubit interface for extremal quantum state engineering
G. Adesso; S. Campbell; F. Illuminati; M. Paternostro
2010-07-02
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 of backward stochastic differential equations: The linear-quadratic case
A. E. B. Lim; Xun Yu Zhou
2000-01-01
This paper is concerned with optimal control of linear backward stochastic differential equations (BSDE) with a quadratic cost criteria, or backward linear-quadratic (BLQ) control. The solution of this problem is obtained completely and explicitly by using an approach which is based primarily on the completion-of-squares technique. Two alternative, though equivalent, expressions for the optimal control are obtained. The first of
Constructive Stabilization of Quadratic-Input Nonlinear Systems with Bounded Controls
Jianghua Zhong; Daizhan Cheng; Xiaoming Hu
2008-01-01
In this paper, the stabilization of quadratic-input nonlinear systems with bounded controls is considered. According to the\\u000a type of quadratic-input forms, two cases, namely, positive definite and positive semi-definite, are considered. For the case\\u000a of positive definiteness, a universal formula for bounded stabilizers is given via a known Lyapunov control function. For\\u000a the case of positive semidefiniteness, a constructive parametrization
Optimal control development for chilled water plants using a quadratic representation
B. C. Ahn; J. W. Mitchell
2001-01-01
Optimal supervisory control strategy for the set points of controlled variables in the cooling plants has been studied by computer simulation. A quadratic linear regression equation for predicting the total cooling system power in terms of the controlled and uncontrolled variables was developed using simulated data collected under different values of controlled and uncontrolled variables. The optimal set temperatures such
Central Control, Sewers and (0,1) quadratic programming
NASA Astrophysics Data System (ADS)
Kolechkina, Alla; van Nooijen, Ronald
2013-04-01
We consider small sewer systems that combine foul water and storm water sewer functions in flat terrain. These systems are a combination of local gravity flow networks connected by pumps. The pumps are usually fixed speed, so they are on or off. We formulate a (0,1) quadratic programming problem, provide an overview of known solution methods and examine the relative speed of different solution methods.
Gaussian Networks for Direct Adaptive Control
Robert M. Sanner; Jean-Jacques E. Slotine
1991-01-01
A direct adaptive tracking control architecture is proposed and evaluated for a class of continuous-time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible. The architecture employs a network of gausian radial basis functions to adaptively compensate for the plant nonlinearities. Under mild assumptions about the degree of smoothness
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.
NASA Technical Reports Server (NTRS)
Milman, Mark H.
1988-01-01
The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary schemes. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.
Ge, Shuzhi Sam
reference feed- forward control was combined with a modified linear quadratic Gaussian (LQG) feedback was used to obtain a globally exponentially stable output feedback controller for dynamic positioning
Quadratic stability analysis and design of continuous-time fuzzy control systems
S. G. CAO; N. W. REES; G. FENG
1996-01-01
This paper presents a design method for fuzzy control systems. The method is based on a fuzzy state-space model A suitable piecewise smooth quadratic (PSQ) Lyapunov function is used to establish asymptotic stability of the closed-loop system. With the PSQ Lyapunov function a kind of global controller design method can be developed, and thus the disadvantage of using fixed P
Fast computation of the quadratic programming subproblem in model predictive control
Ruth Milman; E. J. Davidson
2003-01-01
One of the main drawbacks of model predictive control (MPC) is that large MPC horizon times can cause requirements of excessive computational time to solve the quadratic programming (QP) minimization which occurs in the calculation of the controller at each sampling interval. This motivates the study of finding faster ways for computing the QP problem associated with MPC. In this
New approaches to relaxed quadratic stability condition of fuzzy control systems
Euntai Kim; Heejin Lee
2000-01-01
This paper deals with the quadratic stability conditions of fuzzy control systems that relax the existing conditions reported in the previous literatures. Two new conditions are proposed and shown to be useful in analyzing and designing fuzzy control systems. The first one employs the S-procedure to utilize information regarding the premise parts of the fuzzy systems. The next one enlarges
Asymptotics of the solution to a singularly perturbed linear-quadratic optimal control problem
NASA Astrophysics Data System (ADS)
Kalinin, A. I.; Lavrinovich, L. I.
2015-02-01
The optimization of a transient process in a linear singularly perturbed system is considered. The goal is to find an admissible control that minimizes an integral quadratic cost functional. Asymptotic approximations to optimal open-loop and feedback controls are constructed for this problem. The basic advantage of the algorithms proposed is that the original optimal control problem splits into two unperturbed problems of lower dimension.
Andrzej Bartoszewicz
2008-01-01
In this paper, a new sliding-mode flow controller for connection-oriented communication networks is proposed. The networks are modeled as discrete-time nth-order systems. On the basis of the system state space description, a novel sliding-mode controller with a linear quadratic optimal switching plane is designed. Two control laws are proposed, each derived by minimizing different cost functionals. The first law is
Jian Sun
2010-01-01
A new methodology for adapting rigorous simulation programs to optimal supervisory control of a central chilled water plant is proposed in this article, which solves plant operation mode optimization and set points optimization by combining heuristic search with sequential quadratic programming. The mathematical basis of this algorithm is developed. A new derivative calculation strategy is introduced in set points optimization.
Paris-Sud XI, Université de
The Trust Region Sequential Quadratic Programming method applied to two-aircraft acoustic optimal University of Orléans. CNRS-MAPMO (France) Abstract: This paper aims to reduce noise levels of two-aircraft on approach. Keywords: TRSQP algorithm, optimal control problem, aircraft noise levels, AMPL programming
Zigang Pan; T. Basar
1994-01-01
Studies the optimal control of a class of stochastic singularly perturbed linear systems with noisy state measurements under positively and negatively exponentiated quadratic cost the so-called LEQG problem. The authors identify appropriate “slow” and “fast” subproblems, obtain their optimum solutions (compatible with the corresponding measurement structures), and subsequently study the performances they achieve on the full-order system as the singular
A. I. Kalinin
2010-01-01
A quadratic terminal cost functional is minimized on the trajectories of a linear singularly perturbed system. Equality constraints\\u000a are imposed on the right end of the trajectories, while the multidimensional controls are bounded in the Euclidean norm. An\\u000a algorithm is proposed for constructing asymptotic approximations to the solution of the problem.
On some dynamical and geometrical properties of the Maxwell-Bloch equations with a quadratic control
Tudor Binzar; Cristian Lazureanu
2014-02-24
In this paper, we analyze the stability of the real-valued Maxwell-Bloch equations with a control that depends on state variables quadratically. We also investigate the topological properties of the energy-Casimir map, as well as the existence of periodic orbits and explicitly construct the heteroclinic orbits.
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.
Heinkenschloss, Matthias (Rice University, Houston, TX); Bartlett, Roscoe Ainsworth; Van Bloeman Waanders, Paul; Ridzal, Denis (Rice University, Houston, TX)
2005-04-01
We present an optimization-level domain decomposition (DD) preconditioner for the solution of advection dominated elliptic linear-quadratic optimal control problems. The DD preconditioner is based on a decomposition of the optimality conditions for the elliptic linear-quadratic optimal control problem into smaller subdomain optimality conditions with Dirichlet boundary conditions for the states and the adjoints on the subdomain interfaces. These subdomain optimality conditions are coupled through Robin transmission conditions for the states and the adjoints. The parameters in the Robin transmission condition depend on the advection. This decomposition leads to a Schur complement system in which the unknowns are the state and adjoint variables on the subdomain interfaces. The Schur complement operator is the sum of subdomain Schur complement operators, the application of which is shown to correspond to the solution of subdomain optimal control problems, which are essentially smaller copies of the original optimal control problem. We show that, under suitable conditions, the application of the inverse of the subdomain Schur complement operators requires the solution of a subdomain elliptic linear-quadratic optimal control problem with Robin boundary conditions for the state. Numerical tests for problems with distributed and with boundary control show that the dependence of the preconditioners on mesh size and subdomain size is comparable to its counterpart applied to a single advection dominated equation. These tests also show that the preconditioners are insensitive to the size of the control regularization parameter.
Optimal Control of Linear Backward Stochastic Differential Equations with a Quadratic Cost Criterion
Andrew Lim; Xun Zhou
Backward Stochastic Differential Equations (BSDEs) are Ito SDEs with a random terminal condition. While it is the case that uncontrolled BSDEs have been the topic of extensive research for a number of years, little has been done on optimal control of BSDEs.\\u000a In this paper, we consider the problem of linear-quadratic control of a BSDE. A complete solution to this
Felipe Álvarez; Jérôme Bolte; J. Frédéric Bonnans; Francisco J. Silva
We consider a quadratic optimal control problem governed by a nonautonomous affine ordinary differential equation subject\\u000a to nonnegativity control constraints. For a general class of interior penalty functions, we provide a first order expansion\\u000a for the penalized states and adjoint states around the state and adjoint state of the original problem. Our main argument\\u000a relies on the following fact: if
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.
Blanes, Sergio
Structure preserving integrators for solving linear quadratic optimal control problems Valencia, Spain. Abstract We present structure preserving integrators for solving linear quadratic optimal of the equation for the state. This property is not preserved, in general, by the numerical methods. We propose
NASA Technical Reports Server (NTRS)
Ito, K.; Teglas, R.
1984-01-01
The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.
NASA Technical Reports Server (NTRS)
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)
Becus, G. A.; Lui, C. Y.; Venkayya, V. B.; Tischler, V. A.
1987-01-01
A method for simultaneous structural and control design of large flexible space structures (LFSS) to reduce vibration generated by disturbances is presented. Desired natural frequencies and damping ratios for the closed loop system are achieved by using a combination of linear quadratic regulator (LQR) synthesis and numerical optimization techniques. The state and control weighing matrices (Q and R) are expressed in terms of structural parameters such as mass and stiffness. The design parameters are selected by numerical optimization so as to minimize the weight of the structure and to achieve the desired closed-loop eigenvalues. An illustrative example of the design of a two bar truss is presented.
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)
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.
Singular linear-quadratic control problem for systems with linear delay
NASA Astrophysics Data System (ADS)
Sesekin, A. N.
2013-12-01
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.
Singular linear-quadratic control problem for systems with linear delay
Sesekin, A. N. [Ural Federal University, 19 S. Mira, Ekaterinburg, 620002 (Russian Federation); Institute of Mathematics and Mechanics, Ural Division of Russian Academy of Sciences, 16 S. Kovalevskaya, Ekaterinburg, 620990 (Russian Federation)
2013-12-18
A singular linear-quadratic optimization problem on the trajectories of non-autonomous linear differential equations with linear delay is considered. The peculiarity of this problem is the fact that this problem has no solution in the class of integrable controls. To ensure the existence of solutions is required to expand the class of controls including controls with impulse components. Dynamical systems with linear delay are used to describe the motion of pantograph from the current collector with electric traction, biology, etc. It should be noted that for practical problems fact singularity criterion of quality is quite commonly occurring, and therefore the study of these problems is surely important. For the problem under discussion optimal programming control contained impulse components at the initial and final moments of time is constructed under certain assumptions on the functional and the right side of the control system.
CAD of control systems: Application of nonlinear programming to a linear quadratic formulation
NASA Technical Reports Server (NTRS)
Fleming, P.
1983-01-01
The familiar suboptimal regulator design approach is recast as a constrained optimization problem and incorporated in a Computer Aided Design (CAD) package where both design objective and constraints are quadratic cost functions. This formulation permits the separate consideration of, for example, model following errors, sensitivity measures and control energy as objectives to be minimized or limits to be observed. Efficient techniques for computing the interrelated cost functions and their gradients are utilized in conjunction with a nonlinear programming algorithm. The effectiveness of the approach and the degree of insight into the problem which it affords is illustrated in a helicopter regulation design example.
Submersible control using the Linear Quadratic Gaussian with Loop Transfer Recovery (LQG/LTR) method
Juul, Douglas Lawton
1993-01-01
24 24 24 . . 25 29 . . 30 31 35 44 44 45 45 45 49 49 LIST OF FIGURES (Continued) HGURE 4. 8: Singular Values of the Recovered Loop Transfer Function, G(s)K(s), 5. 0 m/s Model HGURE 4. 9: Singular Values of the Closed Loop System, 5.... Om, h'P=90. 0' HGURE 4. 24b: Heading Angle, 5. 0 m/s, hZ=0. Om, M'=90. 0' . . FIGURE 4. 24c: Sternplane Angle, 5. 0 m/s, d, Z=O. Om, M'=90. 0' HGURE 4. 24d: Rudder Angle, 5. 0m/s, hZ=0. Om, M'=90. 0' HGURE 4. 25a: Vehicle Depth, 5. 0 m/s, hZ=50. 0...
Pan, Z.; Basar, T. [Univ. of Illinois, Urbana, IL (United States)
1994-12-31
We study the optimal control of a class of stochastic singularly perturbed linear systems with noisy state measurements under positively and negatively exponentiated quadratic cost the so-called LEQG problem. We identify appropriate {open_quotes}slow{close_quotes} and {open_quotes}fast{close_quotes} subproblems, obtain their optimum solutions (compatible with the corresponding measurement structures), and subsequently study the performances they achieve on the full-order system as the singular perturbation parameter {epsilon} becomes sufficiently small. A by-product of this analysis is a more direct derivation (than heretofore available) of the solution to the LEQG problem under noisy state measurements, which allows for a general quadratic cost (with cross terms) in the exponent and correlation between system and measurement noises. Such a general LEQG problem is encountered in the slow-fast decomposition of the full-order problem, even if the original problem does not feature correlated noises. In this general context, the paper also establishes a complete equivalence between the LEQG problem and the H{sup {infinity}}-optimal control problem with measurement feedback, though this equivalence does not extend to the slow and fast subproblems arrived at after time-scale separation.
Paris-Sud XI, Université de
Characterization of local quadratic growth for strong minima in the optimal control of semi-linear elliptic equations T´erence Bayen J. Fr´ed´eric Bonnans Francisco J. Silva§ September 11, 2013 Abstract In this article we consider an optimal control problem of a semi-linear elliptic equation, with bound constraints
Soliton transmission control by super-Gaussian filters
NASA Astrophysics Data System (ADS)
Peral, E.; Capmany, J.; Marti, J.
1996-12-01
Bandwidth-limited filtering has been proven to overcome certain limitations in soliton transmission systems. We propose super-Gaussian filters instead of Butterworth filter response obtained with conventionally used Fabry-Perot etalons as a method to improve soliton stability and reduce dispersion degradation and theoretically demonstrate their practical implementation in the form of holographic fiber gratings.
Lyapunov functions for quadratic differential equations with applications to adaptive control
G. Luders; K. Narendra
1972-01-01
Conditions are derived for the existence of quadratic Lyapunov functions for vector differential equations with quadratic terms. These conditions are used to establish a set of nonlinear equations for which the null solution is asymptotically stable in the whole. Many of the recent results in the stability of model reference adaptive systems are particular cases of these general conditions.
Ayvaz, Muzaffer; Demiralp, Metin [Istanbul Technical University, Informatics Institute, Maslak, 34469, Istanbul (Turkey)
2011-09-14
In this study, the optimal control equations for one dimensional quantum harmonic oscillator under the quadratic control operators together with linear dipole polarizability effects are constructed in the sense of Heisenberg equation of motion. A numerical technique based on the approximation to the non-commuting quantum mechanical operators from the fluctuation free expectation value dynamics perspective in the classical limit is also proposed for the solution of optimal control equations which are ODEs with accompanying boundary conditions. The dipole interaction of the system is considered to be linear, and the observable whose expectation value will be suppressed during the control process is considered to be quadratic in terms of position operator x. The objective term operator is also assumed to be quadratic.
Peter Benner; Jing-Rebecca Li; Thilo Penzl
2008-01-01
SUMMARY We study large-scale, continuous-time linear time-invariant control systems with a sparse or structured state matrix and a relatively small number of inputs and outputs. The main contributions of this paper are numerical algorithms for the solution of large algebraic Lyapunov and Riccati equations and linear- quadratic optimal control problems, which arise from such systems. First, we review an alternating
NASA Astrophysics Data System (ADS)
Badreddine, Hassan; Vandewalle, Stefan; Meyers, Johan
2014-01-01
The current work focuses on the development and application of an efficient algorithm for optimization of three-dimensional turbulent flows, simulated using Direct Numerical Simulation (DNS) or Large-Eddy Simulations, and further characterized by large-dimensional optimization-parameter spaces. The optimization algorithm is based on Sequential Quadratic Programming (SQP) in combination with a damped formulation of the limited-memory BFGS method. The latter is suitable for solving large-scale constrained optimization problems whose Hessian matrices cannot be computed and stored at a reasonable cost. We combine the algorithm with a line-search merit function based on an L1-norm to enforce the convergence from any remote point. It is first shown that the proposed form of the damped L-BFGS algorithm is suitable for solving equality constrained Rosenbrock type functions. Then, we apply the algorithm to an optimal-control test problem that consists of finding the optimal initial perturbations to a turbulent temporal mixing layer such that mixing is improved at the end of a simulation time horizon T. The controls are further subject to a non-linear equality constraint on the total control energy. DNSs are used to resolve all turbulent scales of motion, and a continuous adjoint formulation is employed to calculate the gradient of the cost functionals. We compare the convergence speed of the SQP L-BFGS algorithm to a conventional non-linear conjugate-gradient method (i.e. the current standard in DNS-based optimal control), and find that the SQP algorithm is more than an order of magnitude faster than the conjugate-gradient method.
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. PMID:25273197
NSDL National Science Digital Library
2013-06-21
The quadratic formula is easy to solve, yet sufficiently sophisticated that it provides insight into oscillations of masses connected by springs, as well as insight into chemical bonds between atoms. The purpose of this video is to illustrate what it means to find the "zeros" or "roots" of the quadratic equation, both using a graphical description, as well as by analytically completing the square to obtain the famous quadratic formula.
Gravdahl, Jan Tommy
of spacecrafts. Stability proofs are not considered at this point. A poten- tial approach is to search inputs on a predefined horizon, once for each time sample. The first control input in the sequence is then applied to the plant, and the optimization is repeated with the new initial conditions and on the new
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…
Ryo Namiki
2009-06-09
We provide a family of Non-Gaussian pure entangled states in a bipartite system as the eigen states of a quadratic Hamiltonian composed of the Einstein-Podolsky-and-Rosen-like operators. The ground state of the Hamiltonian corresponds to the two-mode-squeezed vacuum state, and belongs to the Gaussian states. In contrast, all of the excited states are Non-Gaussian states. A separable inequality maximally violated by the eigen states is derived.
NASA Astrophysics Data System (ADS)
El Jarbi, M.; Rückelt, J.; Slawig, T.; Oschlies, A.
2012-08-01
This paper presents the application of the Linear Quadratic Optimal Control (LQOC) method for a parameter optimization problem in a marine ecosystem model. The ecosystem model simulates the distribution of nitrogen, phytoplankton, zooplankton and detritus in a water column with temperature and turbulent diffusivity profiles taken from a three-dimensional ocean circulation model. We present the linearization method which is based on the available observations. The linearization is necessary to apply the LQOC method on the nonlinear system of state equations. We show the form of the linearized time-variant problems and the resulting two algebraic Riccati Equations. By using the LQOC method, we are able to introduce temporally varying periodic model parameters and to significantly improve - compared to the use of constant parameters - the fit of the model output to given observational data.
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.
Venuti, Lorenzo Campos; Zanardi, Paolo
2013-01-01
A finite quantum system evolving unitarily equilibrates in a probabilistic fashion. In the general many-body setting the time fluctuations of an observable A are typically exponentially small in the system size. We consider here quasifree Fermi systems where the Hamiltonian and observables are quadratic in the Fermi operators. We first prove a bound on the temporal fluctuations ?A(2) and then map the equilibration dynamics to a generalized classical XY model in the infinite temperature limit. Using this insight, we conjecture that, in most cases, a central limit theorem can be formulated, leading to what we call Gaussian equilibration: observables display a Gaussian distribution with relative error ?A/A[over Ż]=O(L(-1/2)), where L is the dimension of the single-particle space. The conjecture, corroborated by numerical evidence, is proven analytically under mild assumptions for the magnetization in the quantum XY model and for a class of observables in a tight-binding model. We also show that the variance is discontinuous at the transition between a quasifree model and a nonintegrable one. PMID:23410282
Control Barrier Function Based Quadratic Programs with Application to Bipedal Robotic Walking
Hsu, Shao-Chen
2014-12-12
that can be explicitly derived. To demonstrate these formal results, they are applied in the context of bipedal robotic walking. Physical constraints, e.g., joint limits, are represented by control barrier functions and unified with control objectives...
Hak-Keung Lam; Mohammad Narimani
2010-01-01
This paper presents the stability analysis of fuzzy-model-based (FMB) control systems. Staircase membership functions are introduced to facilitate the stability analysis. Through the staircase membership functions approximating those of the fuzzy model and fuzzy controller, the information of the membership functions can be brought into the stability analysis. Based on the Lyapunov-stability theory, stability conditions in terms of linear-matrix inequalities
Solving quadratic Introduction
Vickers, James
Solving quadratic equations 3.2 Introduction A quadratic equation is one which can be written. In this section we describe several ways in which quadratic equations can be solved. ' & $ % Prerequisites Before completing this Section you should be able to . . . recognise a quadratic equation solve a quadratic
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.
Burton, Geoffrey R.
Quadratic Forms Hyperbolic surfaces Closed Geodesics Spectral Theory Pell's Equation Algorithm for solving x Geodesics Y. Petridis Quadratic Forms Hyperbolic surfaces Closed Geodesics Spectral Theory Pell's EquationQuadratic Forms and Closed Geodesics Y. Petridis Outline Quadratic Forms and Closed Geodesics
Symplectic structure for Gaussian diffusions
NASA Astrophysics Data System (ADS)
Brandăo, Augusto
1998-09-01
Using information exclusively about classical Hamiltonian boundary value problems (with quadratic time-dependent potentials) we construct probability measures providing a symplectic structure associated with some inhomogeneous Gaussian diffusion processes introduced earlier [T. Kolsrod and J. C. Zambrini, J. Math. Phys. 33, 1301 (1992)].
Improved temperature control of a PWR nuclear reactor using an LQG\\/LTR based controller
Hussein Arab-Alibeik; Saeed Setayeshi
2003-01-01
State feedback assisted classical (SFAC) control has been developed to improve the temperature response performance of nuclear reactors via modifying the embedded classical controller reference signal. This is done by means of an outermost state feedback controller. A linear quadratic Gaussian with loop transfer recovery (LQG\\/LTR) at the plant output seems a good candidate for the state feedback loop of
VTOL controls for shipboard landing. M.S.Thesis
NASA Technical Reports Server (NTRS)
Mcmuldroch, C. G.
1979-01-01
The problem of landing a VTOL aircraft on a small ship in rough seas using an automatic controller is examined. The controller design uses the linear quadratic Gaussian results of modern control theory. Linear time invariant dynamic models are developed for the aircraft, ship, and wave motions. A hover controller commands the aircraft to track position and orientation of the ship deck using only low levels of control power. Commands for this task are generated by the solution of the steady state linear quadratic gaussian regulator problem. Analytical performance and control requirement tradeoffs are obtained. A landing controller commands the aircraft from stationary hover along a smooth, low control effort trajectory, to a touchdown on a predicted crest of ship motion. The design problem is formulated and solved as an approximate finite-time linear quadratic stochastic regulator. Performance and control results are found by Monte Carlo simulations.
?p-norms of codewords from capacity- and dispersion-achieveing Gaussian codes
Polyanskiy, Yury
It is demonstrated that codewords of good codes for the additive white Gaussian noise (AWGN) channel become more and more isotropically distributed (in the sense of evaluating quadratic forms) and resemble white Gaussian ...
Williamson, John
. It is a non-parametric model which retains the available data and performs inference conditionalNonparametric Identification of Linearizations and Uncertainty using Gaussian Process Models complexity to the available data, and which give not only mean predictions but also the variance
A new eddy current model for magnetic bearing control system design
NASA Technical Reports Server (NTRS)
Feeley, Joseph J.; Ahlstrom, Daniel J.
1992-01-01
This paper describes a new VLSI-based controller for the implementation of a Linear-Quadratic-Gaussian (LQG) theory-based control system. Use of the controller is demonstrated by design of a controller for a magnetic bearing and its performance is evaluated by computer simulation.
Design of a candidate flutter suppression control law for DAST ARW-2
NASA Technical Reports Server (NTRS)
Adams, W. M., Jr.; Tiffany, S. H.
1984-01-01
A control law is developed to suppress symmetric flutter for a mathematical model of an aeroelastic research vehicle. An implementable control law is attained by including modified LQC (Linear Quadratic Gaussian) design techniques, controller order reduction, and gain scheduling. An alternate (complementary) design approach is illustrated for one flight condition wherein nongradient-based constrained optimization techniques are applied to maximize controller robustness.
NSDL National Science Digital Library
Robert Lengacher
2012-07-05
This is an introductory lesson to graphing quadratic equations. This lesson uses graphing technology to illustrate the differences between quadratic equations and linear equations. In addition, it allows students to identify important parts of the quadratic equation and how each piece changes the look of the graph.
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…
PIECEWISE QUADRATIC APPROXIMATIONS IN CONVEX ...
2010-12-11
even if the newly obtained point is inserted in I (which is possible, although not ...... As far as control of the bundle size is concerned, a classical approach (again .... towards the optimum, and the “noise” provided by the extra quadratic terms in the .... Contraints, International Journal of Electrical Power and Energy Systems,.
Homotopy approach to optimal, linear quadratic, fixed architecture compensation
NASA Technical Reports Server (NTRS)
Mercadal, Mathieu
1991-01-01
Optimal linear quadratic Gaussian compensators with constrained architecture are a sensible way to generate good multivariable feedback systems meeting strict implementation requirements. The optimality conditions obtained from the constrained linear quadratic Gaussian are a set of highly coupled matrix equations that cannot be solved algebraically except when the compensator is centralized and full order. An alternative to the use of general parameter optimization methods for solving the problem is to use homotopy. The benefit of the method is that it uses the solution to a simplified problem as a starting point and the final solution is then obtained by solving a simple differential equation. This paper investigates the convergence properties and the limitation of such an approach and sheds some light on the nature and the number of solutions of the constrained linear quadratic Gaussian problem. It also demonstrates the usefulness of homotopy on an example of an optimal decentralized compensator.
Chu, Shu-Chun; Ohtomo, Takayuki; Otsuka, Kenju
2008-05-10
This study demonstrates successive higher-order Hermite-Gaussian (HG(0,m)) mode operations in a microchip solid-state laser with a controlled off-axis laser diode (LD) pumping and generation of the corresponding doughnutlike laser beam of tunable ring diameter and orbital angular momentum, by experimentally focusing a Hermite-Gaussian mode (HGM) lasing beam into an astigmatic mode converter (AMC) with a mode-matching lens. Based on the successful generation of stable doughnutlike vortex beams by combining the LD off-axis pumping of microchip lasers and an AMC, this study proposes a design for a compact, solid doughnutlike vortex laser beam generator that combines three elements (i.e., laser cavity, mode-matching lens, and AMC) into one practical device. The desired doughnutlike vortex beam with different orbital angular momentum is easily generated by simply controlling the lateral off-axis pump position and pump beam shape on the laser crystal by numerical simulation. PMID:18470253
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.
Naresh C. Jain; Ditlev Monrad
1982-01-01
Necessary and sufficient conditions in terms of the mean function and covariance are obtained for a separable Gaussian process to have paths of bounded variation, absolutely continuous or continuous singular. If almost all paths are of bounded variation, the L2 expansion of the Gaussian process is shown to converge in the total variation norm. One then obtains a decomposition of
Schaal, Stefan
that is higher than the dimensionality of the controls. Furthermore, by a modified inverse dynamics controller with quadratic cost functions and gaussian noise profiles [1]. The goal of applying learning control to robots the complexity from exponential, with respect to the number of states, to polynomial it requires
P. Eserin
1999-01-01
The paper describes an application of canonical variate analysis (CVA) and 9-element LQG-optimal control (linear quadratic Gaussian) to boiler drum level control on a 400 kpph gas fired power boiler. Consumed air and flue gas temperatures are investigated for their value as clean fuel flow proxy variables. The work thus has relevance for drum level control of dirty fuel boilers.
Fuzzy and optimal control of a two-link flexible manipulator
Anthony Green; J. Z. Sasiadek
2001-01-01
A linear quadratic Gaussian (LQG) strategy controls a two-link flexible robot manipulator tracking a two-dimensional square trajectory 12.6 m×12.6 m. Slew angles together with a Gaussian white process and white or non-white measurement noise are fed into a LQG regulator (Kalman filter). A FLC strategy incorporates two fuzzy controllers substituted for the LQR state-space dynamics equations. Trajectories were obtained for
Quadratic Forms, Geodesics and
Wirosoetisno, Djoko
Forms Hyperbolic surfaces Closed Geodesics Spectral Theory Propaganda Outline Quadratic Forms Hyperbolic surfaces Closed Geodesics Spectral Theory Propaganda #12;Indefinite Quadratic Forms, Closed Geodesics Propaganda Pell's Equation Algorithm for solving x2 - 2y2 = ±1 (Pythagoreans) Start with x1 = 1, y1 = 1 We
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.
On Convex Relaxations for Quadratically Constrained Quadratic ...
2010-07-28
Jul 28, 2010 ... relaxation of the convex hull of the quadratic form that imposes ... of QCQP problems, corresponding to planar circle-packing (or ..... the algorithm of [18], but still required up to 104 CPU seconds on a 2.7 GHz Linux-based.
Frequency weighted LQG control of spacecraft attitude
M. E. Pittelkau
1992-01-01
A frequency-weighted linear-quadratic-Gaussian (LQG) approach to control of pitch attitude and pitch wheel momentum of an Earth-orbiting spacecraft is presented. Attitude is measured by an Earth horizon sensor, and control torque is produced by magnetic torquer bars and a pitch momentum or reaction wheel. Environmental disturbances are estimated for disturbance rejection. The design features control weighting so that low-frequency control
Direct adaptive control of wind energy conversion systems using Gaussian networks.
Mayosky, M A; Cancelo, I E
1999-01-01
Grid connected wind energy conversion systems (WECS) present interesting control demands, due to the intrinsic nonlinear characteristics of windmills and electric generators. In this paper a direct adaptive control strategy for WECS control is proposed. It is based on the combination of two control actions: a radial basis zfunction network-based adaptive controller, which drives the tracking error to zero with user specified dynamics, and a supervisory controller, based on crude bounds of the system's nonlinearities. The supervisory controller fires when the finite neural-network approximation properties cannot be guaranteed. The form of the supervisor control and the adaptation law for the neural controller are derived from a Lyapunov analysis of stability. The results are applied to a typical turbine/generator pair, showing the feasibility of the proposed solution. PMID:18252585
Twisted Gaussian Schell-model beams
R. Simon; N. Mukunda
1993-01-01
The authors introduce a new class of partially coherent axially symmetric Gaussian Schell-model (GSM) beams incorporating a new twist phase quadratic in configuration variables. This phase twists the beam about its axis during propagation and is shown to be bounded in strength because of the positive semidefiniteness of the cross-spectral density. Propagation characteristics and invariants for such beams are derived
Design issues in the control of large flexible spacecraft slew maneuvers
H. H. Chan; Y. P. Kakad
1990-01-01
Linearized dynamical models of slew maneuvers of a large flexible spacecraft are utilized to design state feedback control systems to perform arbitrary slew maneuvers and to achieve total vibration suppression of flexible appendages. The control system designs are based on linear quadratic Gaussian loop transfer recovery (LQG\\/LTR) design methodology. The linearized slew maneuver equations used are derived from a nonlinear
LQG controller design using GUI: Application to antennas and radio-telescopes
Erin Maneri; Wodek Gawronski
2000-01-01
The Linear Quadratic Gaussian (LQG) algorithm has been used to control the JPL's beam wave-guide, and 70-m antennas. This algorithm significantly improves tracking precision in a wind disturbed environment. Based on this algorithm and the implementation experience a Matlab based Graphical User Interface (GUI) was developed to design the LQG controllers applicable to antennas and radiotelescopes. The GUI is described
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.
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.
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.
Sloane, Neil J. A.
1980-01-01
INFORMATION AND CONTROL 46, 270-272 (1980) A Note on the Leech Lattice as a Code for the Gaussian Channel N. J. A. SLOANE Bell Laboratories, Murray Hill, New Jersey 07974 The Leech lattice A is a very dense packing of spheres in 24-dimensional Euclidean space, discovered by Leech (1967). Its automorphism
Quadratic Functions: Workshop 4
NSDL National Science Digital Library
Annenberg Media, Insights into Algebra, Teaching for Learning
2009-12-23
Lesson 1 of two lessons requires students to explore quadratic functions by examining the family of functions described by y = a (x - h)squared+ k. In Lesson 2 students explore quadratic functions by using a motion detector known as a Calculator Based Ranger (CBR) to examine the heights of the different bounces of a ball. Students will represent each bounce with a quadratic function of the form y = a (x - h)squared + k. Background information, resources, references and videos of the lessons are included. Students work in teams of four.
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.
Quadratic Liénard Equations with Quadratic Damping
Freddy Dumortier; Chengzhi Li
1997-01-01
In this paper we study the generalized Liénard equations x+f(x)x+g(x)=0 with quadratic polynomialsfandg. We prove that these kind of equations can have at most one limit cycle, and we give the complete bifurcation diagram and classification of the phase portraits. The paper also contains a shorter proof for the result in A. Lins, W. de Melo, and C. C. Pugh,
Patrick Devlin
2014-05-08
This only works for zero; that is why when a quadratic equation is factorable, we ... to solve an equation that involves a perfect square, isolate the perfect ... changed into perfect squares by using a procedure called completing the square.
Main graphs: Quadratic equation
Utrecht, Universiteit
a>0 OR OR OR x x x xxx x x x y y y Quadratic equation: The general solution of a quadratic equation equations: Equation dN dt = kN has the solution: N(t) = N0ekt; N0 is an (arbitrary) initial value of N. Systems of linear differential equations: For system dx dt = ax+by dy dt = cx+dy , the characteristic
Constraint propagation on quadratic constraints
Ferenc Domes; Arnold Neumaier
2010-01-01
This paper considers constraint propagation methods for continuous constraint satisfaction problems consisting of linear and quadratic constraints. All methods can be applied after suitable preprocessing to arbitrary algebraic constraints. The basic new techniques consist in eliminating bilinear entries from a quadratic constraint, and solving the resulting separable quadratic constraints by means of a sequence of univariate quadratic problems. Care is
An efficiently solvable quadratic program for stabilizing dynamic locomotion
Kuindersma, Scott
We describe a whole-body dynamic walking controller implemented as a convex quadratic program. The controller solves an optimal control problem using an approximate value function derived from a simple walking model while ...
Asymptotically safe inflation from quadratic gravity
Bonanno, Alfio
2015-01-01
Asymptotically Safe theories of gravity have recently received much attention. In this work we discuss a class of inflationary models derived from quantum-gravity modification of quadratic gravity according to the induced scaling around the non-Gaussian fixed point at very high energies. It is argued that the presence of a three dimensional ultraviolet critical surface generates operators of non-integer power of the type $R^{2-\\theta/2}$ in the effective Lagrangian, where $\\theta>0$ is a critical exponent. The requirement of a successful inflationary model in agreement with the recent Planck 2015 data puts important constraints on the strenght of this new type of couplings.
A hypothesis-based algorithm for planning and control in non-Gaussian belief spaces
Platt, Robert, Jr.
2011-08-27
We consider the partially observable control problem where it is potentially necessary to perform complex information-gathering operations in order to localize state. One approach to solving these problems is to create ...
D. N. Vadiraja; A. D. Sahasrabudhe
2009-01-01
Structural modeling of rotating pre-twisted thin-walled composite beams with embedded macro fiber composite (MFC) actuators and sensors using higher shear deformation theory (HSDT) is presented in the present work. The governing system of equations is derived from Hamilton's principle and solution is obtained by extended Galerkin's method. Optimal control problem is solved using linear quadratic Gaussian (LQG) control algorithm. Vibration
High performance linear-quadratic and H-infinity designs for a 'supermaneuverable' aircraft
NASA Technical Reports Server (NTRS)
Voulgaris, Petros; Valavani, Lena
1989-01-01
Recent efforts by the National Aeronautics and Space Administration Langley Research Center have focused on expanding the flight envelope of the F/A-18 aircraft. Of particular concern has been the low speed, high angle-of-attack regime over which the conventional aerodynamic controls of the F/A-18 lose their effectiveness. In order to address this problem the F18 high alpha research vehicle was developed. This aircraft is essentially a modified F/A-18 which possesses thrust vectoring capabilities and hence increased maneuverability in this flight regime. The linear-quadratic-Gaussian with loop-transfer-recovery and H(infinity) design methodologies are used to design high performance controllers for the F18 at an operating point within the expanded envelope. In addition, how the control redundancy of the F18 can be used to maintain nominal performance, as well as nominal stability, in situations where failures occur, is shown.
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.
Optimal feedback control as a theory of motor coordination: Supplementary Notes
Todorov, Emanuel
, Michael I. Jordan 1. Optimal control of modified Linear-Quadratic-Gaussian (LQG) systems All simulations this problem. The state estimate is updated using a modified Kalman filter which takes into account that the iteration always converges exponentially, and to the same answer (regardless of initialization
LQG\\/LTR robust control of nuclear reactors with improved temperature performance
Adel Ben-Abdennour; Robert M. Edwards; Kwang Y. Lee
1992-01-01
The authors present the design of a robust controller using the linear quadratic Gaussian with loop transfer recovery (LQG\\/LTR) for nuclear reactors with the objective of maintaining a desirable performance for reactor fuel temperature and the temperature of the coolant leaving the reactor for a wide range of reactor powers. The results obtained are compared to those for an observer-based
Jongeun Choi; Joji Yamaguchi; Simon Morales; Roberto Horowitz; Yang Zhao; Arunava Majumdar
2003-01-01
In this paper, the design and control of a thermal stabilizing system for an optomechanical uncooled infrared (IR) imaging camera is presented, which uses an array of MEMS bimaterial cantilever beams to sense an IR image source. A one-dimensional lumped parameter model of the thermal stabilization system was derived and experimentally validated. A model-based discrete time linear quadratic gaussian regulator
Alvarez-Gaume, Luis; Kounnas, Costas; Lust, Dieter; Riotto, Antonio
2015-01-01
We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure $R^2$ theory is indeed ghost free. Then we point out that for flat backgrounds the pure $R^2$ theory propagates only a scalar massless mode and no spin-two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti-de Sitter, or by changing the long-distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string- or M-...
Luis Alvarez-Gaume; Alex Kehagias; Costas Kounnas; Dieter Lust; Antonio Riotto
2015-05-28
We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure $R^2$ theory is indeed ghost free. Then we point out that for flat backgrounds the pure $R^2$ theory propagates only a scalar massless mode and no spin-two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti-de Sitter, or by changing the long-distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string- or M-theory. We demonstrate that string theory on non-compact $CY_3$ manifolds, like a line bundle over $\\mathbb{CP}^2$, may indeed lead to gravity dynamics determined by a higher curvature action.
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]…
Generalized quadratic Liénard equations
S. Lynch
1998-01-01
In this article we give explicit formulae for the Liapunov quantities of generalized Liénard systems with either quadratic damping or restoring coefficients. These quantities provide necessary conditions in order for the origin to be a centre. Recent results are also presented for these systems.
A Quadratic Programming Bibliography
2001-02-27
Feb 27, 2001 ... programming is often used as the basis for ”program trading” where stocks are ..... this defect, the extension of the quadratic programming method is .... for such a behaviour to be accurately predicted and the previously mentioned ..... in the framework of the probabilistic adequacy assessment of large inter-.
Mating Siegel Quadratic Polynomials
Michael Yampolsky; Saeed Zakeri
1998-01-01
Let F be a quadratic rational map of the sphere which has two fixed Siegel disks with bounded type rotation numbers theta and nu. Using a new degree 3 Blaschke product model for the dynamics of F and an adaptation of complex a priori bounds for renormalization of critical circle maps, we prove that F can be realized as the
The explicit linear quadratic regulator for constrained systems
Alberto Bemporad; Manfred Morari; Vivek Dua; Efstratios N. Pistikopoulos
2002-01-01
We present a technique to compute the explicit state-feedback solution to both the xnite and inxnite horizon linear quadratic optimal control problem subject to state and input constraints. We show that this closed form solution is piecewise linear and continuous. As a practical consequence of the result, constrained linear quadratic regulation becomes attractive also for systems with high sampling rates,
Improved perturbation bounds for general quadratic matrix equations
M. M. Konstantinov; P. Hr. Petkov; D. W. Gu
1999-01-01
Perturbation analysis of general algebraic quadratic matrix equations is presented, which include as particular cases the standard and descriptor algebraic matrix Riccati equations, arising in the optimal control and filtering of continuous, time-invariant, linear systems. The perturbation bounds derived are superior to the bounds, already available in the literature. They are applicable to the error analysis of general quadratic matrix
Control for high-speed archimedean spiral nanopositioning
A. Kotsopoulos; Angeliki Pantazi; Theodore Antonakopoulos
2010-01-01
Scanning probes are being considered as the basis for a variety of emerging nanoscale applications including sample imaging and ultra-high-density probe storage. In this work, a controller for track-follow in Archimedean spiral nanopositioning is presented. The proposed tracking controller is based on a Linear Quadratic Gaussian (LQG) component and a tracking controller, extended with frequency-sliding peak filters in order to
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.
Gesture Recognition Using Quadratic Curves
Qiulei Dong; Yihong Wu; Zhanyi Hu
2006-01-01
This paper presents a novel method for human gesture recog- nition based on quadratic curves. Firstly, face and hands in the images are extracted by skin color and their central points are kept tracked by a modifled Greedy Exchange algorithm. Then in each trajectory, the cen- tral points are fltted into a quadratic curve and 6 invariants from this quadratic
Guises and disguises of quadratic divergences
NASA Astrophysics Data System (ADS)
Cherchiglia, A. L.; Vieira, A. R.; Hiller, Brigitte; Baęta Scarpelli, A. P.; Sampaio, Marcos
2014-12-01
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 ?. 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.
Non-gaussianity in axion Nflation models
Soo A. Kim; Andrew R. Liddle; David Seery
2010-01-01
We study perturbations in the multi-field axion Nflation model, taking\\u000aaccount of the full cosine potential. We find significant differences with\\u000aprevious analyses which made a quadratic approximation to the potential. The\\u000atensor-to-scalar ratio and the scalar spectral index move to lower values,\\u000awhich nevertheless provide an acceptable fit to observation. Most\\u000asignificantly, we find that the bispectrum non-gaussianity parameter
Smart base-isolated benchmark building Part III: a sample controller for bilinear isolation
Baris Erkus; Erik A. Johnson
2006-01-01
This paper presents a sample control design for the base isolated benchmark building with bilinear hys- teretic bearings ( e.g. , lead-rubber bearings). Since there is no well-defined control strategy for nonlinear structures, and available linear strategies are well-known among the civil engineering community, a linear quadratic Gaussian (LQG) controller is selected for this purpose. To utilize an LQG controller,
Neuromuscular stochastic optimal control of a tendon driven index finger model
Evangelos Theodorou; Emanuel Todorov; Francisco J. Valero-Cuevas
2011-01-01
Our long-term goal is to find control princi- ples to control robotic hands with dexterity and robustness comparable to that of the human hand. Here we explore a control strategy capable of accommodating the nonlinearities, high dimensionality and endogenous noise intrinsic to complex, tendon-driven biomechanical structures. We present the first stochastic optimal feedback controller (i.e., an iterative Linear Quadratic Gaussian
Main graphs: Quadratic equation
Utrecht, Universiteit
Main graphs: Quadratic equation: Equation A2 +B+C = 0, has solutions given by the following 'abc equations: Equation dN dt = kN has the solution: N(t) = N0ekt; N0 is an (arbitrary) initial value of N. Characteristic time of change is = 1/k. Systems of linear differential equations: For system dx dt = ax+by dy dt
Properties of quadratic equations and their application to power system analysis
Hiskens, Ian A.
Properties of quadratic equations and their application to power system analysis Y.V. Makarova,1 and control can be described by algebraic sets of quadratic equations of the form fx y gx 0 1 where x Rn x as a quadratic equations set with the Jacobian matrix Jx being a linear function of unknown variables. In any
Lesson 17: Quadratic Inequalities
NSDL National Science Digital Library
2011-01-01
The lesson begins with using graphs to solve quadratic inequalities. AN equation modeling the height of a rocket is graphed along with a second equation that represents the minimum height at which the rocket can legally and safely be exploded. The intersections of the graphs provide the solution interval. A second method is then presented where the inequality is put into standard form and then solved for its x-intercepts. Interval notation and union of sets is reviewed before a purely algebraic procedure for solving the inequalities is presented. The lesson concludes with an application problem.
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.
Solving quadratic equations using reduced unimodular quadratic forms
Denis Simon
2005-01-01
Let Q be an n × n symmetric matrix with integral entries and with detQ ?= 0, but not necesarily positive definite. We describe a generalized LLL algorithm to reduce this quadratic form. This algorithm either reduces the quadratic form or stops with some isotropic vector. It is proved to run in polynomial time. We also describe an algorithm for
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.
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 degrees rotation, was measured in the experiments performed. The parameters relevant for characterizing soliton collision processes were also studied in detail. Measurements were performed for various collision angles (from 0.2 to 4 degrees), phase mismatch, relative phase between the solitons and the distance to the collision point within the sample (which affects soliton formation). Both the individual and combined effects of these collision variables were investigated. Based on the research conducted, several all-optical switching scenarios were proposed.
Manfred Knebusch Specialization of Quadratic
= 2. It served me in the first place as the foundation for a theory of generic splitting of quadratic-Kahn-Karpenko- Vishik for instance. One should note that there exists a theory of (partial) generic splitting of central a specialization theory of quadratic and symmetric bilinear forms with respect to a place ~: K ! L [ 1, without
Manfred Knebusch Specialization of Quadratic
#= 2. It served me in the first place as the foundation for a theory of generic splitting of quadratic) generic splitting of central simple algebras and reductive algebraic groups, parallel to the theory during a talk by T.Y. Lam on field invariants from the theory of quadratic forms. 1 It is -- poetic
Gaussian cloning of coherent states with known phases
Alexanian, Moorad [Department of Physics and Physical Oceanography, University of North Carolina at Wilmington, Wilmington, North Carolina 28403 (United States)
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.
Chun-Yao Lien; Tse-Wei Wang
1988-01-01
In previous work by T.W. Wang et al. (1987) the robust multivariable linear quadratic Gaussian\\/loop transfer recovery (LQG\\/LTR) control design methodology was used in designing for the control of the linearized version of a generalized nonlinear bacterial growth system. Here, the effect of applying an extended Kalman filter (EKF) in conjunction with the same linear feedback regulator in the control
Gaussian process based recursive system identification
NASA Astrophysics Data System (ADS)
Prüher, Jakub; Šimandl, Miroslav
2014-12-01
This paper is concerned with the problem of recursive system identification using nonparametric Gaussian process model. Non-linear stochastic system in consideration is affine in control and given in the input-output form. The use of recursive Gaussian process algorithm for non-linear system identification is proposed to alleviate the computational burden of full Gaussian process. The problem of an online hyper-parameter estimation is handled using proposed ad-hoc procedure. The approach to system identification using recursive Gaussian process is compared with full Gaussian process in terms of model error and uncertainty as well as computational demands. Using Monte Carlo simulations it is shown, that the use of recursive Gaussian process with an ad-hoc learning procedure offers converging estimates of hyper-parameters and constant computational demands.
Linear and quadratic programming neural network analysis.
Maa, C Y; Shanblatt, M A
1992-01-01
Neural networks for linear and quadratic programming are analyzed. The network proposed by M.P. Kennedy and L.O. Chua (IEEE Trans. Circuits Syst., vol.35, pp.554-562, May 1988) is justified from the viewpoint of optimization theory and the technique is extended to solve optimization problems, such as the least-squares problem. For quadratic programming, the network converges either to an equilibrium or to an exact solution, depending on whether the problem has constraints or not. The results also suggest an analytical approach to solve the linear system Bx =b without calculating the matrix inverse. The results are directly applicable to optimization problems with C(2) convex objective functions and linear constraints. The dynamics and applicability of the networks are demonstrated by simulation. The distance between the equilibria of the networks and the problem solutions can be controlled by the appropriate choice of a network parameter. PMID:18276458
Performance study of multi-rate output controllers under noise disturbances
MENG J. ER; BRIAN D. O. ANDERSON
1992-01-01
This paper presents a comparative study of the performance of a multi-rate output controller (MROC) with a linear quadratic gaussian (LQG) controller in the presence of noise disturbances and anti-aliasing filters. The basis of comparison is to apply an LQG law with a one-step-ahead prediction-type Kalman filter (hereafter called LQG law I) and an LQG law with a current estimation-type
The Solution of Quadratic Equations
E. Cuthbert Atkinson
1898-01-01
IN your issue of February 24 a review appears of ``Chambers's Algebra for Schools.'' Your reviewer concludes with a lament of the probable uselessness of protesting against the method of solving quadratics by ``completing the square.''
An Investigation on Quadratic Equations.
ERIC Educational Resources Information Center
Hirst, Keith
1988-01-01
Argues that exploring a familiar topic or examination question in a novel manner is a useful way to find topics for mathematical investigation in the classroom. The example used to illustrate the premise is a quadratic equation. (PK)
Quadratics, polynomial form in y
NSDL National Science Digital Library
ExploreMath.com
2001-01-01
Explore the graph of a quadratic of the form x = ay2 + by + c. Vary the coefficients of the equation and examine how the graph changes in response. Calculate the location of the vertex and y-intercepts.
Reactive-power dispatch by successive quadratic programming
Quintana, V.H. (Waterloo Univ., ON (Canada)); Santos-Nieto, M. (Energy Management Systems Div., Control Data Corp., Plymouth, MN (US))
1989-09-01
In this paper the reactive-power dispatch is formulated as the minimization of real-power losses in the system, utilizing a full set of control variables: generator voltages, switchable shunt susceptances and transformer taps. The solution of the loss problem is obtained by successively solving quadratic programming problems. First- and second-order loss sensitivity coefficients are derived for the quadratic problem formulation. The derivations are based on the Jacobian method for sensitivity calculations. Sensitivity relations for the dependent constraints are based on the complete reactive-power model of the fast decoupled load flow method. The active-set projection method for quadratic programming is described and utilized as the solution algorithm for the quadratic reactive-power dispatch problems. Tests are conducted on the IEEE 30-bus and Mexican 253-bus systems. A discussion of the computer results is also presented.
Detecting and Solving Hyperbolic Quadratic Eigenvalue Problems
Higham, Nicholas J.
, overdamped, weakly overdamped, quadratic matrix polynomial, quadratic matrix equation, solvent, cyclicDetecting and Solving Hyperbolic Quadratic Eigenvalue Problems Chun-Hua Guo, Nicholas J. Higham1613 DETECTING AND SOLVING HYPERBOLIC QUADRATIC EIGENVALUE PROBLEMS CHUN-HUA GUO, NICHOLAS J. HIGHAM, AND FRANC
Real Homotopies 1 Quadratic Turning Points
Verschelde, Jan
Real Homotopies 1 Quadratic Turning Points deforming real polynomials quadratic turning points 2 shooting for a turning point MCS 563 Lecture 13 Analytic Symbolic Computation Jan Verschelde, 12 February Homotopies 1 Quadratic Turning Points deforming real polynomials quadratic turning points 2 The Newtonian n
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.
Sparse gaussian graphical models for speech recognition.
Bell, Peter; King, Simon
2007-01-01
We address the problem of learning the structure of Gaussian graphical models for use in automatic speech recognition, a means of controlling the form of the inverse covariance matrices of such systems. With particular focus on data sparsity issues...
Attitude and vibration control of a large flexible space-based antenna
NASA Technical Reports Server (NTRS)
Joshi, S. M.
1982-01-01
Control systems synthesis is considered for controlling the rigid body attitude and elastic motion of a large deployable space-based antenna. Two methods for control systems synthesis are considered. The first method utilizes the stability and robustness properties of the controller consisting of torque actuators and collocated attitude and rate sensors. The second method is based on the linear-quadratic-Gaussian control theory. A combination of the two methods, which results in a two level hierarchical control system, is also briefly discussed. The performance of the controllers is analyzed by computing the variances of pointing errors, feed misalignment errors and surface contour errors in the presence of sensor and actuator noise.
Quadratic stabilization and tracking - Applications to the benchmark problem
NASA Technical Reports Server (NTRS)
Schmitendorf, W. E.; Dolphus, R. M.; Benson, R. W.
1992-01-01
Recent results regarding quadratic stabilization and disturbance attenuation are applied to the benchmark problem. The authors investigate the minimum achievable levels of disturbance attenuation for different disturbance inputs and controlled outputs. They then design a feedforward tracking controller which tracks step inputs while maintaining the disturbance attenuation properties of the regulator.
Circuit analog of quadratic optomechanics
Eun-jong Kim; J. R. Johansson; Franco Nori
2014-12-22
We propose a superconducting electrical circuit that simulates a quadratic optomechanical system. A capacitor placed between two transmission-line (TL) resonators acts like a semi-transparent membrane, and a superconducting quantum interference device (SQUID) that terminates a TL resonator behaves like a movable mirror. Combining these circuit elements, it is possible to simulate a quadratic optomechanical coupling whose coupling strength is determined by the coupling capacitance and the tunable bias flux through the SQUIDs. Estimates using realistic parameters suggest that an improvement in the coupling strength could be realized, to five orders of magnitude from what has been observed in membrane-in-the-middle cavity optomechanical systems. This leads to the possibility of achieving the strong-coupling regime of quadratic optomechanics.
Circuit analog of quadratic optomechanics
NASA Astrophysics Data System (ADS)
Kim, Eun-jong; Johansson, J. R.; Nori, Franco
2015-03-01
We propose a superconducting electrical circuit that simulates a quadratic optomechanical system. A capacitor placed between two transmission-line (TL) resonators acts like a semitransparent membrane, and a superconducting quantum interference device (SQUID) that terminates a TL resonator behaves like a movable mirror. Combining these circuit elements, it is possible to simulate a quadratic optomechanical coupling whose coupling strength is determined by the coupling capacitance and the tunable bias flux through the SQUIDs. Estimates using realistic parameters suggest that an improvement in the coupling strength could be realized, to five orders of magnitude from what has been observed in membrane-in-the-middle cavity optomechanical systems. This leads to the possibility of achieving the strong-coupling regime of quadratic optomechanics.
Estimation of Clustering Parameters Using Gaussian Process Regression
Rigby, Paul; Pizarro, Oscar; Williams, Stefan B.
2014-01-01
We propose a method for estimating the clustering parameters in a Neyman-Scott Poisson process using Gaussian process regression. It is assumed that the underlying process has been observed within a number of quadrats, and from this sparse information the distribution is modelled as a Gaussian process. The clustering parameters are then estimated numerically by fitting to the covariance structure of the model. It is shown that the proposed method is resilient to any sampling regime. The method is applied to simulated two-dimensional clustered populations and the results are compared to a related method from the literature. PMID:25383766
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.
Charalambos D. Charalambous; Joseph L. Hibey
1996-01-01
This paper is concerned with the application of a minimum principle derived for general nonlinear partially observable exponential-of-integral control problems, to solve linear-exponential-quadratic-Gaussian problems. This minimum principle is the stochastic analog of Pontryagin's minimum principle for deterministic systems. It consists of an information state equation, an adjoint process governed by a stochastic partial differential equation with terminal condition, and a
Manfred Knebusch Specialization of Quadratic
, and therefore also K, had characteristic #= 2. It served me in the first place as the foundation for a theory a theory of (partial) generic splitting of central simple algebras and reductive algebraic groups, parallel the theory of quadratic forms. 1 It is -- poetic exaggeration allowed -- a suitable motto for this monograph
New quadratic baryon mass relations
Burakovsky, L.; Goldman, T. [Theoretical Division, MS B285, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)] [Theoretical Division, MS B285, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Horwitz, L.P. [School of Physics and Astronomy, Tel-Aviv University, Ramat-Aviv, 69978 (Israel)] [School of Physics and Astronomy, Tel-Aviv University, Ramat-Aviv, 69978 (Israel)
1997-12-01
By assuming the existence of (quasi)linear baryon Regge trajectories, we derive new quadratic Gell-Mann{endash}Okubo-type baryon mass relations. These relations are used to predict the masses of the charmed baryons absent from the baryon summary table so far, in good agreement with the predictions of many other approaches. {copyright} {ital 1997} {ital The American Physical Society}
Gaussian entanglement of formation
Wolf, M.M. [Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Strasse 1, Garching, D-85748 (Germany); Institut fuer Mathematische Physik, Mendelssohnstrasse. 3, D-38106 Braunschweig (Germany); Giedke, G. [Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Strasse 1, Garching, D-85748 (Germany); Institut fuer Quantenelektronik, ETH Zuerich, Wolfgang-Pauli-Strasse 16, CH-8093 Zurich (Switzerland); Krueger, O.; Werner, R. F. [Institut fuer Mathematische Physik, Mendelssohnstrasse. 3, D-38106 Braunschweig (Germany); Cirac, J.I. [Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Strasse 1, Garching, D-85748 (Germany)
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.
OPTICAL SOLITONS: Excitation of two-dimensional soliton matrices by fundamental Gaussian beams
NASA Astrophysics Data System (ADS)
Borovkova, O. V.; Chuprakov, D. A.; Sukhorukov, Anatolii P.
2005-01-01
The excitation of two-dimensional periodic structures of fields of the first and second radiation harmonics due to the modulation instability of fundamental Gaussian beams is studied in a medium with a quadratic nonlinearity. The distances are found at which soliton matrix structures with a specified period are formed and destroyed. Optical gratings formed due to nonlinear aberration of broad Gaussian beams are considered.
Aeroelastic control of oblique-wing aircraft
NASA Technical Reports Server (NTRS)
Burken, J. J.; Alag, G. S.; Gilyard, G. B.
1986-01-01
The U.S. Navy and NASA are currently involved in the design and development of an unsymmetric-skew-wing aircraft capable of 65 deg wing sweep and flight at Mach 1.6. A generic skew-wing aircraft model was developed for 45 deg wing skew at a flight condition of Mach 0.70 and 3048 m altitude. At this flight condition the aircraft has a wing flutter mode. An active implementable control law was developed using the linear quadratic Gaussian design technique. A method of modal residualization was used to reduce the order of the controller used for flutter suppression.
ON QUADRATIC POLYNOMIALS. by F. Lazebnik.
Lazebnik, Felix
not exist. 3. Quadratic equations. Another most useful applications of the completion of the square in the "completed square form", and this made the finding of its minimum or maximum easy. In case when the quadratic transformation is that it allows to derive a formula for solving quadratic equations or show that no solutions
Stephen F Austin Linear, Quadratic, Polynomial,
Hubbard, Keith
the useful algebraic operation of completing the square, and how to solve quadratic equations. Then we sections--one discusses com- plex numbers (needed to solve arbitrary quadratic equations) and one dis- cusses systems of equations and matrices. 117 #12;Stephen F Austin 118 chapter 2 Linear, Quadratic
Quadratic Residues a is a quadratic residue mod m if x2
Ikenaga, Bruce
if the following equation has a solution: x2 = a (mod m) . Otherwise, a is a quadratic nonresidue mod m. Example. 8 a quadratic equation mod p has at most two solutions (Prove it!), there are exactly two. Example. x2 = 8 (mod6-21-2013 Quadratic Residues · a is a quadratic residue mod m if x2 = a (mod m). Otherwise
Quadratic stability analysis of the Takagi-Sugeno fuzzy model
Kiriakos Kiriakidis; Apostolos Grivas; Anthony Tzes
1998-01-01
The nonlinear dynamic Takagi-Sugeno fuzzy model with offset terms is analyzed as a perturbed linear system. A sufficient criterion for the robust stability of this nominal system against nonlinear perturbations guarantees quadratic stability of the fuzzy model. The criterion accepts a convex programming formulation of reduced computational cost compared to the common Lyapunov matrix approach. Parametric robust control techniques suggest
Linear quadratic regulators with eigenvalue placement in a horizontal strip
NASA Technical Reports Server (NTRS)
Shieh, Leang S.; Dib, Hani M.; Ganesan, Sekar
1987-01-01
A method for optimally shifting the imaginary parts of the open-loop poles of a multivariable control system to the desirable closed-loop locations is presented. The optimal solution with respect to a quadratic performance index is obtained by solving a linear matrix Liapunov equation.
Rational quadratic Bézier curve fitting by simulated annealing technique
NASA Astrophysics Data System (ADS)
Mohamed, Najihah; Abd Majid, Ahmad; Mt Piah, Abd Rahni
2013-04-01
A metaheuristic algorithm, which is an approximation method called simulated annealing is implemented in order to have the best rational quadratic Bézier curve from a given data points. This technique is used to minimize sum squared errors in order to improve the middle control point position and the value of weight. As a result, best fitted rational quadratic Bézier curve and its mathematical function that represents all the given data points is obtained. Numerical and graphical examples are also presented to demonstrate the effectiveness and robustness of the proposed method.
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.
No-activation theorem for Gaussian nonclassical correlations by Gaussian operations
NASA Astrophysics Data System (ADS)
Mišta, Ladislav; McNulty, Daniel; Adesso, Gerardo
2014-08-01
We study general quantum correlations of continuous variable Gaussian states and their interplay with entanglement. Specifically, we investigate the existence of a quantum protocol activating all nonclassical correlations between the subsystems of an input bipartite continuous variable system, into output entanglement between the system and a set of ancillae. For input Gaussian states, we prove that such an activation protocol cannot be accomplished with Gaussian operations, as the latter are unable to create any output entanglement from an initial separable yet nonclassical state in a worst-case scenario. We then construct a faithful non-Gaussian activation protocol, encompassing infinite-dimensional generalizations of controlled-not gates to generate entanglement between system and ancillae, in direct analogy with the finite-dimensional case. We finally calculate the negativity of quantumness, an operational measure of nonclassical correlations defined in terms of the performance of the activation protocol, for relevant classes of two-mode Gaussian states.
Geometrical Solutions of Quadratic Equations.
ERIC Educational Resources Information Center
Grewal, A. S.; Godloza, L.
1999-01-01
Demonstrates that the equation of a circle (x-h)2 + (y-k)2 = r2 with center (h; k) and radius r reduces to a quadratic equation x2-2xh + (h2 + k2 -r2) = O at the intersection with the x-axis. Illustrates how to determine the center of a circle as well as a point on a circle. (Author/ASK)
Quadratic algebras and integrable chains
F. Soloviev
2009-10-26
Using Krichever-Phong's universal formula, we show that a multiplicative representation linearizes Sklyanin quadratic brackets for a multi-pole Lax function with a spectral parameter. The spectral parameter can be either rational or elliptic. As a by-product, we obtain an extension of a Sklyanin algebra in the elliptic case. Krichever-Phong's formula provides a hierarchy of symplectic structures, and we show that there exists a non-trivial cubic bracket in Sklyanin's case.
Second-order phase transition in lambdař24 with non-gaussian variational approximation
L. Polley; U. Ritschel
1989-01-01
We study the ř24 model in the continuum. Approximations for the effective potential and the global ground state are computed variationally using trial states which are quartic exponentials rather than gaussians (quadratic exponentials). We observe a second-order phase transition at gl=6.88 which is in good agreement with existing calculations. Supported by Bundesministerium für Forschung und Technologie.
Complex Gaussian Multiplicative Chaos
NASA Astrophysics Data System (ADS)
Lacoin, Hubert; Rhodes, Rémi; Vargas, Vincent
2015-07-01
In this article, we study complex Gaussian multiplicative chaos. More precisely, we study the renormalization theory and the limit of the exponential of a complex log-correlated Gaussian field in all dimensions (including Gaussian Free Fields in dimension 2). Our main working assumption is that the real part and the imaginary part are independent. We also discuss applications in 2 D string theory; in particular we give a rigorous mathematical definition of the so-called Tachyon fields, the conformally invariant operators in critical Liouville Quantum Gravity with a c = 1 central charge, and derive the original KPZ formula for these fields.
Reduced-order model based feedback control of the modified Hasegawa-Wakatani model
Goumiri, I. R.; Rowley, C. W.; Ma, Z. [Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544 (United States); Gates, D. A.; Krommes, J. A.; Parker, J. B. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08544 (United States)
2013-04-15
In this work, the development of model-based feedback control that stabilizes an unstable equilibrium is obtained for the Modified Hasegawa-Wakatani (MHW) equations, a classic model in plasma turbulence. First, a balanced truncation (a model reduction technique that has proven successful in flow control design problems) is applied to obtain a low dimensional model of the linearized MHW equation. Then, a model-based feedback controller is designed for the reduced order model using linear quadratic regulators. Finally, a linear quadratic Gaussian controller which is more resistant to disturbances is deduced. The controller is applied on the non-reduced, nonlinear MHW equations to stabilize the equilibrium and suppress the transition to drift-wave induced turbulence.
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.
Explicit Solution to a Certain Non-ELQG Risk-sensitive Stochastic Control Problem
Hata, Hiroaki, E-mail: hata@math.sinica.edu.t [Academia Sinica, Institute of Mathematics (China); Sekine, Jun, E-mail: sekine@kier.kyoto-u.ac.j [Kyoto University, Institute of Economic Research (Japan)
2010-12-15
A risk-sensitive stochastic control problem with finite/infinite horizon is studied with a 1-dimensional controlled process defined by a linear SDE with a linear control-term in the drift. In the criterion function, a non-linear/quadratic term is introduced by using the solution to a Riccati differential equation, and hence, the problem is not ELQG (Exponential Linear Quadratic Gaussian) in general. For the problem, optimal value and control are calculated in explicit forms and the set of admissible risk-sensitive parameters is given in a concrete form. As applications, two types of large deviations control problems, i.e., maximizing an upside large deviations probability and minimizing a downside large deviations probability, are mentioned.
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.
NASA Astrophysics Data System (ADS)
Tang, Chun-Ming; Jian, Jin-Bao
2008-10-01
Based on an augmented Lagrangian line search function, a sequential quadratically constrained quadratic programming method is proposed for solving nonlinearly constrained optimization problems. Compared to quadratic programming solved in the traditional SQP methods, a convex quadratically constrained quadratic programming is solved here to obtain a search direction, and the Maratos effect does not occur without any other corrections. The "active set" strategy used in this subproblem can avoid recalculating the unnecessary gradients and (approximate) Hessian matrices of the constraints. Under certain assumptions, the proposed method is proved to be globally, superlinearly, and quadratically convergent. As an extension, general problems with inequality and equality constraints as well as nonmonotone line search are also considered.
Valeriano Parravicini; Carla Morri; Giada Ciribilli; Monica Montefalcone; Giancarlo Albertelli; Carlo Nike Bianchi
2009-01-01
The performances of two commonly used non-destructive sampling procedures for rocky benthic assemblages (i.e. photography and visually assessed quadrats) were compared. A damaging human activity, date mussel (Lithophaga lithophaga) harvesting (DMH), was chosen. Directly impacted sites were compared with reference conditions (controls). Both visual quadrats and photography were equally able to detect differences between impacted situations and controls. However, visual
Ebrahim Karimi; Gianluigi Zito; Bruno Piccirillo; Lorenzo Marrucci; Enrico Santamato
2007-12-05
We studied a novel family of paraxial laser beams forming an overcomplete yet nonorthogonal set of modes. These modes have a singular phase profile and are eigenfunctions of the photon orbital angular momentum. The intensity profile is characterized by a single brilliant ring with the singularity at its center, where the field amplitude vanishes. The complex amplitude is proportional to the degenerate (confluent) hypergeometric function, and therefore we term such beams hypergeometric gaussian (HyGG) modes. Unlike the recently introduced hypergeometric modes (Opt. Lett. {\\textbf 32}, 742 (2007)), the HyGG modes carry a finite power and have been generated in this work with a liquid-crystal spatial light modulator. We briefly consider some sub-families of the HyGG modes as the modified Bessel Gaussian modes, the modified exponential Gaussian modes and the modified Laguerre-Gaussian modes.
Karimi, Ebrahim; Piccirillo, Bruno; Marrucci, Lorenzo; Santamato, Enrico
2007-01-01
We studied a novel family of paraxial laser beams forming an overcomplete yet nonorthogonal set of modes. These modes have a singular phase profile and are eigenfunctions of the photon orbital angular momentum. The intensity profile is characterized by a single brilliant ring with the singularity at its center, where the field amplitude vanishes. The complex amplitude is proportional to the degenerate (confluent) hypergeometric function, and therefore we term such beams hypergeometric gaussian (HyGG) modes. Unlike the recently introduced hypergeometric modes (Opt. Lett. {\\textbf 32}, 742 (2007)), the HyGG modes carry a finite power and have been generated in this work with a liquid-crystal spatial light modulator. We briefly consider some sub-families of the HyGG modes as the modified Bessel Gaussian modes, the modified exponential Gaussian modes and the modified Laguerre-Gaussian modes.
David Langlois
2011-01-01
This contribution gives an overview on primordialnon-Gaussianities from a theoretical perspective. After presenting a general formalism to describe nonlinear cosmological perturbations, several classes of models, illustrated with examples, are discussed: multi-field inflation with non-standard Lagrangians, modulaton fields, curvaton fields. In the latter case, a special emphasis is put on the isocurvature perturbations, which could leave a specific signature in non-Gaussianities.
Gray, Morgan; Petit, Cyril; Rodionov, Sergey; Bocquet, Marc; Bertino, Laurent; Ferrari, Marc; Fusco, Thierry
2014-08-25
We propose a new algorithm for an adaptive optics system control law, based on the Linear Quadratic Gaussian approach and a Kalman Filter adaptation with localizations. It allows to handle non-stationary behaviors, to obtain performance close to the optimality defined with the residual phase variance minimization criterion, and to reduce the computational burden with an intrinsically parallel implementation on the Extremely Large Telescopes (ELTs). PMID:25321291
NASA Astrophysics Data System (ADS)
Weedbrook, Christian; Pirandola, Stefano; García-Patrón, Raúl; Cerf, Nicolas J.; Ralph, Timothy C.; Shapiro, Jeffrey H.; Lloyd, Seth
2012-04-01
The science of quantum information has arisen over the last two decades centered on the manipulation of individual quanta of information, known as quantum bits or qubits. Quantum computers, quantum cryptography, and quantum teleportation are among the most celebrated ideas that have emerged from this new field. It was realized later on that using continuous-variable quantum information carriers, instead of qubits, constitutes an extremely powerful alternative approach to quantum information processing. This review focuses on continuous-variable quantum information processes that rely on any combination of Gaussian states, Gaussian operations, and Gaussian measurements. Interestingly, such a restriction to the Gaussian realm comes with various benefits, since on the theoretical side, simple analytical tools are available and, on the experimental side, optical components effecting Gaussian processes are readily available in the laboratory. Yet, Gaussian quantum information processing opens the way to a wide variety of tasks and applications, including quantum communication, quantum cryptography, quantum computation, quantum teleportation, and quantum state and channel discrimination. This review reports on the state of the art in this field, ranging from the basic theoretical tools and landmark experimental realizations to the most recent successful developments.
NASA Astrophysics Data System (ADS)
Zhou, GuoQuan; Cai, YangJian; Dai, ChaoQing
2013-05-01
A kind of hollow vortex Gaussian beam is introduced. Based on the Collins integral, an analytical propagation formula of a hollow vortex Gaussian beam through a paraxial ABCD optical system is derived. Due to the special distribution of the optical field, which is caused by the initial vortex phase, the dark region of a hollow vortex Gaussian beam will not disappear upon propagation. The analytical expressions for the beam propagation factor, the kurtosis parameter, and the orbital angular momentum density of a hollow vortex Gaussian beam passing through a paraxial ABCD optical system are also derived, respectively. The beam propagation factor is determined by the beam order and the topological charge. The kurtosis parameter and the orbital angular momentum density depend on beam order n, topological charge m, parameter ?, and transfer matrix elements A and D. As a numerical example, the propagation properties of a hollow vortex Gaussian beam in free space are demonstrated. The hollow vortex Gaussian beam has eminent propagation stability and has crucial application prospects in optical micromanipulation.
Gravitational Energy in Quadratic-Curvature Gravities
S. Deser; Bayram Tekin
2002-01-01
We define energy (E) and compute its values for gravitational systems involving terms quadratic in curvature. There are significant differences, both conceptually and concretely, from Einstein theory. For D=4, all purely quadratic models admit constant curvature vacua with arbitrary Lambda, and E is the ``cosmological'' Abbott-Deser (AD) expression; instead, E always vanishes in flat, Lambda=0, background. For combined Einstein-quadratic curvature
Geometrical and Graphical Solutions of Quadratic Equations.
ERIC Educational Resources Information Center
Hornsby, E. John, Jr.
1990-01-01
Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)
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.
Quadratic Isocurvature Cross-Correlation, Ward Identity, and Dark Matter
Daniel J. H. Chung; Hojin Yoo; Peng Zhou
2013-03-25
Sources of isocurvature perturbations and large non-Gaussianities include field degrees of freedom whose vacuum expectation values are smaller than the expansion rate of inflation. The inhomogeneities in the energy density of such fields are quadratic in the fields to leading order in the inhomogeneity expansion. Although it is often assumed that such isocurvature perturbations and inflaton-driven curvature perturbations are uncorre- lated, this is not obvious from a direct computational point of view due to the form of the minimal gravitational interactions. We thus compute the irreducible gravitational contributions to the quadratic isocurvature-curvature cross-correlation. We find a small but non-decaying cross-correlation, which in principle serves as a consistency prediction of this large class of isocurvature perturbations. We apply our cross-correlation result to two dark matter isocurvature perturbation scenarios: QCD axions and WIMPZILLAs. On the technical side, we utilize a gravita- tional Ward identity in a novel manner to demonstrate the gauge invariance of the computation. Furthermore, the detailed computation is interpreted in terms of a soft-{\\zeta} theorem and a gravitational Ward identity. Finally, we also identify explicitly all the counterterms that are necessary for renormalizing the isocurvature perturbation composite operator in inflationary cosmological backgrounds.
Wortman, Kevin
Quadratic Equations and Conics A quadratic equation in two variables is an equation that's equivalent to an equation of the form p(x, y) = 0 where p(x, y) is a quadratic polynomial. Examples. · 4x2 - 3xy - 2y2 + x - y + 6 = 0 is a quadratic equation, as are x2 - y2 = 0 and x2 + y2 = 0 and x2 - 1 = 0
Operational discord measure for Gaussian states with Gaussian measurements
NASA Astrophysics Data System (ADS)
Rahimi-Keshari, Saleh; Ralph, Timothy C.; Caves, Carlton M.
2015-06-01
We introduce an operational discord-type measure for quantifying nonclassical correlations in bipartite Gaussian states based on using Gaussian measurements. We refer to this measure as operational Gaussian discord (OGD). It is defined as the difference between the entropies of two conditional probability distributions associated to one subsystem, which are obtained by performing optimal local and joint Gaussian measurements. We demonstrate the operational significance of this measure in terms of a Gaussian quantum protocol for extracting maximal information about an encoded classical signal. As examples, we calculate OGD for several Gaussian states in the standard form.
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.
Non-Gaussianities in Multi-field Inflation
Thorsten Battefeld; Richard Easther
2007-03-02
We compute the amplitude of the non-Gaussianities in inflationary models with multiple, uncoupled scalar fields. This calculation thus applies to all models of assisted inflation, including N-flation, where inflation is driven by multiple axion fields arising from shift symmetries in a flux stabilized string vacuum. The non-Gaussianities are associated with nonlinear evolution of the field (and density) perturbations, characterized by the parameter $f_{NL}$. We derive a general expression for the nonlinear parameter, incorporating the evolution of perturbations after horizon-crossing. This is valid for arbitrary separable potentials during slow roll. To develop an intuitive understanding of this system and to demonstrate the applicability of the formalism we examine several cases with quadratic potentials: two-field models with a wide range of mass ratios, and a general N-field model with a narrow mass spectrum. We uncover that $f_{NL}$ is suppressed as the number of e-foldings grows, and that this suppression is increased in models with a broad spectrum of masses. On the other hand, we find no enhancement to $f_{NL}$ that increases with the number of fields. We thus conclude that the production of a large non-Gaussian signal in multi-field models of inflation is very unlikely as long as fields are slowly rolling and potentials are of simple, quadratic form. Finally, we compute a spectrum for the scalar spectral index that incorporates the nonlinear corrections to the fields' evolution.
Xiu-Xiang Chu; Ze-Jin Liu; Yi Wu
2010-01-01
The relay propagation of Gaussian-Schell-model in turbulent atmosphere along a slant path is studied in this paper. Based on the extended Huygens-Fresnel principle and a quadratic approximation, an analytical formula of average intensity for Gaussian-Schell-model beams in turbulent atmosphere along a slant path is derived, and some special cases are discussed. From the study and the comparison with the direct
Mohammad Ali Maddah-Ali; David N. C. Tse
2009-01-01
The rate-distortion region for the distributed source coding of the three jointly-Gaussian tree-structured sources with the quadratic distortion measure, is characterized within a constant gap. As a simplified counterpart of the Gaussian problem, we first investigate the rate region of a three binary-expanded sources where each pair of the sources have a certain number of the most-significant bits in common,
Spinor condensates with a laser-induced quadratic Zeeman effect
Santos, L. [Institut fuer Theoretische Physik, Leibniz Universitaet Hannover, Appelstr. 2, D-30167 Hannover (Germany); Fattori, M.; Stuhler, J.; Pfau, T. [5. Physikalisches Institut, Universitaet Stuttgart, Pfaffenwaldring 57 V, D-70550 Stuttgart (Germany)
2007-05-15
We show that an effective quadratic Zeeman effect for trapped atoms can be generated by proper laser configurations and, in particular, by the dipole trap itself. The induced quadratic Zeeman effect leads to a rich ground-state phase diagram, e.g., for a degenerate {sup 52}Cr gas, can be used to induce topological defects by controllably quenching across transitions between phases of different symmetries, allows for the observability of the Einstein-de Haas effect for relatively large magnetic fields, and may be employed to create S=1/2 systems with spinor dynamics. Similar ideas could be explored in other atomic species opening an exciting new control tool in spinor systems.
Ikenaga, Bruce
is a root of a quadratic equation with integer coefficients. · Quadratic irrationals can be expressed. Definition. A quadratic irrational is an irrational number which is a root of a quadratic equation ax2 + bx)2 = q, r2 x2 - 2rpx + (p2 - q) = 0. This is a quadratic equation with integer coefficients, and r2
Detecting and Solving Hyperbolic Quadratic Eigenvalue Problems
Chun-Hua Guo; Nicholas J. Higham; Françoise Tisseur
2008-01-01
Hyperbolic quadratic matrix polynomials Q(? )= ?2A + ?B + C are an important class of Hermitian matrix polynomials with real eigenvalues, among which the overdamped quadratics are those with nonpositive eigenvalues. Neither the definition of overdamped nor any of the standard characterizations provides an efficient way to test if a given Q has this property. We show that a
An Unexpected Influence on a Quadratic
ERIC Educational Resources Information Center
Davis, Jon D.
2013-01-01
Using technology to explore the coefficients of a quadratic equation can lead to an unexpected result. This article describes an investigation that involves sliders and dynamically linked representations. It guides students to notice the effect that the parameter "a" has on the graphical representation of a quadratic function in the form…
Existence Theorems for Some Quadratic Integral Equations
Józef Bana?; Millenia Lecko; Wagdy Gomaa El-Sayed
1998-01-01
Using the theory of measures of noncompactness, we prove a few existence theorems for some quadratic integral equations. The class of quadratic integral equations considered below contains as a special case numerous integral equations encountered in the theories of radiative transfer and neutron transport, and in the kinetic theory of gases. In particular, the well-known Chandrasekhar integral equation also belongs
Quadratic dynamics in binary number systems
Paul E. Fishback
2005-01-01
We describe the quadratic dynamics in certain two-component number systems, which like the complex numbers, can be expressed as rings of two by two real matrices. This description is accomplished using the properties of the real quadratic family and its derivative. We also demonstrate that the Mandelbrot set for any of these systems may be defined in two equivalent ways
On Quadratic Bent Functions in Polynomial Forms
Honggang Hu; Dengguo Feng
2007-01-01
In this correspondence, we construct some new quadratic bent functions in polynomial forms by using the theory of quadratic forms over finite fields. The results improve some previous work. Moreover, we solve a problem left by Yu and Gong in 2006.
Best Quadratic Approximations of Cubic Boolean Functions
, n). Key words: Bent functions; boolean functions; covering radius; lower order approximationsBest Quadratic Approximations of Cubic Boolean Functions Nicholas Kolokotronis1,2, Konstantinos of Boolean functions is treated in this paper. We focus on the case of best quadratic approximations
Single-photon quadratic optomechanics
Jie-Qiao Liao; Franco Nori
2014-09-10
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.
NASA Technical Reports Server (NTRS)
Dembo, Amir
1989-01-01
Pinsker and Ebert (1970) proved that in channels with additive Gaussian noise, feedback at most doubles the capacity. Cover and Pombra (1989) proved that feedback at most adds half a bit per transmission. Following their approach, the author proves that in the limit as signal power approaches either zero (very low SNR) or infinity (very high SNR), feedback does not increase the finite block-length capacity (which for nonstationary Gaussian channels replaces the standard notion of capacity that may not exist). Tighter upper bounds on the capacity are obtained in the process. Specializing these results to stationary channels, the author recovers some of the bounds recently obtained by Ozarow.
Efficient Reduced Basis Solution of Quadratically Nonlinear Diffusion
Efficient Reduced Basis Solution of Quadratically Nonlinear Diffusion Equations M. Rasty M for a steady quadratically nonlinear diffusion equation. We develop an efficient computational procedure- diction of quadratically nonlinear parametrized diffusion equations. To achieve this goal we pursue
Markovian quadratic and superquadratic BSDEs with an unbounded terminal condition
Boyer, Edmond
parabolic partial differen- tial equation with nonlinearity having quadratic or superquadratic growthMarkovian quadratic and superquadratic BSDEs with an unbounded terminal condition Adrien Richou Abstract This article deals with the existence and the uniqueness of solutions to quadratic
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)
Autonomous Gaussian Decomposition
NASA Astrophysics Data System (ADS)
Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirovi?, Snežana; Babler, Brian; Heiles, Carl; Hennebelle, Patrick; Goss, W. M.; Dickey, John
2015-04-01
We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of Gaussian components in the data, and also their locations, widths, and amplitudes. We test AGD and find that it produces results comparable to human-derived solutions on 21 cm absorption spectra from the 21 cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the H i line completeness as a function of peak optical depth and velocity width for the 21-SPONGE data, and also show that the results of AGD are stable against varying observational noise intensity. The autonomy and computational efficiency of the method over traditional manual Gaussian fits allow for truly unbiased comparisons between observations and simulations, and for the ability to scale up and interpret the very large data volumes from the upcoming Square Kilometer Array and pathfinder telescopes.
Sequential design of discrete linear quadratic regulators via optimal root-locus techniques
NASA Technical Reports Server (NTRS)
Shieh, Leang S.; Yates, Robert E.; Ganesan, Sekar
1989-01-01
A sequential method employing classical root-locus techniques has been developed in order to determine the quadratic weighting matrices and discrete linear quadratic regulators of multivariable control systems. At each recursive step, an intermediate unity rank state-weighting matrix that contains some invariant eigenvectors of that open-loop matrix is assigned, and an intermediate characteristic equation of the closed-loop system containing the invariant eigenvalues is created.
Gaussian Processes For Machine Learning
Matthias Seeger
2004-01-01
Gaussian processes (GPs) are natural generalisations of multivariate Gaussian ran- dom variables to innite (countably or continuous) index sets. GPs have been applied in a large number of elds to a diverse range of ends, and very many deep theoretical anal- yses of various properties are available. This paper gives an introduction to Gaussian processes on a fairly elementary level
Non-Gaussianity in axion N-flation models.
Kim, Soo A; Liddle, Andrew R; Seery, David
2010-10-29
We study perturbations in the multifield axion N-flation model, taking account of the full cosine potential. We find significant differences from previous analyses which made a quadratic approximation to the potential. The tensor-to-scalar ratio and the scalar spectral index move to lower values, which nevertheless provide an acceptable fit to observation. Most significantly, we find that the bispectrum non-Gaussianity parameter f{NL} may be large, typically of order 10 for moderate values of the axion decay constant, increasing to of order 100 for decay constants slightly smaller than the Planck scale. Such a non-Gaussian fraction is detectable. We argue that this property is generic in multifield models of hilltop inflation. PMID:21231095
Non-Gaussianity in Axion N-flation Models
Kim, Soo A. [Department of Astronomy and Space Science, Kyung Hee University, Yong-in 446-701 (Korea, Republic of); Liddle, Andrew R.; Seery, David [Astronomy Centre, University of Sussex, Brighton BN1 9QH (United Kingdom)
2010-10-29
We study perturbations in the multifield axion N-flation model, taking account of the full cosine potential. We find significant differences from previous analyses which made a quadratic approximation to the potential. The tensor-to-scalar ratio and the scalar spectral index move to lower values, which nevertheless provide an acceptable fit to observation. Most significantly, we find that the bispectrum non-Gaussianity parameter f{sub NL} may be large, typically of order 10 for moderate values of the axion decay constant, increasing to of order 100 for decay constants slightly smaller than the Planck scale. Such a non-Gaussian fraction is detectable. We argue that this property is generic in multifield models of hilltop inflation.
Repeatability for Gaussian and non-Gaussian data: a practical guide for biologists.
Nakagawa, Shinichi; Schielzeth, Holger
2010-11-01
Repeatability (more precisely the common measure of repeatability, the intra-class correlation coefficient, ICC) is an important index for quantifying the accuracy of measurements and the constancy of phenotypes. It is the proportion of phenotypic variation that can be attributed to between-subject (or between-group) variation. As a consequence, the non-repeatable fraction of phenotypic variation is the sum of measurement error and phenotypic flexibility. There are several ways to estimate repeatability for Gaussian data, but there are no formal agreements on how repeatability should be calculated for non-Gaussian data (e.g. binary, proportion and count data). In addition to point estimates, appropriate uncertainty estimates (standard errors and confidence intervals) and statistical significance for repeatability estimates are required regardless of the types of data. We review the methods for calculating repeatability and the associated statistics for Gaussian and non-Gaussian data. For Gaussian data, we present three common approaches for estimating repeatability: correlation-based, analysis of variance (ANOVA)-based and linear mixed-effects model (LMM)-based methods, while for non-Gaussian data, we focus on generalised linear mixed-effects models (GLMM) that allow the estimation of repeatability on the original and on the underlying latent scale. We also address a number of methods for calculating standard errors, confidence intervals and statistical significance; the most accurate and recommended methods are parametric bootstrapping, randomisation tests and Bayesian approaches. We advocate the use of LMM- and GLMM-based approaches mainly because of the ease with which confounding variables can be controlled for. Furthermore, we compare two types of repeatability (ordinary repeatability and extrapolated repeatability) in relation to narrow-sense heritability. This review serves as a collection of guidelines and recommendations for biologists to calculate repeatability and heritability from both Gaussian and non-Gaussian data. PMID:20569253
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.
Quantum integrability of quadratic Killing tensors
Duval, C.; Valent, G. [Centre de Physique Theorique, CNRS, Luminy, Case 907, F-13288 Marseille Cedex 9 (France); Laboratoire de Physique Theorique et des Hautes Energies, 2, Place Jussieu, F-75251 Paris Cedex 5 (France)
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.
sensitivity analysis in convex quadratic optimization: invariant ...
Aug 20, 2004 ... Keywords: Parametric optimization; Sensitivity analysis; Quadratic opti- ... when the problem has multiple optimal (and thus degenerate) solutions, ...... present, and future, Computers and Chemical Engineering, 23, 667–. 682.
Schur Stability Regions for Complex Quadratic Polynomials
ERIC Educational Resources Information Center
Cheng, Sui Sun; Huang, Shao Yuan
2010-01-01
Given a quadratic polynomial with complex coefficients, necessary and sufficient conditions are found in terms of the coefficients such that all its roots have absolute values less than 1. (Contains 3 figures.)
Quadratic Equations...Origins, Development and Use.
ERIC Educational Resources Information Center
McQualter, J. W.
1988-01-01
There may be a social and an intellectual aspect to the process of development of mathematical knowledge. This paper describes quadratic equations as intellectual mathematics and as colloquial mathematics. Provides some historical data. (YP)
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.
a Quadratic Programming Approach to the Design of ACTIVE-PASSIVE Vibration Isolation Systems
NASA Astrophysics Data System (ADS)
Leo, D. J.; Inman, D. J.
1999-03-01
A quadratic programming algorithm is presented for studying the design tradeoffs of active-passive vibration isolation systems. The novelty of the technique is that the optimal control problem is posed as a quadratic optimization with linear constraints. The quadratic cost function represents the mean square response of the payload acceleration and isolator stroke, and the linear constraints represent asymptotic tracking requirements and peak response constraints. Posing the problem as a quadratic optimization guarantees that a global optimal solution can be found if one exists, and the existence of an optimal solution guarantees that the vibration isolation system satisfies the specified design constraints. The utility of the technique is demonstrated on a comparison of passive vibration isolation and active-passive vibration isolation utilizing relative displacement feedback.
Linear and quadratic programming neural network analysis
Chia-Yiu Maa; Michael A. Shanblatt
1992-01-01
Neural networks for linear and quadratic programming are analyzed. The network proposed by M.P. Kennedy and L.O. Chua (IEEE Trans. Circuits Syst., vol.35, pp.554-562, May 1988) is justified from the viewpoint of optimization theory and the technique is extended to solve optimization problems, such as the least-squares problem. For quadratic programming, the network converges either to an equilibrium or to
Flauger, Raphael [Department of Physics, Yale University, New Haven, CT 06520 (United States); Pajer, Enrico, E-mail: raphael.flauger@yale.edu, E-mail: ep295@cornell.edu [Department of Physics, Cornell University, Ithaca, NY 14853 (United States)
2011-01-01
We provide a derivation from first principles of the primordial bispectrum of scalar perturbations produced during inflation driven by a canonically normalized scalar field whose potential exhibits small sinusoidal modulations. A potential of this type has been derived in a class of string theory models of inflation based on axion monodromy. We use this model as a concrete example, but we present our derivations and results for a general slow-roll potential with superimposed modulations. We show analytically that a resonance between the oscillations of the background and the oscillations of the fluctuations is responsible for the production of an observably large non-Gaussian signal. We provide an explicit expression for the shape of this resonant non-Gaussianity. We show that there is essentially no overlap between this shape and the local, equilateral, and orthogonal shapes, and we stress that resonant non-Gaussianity is not captured by the simplest version of the effective field theory of inflation. We hope our analytic expression will be useful to further observationally constrain this class of models.
Control systems synthesis for a large flexible space antenna
NASA Technical Reports Server (NTRS)
Joshi, S. M.
1982-01-01
The problem of control systems synthesis is considered for controlling the rigid-body attitude and elastic motion of a large deployable space-based antenna. Two methods for control systems synthesis are considered. The first method utilizes the stability and robustness properties of the controller consisting of torque actuators and collocated attitude and rate sensors. The second method is based on the linear-quadratic-Gaussian (LQG) control theory. A combination of the two methods, which results in a two-level hierarchical control system, is also briefly discussed. The performance of the controllers is analyzed by computing the variances of pointing errors, feed misalignment errors and surface contour errors in the presence of sensor and actuator noise.
Note on an Additive Characterization of Quadratic Residues Modulo p
Monico, Chris
if the quadratic equation x2 = a mod p has a solution. If it has no solution then a is called a quadratic nonNote on an Additive Characterization of Quadratic Residues Modulo p Chris Monico, Michele Elia, . . . , p - 1} of positive residues modulo an odd prime p is the partition into quadratic residues
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,…
Quadratic functions with prescribed spectra Wilfried Meidl and Alev Topuzoglu
Paris-Sud XI, Université de
study quadratic Boolean functions f from F2n to F2, which are well-known to have plateaued Fourier of Fitzgerald ([2]) on degenerate quadratic forms. Keywords: Quadratic Boolean functions, s-plateaued functions, near- bent functions, self-reciprocal polynomials, linear complexity 1 Introduction We study quadratic
Interconversion of pure Gaussian states using non-Gaussian operations
Michael G. Jabbour; Raúl García-Patrón; Nicolas J. Cerf
2014-09-29
We analyze the conditions under which local operations and classical communication enable entanglement transformations within the set of bipartite pure Gaussian states. A set of necessary and sufficient conditions had been found in [Quant. Inf. Comp. 3, 211 (2003)] for the interconversion between such states that is restricted to Gaussian local operations and classical communication. Here, we exploit majorization theory in order to derive more general (sufficient) conditions for the interconversion between bipartite pure Gaussian states that goes beyond Gaussian local operations. While our technique is applicable to an arbitrary number of modes for each party, it allows us to exhibit surprisingly simple examples of 2 x 2 Gaussian states that necessarily require non-Gaussian local operations to be transformed into each other.
Non-Gaussian fingerprints of self-interacting curvaton
Enqvist, Kari; Taanila, Olli [Physics Department, University of Helsinki, FIN-00014 (Finland); Nurmi, Sami [Institute for Theoretical Physics, University of Heidelberg, 69120 Heidelberg (Germany); Takahashi, Tomo, E-mail: kari.enqvist@helsinki.fi, E-mail: s.nurmi@thphys.uni-heidelberg.de, E-mail: olli.taanila@iki.fi, E-mail: tomot@cc.saga-u.ac.jp [Department of Physics, Saga University, Saga 840-8502 (Japan)
2010-04-01
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.
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. PMID:20434153
NASA Astrophysics Data System (ADS)
Curtiss, Larry A.; Redfern, Paul C.; Raghavachari, Krishnan
2007-02-01
The Gaussian-4 theory (G4 theory) for the calculation of energies of compounds containing first- (Li-F), second- (Na-Cl), and third-row main group (K, Ca, and Ga-Kr) atoms is presented. This theoretical procedure is the fourth in the Gaussian-n series of quantum chemical methods based on a sequence of single point energy calculations. The G4 theory modifies the Gaussian-3 (G3) theory in five ways. First, an extrapolation procedure is used to obtain the Hartree-Fock limit for inclusion in the total energy calculation. Second, the d-polarization sets are increased to 3d on the first-row atoms and to 4d on the second-row atoms, with reoptimization of the exponents for the latter. Third, the QCISD(T) method is replaced by the CCSD(T) method for the highest level of correlation treatment. Fourth, optimized geometries and zero-point energies are obtained with the B3LYP density functional. Fifth, two new higher level corrections are added to account for deficiencies in the energy calculations. The new method is assessed on the 454 experimental energies in the G3/05 test set [L. A. Curtiss, P. C. Redfern, and K. Raghavachari, J. Chem. Phys. 123, 124107 (2005)], and the average absolute deviation from experiment shows significant improvement from 1.13kcal /mol (G3 theory) to 0.83kcal/mol (G4 theory). The largest improvement is found for 79 nonhydrogen systems (2.10kcal/mol for G3 versus 1.13kcal/mol for G4). The contributions of the new features to this improvement are analyzed and the performance on different types of energies is discussed.
Overview of computational control research at UT Austin
NASA Technical Reports Server (NTRS)
Bong, Wie
1989-01-01
An overview of current research activities at UT Austin is presented to discuss certain technical issues in the following areas: (1) Computer-Aided Nonlinear Control Design: In this project, the describing function method is employed for the nonlinear control analysis and design of a flexible spacecraft equipped with pulse modulated reaction jets. INCA program has been enhanced to allow the numerical calculation of describing functions as well as the nonlinear limit cycle analysis capability in the frequency domain; (2) Robust Linear Quadratic Gaussian (LQG) Compensator Synthesis: Robust control design techniques and software tools are developed for flexible space structures with parameter uncertainty. In particular, an interactive, robust multivariable control design capability is being developed for INCA program; and (3) LQR-Based Autonomous Control System for the Space Station: In this project, real time implementation of LQR-based autonomous control system is investigated for the space station with time-varying inertias and with significant multibody dynamic interactions.
NASA Astrophysics Data System (ADS)
Przybytek, Michal; Helgaker, Trygve
2013-08-01
We analyze the accuracy of the Coulomb energy calculated using the Gaussian-and-finite-element-Coulomb (GFC) method. In this approach, the electrostatic potential associated with the molecular electronic density is obtained by solving the Poisson equation and then used to calculate matrix elements of the Coulomb operator. The molecular electrostatic potential is expanded in a mixed Gaussian-finite-element (GF) basis set consisting of Gaussian functions of s symmetry centered on the nuclei (with exponents obtained from a full optimization of the atomic potentials generated by the atomic densities from symmetry-averaged restricted open-shell Hartree-Fock theory) and shape functions defined on uniform finite elements. The quality of the GF basis is controlled by means of a small set of parameters; for a given width of the finite elements d, the highest accuracy is achieved at smallest computational cost when tricubic (n = 3) elements are used in combination with two (?H = 2) and eight (?1st = 8) Gaussians on hydrogen and first-row atoms, respectively, with exponents greater than a given threshold (? _min^G=0.5). The error in the calculated Coulomb energy divided by the number of atoms in the system depends on the system type but is independent of the system size or the orbital basis set, vanishing approximately like d4 with decreasing d. If the boundary conditions for the Poisson equation are calculated in an approximate way, the GFC method may lose its variational character when the finite elements are too small; with larger elements, it is less sensitive to inaccuracies in the boundary values. As it is possible to obtain accurate boundary conditions in linear time, the overall scaling of the GFC method for large systems is governed by another computational step—namely, the generation of the three-center overlap integrals with three Gaussian orbitals. The most unfavorable (nearly quadratic) scaling is observed for compact, truly three-dimensional systems; however, this scaling can be reduced to linear by introducing more effective techniques for recognizing significant three-center overlap distributions.
2D Gaussian distributions. Equal height.
Oakes, Terry
2D Gaussian distributions. Equal height. Noise-free. Well separated. #12;2D Gaussian distributions. Equal height. Noise-free. Well separated. #12;2D Gaussian distributions. Equal height. Noise-free. Somewhat separated. #12;2D Gaussian distributions. Equal height. Noise-free. Overlapping. #12;2D Gaussian
Martin, Kimball
7 Quadratic forms in n variables In order to understand quadratic forms in n variables over Z, one is let to study quadratic forms over various rings and fields such as Q, Qp, R and Zp. This is consistent equation in Z, it is useful study the equation over other rings. Definition 7.0.8. Let R be a ring
Coding using Gaussian mixture and generalized Gaussian models
Jonathan K. Su; Russell M. Mersereau
1996-01-01
In transform image coding, the histograms of transform coefficients can be approximately modeled by generalized Gaussian (GG) random variables. However, the GG models may not fit the DC distribution. One approach uses DPCM for the DC data, which greatly complicates bit allocation; another assumes a single Gaussian (SG) model, which may be a poor model. As an alternative, this paper
On Exponential Hedging and Related Quadratic Backward Stochastic Differential Equations
Sekine, Jun [Institute of Economic Research, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501 (Japan)], E-mail: sekine@kier.kyoto-u.ac.jp
2006-09-15
The dual optimization problem for the exponential hedging problem is addressed with a cone constraint. Without boundedness conditions on the terminal payoff and the drift of the Ito-type controlled process, the backward stochastic differential equation, which has a quadratic growth term in the drift, is derived as a necessary and sufficient condition for optimality via a variational method and dynamic programming. Further, solvable situations are given, in which the value and the optimizer are expressed in closed forms with the help of the Clark-Haussmann-Ocone formula.
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
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 [Department of Mathematics and Institute of Origins, University College London, London WC1E 6BT (United Kingdom); Caldera-Cabral, Gabriela [Department of Mathematics and Institute of Origins, University College London, London WC1E 6BT (United Kingdom); Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX (United Kingdom); Lazkoz, Ruth [Fisika Teorikoa, Euskal Herriko Unibertsitatea, 48080 Bilbao (Spain); Maartens, Roy [Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX (United Kingdom)
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.
Geometry of Gaussian quantum states
NASA Astrophysics Data System (ADS)
Link, Valentin; Strunz, Walter T.
2015-07-01
We study the Hilbert–Schmidt measure on the manifold of mixed Gaussian states in multi-mode continuous variable quantum systems. An analytical expression for the Hilbert–Schmidt volume element is derived. Its corresponding probability measure can be used to study typical properties of Gaussian states. It turns out that although the manifold of Gaussian states is unbounded, an ensemble of Gaussian states distributed according to this measure still has a normalizable distribution of symplectic eigenvalues, from which unitarily invariant properties can be obtained. By contrast, we find that for an ensemble of one-mode Gaussian states based on the Bures measure the corresponding distribution cannot be normalized. As important applications, we determine the distribution and the mean value of von Neumann entropy and purity for the Hilbert–Schmidt measure.
Geometry of Gaussian quantum states
Valentin Link; Walter T. Strunz
2015-03-09
We study the Hilbert-Schmidt measure on the manifold of mixed Gaussian states in multi mode continuous variable quantum systems. An analytical expression for the Hilbert-Schmidt volume element is derived. Its corresponding probability measure can be used to study typical properties of Gaussian states. It turns out that although the manifold of Gaussian states is unbounded, an ensemble of Gaussian states distributed according to this measure still has a normalizable distribution of symplectic eigenvalues, from which unitarily invariant properties can be obtained. By contrast, we find that for an ensemble of one-mode Gaussian states based on the Bures measure the corresponding distribution cannot be normalized. As important applications, we determine the distribution and the mean value of von Neumann entropy and purity for the Hilbert-Schmidt measure.
McFadden, Paul; Skenderis, Kostas, E-mail: P.L.McFadden@uva.nl, E-mail: K.Skenderis@uva.nl [Institute for Theoretical Physics, Science Park 904, 1090 GL Amsterdam (Netherlands)
2011-05-01
We investigate the non-Gaussianity of primordial cosmological perturbations within our recently proposed holographic description of inflationary universes. We derive a holographic formula that determines the bispectrum of cosmological curvature perturbations in terms of correlation functions of a holographically dual three-dimensional non-gravitational quantum field theory (QFT). This allows us to compute the primordial bispectrum for a universe which started in a non-geometric holographic phase, using perturbative QFT calculations. Strikingly, for a class of models specified by a three-dimensional super-renormalisable QFT, the primordial bispectrum is of exactly the factorisable equilateral form with f{sub NL}{sup equil.} = 5/36, irrespective of the details of the dual QFT. A by-product of this investigation is a holographic formula for the three-point function of the trace of the stress-energy tensor along general holographic RG flows, which should have applications outside the remit of this work.
Normal form decomposition for Gaussian-to-Gaussian superoperators
NASA Astrophysics Data System (ADS)
De Palma, Giacomo; Mari, Andrea; Giovannetti, Vittorio; Holevo, Alexander S.
2015-05-01
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.
Gaussian laser beam tailoring using acoustooptic cell
NASA Astrophysics Data System (ADS)
Bencheikh, Abdelhalim; Ferria, Kouider
2012-06-01
Profile shaping of a Gaussian laser beam by an acoustic wave is well described using Collins integral and ABCD matrix formalism. It is shown by a numerical simulation that the relative width of the laser beam to the ultrasonic wavelength and the acoustic pressure inside the acoustooptic cell act on the light intensity diffraction pattern. Obtained results show that the output intensity profile differs from the incident Gaussian beam shape, and it is more broadened with an increase in the acoustic pressure. The intensity of a focused laser beam is transformed in a flat form in the central region if the acoustic pressure is proprely controlled. On the other hand the intensity longitudinal range (ILR) of the flat shape is discussed along the propagation axes, we have found the ILR is about 2 mm for a focal length distance f=100 mm.
Turbofan engine control system design using the LQG/LTR methodology
NASA Technical Reports Server (NTRS)
Garg, Sanjay
1989-01-01
Application of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery methodology to design of a control system for a simplified turbofan engine model is considered. The importance of properly scaling the plant to achieve the desired Target-Feedback-Loop is emphasized. The steps involved in the application of the methodology are discussed via an example, and evaluation results are presented for a reduced-order compensator. The effect of scaling the plant on the stability robustness evaluation of the closed-loop system is studied in detail.
On the time optimal thermalization of single mode Gaussian states
Alberto Carlini; Andrea Mari; Vittorio Giovannetti
2014-09-25
We consider the problem of time optimal control of a continuous bosonic quantum system subject to the action of a Markovian dissipation. In particular, we consider the case of a one mode Gaussian quantum system prepared in an arbitrary initial state and which relaxes to the steady state due to the action of the dissipative channel. We assume that the unitary part of the dynamics is represented by Gaussian operations which preserve the Gaussian nature of the quantum state, i.e. arbitrary phase rotations, bounded squeezing and unlimited displacements. In the ideal ansatz of unconstrained quantum control (i.e. when the unitary phase rotations, squeezing and displacement of the mode can be performed instantaneously), we study how control can be optimized for speeding up the relaxation towards the fixed point of the dynamics and we analytically derive the optimal relaxation time. Our model has potential and interesting applications to the control of modes of electromagnetic radiation and of trapped levitated nanospheres.
Diagonalization of Quadratic Forms by Gauss Elimination
Charles S. Beightler; Douglass J. Wilde
1966-01-01
The La Grange linear similarity transformation (completing the square) can be used to remove all cross-product terms from a quadratic form. It is shown that the La Grange transformation may be found conveniently by adapting the well-known Gauss elimination procedure for solving linear equations. A simple algorithm for finding the inverse transformation is given. This diagonalization scheme takes much less
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…
Process setup adjustment with quadratic loss
DAN TRIETSCH
2000-01-01
A classic adjustment method, the harmonic adjustment rule, minimizes expected quadratic loss where adjustments are easy and cheap, and the items produced during the adjustment process should be as close to target as possible. This paper generalizes the harmonic adjustment rule by explicitly taking into account measurement and adjustment costs. The generalizationis static, in that adjustments are performed at predetermined
Process setup adjustment with quadratic loss
Dan Trietsch
2000-01-01
A classic adjustment method, the harmonic adjustment rule, minimizes expected quadratic loss where adjustments are easy and cheap, and the items produced during the adjustment process should be as close to target as possible. This paper generalizes the harmonic adjustment rule by explicitly taking into account measurement and adjustment costs. The generalization is static, in that adjustments are performed at
A Repository of Convex Quadratic Programming Problems
Istvan Maros; Csaba Meszaros
1997-01-01
The introduction of a standard set of linear programming problems, to be found in NETLIB\\/LP\\/DATA, had an important impact on measuring, comparing and re- porting the performance of LP solvers .Until recently the eciency of new algorith- mic developments has been measured using this important reference set .Presently, we are witnessing an ever growing interest in the area of quadratic
Multiplicative Updates for Nonnegative Quadratic Programming
Fei Sha; Yuanqing Lin; Lawrence K. Saul; Daniel D. Lee
2007-01-01
Many problems in neural computation and statistical learning involve optimizations with nonnegativity constraints. In this paper, we study convex problems in quadratic program- ming where the optimization is confined to an axis-aligned region in the nonnegative orthant. For these problems, we derive multiplicative updates that improve the value of the objective function at each iteration and converge monotonically to the
Class numbers of complex quadratic fields
Ezra Brown
1974-01-01
Congruence conditions on the class numbers of complex quadratic fields have recently been studied by various investigators, including Barrucand and Cohn, Hasse, and the author. In this paper, we study the class number of Q([radical sign] - pq), where p [reverse not equivalent] q (mod 4) are distinct primes.
MINIMAL CANONICAL DIMENSIONS OF QUADRATIC FORMS
11 11. Fifth canonical dimension 12 References 14 Date: September 2013. Key words and phrasesMINIMAL CANONICAL DIMENSIONS OF QUADRATIC FORMS NIKITA A. KARPENKO Abstract. Canonical dimension of a smooth complete connected variety is the minimal dimension of image of its rational endomorphism. The i
MINIMAL CANONICAL DIMENSIONS OF QUADRATIC FORMS
Karpenko, Nikita - Institut de MathĂ©matiques de Jussieu, UniversitĂ© Paris 7
11 11. Fifth canonical dimension 13 12. Final comments 15 References 16 Date: September 2013. RevisedMINIMAL CANONICAL DIMENSIONS OF QUADRATIC FORMS NIKITA A. KARPENKO Abstract. Canonical dimension of a smooth complete connected variety is the minimal dimension of image of its rational endomorphism. The i
Theory of the Quadratic Zeeman Effect
L. I. Schiff; H. Snyder
1939-01-01
The experiments of Jenkins and Segrč, reported in the accompanying paper, are considered theoretically. The quadratic Zeeman effect observed in absorption to large orbits in strong magnetic fields is due to the diamagnetic term in the Hamiltonian, which is proportional to the square of the vector potential and hence to the square of the magnetic field. For the alkalis, the
Block Ciphers and Systems of Quadratic Equations
Alex Biryukov; Christophe De Canničre
2003-01-01
In this paper we compare systems of multivariate poly- nomials, which completely define the block ciphers Khazad, Misty1, Kasumi, Camellia, Rijndael and Serpent in the view of a potential danger of an algebraic re-linearization attack. Keywords: Block ciphers, multivariate quadratic equations, lineariza- tion, Khazad, Misty, Camellia, Rijndael, Serpent.
A Practical Approach to Quadratic Equations.
ERIC Educational Resources Information Center
Light, Peter
1983-01-01
The usual methods for solving quadratic equations are noted to require either the use of numerical formula or curve plotting on graph paper. The method described here enables pupils to solve equations using only a 45 degree setsquare, graph paper, and a pencil for those which have both real roots and real coefficients. (Author/MP)
On quadratic integral equation of fractional orders
Mohamed Abdalla Darwish
2005-01-01
We present an existence theorem for a nonlinear quadratic integral equations of fractional orders, arising in the queuing theory and biology, in the Banach space of real functions defined and continuous on a bounded and closed interval. The concept of measure of noncompactness and a fixed point theorem due to Darbo are the main tool in carrying out our proof.
Quadratic equations and monodromy evolving deformations
Yousuke Ohyama
2007-09-28
We give a basic theory on monodromy evolving deformations. proposed by Chakravarty and Ablowitz in 1996. We show that Halphen's second quadratic system can be described by monodromy evolving deformations. Our result is a generalization of the work on the DH-V system by Chakravarty and Ablowitz.
Solving Underdefined Systems of Multivariate Quadratic Equations
Nicolas Courtois; Louis Goubin; Willi Meier; Jean-daniel Tacier
2002-01-01
The security of several recent digital signature schemes is based on the difficulty of solving large systems of quadratic multivariate polynomial equations over a finite field F. This problem, sometimes called MQ, is known to be NP-hard. When the number m of equations is equal to the number n of variables, and if n< 15, Grobner base algorithms have been
Width of homoclinic zone for quadratic maps
Vassili Gelfreich; Vincent Naudot
2008-01-01
We study several families of planar quadratic diffeomorphisms near a Bogdanov-Takens bifurcation. For each family, the associate bifurcation diagram can be deduced from the interpolating flow. However, a zone of chaos confined between two lines of homoclinic bifurcation that are exponentially close to one-another is observed. The goal of this paper is to test numerically an accurate asymptotic expansion for
Energy definition for quadratic curvature gravities
Ahmet Baykal
2012-12-03
A conserved current for generic quadratic curvature gravitational models is defined, and it is shown that, at the linearized level, it corresponds to the Deser-Tekin charges. An explicit expression for the charge for new massive gravity in three dimensions is given. Some implications of the linearized equations are discussed.
Directed modified Cholesky factorizations and convex quadratic ...
2014-07-03
Jul 3, 2014 ... the quadratic coefficient matrix is positive definite but nearly singular. For the new .... Partition the permuted interval matrix Ak as: Ak = ( ?k. aT ak. Bk. ) ..... particular the column diagpert shows the average diagonal perturbation med i. (max k. (D ... Integer Global Optimization of Nonlinear Equations. Journal of ...
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.
Robust linear quadratic designs with respect to parameter uncertainty
NASA Technical Reports Server (NTRS)
Douglas, Joel; Athans, Michael
1992-01-01
The authors derive a linear quadratic regulator (LQR) which is robust to parametric uncertainty by using the overbounding method of I. R. Petersen and C. V. Hollot (1986). The resulting controller is determined from the solution of a single modified Riccati equation. It is shown that, when applied to a structural system, the controller gains add robustness by minimizing the potential energy of uncertain stiffness elements, and minimizing the rate of dissipation of energy through uncertain damping elements. A worst-case disturbance in the direction of the uncertainty is also considered. It is proved that performance robustness has been increased with the robust LQR when compared to a mismatched LQR design where the controller is designed on the nominal system, but applied to the actual uncertain system.
Ruban, V P
2015-01-01
The nonlinear dynamics of an obliquely oriented wave packet at sea surface is studied both analytically and numerically for various initial parameters of the packet, in connection with the problem of oceanic rogue waves. In the framework of Gaussian variational ansatz applied to the corresponding (1+2D) hyperbolic nonlinear Schr\\"odinger equation, a simplified Lagrangian system of differential equations is derived, which determines the evolution of coefficients of the real and imaginary quadratic forms appearing in the Gaussian. This model provides a semi-quantitative description for the process of nonlinear spatio-temporal focusing, which is one of the most probable mechanisms of rogue wave formation in random wave fields. The system is integrated in quadratures, which fact allows us to understand qualitative differences between the linear and nonlinear regimes of the focusing of wave packet. Comparison of the Gaussian model predictions with results of direct numerical simulation of fully nonlinear long-cres...
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)
A quadratic assignment formulation of the molecular conformation problem
A. T. Phillips; J. B. Rosen
1994-01-01
The molecular conformation problem is discussed, and a concave quadratic global minimization approach for solving it is described. This approach is based on a quadratic assignment formulation of a discrete approximation to the original problem.
Anonymous IBE from Quadratic Residuosity with Improved Performance
Anonymous IBE from Quadratic Residuosity with Improved Performance Michael Clear , Hitesh Tewari Based Encryption, Anonymous IBE, Cocks Scheme, Quadratic Residuosity Abstract. Identity Based Encryption. Cocks constructed the first such scheme, and subsequent improvements have been made to achieve anonymity
Deflating Quadratic Matrix Polynomials with Structure Preserving Transformations
Tisseur, Francoise
polynomials, both theoretically and numerically, is to convert them into equivalent linear matrix pencilsDeflating Quadratic Matrix Polynomials with Structure Preserving Transformations Francoise Tisseur ISSN 1749-9097 #12;Deflating Quadratic Matrix Polynomials with Structure Preserving Transformations
Dissipative control for linear discrete-time systems
Zhiqiang Tan; Yeng Chai Soh; Lihua Xie
1999-01-01
This paper focuses on the problem of quadratic dissipative control for linear discrete-time systems. We consider the design of feedback controllers to achieve asymptotic stability and strict quadratic dissipativeness. Both the linear static state feedback and the dynamic output feedback controllers are considered. Necessary and sufficient conditions for the solutions of the quadratic dissipative control problems are obtained using the
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.
Attitude and vibration control of a large flexible space-based antenna
NASA Technical Reports Server (NTRS)
Joshi, S. M.; Goglia, G. L.
1982-01-01
The problem of control systems synthesis is considered for controlling the rigid body attitude and elastic motion of a large deployable space based antenna. Two methods for control systems synthesis are considered. The first method utilizes the stability and robustness properties of the controller consisting of torque actuators and collocated attitude and rate sensors. The second method is based on the linear quadratic Gaussian (LQG) control theory. A combination of the two methods, which results in a two level hierarchical control system, is also briefly discussed. The performance of the controllers is analyzed by computing the variances of pointing errors, feed misalignment errors and surface contour errors in the presence of sensor and actuator noise.
Antonio S. de Castro
2003-11-10
The Dirac equation is exactly solved for a pseudoscalar linear plus Coulomb-like potential in a two-dimensional world. This sort of potential gives rise to an effective quadratic plus inversely quadratic potential in a Sturm-Liouville problem, regardless the sign of the parameter of the linear potential, in sharp contrast with the Schroedinger case. The generalized Dirac oscillator already analyzed in a previous work is obtained as a particular case.
Vestibular integrator neurons have quadratic functions due to voltage dependent conductances.
Magnani, Christophe; Eugčne, Daniel; Idoux, Erwin; Moore, Lee E
2013-12-01
The nonlinear properties of the dendrites of the prepositus hypoglossi nucleus (PHN) neurons are essential for the operation of the vestibular neural integrator that converts a head velocity signal to one that controls eye position. A novel system of frequency probing, namely quadratic sinusoidal analysis (QSA), was used to decode the intrinsic nonlinear behavior of these neurons under voltage clamp conditions. Voltage clamp currents were measured at harmonic and interactive frequencies using specific nonoverlapping stimulation frequencies. Eigenanalysis of the QSA matrix reduces it to a remarkably compact processing unit, composed of just one or two dominant components (eigenvalues). The QSA matrix of rat PHN neurons provides signatures of the voltage dependent conductances for their particular dendritic and somatic distributions. An important part of the nonlinear response is due to the persistent sodium conductance (gNaP), which is likely to be essential for sustained effects needed for a neural integrator. It was found that responses in the range of 10 mV peak to peak could be well described by quadratic nonlinearities suggesting that effects of higher degree nonlinearities would add only marginal improvement. Therefore, the quadratic response is likely to sufficiently capture most of the nonlinear behavior of neuronal systems except for extremely large synaptic inputs. Thus, neurons have two distinct linear and quadratic functions, which shows that piecewise linear?+?quadratic analysis is much more complete than just piecewise linear analysis; in addition quadratic analysis can be done at a single holding potential. Furthermore, the nonlinear neuronal responses contain more frequencies over a wider frequency band than the input signal. As a consequence, they convert limited amplitude and bandwidth input signals to wider bandwidth and more complex output responses. Finally, simulations at subthreshold membrane potentials with realistic PHN neuron models suggest that the quadratic functions are fundamentally dominated by active dendritic structures and persistent sodium conductances. PMID:23519443
Recall: Gaussian smoothing/sampling Gaussian 1/2
Oliensis, John
] · In computer graphics, a mip map [Williams, 1983] · A precursor to wavelet transform #12;Motivations #12, then subsample · Filter size should double for each ˝ size reduction. #12;Subsampling with Gaussian smoothing G 1
Economic Dispatch with Network Security Constraints Using Parametric Quadratic Programming
K. Aoki; T. Satoh
1982-01-01
This paper presents an efficient method to solve an economic load dispatch problem with dc load flow type network security constraints. The conventional linear programming and quadratic programming methods cannot deal with transmission losses as a quadratic form of generator outputs. In order to overcome this defect, the extension of the quadratic programming method is proposed, which is designated as
On isotropy of quadratic spaces in finite and infinite dimension
on the right hand side of the equation, which then readily establishes the fact that quadratic and bilinearOn isotropy of quadratic spaces in finite and infinite dimension Karim Johannes Becher, Detlev Hoffmann Abstract Herbert Gross asked whether there exist fields admitting anisotropic quadratic spaces
Linear and quadratic time-frequency signal representations
F. Hlawatsch; G. F. Boudreaux-Bartels
1992-01-01
A tutorial review of both linear and quadratic representations is given. The linear representations discussed are the short-time Fourier transform and the wavelet transform. The discussion of quadratic representations concentrates on the Wigner distribution, the ambiguity function, smoothed versions of the Wigner distribution, and various classes of quadratic time-frequency representations. Examples of the application of these representations to typical problems
Class Groups and Quadratic Diophantine R.A. Mollin
Mollin, R.A.
Class Groups and Quadratic Diophantine Equations R.A. Mollin Abstract First, we consider of the underlying real quadratic orders. This is a generalized Eisenstein criterion in the sense that the equation x words and phrases: Quadratic Diophantine equations, Continued Fractions, Central Norms, Class group
A Quadratic Gradient Equation for pricing Mortgage-Backed Securities
Monneau, Régis
A Quadratic Gradient Equation for pricing Mortgage-Backed Securities Marco Papi Institute for Applied Computing - CNR Rome (Italy) A Quadratic Gradient Equation for pricing Mortgage-Backed Securities call option on a corresponding fixed-rate bond. A Quadratic Gradient Equation for pricing Mortgage
HOW DO YOU SOLVE A QUADRATIC EQUATION? GEORGE E._ FORSYTHE
Jiang, Shidong
cs40 HOW DO YOU SOLVE A QUADRATIC EQUATION? BY GEORGE E._ FORSYTHE TECHNICAL REPORT NO. CS40 JUNE;1 \\- c. `L L t HOW DO YOU SOLVE A QUADRATIC EQUATION? bY George E. Forsythe Abstract The nature-point computation are illustrated by the formula for solving a quadratic equation. An accurate way of solving
QUADRATIC SYSTEMS OF CONSERVATION LAWS WITH GENERIC BEHAVIOR AT INFINITY
Canic, Suncica
QUADRATIC SYSTEMS OF CONSERVATION LAWS WITH GENERIC BEHAVIOR AT INFINITY SUN Ĺ¸ CICA Ĺ¸ CANI ' C Abstract. We identify quadratic systems of conservation laws with ``generic'' behavior at infinity, where properties at infinity that are true for an open and dense subset of the set of all planar quadratic vector
Gaussian Decomposition of HI Surveys - II. Separation of Problematic Gaussians
U. Haud; P. M. W. Kalberla
2006-04-28
We have analyzed the Gaussian decomposition of the Leiden/Dwingeloo Survey (LDS) of galactic neutral hydrogen for the presence of Gaussians probably not directly related to galactic HI emission. It is demonstrated that at least three classes of such components can be distinguished. The narrowest Gaussians mostly represent stronger random noise peaks in profiles and some still uncorrected radio-interferences. Many of slightly wider weak Gaussians are caused by increased uncertainties near the profile edges and with the still increasing width the baseline problems become dominating among weak components. Statistical criteria are given for separation of the parameter space regions, most likely populated with the problematic components from those where the Gaussians are with higher probability describing the actual Milky Way HI emission. The same analysis is applied to the Leiden/Argentina/Bonn survey (LAB). It is demonstrated that the selection criteria for dividing the parameter space are to a great extent independent of the particular survey in use. The presence of the baseline problems in the LDS is indicated by the peculiarities of the distribution of the widest Gaussians in the sky. A similar plot for the northern part of the LAB demonstrates considerably lower numbers of spurious components, but there are still problems with the southern part of the LAB. The strange characteristics of the observational noise in the southern part of the LAB are pointed out.
Observer-based control of Rijke-type combustion instability
NASA Astrophysics Data System (ADS)
Hervas, Jaime Rubio; Zhao, Dan; Reyhanoglu, Mahmut
2014-12-01
In this work, observer-based feedback control of combustion instability in a Rijke-type thermoacoustic system is considered. A generalized thermoacoustic model with distributed monopole-like actuators is developed. The model is linearized and formulated in state-space and it is assumed that pressure sensors are the only information available for feedback. It is shown that a system of this form is observable. As a Linear-Quadratic-Gaussian (LQG) controller is implemented to tune the actuators, the system becomes asymptotically stable. The performance of the controller is evaluated with a system involving two modes. The successful demonstration indicates that the observer-based feedback controller can be applied to a real combustion system with multiple modes.
NASA Technical Reports Server (NTRS)
Fleming, P.
1983-01-01
A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a nonlinear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer. One concerns helicopter longitudinal dynamics and the other the flight dynamics of an aerodynamically unstable aircraft.
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
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
INTERFERENCE DETECTION IN GAUSSIAN NOISE
Baddi, Raju [Raman Research Institute, C.V. Raman Avenue., Bangalore 560 080 (India)
2011-06-15
Interference detection in Gaussian noise is proposed. It can be applied for easy detection and editing of interference lines in radio spectral line observations. One does not need to know the position of occurrence or keep track of interference in the band. By using statistical properties of N-channel Gaussian noise it is possible to differentiate interference from normal Gaussian noise. These statistical properties are three quantities which are calculated on the subject spectrum. The first is the expected absolute maximum from the mean level across the spectrum. The second is the expected absolute difference maximum (array of adjacent differences of channel values taken across the spectrum), and the third is the expected absolute added difference maximum. For N-channel Gaussian noise, these quantities have a well-defined value. Any deviation across the spectrum that violates an upper limit formed by these expected maxima is attributed to interference. Results obtained on real data by applying this technique have been displayed.
The Gaussian parallel relay network
B. Schein; R. Gallager
2000-01-01
We introduce the real, discrete-time Gaussian parallel relay network. This simple network is theoretically important in the context of network information theory. We present upper and lower bounds to capacity and explain where they coincide
Hypergeometric-Gaussian modes Ebrahim Karimi,1
Marrucci, Lorenzo
modes, the modified exponential Gaussian modes, and the modified LaguerreGaussian modes. © 2007 Optical light modulator. We briefly consider some subfamilies of the HyGG modes as the modified Bessel GaussianHypergeometric-Gaussian modes Ebrahim Karimi,1 Gianluigi Zito,1 Bruno Piccirillo,1 Lorenzo Marrucci
The Generalized Gaussian Mixture Model Using ICA
Te-won Lee; Michael S. Lewicki
2000-01-01
An extension of the Gaussian mixture model is presentedusing Independent Component Analysis (ICA)and the generalized Gaussian density model. The mixturemodel assumes that the observed data can be categorizedinto mutually exclusive classes whose componentsare generated by a linear combination of independentsources. The source densities are modeled bygeneralized Gaussians (Box and Tiao, 1973) that providea general method for modeling non-Gaussian statisticalstructure of
Weighted Inverse Gaussian -a Versatile Lifetime Model
Kundu, Debasis
-parameter generalized inverse Gaussian distribution, which is a mixture of the inverse Gaussian distribution and lengthWeighted Inverse Gaussian - a Versatile Lifetime Model Ramesh C. Gupta1 & Debasis Kundu2 Abstract biased inverse Gaussian distri- bution. Also Birnbaum-Saunders distribution is a special case for p = 1
WKB Propagation of Gaussian Wavepackets
Raphael N. P. Maia; Fernando Nicacio; Raul O. Vallejos; Fabricio Toscano
2008-02-12
We analyze the semiclassical evolution of Gaussian wavepackets in chaotic systems. We prove that after some short time a Gaussian wavepacket becomes a primitive WKB state. From then on, the state can be propagated using the standard TDWKB scheme. Complex trajectories are not necessary to account for the long-time propagation. The Wigner function of the evolving state develops the structure of a classical filament plus quantum oscillations, with phase and amplitude being determined by geometric properties of a classical manifold.
Relativistic pseudo-Gaussian oscillators
Felix Iacob
2014-10-07
The quantum models of a massive scalar particle inside of an open bag generated by a pseudo-Gaussian conformaly flat (1+1) metrics are investigated. The potential of a free moving test particle, in the generated metric, has Gaussian asymptotic behavior, approaching to the potential of harmonic oscillator in the limit of zero. The energy levels are calculated using numerical methods, calculations are based on efficient method of generating functionals.
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.
The halo bispectrum in N-body simulations with non-Gaussian initial conditions
NASA Astrophysics Data System (ADS)
Sefusatti, E.; Crocce, M.; Desjacques, V.
2012-10-01
We present measurements of the bispectrum of dark matter haloes in numerical simulations with non-Gaussian initial conditions of local type. We show, in the first place, that the overall effect of primordial non-Gaussianity on the halo bispectrum is larger than on the halo power spectrum when all measurable configurations are taken into account. We then compare our measurements with a tree-level perturbative prediction, finding good agreement at large scales when the constant Gaussian bias parameter, both linear and quadratic, and their constant non-Gaussian corrections are fitted for. The best-fitting values of the Gaussian bias factors and their non-Gaussian, scale-independent corrections are in qualitative agreement with the peak-background split expectations. In particular, we show that the effect of non-Gaussian initial conditions on squeezed configurations is fairly large (up to 30 per cent for fNL = 100 at redshift z = 0.5) and results from contributions of similar amplitude induced by the initial matter bispectrum, scale-dependent bias corrections as well as from non-linear matter bispectrum corrections. We show, in addition, that effects at second order in fNL are irrelevant for the range of values allowed by cosmic microwave background and galaxy power spectrum measurements, at least on the scales probed by our simulations (k > 0.01 h Mpc-1). Finally, we present a Fisher matrix analysis to assess the possibility of constraining primordial non-Gaussianity with future measurements of the galaxy bispectrum. We find that a survey with a volume of about 10 h-3 Gpc3 at mean redshift z ? 1 could provide an error on fNL of the order of a few. This shows the relevance of a joint analysis of galaxy power spectrum and bispectrum in future redshift surveys.
Use of quadratic components for buckling calculations
Dohrmann, C.R.; Segalman, D.J. [Sandia National Labs., Albuquerque, NM (United States). Structural Dynamics Dept.] [Sandia National Labs., Albuquerque, NM (United States). Structural Dynamics Dept.
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.
Regular models with quadratic equation of state
S. D. Maharaj; P. Mafa Takisa
2013-01-08
We provide new exact solutions to the Einstein-Maxwell system of equations which are physically reasonable. The spacetime is static and spherically symmetric with a charged matter distribution. We utilise an equation of state which is quadratic relating the radial pressure to the energy density. Earlier models, with linear and quadratic equations of state, are shown to be contained in our general class of solutions. The new solutions to the Einstein-Maxwell are found in terms of elementary functions. A physical analysis of the matter and electromagnetic variables indicates that the model is well behaved and regular. In particular there is no singularity in the proper charge density at the stellar centre unlike earlier anisotropic models in the presence of the electromagnetic field.
Stellar objects in the quadratic regime
P. Mafa Takisa; S. D. Maharaj; Subharthi Ray
2014-12-28
We model a charged anisotropic relativistic star with a quadratic equation of state. Physical features of an exact solution of the Einstein-Maxwell system are studied by incorporating the effect of the nonlinear term from the equation of state. It is possible to regain the masses, radii and central densities for a linear equation of state in our analysis. We generate masses for stellar compact objects and perform a detailed study of PSR J1614-2230 in particular. We also show the influence of the nonlinear equation of state on physical features of the matter distribution. We demonstrate that it is possible to incorporate the effects of charge, anisotropy and a quadratic term in the equation of state in modelling a compact relativistic body.
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.
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.
Coherent States of Systems with Quadratic Hamiltonians
NASA Astrophysics Data System (ADS)
Bagrov, V. G.; Gitman, D. M.; Pereira, A. S.
2015-06-01
Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schrödinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency.
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.
QUADRATIC RECIPROCITY VIA LINEAR ALGEBRA 1. Introduction ...
2005-03-12
Gauss sum and derive from this, the law of quadratic reciprocity. 1. ... be 1 if p is a square modulo q and ?1 otherwise. The law of ... system of equations xn?j = xj, 1 ? j ? n ? 1. For n odd, we find ... case using (2.1), we solve the system a + b = (n + 1)/2, a ? b = ±1 and deduce .... a complete set of residue classes modulo mn.
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.
Numerical analysis of a quadratic matrix equation
NICHOLAS J. HIGHAM; HYUN-MIN KIM
1999-01-01
The quadratic matrix equation AX2+BX +C = 0 in n \\\\Theta n matrices arises inapplications and is of intrinsic interest as one of the simplest nonlinear matrix equations.We give a complete characterization of solutions in terms of the generalizedSchur decomposition and describe and compare various numerical solution techniques.In particular, we give a thorough treatment of functional iteration methodsbased on Bernoulli's
An alternative method on quadratic programming problems
NASA Astrophysics Data System (ADS)
Dasril, Y.; Mohd, I. B.; Mustaffa, I.; Aminuddin, MMM.
2015-05-01
In this paper we proposed an alternative approach to find the optimum solution of quadratic programming problems (QPP) in its original form without additional information such as slack variable, surplus variable or artificial variable as done in other favourite methods. This approached is based on the violated constraints by the unconstrained optimum. The optimal solution of QPP obtained by searching from initial point to another point alongside of feasible region.
Ever-expanding, Isotropizing, Quadratic Cosmologies
Spiros Cotsakis; George Flessas; Peter Leach; Laurent Querella
2000-11-06
We consider some aspects of the global evolution problem of Hamiltonian homogeneous, anisotropic cosmologies derived from a purely quadratic action functional of the scalar curvature. We show that models can isotropize in the positive asymptotic direction and that quadratic diagonal Bianchi IX models do not recollapse and may be regular initially. Although the global existence and isotropization results we prove hold quite generally, they are applied to specific Bianchi models in an attempt to describe how certain dynamical properties uncommon to the general relativity case, become generic features of these quadratic universes. The question of integrability of the models is also considered. Our results point to the fact that the more general models are not integrable in the sense of Painlev\\'e and for the Bianchi IX case this may be connected to the validity of a BKL oscillatory picture on approach to the singularity in sharp contrast with other higher order gravity theories that contain an Einstein term and show a monotonic evolution towards the initial singularity.
Constrained quadratic correlation filters for target detection.
Muise, Robert; Mahalanobis, Abhijit; Mohapatra, Ram; Li, Xin; Han, Deguang; Mikhael, Wasfy
2004-01-10
A method for designing and implementing quadratic correlation filters (QCFs) for shift-invariant target detection in imagery is presented. The QCFs are quadratic classifiers that operate directly on the image data without feature extraction or segmentation. In this sense the QCFs retain the main advantages of conventional linear correlation filters while offering significant improvements in other respects. Not only is more processing required for detection of peaks in the outputs of multiple linear filters but choosing the most suitable among them is an error-prone task. All channels in a QCF work together to optimize the same performance metric and to produce a combined output that leads to considerable simplification of the postprocessing scheme. The QCFs that are developed involve hard constraints on the output of the filter. Inasmuch as this design methodology is indicative of the synthetic discriminant function (SDF) approach for linear filters, the filters that we develop here are referred to as quadratic SDFs (QSDFs). Two methods for designing QSDFs are presented, an efficient architecture for achieving them is discussed, and results from the Moving and Stationary Target Acquisition and Recognition synthetic aperture radar data set are presented. PMID:14735950
Moments for general quadratic densities in n dimensions
Furman, Miguel A.
2002-03-20
We present the calculation of the generating functions and the rth-order correlations for densities of the form {rho}(x) {proportional_to} where g(s) is a non-negative function of the quadratic ''action'' s(x)={summation}{sub i,j}H{sub ij}x{sub i}x{sub j}, where x = (x{sub 1},x{sub 2}...,x{sub n}) is a real n-dimensional vector and H is a real, symmetric n x n matrix whose eigenvalues are strictly positive. In particular, we find the connection between the (r+2)th-order and rth-order correlations, which constitutes a generalization of the Gaussian moment theorem, which corresponds to the particular choice g(s)=e{sup -s/2}. We present several examples for specific choices for g(s), including the explicit expression for the generating function for each case and the subspace projection of {rho}(x) in a few cases. We also provide the straightforward generalizations to: (1) the case where g=g(s(x)+a {center_dot} x), where a=(a{sub 1},a{sub 2},...,a{sub n}) is an arbitrary real n-dimensional vector, and (2) the complex case, in which the action is of the form s(z) = {summation}{sub i,j}H{sub ij}z{sup *}{sub i} z{sub j} where z=(z{sub 1},z{sub 2}...z{sub n}) is an n-dimensional complex vector and H is a Hermitian n x n matrix whose eigenvalues are strictly positive.
Information geometry of Gaussian channels
Monras, Alex [Dipartimento di Matematica e Informatica, Universita degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (Italy); CNR-INFM Coherentia, Napoli (Italy); CNISM Unita di Salerno (Italy) and INFN Sezione di Napoli, Gruppo collegato di Salerno, Baronissi (Italy); Illuminati, Fabrizio [Dipartimento di Matematica e Informatica, Universita degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (Italy); CNR-INFM Coherentia, Napoli (Italy) and CNISM Unita di Salerno; and INFN Sezione di Napoli, Gruppo collegato di Salerno, Baronissi (Italy); ISI Foundation for Scientific Interchange, Villa Gualino, Viale Settimio Severo 65, I-10133 Torino (Italy)
2010-06-15
We define a local Riemannian metric tensor in the manifold of Gaussian channels and the distance that it induces. We adopt an information-geometric approach and define a metric derived from the Bures-Fisher metric for quantum states. The resulting metric inherits several desirable properties from the Bures-Fisher metric and is operationally motivated by distinguishability considerations: It serves as an upper bound to the attainable quantum Fisher information for the channel parameters using Gaussian states, under generic constraints on the physically available resources. Our approach naturally includes the use of entangled Gaussian probe states. We prove that the metric enjoys some desirable properties like stability and covariance. As a by-product, we also obtain some general results in Gaussian channel estimation that are the continuous-variable analogs of previously known results in finite dimensions. We prove that optimal probe states are always pure and bounded in the number of ancillary modes, even in the presence of constraints on the reduced state input in the channel. This has experimental and computational implications. It limits the complexity of optimal experimental setups for channel estimation and reduces the computational requirements for the evaluation of the metric: Indeed, we construct a converging algorithm for its computation. We provide explicit formulas for computing the multiparametric quantum Fisher information for dissipative channels probed with arbitrary Gaussian states and provide the optimal observables for the estimation of the channel parameters (e.g., bath couplings, squeezing, and temperature).
Controller design and parameter identifiability studies for a large space antenna
NASA Technical Reports Server (NTRS)
Joshi, S. M.
1985-01-01
The problem of control systems synthesis and parameter identifiability are considered for a large, space-based antenna. Two methods are considered for control system synthesis, the first of which uses torque actuators and collocated attitude and rate sensors, and the second method is based on the linear-quadratic-Gaussian (LQG) control theory. The predicted performance obtained by computing variances of pointing, surface and feed misalignment errors in the presence of sensor noise indicates that the LQG-based controller yields superior results. Since controller design requires the knowledge of the system parameters, the identifiability of the structural parameters is investigated by obtaining Cramer-Rao lower bounds. The modal frequencies are found to have the best identifiability, followed by damping ratios, and mode-slopes.
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.
ChemXSeer Digital Library Gaussian Search
Lahiri, Shibamouli; Nangia, Shikha; Mitra, Prasenjit; Giles, C Lee; Mueller, Karl T
2011-01-01
We report on the Gaussian file search system designed as part of the ChemXSeer digital library. Gaussian files are produced by the Gaussian software [4], a software package used for calculating molecular electronic structure and properties. The output files are semi-structured, allowing relatively easy access to the Gaussian attributes and metadata. Our system is currently capable of searching Gaussian documents using a boolean combination of atoms (chemical elements) and attributes. We have also implemented a faceted browsing feature on three important Gaussian attribute types - Basis Set, Job Type and Method Used. The faceted browsing feature enables a user to view and process a smaller, filtered subset of documents.
A quadratic programming framework for constrained and robust jet engine health monitoring
NASA Astrophysics Data System (ADS)
Borguet, S.; Léonard, O.
2009-09-01
Kalman filters are largely used in the jet engine community for condition monitoring purpose. This algorithm gives a good estimate of the engine condition provided that the residuals between the model prediction and the measurements are zero-mean, Gaussian random variables. In the case of sensor faults, this assumption does not hold anymore and consequently, the diagnosis is spoiled. This contribution presents a recursive estimation algorithm based on a Quadratic Programming (QP) formulation which provides robustness against sensor faults and allows constraints on the health parameters to be specified. The improvements in estimation accuracy brought by this new algorithm are illustrated on a series of typical test-cases that may be encountered on current turbofan engines.
Quadratic Equation over Associative D-Algebra
Aleks Kleyn
2015-05-30
In this paper, I treat quadratic equation over associative $D$-algebra. In quaternion algebra $H$, the equation $x^2=a$ has either $2$ roots, or infinitely many roots. Since $a\\in R$, $aequation has infinitely many roots. Otherwise, the equation has roots $x_1$, $x_2$, $x_2=-x_1$. I considered different forms of the Viete's theorem and a possibility to apply the method of completing the square. Assumed the hypothesis that, in noncommutative algebra, the equation $$(x-b)(x-a)+(x-a)(x-c)=0$$ $b\
Coupled detection- estimation of Gaussian processes in Gaussian noise
A. Jaffer; S. Gupta
1972-01-01
This paper considers the joint detection and estimation of Gauss-Markov processes in white Gaussian noise, where the operations of detection and estimation are strongly coupled. Explicit Bayes' optimal recursive estimation and detection rules are derived, and it is shown that the resulting optimal receiver is amenable to a causal estimator-correlator-type interpretation.
On the generation of a non-gaussian curvature perturbation during preheating
Kohri, Kazunori; Lyth, David H. [Department of Physics, Lancaster University, Lancaster LA1 4YB (United Kingdom); Valenzuela-Toledo, Cesar A., E-mail: k.kohri@lancaster.ac.uk, E-mail: d.lyth@lancaster.ac.uk, E-mail: cavalto@ciencias.uis.edu.co [Escuela de Física, Universidad Industrial de Santander, Ciudad Universitaria, Bucaramanga (Colombia)
2010-02-01
The perturbation of a light field might affect preheating and hence generate a contribution to the spectrum and non-gaussianity of the curvature perturbation ?. The field might appear directly in the preheating model (curvaton-type preheating) or indirectly through its effect on a mass or coupling (modulated preheating). We give general expressions for ? based on the ?N formula, and apply them to the cases of quadratic and quartic chaotic inflation. For the quadratic case, curvaton-type preheating is ineffective in contributing to ?, but modulated preheating can be effective. For quartic inflation, curvaton-type preheating may be effective but the usual ?N formalism has to be modified. We see under what circumstances the recent numerical simulation of Bond et al. [0903.3407] may be enough to provide a rough estimate for this case.
LARGE TIME SOLUTION FOR QUADRATIC SCHRODINGER EQUATIONS IN HANTAEK BAE
Yorke, James
LARGE TIME SOLUTION FOR QUADRATIC SCHR¨ODINGER EQUATIONS IN 2D AND 3D HANTAEK BAE Abstract. The aim of this paper is to establish the large time well-posedness of the quadratic Schr¨odinger equation in 2D and 3D for the solvability of (1.1), see [5]. In this paper, we consider the Schr¨odinger equation with quadratic
Runge-Kutta methods for quadratic ordinary differential equations
Arieh Iserles; Geetha Ramaswami; Mark Sofroniou
1998-01-01
Many systems of ordinary differential equations are quadratic: the derivative can be expressed as a quadratic function of\\u000a the dependent variable. We demonstrate that this feature can be exploited in the numerical solution by Runge-Kutta methods,\\u000a since the quadratic structure serves to decrease the number of order conditions. We discuss issues related to construction\\u000a design and implementation and present a
A quadratic pulse height analyzer for space applications.
NASA Technical Reports Server (NTRS)
Burtis, D. W.; Aalami, D.; Evelyn-Veere, R. H.; Sarkady, A. A.
1972-01-01
A flight-worthy pulse height analyzer that has a quadratic transfer function is described. This quadratic function permits optimum usage of the entire PHA dynamic range due to the quadratic nature of the gamma ray spectrometer's resolution vs energy. After the theoretical design discussion, the implementation of the design is examined and test results described. The analyzer is part of the University of New Hampshire gamma ray monitor for OSO-H.
A Gradient Descent Approach to Optimal Coherent Quantum LQG Controller Design
Arash Kh. Sichani; Igor G. Vladimirov; Ian R. Petersen
2015-02-01
This paper is concerned with the Coherent Quantum Linear Quadratic Gaussian (CQLQG) control problem of finding a stabilizing measurement-free quantum controller for a quantum plant so as to minimize an infinite-horizon mean square performance index for the fully quantum closed-loop system. In comparison with the observation-actuation structure of classical controllers, the coherent quantum feedback is less invasive to the quantum dynamics and quantum information. Both the plant and the controller are open quantum systems whose dynamic variables satisfy the canonical commutation relations (CCRs) of a quantum harmonic oscillator and are governed by linear quantum stochastic differential equations (QSDEs). In order to correspond to such oscillators, these QSDEs must satisfy physical realizability (PR) conditions, which are organised as quadratic constraints on the controller matrices and reflect the preservation of CCRs in time. The CQLQG problem is a constrained optimization problem for the steady-state quantum covariance matrix of the plant-controller system satisfying an algebraic Lyapunov equation. We propose a gradient descent algorithm equipped with adaptive stepsize selection for the numerical solution of the problem. The algorithm finds a local minimum of the LQG cost over the parameters of the Hamiltonian and coupling operators of a stabilizing PR quantum controller, thus taking the PR constraints into account. A convergence analysis of the proposed algorithm is presented. A numerical example of a locally optimal CQLQG controller design is provided to demonstrate the algorithm performance.
V. V. Kozlov
2005-01-01
We discuss the symplectic geometry of linear Hamiltonian systems with nondegenerate Hamiltonians. These systems can be reduced to linear second-order differential equations characteristic of linear oscillation theory. This reduction is related to the problem on the signatures of restrictions of quadratic forms to Lagrangian planes. We study vortex symplectic planes invariant with respect to linear Hamiltonian systems. These planes are
Economic dispatch with network security constraints using parametric quadratic programming
Aoki, K.; Satoh, T.
1982-12-01
This paper presents an efficient method to solve an economic load dispatch problem with dc load flow type network security constraints. The conventional linear programming and quadratic programming methods cannot deal with transmission losses as a quadratic form of generator outputs. In order to overcome this defect, the extension of the quadratic programming method is proposed, which is designated as the parametric quadratic programming method. The upper bounding technique and the relaxation method are coupled with the proposed method for the purpose of computational efficiency. The test results show that the proposed method is practical for real-time applications.
Generalized symmetry transformation with Gaussian phase weight function
NASA Astrophysics Data System (ADS)
Lee, Hee-Yul; Kim, Tae-Hun; Jeon, Joon-Hyung; Choi, Il; Park, Kil-Houm
2012-03-01
The generalized symmetry transformation (GST) is a symmetry operator detecting objects by using edge gradient directions. Conventional GST uses the cosine function to define the phase weight function (PWF), which represents the symmetry of two gradient directions. The cosine function of PWF leads to a good performance in detecting symmetrical objects. However, the weights of gradient pairs, which are considered to be asymmetrical, are relatively high, so side effects appear near the symmetry pick regions. (Note that side effects disturb the multiple object detection.) In this paper, we use the Gaussian function in calculating the symmetric weights of gradient pairs. The Gaussian function can suppress the weights of less symmetric gradient pairs. In addition, the symmetry for elliptically shaped objects can be more emphasized by controlling the width of the Gaussian function. The proposed GST is evaluated through experiments on synthetic images, which include various bright and dark plane figures, and on real images, which requires the detection of elliptical shapes.
Non-gaussian shape recognition
Byun, Joyce; Bean, Rachel, E-mail: byun@astro.cornell.edu, E-mail: rbean@astro.cornell.edu [Department of Astronomy, Cornell University, Ithaca, NY 14853 (United States)
2013-09-01
A detection of primordial non-Gaussianity could transform our understanding of the fundamental theory of inflation. The precision promised by upcoming cosmic microwave background (CMB) and large-scale structure (LSS) surveys raises a natural question: if a detection given a particular template is made, what does this truly tell us about the underlying theory? Even in the case of non-detections and upper bounds on deviations from Gaussianity, what can we then infer about the viable theories that remain? In this paper we present a systematic way to constrain a wide range of non-Gaussian shapes, including general single and multi-field models and models with excited initial states. We present a separable, divergent basis able to recreate many shapes in the literature to high accuracy with between three and seven basis functions. The basis allows shapes to be grouped into broad ''template classes'', satisfying theoretically-relevant priors on their divergence properties in the squeezed limit. We forecast how well a Planck-like CMB survey could not only detect a general non-Gaussian signal but discern more about its shape, using existing templates and new ones we propose. This approach offers an opportunity to tie together minimal theoretical priors with observational constraints on the shape in general, and in the squeezed limit, to gain a deeper insight into what drove inflation.
Gaussian processes for machine learning.
Seeger, Matthias
2004-04-01
Gaussian processes (GPs) are natural generalisations of multivariate Gaussian random variables to infinite (countably or continuous) index sets. GPs have been applied in a large number of fields to a diverse range of ends, and very many deep theoretical analyses of various properties are available. This paper gives an introduction to Gaussian processes on a fairly elementary level with special emphasis on characteristics relevant in machine learning. It draws explicit connections to branches such as spline smoothing models and support vector machines in which similar ideas have been investigated. Gaussian process models are routinely used to solve hard machine learning problems. They are attractive because of their flexible non-parametric nature and computational simplicity. Treated within a Bayesian framework, very powerful statistical methods can be implemented which offer valid estimates of uncertainties in our predictions and generic model selection procedures cast as nonlinear optimization problems. Their main drawback of heavy computational scaling has recently been alleviated by the introduction of generic sparse approximations.13,78,31 The mathematical literature on GPs is large and often uses deep concepts which are not required to fully understand most machine learning applications. In this tutorial paper, we aim to present characteristics of GPs relevant to machine learning and to show up precise connections to other "kernel machines" popular in the community. Our focus is on a simple presentation, but references to more detailed sources are provided. PMID:15112367
LQG controller design using GUI: application to antennas and radio-telescopes
Maneri; Gawronski
2000-01-01
The Linear Quadratic Gaussian (LQG) algorithm has been used to control the JPL's beam wave-guide, and 70-m antennas. This algorithm significantly improves tracking precision in a wind disturbed environment. Based on this algorithm and the implementation experience a Matlab based Graphical User Interface (GUI) was developed to design the LQG controllers applicable to antennas and radiotelescopes. The GUI is described in this paper. It consists of two parts the basic LQG design and the fine-tuning of the basic design using a constrained optimization algorithm. The presented GUI was developed to simplify the design process, to make the design process user-friendly, and to enable design of an LQG controller for one with a limited control engineering background. The user is asked to manipulate the GUI sliders and radio buttons to watch the antenna performance. Simple rules are given at the GUI display. PMID:10871218
Development and modification of a Gaussian and non-Gaussian noise exposure system
NASA Astrophysics Data System (ADS)
Schlag, Adam W.
Millions of people across the world currently have noise induced hearing loss, and many are working in conditions with both continuous Gaussian and non-Gaussian noises that could affect their hearing. It was hypothesized that the energy of the noise was the cause of the hearing loss and did not depend on temporal pattern of a noise. This was referred to as the equal energy hypothesis. This hypothesis has been shown to have limitations though. This means that there is a difference in the types of noise a person receives to induce hearing loss and it is necessary to build a system that can easily mimic various conditions to conduct research. This study builds a system that can produce both non-Gaussian impulse/impact noises and continuous Gaussian noise. It was found that the peak sound pressure level of the system could reach well above the needed 120 dB level to represent acoustic trauma and could replicate well above the 85 dB A-weighted sound pressure level to produce conditions of gradual developing hearing loss. The system reached a maximum of 150 dB sound peak pressure level and a maximum of 133 dB A-weighted sound pressure level. Various parameters could easily be adjusted to control the sound, such as the high and low cutoff frequency to center the sound at 4 kHz. The system build can easily be adjusted to create numerous sound conditions and will hopefully be modified and improved in hopes of eventually being used for animal studies to lead to the creation of a method to treat or prevent noise induced hearing loss.
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.
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.
A modified Gaussian sum approach to estimation of non-Gaussian signals
MAURO J. CAPUTI; RICHARD L. MOOSE
1993-01-01
A Gaussian sum estimation algorithm has previously been developed to deal with noise processes that are non-Gaussian. Inherent in this algorithm is a serious growing memory problem that causes the number of terms in the Gaussian sum to increase exponentially at each iteration. A modified Gaussian sum estimation algorithm using an adaptive filter is developed that avoids the growing memory
A modified Gaussian sum approach to estimation of non-Gaussian signals
Mauro J. Caputi; Richard L. Moose
1993-01-01
A Gaussian sum estimation algorithm has previously been developed to deal with noise processes that are non-Gaussian. Inherent in this algorithm is a serious growing memory problem that causes the number of terms in the Gaussian sum to increase exponentially at each iteration. A modified Gaussian sum estimation algorithm is developed here that avoids the growing memory problem of the
SELF-ADAPTIVE INDEPENDENT COMPONENT ANALYSIS for SUB-GAUSSIAN and SUPER-GAUSSIAN MIXTURES with
Vialatte, François
SELF-ADAPTIVE INDEPENDENT COMPONENT ANALYSIS for SUB-GAUSSIAN and SUPER-GAUSSIAN MIXTURES that source have general- ized Gaussian, Cauchy or Rayleigh distributions. Ex- tensive computer simulations mixture of sub and super-Gaussian sources. I. INTRODUCTION The problem of independent component analy- sis
Nonlinear Predictive Control with Gaussian Process Model
Kocijan, J.; Murray-Smith, R.
Kocijan,J. Murray-Smith,R. Proceedings of the Hamilton Summer School on Switching and Learning in Feedback systems, Ed. R. Murray-Smith, R. Shorten, Springer-Verlag, Lecture Notes in Computing Science, Vol. 3355 pp p185-200 Springer Verlag
Mixtures of Gaussian Processes Volker Tresp
Tresp, Volker
a Gaussian like- lihood model. GPR can be generalized by using likelihood models from the exponential familyMixtures of Gaussian Processes Volker Tresp Siemens AG, Corporate Technology, Department of Neural the mixture of Gaussian processes (MGP) model which is useful for applications in which the optimal bandwidth
Broadcasting Correlated Gaussian Sources with Bandwidth Expansion
Alajaji, Fady
-power-limited Gaussian channel with matched bandwidth. Tian and Shamai generalize This work was supported in part region in broadcasting a Gaussian mixture source are provided. In this work, we consider the problemBroadcasting Correlated Gaussian Sources with Bandwidth Expansion Hamid Behroozi, Fady Alajaji
Bipartite and Multipartite Entanglement of Gaussian States
Gerardo Adesso; Fabrizio Illuminati
2005-01-01
In this chapter we review the characterization of entanglement in Gaussian states of continuous variable systems. For two-mode Gaussian states, we discuss how their bipartite entanglement can be accurately quantified in terms of the global and local amounts of mixedness, and efficiently estimated by direct measurements of the associated purities. For multimode Gaussian states endowed with local symmetry with respect
Monogamy Inequality for Distributed Gaussian Entanglement
Tohya Hiroshima; Gerardo Adesso; Fabrizio Illuminati
2007-01-01
We show that for all n-mode Gaussian states of continuous variable systems, the entanglement shared among n parties exhibits the fundamental monogamy property. The monogamy inequality is proven by introducing the Gaussian tangle, an entanglement monotone under Gaussian local operations and classical communication, which is defined in terms of the squared negativity in complete analogy with the case of n-qubit
Improving stability margins in discrete-time LQG controllers
NASA Technical Reports Server (NTRS)
Oranc, B. Tarik; Phillips, Charles L.
1987-01-01
Some of the problems are discussed which are encountered in the design of discrete-time stochastic controllers for problems that may adequately be described by the Linear Quadratic Gaussian (LQG) assumptions; namely, the problems of obtaining acceptable relative stability, robustness, and disturbance rejection properties. A dynamic compensator is proposed to replace the optimal full state feedback regulator gains at steady state, provided that all states are measurable. The compensator increases the stability margins at the plant input, which may possibly be inadequate in practical applications. Though the optimal regulator has desirable properties the observer based controller as implemented with a Kalman filter, in a noisy environment, has inadequate stability margins. The proposed compensator is designed to match the return difference matrix at the plant input to that of the optimal regulator while maintaining the optimality of the state estimates as directed by the measurement noise characteristics.
AESOP- INTERACTIVE DESIGN OF LINEAR QUADRATIC REGULATORS AND KALMAN FILTERS
NASA Technical Reports Server (NTRS)
Lehtinen, B.
1994-01-01
AESOP was developed to solve a number of problems associated with the design of controls and state estimators for linear time-invariant systems. The systems considered are modeled in state-variable form by a set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are the linear quadratic regulator (LQR) design problem and the steady-state Kalman filter design problem. AESOP is designed to be used in an interactive manner. The user can solve design problems and analyze the solutions in a single interactive session. Both numerical and graphical information are available to the user during the session. The AESOP program is structured around a list of predefined functions. Each function performs a single computation associated with control, estimation, or system response determination. AESOP contains over sixty functions and permits the easy inclusion of user defined functions. The user accesses these functions either by inputting a list of desired functions in the order they are to be performed, or by specifying a single function to be performed. The latter case is used when the choice of function and function order depends on the results of previous functions. The available AESOP functions are divided into several general areas including: 1) program control, 2) matrix input and revision, 3) matrix formation, 4) open-loop system analysis, 5) frequency response, 6) transient response, 7) transient function zeros, 8) LQR and Kalman filter design, 9) eigenvalues and eigenvectors, 10) covariances, and 11) user-defined functions. The most important functions are those that design linear quadratic regulators and Kalman filters. The user interacts with AESOP when using these functions by inputting design weighting parameters and by viewing displays of designed system response. Support functions obtain system transient and frequency responses, transfer functions, and covariance matrices. AESOP can also provide the user with open-loop system information including stability, controllability, and observability. The AESOP program is written in FORTRAN IV for interactive execution and has been implemented on an IBM 3033 computer using TSS 370. As currently configured, AESOP has a central memory requirement of approximately 2 Megs of 8 bit bytes. Memory requirements can be reduced by redimensioning arrays in the AESOP program. Graphical output requires adaptation of the AESOP plot routines to whatever device is available. The AESOP program was developed in 1984.
Integrated structural control design of large space structures
Allen, J.J.; Lauffer, J.P.
1995-01-01
Active control of structures has been under intensive development for the last ten years. Reference 2 reviews much of the identification and control technology for structural control developed during this time. The technology was initially focused on space structure and weapon applications; however, recently the technology is also being directed toward applications in manufacturing and transportation. Much of this technology focused on multiple-input/multiple-output (MIMO) identification and control methodology because many of the applications require a coordinated control involving multiple disturbances and control objectives where multiple actuators and sensors are necessary for high performance. There have been many optimal robust control methods developed for the design of MIMO robust control laws; however, there appears to be a significant gap between the theoretical development and experimental evaluation of control and identification methods to address structural control applications. Many methods have been developed for MIMO identification and control of structures, such as the Eigensystem Realization Algorithm (ERA), Q-Markov Covariance Equivalent Realization (Q-Markov COVER) for identification; and, Linear Quadratic Gaussian (LQG), Frequency Weighted LQG and H-/ii-synthesis methods for control. Upon implementation, many of the identification and control methods have shown limitations such as the excitation of unmodelled dynamics and sensitivity to system parameter variations. As a result, research on methods which address these problems have been conducted.
Quadratic diophantine equations and orders in quaternion algebras
Goro Shimura
2006-01-01
We first reformulate the main theorem on quadratic Diophantine equations given in our recent book in terms of the even Clifford group. In the quaternary case the group is the multiplicative group of a quaternion algebra, and the reformulated theorem connects a class of primitive solutions of a quadratic equation with a class of an order in the algebra. In
Collisions between type II two-dimensional quadratic solitons.
Costantini, B; De Angelis, C; Barthelemy, A; Bourliaguet, B; Kermene, V
1998-03-15
We report experimental and numerical results that describe collisions between two-dimensional type II quadratic solitons excited in a KTP crystal by fundamental waves of orthogonal polarization. Our results provide experimental evidence of the possibility of both inelastic collision (when two quadratic solitons merge at input into a single soliton at output) and quasi-elastic collision. PMID:18084532
ELLIPTICAL RANGE THEOREMS FOR GENERALIZED NUMERICAL RANGES OF QUADRATIC OPERATORS
Li, Chi-Kwong
ELLIPTICAL RANGE THEOREMS FOR GENERALIZED NUMERICAL RANGES OF QUADRATIC OPERATORS CHI-KWONG LI, YIU-TUNG POON, AND NUNG-SING SZE Abstract. The classical numerical range of a quadratic operator is an elliptical disk. This result is extended to different kinds of generalized numerical ranges. In particular
June 23, 2005 THE QUADRATIC EQUATION AS SOLVED BY PERSIAN
Osler, Thomas
1 June 23, 2005 THE QUADRATIC EQUATION AS SOLVED BY PERSIAN MATHEMATICANS OF THE MIDDLE AGES mathematicians. We will look at the solution of the quadratic as viewed by two Persian mathematicians Al in Sanskrit, Pahlavi, `the classical language of Persia', Syriac and Greek [4]. Khwarazmi's most famous
THE PARALLELIZED POLLARD KANGAROO METHOD IN REAL QUADRATIC FUNCTION FIELDS
Bernstein, Daniel
THE PARALLELIZED POLLARD KANGAROO METHOD IN REAL QUADRATIC FUNCTION FIELDS ANDREAS STEIN AND EDLYN TESKE Abstract. We show how to use the parallelized kangaroo method for computing invariants in real quadratic function #12;elds. Speci#12;cally, we show how to apply the kangaroo method to the infrastructure
Some Paradoxical Results for the Quadratically Weighted Kappa
ERIC Educational Resources Information Center
Warrens, Matthijs J.
2012-01-01
The quadratically weighted kappa is the most commonly used weighted kappa statistic for summarizing interrater agreement on an ordinal scale. The paper presents several properties of the quadratically weighted kappa that are paradoxical. For agreement tables with an odd number of categories "n" it is shown that if one of the raters uses the same…
Quadratic elongation: A quantitative measure of distortion in coordination polyhedra
Robinson, 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.
Quadratic Elongation: A Quantitative Measure of Distortion in Coordination Polyhedra
Keith Robinson; G. V. Gibbs; P. H. Ribbe
1971-01-01
Quadratic elongation and the variance of bond angles are linearly correlated for distorted octahedral and tetrahedral coordination complexes, both of which show variations in bond length and bond angle. The quadratic elongation is dimensionless, giving a quantitative measure of polyhedral distortion which is independent of the effective size of the polyhedron.
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…
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.)
Problems in Presenting Quadratics as a Unifying Topic.
ERIC Educational Resources Information Center
MacDonald, Theodore H.
1986-01-01
A sequence for teaching quadratic equations is presented. Considered are: multiplying arithmetic binomials, multiplying algebraic polynomials, reversing the process, missing terms, perfect squares, other special forms and diagrams, quadratic equations, completing the square, systematizing the process, the general form, graphing equations, and…
Effects of Classroom Instruction on Students' Understanding of Quadratic Equations
ERIC Educational Resources Information Center
Vaiyavutjamai, Pongchawee; Clements, M. A.
2006-01-01
Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of…
Complex digital signal processing using quadratic residue number systems
R. Krishnan; G. Jullien; W. Miller
1985-01-01
Recently, the Quadratic Residue Number System (QRNS) has been introduced [4,5,6], which allows the multiplication of complex integers with two real multiplications. Restrictions on the form of the moduli can be removed if an increase in real multiplications from two to three can be tolerated; the resulting number system has been termed the Modified Quadratic Residue Number System (MQRNS). In
THE KAPLANSKY RADICAL OF A QUADRATIC FIELD EXTENSION
THE KAPLANSKY RADICAL OF A QUADRATIC FIELD EXTENSION KARIM JOHANNES BECHER AND DAVID B. LEEP Abstract. The radical of a field consists of all nonzero elements that are represented by every binary quadratic form representing 1. Here, the radical is studied in relation to localglobal principles
THE KAPLANSKY RADICAL OF A QUADRATIC FIELD EXTENSION
THE KAPLANSKY RADICAL OF A QUADRATIC FIELD EXTENSION KARIM JOHANNES BECHER AND DAVID B. LEEP Abstract. The radical of a field consists of all nonzero elements that are represented by every binary quadratic form representing 1. Here, the radical is studied in relation to local-global principles
Semidefinite Relaxations for Non-Convex Quadratic Mixed-Integer ...
2011-11-08
Most algorithms and software tools for quadratic mixed-integer optimization ... closest vector problem (domains Z), and quadratic minimization with box con- .... The point to be separated is a pair (x0i,xii) from a positive semidefinite matrix X. By ...
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 formulate the inverse problem, and how to estimate the mean and variance of the magnetic vector field, even when the data consist of mixed combinations of directions and intensities. We examine palaeomagnetic secular-variation data from Hawaii and Re??union, and although these two sites are on almost opposite latitudes, we find significant differences in the mean vector and differences in the local vectorial variances, with the Hawaiian data being particularly anisotropic. These observations are inconsistent with a description of the mean field as being a simple geocentric axial dipole and with secular variation being statistically symmetrical with respect to reflection through the equatorial plane. Finally, our analysis of palaeomagnetic acquisition data from the 1960 Kilauea flow in Hawaii and the Holocene Xitle flow in Mexico, is consistent with the widely held suspicion that directional data are more accurate than intensity data.
Linear stability analysis of dynamical quadratic gravity
NASA Astrophysics Data System (ADS)
Ayzenberg, Dimitry; Yagi, Kent; Yunes, Nicolás
2014-02-01
We study the linear stability of dynamical, quadratic gravity, focusing on two particular subclasses (the even-parity sector, exemplified by Einstein-Dilaton-Gauss-Bonnet gravity, and the odd-parity sector, exemplified by dynamical Chern-Simons modified gravity) in the high-frequency, geometric optics approximation. This analysis is carried out by studying gravitational and scalar modes propagating on spherically symmetric and axially symmetric, vacuum solutions of the theory and finding the associated dispersion relations. These relations are solved in two separate cases (the scalar regime and the gravitational wave regime, defined by requiring the ratio of the amplitude of the perturbations to be much greater or smaller than unity) and found in both cases to not lead to exponential growth of the propagating modes, suggesting linearly stability. The modes are found to propagate at subluminal and superluminal speeds, depending on the propagating modes' direction relative to the background geometry, just as in dynamical Chern-Simons gravity.
Compact stars with quadratic equation of state
NASA Astrophysics Data System (ADS)
Ngubelanga, Sifiso A.; Maharaj, Sunil D.; Ray, Subharthi
2015-05-01
We provide new exact solutions to the Einstein-Maxwell system of equations for matter configurations with anisotropy and charge. The spacetime is static and spherically symmetric. A quadratic equation of state is utilised for the matter distribution. By specifying a particular form for one of the gravitational potentials and the electric field intensity we obtain new exact solutions in isotropic coordinates. In our general class of models, an earlier model with a linear equation of state is regained. For particular choices of parameters we regain the masses of the stars PSR J1614-2230, 4U 1608-52, PSR J1903+0327, EXO 1745-248 and SAX J1808.4-3658. A comprehensive physical analysis for the star PSR J1903+0327 reveals that our model is reasonable.
Digital image restoration using quadratic programming.
Abdelmalek, N N; Kasvand, T
1980-10-01
The problem of digital image restoration is considered by obtaining an approximate solution to the Fredholm integral equation of the first kind in two variables. The system of linear equations resulting from the discretization of the integral equation is converted to a consistent system of linear equations. The problem is then solved as a quadratic programming problem with bounded variables where the unknown solution is minimized in the L(2) norm. In this method minimum computer storage is needed, and the repeated solutions are obtained in an efficient way. Also the rank of the consistent system which gives a best or near best solution is estimated. Computer simulated examples using spatially separable pointspread functions are presented. Comments and conclusion are given. PMID:20234627
Multiplicative updates for nonnegative quadratic programming.
Sha, Fei; Lin, Yuanqing; Saul, Lawrence K; Lee, Daniel D
2007-08-01
Many problems in neural computation and statistical learning involve optimizations with nonnegativity constraints. In this article, we study convex problems in quadratic programming where the optimization is confined to an axis-aligned region in the nonnegative orthant. For these problems, we derive multiplicative updates that improve the value of the objective function at each iteration and converge monotonically to the global minimum. The updates have a simple closed form and do not involve any heuristics or free parameters that must be tuned to ensure convergence. Despite their simplicity, they differ strikingly in form from other multiplicative updates used in machine learning. We provide complete proofs of convergence for these updates and describe their application to problems in signal processing and pattern recognition. PMID:17571937
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.
Quadratic algebras for three-dimensional superintegrable systems
Daskaloyannis, C., E-mail: daskalo@math.auth.gr; Tanoudis, Y. [Aristotle University of Thessaloniki, Mathematics Department (Greece)
2010-02-15
The three-dimensional superintegrable systems with quadratic integrals of motion have five functionally independent integrals, one among them is the Hamiltonian. Kalnins, Kress, and Miller have proved that in the case of nondegenerate potentials with quadratic integrals of motion there is a sixth quadratic integral, which is linearly independent of the other integrals. The existence of this sixth integral implies that the integrals of motion form a ternary parafermionic-like quadratic Poisson algebra with five generators. In this contribution we investigate the structure of this algebra. We show that in all the nondegenerate cases there is at least one subalgebra of three integrals having a Poisson quadratic algebra structure, which is similar to the two-dimensional case.
Ikenaga, Bruce
of a quadratic equation. It depends on a procedure called completing the square. Here's the idea. Suppose you can for the variable-stuff by taking the square root of both sides. Example. Solve the equation for x. (a) x2 - 49 = 0 and x = 3. Suppose you start out with a quadratic equation where you don't have a perfect square on one
Wirosoetisno, Djoko
Quadratic Forms Elliptic Curves Modular Forms Elliptic Curves vs. Modular Forms Langlands My stuff. Modular Forms Langlands My stuff Some very classical number theory Number of ways a number N can. Modular Forms Langlands My stuff Three quadratic forms(1) P(x, y, u, v) P(x, y, u, v) = x2 + xy + 3y2 + u2
Inflation and non--Gaussianity
Alejandro Gangui; Jerome Martin; Mairi Sakellariadou
2002-05-14
We study non-Gaussian signatures on the cosmic microwave background (CMB) radiation predicted within inflationary models with non-vacuum initial states for cosmological perturbations. The model incorporates a privileged scale, which implies the existence of a feature in the primordial power spectrum. This broken-scale-invariant model predicts a vanishing three-point correlation function for the CMB temperature anisotropies (or any other odd-numbered-point correlation function) whilst an intrinsic non-Gaussian signature arises for any even-numbered-point correlation function. We thus focus on the first non-vanishing moment, the CMB four-point function at zero lag, namely the kurtosis, and compute its expected value for different locations of the primordial feature in the spectrum, as suggested in the literature to conform to observations of large scale structure. The excess kurtosis is found to be negative and the signal to noise ratio for the dimensionless excess kurtosis parameter is equal to $| S/N | \\simeq 4 \\times 10^{-4}$, almost independently of the free parameters of the model. This signature turns out to be undetectable. We conclude that, subject to current tests, Gaussianity is a generic property of single field inflationary models. The only uncertainty concerning this prediction is that the effect of back-reaction has not yet been properly incorporated. The implications for the trans-Planckian problem of inflation are also briefly discussed.
Nurmi, Sami [Department of Physics and Helsinki Institute of Physics, University of Helsinki, P.O. Box 64, FIN-00014 University of Helsinki (Finland); Byrnes, Christian T. [Astronomy Centre, University of Sussex, Brighton, BN1 9QH (United Kingdom); Tasinato, Gianmassimo, E-mail: sami.nurmi@helsinki.fi, E-mail: ctb22@sussex.ac.uk, E-mail: gianmassimo.tasinato@port.ac.uk [Institute of Cosmology and Gravitation, University of Portsmouth, PO1 3FX (United Kingdom)
2013-06-01
Primordial perturbations with wavelengths greater than the observable universe shift the effective background fields in our observable patch from their global averages over the inflating space. This leads to a landscape picture where the properties of our observable patch depend on its location and may significantly differ from the expectation values predicted by the underlying fundamental inflationary model. We show that if multiple fields are present during inflation, this may happen even if our horizon exit would be preceded by only a few e-foldings of inflation. Non-Gaussian statistics are especially affected: for example models of local non-Gaussianity predicting |f{sub NL}{sup 0}| >> 10 over the entire inflating volume can have a probability up to a few tens of percent to generate a non-detectable bispectrum in our observable patch |f{sub NL}{sup obs.}|?<10. In this work we establish systematic connections between the observable local properties of primordial perturbations and the global properties of the inflating space which reflect the underlying high energy physics. We study in detail the implications of both a detection and non-detection of primordial non-Gaussianity by Planck, and discover novel ways of characterising the naturalness of different observational configurations.
A Comparison of Multivariable Control Design Techniques for a Turbofan Engine Control
NASA Technical Reports Server (NTRS)
Garg, Sanjay; Watts, Stephen R.
1995-01-01
This paper compares two previously published design procedures for two different multivariable control design techniques for application to a linear engine model of a jet engine. The two multivariable control design techniques compared were the Linear Quadratic Gaussian with Loop Transfer Recovery (LQG/LTR) and the H-Infinity synthesis. The two control design techniques were used with specific previously published design procedures to synthesize controls which would provide equivalent closed loop frequency response for the primary control loops while assuring adequate loop decoupling. The resulting controllers were then reduced in order to minimize the programming and data storage requirements for a typical implementation. The reduced order linear controllers designed by each method were combined with the linear model of an advanced turbofan engine and the system performance was evaluated for the continuous linear system. Included in the performance analysis are the resulting frequency and transient responses as well as actuator usage and rate capability for each design method. The controls were also analyzed for robustness with respect to structured uncertainties in the unmodeled system dynamics. The two controls were then compared for performance capability and hardware implementation issues.
Francesca Aicardi
2008-03-27
The continue fractions of quadratic surds are periodic, according to a theorem by Lagrange. Their periods may have differing types of symmetries. This work relates these types of symmetries to the symmetries of the classes of the corresponding indefinite quadratic forms. This allows to classify the periods of quadratic surds and at the same time to find, for an arbitrary indefinite quadratic form, the symmetry type of its class and the number of integer points, for that class, contained in each domain of the Poincare' model of the de Sitter world, introduced in Part I. Moreover, we obtain the same information for every class of forms representing zero, by the finite continue fraction related to a special representative of that class. We will see finally the relation between the reduction procedure for indefinite quadratic forms, defined by the continued fractions, and the classical reduction theory, which acquires a geometrical description by the results of Part I.
Aicardi, Francesca
2007-01-01
The continue fractions of quadratic surds are periodic, according to a theorem by Lagrange. Their periods may have differing types of symmetries. This work relates these types of symmetries to the symmetries of the classes of the corresponding indefinite quadratic forms. This allows to classify the periods of quadratic surds and at the same time to find, for an arbitrary indefinite quadratic form, the symmetry type of its class and the number of integer points, for that class, contained in each domain of the Poincare' model of the de Sitter world, introduced in Part I. Moreover, we obtain the same information for every class of forms representing zero, by the finite continue fraction related to a special representative of that class. We will see finally the relation between the reduction procedure for indefinite quadratic forms, defined by the continued fractions, and the classical reduction theory, which acquires a geometrical description by the results of Part I.
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.
Control Law Synthesis for Vertical Fin Buffeting Alleviation Using Strain Actuation
NASA Technical Reports Server (NTRS)
Nitzsche, F.; Zimcik, D. G.; Ryall, T. G.; Moses, R. W.; Henderson, D. A.
1999-01-01
In the present investigation, the results obtained during the ground test of a closed-loop control system conducted on a full-scale fighter to attenuate vertical fin buffeting response using strain actuation are presented. Two groups of actuators consisting of piezoelectric elements distributed over the structure were designed to achieve authority over the first and second modes of the vertical fin. The control laws were synthesized using the Linear Quadratic Gaussian (LQG) method for a time-invariant control system. Three different pairs of sensors including strain gauges and accelerometers at different locations were used to close the feedback loop. The results demonstrated that measurable reductions in the root-mean-square (RMS) values of the fin dynamic response identified by the strain transducer at the critical point for fatigue at the root were achieved under the most severe buffet condition. For less severe buffet conditions, reductions of up to 58% were achieved.
NASA Technical Reports Server (NTRS)
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.
Cooling and squeezing via quadratic optomechanical coupling
Nunnenkamp, A.; Boerkje, K.; Harris, J. G. E.; Girvin, S. M. [Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520 (United States)
2010-08-15
We explore the physics of optomechanical systems in which an optical cavity mode is coupled parametrically to the square of the position of a mechanical oscillator. We derive an effective master equation describing two-phonon cooling of the mechanical oscillator. We show that for high temperatures and weak coupling, the steady-state phonon number distribution is nonthermal (Gaussian) and that even for strong cooling the mean phonon number remains finite. Moreover, we demonstrate how to achieve mechanical squeezing by driving the cavity with two beams. Finally, we calculate the optical output and squeezing spectra. Implications for optomechanics experiments with the membrane-in-the-middle geometry or ultracold atoms in optical resonators are discussed.
Breaking Gaussian incompatibility on continuous variable quantum systems
Teiko Heinosaari; Jukka Kiukas; Jussi Schultz
2015-05-11
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.
Models for the 3D singular isotropic oscillator quadratic algebra
Kalnins, E. G., E-mail: math0236@waikato.ac.n [University of Waikato, Department of Mathematics (New Zealand); Miller, W.; Post, S. [University of Minnesota, School of Mathematics (United States)
2010-02-15
We give the first explicit construction of the quadratic algebra for a 3D quantum superintegrable system with nondegenerate (4-parameter) potential together with realizations of irreducible representations of the quadratic algebra in terms of differential-differential or differential-difference and difference-difference operators in two variables. The example is the singular isotropic oscillator. We point out that the quantum models arise naturally from models of the Poisson algebras for the corresponding classical superintegrable system. These techniques extend to quadratic algebras for superintegrable systems in n dimensions and are closely related to Hecke algebras and multivariable orthogonal polynomials.
Quadratic integer programming for large scale banded matrices
NASA Technical Reports Server (NTRS)
Yan, T. Y.; Tan, H. H.
1982-01-01
This paper is concerned with the integer quadratic program where the variables are constrained to belong to a given set of discrete values. This quadratic integer program is shown to be equivalent to a problem of finding the shortest path in a particular directed graph called a trellis when the matrix is a positive-definite symmetric banded matrix. An efficient procedure for solving this shortest path problem is presented which allows the solution of the integer quadratic program. This method is particularly effective when the half-bandwidth of the matrix is significantly smaller than its dimension.
Time-optimal thermalization of single-mode Gaussian states
NASA Astrophysics Data System (ADS)
Carlini, Alberto; Mari, Andrea; Giovannetti, Vittorio
2014-11-01
We consider the problem of time-optimal control of a continuous bosonic quantum system subject to the action of a Markovian dissipation. In particular, we consider the case of a one-mode Gaussian quantum system prepared in an arbitrary initial state and which relaxes to the steady state due to the action of the dissipative channel. We assume that the unitary part of the dynamics is represented by Gaussian operations which preserve the Gaussian nature of the quantum state, i.e., arbitrary phase rotations, bounded squeezing, and unlimited displacements. In the ideal ansatz of unconstrained quantum control (i.e., when the unitary phase rotations, squeezing, and displacement of the mode can be performed instantaneously), we study how control can be optimized for speeding up the relaxation towards the fixed point of the dynamics and we analytically derive the optimal relaxation time. Our model has potential and interesting applications to the control of modes of electromagnetic radiation and of trapped levitated nanospheres.
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
A linear quadratic regulator approach to the stabilization of uncertain linear systems
NASA Technical Reports Server (NTRS)
Shieh, L. S.; Sunkel, J. W.; Wang, Y. J.
1990-01-01
This paper presents a linear quadratic regulator approach to the stabilization of uncertain linear systems. The uncertain systems under consideration are described by state equations with the presence of time-varying unknown-but-bounded uncertainty matrices. The method is based on linear quadratic regulator (LQR) theory and Liapunov stability theory. The robust stabilizing control law for a given uncertain system can be easily constructed from the symmetric positive-definite solution of the associated augmented Riccati equation. The proposed approach can be applied to matched and/or mismatched systems with uncertainty matrices in which only their matrix norms are bounded by some prescribed values and/or their entries are bounded by some prescribed constraint sets. Several numerical examples are presented to illustrate the results.
Minkowski Functional Description of Microwave Background Gaussianity
Serge Winitzki; Arthur Kosowsky
1997-10-15
A Gaussian distribution of cosmic microwave background temperature fluctuations is a generic prediction of inflation. Upcoming high-resolution maps of the microwave background will allow detailed tests of Gaussianity down to small angular scales, providing a crucial test of inflation. We propose Minkowski functionals as a calculational tool for testing Gaussianity and characterizing deviations from it. We review the mathematical formalism of Minkowski functionals of random fields; for Gaussian fields the functionals can be calculated exactly. We then apply the results to pixelized maps, giving explicit expressions for calculating the functionals from maps as well as the Gaussian predictions, including corrections for map boundaries, pixel noise, and pixel size and shape. Variances of the functionals for Gaussian distributions are derived in terms of the map correlation function. Applications to microwave background maps are discussed.
Local classifier weighting by quadratic programming.
Cevikalp, Hakan; Polikar, Robi
2008-10-01
It has been widely accepted that the classification accuracy can be improved by combining outputs of multiple classifiers. However, how to combine multiple classifiers with various (potentially conflicting) decisions is still an open problem. A rich collection of classifier combination procedures -- many of which are heuristic in nature -- have been developed for this goal. In this brief, we describe a dynamic approach to combine classifiers that have expertise in different regions of the input space. To this end, we use local classifier accuracy estimates to weight classifier outputs. Specifically, we estimate local recognition accuracies of classifiers near a query sample by utilizing its nearest neighbors, and then use these estimates to find the best weights of classifiers to label the query. The problem is formulated as a convex quadratic optimization problem, which returns optimal nonnegative classifier weights with respect to the chosen objective function, and the weights ensure that locally most accurate classifiers are weighted more heavily for labeling the query sample. Experimental results on several data sets indicate that the proposed weighting scheme outperforms other popular classifier combination schemes, particularly on problems with complex decision boundaries. Hence, the results indicate that local classification-accuracy-based combination techniques are well suited for decision making when the classifiers are trained by focusing on different regions of the input space. PMID:18842488
Monogamy inequality for distributed Gaussian entanglement
Tohya Hiroshima; Gerardo Adesso; Fabrizio Illuminati
2006-11-08
We show that for all n-mode Gaussian states of continuous variable systems, the entanglement shared among n parties exhibits the fundamental monogamy property. The monogamy inequality is proven by introducing the Gaussian tangle, an entanglement monotone under Gaussian local operations and classical communication, which is defined in terms of the squared negativity in complete analogy with the case of n-qubit systems. Our results elucidate the structure of quantum correlations in many-body harmonic lattice systems.
Monogamy inequality for distributed gaussian entanglement.
Hiroshima, Tohya; Adesso, Gerardo; Illuminati, Fabrizio
2007-02-01
We show that for all n-mode Gaussian states of continuous variable systems, the entanglement shared among n parties exhibits the fundamental monogamy property. The monogamy inequality is proven by introducing the Gaussian tangle, an entanglement monotone under Gaussian local operations and classical communication, which is defined in terms of the squared negativity in complete analogy with the case of n-qubit systems. Our results elucidate the structure of quantum correlations in many-body harmonic lattice systems. PMID:17358836
Bulk-Synchronous Parallel Gaussian Elimination
A. Tiskin
2002-01-01
The model of bulk-synchronous parallel (BSP) computation is an emerging paradigm of general-purpose parallel computing. We study the BSP complexity of Gaussian elimination and related problems. First, we analyze the Gaussian elimination without pivoting, which can be applied to the LU decomposition of symmetric positive-definite or diagonally dominant real matrices. Then we analyze the Gaussian elimination with Schönhage's recursive local
Pinning and disorder relevance for the lattice Gaussian free field
Giambattista Giacomin; Hubert Lacoin
2015-02-26
This paper provides a rigorous study of the localization transition for a Gaussian free field on $\\mathbb{Z}^d$ interacting with a quenched disordered substrate that acts on the interface when the interface height is close to zero. The substrate has the tendency to localize or repel the interface at different sites and one can show that a localization-delocalization transition takes place when varying the average pinning potential $h$: the free energy density is zero in the delocalized regime, that is for $h$ smaller than a threshold $h_c$, and it is positive for $h>h_c$. For $d\\ge 3$ we compute $h_c$ and we show that the transition happens at the same value as for the annealed model. However we can show that the critical behavior of the quenched model differs from the one of the annealed one. While the phase transition of the annealed model is of first order, we show that the quenched free energy is bounded above by $ (h-h_c)_+^2$ times a positive constant and that, for Gaussian disorder, the quadratic behavior is sharp. Therefore this provides an example in which a {\\sl relevant disorder critical exponent} can be made explicit: in theoretical physics disorder is said to be {\\sl relevant} when the disorder changes the critical behavior of a system and, while there are cases in which it is known that disorder is relevant, the exact critical behavior is typically unknown. For $d=2$ we are not able to decide whether the quenched and annealed critical points coincide, but we provide an upper bound for the difference between them.
Elegant Gaussian beams for enhanced optical manipulation
NASA Astrophysics Data System (ADS)
Alpmann, Christina; Schöler, Christoph; Denz, Cornelia
2015-06-01
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.
Optimal scaling of the ADMM algorithm for distributed quadratic ...
2014-12-11
Dec 11, 2014 ... algorithm for a class of distributed quadratic programming problems. ... Numerical simulations justify our results and highlight the benefits of optimally .... the past iterates when computing the next. ...... E. Chu, B. Peleato, and J. Eckstein, “
An Effective Branch-and-Bound Algorithm for Convex Quadratic ...
Christoph Buchheim,,,
singular, so that E(Q ,x ) may be a degenerate ellipsoid. Moreover, for ? ? R+, ...... vectors, we use the Block Korkin-Zolotarev basis reduction algorithm [16] implemented in NTL [17]. ..... by ?? modulation: the case of circulant quadratic forms.
Regular zeros of quadratic maps and their application
Arutyunov, Aram V; Karamzin, Dmitry Yu
2011-06-30
Sufficient conditions for the existence of regular zeros of quadratic maps are obtained. Their applications are indicated to certain problems of analysis related to the inverse function theorem in a neighbourhood of an abnormal point. Bibliography: 13 titles.
Geometric Procedures for Graphing the General Quadratic Equation.
ERIC Educational Resources Information Center
DeTemple, Duane W.
1984-01-01
How tedious algebraic manipulations for simplifying general quadratic equations can be supplemented with simple geometric procedures is discussed. These procedures help students determine the type of conic and its axes and allow a graph to be sketched quickly. (MNS)
Stability and control of singularly perturbed systems. Second annual report
Khalil, H.; El-Ansary, M.; Gajic, Z.; Litkouhi, B.; Saberi, A.
1982-09-01
This report surveys the results obtained during the second year of the three-year project entitled, Multimodel Strategies for Stochastic Models, and supported by the US Department of Energy, Electric Energy Systems Division. The report is divided into four parts. Part One presents a new method for studying stability of singularly perturbed systems using quadratic-type Lyapunov functions. The method is less conservative than the previous methods reported in the literature. Several examples are included to demonstrate that. Part Two is a continuation of our effort to study sampled-data control of singularly perturbed systems (see Part Three of the first annual report). Here we study singularly perturbed difference equations resulting from discretizing continious-time singularly perturbed systems. Part Three presents an important development in linear-quadratic Gaussian estimation and control of singularly perturbed systems. Near-optimum estimators and regulators are obtained using a special transformation to decouple slow and fast dynamics. Part Four considers a class of nonlinear singularly perturbed systems driven by wide-band noise and derives a reduced-order diffusion model that represents the behavior of the slow variables.
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.
Effects of classroom instruction on students’ understanding of quadratic equations
Pongchawee Vaiyavutjamai
2006-01-01
Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand,\\u000a attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data\\u000a from the students’ written responses to the equations, together with data in the form of transcripts of 36 interviews with\\u000a 18
Scale-invariant rotating black holes in quadratic gravity
Cognola, Guido; Vanzo, Luciano
2015-01-01
Black hole solutions in pure quadratic theories of gravity are interesting since they allow to formulate a set of scale-invariant thermodynamics laws. Recently, we have proven that static scale-invariant black holes have a well-defined entropy, which characterizes equivalent classes of solutions. In this paper, we generalize these results and explore the thermodynamics of rotating black holes in pure quadratic gravity.
Quadratic fluctuation-dissipation theorem: The quantum domain
G. Kalman; Xiao-Yue Gu
1987-01-01
A derivation of a general relationship between the frequency- and wave-number-dependent longitudinal quadratic response functions and the three-point dynamical structure function (the Fourier transform of the equilibrium three-point density-density correlations) is presented. This relationship is the full quadratic equivalent, valid for quantum systems of arbitrary degeneracy, of the customary (linear) fluctuation-dissipation theorem. The high-temperature limit reproduces earlier classical results, while
Quadratic function approaching method for magnetotelluric soundingdata inversion
Liangjun, Yan; Wenbao, Hu; Zhang, Keni
2004-04-05
The quadratic function approaching method (QFAM) is introduced for magnetotelluric sounding (MT) data inversion. The method takes the advantage of that quadratic function has single extreme value, which avoids leading to an inversion solution for local minimum and ensures the solution for global minimization of an objective function. The method does not need calculation of sensitivity matrix and not require a strict initial earth model. Examples for synthetic data and field measurement data indicate that the proposed inversion method is effective.
AdS waves as exact solutions to quadratic gravity
Guellue, Ibrahim; Sisman, Tahsin Cagri; Tekin, Bayram [Department of Physics, Middle East Technical University, 06531 Ankara (Turkey); Guerses, Metin [Department of Mathematics, Faculty of Sciences Bilkent University, 06800 Ankara (Turkey)
2011-04-15
We give an exact solution of the quadratic gravity in D dimensions. The solution is a plane-fronted wave metric with a cosmological constant. This metric solves not only the full quadratic gravity field equations but also the linearized ones which include the linearized equations of the recently found critical gravity. A subset of the solutions change the asymptotic structure of the anti-de Sitter space due to their logarithmic behavior.
On active-set methods for the quadratic programming problem
NASA Astrophysics Data System (ADS)
Daryina, A. N.; Izmailov, A. F.
2012-04-01
The active-set Newton method developed earlier by the authors for mixed complementarity problems is applied to solving the quadratic programming problem with a positive definite matrix of the objective function. A theoretical justification is given to the fact that the method is guaranteed to find the exact solution in a finite number of steps. Numerical results indicate that this approach is competitive with other available methods for quadratic programming problems.
Psiaki, Mark L.
has been developed to approximate one Gaussian mixture by another in a process that generalizes. 5. A sensible generalization of the PF is to use Gaussian mixtures to represent probability density of Dirac delta functions. A Gaussian mixture generalizes this concept by using elements that have finite
Inflation and non--Gaussianity
Gangui, A; Sakellariadou, M; Gangui, Alejandro; Martin, Jerome; Sakellariadou, Mairi
2002-01-01
We study non-Gaussian signatures on the cosmic microwave background (CMB) radiation predicted within inflationary models with non-vacuum initial states for cosmological perturbations. The model incorporates a privileged scale, which implies the existence of a feature in the primordial power spectrum. This broken-scale-invariant model predicts a vanishing three-point correlation function for the CMB temperature anisotropies (or any other odd-numbered-point correlation function) whilst an intrinsic non-Gaussian signature arises for any even-numbered-point correlation function. We thus focus on the first non-vanishing moment, the CMB four-point function at zero lag, namely the kurtosis, and compute its expected value for different locations of the primordial feature in the spectrum, as suggested in the literature to conform to observations of large scale structure. The excess kurtosis is found to be negative and the signal to noise ratio for the dimensionless excess kurtosis parameter is equal to $| S/N | \\simeq...
Time-Inconsistent Stochastic LinearQuadratic Control Hanqing Jin
well-known examples of time- inconsistency. Probability distortion, as in behavioral finance models [11.213841/2008. Mathematical Institute and Nomura Centre for Mathematical Finance, and OxfordMan Institute of Quantitative Finance, The University of Oxford, 2429 St Giles, Oxford OX1 3LB, UK. This author is partially
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
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.
REGULATORS OF RANK ONE QUADRATIC TWISTS CHRISTOPHE DELAUNAY AND XAVIER-FRANCOIS ROBLOT
Paris-Sud XI, Université de
) quadratic twist of E is a quadratic twist such that the sign of the func- tional equation of its LREGULATORS OF RANK ONE QUADRATIC TWISTS CHRISTOPHE DELAUNAY AND XAVIER-FRANC¸OIS ROBLOT Abstract. We investigate the regulators of elliptic curves with rank 1 in some families of quadratic twists
hp calculators HP 50g Solving for roots of polynomials and quadratics
Vetter, Frederick J.
hp calculators HP 50g Solving for roots of polynomials and quadratics The Numeric Solver Practice finding roots of polynomials and quadratics #12;hp calculators HP 50g Solving for roots of polynomials and quadratics hp calculators - 2 - HP 50g Solving for roots of polynomials and quadratics The Numeric Solver
Chi, Sung Goo; Cho, Nam Zin [Korea Advanced Institute of Science and Technology (Korea, Republic of)
2002-02-15
A robust controller is designed by applying the H{sub {infinity}} optimal control theory to the xenon control for the load-following operation of a nuclear reactor. The set of reactor model equations for controller design is a stiff system. This singularly perturbed system arises from the interaction of slow dynamics modes (iodine and xenon concentrations) and fast dynamics modes (neutron density, fuel and coolant temperatures). The singular perturbation technique is used to overcome this stiffness problem. The design specifications are incorporated by the frequency weights using the mixed-sensitivity problem approach. The robustness of H{sub {infinity}} control is demonstrated by comparing it with linear quadratic Gaussian (LQG) control in the case of a measurement delay of the power measurement system.Since the gains and phase margins of H{sub {infinity}} control are larger than those of LQG control, the H{sub {infinity}} control is expected to provide excellent stability robustness and performance robustness against external disturbances and noises, model parameter variations, and modeling errors as well as hardware failures. It may also provide a practical design method because the design specifications can be easily implemented by the frequency weights.
Particle swarm optimization with Gaussian mutation
Natsuki Higashi; Hitoshi Iba
2003-01-01
In this paper we present particle swarm optimization with Gaussian mutation combining the idea of the particle swarm with concepts from evolutionary algorithms. This method combines the traditional velocity and position update rules with the ideas of Gaussian mutation. This model is tested and compared with the standard PSO and standard GA. The comparative experiments have been conducted on unimodal
The peak width of nearly Gaussian peaks
R. Delley
1984-01-01
In chromatography the peak shape is often described by the method of statistical moments and therefore the second central moment is considered as the correct measure of peak width. Using the exponentially modified Gaussian peak model as an example and a criterion more related to chromatography, the extent of separation, it is shown that for nearly Gaussian peaks the width
Twin Gaussian Processes for Structured Prediction
Liefeng Bo; Cristian Sminchisescu
2010-01-01
We describe twin Gaussian processes (TGP), a generic structured prediction method that uses Gaussian process (GP) priors on both covariates and responses, both multivariate, and estimates outputs by minimizing the Kullback-Leibler divergence between two GP modeled as normal distributions over finite index sets of training and testing examples, emphasizing the goal that similar inputs should produce similar percepts and this
Partially polarized Gaussian Schell-model beams
F. Gori; M. Santarsiero; G. Piquero; R. Borghi; A. Mondello; R. Simon
2001-01-01
We consider a class of beams that are both partially polarized and partially coherent from the spatial standpoint. They are characterized by a correlation matrix whose elements have the same form as the mutual intensity of a Gaussian Schell-model beam. We focus our attention on those beams that would appear identical to ordinary Gaussian Schell-model beams in a scalar treatment.
Iterative Gaussianization: From ICA to Random Rotations
Valero Laparra; Gustavo Camps-Valls; Jesus Malo
2011-01-01
Most signal processing problems involve the chal- lenging 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 Gaussian- ization (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
H? Gaussian filter on infinite time horizon
Xiang Chen; Kemin Zhou
2002-01-01
Addresses design of H? Gaussian filters on infinite time horizon. In particular, we are interested in the robust filter design in a Gaussian noisy environment for a target plant which is subject to model uncertainty. The proposed filter can be treated as a natural extension of the Kalman filter for plants with model uncertainty in their worst cases. It is
Entanglement in Gaussian matrix-product states
Adesso, Gerardo [Centre for Quantum Computation, DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Dipartimento di Fisica 'E. R. Caianiello', Universita degli Studi di Salerno, INFN Sezione di Napoli-Gruppo Collegato di Salerno, Via S. Allende, 84081 Baronissi (Saudi Arabia) (Italy); Ericsson, Marie [Centre for Quantum Computation, DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
2006-09-15
Gaussian matrix-product states are obtained as the outputs of projection operations from an ancillary space of M infinitely entangled bonds connecting neighboring sites, applied at each of N sites of a harmonic chain. Replacing the projections by associated Gaussian states, the building blocks, we show that the entanglement range in translationally invariant Gaussian matrix-product states depends on how entangled the building blocks are. In particular, infinite entanglement in the building blocks produces fully symmetric Gaussian states with maximum entanglement range. From their peculiar properties of entanglement sharing, a basic difference with spin chains is revealed: Gaussian matrix-product states can possess unlimited, long-range entanglement even with minimum number of ancillary bonds (M=1). Finally we discuss how these states can be experimentally engineered from N copies of a three-mode building block and N two-mode finitely squeezed states.
On Gaussian Beams Described by Jacobi's Equation
Steven Thomas Smith
2014-04-18
Gaussian beams describe the amplitude and phase of rays and are widely used to model acoustic propagation. This paper describes four new results in the theory of Gaussian beams. (1) A new version of the \\v{C}erven\\'y equations for the amplitude and phase of Gaussian beams is developed by applying the equivalence of Hamilton-Jacobi theory with Jacobi's equation that connects Riemannian curvature to geodesic flow. Thus the paper makes a fundamental connection between Gaussian beams and an acoustic channel's so-called intrinsic Gaussian curvature from differential geometry. (2) A new formula $\\pi(c/c")^{1/2}$ for the distance between convergence zones is derived and applied to several well-known profiles. (3) A class of "model spaces" are introduced that connect the acoustics of ducting/divergence zones with the channel's Gaussian curvature $K=cc"-(c')^2$. The "model" SSPs yield constant Gaussian curvature in which the geometry of ducts corresponds to great circles on a sphere and convergence zones correspond to antipodes. The distance between caustics $\\pi(c/c")^{1/2}$ is equated with an ideal hyperbolic cosine SSP duct. (4) An "intrinsic" version of \\v{C}erven\\'y's formulae for the amplitude and phase of Gaussian beams is derived that does not depend on an "extrinsic" arbitrary choice of coordinates such as range and depth. Direct comparisons are made between the computational frameworks used by the three different approaches to Gaussian beams: Snell's law, the extrinsic Frenet-Serret formulae, and the intrinsic Jacobi methods presented here. The relationship of Gaussian beams to Riemannian curvature is explained with an overview of the modern covariant geometric methods that provide a general framework for application to other special cases.
Optimal Power Management in Wireless Control Systems
Plotkin, Joshua B.
Optimal Power Management in Wireless Control Systems Konstantinos Gatsis, Student Member, IEEE to the controller over a wireless fading channel. The power allocated to these transmissions determines channels, power adaptation, linear quadratic control, con- trol/communication separation, event
Generation of radially polarized Bessel-Gaussian beams from c-cut Nd:YVO? laser.
Vyas, Sunil; Kozawa, Yuichi; Sato, Shunichi
2014-02-15
We experimentally demonstrate the generation of radially polarized Bessel-Gaussian beams from a c-cut Nd:YVO? laser with a hemispherical cavity configuration by proper mode control. The output beam has an annular-shaped intensity distribution with radial polarization. When the beam is focused, the intensity pattern changes to a multi-ring, which is a typical characteristic of the lowest transverse mode of vector Bessel-Gaussian beam. Higher-order modes of vector Bessel-Gaussian beam are also observed from the same cavity by slightly changing the cavity alignment. The experimental results show a good agreement with the simulation results for both focal and far fields. The present method is a simple and direct way for generating vector Bessel-Gaussian beams. PMID:24562288
Engineering extremal two-qubit entangled states with maximally entangled Gaussian light
Adesso, G; Illuminati, F; Paternostro, M
2010-01-01
We study state engineering induced by bilinear interactions between two remote qubits and light fields prepared in two-mode Gaussian states. The attainable two-qubit states span the entire physically allowed region in the entanglement-vs-global-purity plane. We show that two-mode Gaussian states with maximal entanglement at fixed global and marginal entropies produce maximally entangled two-qubit states in the corresponding entropic diagram. The target two-qubit entanglement is determined quantitatively only by the purities of the two-mode Gaussian resource. Thus, a small set of parameters characterizing extremally entangled two-mode Gaussian states is sufficient to control completely the engineering of extremally entangled two-qubit states, which can be realized in realistic scenarios of cavity and circuit quantum electrodynamics.
Effects of classroom instruction on students' understanding of quadratic equations
NASA Astrophysics Data System (ADS)
Vaiyavutjamai, Pongchawee; Clements, M. A. (Ken)
2006-05-01
Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of transcripts of 36 interviews with 18 interviewees (a high performer, a medium performer, and a low performer from each of the six classes), were analysed. Using a rubric for assessing students' understanding, the analysis revealed that at the post-teaching stage students improved their performance on quadratic equations and had a better understanding of associated concepts than they had at the pre-teaching stage. However, many were still confused about the concepts of a variable and of a "solution" to a quadratic equation. After the lessons, most students had acquired neither an instrumental nor a relational understanding of the mathematics associated with solving elementary quadratic equations.
Gaussian measures of entanglement versus negativities: Ordering of two-mode Gaussian states
Adesso, Gerardo; Illuminati, Fabrizio [Dipartimento di Fisica 'E. R. Caianiello', Universita di Salerno, CNR-Coherentia, Gruppo di Salerno (Italy); INFN Sezione di Napoli-Gruppo Collegato di Salerno, Via S. Allende, 84081 Baronissi, SA (Italy)
2005-09-15
We study the entanglement of general (pure or mixed) two-mode Gaussian states of continuous-variable systems by comparing the two available classes of computable measures of entanglement: entropy-inspired Gaussian convex-roof measures and positive partial transposition-inspired measures (negativity and logarithmic negativity). We first review the formalism of Gaussian measures of entanglement, adopting the framework introduced in M. M. Wolf et al., Phys. Rev. A 69, 052320 (2004), where the Gaussian entanglement of formation was defined. We compute explicitly Gaussian measures of entanglement for two important families of nonsymmetric two-mode Gaussian state: namely, the states of extremal (maximal and minimal) negativities at fixed global and local purities, introduced in G. Adesso et al., Phys. Rev. Lett. 92, 087901 (2004). This analysis allows us to compare the different orderings induced on the set of entangled two-mode Gaussian states by the negativities and by the Gaussian measures of entanglement. We find that in a certain range of values of the global and local purities (characterizing the covariance matrix of the corresponding extremal states), states of minimum negativity can have more Gaussian entanglement of formation than states of maximum negativity. Consequently, Gaussian measures and negativities are definitely inequivalent measures of entanglement on nonsymmetric two-mode Gaussian states, even when restricted to a class of extremal states. On the other hand, the two families of entanglement measures are completely equivalent on symmetric states, for which the Gaussian entanglement of formation coincides with the true entanglement of formation. Finally, we show that the inequivalence between the two families of continuous-variable entanglement measures is somehow limited. Namely, we rigorously prove that, at fixed negativities, the Gaussian measures of entanglement are bounded from below. Moreover, we provide some strong evidence suggesting that they are as well bounded from above.
Goyal, Vivek K
Matching to Interference Lav R. Varshney, Member, IEEE, and Sanjoy K. Mitter, Life Fellow, IEEE Abstract of Technology. L. R. Varshney was with and S. K. Mitter is with the Department of Elec- trical Engineering of Technology, Cambridge, MA, 02139 USA (e-mail: varshney@alum.mit.edu; mitter@mit.edu). Digital Object
Gaussian coordinate systems for the Kerr metric
M. Novello; E. Bittencourt
2010-04-22
We present the whole class of Gaussian coordinate systems for the Kerr metric. This is achieved through the uses of the relationship between Gaussian observers and the relativistic Hamilton-Jacobi equation. We analyze the completeness of this coordinate system. In the appendix we present the equivalent JEK formulation of General Relativity -- the so-called quasi-Maxwellian equations -- which acquires a simpler form in the Gaussian coordinate system. We show how this set of equations can be used to obtain the internal metric of the Schwazschild solution, as a simple example. We suggest that this path can be followed to the search of the internal Kerr metric.
Nonparametric Bayesian Density Modeling with Gaussian Processes
Adams, Ryan Prescott; MacKay, David J C
2009-01-01
We present the Gaussian process density sampler (GPDS), an exchangeable generative model for use in nonparametric Bayesian density estimation. Samples drawn from the GPDS are consistent with exact, independent samples from a distribution defined by a density that is a transformation of a function drawn from a Gaussian process prior. Our formulation allows us to infer an unknown density from data using Markov chain Monte Carlo, which gives samples from the posterior distribution over density functions and from the predictive distribution on data space. We describe two such MCMC methods. Both methods also allow inference of the hyperparameters of the Gaussian process.
Cloning of Gaussian states by linear optics
Olivares, Stefano; Paris, Matteo G. A.; Andersen, Ulrik L. [Dipartimento di Fisica dell'Universita degli Studi di Milano (Italy); Institut fuer Optik, Information und Photonik, Max-Planck Forschungsgruppe, Universitaet Erlangen-Nuernberg, Guenther-Scharowsky strasse 1, 91058, Erlangen (Germany)
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. PMID:18518022
Non-Gaussian signatures of tachyacoustic cosmology
Bessada, Dennis, E-mail: dennis.bessada@unifesp.br [UNIFESP — Universidade Federal de Săo Paulo, Laboratório de Física Teórica e Computaçăo Científica, Rua Săo Nicolau, 210, 09913-030, Diadema, SP (Brazil)
2012-09-01
I investigate non-Gaussian signatures in the context of tachyacoustic cosmology, that is, a noninflationary model with superluminal speed of sound. I calculate the full non-Gaussian amplitude A, its size f{sub NL}, and corresponding shapes for a red-tilted spectrum of primordial scalar perturbations. Specifically, for cuscuton-like models I show that f{sub NL} ? O(1), and the shape of its non-Gaussian amplitude peaks for both equilateral and local configurations, the latter being dominant. These results, albeit similar, are quantitatively distinct from the corresponding ones obtained by Magueijo et al. in the context of superluminal bimetric models.
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.
Driving/Braking Force Distribution of Four Wheel Vehicle by Quadratic Programming with Constraints
NASA Astrophysics Data System (ADS)
Ikeda, Yuichi; Suzuki, Ryo; Chida, Yuichi
This paper proposes a yaw rate tracking control method that distributes the driving/ braking force exerted on vehicles at the time of negotiating sharp turns and driving at high speeds. The proposed method employs quadratic programming to distribute the driving/braking force in order to equalize the tire load factor on all wheels and consider the limits of the driving/braking force. The yaw rate tracking performance can be improved even while driving at high speeds and negotiating sharp turns by setting limits for the driving/braking force, differential moment, etc. The effectiveness of our proposed method is proven by a numerical simulation.
Equi-ripple design of quadratic-phase RF pulses
NASA Astrophysics Data System (ADS)
Schulte, Rolf F.; Tsao, Jeffrey; Boesiger, Peter; Pruessmann, Klaas P.
2004-01-01
An improved strategy for the design of quadratic-phase RF pulses with high selectivity and broad bandwidths using the Shinnar-Le Roux (SLR) transformation is proposed. Unlike previous implementations, the required quadratic-phase finite impulse response (FIR) filters are generated using the complex Remez exchange algorithm, which ensures an equi-ripple deviation from the ideal response function. It is argued analytically that quadratic-phase pulses are near-optimal in terms of minimising the B1-amplitude for a given bandwidth and flip angle. Furthermore, several parameter relations are derived, providing practical design guidelines. The effectiveness of the proposed design method is demonstrated by examples of excitation and saturation pulses applied in vitro and in vivo.
A class of quadratic deformations of Lie superalgebras
Peter Jarvis; Gerd Rudolph; Luke Yates
2011-06-24
We study certain Z_2-graded, finite-dimensional polynomial algebras of degree 2 which are a special class of deformations of Lie superalgebras, which we call quadratic Lie superalgebras. Starting from the formal definition, we discuss the generalised Jacobi relations in the context of the Koszul property, and give a proof of the PBW basis theorem. We give several concrete examples of quadratic Lie superalgebras for low dimensional cases, and discuss aspects of their structure constants for the `type I' class. We derive the equivalent of the Kac module construction for typical and atypical modules, and a related direct construction of irreducible modules due to Gould. We investigate in detail one specific case, the quadratic generalisation gl_2(n/1) of the Lie superalgebra sl(n/1). We formulate the general atypicality conditions at level 1, and present an analysis of zero-and one-step atypical modules for a certain family of Kac modules.
Quadratic algebra approach to relativistic quantum Smorodinsky-Winternitz systems
Marquette, Ian [Department of Mathematics, University of York, Heslington, York YO10 5DD (United Kingdom)
2011-04-15
There exists a relation between the Klein-Gordon and the Dirac equations with scalar and vector potentials of equal magnitude and the Schroedinger equation. We obtain the relativistic energy spectrum for the four relativistic quantum Smorodinsky-Winternitz systems from their quasi-Hamiltonian and the quadratic algebras studied by Daskaloyannis in the nonrelativistic context. We also apply the quadratic algebra approach directly to the initial Dirac equation for these four systems and show that the quadratic algebras obtained are the same than those obtained from the quasi-Hamiltonians. We point out how results obtained in context of quantum superintegrable systems and their polynomial algebras can be applied to the quantum relativistic case.
The generalized quadratic knapsack problem. A neuronal network approach.
Talaván, Pedro M; Yáńez, Javier
2006-05-01
The solution of an optimization problem through the continuous Hopfield network (CHN) is based on some energy or Lyapunov function, which decreases as the system evolves until a local minimum value is attained. A new energy function is proposed in this paper so that any 0-1 linear constrains programming with quadratic objective function can be solved. This problem, denoted as the generalized quadratic knapsack problem (GQKP), includes as particular cases well-known problems such as the traveling salesman problem (TSP) and the quadratic assignment problem (QAP). This new energy function generalizes those proposed by other authors. Through this energy function, any GQKP can be solved with an appropriate parameter setting procedure, which is detailed in this paper. As a particular case, and in order to test this generalized energy function, some computational experiments solving the traveling salesman problem are also included. PMID:16488117
Quadratic $n$-ary Hom-Nambu algebras
Faouzi Ammar; Sami Mabrouk; Abdenacer Makhlouf
2011-10-10
The purpose of this paper is to introduce and study quadratic $n$-ary Hom-Nambu algebras, which are $n$-ary Hom-Nambu algebras with an invariant, nondegenerate and symmetric bilinear forms that are also $\\alpha$-symmetric and $\\beta$-invariant where $\\alpha$ and $\\beta$ are twisting maps. We provide constructions of these $n$-ary algebras by using twisting principles, tensor product and T*-extension. Also is discussed their connections with representation theory and centroids. Moreover we show that one may derive from quadratic $n$-ary Hom-Nambu algebra ones of increasingly higher arities and that under suitable assumptions it reduces to a quadratic $(n-1)$-ary Hom-Nambu algebra.
The bounds of feasible space on constrained nonconvex quadratic programming
NASA Astrophysics Data System (ADS)
Zhu, Jinghao
2008-03-01
This paper presents a method to estimate the bounds of the radius of the feasible space for a class of constrained nonconvex quadratic programmingsE Results show that one may compute a bound of the radius of the feasible space by a linear programming which is known to be a P-problem [N. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica 4 (1984) 373-395]. It is proposed that one applies this method for using the canonical dual transformation [D.Y. Gao, Canonical duality theory and solutions to constrained nonconvex quadratic programming, J. Global Optimization 29 (2004) 377-399] for solving a standard quadratic programming problem.
Design, test, and evaluation of three active flutter suppression controllers
NASA Technical Reports Server (NTRS)
Adams, William M., Jr.; Christhilf, David M.; Waszak, Martin R.; Mukhopadhyay, Vivek; Srinathkumar, S.
1992-01-01
Three control law design techniques for flutter suppression are presented. Each technique uses multiple control surfaces and/or sensors. The first method uses traditional tools (such as pole/zero loci and Nyquist diagrams) for producing a controller that has minimal complexity and which is sufficiently robust to handle plant uncertainty. The second procedure uses linear combinations of several accelerometer signals and dynamic compensation to synthesize the model rate of the critical mode for feedback to the distributed control surfaces. The third technique starts with a minimum-energy linear quadratic Gaussian controller, iteratively modifies intensity matrices corresponding to input and output noise, and applies controller order reduction to achieve a low-order, robust controller. The resulting designs were implemented digitally and tested subsonically on the active flexible wing wind-tunnel model in the Langley Transonic Dynamics Tunnel. Only the traditional pole/zero loci design was sufficiently robust to errors in the nominal plant to successfully suppress flutter during the test. The traditional pole/zero loci design provided simultaneous suppression of symmetric and antisymmetric flutter with a 24-percent increase in attainable dynamic pressure. Posttest analyses are shown which illustrate the problems encountered with the other laws.
Fermionic Meixner probability distributions, Lie algebras and quadratic Hamiltonians
L. Accardi; I. Ya. Aref'eva; I. V. Volovich
2014-11-17
We introduce the quadratic Fermi algebra, which is a Lie algebra, and show that the vacuum distributions of the associated Hamiltonians define the fermionic Meixner probability distributions. In order to emphasize the difference with the Bose case, we apply a modification of the method used in the above calculation to obtain a simple and straightforward classification of the 1--dimensional Meixner laws in terms of homogeneous quadratic expressions in the Bose creation and annihilation operators. There is a huge literature of the Meixner laws but this, purely quantum probabilistic, derivation seems to be new. Finally we briefly discuss the possible multi-dimensional extensions of the above results.
FRW in quadratic form of f( T) gravitational theories
NASA Astrophysics Data System (ADS)
Nashed, G. L.
2015-07-01
We derive asymptote solution of a homogeneous and isotropic universe governed by the quadratic form of the field equation of f( T) gravity. We explain how the higher order of the torsion can provide an origin for late accelerated phase of the universe in the FRW. The solution makes the scalar torsion T to be a function of the cosmic time t. We show that for the equation of state with the scale factor represent late phase of universe. We perform the cosmological studies and show how the quadratic form of f( T) effect on the behavior of these studies.
Stability of the Quadratic Equation of Pexider Type
Soon-Mo Jung
2000-01-01
We will investigate the stability problem of the quadratic equation (1) and extend the results of Borelli and Forti, Czerwik,\\u000a and Rassias. By applying this result and an improved theorem of the author, we will also prove the stability of the quadratic\\u000a functional equation of Pexider type,f\\u000a 1 (x +y) + f2(x -y) =f\\u000a 3(x) +f\\u000a 4(y), for a large
On Evgrafov-Fedoryuk's theory and quadratic differentials
NASA Astrophysics Data System (ADS)
Shapiro, Boris
2015-02-01
The purpose of this note is to recall the theory of the (homogenized) spectral problem for Schrödinger equation with a polynomial potential and its relation with quadratic differentials. We derive from results of this theory that the accumulation rays of the eigenvalues of the latter problem are in 1-1 -correspondence with the short geodesics of the singular planar metrics induced by the corresponding quadratic differential. We prove that for a polynomial potential of degree d, the number of such accumulation rays can be any positive integer between (d-1) and d atopwithdelims ()2.
On the Dual of Monomial Quadratic p -ary Bent Functions
Tor Helleseth; Alexander Kholosha
2007-01-01
Considered are quadratic p-ary bent functions having the form \\u000a f(x)=Trn(a xpj+1)f(x)={\\\\rm Tr}_n(a x^{p^j+1})\\u000a . Described is the general Gold-like class of bent functions that covers all the previously known monomial quadratic cases.\\u000a Obtained is the exact value of the Walsh transform coefficients for a bent function in this class. In particular, presented\\u000a is an explicit expressions for a dual of
On Evgrafov-Fedoryuk's theory and quadratic differentials
NASA Astrophysics Data System (ADS)
Shapiro, Boris
2015-06-01
The purpose of this note is to recall the theory of the (homogenized) spectral problem for Schrödinger equation with a polynomial potential and its relation with quadratic differentials. We derive from results of this theory that the accumulation rays of the eigenvalues of the latter problem are in -correspondence with the short geodesics of the singular planar metrics induced by the corresponding quadratic differential. We prove that for a polynomial potential of degree the number of such accumulation rays can be any positive integer between and.
Approximate inference in Gaussian graphical models
Malioutov, Dmitry M., 1981-
2008-01-01
The focus of this thesis is approximate inference in Gaussian graphical models. A graphical model is a family of probability distributions in which the structure of interactions among the random variables is captured by a ...
Optimal unitary dilation for bosonic Gaussian channels
Caruso, Filippo [Institut fuer Theoretische Physik, Universitaet Ulm, Albert-Einstein-Allee 11, D-89069 Ulm (Germany); Eisert, Jens [Dahlem Center for Complex Quantum Systems, Freie Universitaet Berlin, D-14195 Berlin (Germany); Giovannetti, Vittorio [NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, Piazza dei Cavalieri 7, I-56126 Pisa (Italy); Holevo, Alexander S. [Steklov Mathematical Institute, Gubkina 8, RU-119991 Moscow (Russian Federation)
2011-08-15
A general quantum channel can be represented in terms of a unitary interaction between the information-carrying system and a noisy environment. In this paper the minimal number of quantum Gaussian environmental modes required to provide a unitary dilation of a multimode bosonic Gaussian channel is analyzed for both pure and mixed environments. We compute this quantity in the case of pure environment corresponding to the Stinespring representation and give an improved estimate in the case of mixed environment. The computations rely, on one hand, on the properties of the generalized Choi-Jamiolkowski state and, on the other hand, on an explicit construction of the minimal dilation for arbitrary bosonic Gaussian channel. These results introduce a new quantity reflecting ''noisiness'' of bosonic Gaussian channels and can be applied to address some issues concerning transmission of information in continuous variables systems.
Optimal cloning of mixed Gaussian states
Guta, Madalin [University of Nijmegen, Toernooiveld 1, Postbus 9010, 6500 GL Nijmegen (Netherlands); Matsumoto, Keiji [National Inatitute of Informatics, 2-1-2, Hitotsubashi, Chiyoda-ku, Tokyo, 101-8430 (Japan); Quantum Computation and Information Project, JST, Hongo 5-28-3, Bunkyo-ku, Tokyo 113-0033 (Japan)
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.
Generalized competitive learning of gaussian mixture models.
Lu, Zhiwu; Ip, Horace H S
2009-08-01
When fitting Gaussian mixtures to multivariate data, it is crucial to select the appropriate number of Gaussians, which is generally referred to as the model selection problem. Under regularization theory, we aim to solve this model selection problem through developing an entropy regularized likelihood (ERL) learning on Gaussian mixtures. We further present a gradient algorithm for this ERL learning. Through some theoretic analysis, we have shown a mechanism of generalized competitive learning that is inherent in the ERL learning, which can lead to automatic model selection on Gaussian mixtures and also make our ERL learning algorithm less sensitive to the initialization as compared to the standard expectation-maximization algorithm. The experiments on simulated data using our algorithm verified our theoretic analysis. Moreover, our ERL learning algorithm has been shown to outperform other competitive learning algorithms in the application of unsupervised image segmentation. PMID:19362913
Gaussian Faithful Markov Trees Dhafer Malouche 1
Paris-Sud XI, Université de
Gaussian Faithful Markov Trees Dhafer Malouche 1 & Bala Rajaratnam 2 1 Ecole Sup´erieure de la Statistique et de l'Analyse de l'Information. dhafer.malouche@essai.rnu.tn 2 Stanford University brajarat
Effect of different Gaussian width on disappearance of flow
Rajni; Suneel Kumar
2011-08-04
In the present paper, we reduce and enhance the scaled Gaussian width(SGW) by 30% from the normal SGW of the systems and see its effect on balance energy. The scaled Gaussian width can be defined as the ratio of Gaussian width used for any nuclei to the Gaussian width used for Au nuclei(i.e. 8.66 $fm^2$).
Effect of different Gaussian width on disappearance of flow
Rajni,
2011-01-01
In the present paper, we reduce and enhance the scaled Gaussian width(SGW) by 30% from the normal SGW of the systems and see its effect on balance energy. The scaled Gaussian width can be defined as the ratio of Gaussian width used for any nuclei to the Gaussian width used for Au nuclei(i.e. 8.66 $fm^2$).
A Gaussian mixture ensemble transform filter Sebastian Reich
Reich, Sebastian
A Gaussian mixture ensemble transform filter Sebastian Reich August 14, 2011 Abstract We generalize the form of a Gaussian mixture or a Gaussian kernel density estimator. The design of the filter is based Gaussian mix- ture filter (EGMF). The EGMF is implemented for three simple test problems (Brownian dynamics
UNDERDETERMINED BLIND SOURCE SEPARATION BASED ON GENERALIZED GAUSSIAN DISTRIBUTION
Yoo, Chang D.
UNDERDETERMINED BLIND SOURCE SEPARATION BASED ON GENERALIZED GAUSSIAN DISTRIBUTION SangGyun Kim mixtures of sources with both sub- and super- Gaussian distributions is proposed. In order to separate the sub- and super-Gaussian sources in the underdeterminedcase, generalized Gaussian distribution (GGD
Continuous Gaussian Mixture Modeling Stephen Aylward1 and Stephen Pize?
North Carolina at Chapel Hill, University of
Continuous Gaussian Mixture Modeling Stephen Aylward1 and Stephen Pize? 1Department of Radiology 2 vectors has a Gaussian distribution, those samples have a generalized projective Gaussian distribution will demonstrate that GPGDs are better represented by continuous Gaussian mixture models (CGMMs) than fmite
A Gaussian mixture ensemble transform filter
Reich, Sebastian
2011-01-01
We generalize the popular ensemble Kalman filter to an ensemble transform filter where the prior distribution can take the form of a Gaussian mixture. The design of the filter is based on a continuous formulation of the Bayesian filter analysis step. We call the new filter algorithm the ensemble Gaussian mixture filter (EGMF). The EGMF is implemented for two simple test problems (Brownian dynamics in one dimension and a modified Lorenz-96 model).
Speaker Verification Using Adapted Gaussian Mixture Models
Douglas A. Reynolds; Thomas F. Quatieri; Robert B. Dunn
2000-01-01
Reynolds, Douglas A., Quatieri, Thomas F., and Dunn, Robert B., Speaker Verification Using Adapted Gaussian Mixture Models, Digital Signal Processing10(2000), 19–41.In this paper we describe the major elements of MIT Lincoln Laboratory's Gaussian mixture model (GMM)-based speaker verification system used successfully in several NIST Speaker Recognition Evaluations (SREs). The system is built around the likelihood ratio test for verification, using
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).
Unitarily localizable entanglement of Gaussian states
Alessio Serafini; Gerardo Adesso; Fabrizio Illuminati
2005-01-01
We consider generic (m×n) -mode bipartitions of continuous-variable systems, and study the associated bisymmetric multimode Gaussian states. They are defined as (m+n) -mode Gaussian states invariant under local mode permutations on the m -mode and n -mode subsystems. We prove that such states are equivalent, under local unitary transformations, to the tensor product of a two-mode state and of m+n-2
Gaussian beam tracing for ocean acoustics
NASA Astrophysics Data System (ADS)
Porter, Michael B.; Hursky, Paul
2010-09-01
Gaussian beam tracing methods have emerged as a standard approach for modeling sound propagation in the ocean. The first implementations were developed in the 1970's by Bucker and evolved significantly. Today there are actually some four different types of Gaussian beam algorithms. They are quite different in terms of both the beam characteristics and their performance. This paper will review the development of the methods and their application to typical ocean acoustic problems.
NASA Astrophysics Data System (ADS)
Brahma, Sanjoy; Datta, Biswa
2009-07-01
The partial quadratic eigenvalue assignment problem (PQEVAP) concerns the reassignment of a small number of undesirable eigenvalues of a quadratic matrix pencil, while leaving the remaining large number of eigenvalues and the corresponding eigenvectors unchanged. The problem arises in controlling undesirable resonance in vibrating structures and in stabilizing control systems. The solution of this problem requires computations of a pair of feedback matrices. For practical effectiveness, these feedback matrices must be computed in such a way that their norms and the condition number of the closed-loop eigenvector matrix are as small as possible. These considerations give rise to the minimum norm partial quadratic eigenvalue assignment problem (MNPQEVAP) and the robust partial quadratic eigenvalue assignment problem (RPQEVAP), respectively. In this paper we propose new optimization based algorithms for solving these problems. The problems are solved directly in a second-order setting without resorting to a standard first-order formulation so as to avoid the inversion of a possibly ill-conditioned matrix and the loss of exploitable structures of the original model. The algorithms require the knowledge of only the open-loop eigenvalues to be replaced and their corresponding eigenvectors. The remaining open-loop eigenvalues and their corresponding eigenvectors are kept unchanged. The invariance of the large number of eigenvalues and eigenvectors under feedback is guaranteed by a proven mathematical result. Furthermore, the gradient formulas needed to solve the problems by using the quasi-Newton optimization technique employed are computed in terms of the known quantities only. Above all, the proposed methods do not require the reduction of the model order or the order of the controller, even when the underlying finite element model has a very large degree of freedom. These attractive features, coupled with minimal computational requirements, such as solutions of small diagonal Sylvester equations make the proposed algorithms ideally suited for application to large real-life structures. Numerical results show significant improvement in feedback norms and in the condition number of the closed-loop system. Also, the closed-loop eigenvalues have acceptable accuracy.
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.
A contribution to matrix quadratic equations
V. Kucera
1972-01-01
The well-known matrix algebraic equation of the optimal control and filtering theory is considered. A necessary and sufficient condition for its solution to yield an optimal as well as asymptotically stable closed-loop system is given. The condition involves the concepts of stabilizability and detectability.
MODEL PREDICTIVE CONTROL AND STATE ESTIMATION: A NETWORK EXAMPLE
Bitmead, Bob
estimates are provided by a Kalman Filter, which yields an estimate of the plant state and a state estimate is applied to the plant. Then the output response is measured, the state estimate updated. This is to be considered in a constrained linear quadratic gaussian (LQG) problem. Be- cause of the existence of noise
Non-Gaussian halo assembly bias
Reid, Beth A.; Verde, Licia [Institute for Sciences of the Cosmos (ICC), University of Barcelona and IEEC, Barcelona 08028 (Spain); Dolag, Klaus [Max Planck Institute for Astrophysics, P.O. Box 1317, D85741 Garching (Germany); Matarrese, Sabino [Dipartimento di Fisica ''G. Galilei'', Universitŕ degli Studi di Padova, via Marzolo 8, I-35131 Padova (Italy); Moscardini, Lauro, E-mail: beth.ann.reid@gmail.com, E-mail: liciaverde@icc.ub.edu, E-mail: kdolag@mpa-garching.mpg.de, E-mail: sabino.matarrese@pd.infn.it, E-mail: lauro.moscardini@unibo.it [Dipartimento di Astronomia, Universitŕ di Bologna, Via Ranzani 1, I-40127 Bologna (Italy)
2010-07-01
The strong dependence of the large-scale dark matter halo bias on the (local) non-Gaussianity parameter, f{sub NL}, offers a promising avenue towards constraining primordial non-Gaussianity with large-scale structure surveys. In this paper, we present the first detection of the dependence of the non-Gaussian halo bias on halo formation history using N-body simulations. We also present an analytic derivation of the expected signal based on the extended Press-Schechter formalism. In excellent agreement with our analytic prediction, we find that the halo formation history-dependent contribution to the non-Gaussian halo bias (which we call non-Gaussian halo assembly bias) can be factorized in a form approximately independent of redshift and halo mass. The correction to the non-Gaussian halo bias due to the halo formation history can be as large as 100%, with a suppression of the signal for recently formed halos and enhancement for old halos. This could in principle be a problem for realistic galaxy surveys if observational selection effects were to pick galaxies occupying only recently formed halos. Current semi-analytic galaxy formation models, for example, imply an enhancement in the expected signal of ? 23% and ? 48% for galaxies at z = 1 selected by stellar mass and star formation rate, respectively.
Bidhan Chandra Bag; Chin-Kun Hu
2007-01-01
In a previous paper [Bag and Hu, Phys. Rev. E 73, 061107 (2006)], we studied the mean lifetime (MLT) for the escape of a Brownian particle through an unstable limit cycle driven by multiplicative colored Gaussian and additive Gaussian white noises and found resonant activation (RA) behavior. In the present paper we switch from Gaussian to non-Gaussian multiplicative colored noise.
Analysis of non-Gaussian surge response of tension leg platforms under wind loads
Kareem, A. (Univ. of Notre Dame, IN (United States). Dept. of Civil Engineering and Geological Sciences); Zhao, J. (Barnett Casbarian Inc., Houston, TX (United States))
1994-08-01
The nonlinearity in the wind loading expression for a complaint offshore structure, e.g., a tension leg platform (TLP), results in response statistics that deviate from the Gaussian distribution. This paper focuses on the statistical analysis of the response of these structures to random wind loads. The analysis presented here involves a nonlinear system with memory. As an improvement over the commonly used linearization approach, an equivalent statistical quadratization method is presented. The higher-order response cumulants are based on Volterra series. A direct integration scheme and Kac-Siegert technique is utilized to evaluate the response cumulants. Based on the first four cumulants, the response probability density function, crossing rates, and peak value distribution are derived. The results provide a good comparison with simulation. A nonlinear wind gust loading factor based on the derived extreme value distribution of nonlinear wind effects is formulated.
Properties of holograms recorded in a material with quadratic nonlinearity
Yu. N. Denisyuk
2006-01-01
This paper discusses the properties of a hologram recorded in a medium that possesses quadratic nonlinearity when the frequencies of the nonlinear and reference waves are identical and different. It is shown theoretically and experimentally that holograms of this type can form three-dimensional images of objects. Experiments on the recording of holograms were carried out using a pulsed Nd:YAG laser
Quadratic Diophantine equations, the class number, and the massformula
Goro Shimura
2006-01-01
1. The basic setting and two ternary cases We take a finite-dimensional vector space V over a field F and take also an F -bilinear symmetric form ? : V × V ? F. We then put ?(x )= ?(x, x )f or x ? V, thus using the same letter ? for the quadratic form and the corresponding symmetric
Solving quadratically constrained least squares using black box solvers
Tony F. Chan; Julia A. Olkin; Donald W. Cooley
1992-01-01
We present algorithms for solving quadratically constrained linear least squares problems that do not necessarily require expensive dense matrix factorizations. Instead, only “black box” solvers for certain related unconstrained least squares problems, as well as the solution of two related linear systems involving the coefficient matrixA and the constraint matrixB, are required. Special structures in the problem can thus be
Least squares problems with inequality constraints as quadratic constraints
Jodi L. Mead; Rosemary A Renauty
2010-01-01
Linear least squares problems with box constraints are commonly solved to find model parameters within bounds based on physical considerations. Common algorithms include Bounded Variable Least Squares (BVLS) and the Matlab function lsqlin. Here, the goal is to find solutions to ill-posed inverse problems that lie within box constraints. To do this, we formulate the box constraints as quadratic constraints,
On Differences of Two Squares in Some Quadratic Fields
Andrej Dujella; Zrinka Franuši?
2007-01-01
It this paper, we study the problem of determining the el- ements in the rings of integers of quadratic fields Q( p d) which are rep- resentable as a dierence of two squares. The complete solution of the problem is obtained for integers d which satisfy conditions given in terms of solvability of certain Pellian equations.
Solving quadratic programming problems with linear Hopfield networks
Evgeny Dudnikov
2003-01-01
We consider a linear Hopfield network for solving quadratic programming problems with equation constraints. The problem is reduced to the solution of the ordinary linear differential equations with arbitrary square matrix. Because of some properties of this matrix the special methods are required for good convergence of the system. After some comparative study of neural network models for solving this
Solving quadratic programming problems with linear Hopfield networks
Evgeny Dudnikov
2001-01-01
We consider a linear Hopfield network for solving quadratic programming problems with equation constraints. The problem is reduced to the solution of ordinary linear differential equations with arbitrary square matrix. Because of some properties of this matrix special methods are required for good convergence of the system. After some comparative studies of neural network models for solving this problem we
Quantum electroweak symmetry breaking through loop quadratic contributions
NASA Astrophysics Data System (ADS)
Bai, Dong; Cui, Jian-Wei; Wu, Yue-Liang
2015-06-01
Based on two postulations that (i) the Higgs boson has a large bare mass mH ?mh ? 125 GeV at the characteristic energy scale Mc which defines the Standard Model (SM) in the ultraviolet region, and (ii) quadratic contributions of Feynman loop diagrams in quantum field theories are physically meaningful, we show that the SM electroweak symmetry breaking is induced by the quadratic contributions from loop effects. As the quadratic running of Higgs mass parameter leads to an additive renormalization, which distinguishes from the logarithmic running with a multiplicative renormalization, the symmetry breaking occurs once the sliding energy scale ? moves from Mc down to a transition scale ? =?EW at which the additive renormalized Higgs mass parameter mH2 (Mc / ?) gets to change the sign. With the input of current experimental data, this symmetry breaking energy scale is found to be ?EW ? 760 GeV, which provides another basic energy scale for the SM besides Mc. Studying such a symmetry breaking mechanism could play an important role in understanding both the hierarchy problem and naturalness problem. It also provides a possible way to explore the experimental implications of the quadratic contributions as ?EW lies within the probing reach of the LHC and the future Great Collider.
Quadratic assignment problems generated with the Palubetskis algorithm are degenerate
David Cyganski; Richard F. Vaz; V. Glenn Virball
1994-01-01
The quadratic assignment problem (QAP) is a combinatorial optimization problem that arises in many applications such as the allocation of processes in distributed computer systems. The QAP is NP-hard and therefore no algorithms are known for solving the QAP in polynomial time. For this reason a variety of heuristic methods have been proposed for this problem. In order to evaluate
Computing greatest common divisors and factorizations in quadratic number fields
Erich Kaltofen; Heinrich Rolletschek
1989-01-01
In a quadratic number field Q(? + + D ), D a squarefree integer, with class number 1 any algebraic integer can be decomposed uniquely into primes but for only 21 domains Euclidean algorithms are known. It was shown by Cohn (5) that for D ? -19 even remainder sequences with possibly non-decreasing norms cannot determine the GCD of arbitrary