International Nuclear Information System (INIS)
Belyakov, V.; Kavin, A.; Rumyantsev, E.; Kharitonov, V.; Misenov, B.; Ovsyannikov, A.; Ovsyannikov, D.; Veremei, E.; Zhabko, A.; Mitrishkin, Y.
1999-01-01
This paper is focused on the linear quadratic Gaussian (LQG) controller synthesis methodology for the ITER plasma current, position and shape control system as well as power derivative management system. It has been shown that some poloidal field (PF) coils have less influence on reference plasma-wall gaps control during plasma disturbances and hence they have been used to reduce total control power derivative by means of the additional non-linear feedback. The design has been done on the basis of linear models. Simulation was provided for non-linear model and results are presented and discussed. (orig.)
Yang, Kangjian; Yang, Ping; Wang, Shuai; Dong, Lizhi; Xu, Bing
2018-05-01
We propose a method to identify tip-tilt disturbance model for Linear Quadratic Gaussian control. This identification method based on Levenberg-Marquardt method conducts with a little prior information and no auxiliary system and it is convenient to identify the tip-tilt disturbance model on-line for real-time control. This identification method makes it easy that Linear Quadratic Gaussian control runs efficiently in different adaptive optics systems for vibration mitigation. The validity of the Linear Quadratic Gaussian control associated with this tip-tilt disturbance model identification method is verified by experimental data, which is conducted in replay mode by simulation.
Neural network-based nonlinear model predictive control vs. linear quadratic gaussian control
Cho, C.; Vance, R.; Mardi, N.; Qian, Z.; Prisbrey, K.
1997-01-01
One problem with the application of neural networks to the multivariable control of mineral and extractive processes is determining whether and how to use them. The objective of this investigation was to compare neural network control to more conventional strategies and to determine if there are any advantages in using neural network control in terms of set-point tracking, rise time, settling time, disturbance rejection and other criteria. The procedure involved developing neural network controllers using both historical plant data and simulation models. Various control patterns were tried, including both inverse and direct neural network plant models. These were compared to state space controllers that are, by nature, linear. For grinding and leaching circuits, a nonlinear neural network-based model predictive control strategy was superior to a state space-based linear quadratic gaussian controller. The investigation pointed out the importance of incorporating state space into neural networks by making them recurrent, i.e., feeding certain output state variables into input nodes in the neural network. It was concluded that neural network controllers can have better disturbance rejection, set-point tracking, rise time, settling time and lower set-point overshoot, and it was also concluded that neural network controllers can be more reliable and easy to implement in complex, multivariable plants.
ORACLS: A system for linear-quadratic-Gaussian control law design
Armstrong, E. S.
1978-01-01
A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.
Directory of Open Access Journals (Sweden)
Tarek Hassan Mohamed
2015-12-01
Full Text Available This paper presented both the linear quadratic Gaussian technique (LQG and the coefficient diagram method (CDM as load frequency controllers in a multi-area power system to deal with the problem of variations in system parameters and load demand change. The full states of the system including the area frequency deviation have been estimated using the Kalman filter technique. The efficiency of the proposed control method has been checked using a digital simulation. Simulation results indicated that, with the proposed CDM + LQG technique, the system is robust in the face of parameter uncertainties and load disturbances. A comparison between the proposed technique and other schemes is carried out, confirming the superiority of the proposed CDM + LQG technique.
International Nuclear Information System (INIS)
Murphy, G.V.; Bailey, J.M.
1990-01-01
This paper uses the linear quadratic Gaussian with loop transfer recovery (LQG/LTR) control system design method to obtain a level control system for a low-pressure feedwater heater train. The control system performance and stability robustness are evaluated for a given set of system design specifications. The tools for analysis are the return ratio, return difference, and inverse return difference singular-valve plots for a loop break at the plant output. 3 refs., 7 figs., 2 tabs
Optimal control linear quadratic methods
Anderson, Brian D O
2007-01-01
This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material.The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the
Linear quadratic Gaussian balancing for discrete-time infinite-dimensional linear systems
Opmeer, MR; Curtain, RF
2004-01-01
In this paper, we study the existence of linear quadratic Gaussian (LQG)-balanced realizations for discrete-time infinite-dimensional systems. LQG-balanced realizations are those for which the smallest nonnegative self-adjoint solutions of the control and filter Riccati equations are equal. We show
An example in linear quadratic optimal control
Weiss, George; Zwart, Heiko J.
1998-01-01
We construct a simple example of a quadratic optimal control problem for an infinite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme
Self-repeating properties of four-petal Gaussian vortex beams in quadratic index medium
Zou, Defeng; Li, Xiaohui; Chai, Tong; Zheng, Hairong
2018-05-01
In this paper, we investigate the propagation properties of four-petal Gaussian vortex (FPGV) beams propagating through the quadratic index medium, obtaining the analytical expression of FPGV beams. The effects of beam order n, topological charge m and beam waist ω0 are investigated. Results show that quadratic index medium support periodic distributions of FPGV beams. A hollow optical wall or an optical central principal maximum surrounded by symmetrical sidelobes will occur at the center of a period. At length, they will evolve into four petals structure, exactly same as the intensity distributions at source plane.
Time evolution of a Gaussian class of quasi-distribution functions under quadratic Hamiltonian.
Ginzburg, D; Mann, A
2014-03-10
A Lie algebraic method for propagation of the Wigner quasi-distribution function (QDF) under quadratic Hamiltonian was presented by Zoubi and Ben-Aryeh. We show that the same method can be used in order to propagate a rather general class of QDFs, which we call the "Gaussian class." This class contains as special cases the well-known Wigner, Husimi, Glauber, and Kirkwood-Rihaczek QDFs. We present some examples of the calculation of the time evolution of those functions.
Clemens, Joshua William
Game theory has application across multiple fields, spanning from economic strategy to optimal control of an aircraft and missile on an intercept trajectory. The idea of game theory is fascinating in that we can actually mathematically model real-world scenarios and determine optimal decision making. It may not always be easy to mathematically model certain real-world scenarios, nonetheless, game theory gives us an appreciation for the complexity involved in decision making. This complexity is especially apparent when the players involved have access to different information upon which to base their decision making (a nonclassical information pattern). Here we will focus on the class of adversarial two-player games (sometimes referred to as pursuit-evasion games) with nonclassical information pattern. We present a two-sided (simultaneous) optimization solution method for the two-player linear quadratic Gaussian (LQG) multistage game. This direct solution method allows for further interpretation of each player's decision making (strategy) as compared to previously used formal solution methods. In addition to the optimal control strategies, we present a saddle point proof and we derive an expression for the optimal performance index value. We provide some numerical results in order to further interpret the optimal control strategies and to highlight real-world application of this game-theoretic optimal solution.
On the Distribution of Indefinite Quadratic Forms in Gaussian Random Variables
Al-Naffouri, Tareq Y.
2015-10-30
© 2015 IEEE. In this work, we propose a unified approach to evaluating the CDF and PDF of indefinite quadratic forms in Gaussian random variables. Such a quantity appears in many applications in communications, signal processing, information theory, and adaptive filtering. For example, this quantity appears in the mean-square-error (MSE) analysis of the normalized least-meansquare (NLMS) adaptive algorithm, and SINR associated with each beam in beam forming applications. The trick of the proposed approach is to replace inequalities that appear in the CDF calculation with unit step functions and to use complex integral representation of the the unit step function. Complex integration allows us then to evaluate the CDF in closed form for the zero mean case and as a single dimensional integral for the non-zero mean case. Utilizing the saddle point technique allows us to closely approximate such integrals in non zero mean case. We demonstrate how our approach can be extended to other scenarios such as the joint distribution of quadratic forms and ratios of such forms, and to characterize quadratic forms in isotropic distributed random variables.We also evaluate the outage probability in multiuser beamforming using our approach to provide an application of indefinite forms in communications.
Non-Gaussian Stochastic Radiation Transfer in Finite Planar Media with Quadratic Scattering
International Nuclear Information System (INIS)
Sallah, M.
2016-01-01
The stochastic radiation transfer is considered in a participating planar finite continuously fluctuating medium characterized by non-Gaussian variability. The problem is considered for diffuse-reflecting boundaries with quadratic Rayleigh scattering. Random variable transformation (RVT) technique is used to get the complete average for the solution functions that are represented by the probability-density function (PDF) of the solution process. RVT algorithm applies a simple integral transformation to the input stochastic process (the extinction function of the medium). This linear transformation enables us to rewrite the stochastic transport equations in terms of the optical random variable (x) and the optical random thickness (L). Then the radiation transfer equation is solved deterministically to get a closed form for the solution as a function of x and L. So, the solution is used to obtain the PDF of the solution functions applying the RVT technique among the input random variable (L) and the output process (the solution functions). The obtained averages of the solution functions are used to get the complete analytical averages for some interesting physical quantities, namely, reflectivity, transmissivity and partial heat fluxes at the medium boundaries. Numerical results are represented graphically for different non-Gaussian probability distribution functions that compared with the corresponding Gaussian PDF.
Stochastic Linear Quadratic Optimal Control Problems
International Nuclear Information System (INIS)
Chen, S.; Yong, J.
2001-01-01
This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) forward-backward stochastic differential equations are established. Some results involving Riccati equation are discussed as well
Resolving Actuator Redundancy - Control Allocation vs. Linear Quadratic Control
Härkegård, Ola
2004-01-01
When designing control laws for systems with more inputs than controlled variables, one issue to consider is how to deal with actuator redundancy. Two tools for distributing the control effort among a redundant set of actuators are control allocation and linear quadratic control design. In this paper, we investigate the relationship between these two design tools when a quadratic performance index is used for control allocation. We show that for a particular class of linear systems, they give...
Gain scheduled linear quadratic control for quadcopter
Okasha, M.; Shah, J.; Fauzi, W.; Hanouf, Z.
2017-12-01
This study exploits the dynamics and control of quadcopters using Linear Quadratic Regulator (LQR) control approach. The quadcopter’s mathematical model is derived using the Newton-Euler method. It is a highly manoeuvrable, nonlinear, coupled with six degrees of freedom (DOF) model, which includes aerodynamics and detailed gyroscopic moments that are often ignored in many literatures. The linearized model is obtained and characterized by the heading angle (i.e. yaw angle) of the quadcopter. The adopted control approach utilizes LQR method to track several reference trajectories including circle and helix curves with significant variation in the yaw angle. The controller is modified to overcome difficulties related to the continuous changes in the operating points and eliminate chattering and discontinuity that is observed in the control input signal. Numerical non-linear simulations are performed using MATLAB and Simulink to illustrate to accuracy and effectiveness of the proposed controller.
Linear-quadratic control and quadratic differential forms for multidimensional behaviors
Napp, D.; Trentelman, H.L.
2011-01-01
This paper deals with systems described by constant coefficient linear partial differential equations (nD-systems) from a behavioral point of view. In this context we treat the linear-quadratic control problem where the performance functional is the integral of a quadratic differential form. We look
Quadratic theory and feedback controllers for linear time delay systems
International Nuclear Information System (INIS)
Lee, E.B.
1976-01-01
Recent research on the design of controllers for systems having time delays is discussed. Results for the ''open loop'' and ''closed loop'' designs will be presented. In both cases results for minimizing a quadratic cost functional are given. The usefulness of these results is not known, but similar results for the non-delay case are being routinely applied. (author)
Linear Quadratic Controller with Fault Detection in Compact Disk Players
DEFF Research Database (Denmark)
Vidal, Enrique Sanchez; Hansen, K.G.; Andersen, R.S.
2001-01-01
The design of the positioning controllers in Optical Disk Drives are today subjected to a trade off between an acceptable suppression of external disturbances and an acceptable immunity against surfaces defects. In this paper an algorithm is suggested to detect defects of the disk surface combined...... with an observer and a Linear Quadratic Regulator. As a result, the mentioned trade off is minimized and the playability of the tested compact disk player is considerably enhanced....
Linear-quadratic model predictions for tumor control probability
International Nuclear Information System (INIS)
Yaes, R.J.
1987-01-01
Sigmoid dose-response curves for tumor control are calculated from the linear-quadratic model parameters α and Β, obtained from human epidermoid carcinoma cell lines, and are much steeper than the clinical dose-response curves for head and neck cancers. One possible explanation is the presence of small radiation-resistant clones arising from mutations in an initially homogeneous tumor. Using the mutation theory of Delbruck and Luria and of Goldie and Coldman, the authors discuss the implications of such radiation-resistant clones for clinical radiation therapy
Functional Dual Adaptive Control with Recursive Gaussian Process Model
International Nuclear Information System (INIS)
Prüher, Jakub; Král, Ladislav
2015-01-01
The paper deals with dual adaptive control problem, where the functional uncertainties in the system description are modelled by a non-parametric Gaussian process regression model. Current approaches to adaptive control based on Gaussian process models are severely limited in their practical applicability, because the model is re-adjusted using all the currently available data, which keeps growing with every time step. We propose the use of recursive Gaussian process regression algorithm for significant reduction in computational requirements, thus bringing the Gaussian process-based adaptive controllers closer to their practical applicability. In this work, we design a bi-criterial dual controller based on recursive Gaussian process model for discrete-time stochastic dynamic systems given in an affine-in-control form. Using Monte Carlo simulations, we show that the proposed controller achieves comparable performance with the full Gaussian process-based controller in terms of control quality while keeping the computational demands bounded. (paper)
Bayesian nonparametric adaptive control using Gaussian processes.
Chowdhary, Girish; Kingravi, Hassan A; How, Jonathan P; Vela, Patricio A
2015-03-01
Most current model reference adaptive control (MRAC) methods rely on parametric adaptive elements, in which the number of parameters of the adaptive element are fixed a priori, often through expert judgment. An example of such an adaptive element is radial basis function networks (RBFNs), with RBF centers preallocated based on the expected operating domain. If the system operates outside of the expected operating domain, this adaptive element can become noneffective in capturing and canceling the uncertainty, thus rendering the adaptive controller only semiglobal in nature. This paper investigates a Gaussian process-based Bayesian MRAC architecture (GP-MRAC), which leverages the power and flexibility of GP Bayesian nonparametric models of uncertainty. The GP-MRAC does not require the centers to be preallocated, can inherently handle measurement noise, and enables MRAC to handle a broader set of uncertainties, including those that are defined as distributions over functions. We use stochastic stability arguments to show that GP-MRAC guarantees good closed-loop performance with no prior domain knowledge of the uncertainty. Online implementable GP inference methods are compared in numerical simulations against RBFN-MRAC with preallocated centers and are shown to provide better tracking and improved long-term learning.
Fault Tolerant Control Using Gaussian Processes and Model Predictive Control
Directory of Open Access Journals (Sweden)
Yang Xiaoke
2015-03-01
Full Text Available Essential ingredients for fault-tolerant control are the ability to represent system behaviour following the occurrence of a fault, and the ability to exploit this representation for deciding control actions. Gaussian processes seem to be very promising candidates for the first of these, and model predictive control has a proven capability for the second. We therefore propose to use the two together to obtain fault-tolerant control functionality. Our proposal is illustrated by several reasonably realistic examples drawn from flight control.
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.
Cost Cumulant-Based Control for a Class of Linear Quadratic Tracking Problems
National Research Council Canada - National Science Library
Pham, Khanh D
2007-01-01
.... For instance, the present paper extends the application of cost-cumulant controller design to control of a wide class of linear-quadratic tracking systems where output measurements of a tracker...
International Nuclear Information System (INIS)
Curtiss, L.A.; Raghavachari, K.; Pople, J.A.
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) and the use of scaled MP2 zero-point energies rather than scaled Hartree--Fock (HF) zero-point energies have also been examined. The set of 125 energies used for validation of G2 theory [J. Chem. Phys. 94, 7221 (1991)] is used to test out these variations of G2 theory. Inclusion of higher levels of correlation treatment has little effect except in the cases of multiply-bonded systems. In these cases better agreement is obtained in some cases and poorer agreement in others so that there is no improvement in overall performance. The use of QCISD geometries yields significantly better agreement with experiment for several cases including the ionization potentials of CS and O 2 , electron affinity of CN, and dissociation energies of N 2 , O 2 , CN, and SO 2 . This leads to a slightly better agreement with experiment overall. The MP2 zero-point energies gives no overall improvement. These methods may be useful for specific systems
Numerical Methods for Solution of the Extended Linear Quadratic Control Problem
DEFF Research Database (Denmark)
Jørgensen, John Bagterp; Frison, Gianluca; Gade-Nielsen, Nicolai Fog
2012-01-01
In this paper we present the extended linear quadratic control problem, its efficient solution, and a discussion of how it arises in the numerical solution of nonlinear model predictive control problems. The extended linear quadratic control problem is the optimal control problem corresponding...... to the Karush-Kuhn-Tucker system that constitute the majority of computational work in constrained nonlinear and linear model predictive control problems solved by efficient MPC-tailored interior-point and active-set algorithms. We state various methods of solving the extended linear quadratic control problem...... and discuss instances in which it arises. The methods discussed in the paper have been implemented in efficient C code for both CPUs and GPUs for a number of test examples....
Polishchuk, Alexander
2005-01-01
Quadratic algebras, i.e., algebras defined by quadratic relations, often occur in various areas of mathematics. One of the main problems in the study of these (and similarly defined) algebras is how to control their size. A central notion in solving this problem is the notion of a Koszul algebra, which was introduced in 1970 by S. Priddy and then appeared in many areas of mathematics, such as algebraic geometry, representation theory, noncommutative geometry, K-theory, number theory, and noncommutative linear algebra. The book offers a coherent exposition of the theory of quadratic and Koszul algebras, including various definitions of Koszulness, duality theory, Poincar�-Birkhoff-Witt-type theorems for Koszul algebras, and the Koszul deformation principle. In the concluding chapter of the book, they explain a surprising connection between Koszul algebras and one-dependent discrete-time stochastic processes.
An online re-linearization scheme suited for Model Predictive and Linear Quadratic Control
DEFF Research Database (Denmark)
Henriksen, Lars Christian; Poulsen, Niels Kjølstad
This technical note documents the equations for primal-dual interior-point quadratic programming problem solver used for MPC. The algorithm exploits the special structure of the MPC problem and is able to reduce the computational burden such that the computational burden scales with prediction...... horizon length in a linear way rather than cubic, which would be the case if the structure was not exploited. It is also shown how models used for design of model-based controllers, e.g. linear quadratic and model predictive, can be linearized both at equilibrium and non-equilibrium points, making...
International Nuclear Information System (INIS)
Hong-Bin, Zhang; Jian-Wei, Xia; Yong-Bin, Yu; Chuang-Yin, Dang
2010-01-01
This paper investigates the chaos synchronisation between two coupled chaotic Chua's circuits. The sufficient condition presented by linear matrix inequalities (LMIs) of global asymptotic synchronisation is attained based on piecewise quadratic Lyapunov functions. First, we obtain the piecewise linear differential inclusions (pwLDIs) model of synchronisation error dynamics, then we design a switching (piecewise-linear) feedback control law to stabilise it based on the piecewise quadratic Laypunov functions. Then we give some numerical simulations to demonstrate the effectiveness of our theoretical results
Delayed Stochastic Linear-Quadratic Control Problem and Related Applications
Directory of Open Access Journals (Sweden)
Li Chen
2012-01-01
stochastic differential equations (FBSDEs with Itô’s stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. Especially, we present the optimal feedback regulator for the time delay system via a new type of Riccati equations and also apply to a population optimal control problem.
Management of linear quadratic regulator optimal control with full-vehicle control case study
Directory of Open Access Journals (Sweden)
Rodrigue Tchamna
2016-09-01
Full Text Available Linear quadratic regulator is a powerful technique for dealing with the control design of any linear and nonlinear system after linearization of the system around an operating point. For small systems, which have fewer state variables, the transformation of the performance index from scalar to matrix form can be straightforward. On the other hand, as the system becomes large with many state variables and controllers, appropriate design and notations should be defined to make it easy to automatically implement the technique for any large system without the need to redesign from scratch every time one requires a new system. The main aim of this article was to deal with this issue. This article shows how to automatically obtain the matrix form of the performance index matrices from the scalar version of the performance index. Control of a full-vehicle in cornering was taken as a case study in this article.
A Fast Condensing Method for Solution of Linear-Quadratic Control Problems
DEFF Research Database (Denmark)
Frison, Gianluca; Jørgensen, John Bagterp
2013-01-01
consider a condensing (or state elimination) method to solve an extended version of the LQ control problem, and we show how to exploit the structure of this problem to both factorize the dense Hessian matrix and solve the system. Furthermore, we present two efficient implementations. The first......In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is usually the main computational effort. In this paper we...... implementation is formally identical to the Riccati recursion based solver and has a computational complexity that is linear in the control horizon length and cubic in the number of states. The second implementation has a computational complexity that is quadratic in the control horizon length as well...
Modelling and control of dynamic systems using gaussian process models
Kocijan, Juš
2016-01-01
This monograph opens up new horizons for engineers and researchers in academia and in industry dealing with or interested in new developments in the field of system identification and control. It emphasizes guidelines for working solutions and practical advice for their implementation rather than the theoretical background of Gaussian process (GP) models. The book demonstrates the potential of this recent development in probabilistic machine-learning methods and gives the reader an intuitive understanding of the topic. The current state of the art is treated along with possible future directions for research. Systems control design relies on mathematical models and these may be developed from measurement data. This process of system identification, when based on GP models, can play an integral part of control design in data-based control and its description as such is an essential aspect of the text. The background of GP regression is introduced first with system identification and incorporation of prior know...
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.
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.
Gain-scheduled Linear Quadratic Control of Wind Turbines Operating at High Wind Speed
DEFF Research Database (Denmark)
Østergaard, Kasper Zinck; Stoustrup, Jakob; Brath, Per
2007-01-01
This paper addresses state estimation and linear quadratic (LQ) control of variable speed variable pitch wind turbines. On the basis of a nonlinear model of a wind turbine, a set of operating conditions is identified and a LQ controller is designed for each operating point. The controller gains...... are then interpolated linearly to get a control law for the entire operating envelope. A nonlinear state estimator is designed as a combination of two unscented Kalman filters and a linear disturbance estimator. The gain-scheduling variable (wind speed) is then calculated from the output of these state estimators...
Quadratic Stabilization of LPV System by an LTI Controller Based on ILMI Algorithm
Directory of Open Access Journals (Sweden)
Wei Xie
2007-01-01
Full Text Available A linear time-invariant (LTI output feedback controller is designed for a linear parameter-varying (LPV control system to achieve quadratic stability. The LPV system includes immeasurable dependent parameters that are assumed to vary in a polytopic space. To solve this control problem, a heuristic algorithm is proposed in the form of an iterative linear matrix inequality (ILMI formulation. Furthermore, an effective method of setting an initial value of the ILMI algorithm is also proposed to increase the probability of getting an admissible solution for the controller design problem.
Rey, Martin P.; Pontzen, Andrew
2018-02-01
Recent work has studied the interplay between a galaxy's history and its observable properties using `genetically modified' cosmological zoom simulations. The approach systematically generates alternative histories for a halo, while keeping its cosmological environment fixed. Applications to date altered linear properties of the initial conditions, such as the mean overdensity of specified regions; we extend the formulation to include quadratic features, such as local variance, that determines the overall importance of smooth accretion relative to mergers in a galaxy's history. We introduce an efficient algorithm for this new class of modification and demonstrate its ability to control the variance of a region in a one-dimensional toy model. Outcomes of this work are twofold: (i) a clarification of the formulation of genetic modifications and (ii) a proof of concept for quadratic modifications leading the way to a forthcoming implementation in cosmological simulations.
Directory of Open Access Journals (Sweden)
Linlin Gao
2015-11-01
Full Text Available From the perspective of vehicle dynamics, the four-wheel independent steering vehicle dynamics stability control method is studied, and a four-wheel independent steering varying parameter linear quadratic regulator control system is proposed with the help of expert control method. In the article, a four-wheel independent steering linear quadratic regulator controller for model following purpose is designed first. Then, by analyzing the four-wheel independent steering vehicle dynamic characteristics and the influence of linear quadratic regulator control parameters on control performance, a linear quadratic regulator control parameter adjustment strategy based on vehicle steering state is proposed to achieve the adaptive adjustment of linear quadratic regulator control parameters. In addition, to further improve the control performance, the proposed varying parameter linear quadratic regulator control system is optimized by genetic algorithm. Finally, simulation studies have been conducted by applying the proposed control system to the 8-degree-of-freedom four-wheel independent steering vehicle dynamics model. The simulation results indicate that the proposed control system has better performance and robustness and can effectively improve the stability and steering safety of the four-wheel independent steering vehicle.
Parallel Implementation of Riccati Recursion for Solving Linear-Quadratic Control Problems
DEFF Research Database (Denmark)
Frison, Gianluca; Jørgensen, John Bagterp
2013-01-01
In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is usually the main computational effort. In this paper...... an alternative version of the Riccati recursion solver for LQ control problems is presented. The performance of both the classical and the alternative version is analyzed from a theoretical as well as a numerical point of view, and the alternative version is found to be approximately 50% faster than...
Frost, Susan A.; Bodson, Marc; Acosta, Diana M.
2009-01-01
The Next Generation (NextGen) transport aircraft configurations being investigated as part of the NASA Aeronautics Subsonic Fixed Wing Project have more control surfaces, or control effectors, than existing transport aircraft configurations. Conventional flight control is achieved through two symmetric elevators, two antisymmetric ailerons, and a rudder. The five effectors, reduced to three command variables, produce moments along the three main axes of the aircraft and enable the pilot to control the attitude and flight path of the aircraft. The NextGen aircraft will have additional redundant control effectors to control the three moments, creating a situation where the aircraft is over-actuated and where a simple relationship does not exist anymore between the required effector deflections and the desired moments. NextGen flight controllers will incorporate control allocation algorithms to determine the optimal effector commands and attain the desired moments, taking into account the effector limits. Approaches to solving the problem using linear programming and quadratic programming algorithms have been proposed and tested. It is of great interest to understand their relative advantages and disadvantages and how design parameters may affect their properties. In this paper, we investigate the sensitivity of the effector commands with respect to the desired moments and show on some examples that the solutions provided using the l2 norm of quadratic programming are less sensitive than those using the l1 norm of linear programming.
Optimal linear-quadratic control of coupled parabolic-hyperbolic PDEs
Aksikas, I.; Moghadam, A. Alizadeh; Forbes, J. F.
2017-10-01
This paper focuses on the optimal control design for a system of coupled parabolic-hypebolic partial differential equations by using the infinite-dimensional state-space description and the corresponding operator Riccati equation. Some dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the linear-quadratic (LQ)-optimal control problem. A state LQ-feedback operator is computed by solving the operator Riccati equation, which is converted into a set of algebraic and differential Riccati equations, thanks to the eigenvalues and the eigenvectors of the parabolic operator. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ-optimal controller designed in the early portion of the paper is implemented for the original nonlinear model. Numerical simulations are performed to show the controller performances.
Efficient Implementation of the Riccati Recursion for Solving Linear-Quadratic Control Problems
DEFF Research Database (Denmark)
Frison, Gianluca; Jørgensen, John Bagterp
2013-01-01
In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is typically the main computational effort at each iteration....... In this paper, we compare a number of solvers for an extended formulation of the LQ control problem: a Riccati recursion based solver can be considered the best choice for the general problem with dense matrices. Furthermore, we present a novel version of the Riccati solver, that makes use of the Cholesky...... factorization of the Pn matrices to reduce the number of flops. When combined with regularization and mixed precision, this algorithm can solve large instances of the LQ control problem up to 3 times faster than the classical Riccati solver....
International Nuclear Information System (INIS)
Chertkov, Michael; Kolokolov, Igor; Lebedev, Vladimir
2012-01-01
The standard definition of the stochastic risk-sensitive linear–quadratic (RS-LQ) control depends on the risk parameter, which is normally left to be set exogenously. We reconsider the classical approach and suggest two alternatives, resolving the spurious freedom naturally. One approach consists in seeking for the minimum of the tail of the probability distribution function (PDF) of the cost functional at some large fixed value. Another option suggests minimizing the expectation value of the cost functional under a constraint on the value of the PDF tail. Under the assumption of resulting control stability, both problems are reduced to static optimizations over a stationary control matrix. The solutions are illustrated using the examples of scalar and 1D chain (string) systems. The large deviation self-similar asymptotic of the cost functional PDF is analyzed. (paper)
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…
Quadratic obstructions to small-time local controllability for scalar-input systems
Beauchard, Karine; Marbach, Frédéric
2018-03-01
We consider nonlinear finite-dimensional scalar-input control systems in the vicinity of an equilibrium. When the linearized system is controllable, the nonlinear system is smoothly small-time locally controllable: whatever m > 0 and T > 0, the state can reach a whole neighborhood of the equilibrium at time T with controls arbitrary small in Cm-norm. When the linearized system is not controllable, we prove that: either the state is constrained to live within a smooth strict manifold, up to a cubic residual, or the quadratic order adds a signed drift with respect to it. This drift holds along a Lie bracket of length (2 k + 1), is quantified in terms of an H-k-norm of the control, holds for controls small in W 2 k , ∞-norm and these spaces are optimal. Our proof requires only C3 regularity of the vector field. This work underlines the importance of the norm used in the smallness assumption on the control, even in finite dimension.
Musthofa, M.W.; Salmah, S.; Engwerda, Jacob; Suparwanto, A.
This paper studies the robust optimal control problem for descriptor systems. We applied differential game theory to solve the disturbance attenuation problem. The robust control problem was converted into a reduced ordinary zero-sum game. Within a linear quadratic setting, we solved the problem for
A Bernoulli Gaussian Watermark for Detecting Integrity Attacks in Control Systems
Energy Technology Data Exchange (ETDEWEB)
Weerakkody, Sean [Carnegie Mellon Univ., Pittsburgh, PA (United States); Ozel, Omur [Carnegie Mellon Univ., Pittsburgh, PA (United States); Sinopoli, Bruno [Carnegie Mellon Univ., Pittsburgh, PA (United States)
2017-11-02
We examine the merit of Bernoulli packet drops in actively detecting integrity attacks on control systems. The aim is to detect an adversary who delivers fake sensor measurements to a system operator in order to conceal their effect on the plant. Physical watermarks, or noisy additive Gaussian inputs, have been previously used to detect several classes of integrity attacks in control systems. In this paper, we consider the analysis and design of Gaussian physical watermarks in the presence of packet drops at the control input. On one hand, this enables analysis in a more general network setting. On the other hand, we observe that in certain cases, Bernoulli packet drops can improve detection performance relative to a purely Gaussian watermark. This motivates the joint design of a Bernoulli-Gaussian watermark which incorporates both an additive Gaussian input and a Bernoulli drop process. We characterize the effect of such a watermark on system performance as well as attack detectability in two separate design scenarios. Here, we consider a correlation detector for attack recognition. We then propose efficiently solvable optimization problems to intelligently select parameters of the Gaussian input and the Bernoulli drop process while addressing security and performance trade-offs. Finally, we provide numerical results which illustrate that a watermark with packet drops can indeed outperform a Gaussian watermark.
Li, Yanning
2014-03-01
This article presents a new optimal control framework for transportation networks in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi (H-J) equation and the commonly used triangular fundamental diagram, we pose the problem of controlling the state of the system on a network link, in a finite horizon, as a Linear Program (LP). We then show that this framework can be extended to an arbitrary transportation network, resulting in an LP or a Quadratic Program. Unlike many previously investigated transportation network control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e., discontinuities in the state of the system). As it leverages the intrinsic properties of the H-J equation used to model the state of the system, it does not require any approximation, unlike classical methods that are based on discretizations of the model. The computational efficiency of the method is illustrated on a transportation network. © 2014 IEEE.
Li, Yanning; Canepa, Edward S.; Claudel, Christian
2014-01-01
This article presents a new optimal control framework for transportation networks in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi (H-J) equation and the commonly used triangular fundamental diagram, we pose the problem of controlling the state of the system on a network link, in a finite horizon, as a Linear Program (LP). We then show that this framework can be extended to an arbitrary transportation network, resulting in an LP or a Quadratic Program. Unlike many previously investigated transportation network control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e., discontinuities in the state of the system). As it leverages the intrinsic properties of the H-J equation used to model the state of the system, it does not require any approximation, unlike classical methods that are based on discretizations of the model. The computational efficiency of the method is illustrated on a transportation network. © 2014 IEEE.
Interlink Converter with Linear Quadratic Regulator Based Current Control for Hybrid AC/DC Microgrid
Directory of Open Access Journals (Sweden)
Dwi Riana Aryani
2017-11-01
Full Text Available A hybrid alternate current/direct current (AC/DC microgrid consists of an AC subgrid and a DC subgrid, and the subgrids are connected through the interlink bidirectional AC/DC converter. In the stand-alone operation mode, it is desirable that the interlink bidirectional AC/DC converter manages proportional power sharing between the subgrids by transferring power from the under-loaded subgrid to the over-loaded one. In terms of system security, the interlink bidirectional AC/DC converter takes an important role, so proper control strategies need to be established. In addition, it is assumed that a battery energy storage system is installed in one subgrid, and the coordinated control of interlink bidirectional AC/DC converter and battery energy storage system converter is required so that the power sharing scheme between subgrids becomes more efficient. For the purpose of designing a tracking controller for the power sharing by interlink bidirectional AC/DC converter in a hybrid AC/DC microgrid, a droop control method generates a power reference for interlink bidirectional AC/DC converter based on the deviation of the system frequency and voltages first and then interlink bidirectional AC/DC converter needs to transfer the power reference to the over-loaded subgrid. For efficiency of this power transferring, a linear quadratic regulator with exponential weighting for the current regulation of interlink bidirectional AC/DC converter is designed in such a way that the resulting microgrid can operate robustly against various uncertainties and the power sharing is carried out quickly. Simulation results show that the proposed interlink bidirectional AC/DC converter control strategy provides robust and efficient power sharing scheme between the subgrids without deteriorating the secure system operation.
Heinkenschloss, Matthias
2005-01-01
We study a class of time-domain decomposition-based methods for the numerical solution of large-scale linear quadratic optimal control problems. Our methods are based on a multiple shooting reformulation of the linear quadratic optimal control problem as a discrete-time optimal control (DTOC) problem. The optimality conditions for this DTOC problem lead to a linear block tridiagonal system. The diagonal blocks are invertible and are related to the original linear quadratic optimal control problem restricted to smaller time-subintervals. This motivates the application of block Gauss-Seidel (GS)-type methods for the solution of the block tridiagonal systems. Numerical experiments show that the spectral radii of the block GS iteration matrices are larger than one for typical applications, but that the eigenvalues of the iteration matrices decay to zero fast. Hence, while the GS method is not expected to convergence for typical applications, it can be effective as a preconditioner for Krylov-subspace methods. This is confirmed by our numerical tests.A byproduct of this research is the insight that certain instantaneous control techniques can be viewed as the application of one step of the forward block GS method applied to the DTOC optimality system.
A feedback control strategy for the airfoil system under non-Gaussian colored noise excitation
Energy Technology Data Exchange (ETDEWEB)
Huang, Yong, E-mail: hy@njust.edu.cn, E-mail: taogang@njust.edu.cn; Tao, Gang, E-mail: hy@njust.edu.cn, E-mail: taogang@njust.edu.cn [School of Energy and Power Engineering, Nanjing University of Science and Technology, 200 XiaoLingwei Street, Nanjing 210094 (China)
2014-09-01
The stability of a binary airfoil with feedback control under stochastic disturbances, a non-Gaussian colored noise, is studied in this paper. First, based on some approximated theories and methods the non-Gaussian colored noise is simplified to an Ornstein-Uhlenbeck process. Furthermore, via the stochastic averaging method and the logarithmic polar transformation, one dimensional diffusion process can be obtained. At last by applying the boundary conditions, the largest Lyapunov exponent which can determine the almost-sure stability of the system and the effective region of control parameters is calculated.
A feedback control strategy for the airfoil system under non-Gaussian colored noise excitation.
Huang, Yong; 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.
International Nuclear Information System (INIS)
Ayvaz, Muzaffer; Demiralp, Metin
2011-01-01
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.
Directory of Open Access Journals (Sweden)
Jens G. Balchen
1984-10-01
Full Text Available The problem of systematic derivation of a quasi-dynamic optimal control strategy for a non-linear dynamic process based upon a non-quadratic objective function is investigated. The wellknown LQG-control algorithm does not lead to an optimal solution when the process disturbances have non-zero mean. The relationships between the proposed control algorithm and LQG-control are presented. The problem of how to constrain process variables by means of 'penalty' - terms in the objective function is dealt with separately.
Assessment of the GPC Control Quality Using Non–Gaussian Statistical Measures
Directory of Open Access Journals (Sweden)
Domański Paweł D.
2017-06-01
Full Text Available This paper presents an alternative approach to the task of control performance assessment. Various statistical measures based on Gaussian and non-Gaussian distribution functions are evaluated. The analysis starts with the review of control error histograms followed by their statistical analysis using probability distribution functions. Simulation results obtained for a control system with the generalized predictive controller algorithm are considered. The proposed approach using Cauchy and Lévy α-stable distributions shows robustness against disturbances and enables effective control loop quality evaluation. Tests of the predictive algorithm prove its ability to detect the impact of the main controller parameters, such as the model gain, the dynamics or the prediction horizon.
DEFF Research Database (Denmark)
Bergami, Leonardo; Poulsen, Niels Kjølstad
2015-01-01
The paper proposes a smart rotor configuration where adaptive trailing edge flaps (ATEFs) are employed for active alleviation of the aerodynamic loads on the blades of the NREL 5 MW reference turbine. The flaps extend for 20% of the blade length and are controlled by a linear quadratic (LQ....... The effects of active flap control are assessed with aeroelastic simulations of the turbine in normal operation conditions, as prescribed by the International Electrotechnical Commission standard. The turbine lifetime fatigue damage equivalent loads provide a convenient summary of the results achieved...
Self-tuning control of a nuclear reactor using a Gaussian function neural network
International Nuclear Information System (INIS)
Park, M.G.; Cho, N.Z.
1995-01-01
A self-tuning control method is described for a nuclear reactor system that requires only a set of input-output measurements. The use of an artificial neural network in nonlinear model-based adaptive control, both as a plant model and a controller, is investigated. A neural network called a Gaussian function network is used for one-step-ahead predictive control to track the desired plant output. The effectiveness of the controller is demonstrated by the application of the method to the power tracking control of the Korea Multipurpose Research Reactor
Pfeil, W. H.; De Los Reyes, G.; Bobula, G. A.
1985-01-01
A power turbine governor was designed for a recent-technology turboshaft engine coupled to a modern, articulated rotor system using Linear Quadratic Regulator (LQR) and Kalman Filter (KF) techniques. A linear, state-space model of the engine and rotor system was derived for six engine power settings from flight idle to maximum continuous. An integrator was appended to the fuel flow input to reduce the steady-state governor error to zero. Feedback gains were calculated for the system states at each power setting using the LQR technique. The main rotor tip speed state is not measurable, so a Kalman Filter of the rotor was used to estimate this state. The crossover of the system was increased to 10 rad/s compared to 2 rad/sec for a current governor. Initial computer simulations with a nonlinear engine model indicate a significant decrease in power turbine speed variation with the LQR governor compared to a conventional governor.
Directory of Open Access Journals (Sweden)
Ramji Tiwari
2018-02-01
Full Text Available This paper proposes an artificial neural network (ANN based maximum power point tracking (MPPT control strategy for wind energy conversion system (WECS implemented with a DC/DC converter. The proposed topology utilizes a radial basis function network (RBFN based neural network control strategy to extract the maximum available power from the wind velocity. The results are compared with a classical Perturb and Observe (P&O method and Back propagation network (BPN method. In order to achieve a high voltage rating, the system is implemented with a quadratic boost converter and the performance of the converter is validated with a boost and single ended primary inductance converter (SEPIC. The performance of the MPPT technique along with a DC/DC converter is demonstrated using MATLAB/Simulink.
Lien, C.-H.; Vaidyanathan, S.; Sambas, A.; Sukono; Mamat, M.; Sanjaya, W. S. M.; Subiyanto
2018-03-01
A 3-D new two-scroll chaotic attractor with three quadratic nonlinearities is investigated in this paper. First, the qualitative and dynamical properties of the new two-scroll chaotic system are described in terms of phase portraits, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, etc. We show that the new two-scroll dissipative chaotic system has three unstable equilibrium points. As an engineering application, global chaos control of the new two-scroll chaotic system with unknown system parameters is designed via adaptive feedback control and Lyapunov stability theory. Furthermore, an electronic circuit realization of the new chaotic attractor is presented in detail to confirm the feasibility of the theoretical chaotic two-scroll attractor model.
Controlling the ambipolarity and improvement of RF performance using Gaussian Drain Doped TFET
Nigam, Kaushal; Gupta, Sarthak; Pandey, Sunil; Kondekar, P. N.; Sharma, Dheeraj
2018-05-01
Ambipolar conduction in tunnel field-effect transistors (TFETs) has been occurred as an inherent issue due to drain-channel tunneling. It makes TFET less efficient and restricts its application in complementary digital circuits. Therefore, this manuscript reports the application of Gaussian doping profile on nanometer regime silicon channel TFETs to completely eliminate the ambipolarity. For this, Gaussian doping is used in the drain region of conventional gate-drain overlap TFET to control the tunneling of electrons from the valence band of channel to the conduction band of drain. As a result, barrier width at the drain/channel junction increases significantly leading to the suppression of an ambipolar current even when higher doping concentration (1 ? 10 ? cm ?) is considered in the drain region. However, significant improvement in terms of RF figure-of-merits such as cut-off frequency (f ?), gain bandwidth product (GBW), and gate-to-drain capacitance (C ?) is achieved with Gaussian doped gate on drain overlap TFET as compared to its counterpart TFET.
Launching and controlling Gaussian beams from point sources via planar transformation media
Odabasi, Hayrettin; Sainath, Kamalesh; Teixeira, Fernando L.
2018-02-01
Based on operations prescribed under the paradigm of complex transformation optics (CTO) [F. Teixeira and W. Chew, J. Electromagn. Waves Appl. 13, 665 (1999), 10.1163/156939399X01104; F. L. Teixeira and W. C. Chew, Int. J. Numer. Model. 13, 441 (2000), 10.1002/1099-1204(200009/10)13:5%3C441::AID-JNM376%3E3.0.CO;2-J; H. Odabasi, F. L. Teixeira, and W. C. Chew, J. Opt. Soc. Am. B 28, 1317 (2011), 10.1364/JOSAB.28.001317; B.-I. Popa and S. A. Cummer, Phys. Rev. A 84, 063837 (2011), 10.1103/PhysRevA.84.063837], it was recently shown in [G. Castaldi, S. Savoia, V. Galdi, A. Alù, and N. Engheta, Phys. Rev. Lett. 110, 173901 (2013), 10.1103/PhysRevLett.110.173901] that a complex source point (CSP) can be mimicked by parity-time (PT ) transformation media. Such coordinate transformation has a mirror symmetry for the imaginary part, and results in a balanced loss/gain metamaterial slab. A CSP produces a Gaussian beam and, consequently, a point source placed at the center of such a metamaterial slab produces a Gaussian beam propagating away from the slab. Here, we extend the CTO analysis to nonsymmetric complex coordinate transformations as put forth in [S. Savoia, G. Castaldi, and V. Galdi, J. Opt. 18, 044027 (2016), 10.1088/2040-8978/18/4/044027] and verify that, by using simply a (homogeneous) doubly anisotropic gain-media metamaterial slab, one can still mimic a CSP and produce Gaussian beam. In addition, we show that a Gaussian-like beams can be produced by point sources placed outside the slab as well. By making use of the extra degrees of freedom (the real and imaginary parts of the coordinate transformation) provided by CTO, the near-zero requirement on the real part of the resulting constitutive parameters can be relaxed to facilitate potential realization of Gaussian-like beams. We illustrate how beam properties such as peak amplitude and waist location can be controlled by a proper choice of (complex-valued) CTO Jacobian elements. In particular, the beam waist
Quadratic measurement and conditional state preparation in an optomechanical system
DEFF Research Database (Denmark)
A. Brawley, George; Vanner, Michael A.; Bowen, Warwick P.
2014-01-01
We experimentally demonstrate, for the first time, quadratic measurement of mechanical motion in an optomechanical system. We use this nonlinear easurement to conditionally prepare classical non-Gaussian states of motion of a micro-mechanical oscillator.......We experimentally demonstrate, for the first time, quadratic measurement of mechanical motion in an optomechanical system. We use this nonlinear easurement to conditionally prepare classical non-Gaussian states of motion of a micro-mechanical oscillator....
Overlapping quadratic optimal control of linear time-varying commutative systems
Czech Academy of Sciences Publication Activity Database
Bakule, Lubomír; Rodellar, J.; Rossell, J. M.
2002-01-01
Roč. 40, č. 5 (2002), s. 1611-1627 ISSN 0363-0129 R&D Projects: GA AV ČR IAA2075802 Institutional research plan: CEZ:AV0Z1075907 Keywords : overlapping * optimal control * linear time-varying systems Subject RIV: BC - Control Systems Theory Impact factor: 1.441, year: 2002
Non-Gaussian Systems Control Performance Assessment Based on Rational Entropy
Directory of Open Access Journals (Sweden)
Jinglin Zhou
2018-05-01
Full Text Available Control loop Performance Assessment (CPA plays an important role in system operations. Stochastic statistical CPA index, such as a minimum variance controller (MVC-based CPA index, is one of the most widely used CPA indices. In this paper, a new minimum entropy controller (MEC-based CPA method of linear non-Gaussian systems is proposed. In this method, probability density function (PDF and rational entropy (RE are respectively used to describe the characteristics and the uncertainty of random variables. To better estimate the performance benchmark, an improved EDA algorithm, which is used to estimate the system parameters and noise PDF, is given. The effectiveness of the proposed method is illustrated through case studies on an ARMAX system.
Directory of Open Access Journals (Sweden)
Xinying Xu
2018-06-01
Full Text Available In this paper, a novel data-driven single neuron predictive control strategy is proposed for non-Gaussian networked control systems with metrology delays in the information theory framework. Firstly, survival information potential (SIP, instead of minimum entropy, is used to formulate the performance index to characterize the randomness of the considered systems, which is calculated by oversampling method. Then the minimum values can be computed by optimizing the SIP-based performance index. Finally, the proposed strategy, minimum entropy method and mean square error (MSE are applied to a networked motor control system, and results demonstrated the effectiveness of the proposed strategy.
Duality-Based Nonlinear Quadratic Control: Application to Mobile Robot Trajectory-Following
Czech Academy of Sciences Publication Activity Database
Arnesto, L.; Girbés, V.; Sala, A.; Zima, M.; Šmídl, Václav
2015-01-01
Roč. 23, č. 4 (2015), s. 1494-1504 ISSN 1063-6536 R&D Projects: GA ČR(CZ) GAP102/11/0437 Grant - others:GA MŠk(CZ) CZ.1.05/2.1.00/03.0094 Institutional support: RVO:67985556 Keywords : trajectory planning * duality of estimation and control Subject RIV: BC - Control Systems Theory Impact factor: 2.818, year: 2015 http://library.utia.cas.cz/separaty/2015/AS/smidl-0445192.pdf
Vibration control of large linear quadratic symmetric systems. Ph.D. Thesis
Jeon, G. J.
1983-01-01
Some unique properties on a class of the second order lambda matrices were found and applied to determine a damping matrix of the decoupled subsystem in such a way that the damped system would have preassigned eigenvalues without disturbing the stiffness matrix. The resulting system was realized as a time invariant velocity only feedback control system with desired poles. Another approach using optimal control theory was also applied to the decoupled system in such a way that the mode spillover problem could be eliminated. The procedures were tested successfully by numerical examples.
Optimal Quadratic Programming Algorithms
Dostal, Zdenek
2009-01-01
Quadratic programming (QP) is one technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. This title presents various algorithms for solving large QP problems. It is suitable as an introductory text on quadratic programming for graduate students and researchers
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…
Energy Technology Data Exchange (ETDEWEB)
Liu, Yunlong; Wang, Aiping; Guo, Lei; Wang, Hong
2017-07-09
This paper presents an error-entropy minimization tracking control algorithm for a class of dynamic stochastic system. The system is represented by a set of time-varying discrete nonlinear equations with non-Gaussian stochastic input, where the statistical properties of stochastic input are unknown. By using Parzen windowing with Gaussian kernel to estimate the probability densities of errors, recursive algorithms are then proposed to design the controller such that the tracking error can be minimized. The performance of the error-entropy minimization criterion is compared with the mean-square-error minimization in the simulation results.
Energy Technology Data Exchange (ETDEWEB)
Graber, P. Jameson, E-mail: jameson-graber@baylor.edu [Baylor University, Department of Mathematics (United States)
2016-12-15
We study a general linear quadratic mean field type control problem and connect it to mean field games of a similar type. The solution is given both in terms of a forward/backward system of stochastic differential equations and by a pair of Riccati equations. In certain cases, the solution to the mean field type control is also the equilibrium strategy for a class of mean field games. We use this fact to study an economic model of production of exhaustible resources.
International Nuclear Information System (INIS)
Farivar, Faezeh; Aliyari Shoorehdeli, Mahdi; Nekoui, Mohammad Ali; Teshnehlab, Mohammad
2012-01-01
Highlights: ► A systematic procedure for GPS of unknown heavy chaotic gyroscope systems. ► Proposed methods are based on Lyapunov stability theory. ► Without calculating Lyapunov exponents and Eigen values of the Jacobian matrix. ► Capable to extend for a variety of chaotic systems. ► Useful for practical applications in the future. - Abstract: This paper proposes the chaos control and the generalized projective synchronization methods for heavy symmetric gyroscope systems via Gaussian radial basis adaptive variable structure control. Because of the nonlinear terms of the gyroscope system, the system exhibits chaotic motions. Occasionally, the extreme sensitivity to initial states in a system operating in chaotic mode can be very destructive to the system because of unpredictable behavior. In order to improve the performance of a dynamic system or avoid the chaotic phenomena, it is necessary to control a chaotic system with a periodic motion beneficial for working with a particular condition. As chaotic signals are usually broadband and noise like, synchronized chaotic systems can be used as cipher generators for secure communication. This paper presents chaos synchronization of two identical chaotic motions of symmetric gyroscopes. In this paper, the switching surfaces are adopted to ensure the stability of the error dynamics in variable structure control. Using the neural variable structure control technique, control laws are established which guarantees the chaos control and the generalized projective synchronization of unknown gyroscope systems. In the neural variable structure control, Gaussian radial basis functions are utilized to on-line estimate the system dynamic functions. Also, the adaptation laws of the on-line estimator are derived in the sense of Lyapunov function. Thus, the unknown gyro systems can be guaranteed to be asymptotically stable. Also, the proposed method can achieve the control objectives. Numerical simulations are presented to
Gaussian Processes for Data-Efficient Learning in Robotics and Control.
Deisenroth, Marc Peter; Fox, Dieter; Rasmussen, Carl Edward
2015-02-01
Autonomous learning has been a promising direction in control and robotics for more than a decade since data-driven learning allows to reduce the amount of engineering knowledge, which is otherwise required. However, autonomous reinforcement learning (RL) approaches typically require many interactions with the system to learn controllers, which is a practical limitation in real systems, such as robots, where many interactions can be impractical and time consuming. To address this problem, current learning approaches typically require task-specific knowledge in form of expert demonstrations, realistic simulators, pre-shaped policies, or specific knowledge about the underlying dynamics. In this paper, we follow a different approach and speed up learning by extracting more information from data. In particular, we learn a probabilistic, non-parametric Gaussian process transition model of the system. By explicitly incorporating model uncertainty into long-term planning and controller learning our approach reduces the effects of model errors, a key problem in model-based learning. Compared to state-of-the art RL our model-based policy search method achieves an unprecedented speed of learning. We demonstrate its applicability to autonomous learning in real robot and control tasks.
Gravitation and quadratic forms
International Nuclear Information System (INIS)
Ananth, Sudarshan; Brink, Lars; Majumdar, Sucheta; Mali, Mahendra; Shah, Nabha
2017-01-01
The light-cone Hamiltonians describing both pure (N=0) Yang-Mills and N=4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity. We demonstrate how the Hamiltonians of both pure gravity and N=8 supergravity, in four dimensions, may be written as quadratic forms. We examine the effect of residual reparametrizations on the Hamiltonian and the resulting quadratic form.
Gravitation and quadratic forms
Energy Technology Data Exchange (ETDEWEB)
Ananth, Sudarshan [Indian Institute of Science Education and Research,Pune 411008 (India); Brink, Lars [Department of Physics, Chalmers University of Technology,S-41296 Göteborg (Sweden); Institute of Advanced Studies and Department of Physics & Applied Physics,Nanyang Technological University,Singapore 637371 (Singapore); Majumdar, Sucheta [Indian Institute of Science Education and Research,Pune 411008 (India); Mali, Mahendra [School of Physics, Indian Institute of Science Education and Research,Thiruvananthapuram, Trivandrum 695016 (India); Shah, Nabha [Indian Institute of Science Education and Research,Pune 411008 (India)
2017-03-31
The light-cone Hamiltonians describing both pure (N=0) Yang-Mills and N=4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity. We demonstrate how the Hamiltonians of both pure gravity and N=8 supergravity, in four dimensions, may be written as quadratic forms. We examine the effect of residual reparametrizations on the Hamiltonian and the resulting quadratic form.
Gaussian mixed model in support of semiglobal matching leveraged by ground control points
Ma, Hao; Zheng, Shunyi; Li, Chang; Li, Yingsong; Gui, Li
2017-04-01
Semiglobal matching (SGM) has been widely applied in large aerial images because of its good tradeoff between complexity and robustness. The concept of ground control points (GCPs) is adopted to make SGM more robust. We model the effect of GCPs as two data terms for stereo matching between high-resolution aerial epipolar images in an iterative scheme. One term based on GCPs is formulated by Gaussian mixture model, which strengths the relation between GCPs and the pixels to be estimated and encodes some degree of consistency between them with respect to disparity values. Another term depends on pixel-wise confidence, and we further design a confidence updating equation based on three rules. With this confidence-based term, the assignment of disparity can be heuristically selected among disparity search ranges during the iteration process. Several iterations are sufficient to bring out satisfactory results according to our experiments. Experimental results validate that the proposed method outperforms surface reconstruction, which is a representative variant of SGM and behaves excellently on aerial images.
Directory of Open Access Journals (Sweden)
Ronghui ZHENG
2017-12-01
Full Text Available A control method for Multi-Input Multi-Output (MIMO non-Gaussian random vibration test with cross spectra consideration is proposed in the paper. The aim of the proposed control method is to replicate the specified references composed of auto spectral densities, cross spectral densities and kurtoses on the test article in the laboratory. It is found that the cross spectral densities will bring intractable coupling problems and induce difficulty for the control of the multi-output kurtoses. Hence, a sequential phase modification method is put forward to solve the coupling problems in multi-input multi-output non-Gaussian random vibration test. To achieve the specified responses, an improved zero memory nonlinear transformation is utilized first to modify the Fourier phases of the signals with sequential phase modification method to obtain one frame reference response signals which satisfy the reference spectra and reference kurtoses. Then, an inverse system method is used in frequency domain to obtain the continuous stationary drive signals. At the same time, the matrix power control algorithm is utilized to control the spectra and kurtoses of the response signals further. At the end of the paper, a simulation example with a cantilever beam and a vibration shaker test are implemented and the results support the proposed method very well. Keywords: Cross spectra, Kurtosis control, Multi-input multi-output, Non-Gaussian, Random vibration test
Dickmann, M
2015-01-01
In this monograph the authors extend the classical algebraic theory of quadratic forms over fields to diagonal quadratic forms with invertible entries over broad classes of commutative, unitary rings where -1 is not a sum of squares and 2 is invertible. They accomplish this by: (1) Extending the classical notion of matrix isometry of forms to a suitable notion of T-isometry, where T is a preorder of the given ring, A, or T = A^2. (2) Introducing in this context three axioms expressing simple properties of (value) representation of elements of the ring by quadratic forms, well-known to hold in
Ellis, John; Sueiro, Maria
2014-01-01
Inflationary models based on a single scalar field $\\phi$ with a quadratic potential $V = \\frac{1}{2} m^2 \\phi^2$ are disfavoured by the recent Planck constraints on the scalar index, $n_s$, and the tensor-to-scalar ratio for cosmological density perturbations, $r_T$. In this paper we study how such a quadratic inflationary model can be rescued by postulating additional fields with quadratic potentials, such as might occur in sneutrino models, which might serve as either curvatons or supplementary inflatons. Introducing a second scalar field reduces but does not remove the pressure on quadratic inflation, but we find a sample of three-field models that are highly compatible with the Planck data on $n_s$ and $r_T$. We exhibit a specific three-sneutrino example that is also compatible with the data on neutrino mass difference and mixing angles.
Separable quadratic stochastic operators
International Nuclear Information System (INIS)
Rozikov, U.A.; Nazir, S.
2009-04-01
We consider quadratic stochastic operators, which are separable as a product of two linear operators. Depending on properties of these linear operators we classify the set of the separable quadratic stochastic operators: first class of constant operators, second class of linear and third class of nonlinear (separable) quadratic stochastic operators. Since the properties of operators from the first and second classes are well known, we mainly study the properties of the operators of the third class. We describe some Lyapunov functions of the operators and apply them to study ω-limit sets of the trajectories generated by the operators. We also compare our results with known results of the theory of quadratic operators and give some open problems. (author)
Linear quadratic optimization for positive LTI system
Muhafzan, Yenti, Syafrida Wirma; Zulakmal
2017-05-01
Nowaday the linear quadratic optimization subject to positive linear time invariant (LTI) system constitute an interesting study considering it can become a mathematical model of variety of real problem whose variables have to nonnegative and trajectories generated by these variables must be nonnegative. In this paper we propose a method to generate an optimal control of linear quadratic optimization subject to positive linear time invariant (LTI) system. A sufficient condition that guarantee the existence of such optimal control is discussed.
Directory of Open Access Journals (Sweden)
S. Vaidyanathan
2014-11-01
Full Text Available This research work describes a nine-term novel 3-D chaotic system with four quadratic nonlinearities and details its qualitative properties. The phase portraits of the 3-D novel chaotic system simulated using MATLAB, depict the strange chaotic attractor of the system. For the parameter values chosen in this work, the Lyapunov exponents of the novel chaotic system are obtained as L1 = 6.8548, L2 = 0 and L3 = −32.8779. Also, the Kaplan-Yorke dimension of the novel chaotic system is obtained as DKY = 2.2085. Next, an adaptive controller is design to achieve global stabilization of the 3-D novel chaotic system with unknown system parameters. Moreover, an adaptive controller is designed to achieve global chaos synchronization of two identical novel chaotic systems with unknown system parameters. Finally, an electronic circuit realization of the novel chaotic system is presented using SPICE to confirm the feasibility of the theoretical model.
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
Alvarez-Gaume, Luis; Kounnas, Costas; Lust, Dieter; Riotto, Antonio
2016-01-01
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-...
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]…
DEFF Research Database (Denmark)
Nadimi, Esmaeil Sharak; Bak, Thomas; Izadi-Zamanabadi, Roozbeh
2006-01-01
The main objective of this paper is to investigate the erformance and applicability of two GPC (generalized predictive control) based control methods on a complete benchmark model of the Stewart platform made in MATLAB V6.5. The first method involves an LQG controller (Linear Quadratic Gaussian...
Han, Min; Fan, Jianchao; Wang, Jun
2011-09-01
A dynamic feedforward neural network (DFNN) is proposed for predictive control, whose adaptive parameters are adjusted by using Gaussian particle swarm optimization (GPSO) in the training process. Adaptive time-delay operators are added in the DFNN to improve its generalization for poorly known nonlinear dynamic systems with long time delays. Furthermore, GPSO adopts a chaotic map with Gaussian function to balance the exploration and exploitation capabilities of particles, which improves the computational efficiency without compromising the performance of the DFNN. The stability of the particle dynamics is analyzed, based on the robust stability theory, without any restrictive assumption. A stability condition for the GPSO+DFNN model is derived, which ensures a satisfactory global search and quick convergence, without the need for gradients. The particle velocity ranges could change adaptively during the optimization process. The results of a comparative study show that the performance of the proposed algorithm can compete with selected algorithms on benchmark problems. Additional simulation results demonstrate the effectiveness and accuracy of the proposed combination algorithm in identifying and controlling nonlinear systems with long time delays.
Robust Control Design of Wheeled Inverted Pendulum Assistant Robot
Institute of Scientific and Technical Information of China (English)
Magdi S.Mahmoud; Mohammad T.Nasir
2017-01-01
This paper examines the design concept and mobile control strategy of the human assistant robot I-PENTAR（inverted pendulum type assistant robot）. The motion equation is derived considering the non-holonomic constraint of the twowheeled mobile robot. Different optimal control approaches are applied to a linearized model of I-PENTAR. These include linear quadratic regulator（LQR）, linear quadratic Gaussian control（LQG）, H2 control and H∞ control. Simulation is performed for all the approaches yielding good performance results.
Hidden conic quadratic representation of some nonconvex quadratic optimization problems
Ben-Tal, A.; den Hertog, D.
The problem of minimizing a quadratic objective function subject to one or two quadratic constraints is known to have a hidden convexity property, even when the quadratic forms are indefinite. The equivalent convex problem is a semidefinite one, and the equivalence is based on the celebrated
Binary classification posed as a quadratically constrained quadratic ...
Indian Academy of Sciences (India)
Binary classification is posed as a quadratically constrained quadratic problem and solved using the proposed method. Each class in the binary classification problem is modeled as a multidimensional ellipsoid to forma quadratic constraint in the problem. Particle swarms help in determining the optimal hyperplane or ...
Liang, Lihua; Yuan, Jia; Zhang, Songtao; Zhao, Peng
2018-01-01
This work presents optimal linear quadratic regulator (LQR) based on genetic algorithm (GA) to solve the two degrees of freedom (2 DoF) motion control problem in head seas for wave piercing catamarans (WPC). The proposed LQR based GA control strategy is to select optimal weighting matrices (Q and R). The seakeeping performance of WPC based on proposed algorithm is challenged because of multi-input multi-output (MIMO) system of uncertain coefficient problems. Besides the kinematical constraint problems of WPC, the external conditions must be considered, like the sea disturbance and the actuators (a T-foil and two flaps) control. Moreover, this paper describes the MATLAB and LabVIEW software plats to simulate the reduction effects of WPC. Finally, the real-time (RT) NI CompactRIO embedded controller is selected to test the effectiveness of the actuators based on proposed techniques. In conclusion, simulation and experimental results prove the correctness of the proposed algorithm. The percentage of heave and pitch reductions are more than 18% in different high speeds and bad sea conditions. And the results also verify the feasibility of NI CompactRIO embedded controller.
Quadratic Diophantine equations
Andreescu, Titu
2015-01-01
This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems, and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.
Indian Academy of Sciences (India)
V. Suresh University Of Hyderabad Hyderabad
2008-10-31
Oct 31, 2008 ... We say that (a1,··· ,an) is a zero of the polynomial f if f (a1,··· ,an) = 0. One of the main problems in Mathematics is to determine whether the given polynomial has a (non-trivial) zero or not. For example, let us recall the Fermat's last theorem: V. Suresh University Of Hyderabad Hyderabad. Isotropy of quadratic ...
Altin, Necmi
2018-05-01
An interval type-2 fuzzy logic controller-based maximum power point tracking algorithm and direct current-direct current (DC-DC) converter topology are proposed for photovoltaic (PV) systems. The proposed maximum power point tracking algorithm is designed based on an interval type-2 fuzzy logic controller that has an ability to handle uncertainties. The change in PV power and the change in PV voltage are determined as inputs of the proposed controller, while the change in duty cycle is determined as the output of the controller. Seven interval type-2 fuzzy sets are determined and used as membership functions for input and output variables. The quadratic boost converter provides high voltage step-up ability without any reduction in performance and stability of the system. The performance of the proposed system is validated through MATLAB/Simulink simulations. It is seen that the proposed system provides high maximum power point tracking speed and accuracy even for fast changing atmospheric conditions and high voltage step-up requirements.
Quadratic spatial soliton interactions
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
Guises and disguises of quadratic divergences
Energy Technology Data Exchange (ETDEWEB)
Cherchiglia, A.L., E-mail: adriano@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Vieira, A.R., E-mail: arvieira@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Hiller, Brigitte, E-mail: brigitte@teor.fis.uc.pt [Departamento de Física, Faculdade de Ciências e Tecnologia, Universidade de Coimbra, 3004-516 Coimbra (Portugal); Baêta Scarpelli, A.P., E-mail: scarpelli.apbs@dpf.gov.br [Setor Técnico-Científico, Departamento de Polícia Federal, Rua Hugo D’Antola, 95 - Lapa, São Paulo (Brazil); Sampaio, Marcos, E-mail: marcos.sampaio@durham.ac.uk [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Centre for Particle Theory, Department of Mathematical Sciences, Durham University, South Road Durham DH1 3LE (United Kingdom)
2014-12-15
In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.
Quadratic soliton self-reflection at a quadratically nonlinear interface
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.
Binary naive Bayesian classifiers for correlated Gaussian features: a theoretical analysis
CSIR Research Space (South Africa)
Van Dyk, E
2008-11-01
Full Text Available classifier with Gaussian features while using any quadratic decision boundary. Therefore, the analysis is not restricted to Naive Bayesian classifiers alone and can, for instance, be used to calculate the Bayes error performance. We compare the analytical...
Quadratic brackets from symplectic forms
International Nuclear Information System (INIS)
Alekseev, Anton Yu.; Todorov, Ivan T.
1994-01-01
We give a physicist oriented survey of Poisson-Lie symmetries of classical systems. We consider finite-dimensional geometric actions and the chiral WZNW model as examples for the general construction. An essential point is the appearance of quadratic Poisson brackets for group-like variables. It is believed that upon quantization they lead to quadratic exchange algebras. ((orig.))
Students' Understanding of Quadratic Equations
López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael
2016-01-01
Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…
A Sequential Quadratically Constrained Quadratic Programming Method of Feasible Directions
International Nuclear Information System (INIS)
Jian Jinbao; Hu Qingjie; Tang Chunming; Zheng Haiyan
2007-01-01
In this paper, a sequential quadratically constrained quadratic programming method of feasible directions is proposed for the optimization problems with nonlinear inequality constraints. At each iteration of the proposed algorithm, a feasible direction of descent is obtained by solving only one subproblem which consist of a convex quadratic objective function and simple quadratic inequality constraints without the second derivatives of the functions of the discussed problems, and such a subproblem can be formulated as a second-order cone programming which can be solved by interior point methods. To overcome the Maratos effect, an efficient higher-order correction direction is obtained by only one explicit computation formula. The algorithm is proved to be globally convergent and superlinearly convergent under some mild conditions without the strict complementarity. Finally, some preliminary numerical results are reported
On Characterization of Quadratic Splines
DEFF Research Database (Denmark)
Chen, B. T.; Madsen, Kaj; Zhang, Shuzhong
2005-01-01
that the representation can be refined in a neighborhood of a non-degenerate point and a set of non-degenerate minimizers. Based on these characterizations, many existing algorithms for specific convex quadratic splines are also finite convergent for a general convex quadratic spline. Finally, we study the relationship...... between the convexity of a quadratic spline function and the monotonicity of the corresponding LCP problem. It is shown that, although both conditions lead to easy solvability of the problem, they are different in general....
Energy Technology Data Exchange (ETDEWEB)
Hoejstrup, J [NEG Micon Project Development A/S, Randers (Denmark); Hansen, K S [Denmarks Technical Univ., Dept. of Energy Engineering, Lyngby (Denmark); Pedersen, B J [VESTAS Wind Systems A/S, Lem (Denmark); Nielsen, M [Risoe National Lab., Wind Energy and Atmospheric Physics, Roskilde (Denmark)
1999-03-01
The pdf`s of atmospheric turbulence have somewhat wider tails than a Gaussian, especially regarding accelerations, whereas velocities are close to Gaussian. This behaviour is being investigated using data from a large WEB-database in order to quantify the amount of non-Gaussianity. Models for non-Gaussian turbulence have been developed, by which artificial turbulence can be generated with specified distributions, spectra and cross-correlations. The artificial time series will then be used in load models and the resulting loads in the Gaussian and the non-Gaussian cases will be compared. (au)
Gaussian cloning of coherent states with known phases
International Nuclear Information System (INIS)
Alexanian, Moorad
2006-01-01
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
Dynamic Algorithm for LQGPC Predictive Control
DEFF Research Database (Denmark)
Hangstrup, M.; Ordys, A.W.; Grimble, M.J.
1998-01-01
In this paper the optimal control law is derived for a multi-variable state space Linear Quadratic Gaussian Predictive Controller (LQGPC). A dynamic performance index is utilized resulting in an optimal steady state controller. Knowledge of future reference values is incorporated into the control......In this paper the optimal control law is derived for a multi-variable state space Linear Quadratic Gaussian Predictive Controller (LQGPC). A dynamic performance index is utilized resulting in an optimal steady state controller. Knowledge of future reference values is incorporated...... into the controller design and the solution is derived using the method of Lagrange multipliers. It is shown how well-known GPC controller can be obtained as a special case of the LQGPC controller design. The important advantage of using the LQGPC framework for designing predictive, e.g. GPS is that LQGPC enables...
Metin, Baris; Wiersema, Jan R; Verguts, Tom; Gasthuys, Roos; van Der Meere, Jacob J; Roeyers, Herbert; Sonuga-Barke, Edmund
2014-12-06
According to the state regulation deficit (SRD) account, ADHD is associated with a problem using effort to maintain an optimal activation state under demanding task settings such as very fast or very slow event rates. This leads to a prediction of disrupted performance at event rate extremes reflected in higher Gaussian response variability that is a putative marker of activation during motor preparation. In the current study, we tested this hypothesis using ex-Gaussian modeling, which distinguishes Gaussian from non-Gaussian variability. Twenty-five children with ADHD and 29 typically developing controls performed a simple Go/No-Go task under four different event-rate conditions. There was an accentuated quadratic relationship between event rate and Gaussian variability in the ADHD group compared to the controls. The children with ADHD had greater Gaussian variability at very fast and very slow event rates but not at moderate event rates. The results provide evidence for the SRD account of ADHD. However, given that this effect did not explain all group differences (some of which were independent of event rate) other cognitive and/or motivational processes are also likely implicated in ADHD performance deficits.
LQG Controller Design for Pitch Regulated Variable Speed Wind Turbine
DEFF Research Database (Denmark)
Imran, Raja Muhammed; Hussain, Dil Muhammad Akbar; Chen, Zhe
2014-01-01
Variable speed wind turbine is a complex and nonlinear system, a sophisticated control is required to meet the challenges posed by these systems. This paper is presenting a pitch regulation strategy based on LQG (Linear Quadratic Gaussian) to regulate turbine at its rated power and to reject...
Stability in quadratic torsion theories
Energy Technology Data Exchange (ETDEWEB)
Vasilev, Teodor Borislavov; Cembranos, Jose A.R.; Gigante Valcarcel, Jorge; Martin-Moruno, Prado [Universidad Complutense de Madrid, Departamento de Fisica Teorica I, Madrid (Spain)
2017-11-15
We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier. (orig.)
Stability in quadratic torsion theories
International Nuclear Information System (INIS)
Vasilev, Teodor Borislavov; Cembranos, Jose A.R.; Gigante Valcarcel, Jorge; Martin-Moruno, Prado
2017-01-01
We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier. (orig.)
International Nuclear Information System (INIS)
Nishimichi, Takahiro
2012-01-01
The large-scale clustering pattern of biased tracers is known to be a powerful probe of the non-Gaussianities in the primordial fluctuations. The so-called scale-dependent bias has been reported in various type of models of primordial non-Gaussianities. We focus on local-type non-Gaussianities, and unify the derivations in the literature of the scale-dependent bias in the presence of multiple Gaussian source fields as well as higher-order coupling to cover the models described by frequently-discussed f NL , g NL and t NL parameterization. We find that the resultant power spectrum is characterized by two parameters responsible for the shape and the amplitude of the scale-dependent bias in addition to the Gaussian bias factor. We show how (a generalized version of) Suyama-Yamaguchi inequality between f NL and t NL can directly be accessible from the observed power spectrum through the dependence on our new parameter which controls the shape of the scale-dependent bias. The other parameter for the amplitude of the scale-dependent bias is shown to be useful to distinguish the simplest quadratic non-Gaussianities (i.e., f NL -type) from higher-order ones (g NL and higher), if one measures it from multiple species of galaxies or clusters of galaxies. We discuss the validity and limitations of our analytic results by comparison with numerical simulations in an accompanying paper
Quadratic prediction of factor scores
Wansbeek, T
1999-01-01
Factor scores are naturally predicted by means of their conditional expectation given the indicators y. Under normality this expectation is linear in y but in general it is an unknown function of y. II is discussed that under nonnormality factor scores can be more precisely predicted by a quadratic
On quadratic variation of martingales
Indian Academy of Sciences (India)
On quadratic variation of martingales. 459. The proof relied on the theory of stochastic integration. Subsequently, in Karandikar. [4], the formula was derived using only Doob's maximal inequality. Thus this could be the starting point for the development of stochastic calculus for continuous semimartingales without bringing in ...
Impurity solitons with quadratic nonlinearities
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Torres, Juan P-; Torner, Lluis
1998-01-01
We fmd families of solitary waves mediated by parametric mixing in quadratic nonlinear media that are localized at point-defect impurities. Solitons localized at attractive impurities are found to be dynamically stable. It is shown that localization at the impurity modifies strongly the soliton...
Quadratic divergences and dimensional regularisation
International Nuclear Information System (INIS)
Jack, I.; Jones, D.R.T.
1990-01-01
We present a detailed analysis of quadratic and quartic divergences in dimensionally regulated renormalisable theories. We perform explicit three-loop calculations for a general theory of scalars and fermions. We find that the higher-order quartic divergences are related to the lower-order ones by the renormalisation group β-functions. (orig.)
Quadratic third-order tensor optimization problem with quadratic constraints
Directory of Open Access Journals (Sweden)
Lixing Yang
2014-05-01
Full Text Available Quadratically constrained quadratic programs (QQPs problems play an important modeling role for many diverse problems. These problems are in general NP hard and numerically intractable. Semidenite programming (SDP relaxations often provide good approximate solutions to these hard problems. For several special cases of QQP, e.g., convex programs and trust region subproblems, SDP relaxation provides the exact optimal value, i.e., there is a zero duality gap. However, this is not true for the general QQP, or even the QQP with two convex constraints, but a nonconvex objective.In this paper, we consider a certain QQP where the variable is neither vector nor matrix but a third-order tensor. This problem can be viewed as a generalization of the ordinary QQP with vector or matrix as it's variant. Under some mild conditions, we rst show that SDP relaxation provides exact optimal solutions for the original problem. Then we focus on two classes of homogeneous quadratic tensor programming problems which have no requirements on the constraints number. For one, we provide an easily implemental polynomial time algorithm to approximately solve the problem and discuss the approximation ratio. For the other, we show there is no gap between the SDP relaxation and itself.
Gaussian entanglement revisited
Lami, Ludovico; Serafini, Alessio; Adesso, Gerardo
2018-02-01
We present a novel approach to the separability problem for Gaussian quantum states of bosonic continuous variable systems. We derive a simplified necessary and sufficient separability criterion for arbitrary Gaussian states of m versus n modes, which relies on convex optimisation over marginal covariance matrices on one subsystem only. We further revisit the currently known results stating the equivalence between separability and positive partial transposition (PPT) for specific classes of Gaussian states. Using techniques based on matrix analysis, such as Schur complements and matrix means, we then provide a unified treatment and compact proofs of all these results. In particular, we recover the PPT-separability equivalence for: (i) Gaussian states of 1 versus n modes; and (ii) isotropic Gaussian states. In passing, we also retrieve (iii) the recently established equivalence between separability of a Gaussian state and and its complete Gaussian extendability. Our techniques are then applied to progress beyond the state of the art. We prove that: (iv) Gaussian states that are invariant under partial transposition are necessarily separable; (v) the PPT criterion is necessary and sufficient for separability for Gaussian states of m versus n modes that are symmetric under the exchange of any two modes belonging to one of the parties; and (vi) Gaussian states which remain PPT under passive optical operations can not be entangled by them either. This is not a foregone conclusion per se (since Gaussian bound entangled states do exist) and settles a question that had been left unanswered in the existing literature on the subject. This paper, enjoyable by both the quantum optics and the matrix analysis communities, overall delivers technical and conceptual advances which are likely to be useful for further applications in continuous variable quantum information theory, beyond the separability problem.
Exact solutions to quadratic gravity
Czech Academy of Sciences Publication Activity Database
Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.
2017-01-01
Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.084025
On Quadratic Variation of Martingales
Indian Academy of Sciences (India)
where D ( [ 0 , ∞ ) , R ) denotes the class of real valued r.c.l.l. functions on [ 0 , ∞ ) such that for a locally square integrable martingale ( M t ) with r.c.l.l. paths,. Ψ ( M . ( ) ) = A . ( ). gives the quadratic variation process (written usually as [ M , M ] t ) of ( M t ) . We also show that this process ( A t ) is the unique increasing ...
Exact solutions to quadratic gravity
Czech Academy of Sciences Publication Activity Database
Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.
2017-01-01
Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals. aps .org/prd/abstract/10.1103/PhysRevD.95.084025
Orthogonality preserving infinite dimensional quadratic stochastic operators
International Nuclear Information System (INIS)
Akın, Hasan; Mukhamedov, Farrukh
2015-01-01
In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators
Extending the Scope of Robust Quadratic Optimization
Marandi, Ahmadreza; Ben-Tal, A.; den Hertog, Dick; Melenberg, Bertrand
In this paper, we derive tractable reformulations of the robust counterparts of convex quadratic and conic quadratic constraints with concave uncertainties for a broad range of uncertainty sets. For quadratic constraints with convex uncertainty, it is well-known that the robust counterpart is, in
Quadratic time dependent Hamiltonians and separation of variables
International Nuclear Information System (INIS)
Anzaldo-Meneses, A.
2017-01-01
Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green’s function is obtained and a comparison with the classical Hamilton–Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei–Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü–Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems. - Highlights: • Exact unitary transformation reducing time dependent quadratic quantum Hamiltonian to zero. • New separation of variables method and simultaneous uncoupling of modes. • Explicit examples of transformations for one to four dimensional problems. • New general evolution equation for quadratic form in the action, respectively Green’s function.
Noise-induced chaos in a quadratically nonlinear oscillator
International Nuclear Information System (INIS)
Gan Chunbiao
2006-01-01
The present paper focuses on the noise-induced chaos in a quadratically nonlinear oscillator. Simple zero points of the stochastic Melnikov integral theoretically mean the necessary rising of noise-induced chaotic response in the system based on the stochastic Melnikov method. To quantify the noise-induced chaos, the boundary of the system's safe basin is firstly studied and it is shown to be incursively fractal when chaos arises. Three cases are considered in simulating the safe basin of the system, i.e., the system is excited only by the harmonic excitation, by both the harmonic and the Gaussian white noise excitations, and only by the Gaussian white noise excitation. Secondly, the leading Lyapunov exponent by Rosenstein's algorithm is shown to quantify the chaotic nature of the sample time series of the system. The results show that the boundary of the safe basin can also be fractal even if the system is excited only by the external Gaussian white noise. Most importantly, the almost-harmonic, the noise-induced chaotic and the thoroughly random responses can be found in the system
Applications exponential approximation by integer shifts of Gaussian functions
Directory of Open Access Journals (Sweden)
S. M. Sitnik
2013-01-01
Full Text Available In this paper we consider approximations of functions using integer shifts of Gaussians – quadratic exponentials. A method is proposed to find coefficients of node functions by solving linear systems of equations. The explicit formula for the determinant of the system is found, based on it solvability of linear system under consideration is proved and uniqueness of its solution. We compare results with known ones and briefly indicate applications to signal theory.
Data Transmission Over Networks for Estimation and Control
Gupta, Vijay; Dana, Amir F.; Hespanha, Joao P.; Murray, Richard M.; Hassibi, Babak
2009-01-01
We consider the problem of controlling a linear time invariant process when the controller is located at a location remote from where the sensor measurements are being generated. The communication from the sensor to the controller is supported by a communication network with arbitrary topology composed of analog erasure channels. Using a separation principle, we prove that the optimal linear-quadratic-Gaussian (LQG) controller consists of an LQ optimal regulator along with an estimator that e...
The Model and Quadratic Stability Problem of Buck Converter in DCM
Directory of Open Access Journals (Sweden)
Li Xiaojing
2016-01-01
Full Text Available Quadratic stability is an important performance for control systems. At first, the model of Buck Converter in DCM is built based on the theories of hybrid systems and switched linear systems primarily. Then quadratic stability of SLS and hybrid feedback switching rule are introduced. The problem of Buck Converter’s quadratic stability is researched afterwards. In the end, the simulation analysis and verification are provided. Both experimental verification and theoretical analysis results indicate that the output of Buck Converter in DCM has an excellent performance via quadratic stability control and switching rules.
International Nuclear Information System (INIS)
Tsuchida, Takahiro; Kimura, Koji
2016-01-01
Equivalent non-Gaussian excitation method is proposed to obtain the response moments up to the 4th order of dynamic systems under non-Gaussian random excitation. The non-Gaussian excitation is prescribed by the probability density and the power spectrum, and is described by an Ito stochastic differential equation. Generally, moment equations for the response, which are derived from the governing equations for the excitation and the system, are not closed due to the nonlinearity of the diffusion coefficient in the equation for the excitation even though the system is linear. In the equivalent non-Gaussian excitation method, the diffusion coefficient is replaced with the equivalent diffusion coefficient approximately to obtain a closed set of the moment equations. The square of the equivalent diffusion coefficient is expressed by a quadratic polynomial. In numerical examples, a linear system subjected to nonGaussian excitations with bimodal and Rayleigh distributions is analyzed by using the present method. The results show that the method yields the variance, skewness and kurtosis of the response with high accuracy for non-Gaussian excitation with the widely different probability densities and bandwidth. The statistical moments of the equivalent non-Gaussian excitation are also investigated to describe the feature of the method. (paper)
Coherent states for quadratic Hamiltonians
International Nuclear Information System (INIS)
Contreras-Astorga, Alonso; Fernandez C, David J; Velazquez, Mercedes
2011-01-01
The coherent states for a set of quadratic Hamiltonians in the trap regime are constructed. A matrix technique which allows us to directly identify the creation and annihilation operators will be presented. Then, the coherent states as simultaneous eigenstates of the annihilation operators will be derived, and will be compared with those attained through the displacement operator method. The corresponding wavefunction will be found, and a general procedure for obtaining several mean values involving the canonical operators in these states will be described. The results will be illustrated through the asymmetric Penning trap.
Quadratic Variation by Markov Chains
DEFF Research Database (Denmark)
Hansen, Peter Reinhard; Horel, Guillaume
We introduce a novel estimator of the quadratic variation that is based on the the- ory of Markov chains. The estimator is motivated by some general results concerning filtering contaminated semimartingales. Specifically, we show that filtering can in prin- ciple remove the effects of market...... microstructure noise in a general framework where little is assumed about the noise. For the practical implementation, we adopt the dis- crete Markov chain model that is well suited for the analysis of financial high-frequency prices. The Markov chain framework facilitates simple expressions and elegant analyti...
Factorization method of quadratic template
Kotyrba, Martin
2017-07-01
Multiplication of two numbers is a one-way function in mathematics. Any attempt to distribute the outcome to its roots is called factorization. There are many methods such as Fermat's factorization, Dixońs method or quadratic sieve and GNFS, which use sophisticated techniques fast factorization. All the above methods use the same basic formula differing only in its use. This article discusses a newly designed factorization method. Effective implementation of this method in programs is not important, it only represents and clearly defines its properties.
CSIR Research Space (South Africa)
Roux, FS
2009-01-01
Full Text Available , t0)} = P(du, dv) {FR{g(u, v, t0)}} Replacement: u→ du = t− t0 i2 ∂ ∂u′ v → dv = t− t0 i2 ∂ ∂v′ CSIR National Laser Centre – p.13/30 Differentiation i.s.o integration Evaluate the integral over the Gaussian beam (once and for all). Then, instead... . Gaussian beams with vortex dipoles CSIR National Laser Centre – p.2/30 Gaussian beam notation Gaussian beam in normalised coordinates: g(u, v, t) = exp ( −u 2 + v2 1− it ) u = xω0 v = yω0 t = zρ ρ = piω20 λ ω0 — 1/e2 beam waist radius; ρ— Rayleigh range ω ω...
Gaussian operations and privacy
International Nuclear Information System (INIS)
Navascues, Miguel; Acin, Antonio
2005-01-01
We consider the possibilities offered by Gaussian states and operations for two honest parties, Alice and Bob, to obtain privacy against a third eavesdropping party, Eve. We first extend the security analysis of the protocol proposed in [Navascues et al. Phys. Rev. Lett. 94, 010502 (2005)]. Then, we prove that a generalized version of this protocol does not allow one to distill a secret key out of bound entangled Gaussian states
Quadratic reactivity fuel cycle model
International Nuclear Information System (INIS)
Lewins, J.D.
1985-01-01
For educational purposes it is highly desirable to provide simple yet realistic models for fuel cycle and fuel economy. In particular, a lumped model without recourse to detailed spatial calculations would be very helpful in providing the student with a proper understanding of the purposes of fuel cycle calculations. A teaching model for fuel cycle studies based on a lumped model assuming the summability of partial reactivities with a linear dependence of reactivity usefully illustrates fuel utilization concepts. The linear burnup model does not satisfactorily represent natural enrichment reactors. A better model, showing the trend of initial plutonium production before subsequent fuel burnup and fission product generation, is a quadratic fit. The study of M-batch cycles, reloading 1/Mth of the core at end of cycle, is now complicated by nonlinear equations. A complete account of the asymptotic cycle for any order of M-batch refueling can be given and compared with the linear model. A complete account of the transient cycle can be obtained readily in the two-batch model and this exact solution would be useful in verifying numerical marching models. It is convenient to treat the parabolic fit rho = 1 - tau 2 as a special case of the general quadratic fit rho = 1 - C/sub tau/ - (1 - C)tau 2 in suitably normalized reactivity and cycle time units. The parabolic results are given in this paper
Comparison between linear quadratic and early time dose models
International Nuclear Information System (INIS)
Chougule, A.A.; Supe, S.J.
1993-01-01
During the 70s, much interest was focused on fractionation in radiotherapy with the aim of improving tumor control rate without producing unacceptable normal tissue damage. To compare the radiobiological effectiveness of various fractionation schedules, empirical formulae such as Nominal Standard Dose, Time Dose Factor, Cumulative Radiation Effect and Tumour Significant Dose, were introduced and were used despite many shortcomings. It has been claimed that a recent linear quadratic model is able to predict the radiobiological responses of tumours as well as normal tissues more accurately. We compared Time Dose Factor and Tumour Significant Dose models with the linear quadratic model for tumour regression in patients with carcinomas of the cervix. It was observed that the prediction of tumour regression estimated by the Tumour Significant Dose and Time Dose factor concepts varied by 1.6% from that of the linear quadratic model prediction. In view of the lack of knowledge of the precise values of the parameters of the linear quadratic model, it should be applied with caution. One can continue to use the Time Dose Factor concept which has been in use for more than a decade as its results are within ±2% as compared to that predicted by the linear quadratic model. (author). 11 refs., 3 figs., 4 tabs
Dynamical invariants for variable quadratic Hamiltonians
International Nuclear Information System (INIS)
Suslov, Sergei K
2010-01-01
We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value problem for the time-dependent Schroedinger equation are emphasized. An eigenfunction expansion of the solution of the initial value problem is also found. A nonlinear superposition principle for generalized Ermakov systems is established as a result of decomposition of the general quadratic invariant in terms of the linear ones.
Multivariable controller for discrete stochastic amplitude-constrained systems
Directory of Open Access Journals (Sweden)
Hannu T. Toivonen
1983-04-01
Full Text Available A sub-optimal multivariable controller for discrete stochastic amplitude-constrained systems is presented. In the approach the regulator structure is restricted to the class of linear saturated feedback laws. The stationary covariances of the controlled system are evaluated by approximating the stationary probability distribution of the state by a gaussian distribution. An algorithm for minimizing a quadratic loss function is given, and examples are presented to illustrate the performance of the sub-optimal controller.
New robust chaotic system with exponential quadratic term
International Nuclear Information System (INIS)
Bao Bocheng; Li Chunbiao; Liu Zhong; Xu Jianping
2008-01-01
This paper proposes a new robust chaotic system of three-dimensional quadratic autonomous ordinary differential equations by introducing an exponential quadratic term. This system can display a double-scroll chaotic attractor with only two equilibria, and can be found to be robust chaotic in a very wide parameter domain with positive maximum Lyapunov exponent. Some basic dynamical properties and chaotic behaviour of novel attractor are studied. By numerical simulation, this paper verifies that the three-dimensional system can also evolve into periodic and chaotic behaviours by a constant controller. (general)
1983-12-01
34 M4 + + Z + + + E + ass + + Z + + + osi " " + + Z + + + + 9tr"- + t + Z + ++ +" + + L + Z + +0+ + : :L:+: • +: E. . :ce + L+ Z+ + E+ 9 " + L z + K...this guide.) The truth model description is identified by the heading "TRUTH MODELO . The matrices of the continuous-time system are listed first. The
Quadratically convergent MCSCF scheme using Fock operators
International Nuclear Information System (INIS)
Das, G.
1981-01-01
A quadratically convergent formulation of the MCSCF method using Fock operators is presented. Among its advantages the present formulation is quadratically convergent unlike the earlier ones based on Fock operators. In contrast to other quadratically convergent schemes as well as the one based on generalized Brillouin's theorem, this method leads easily to a hybrid scheme where the weakly coupled orbitals (such as the core) are handled purely by Fock equations, while the rest of the orbitals are treated by a quadratically convergent approach with a truncated virtual space obtained by the use of the corresponding Fock equations
Geometrical and Graphical Solutions of Quadratic Equations.
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)
Multiobjective Optimization Involving Quadratic Functions
Directory of Open Access Journals (Sweden)
Oscar Brito Augusto
2014-01-01
Full Text Available Multiobjective optimization is nowadays a word of order in engineering projects. Although the idea involved is simple, the implementation of any procedure to solve a general problem is not an easy task. Evolutionary algorithms are widespread as a satisfactory technique to find a candidate set for the solution. Usually they supply a discrete picture of the Pareto front even if this front is continuous. In this paper we propose three methods for solving unconstrained multiobjective optimization problems involving quadratic functions. In the first, for biobjective optimization defined in the bidimensional space, a continuous Pareto set is found analytically. In the second, applicable to multiobjective optimization, a condition test is proposed to check if a point in the decision space is Pareto optimum or not and, in the third, with functions defined in n-dimensional space, a direct noniterative algorithm is proposed to find the Pareto set. Simple problems highlight the suitability of the proposed methods.
Quadratic Lagrangians and Legendre transformation
International Nuclear Information System (INIS)
Magnano, G.
1988-01-01
In recent years interest is grown about the so-called non-linear Lagrangians for gravitation. In particular, the quadratic lagrangians are currently believed to play a fundamental role both for quantum gravity and for the super-gravity approach. The higher order and high degree of non-linearity of these theories make very difficult to extract physical information out of them. The author discusses how the Legendre transformation can be applied to a wide class of non-linear theories: it corresponds to a conformal transformation whenever the Lagrangian depends only on the scalar curvature, while it has a more general form if the Lagrangian depends on the full Ricci tensor
Decentralized linear quadratic power system stabilizers for multi ...
Indian Academy of Sciences (India)
Linear quadratic stabilizers are well-known for their superior control capabilities when compared to the conventional lead–lag power system stabilizers. However, they have not seen much of practical importance as the state variables are generally not measurable; especially the generator rotor angle measurement is not ...
Nonclassicality by Local Gaussian Unitary Operations for Gaussian States
Directory of Open Access Journals (Sweden)
Yangyang Wang
2018-04-01
Full Text Available A measure of nonclassicality N in terms of local Gaussian unitary operations for bipartite Gaussian states is introduced. N is a faithful quantum correlation measure for Gaussian states as product states have no such correlation and every non product Gaussian state contains it. For any bipartite Gaussian state ρ A B , we always have 0 ≤ N ( ρ A B < 1 , where the upper bound 1 is sharp. An explicit formula of N for ( 1 + 1 -mode Gaussian states and an estimate of N for ( n + m -mode Gaussian states are presented. A criterion of entanglement is established in terms of this correlation. The quantum correlation N is also compared with entanglement, Gaussian discord and Gaussian geometric discord.
Quadratic time dependent Hamiltonians and separation of variables
Anzaldo-Meneses, A.
2017-06-01
Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green's function is obtained and a comparison with the classical Hamilton-Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei-Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü-Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems.
Generalized Gaussian Error Calculus
Grabe, Michael
2010-01-01
For the first time in 200 years Generalized Gaussian Error Calculus addresses a rigorous, complete and self-consistent revision of the Gaussian error calculus. Since experimentalists realized that measurements in general are burdened by unknown systematic errors, the classical, widespread used evaluation procedures scrutinizing the consequences of random errors alone turned out to be obsolete. As a matter of course, the error calculus to-be, treating random and unknown systematic errors side by side, should ensure the consistency and traceability of physical units, physical constants and physical quantities at large. The generalized Gaussian error calculus considers unknown systematic errors to spawn biased estimators. Beyond, random errors are asked to conform to the idea of what the author calls well-defined measuring conditions. The approach features the properties of a building kit: any overall uncertainty turns out to be the sum of a contribution due to random errors, to be taken from a confidence inter...
Learning conditional Gaussian networks
DEFF Research Database (Denmark)
Bøttcher, Susanne Gammelgaard
This paper considers conditional Gaussian networks. The parameters in the network are learned by using conjugate Bayesian analysis. As conjugate local priors, we apply the Dirichlet distribution for discrete variables and the Gaussian-inverse gamma distribution for continuous variables, given...... a configuration of the discrete parents. We assume parameter independence and complete data. Further, to learn the structure of the network, the network score is deduced. We then develop a local master prior procedure, for deriving parameter priors in these networks. This procedure satisfies parameter...... independence, parameter modularity and likelihood equivalence. Bayes factors to be used in model search are introduced. Finally the methods derived are illustrated by a simple example....
A Numerical Approach to Optimal Coherent Quantum LQG Controller Design Using Gradient Descent
Sichani, Arash Kh.; Vladimirov, Igor G.; Petersen, Ian R.
2016-01-01
This paper is concerned with coherent quantum linear quadratic Gaussian (CQLQG) control. The problem is to find a stabilizing measurement-free quantum controller for a quantum plant so as to minimize a mean square cost for the fully quantum closed-loop system. The plant and controller are open quantum systems interconnected through bosonic quantum fields. In comparison with the observation-actuation structure of classical controllers, coherent quantum feedback is less invasive to the quantum ...
Quadratic independence of coordinate functions of certain ...
Indian Academy of Sciences (India)
... are `quadratically independent' in the sense that they do not satisfy any nontrivial homogeneous quadratic relations among them. Using this, it is proved that there is no genuine compact quantum group which can act faithfully on C ( M ) such that the action leaves invariant the linear span of the above coordinate functions.
Sibling curves of quadratic polynomials | Wiggins | Quaestiones ...
African Journals Online (AJOL)
Sibling curves were demonstrated in [1, 2] as a novel way to visualize the zeroes of real valued functions. In [3] it was shown that a polynomial of degree n has n sibling curves. This paper focuses on the algebraic and geometric properites of the sibling curves of real and complex quadratic polynomials. Key words: Quadratic ...
Quadratic Boost A-Source Impedance Network
DEFF Research Database (Denmark)
Siwakoti, Yam Prasad; Blaabjerg, Frede; Chub, Andrii
2016-01-01
A novel quadratic boost A-source impedance network is proposed to realize converters that demand very high voltage gain. To satisfy the requirement, the network uses an autotransformer where the obtained gain is quadratically dependent on the duty ratio and is unmatched by any existing impedance...
Directory of Open Access Journals (Sweden)
Phil Diamond
2003-01-01
Full Text Available Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.
AUTONOMOUS GAUSSIAN DECOMPOSITION
Energy Technology Data Exchange (ETDEWEB)
Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirović, Snežana; Babler, Brian [Department of Astronomy, University of Wisconsin, 475 North Charter Street, Madison, WI 53706 (United States); Heiles, Carl [Radio Astronomy Lab, UC Berkeley, 601 Campbell Hall, Berkeley, CA 94720 (United States); Hennebelle, Patrick [Laboratoire AIM, Paris-Saclay, CEA/IRFU/SAp-CNRS-Université Paris Diderot, F-91191 Gif-sur Yvette Cedex (France); Goss, W. M. [National Radio Astronomy Observatory, P.O. Box O, 1003 Lopezville, Socorro, NM 87801 (United States); Dickey, John, E-mail: rlindner@astro.wisc.edu [University of Tasmania, School of Maths and Physics, Private Bag 37, Hobart, TAS 7001 (Australia)
2015-04-15
We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of Gaussian components in the data, and also their locations, widths, and amplitudes. We test AGD and find that it produces results comparable to human-derived solutions on 21 cm absorption spectra from the 21 cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the H i line completeness as a function of peak optical depth and velocity width for the 21-SPONGE data, and also show that the results of AGD are stable against varying observational noise intensity. The autonomy and computational efficiency of the method over traditional manual Gaussian fits allow for truly unbiased comparisons between observations and simulations, and for the ability to scale up and interpret the very large data volumes from the upcoming Square Kilometer Array and pathfinder telescopes.
Bounded Gaussian process regression
DEFF Research Database (Denmark)
Jensen, Bjørn Sand; Nielsen, Jens Brehm; Larsen, Jan
2013-01-01
We extend the Gaussian process (GP) framework for bounded regression by introducing two bounded likelihood functions that model the noise on the dependent variable explicitly. This is fundamentally different from the implicit noise assumption in the previously suggested warped GP framework. We...... with the proposed explicit noise-model extension....
AUTONOMOUS GAUSSIAN DECOMPOSITION
International Nuclear Information System (INIS)
Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirović, Snežana; Babler, Brian; Heiles, Carl; Hennebelle, Patrick; Goss, W. M.; Dickey, John
2015-01-01
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
Quadratic Hedging of Basis Risk
Directory of Open Access Journals (Sweden)
Hardy Hulley
2015-02-01
Full Text Available This paper examines a simple basis risk model based on correlated geometric Brownian motions. We apply quadratic criteria to minimize basis risk and hedge in an optimal manner. Initially, we derive the Föllmer–Schweizer decomposition for a European claim. This allows pricing and hedging under the minimal martingale measure, corresponding to the local risk-minimizing strategy. Furthermore, since the mean-variance tradeoff process is deterministic in our setup, the minimal martingale- and variance-optimal martingale measures coincide. Consequently, the mean-variance optimal strategy is easily constructed. Simple pricing and hedging formulae for put and call options are derived in terms of the Black–Scholes formula. Due to market incompleteness, these formulae depend on the drift parameters of the processes. By making a further equilibrium assumption, we derive an approximate hedging formula, which does not require knowledge of these parameters. The hedging strategies are tested using Monte Carlo experiments, and are compared with results achieved using a utility maximization approach.
Asymptotic performance of regularized quadratic discriminant analysis based classifiers
Elkhalil, Khalil
2017-12-13
This paper carries out a large dimensional analysis of the standard regularized quadratic discriminant analysis (QDA) classifier designed on the assumption that data arise from a Gaussian mixture model. The analysis relies on fundamental results from random matrix theory (RMT) when both the number of features and the cardinality of the training data within each class grow large at the same pace. Under some mild assumptions, we show that the asymptotic classification error converges to a deterministic quantity that depends only on the covariances and means associated with each class as well as the problem dimensions. Such a result permits a better understanding of the performance of regularized QDA and can be used to determine the optimal regularization parameter that minimizes the misclassification error probability. Despite being valid only for Gaussian data, our theoretical findings are shown to yield a high accuracy in predicting the performances achieved with real data sets drawn from popular real data bases, thereby making an interesting connection between theory and practice.
Quantum information with Gaussian states
International Nuclear Information System (INIS)
Wang Xiangbin; Hiroshima, Tohya; Tomita, Akihisa; Hayashi, Masahito
2007-01-01
Quantum optical Gaussian states are a type of important robust quantum states which are manipulatable by the existing technologies. So far, most of the important quantum information experiments are done with such states, including bright Gaussian light and weak Gaussian light. Extending the existing results of quantum information with discrete quantum states to the case of continuous variable quantum states is an interesting theoretical job. The quantum Gaussian states play a central role in such a case. We review the properties and applications of Gaussian states in quantum information with emphasis on the fundamental concepts, the calculation techniques and the effects of imperfections of the real-life experimental setups. Topics here include the elementary properties of Gaussian states and relevant quantum information device, entanglement-based quantum tasks such as quantum teleportation, quantum cryptography with weak and strong Gaussian states and the quantum channel capacity, mathematical theory of quantum entanglement and state estimation for Gaussian states
Directory of Open Access Journals (Sweden)
Tanwiwat Jaikuna
2017-02-01
Full Text Available Purpose: To develop an in-house software program that is able to calculate and generate the biological dose distribution and biological dose volume histogram by physical dose conversion using the linear-quadratic-linear (LQL model. Material and methods : The Isobio software was developed using MATLAB version 2014b to calculate and generate the biological dose distribution and biological dose volume histograms. The physical dose from each voxel in treatment planning was extracted through Computational Environment for Radiotherapy Research (CERR, and the accuracy was verified by the differentiation between the dose volume histogram from CERR and the treatment planning system. An equivalent dose in 2 Gy fraction (EQD2 was calculated using biological effective dose (BED based on the LQL model. The software calculation and the manual calculation were compared for EQD2 verification with pair t-test statistical analysis using IBM SPSS Statistics version 22 (64-bit. Results: Two and three-dimensional biological dose distribution and biological dose volume histogram were displayed correctly by the Isobio software. Different physical doses were found between CERR and treatment planning system (TPS in Oncentra, with 3.33% in high-risk clinical target volume (HR-CTV determined by D90%, 0.56% in the bladder, 1.74% in the rectum when determined by D2cc, and less than 1% in Pinnacle. The difference in the EQD2 between the software calculation and the manual calculation was not significantly different with 0.00% at p-values 0.820, 0.095, and 0.593 for external beam radiation therapy (EBRT and 0.240, 0.320, and 0.849 for brachytherapy (BT in HR-CTV, bladder, and rectum, respectively. Conclusions : The Isobio software is a feasible tool to generate the biological dose distribution and biological dose volume histogram for treatment plan evaluation in both EBRT and BT.
On a linear-quadratic problem with Caputo derivative
Directory of Open Access Journals (Sweden)
Dariusz Idczak
2016-01-01
Full Text Available In this paper, we study a linear-quadratic optimal control problem with a fractional control system containing a Caputo derivative of unknown function. First, we derive the formulas for the differential and gradient of the cost functional under given constraints. Next, we prove an existence result and derive a maximum principle. Finally, we describe the gradient and projection of the gradient methods for the problem under consideration.
Design of Linear-Quadratic-Regulator for a CSTR process
Meghna, P. R.; Saranya, V.; Jaganatha Pandian, B.
2017-11-01
This paper aims at creating a Linear Quadratic Regulator (LQR) for a Continuous Stirred Tank Reactor (CSTR). A CSTR is a common process used in chemical industries. It is a highly non-linear system. Therefore, in order to create the gain feedback controller, the model is linearized. The controller is designed for the linearized model and the concentration and volume of the liquid in the reactor are kept at a constant value as required.
Gaussian discriminating strength
Rigovacca, L.; Farace, A.; De Pasquale, A.; Giovannetti, V.
2015-10-01
We present a quantifier of nonclassical correlations for bipartite, multimode Gaussian states. It is derived from the Discriminating Strength measure, introduced for finite dimensional systems in Farace et al., [New J. Phys. 16, 073010 (2014), 10.1088/1367-2630/16/7/073010]. As the latter the new measure exploits the quantum Chernoff bound to gauge the susceptibility of the composite system with respect to local perturbations induced by unitary gates extracted from a suitable set of allowed transformations (the latter being identified by posing some general requirements). Closed expressions are provided for the case of two-mode Gaussian states obtained by squeezing or by linearly mixing via a beam splitter a factorized two-mode thermal state. For these density matrices, we study how nonclassical correlations are related with the entanglement present in the system and with its total photon number.
Designing Camera Networks by Convex Quadratic Programming
Ghanem, Bernard; Wonka, Peter; Cao, Yuanhao
2015-01-01
be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution
Schur Stability Regions for Complex Quadratic Polynomials
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 Functionals with General Boundary Conditions
International Nuclear Information System (INIS)
Dosla, Z.; Dosly, O.
1997-01-01
The purpose of this paper is to give the Reid 'Roundabout Theorem' for quadratic functionals with general boundary conditions. In particular, we describe the so-called coupled point and regularity condition introduced in terms of Riccati equation solutions
Radiotherapy treatment planning linear-quadratic radiobiology
Chapman, J Donald
2015-01-01
Understand Quantitative Radiobiology from a Radiation Biophysics PerspectiveIn the field of radiobiology, the linear-quadratic (LQ) equation has become the standard for defining radiation-induced cell killing. Radiotherapy Treatment Planning: Linear-Quadratic Radiobiology describes tumor cell inactivation from a radiation physics perspective and offers appropriate LQ parameters for modeling tumor and normal tissue responses.Explore the Latest Cell Killing Numbers for Defining Iso-Effective Cancer TreatmentsThe book compil
Solitons in quadratic nonlinear photonic crystals
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2001-01-01
We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities, which can be defocusing, and we numerically find previously unknown soliton families....... Because of these induced cubic terms, solitons still exist even when the effective quadratic nonlinearity vanishes and conventional theory predicts that there can be no soliton. We demonstrate that both bright and dark forms of these solitons can propagate stably....
Directory of Open Access Journals (Sweden)
A. L. Senyavskiy
2015-01-01
Full Text Available The article analyzes the robustness of the digital demodulator of the signal with the lowest frequency shift keying at a subcarrier frequency with respect to non-Gaussian interference type of atmospheric, industrial noise and interfering frequency -and phase-shift keyed signals. This type of demodulator is used for the transmission of navigation data in the systems of air traffic control with automatic dependent surveillance.
Yan, Yuan
2017-07-13
Gaussian likelihood inference has been studied and used extensively in both statistical theory and applications due to its simplicity. However, in practice, the assumption of Gaussianity is rarely met in the analysis of spatial data. In this paper, we study the effect of non-Gaussianity on Gaussian likelihood inference for the parameters of the Matérn covariance model. By using Monte Carlo simulations, we generate spatial data from a Tukey g-and-h random field, a flexible trans-Gaussian random field, with the Matérn covariance function, where g controls skewness and h controls tail heaviness. We use maximum likelihood based on the multivariate Gaussian distribution to estimate the parameters of the Matérn covariance function. We illustrate the effects of non-Gaussianity of the data on the estimated covariance function by means of functional boxplots. Thanks to our tailored simulation design, a comparison of the maximum likelihood estimator under both the increasing and fixed domain asymptotics for spatial data is performed. We find that the maximum likelihood estimator based on Gaussian likelihood is overall satisfying and preferable than the non-distribution-based weighted least squares estimator for data from the Tukey g-and-h random field. We also present the result for Gaussian kriging based on Matérn covariance estimates with data from the Tukey g-and-h random field and observe an overall satisfactory performance.
Yan, Yuan; Genton, Marc G.
2017-01-01
Gaussian likelihood inference has been studied and used extensively in both statistical theory and applications due to its simplicity. However, in practice, the assumption of Gaussianity is rarely met in the analysis of spatial data. In this paper, we study the effect of non-Gaussianity on Gaussian likelihood inference for the parameters of the Matérn covariance model. By using Monte Carlo simulations, we generate spatial data from a Tukey g-and-h random field, a flexible trans-Gaussian random field, with the Matérn covariance function, where g controls skewness and h controls tail heaviness. We use maximum likelihood based on the multivariate Gaussian distribution to estimate the parameters of the Matérn covariance function. We illustrate the effects of non-Gaussianity of the data on the estimated covariance function by means of functional boxplots. Thanks to our tailored simulation design, a comparison of the maximum likelihood estimator under both the increasing and fixed domain asymptotics for spatial data is performed. We find that the maximum likelihood estimator based on Gaussian likelihood is overall satisfying and preferable than the non-distribution-based weighted least squares estimator for data from the Tukey g-and-h random field. We also present the result for Gaussian kriging based on Matérn covariance estimates with data from the Tukey g-and-h random field and observe an overall satisfactory performance.
Interconversion of pure Gaussian states requiring non-Gaussian operations
Jabbour, Michael G.; García-Patrón, Raúl; Cerf, Nicolas J.
2015-01-01
We analyze the conditions under which local operations and classical communication enable entanglement transformations between bipartite pure Gaussian states. A set of necessary and sufficient conditions had been found [G. Giedke et al., Quant. Inf. Comput. 3, 211 (2003)] for the interconversion between such states that is restricted to Gaussian local operations and classical communication. Here, we exploit majorization theory in order to derive more general (sufficient) conditions for the interconversion between bipartite pure Gaussian states that goes beyond Gaussian local operations. While our technique is applicable to an arbitrary number of modes for each party, it allows us to exhibit surprisingly simple examples of 2 ×2 Gaussian states that necessarily require non-Gaussian local operations to be transformed into each other.
Yurinsky, Vadim Vladimirovich
1995-01-01
Surveys the methods currently applied to study sums of infinite-dimensional independent random vectors in situations where their distributions resemble Gaussian laws. Covers probabilities of large deviations, Chebyshev-type inequalities for seminorms of sums, a method of constructing Edgeworth-type expansions, estimates of characteristic functions for random vectors obtained by smooth mappings of infinite-dimensional sums to Euclidean spaces. A self-contained exposition of the modern research apparatus around CLT, the book is accessible to new graduate students, and can be a useful reference for researchers and teachers of the subject.
Chimera states in Gaussian coupled map lattices
Li, Xiao-Wen; Bi, Ran; Sun, Yue-Xiang; Zhang, Shuo; Song, Qian-Qian
2018-04-01
We study chimera states in one-dimensional and two-dimensional Gaussian coupled map lattices through simulations and experiments. Similar to the case of global coupling oscillators, individual lattices can be regarded as being controlled by a common mean field. A space-dependent order parameter is derived from a self-consistency condition in order to represent the collective state.
LQG Control of Networked Control Systems with Limited Information
Directory of Open Access Journals (Sweden)
Qing-Quan Liu
2014-01-01
Full Text Available This paper addresses linear quadratic Gaussian (LQG control problems for multi-input multioutput (MIMO, linear time-invariant (LTI systems, where the sensors and controllers are geographically separated and connected via a digital communication channel with limited data rates. An observer-based, quantized state feedback control scheme is employed in order to achieve the minimum data rate for mean square stabilization of the unstable plant. An explicit expression is presented to state the tradeoff between the LQ cost and the data rate. Sufficient conditions on the data rate for mean square stabilization are derived. An illustrative example is given to demonstrate the effectiveness of the proposed scheme.
Rotating quantum Gaussian packets
International Nuclear Information System (INIS)
Dodonov, V V
2015-01-01
We study two-dimensional quantum Gaussian packets with a fixed value of mean angular momentum. This value is the sum of two independent parts: the ‘external’ momentum related to the motion of the packet center and the ‘internal’ momentum due to quantum fluctuations. The packets minimizing the mean energy of an isotropic oscillator with the fixed mean angular momentum are found. They exist for ‘co-rotating’ external and internal motions, and they have nonzero correlation coefficients between coordinates and momenta, together with some (moderate) amount of quadrature squeezing. Variances of angular momentum and energy are calculated, too. Differences in the behavior of ‘co-rotating’ and ‘anti-rotating’ packets are shown. The time evolution of rotating Gaussian packets is analyzed, including the cases of a charge in a homogeneous magnetic field and a free particle. In the latter case, the effect of initial shrinking of packets with big enough coordinate-momentum correlation coefficients (followed by the well known expansion) is discovered. This happens due to a competition of ‘focusing’ and ‘de-focusing’ in the orthogonal directions. (paper)
DEFF Research Database (Denmark)
Mak, Vicky; Thomadsen, Tommy
2006-01-01
This paper considers the cardinality constrained quadratic knapsack problem (QKP) and the quadratic selective travelling salesman problem (QSTSP). The QKP is a generalization of the knapsack problem and the QSTSP is a generalization of the travelling salesman problem. Thus, both problems are NP...
Indirect quantum tomography of quadratic Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)
2011-01-15
A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.
Nonlinear dynamics of quadratically cubic systems
International Nuclear Information System (INIS)
Rudenko, O V
2013-01-01
We propose a modified form of the well-known nonlinear dynamic equations with quadratic relations used to model a cubic nonlinearity. We show that such quadratically cubic equations sometimes allow exact solutions and sometimes make the original problem easier to analyze qualitatively. Occasionally, exact solutions provide a useful tool for studying new phenomena. Examples considered include nonlinear ordinary differential equations and Hopf, Burgers, Korteweg–de Vries, and nonlinear Schrödinger partial differential equations. Some problems are solved exactly in the space–time and spectral representations. Unsolved problems potentially solvable by the proposed approach are listed. (methodological notes)
PSQP: Puzzle Solving by Quadratic Programming.
Andalo, Fernanda A; Taubin, Gabriel; Goldenstein, Siome
2017-02-01
In this article we present the first effective method based on global optimization for the reconstruction of image puzzles comprising rectangle pieces-Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.
Cascaded Quadratic Soliton Compression in Waveguide Structures
DEFF Research Database (Denmark)
Guo, Hairun
between the Kerr nonlinear effects and the dispersive effects in the medium. A Kerr-like nonlinearity is produced through the cascaded phase mismatched quadratic process, e.g. the second harmonic generation process, which can be flexibly tuned in both the sign and the amplitude, making possible a strong......-phase-matching technology is not necessarily needed. In large-RI-changed waveguides, CQSC is extended to the mid-infrared range to generate single-cycle pulses with purely nonlinear interactions, since an all-normal dispersion profile could be achieved within the guidance band. We believe that CQSC in quadratic waveguides...
On orthogonality preserving quadratic stochastic operators
Energy Technology Data Exchange (ETDEWEB)
Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd [Department of Computational and Theoretical Sciences, Faculty of Science International Islamic University Malaysia, P.O. Box 141, 25710 Kuantan, Pahang Malaysia (Malaysia)
2015-05-15
A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.
Bound constrained quadratic programming via piecewise
DEFF Research Database (Denmark)
Madsen, Kaj; Nielsen, Hans Bruun; Pinar, M. C.
1999-01-01
of a symmetric, positive definite matrix, and is solved by Newton iteration with line search. The paper describes the algorithm and its implementation including estimation of lambda/sub 1/ , how to get a good starting point for the iteration, and up- and downdating of Cholesky factorization. Results of extensive......We consider the strictly convex quadratic programming problem with bounded variables. A dual problem is derived using Lagrange duality. The dual problem is the minimization of an unconstrained, piecewise quadratic function. It involves a lower bound of lambda/sub 1/ , the smallest eigenvalue...
On orthogonality preserving quadratic stochastic operators
International Nuclear Information System (INIS)
Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd
2015-01-01
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
Eigenfunctions of quadratic hamiltonians in Wigner representation
International Nuclear Information System (INIS)
Akhundova, Eh.A.; Dodonov, V.V.; Man'ko, V.I.
1984-01-01
Exact solutions of the Schroedinger equation in Wigner representation are obtained for an arbitrary non-stationary N-dimensional quadratic Hamiltonian. It is shown that the complete system of the solutions can always be chosen in the form of the products of Laguerre polynomials, the arguments of which are the quadratic integrals of motion of the corresponding classical problem. The generating function is found for the transition probabilities between Fock states which represent a many-dimensional generatization of a well-known Husimi formula for the oscillator of variable frequency. As an example, the motion of a charged particle in an uniform alternate electromagnetic field is considered in detail
International Nuclear Information System (INIS)
McFadden, Paul; Skenderis, Kostas
2011-01-01
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 NL 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
Palm distributions for log Gaussian Cox processes
DEFF Research Database (Denmark)
Coeurjolly, Jean-Francois; Møller, Jesper; Waagepetersen, Rasmus Plenge
2017-01-01
This paper establishes a remarkable result regarding Palm distributions for a log Gaussian Cox process: the reduced Palm distribution for a log Gaussian Cox process is itself a log Gaussian Cox process that only differs from the original log Gaussian Cox process in the intensity function. This new...... result is used to study functional summaries for log Gaussian Cox processes....
Geometry of Gaussian quantum states
International Nuclear Information System (INIS)
Link, Valentin; Strunz, Walter T
2015-01-01
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. (paper)
Quadratic mass relations in topological bootstrap theory
International Nuclear Information System (INIS)
Jones, C.E.; Uschersohn, J.
1980-01-01
From the requirement of reality of discontinuities of scattering amplitudes at the spherical level of the topological bootstrap theory, a large number of mass relations for hadrons is derived. Quadratic mass formulas for the symmetry-breaking pattern of both mesons and baryon is obtained and their relation to conventional models of symmetry breaking is briefly discussed
STABILIZED SEQUENTIAL QUADRATIC PROGRAMMING: A SURVEY
Directory of Open Access Journals (Sweden)
Damián Fernández
2014-12-01
Full Text Available We review the motivation for, the current state-of-the-art in convergence results, and some open questions concerning the stabilized version of the sequential quadratic programming algorithm for constrained optimization. We also discuss the tools required for its local convergence analysis, globalization challenges, and extentions of the method to the more general variational problems.
The Quadratic Selective Travelling Salesman Problem
DEFF Research Database (Denmark)
Thomadsen, Tommy; Stidsen, Thomas K.
2003-01-01
A well-known extension of the Travelling Salesman Problem (TSP) is the Selective TSP (STSP): Each node has an associated profit and instead of visiting all nodes, the most profitable set of nodes, taking into account the tour cost, is visited. The Quadratic STSP (QSTSP) adds the additional...
orthogonal and scaling transformations of quadratic functions
African Journals Online (AJOL)
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functions of sub-problems of various nonlinear programming problems that employ methods such as sequential quadratic programming and trust-region methods (Sorensen, 1982; Eldersveld,. 1991; Nocedal and Wright, 1999). Various problems in Algebra, Functional Analysis,. Analytic Geometry and Computational Mathe-.
Fundamental quadratic variational principle underlying general relativity
International Nuclear Information System (INIS)
Atkins, W.K.
1983-01-01
The fundamental result of Lanczos is used in a new type of quadratic variational principle whose field equations are the Einstein field equations together with the Yang-Mills type equations for the Riemann curvature. Additionally, a spin-2 theory of gravity for the special case of the Einstein vacuum is discussed
Investigating Students' Mathematical Difficulties with Quadratic Equations
O'Connor, Bronwyn Reid; Norton, Stephen
2016-01-01
This paper examines the factors that hinder students' success in working with and understanding the mathematics of quadratic equations using a case study analysis of student error patterns. Twenty-five Year 11 students were administered a written test to examine their understanding of concepts and procedures associated with this topic. The…
Commuting quantum traces for quadratic algebras
International Nuclear Information System (INIS)
Nagy, Zoltan; Avan, Jean; Doikou, Anastasia; Rollet, Genevieve
2005-01-01
Consistent tensor products on auxiliary spaces, hereafter denoted 'fusion procedures', and commuting transfer matrices are defined for general quadratic algebras, nondynamical and dynamical, inspired by results on reflection algebras. Applications of these procedures then yield integer-indexed families of commuting Hamiltonians
How Gaussian can our Universe be?
Cabass, G.; Pajer, E.; Schmidt, F.
2017-01-01
Gravity is a non-linear theory, and hence, barring cancellations, the initial super-horizon perturbations produced by inflation must contain some minimum amount of mode coupling, or primordial non-Gaussianity. In single-field slow-roll models, where this lower bound is saturated, non-Gaussianity is controlled by two observables: the tensor-to-scalar ratio, which is uncertain by more than fifty orders of magnitude; and the scalar spectral index, or tilt, which is relatively well measured. It is well known that to leading and next-to-leading order in derivatives, the contributions proportional to the tilt disappear from any local observable, and suspicion has been raised that this might happen to all orders, allowing for an arbitrarily low amount of primordial non-Gaussianity. Employing Conformal Fermi Coordinates, we show explicitly that this is not the case. Instead, a contribution of order the tilt appears in local observables. In summary, the floor of physical primordial non-Gaussianity in our Universe has a squeezed-limit scaling of kl2/ks2, similar to equilateral and orthogonal shapes, and a dimensionless amplitude of order 0.1 × (ns-1).
How Gaussian can our Universe be?
Energy Technology Data Exchange (ETDEWEB)
Cabass, G. [Physics Department and INFN, Università di Roma ' ' La Sapienza' ' , P.le Aldo Moro 2, 00185, Rome (Italy); Pajer, E. [Institute for Theoretical Physics and Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht (Netherlands); Schmidt, F., E-mail: giovanni.cabass@roma1.infn.it, E-mail: e.pajer@uu.nl, E-mail: fabians@mpa-garching.mpg.de [Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching (Germany)
2017-01-01
Gravity is a non-linear theory, and hence, barring cancellations, the initial super-horizon perturbations produced by inflation must contain some minimum amount of mode coupling, or primordial non-Gaussianity. In single-field slow-roll models, where this lower bound is saturated, non-Gaussianity is controlled by two observables: the tensor-to-scalar ratio, which is uncertain by more than fifty orders of magnitude; and the scalar spectral index, or tilt, which is relatively well measured. It is well known that to leading and next-to-leading order in derivatives, the contributions proportional to the tilt disappear from any local observable, and suspicion has been raised that this might happen to all orders, allowing for an arbitrarily low amount of primordial non-Gaussianity. Employing Conformal Fermi Coordinates, we show explicitly that this is not the case. Instead, a contribution of order the tilt appears in local observables. In summary, the floor of physical primordial non-Gaussianity in our Universe has a squeezed-limit scaling of k {sub ℓ}{sup 2}/ k {sub s} {sup 2}, similar to equilateral and orthogonal shapes, and a dimensionless amplitude of order 0.1 × ( n {sub s}−1).
Resource theory of non-Gaussian operations
Zhuang, Quntao; Shor, Peter W.; Shapiro, Jeffrey H.
2018-05-01
Non-Gaussian states and operations are crucial for various continuous-variable quantum information processing tasks. To quantitatively understand non-Gaussianity beyond states, we establish a resource theory for non-Gaussian operations. In our framework, we consider Gaussian operations as free operations, and non-Gaussian operations as resources. We define entanglement-assisted non-Gaussianity generating power and show that it is a monotone that is nonincreasing under the set of free superoperations, i.e., concatenation and tensoring with Gaussian channels. For conditional unitary maps, this monotone can be analytically calculated. As examples, we show that the non-Gaussianity of ideal photon-number subtraction and photon-number addition equal the non-Gaussianity of the single-photon Fock state. Based on our non-Gaussianity monotone, we divide non-Gaussian operations into two classes: (i) the finite non-Gaussianity class, e.g., photon-number subtraction, photon-number addition, and all Gaussian-dilatable non-Gaussian channels; and (ii) the diverging non-Gaussianity class, e.g., the binary phase-shift channel and the Kerr nonlinearity. This classification also implies that not all non-Gaussian channels are exactly Gaussian dilatable. Our resource theory enables a quantitative characterization and a first classification of non-Gaussian operations, paving the way towards the full understanding of non-Gaussianity.
Optimality Conditions for Fuzzy Number Quadratic Programming with Fuzzy Coefficients
Directory of Open Access Journals (Sweden)
Xue-Gang Zhou
2014-01-01
Full Text Available The purpose of the present paper is to investigate optimality conditions and duality theory in fuzzy number quadratic programming (FNQP in which the objective function is fuzzy quadratic function with fuzzy number coefficients and the constraint set is fuzzy linear functions with fuzzy number coefficients. Firstly, the equivalent quadratic programming of FNQP is presented by utilizing a linear ranking function and the dual of fuzzy number quadratic programming primal problems is introduced. Secondly, we present optimality conditions for fuzzy number quadratic programming. We then prove several duality results for fuzzy number quadratic programming problems with fuzzy coefficients.
Handbook of Gaussian basis sets
International Nuclear Information System (INIS)
Poirier, R.; Kari, R.; Csizmadia, I.G.
1985-01-01
A collection of a large body of information is presented useful for chemists involved in molecular Gaussian computations. Every effort has been made by the authors to collect all available data for cartesian Gaussian as found in the literature up to July of 1984. The data in this text includes a large collection of polarization function exponents but in this case the collection is not complete. Exponents for Slater type orbitals (STO) were included for completeness. This text offers a collection of Gaussian exponents primarily without criticism. (Auth.)
Sensitivity analysis in Gaussian Bayesian networks using a symbolic-numerical technique
International Nuclear Information System (INIS)
Castillo, Enrique; Kjaerulff, Uffe
2003-01-01
The paper discusses the problem of sensitivity analysis in Gaussian Bayesian networks. The algebraic structure of the conditional means and variances, as rational functions involving linear and quadratic functions of the parameters, are used to simplify the sensitivity analysis. In particular the probabilities of conditional variables exceeding given values and related probabilities are analyzed. Two examples of application are used to illustrate all the concepts and methods
Geometric Approaches to Quadratic Equations from Other Times and Places.
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)
On Exponential Hedging and Related Quadratic Backward Stochastic Differential Equations
International Nuclear Information System (INIS)
Sekine, Jun
2006-01-01
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
C1 Rational Quadratic Trigonometric Interpolation Spline for Data Visualization
Directory of Open Access Journals (Sweden)
Shengjun Liu
2015-01-01
Full Text Available A new C1 piecewise rational quadratic trigonometric spline with four local positive shape parameters in each subinterval is constructed to visualize the given planar data. Constraints are derived on these free shape parameters to generate shape preserving interpolation curves for positive and/or monotonic data sets. Two of these shape parameters are constrained while the other two can be set free to interactively control the shape of the curves. Moreover, the order of approximation of developed interpolant is investigated as O(h3. Numeric experiments demonstrate that our method can construct nice shape preserving interpolation curves efficiently.
Coherent states of systems with quadratic Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Bagrov, V.G., E-mail: bagrov@phys.tsu.ru [Department of Physics, Tomsk State University, Tomsk (Russian Federation); Gitman, D.M., E-mail: gitman@if.usp.br [Tomsk State University, Tomsk (Russian Federation); Pereira, A.S., E-mail: albertoufcg@hotmail.com [Universidade de Sao Paulo (USP), Sao Paulo, SP (Brazil). Instituto de Fisica
2015-06-15
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 Schroedinger 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. (author)
Coherent states of systems with quadratic Hamiltonians
International Nuclear Information System (INIS)
Bagrov, V.G.; Gitman, D.M.; Pereira, A.S.
2015-01-01
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 Schroedinger 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. (author)
On quadratic residue codes and hyperelliptic curves
Directory of Open Access Journals (Sweden)
David Joyner
2008-01-01
Full Text Available For an odd prime p and each non-empty subset S⊂GF(p, consider the hyperelliptic curve X S defined by y 2 =f S (x, where f S (x = ∏ a∈S (x-a. Using a connection between binary quadratic residue codes and hyperelliptic curves over GF(p, this paper investigates how coding theory bounds give rise to bounds such as the following example: for all sufficiently large primes p there exists a subset S⊂GF(p for which the bound |X S (GF(p| > 1.39p holds. We also use the quasi-quadratic residue codes defined below to construct an example of a formally self-dual optimal code whose zeta function does not satisfy the ``Riemann hypothesis.''
Quaternion orders, quadratic forms, and Shimura curves
Alsina, Montserrat
2004-01-01
Shimura curves are a far-reaching generalization of the classical modular curves. They lie at the crossroads of many areas, including complex analysis, hyperbolic geometry, algebraic geometry, algebra, and arithmetic. The text provides an introduction to the subject from a theoretic and algorithmic perspective. The main topics covered in it are Shimura curves defined over the rational number field, the construction of their fundamental domains, and the determination of their complex multiplication points. The study of complex multiplication points in Shimura curves leads to the study of families of binary quadratic forms with algebraic coefficients and to their classification by arithmetic Fuchsian groups. In this regard, the authors develop a theory full of new possibilities which parallels Gauss' theory on the classification of binary quadratic forms with integral coefficients by the action of the modular group. Each topic covered in the book begins with a theoretical discussion followed by carefully worked...
Quadratic hamiltonians and relativistic quantum mechanics
International Nuclear Information System (INIS)
Razumov, A.V.; Solov'ev, V.O.; Taranov, A.Yu.
1981-01-01
For the case of a charged scalar field described by a quadratic hamiltonian the equivalent relativistic quantum mechanics is constructed in one-particle sector. Complete investigation of a charged relativistic particle motion in the Coulomb field is carried out. Subcritical as well as supercritical cases are considered. In the course of investigation of the charged scalar particle in the Coulomb field the diagonalization of the quadratic hamiltonian describing the charged scalar quantized field interaction with the external Coulomb field has taken place. Mathematically this problem is bound to the construction of self-conjugated expansions of the symmetric operator. The construction of such expansion is necessary at any small external field magnitude [ru
Lambda-lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, O.; Schultz, U.P.
2004-01-01
-lifting transforms a block-structured program into a set of recursive equations, one for each local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters......Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...
Quadratic Interpolation and Linear Lifting Design
Directory of Open Access Journals (Sweden)
Joel Solé
2007-03-01
Full Text Available A quadratic image interpolation method is stated. The formulation is connected to the optimization of lifting steps. This relation triggers the exploration of several interpolation possibilities within the same context, which uses the theory of convex optimization to minimize quadratic functions with linear constraints. The methods consider possible knowledge available from a given application. A set of linear equality constraints that relate wavelet bases and coefficients with the underlying signal is introduced in the formulation. As a consequence, the formulation turns out to be adequate for the design of lifting steps. The resulting steps are related to the prediction minimizing the detail signal energy and to the update minimizing the l2-norm of the approximation signal gradient. Results are reported for the interpolation methods in terms of PSNR and also, coding results are given for the new update lifting steps.
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2002-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2003-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2004-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....
Temporal quadratic expansion nodal Green's function method
International Nuclear Information System (INIS)
Liu Cong; Jing Xingqing; Xu Xiaolin
2000-01-01
A new approach is presented to efficiently solve the three-dimensional space-time reactor dynamics equation which overcomes the disadvantages of current methods. In the Temporal Quadratic Expansion Nodal Green's Function Method (TQE/NGFM), the Quadratic Expansion Method (QEM) is used for the temporal solution with the Nodal Green's Function Method (NGFM) employed for the spatial solution. Test calculational results using TQE/NGFM show that its time step size can be 5-20 times larger than that of the Fully Implicit Method (FIM) for similar precision. Additionally, the spatial mesh size with NGFM can be nearly 20 times larger than that using the finite difference method. So, TQE/NGFM is proved to be an efficient reactor dynamics analysis method
Walking solitons in quadratic nonlinear media
Torner Sabata, Lluís; Mazilu, D; Mihalache, Dumitru
1996-01-01
We study self-action of light in parametric wave interactions in nonlinear quadratic media. We show the existence of stationary solitons in the presence of Poynting vector beam walk-off or different group velocities between the waves. We discover that the new solitons constitute a two-parameter family, and they exist for different wave intensities and transverse velocities. We discuss the properties of the walking solitons and their experimental implications. Peer Reviewed
Quadratic Term Structure Models in Discrete Time
Marco Realdon
2006-01-01
This paper extends the results on quadratic term structure models in continuos time to the discrete time setting. The continuos time setting can be seen as a special case of the discrete time one. Recursive closed form solutions for zero coupon bonds are provided even in the presence of multiple correlated underlying factors. Pricing bond options requires simple integration. Model parameters may well be time dependent without scuppering such tractability. Model estimation does not require a r...
Least Squares Problems with Absolute Quadratic Constraints
Directory of Open Access Journals (Sweden)
R. Schöne
2012-01-01
Full Text Available This paper analyzes linear least squares problems with absolute quadratic constraints. We develop a generalized theory following Bookstein's conic-fitting and Fitzgibbon's direct ellipse-specific fitting. Under simple preconditions, it can be shown that a minimum always exists and can be determined by a generalized eigenvalue problem. This problem is numerically reduced to an eigenvalue problem by multiplications of Givens' rotations. Finally, four applications of this approach are presented.
Non-Gaussian bias: insights from discrete density peaks
Desjacques, Vincent; Riotto, Antonio
2013-01-01
Corrections induced by primordial non-Gaussianity to the linear halo bias can be computed from a peak-background split or the widespread local bias model. However, numerical simulations clearly support the prediction of the former, in which the non-Gaussian amplitude is proportional to the linear halo bias. To understand better the reasons behind the failure of standard Lagrangian local bias, in which the halo overdensity is a function of the local mass overdensity only, we explore the effect of a primordial bispectrum on the 2-point correlation of discrete density peaks. We show that the effective local bias expansion to peak clustering vastly simplifies the calculation. We generalize this approach to excursion set peaks and demonstrate that the resulting non-Gaussian amplitude, which is a weighted sum of quadratic bias factors, precisely agrees with the peak-background split expectation, which is a logarithmic derivative of the halo mass function with respect to the normalisation amplitude. We point out tha...
Quadratic tracer dynamical models tobacco growth
International Nuclear Information System (INIS)
Qiang Jiyi; Hua Cuncai; Wang Shaohua
2011-01-01
In order to study the non-uniformly transferring process of some tracer dosages, we assume that the absorption of some tracer by tobacco is a quadratic function of the tracer quantity of the tracer in the case of fast absorption, whereas the exclusion of the tracer from tobacco is a linear function of the tracer quantity in the case of slow exclusion, after the tracer is introduced into tobacco once at zero time. A single-compartment quadratic dynamical model of Logistic type is established for the leaves of tobacco. Then, a two-compartment quadratic dynamical model is established for leaves and calms of the tobacco. Qualitative analysis of the models shows that the tracer applied to the leaves of the tobacco is excluded finally; however, the tracer stays at the tobacco for finite time. Two methods are also given for computing the parameters in the models. Finally, the results of the models are verified by the 32 P experiment for the absorption of tobacco. (authors)
Non-Gaussian lineshapes and dynamics of time-resolved linear and nonlinear (correlation) spectra.
Dinpajooh, Mohammadhasan; Matyushov, Dmitry V
2014-07-17
Signatures of nonlinear and non-Gaussian dynamics in time-resolved linear and nonlinear (correlation) 2D spectra are analyzed in a model considering a linear plus quadratic dependence of the spectroscopic transition frequency on a Gaussian nuclear coordinate of the thermal bath (quadratic coupling). This new model is contrasted to the commonly assumed linear dependence of the transition frequency on the medium nuclear coordinates (linear coupling). The linear coupling model predicts equality between the Stokes shift and equilibrium correlation functions of the transition frequency and time-independent spectral width. Both predictions are often violated, and we are asking here the question of whether a nonlinear solvent response and/or non-Gaussian dynamics are required to explain these observations. We find that correlation functions of spectroscopic observables calculated in the quadratic coupling model depend on the chromophore's electronic state and the spectral width gains time dependence, all in violation of the predictions of the linear coupling models. Lineshape functions of 2D spectra are derived assuming Ornstein-Uhlenbeck dynamics of the bath nuclear modes. The model predicts asymmetry of 2D correlation plots and bending of the center line. The latter is often used to extract two-point correlation functions from 2D spectra. The dynamics of the transition frequency are non-Gaussian. However, the effect of non-Gaussian dynamics is limited to the third-order (skewness) time correlation function, without affecting the time correlation functions of higher order. The theory is tested against molecular dynamics simulations of a model polar-polarizable chromophore dissolved in a force field water.
A Finite Continuation Algorithm for Bound Constrained Quadratic Programming
DEFF Research Database (Denmark)
Madsen, Kaj; Nielsen, Hans Bruun; Pinar, Mustafa C.
1999-01-01
The dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear $\\ell_1$ minimization problem with quadratic terms. A smooth approximation to the linear $\\ell_1$ function is used to obtain a parametric family of piecewise-quadratic approximation problems...
Graphical Solution of the Monic Quadratic Equation with Complex Coefficients
Laine, A. D.
2015-01-01
There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…
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. 2010 ISA. Published by Elsevier Ltd. All rights reserved.
Stochastic Control of Energy Efficient Buildings: A Semidefinite Programming Approach
Energy Technology Data Exchange (ETDEWEB)
Ma, Xiao [ORNL; Dong, Jin [ORNL; Djouadi, Seddik M [ORNL; Nutaro, James J [ORNL; Kuruganti, Teja [ORNL
2015-01-01
The key goal in energy efficient buildings is to reduce energy consumption of Heating, Ventilation, and Air- Conditioning (HVAC) systems while maintaining a comfortable temperature and humidity in the building. This paper proposes a novel stochastic control approach for achieving joint performance and power control of HVAC. We employ a constrained Stochastic Linear Quadratic Control (cSLQC) by minimizing a quadratic cost function with a disturbance assumed to be Gaussian. The problem is formulated to minimize the expected cost subject to a linear constraint and a probabilistic constraint. By using cSLQC, the problem is reduced to a semidefinite optimization problem, where the optimal control can be computed efficiently by Semidefinite programming (SDP). Simulation results are provided to demonstrate the effectiveness and power efficiency by utilizing the proposed control approach.
Modelling and control of a diffusion/LPCVD furnace
Dewaard, H.; Dekoning, W. L.
1988-12-01
Heat transfer inside a cylindrical resistance diffusion/Low Pressure Chemical Vapor Deposition (LPCVD) furnace is studied with the aim of developing an improved temperature controller. A model of the thermal behavior is derived, which covers the important class of furnaces equipped with semitransparent quartz process tubes. The model takes into account the thermal behavior of the thermocouples. Currently used temperature controllers are shown to be highly inefficient for very large scale integration applications. Based on the model an alternative temperature controller of the LQG (linear quadratic Gaussian) type is proposed which features direct wafer temperature control. Some simulation results are given.
Przybytek, Michal; Helgaker, Trygve
2013-08-07
We analyze the accuracy of the Coulomb energy calculated using the Gaussian-and-finite-element-Coulomb (GFC) method. In this approach, the electrostatic potential associated with the molecular electronic density is obtained by solving the Poisson equation and then used to calculate matrix elements of the Coulomb operator. The molecular electrostatic potential is expanded in a mixed Gaussian-finite-element (GF) basis set consisting of Gaussian functions of s symmetry centered on the nuclei (with exponents obtained from a full optimization of the atomic potentials generated by the atomic densities from symmetry-averaged restricted open-shell Hartree-Fock theory) and shape functions defined on uniform finite elements. The quality of the GF basis is controlled by means of a small set of parameters; for a given width of the finite elements d, the highest accuracy is achieved at smallest computational cost when tricubic (n = 3) elements are used in combination with two (γ(H) = 2) and eight (γ(1st) = 8) Gaussians on hydrogen and first-row atoms, respectively, with exponents greater than a given threshold (αmin (G)=0.5). The error in the calculated Coulomb energy divided by the number of atoms in the system depends on the system type but is independent of the system size or the orbital basis set, vanishing approximately like d(4) with decreasing d. If the boundary conditions for the Poisson equation are calculated in an approximate way, the GFC method may lose its variational character when the finite elements are too small; with larger elements, it is less sensitive to inaccuracies in the boundary values. As it is possible to obtain accurate boundary conditions in linear time, the overall scaling of the GFC method for large systems is governed by another computational step-namely, the generation of the three-center overlap integrals with three Gaussian orbitals. The most unfavorable (nearly quadratic) scaling is observed for compact, truly three-dimensional systems
On the Shaker Simulation of Wind-Induced Non-Gaussian Random Vibration
Directory of Open Access Journals (Sweden)
Fei Xu
2016-01-01
Full Text Available Gaussian signal is produced by ordinary random vibration controllers to test the products in the laboratory, while the field data is usually non-Gaussian. Two methodologies are presented in this paper for shaker simulation of wind-induced non-Gaussian vibration. The first methodology synthesizes the non-Gaussian signal offline and replicates it on the shaker in the Time Waveform Replication (TWR mode. A new synthesis method is used to model the non-Gaussian signal as a Gaussian signal multiplied by an amplitude modulation function (AMF. A case study is presented to show that the synthesized non-Gaussian signal has the same power spectral density (PSD, probability density function (PDF, and loading cycle distribution (LCD as the field data. The second methodology derives a damage equivalent Gaussian signal from the non-Gaussian signal based on the fatigue damage spectrum (FDS and the extreme response spectrum (ERS and reproduces it on the shaker in the closed-loop frequency domain control mode. The PSD level and the duration time of the derived Gaussian signal can be manipulated for accelerated testing purpose. A case study is presented to show that the derived PSD matches the damage potential of the non-Gaussian environment for both fatigue and peak response.
Information geometry of Gaussian channels
International Nuclear Information System (INIS)
Monras, Alex; Illuminati, Fabrizio
2010-01-01
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).
International Nuclear Information System (INIS)
Yu, Jie; Chen, Kuilin; Mori, Junichi; Rashid, Mudassir M.
2013-01-01
Optimizing wind power generation and controlling the operation of wind turbines to efficiently harness the renewable wind energy is a challenging task due to the intermittency and unpredictable nature of wind speed, which has significant influence on wind power production. A new approach for long-term wind speed forecasting is developed in this study by integrating GMCM (Gaussian mixture copula model) and localized GPR (Gaussian process regression). The time series of wind speed is first classified into multiple non-Gaussian components through the Gaussian mixture copula model and then Bayesian inference strategy is employed to incorporate the various non-Gaussian components using the posterior probabilities. Further, the localized Gaussian process regression models corresponding to different non-Gaussian components are built to characterize the stochastic uncertainty and non-stationary seasonality of the wind speed data. The various localized GPR models are integrated through the posterior probabilities as the weightings so that a global predictive model is developed for the prediction of wind speed. The proposed GMCM–GPR approach is demonstrated using wind speed data from various wind farm locations and compared against the GMCM-based ARIMA (auto-regressive integrated moving average) and SVR (support vector regression) methods. In contrast to GMCM–ARIMA and GMCM–SVR methods, the proposed GMCM–GPR model is able to well characterize the multi-seasonality and uncertainty of wind speed series for accurate long-term prediction. - Highlights: • A novel predictive modeling method is proposed for long-term wind speed forecasting. • Gaussian mixture copula model is estimated to characterize the multi-seasonality. • Localized Gaussian process regression models can deal with the random uncertainty. • Multiple GPR models are integrated through Bayesian inference strategy. • The proposed approach shows higher prediction accuracy and reliability
Quadratic stochastic operators: Results and open problems
International Nuclear Information System (INIS)
Ganikhodzhaev, R.N.; Rozikov, U.A.
2009-03-01
The history of the quadratic stochastic operators can be traced back to the work of S. Bernshtein (1924). For more than 80 years this theory has been developed and many papers were published. In recent years it has again become of interest in connection with numerous applications in many branches of mathematics, biology and physics. But most results of the theory were published in non English journals, full text of which are not accessible. In this paper we give a brief description of the results and discuss several open problems. (author)
Sequential Quadratic Programming Algorithms for Optimization
1989-08-01
quadratic program- ma ng (SQ(2l ) aIiatain.seenis to be relgarded aIs tie( buest choice for the solution of smiall. dlense problema (see S tour L)toS...For the step along d, note that a < nOing + 3 szH + i3.ninA A a K f~Iz,;nd and from Id1 _< ,,, we must have that for some /3 , np , 11P11 < dn"p. 5.2...Nevertheless, many of these problems are considered hard to solve. Moreover, for some of these problems the assumptions made in Chapter 2 to establish the
Results of radiotherapy in craniopharyngiomas analysed by the linear quadratic model
Energy Technology Data Exchange (ETDEWEB)
Guerkaynak, M. [Dept. of Radiation Oncology, Hacettepe Univ., Ankara (Turkey); Oezyar, E. [Dept. of Radiation Oncology, Hacettepe Univ., Ankara (Turkey); Zorlu, F. [Dept. of Radiation Oncology, Hacettepe Univ., Ankara (Turkey); Akyol, F.H. [Dept. of Radiation Oncology, Hacettepe Univ., Ankara (Turkey); Lale Atahan, I. [Dept. of Radiation Oncology, Hacettepe Univ., Ankara (Turkey)
1994-12-31
In 23 craniopharyngioma patients treated by limited surgery and external radiotherapy, the results concerning local control were analysed by linear quadratic formula. A biologically effective dose (BED) of 55 Gy, calculated with time factor and an {alpha}/{beta} value of 10 Gy, seemed to be adequate for local control. (orig.).
International Nuclear Information System (INIS)
Chingangbam, Pravabati; Park, Changbom
2009-01-01
We simulate CMB maps including non-Gaussianity arising from cubic order perturbations of the primordial gravitational potential, characterized by the non-linearity parameter g NL . The maps are used to study the characteristic nature of the resulting non-Gaussian temperature fluctuations. We measure the genus and investigate how it deviates from Gaussian shape as a function of g NL and smoothing scale. We find that the deviation of the non-Gaussian genus curve from the Gaussian one has an antisymmetric, sine function like shape, implying more hot and more cold spots for g NL > 0 and less of both for g NL NL and also exhibits mild increase as the smoothing scale increases. We further study other statistics derived from the genus, namely, the number of hot spots, the number of cold spots, combined number of hot and cold spots and the slope of the genus curve at mean temperature fluctuation. We find that these observables carry signatures of g NL that are clearly distinct from the quadratic order perturbations, encoded in the parameter f NL . Hence they can be very useful tools for distinguishing not only between non-Gaussian temperature fluctuations and Gaussian ones but also between g NL and f NL type non-Gaussianities
Rational quadratic trigonometric Bézier curve based on new basis with exponential functions
Directory of Open Access Journals (Sweden)
Wu Beibei
2017-06-01
Full Text Available We construct a rational quadratic trigonometric Bézier curve with four shape parameters by introducing two exponential functions into the trigonometric basis functions in this paper. It has the similar properties as the rational quadratic Bézier curve. For given control points, the shape of the curve can be flexibly adjusted by changing the shape parameters and the weight. Some conics can be exactly represented when the control points, the shape parameters and the weight are chosen appropriately. The C0, C1 and C2 continuous conditions for joining two constructed curves are discussed. Some examples are given.
Characterisation of random Gaussian and non-Gaussian stress processes in terms of extreme responses
Directory of Open Access Journals (Sweden)
Colin Bruno
2015-01-01
Full Text Available In the field of military land vehicles, random vibration processes generated by all-terrain wheeled vehicles in motion are not classical stochastic processes with a stationary and Gaussian nature. Non-stationarity of processes induced by the variability of the vehicle speed does not form a major difficulty because the designer can have good control over the vehicle speed by characterising the histogram of instantaneous speed of the vehicle during an operational situation. Beyond this non-stationarity problem, the hard point clearly lies in the fact that the random processes are not Gaussian and are generated mainly by the non-linear behaviour of the undercarriage and the strong occurrence of shocks generated by roughness of the terrain. This non-Gaussian nature is expressed particularly by very high flattening levels that can affect the design of structures under extreme stresses conventionally acquired by spectral approaches, inherent to Gaussian processes and based essentially on spectral moments of stress processes. Due to these technical considerations, techniques for characterisation of random excitation processes generated by this type of carrier need to be changed, by proposing innovative characterisation methods based on time domain approaches as described in the body of the text rather than spectral domain approaches.
Comparison of Gaussian and non-Gaussian Atmospheric Profile Retrievals from Satellite Microwave Data
Kliewer, A.; Forsythe, J. M.; Fletcher, S. J.; Jones, A. S.
2017-12-01
The Cooperative Institute for Research in the Atmosphere at Colorado State University has recently developed two different versions of a mixed-distribution (lognormal combined with a Gaussian) based microwave temperature and mixing ratio retrieval system as well as the original Gaussian-based approach. These retrieval systems are based upon 1DVAR theory but have been adapted to use different descriptive statistics of the lognormal distribution to minimize the background errors. The input radiance data is from the AMSU-A and MHS instruments on the NOAA series of spacecraft. To help illustrate how the three retrievals are affected by the change in the distribution we are in the process of creating a new website to show the output from the different retrievals. Here we present initial results from different dynamical situations to show how the tool could be used by forecasters as well as for educators. However, as the new retrieved values are from a non-Gaussian based 1DVAR then they will display non-Gaussian behaviors that need to pass a quality control measure that is consistent with this distribution, and these new measures are presented here along with initial results for checking the retrievals.
Gaussian entanglement distribution via satellite
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.
Current inversion induced by colored non-Gaussian noise
International Nuclear Information System (INIS)
Bag, Bidhan Chandra; Hu, Chin-Kung
2009-01-01
We study a stochastic process driven by colored non-Gaussian noises. For the flashing ratchet model we find that there is a current inversion in the variation of the current with the half-cycle period which accounts for the potential on–off operation. The current inversion almost disappears if one switches from non-Gaussian (NG) to Gaussian (G) noise. We also find that at low value of the asymmetry parameter of the potential the mobility controlled current is more negative for NG noise as compared to G noise. But at large magnitude of the parameter the diffusion controlled positive current is higher for the former than for the latter. On increasing the noise correlation time (τ), keeping the noise strength fixed, the mean velocity of a particle first increases and then decreases after passing through a maximum if the noise is non-Gaussian. For Gaussian noise, the current monotonically decreases. The current increases with the noise parameter p, 0< p<5/3, which is 1 for Gaussian noise
Tachyon mediated non-Gaussianity
International Nuclear Information System (INIS)
Dutta, Bhaskar; Leblond, Louis; Kumar, Jason
2008-01-01
We describe a general scenario where primordial non-Gaussian curvature perturbations are generated in models with extra scalar fields. The extra scalars communicate to the inflaton sector mainly through the tachyonic (waterfall) field condensing at the end of hybrid inflation. These models can yield significant non-Gaussianity of the local shape, and both signs of the bispectrum can be obtained. These models have cosmic strings and a nearly flat power spectrum, which together have been recently shown to be a good fit to WMAP data. We illustrate with a model of inflation inspired from intersecting brane models.
On a quadratic inverse eigenvalue problem
International Nuclear Information System (INIS)
Cai, Yunfeng; Xu, Shufang
2009-01-01
This paper concerns the quadratic inverse eigenvalue problem (QIEP) of constructing real symmetric matrices M, C and K of size n × n, with M nonsingular, so that the quadratic matrix polynomial Q(λ) ≡ λ 2 M + λC + K has a completely prescribed set of eigenvalues and eigenvectors. It is shown via construction that the QIEP has a solution if and only if r 0, where r and δ are computable from the prescribed spectral data. A necessary and sufficient condition for the existence of a solution to the QIEP with M being positive definite is also established in a constructive way. Furthermore, two algorithms are developed: one is to solve the QIEP; another is to find a particular solution to the QIEP with the leading coefficient matrix being positive definite, which also provides us an approach to a simultaneous reduction of real symmetric matrix triple (M, C, K) by real congruence. Numerical results show that the two algorithms are feasible and numerically reliable
Phase space eigenfunctions of multidimensional quadratic Hamiltonians
International Nuclear Information System (INIS)
Dodonov, V.V.; Man'ko, V.I.
1986-01-01
We obtain the explicit expressions for phace space eigenfunctions (PSE),i.e. Weyl's symbols of dyadic operators like vertical stroken> ,vertical strokem>, being the solution of the Schroedinger equation with the Hamiltonian which is a quite arbitrary multidimensional quadratic form of the operators of Cartesian coordinates and conjugated to them momenta with time-dependent coefficients. It is shown that for an arbitrary quadratic Hamiltonian one can always construct the set of completely factorized PSE which are products of N factors, each factor being dependent only on two arguments for nnot=m and on a single argument for n=m. These arguments are nothing but constants of motion of the correspondent classical system. PSE are expressed in terms of the associated Laguerre polynomials in the case of a discrete spectrum and in terms of the Airy functions in the continuous spectrum case. Three examples are considered: a harmonic oscillator with a time-dependent frequency, a charged particle in a nonstationary uniform magnetic field, and a particle in a time-dependent uniform potential field. (orig.)
Quadratic forms for Feynman-Kac semigroups
International Nuclear Information System (INIS)
Hibey, Joseph L.; Charalambous, Charalambos D.
2006-01-01
Some problems in a stochastic setting often involve the need to evaluate the Feynman-Kac formula that follows from models described in terms of stochastic differential equations. Equivalent representations in terms of partial differential equations are also of interest, and these establish the well-known connection between probabilistic and deterministic formulations of these problems. In this Letter, this connection is studied in terms of the quadratic form associated with the Feynman-Kac semigroup. The probability measures that naturally arise in this approach, and thus define how Brownian motion is killed at a specified rate while exiting a set, are interpreted as a random time change of the original stochastic differential equation. Furthermore, since random time changes alter the diffusion coefficients in stochastic differential equations while Girsanov-type measure transformations alter their drift coefficients, their simultaneous use should lead to more tractable solutions for some classes of problems. For example, the minimization of some quadratic forms leads to solutions that satisfy certain partial differential equations and, therefore, the techniques discussed provide a variational approach for finding these solutions
DEFF Research Database (Denmark)
Mak, Vicky; Thomadsen, Tommy
2004-01-01
A well-known extension of the Travelling Salesman Problem (TSP) is the Selective (or Prize-collecting) TSP: In addition to the edge-costs, each node has an associated reward (denoted the node-reward) and instead of visiting all nodes, only profitable nodes are visited. The Quadratic Selective TSP...
Advanced control of a doubly-fed induction generator for wind energy conversion
Energy Technology Data Exchange (ETDEWEB)
Poitiers, F.; Bouaouiche, T.; Machmoum, M. [Institut de Recherche en Electronique et Electrotechnique de Nantes Atlantique, rue Christian Pauc, 44306 Nantes (France)
2009-07-15
The aim of this paper is to propose a control method for a doubly-fed induction generator used in wind energy conversion systems. First, stator active and reactive powers are regulated by controlling the machine inverter with three different controllers: proportional-integral, polynomial RST based on pole placement theory and Linear Quadratic Gaussian. The machine is tested in association with a wind-turbine emulator. Secondly a control strategy for the grid-converter is proposed. Simulations results are presented and discussed for each converter control and for the whole system. (author)
Trajectory generation for manipulators using linear quadratic optimal tracking
Directory of Open Access Journals (Sweden)
Olav Egeland
1989-04-01
Full Text Available The reference trajectory is normally known in advance in manipulator control which makes it possible to apply linear quadratic optimal tracking. This gives a control system which rounds corners and generates optimal feedforward. The method may be used for references consisting of straight-line segments as an alternative to the two-step method of using splines to smooth the reference and then applying feedforward. In addition, the method can be used for more complex trajectories. The actual dynamics of the manipulator are taken into account, and this results in smooth and accurate tracking. The method has been applied in combination with the computed torque technique and excellent performance was demonstrated in a simulation study. The method has also been applied experimentally to an industrial spray-painting robot where a saw-tooth reference was tracked. The corner was rounded extremely well, and the steady-state tracking error was eliminated by the optimal feedforward.
The halo bispectrum in N-body simulations with non-Gaussian initial conditions
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.
Directory of Open Access Journals (Sweden)
Yong Li
2014-01-01
Full Text Available 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.
The Multivariate Gaussian Probability Distribution
DEFF Research Database (Denmark)
Ahrendt, Peter
2005-01-01
This technical report intends to gather information about the multivariate gaussian distribution, that was previously not (at least to my knowledge) to be found in one place and written as a reference manual. Additionally, some useful tips and tricks are collected that may be useful in practical ...
On Gaussian conditional independence structures
Czech Academy of Sciences Publication Activity Database
Lněnička, Radim; Matúš, František
2007-01-01
Roč. 43, č. 3 (2007), s. 327-342 ISSN 0023-5954 R&D Projects: GA AV ČR IAA100750603 Institutional research plan: CEZ:AV0Z10750506 Keywords : multivariate Gaussian distribution * positive definite matrices * determinants * gaussoids * covariance selection models * Markov perfectness Subject RIV: BA - General Mathematics Impact factor: 0.552, year: 2007
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.
Quadratic residues and non-residues selected topics
Wright, Steve
2016-01-01
This book offers an account of the classical theory of quadratic residues and non-residues with the goal of using that theory as a lens through which to view the development of some of the fundamental methods employed in modern elementary, algebraic, and analytic number theory. The first three chapters present some basic facts and the history of quadratic residues and non-residues and discuss various proofs of the Law of Quadratic Reciprosity in depth, with an emphasis on the six proofs that Gauss published. The remaining seven chapters explore some interesting applications of the Law of Quadratic Reciprocity, prove some results concerning the distribution and arithmetic structure of quadratic residues and non-residues, provide a detailed proof of Dirichlet’s Class-Number Formula, and discuss the question of whether quadratic residues are randomly distributed. The text is a valuable resource for graduate and advanced undergraduate students as well as for mathematicians interested in number theory.
Exact cancellation of quadratic divergences in top condensation models
International Nuclear Information System (INIS)
Blumhofer, A.
1995-01-01
We discuss the hierarchy problem and the corresponding quadratic divergences in the top mode Standard Model. Quadratic divergences appear at each order 1/N c since fermionic and bosonic contributions are of different order 1/N c . It is shown that the full dynamical system to all orders in 1/N c admits a solution, where the sum of all quadratic divergent contributions disappears. ((orig.))
International Nuclear Information System (INIS)
Tao Ganqiang; Yu Qing; Xiao Xiao
2011-01-01
Viscous and incompressible fluid flow is important for numerous engineering mechanics problems. Because of high non linear and incompressibility for Navier-Stokes equation, it is very difficult to solve Navier-Stokes equation by numerical method. According to its characters of Navier-Stokes equation, quartic derivation controlling equation of the two dimensional incompressible Navier-Stokes equation is set up firstly. The method solves the problem for dealing with vorticity boundary and automatically meets incompressibility condition. Then Finite Element equation for Navier-Stokes equation is proposed by using quadratic quadrilateral unit with 8 nodes in which the unit function is quadratic and non linear.-Based on it, the Finite Element program of quadratic quadrilateral unit with 8 nodes is developed. Lastly, numerical experiment proves the accuracy and dependability of the method and also shows the method has good application prospect in computational fluid mechanics. (authors)
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.
Distance matrices and quadratic embedding of graphs
Directory of Open Access Journals (Sweden)
Nobuaki Obata
2018-04-01
Full Text Available A connected graph is said to be of QE class if it admits a quadratic embedding in a Hilbert space, or equivalently, if the distance matrix is conditionally negative definite. Several criteria for a graph to be of QE class are derived from the point of view of graph operations. For a quantitative criterion the QE constant is introduced and concrete examples are shown with explicit calculation. If the distance matrix admits a constant row sum, the QE constant coincides with the second largest eigenvalue of the distance matrix. The QE constants are determined for all graphs on $n$ vertices with $n\\le5$, among which two are not of QE class.
Low-rank quadratic semidefinite programming
Yuan, Ganzhao
2013-04-01
Low rank matrix approximation is an attractive model in large scale machine learning problems, because it can not only reduce the memory and runtime complexity, but also provide a natural way to regularize parameters while preserving learning accuracy. In this paper, we address a special class of nonconvex quadratic matrix optimization problems, which require a low rank positive semidefinite solution. Despite their non-convexity, we exploit the structure of these problems to derive an efficient solver that converges to their local optima. Furthermore, we show that the proposed solution is capable of dramatically enhancing the efficiency and scalability of a variety of concrete problems, which are of significant interest to the machine learning community. These problems include the Top-k Eigenvalue problem, Distance learning and Kernel learning. Extensive experiments on UCI benchmarks have shown the effectiveness and efficiency of our proposed method. © 2012.
Polarization Nonlinear Optics of Quadratically Nonlinear Azopolymers
International Nuclear Information System (INIS)
Konorov, S.O.; Akimov, D.A.; Ivanov, A.A.; Petrov, A.N.; Alfimov, M.V.; Yakimanskii, A.V.; Smirnov, N.N.; Ivanova, V.N.; Kudryavtsev, V.V.; Podshivalov, A.A.; Sokolova, I.M.; Zheltikov, A.M.
2005-01-01
The polarization properties of second harmonic and sum-frequency signals generated by femtosecond laser pulses in films of polymers containing covalent groups of an azobenzothiazole chromophore polarized by an external electric field are investigated. It is shown that the methods of polarization nonlinear optics make it possible to determine the structure of oriented molecular dipoles and reveal important properties of the motion of collectivized πelectrons in organic molecules with strong optical nonlinearities. The polarization measurements show that the tensor of quadratic nonlinear optical susceptibility of chromophore fragments oriented by an external field in macromolecules of the noted azopolymers has a degenerate form. This is indicative of a predominantly one-dimensional character of motion of collectivized π electrons along an extended group of atoms in such molecules
Charged black holes in quadratic gravity
International Nuclear Information System (INIS)
Matyjasek, Jerzy; Tryniecki, Dariusz
2004-01-01
Iterative solutions to fourth-order gravity describing static and electrically charged black holes are constructed. The obtained solutions are parametrized by two integration constants which are related to the electric charge and the exact location of the event horizon. Special emphasis is put on the extremal black holes. It is explicitly demonstrated that in the extremal limit the exact location of the (degenerate) event horizon is given by r + =|e|. Similarly to the classical Reissner-Nordstroem solution, the near-horizon geometry of the charged black holes in quadratic gravity, when expanded into the whole manifold, is simply that of Bertotti and Robinson. Similar considerations have been carried out for boundary conditions of the second type which employ the electric charge and the mass of the system as seen by a distant observer. The relations between results obtained within the framework of each method are briefly discussed
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2002-01-01
Lambda-lifting is a program transformation used in compilers and in partial evaluators and that operates in cubic time. In this article, we show how to reduce this complexity to quadratic time. Lambda-lifting transforms a block-structured program into a set of recursive equations, one for each...... local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters that yields the cubic factor in the traditional formulation of lambda-lifting, which...... is not needed. We therefore simplify the search for extra parameters by treating each strongly connected component instead of each function as a unit, thereby reducing the time complexity of lambda-lifting from O(n 3 log n)toO(n2 log n), where n is the size of the program. Since a lambda-lifter can output...
Low-rank quadratic semidefinite programming
Yuan, Ganzhao; Zhang, Zhenjie; Ghanem, Bernard; Hao, Zhifeng
2013-01-01
Low rank matrix approximation is an attractive model in large scale machine learning problems, because it can not only reduce the memory and runtime complexity, but also provide a natural way to regularize parameters while preserving learning accuracy. In this paper, we address a special class of nonconvex quadratic matrix optimization problems, which require a low rank positive semidefinite solution. Despite their non-convexity, we exploit the structure of these problems to derive an efficient solver that converges to their local optima. Furthermore, we show that the proposed solution is capable of dramatically enhancing the efficiency and scalability of a variety of concrete problems, which are of significant interest to the machine learning community. These problems include the Top-k Eigenvalue problem, Distance learning and Kernel learning. Extensive experiments on UCI benchmarks have shown the effectiveness and efficiency of our proposed method. © 2012.
A ''quadratized'' augmented plane wave method
International Nuclear Information System (INIS)
Smrcka, L.
1982-02-01
The exact radial solution inside the muffin-tin sphere is replaced by its Taylor expansion with respect to the energy, truncated after the quadratic term. Making use of it the energy independent augmented plane waves are formed which lead to the secular equations linear in energy. The method resembles the currently used linearized APW method but yields higher accuracy. The analysis of solution inside one muffin-tin sphere shows that the eigenvalue error is proportional to (E-E 0 ) 6 as compared with (E-E 0 ) 4 for LAPW. The error of eigenfunctions is (E-E 0 ) 3 ((E-E 0 ) 2 for LAPW). These conclusions are confirmed by direct numerical calculation of band structure of Cu and Al. (author)
Quadratic gravity in first order formalism
Energy Technology Data Exchange (ETDEWEB)
Alvarez, Enrique; Anero, Jesus; Gonzalez-Martin, Sergio, E-mail: enrique.alvarez@uam.es, E-mail: jesusanero@gmail.com, E-mail: sergio.gonzalez.martin@uam.es [Departamento de Física Teórica and Instituto de Física Teórica (IFT-UAM/CSIC), Universidad Autónoma de Madrid, Cantoblanco, 28049, Madrid (Spain)
2017-10-01
We consider the most general action for gravity which is quadratic in curvature. In this case first order and second order formalisms are not equivalent. This framework is a good candidate for a unitary and renormalizable theory of the gravitational field; in particular, there are no propagators falling down faster than 1/ p {sup 2}. The drawback is of course that the parameter space of the theory is too big, so that in many cases will be far away from a theory of gravity alone. In order to analyze this issue, the interaction between external sources was examined in some detail. We find that this interaction is conveyed mainly by propagation of the three-index connection field. At any rate the theory as it stands is in the conformal invariant phase; only when Weyl invariance is broken through the coupling to matter can an Einstein-Hilbert term (and its corresponding Planck mass scale) be generated by quantum corrections.
Large-scale sequential quadratic programming algorithms
Energy Technology Data Exchange (ETDEWEB)
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.
Laguerre Gaussian beam multiplexing through turbulence
CSIR Research Space (South Africa)
Trichili, A
2014-08-17
Full Text Available We analyze the effect of atmospheric turbulence on the propagation of multiplexed Laguerre Gaussian modes. We present a method to multiplex Laguerre Gaussian modes using digital holograms and decompose the resulting field after encountering a...
An Analysis and Design for Nonlinear Quadratic Systems Subject to Nested Saturation
Directory of Open Access Journals (Sweden)
Minsong Zhang
2013-01-01
Full Text Available This paper considers the stability problem for nonlinear quadratic systems with nested saturation input. The interesting treatment method proposed to nested saturation here is put into use a well-established linear differential control tool. And the new conclusions include the existing conclusion on this issue and have less conservatism than before. Simulation example illustrates the effectiveness of the established methodologies.
Quadratic head loss approximations for optimisation problems in water supply networks
Pecci, Filippo; Abraham, E.; I, Stoianov
2017-01-01
This paper presents a novel analysis of the accuracy of quadratic approximations for the Hazen–Williams (HW) head loss formula, which enables the control of constraint violations in optimisation problems for water supply networks. The two smooth polynomial approximations considered here minimise the
Differentiated Learning Environment--A Classroom for Quadratic Equation, Function and Graphs
Dinç, Emre
2017-01-01
This paper will cover the design of a learning environment as a classroom regarding the Quadratic Equations, Functions and Graphs. The goal of the learning environment offered in the paper is to design a classroom where students will enjoy the process, use their skills they already have during the learning process, control and plan their learning…
Analytic matrix elements with shifted correlated Gaussians
DEFF Research Database (Denmark)
Fedorov, D. V.
2017-01-01
Matrix elements between shifted correlated Gaussians of various potentials with several form-factors are calculated analytically. Analytic matrix elements are of importance for the correlated Gaussian method in quantum few-body physics.......Matrix elements between shifted correlated Gaussians of various potentials with several form-factors are calculated analytically. Analytic matrix elements are of importance for the correlated Gaussian method in quantum few-body physics....
Gaussian process regression analysis for functional data
Shi, Jian Qing
2011-01-01
Gaussian Process Regression Analysis for Functional Data presents nonparametric statistical methods for functional regression analysis, specifically the methods based on a Gaussian process prior in a functional space. The authors focus on problems involving functional response variables and mixed covariates of functional and scalar variables.Covering the basics of Gaussian process regression, the first several chapters discuss functional data analysis, theoretical aspects based on the asymptotic properties of Gaussian process regression models, and new methodological developments for high dime
Describing Quadratic Cremer Point Polynomials by Parabolic Perturbations
DEFF Research Database (Denmark)
Sørensen, Dan Erik Krarup
1996-01-01
We describe two infinite order parabolic perturbation proceduresyielding quadratic polynomials having a Cremer fixed point. The main ideais to obtain the polynomial as the limit of repeated parabolic perturbations.The basic tool at each step is to control the behaviour of certain externalrays.......Polynomials of the Cremer type correspond to parameters at the boundary of ahyperbolic component of the Mandelbrot set. In this paper we concentrate onthe main cardioid component. We investigate the differences between two-sided(i.e. alternating) and one-sided parabolic perturbations.In the two-sided case, we prove...... the existence of polynomials having an explicitlygiven external ray accumulating both at the Cremer point and at its non-periodicpreimage. We think of the Julia set as containing a "topologists double comb".In the one-sided case we prove a weaker result: the existence of polynomials havingan explicitly given...
Modeling and control of diffusion and low-pressure chemical vapor deposition furnaces
De Waard, H.; De Koning, W. L.
1990-03-01
In this paper a study is made of the heat transfer inside cylindrical resistance diffusion and low-pressure chemical vapor deposition furnaces, aimed at developing an improved temperature controller. A model of the thermal behavior is derived which also covers the important class of furnaces equipped with semitransparent quartz process tubes. The model takes into account the thermal behavior of the thermocouples. It is shown that currently used temperature controllers are highly inefficient for very large scale integration applications. Based on the model an alternative temperature controller of the linear-quadratic-Gaussian type is proposed which features direct wafer temperature control. Some simulation results are given.
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
Gaussian statistics for palaeomagnetic vectors
Love, J. J.; Constable, C. G.
2003-03-01
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 (unimodal) 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
Reproducing kernel Hilbert spaces of Gaussian priors
Vaart, van der A.W.; Zanten, van J.H.; Clarke, B.; Ghosal, S.
2008-01-01
We review definitions and properties of reproducing kernel Hilbert spaces attached to Gaussian variables and processes, with a view to applications in nonparametric Bayesian statistics using Gaussian priors. The rate of contraction of posterior distributions based on Gaussian priors can be described
Inflation in random Gaussian landscapes
Energy Technology Data Exchange (ETDEWEB)
Masoumi, Ali; Vilenkin, Alexander; Yamada, Masaki, E-mail: ali@cosmos.phy.tufts.edu, E-mail: vilenkin@cosmos.phy.tufts.edu, E-mail: Masaki.Yamada@tufts.edu [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155 (United States)
2017-05-01
We develop analytic and numerical techniques for studying the statistics of slow-roll inflation in random Gaussian landscapes. As an illustration of these techniques, we analyze small-field inflation in a one-dimensional landscape. We calculate the probability distributions for the maximal number of e-folds and for the spectral index of density fluctuations n {sub s} and its running α {sub s} . These distributions have a universal form, insensitive to the correlation function of the Gaussian ensemble. We outline possible extensions of our methods to a large number of fields and to models of large-field inflation. These methods do not suffer from potential inconsistencies inherent in the Brownian motion technique, which has been used in most of the earlier treatments.
General Galilei Covariant Gaussian Maps
Gasbarri, Giulio; Toroš, Marko; Bassi, Angelo
2017-09-01
We characterize general non-Markovian Gaussian maps which are covariant under Galilean transformations. In particular, we consider translational and Galilean covariant maps and show that they reduce to the known Holevo result in the Markovian limit. We apply the results to discuss measures of macroscopicity based on classicalization maps, specifically addressing dissipation, Galilean covariance and non-Markovianity. We further suggest a possible generalization of the macroscopicity measure defined by Nimmrichter and Hornberger [Phys. Rev. Lett. 110, 16 (2013)].
Gaussian Embeddings for Collaborative Filtering
Dos Santos , Ludovic; Piwowarski , Benjamin; Gallinari , Patrick
2017-01-01
International audience; Most collaborative ltering systems, such as matrix factorization, use vector representations for items and users. Those representations are deterministic, and do not allow modeling the uncertainty of the learned representation, which can be useful when a user has a small number of rated items (cold start), or when there is connict-ing information about the behavior of a user or the ratings of an item. In this paper, we leverage recent works in learning Gaussian embeddi...
Orthogonal and Scaling Transformations of Quadratic Functions with ...
African Journals Online (AJOL)
In this paper we present a non-singular transformation that can reduce a given quadratic function defined on Rn to another simpler quadratic function and study the impact of the transformation in relation to the problem of minimization of the function. In particular, we construct a non-singular transformation that can reduce a ...
Quadratic Twists of Rigid Calabi–Yau Threefolds Over
DEFF Research Database (Denmark)
Gouvêa, Fernando Q.; Kiming, Ian; Yui, Noriko
2013-01-01
of weight 4 on some Γ 0(N). We show that quadratic twisting of a threefold corresponds to twisting the attached newform by quadratic characters and illustrate with a number of obvious and not so obvious examples. The question is motivated by the deeper question of which newforms of weight 4 on some Γ 0(N...
Approximate *-derivations and approximate quadratic *-derivations on C*-algebras
Directory of Open Access Journals (Sweden)
Park Choonkil
2011-01-01
Full Text Available Abstract In this paper, we prove the stability of *-derivations and of quadratic *-derivations on Banach *-algebras. We moreover prove the superstability of *-derivations and of quadratic *-derivations on C*-algebras. 2000 Mathematics Subject Classification: 39B52; 47B47; 46L05; 39B72.
A Linear Programming Reformulation of the Standard Quadratic Optimization Problem
de Klerk, E.; Pasechnik, D.V.
2005-01-01
The problem of minimizing a quadratic form over the standard simplex is known as the standard quadratic optimization problem (SQO).It is NPhard, and contains the maximum stable set problem in graphs as a special case.In this note we show that the SQO problem may be reformulated as an (exponentially
Effects of Classroom Instruction on Students' Understanding of Quadratic Equations
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…
Analysis of Students' Error in Learning of Quadratic Equations
Zakaria, Effandi; Ibrahim; Maat, Siti Mistima
2010-01-01
The purpose of the study was to determine the students' error in learning quadratic equation. The samples were 30 form three students from a secondary school in Jambi, Indonesia. Diagnostic test was used as the instrument of this study that included three components: factorization, completing the square and quadratic formula. Diagnostic interview…
Sketching the General Quadratic Equation Using Dynamic Geometry Software
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
Carroll, William J.
2009-01-01
In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)
Visualising the Roots of Quadratic Equations with Complex Coefficients
Bardell, Nicholas S.
2014-01-01
This paper is a natural extension of the root visualisation techniques first presented by Bardell (2012) for quadratic equations with real coefficients. Consideration is now given to the familiar quadratic equation "y = ax[superscript 2] + bx + c" in which the coefficients "a," "b," "c" are generally…
Quadratic Polynomial Regression using Serial Observation Processing:Implementation within DART
Hodyss, D.; Anderson, J. L.; Collins, N.; Campbell, W. F.; Reinecke, P. A.
2017-12-01
Many Ensemble-Based Kalman ltering (EBKF) algorithms process the observations serially. Serial observation processing views the data assimilation process as an iterative sequence of scalar update equations. What is useful about this data assimilation algorithm is that it has very low memory requirements and does not need complex methods to perform the typical high-dimensional inverse calculation of many other algorithms. Recently, the push has been towards the prediction, and therefore the assimilation of observations, for regions and phenomena for which high-resolution is required and/or highly nonlinear physical processes are operating. For these situations, a basic hypothesis is that the use of the EBKF is sub-optimal and performance gains could be achieved by accounting for aspects of the non-Gaussianty. To this end, we develop here a new component of the Data Assimilation Research Testbed [DART] to allow for a wide-variety of users to test this hypothesis. This new version of DART allows one to run several variants of the EBKF as well as several variants of the quadratic polynomial lter using the same forecast model and observations. Dierences between the results of the two systems will then highlight the degree of non-Gaussianity in the system being examined. We will illustrate in this work the differences between the performance of linear versus quadratic polynomial regression in a hierarchy of models from Lorenz-63 to a simple general circulation model.
Engineering quadratic nonlinear photonic crystals for frequency conversion of lasers
Chen, Baoqin; Hong, Lihong; Hu, Chenyang; Zhang, Chao; Liu, Rongjuan; Li, Zhiyuan
2018-03-01
Nonlinear frequency conversion offers an effective way to extend the laser wavelength range. Quadratic nonlinear photonic crystals (NPCs) are artificial materials composed of domain-inversion structures whose sign of nonlinear coefficients are modulated with desire to implement quasi-phase matching (QPM) required for nonlinear frequency conversion. These structures can offer various reciprocal lattice vectors (RLVs) to compensate the phase-mismatching during the quadratic nonlinear optical processes, including second-harmonic generation (SHG), sum-frequency generation and the cascaded third-harmonic generation (THG). The modulation pattern of the nonlinear coefficients is flexible, which can be one-dimensional or two-dimensional (2D), be periodic, quasi-periodic, aperiodic, chirped, or super-periodic. As a result, these NPCs offer very flexible QPM scheme to satisfy various nonlinear optics and laser frequency conversion problems via design of the modulation patterns and RLV spectra. In particular, we introduce the electric poling technique for fabricating QPM structures, a simple effective nonlinear coefficient model for efficiently and precisely evaluating the performance of QPM structures, the concept of super-QPM and super-periodically poled lithium niobate for finely tuning nonlinear optical interactions, the design of 2D ellipse QPM NPC structures enabling continuous tunability of SHG in a broad bandwidth by simply changing the transport direction of pump light, and chirped QPM structures that exhibit broadband RLVs and allow for simultaneous radiation of broadband SHG, THG, HHG and thus coherent white laser from a single crystal. All these technical, theoretical, and physical studies on QPM NPCs can help to gain a deeper insight on the mechanisms, approaches, and routes for flexibly controlling the interaction of lasers with various QPM NPCs for high-efficiency frequency conversion and creation of novel lasers.
On the generation of a non-gaussian curvature perturbation during preheating
Energy Technology Data Exchange (ETDEWEB)
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 ζ. 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 ζ based on the δN 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 ζ, but modulated preheating can be effective. For quartic inflation, curvaton-type preheating may be effective but the usual δN 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.
On the generation of a non-gaussian curvature perturbation during preheating
International Nuclear Information System (INIS)
Kohri, Kazunori; Lyth, David H.; Valenzuela-Toledo, Cesar A.
2010-01-01
The perturbation of a light field might affect preheating and hence generate a contribution to the spectrum and non-gaussianity of the curvature perturbation ζ. 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 ζ based on the δN 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 ζ, but modulated preheating can be effective. For quartic inflation, curvaton-type preheating may be effective but the usual δN 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
International Nuclear Information System (INIS)
2005-01-01
Nature of physical problem solved: AUTOJOM is a computer program that will generate the coefficients of any quadratic equation used to define conic volumes and also the coefficients of the planes needed to define parallelepipeds, wedges, and pyramids. JOMREAD is a computer code to check any 3D geometry composed of and constructed with quadratic surfaces
Are ghost surfaces quadratic-flux-minimizing?
International Nuclear Information System (INIS)
Hudson, S.R.; Dewar, R.L.
2009-01-01
Two candidates for 'almost-invariant' toroidal surfaces passing through magnetic islands, namely quadratic-flux-minimizing (QFMin) surfaces and ghost surfaces, use families of periodic pseudo-orbits (i.e. paths for which the action is not exactly extremal). QFMin pseudo-orbits, which are coordinate-dependent, are field lines obtained from a modified magnetic field, and ghost-surface pseudo-orbits are obtained by displacing closed field lines in the direction of steepest descent of magnetic action, ∫A.dl. A generalized Hamiltonian definition of ghost surfaces is given and specialized to the usual Lagrangian definition. A modified Hamilton's Principle is introduced that allows the use of Lagrangian integration for calculation of the QFMin pseudo-orbits. Numerical calculations show QFMin and Lagrangian ghost surfaces give very similar results for a chaotic magnetic field perturbed from an integrable case, and this is explained using a perturbative construction of an auxiliary poloidal angle for which QFMin and Lagrangian ghost surfaces are the same up to second order. While presented in the context of 3-dimensional magnetic field line systems, the concepts are applicable to defining almost-invariant tori in other 11/2 degree-of-freedom nonintegrable Lagrangian/Hamiltonian systems.
Securing Digital Audio using Complex Quadratic Map
Suryadi, MT; Satria Gunawan, Tjandra; Satria, Yudi
2018-03-01
In This digital era, exchanging data are common and easy to do, therefore it is vulnerable to be attacked and manipulated from unauthorized parties. One data type that is vulnerable to attack is digital audio. So, we need data securing method that is not vulnerable and fast. One of the methods that match all of those criteria is securing the data using chaos function. Chaos function that is used in this research is complex quadratic map (CQM). There are some parameter value that causing the key stream that is generated by CQM function to pass all 15 NIST test, this means that the key stream that is generated using this CQM is proven to be random. In addition, samples of encrypted digital sound when tested using goodness of fit test are proven to be uniform, so securing digital audio using this method is not vulnerable to frequency analysis attack. The key space is very huge about 8.1×l031 possible keys and the key sensitivity is very small about 10-10, therefore this method is also not vulnerable against brute-force attack. And finally, the processing speed for both encryption and decryption process on average about 450 times faster that its digital audio duration.
Designing Camera Networks by Convex Quadratic Programming
Ghanem, Bernard
2015-05-04
In this paper, we study the problem of automatic camera placement for computer graphics and computer vision applications. We extend the problem formulations of previous work by proposing a novel way to incorporate visibility constraints and camera-to-camera relationships. For example, the placement solution can be encouraged to have cameras that image the same important locations from different viewing directions, which can enable reconstruction and surveillance tasks to perform better. We show that the general camera placement problem can be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution is almost as fast as a greedy treatment of the problem, but the quality is significantly higher, so much so that it is comparable to exact solutions that take orders of magnitude more computation time. Because it is computationally attractive, our method also allows users to explore the space of solutions for variations in input parameters. To evaluate its effectiveness, we show a range of 3D results on real-world floorplans (garage, hotel, mall, and airport).
Won, Chang-Hee; Michel, Anthony N
2008-01-01
This volume - dedicated to Michael K. Sain on the occasion of his seventieth birthday - is a collection of chapters covering recent advances in stochastic optimal control theory and algebraic systems theory. Written by experts in their respective fields, the chapters are thematically organized into four parts: Part I focuses on statistical control theory, where the cost function is viewed as a random variable and performance is shaped through cost cumulants. In this respect, statistical control generalizes linear-quadratic-Gaussian and H-infinity control. Part II addresses algebraic systems th
Halyo, N.; Caglayan, A. K.
1976-01-01
This paper considers the control of a continuous linear plant disturbed by white plant noise when the control is constrained to be a piecewise constant function of time; i.e. a stochastic sampled-data system. The cost function is the integral of quadratic error terms in the state and control, thus penalizing errors at every instant of time while the plant noise disturbs the system continuously. The problem is solved by reducing the constrained continuous problem to an unconstrained discrete one. It is shown that the separation principle for estimation and control still holds for this problem when the plant disturbance and measurement noise are Gaussian.
A revisit to quadratic programming with fuzzy parameters
International Nuclear Information System (INIS)
Liu, S.-T.
2009-01-01
Quadratic programming has been widely applied to solving real-world problems. Recently, Liu describes a solution method for solving a class of fuzzy quadratic programming problems, where the cost coefficients of the linear terms in objective function, constraint coefficients, and right-hand sides are fuzzy numbers [Liu ST. Quadratic programming with fuzzy parameters: a membership function approach. Chaos, Solitons and Fractals 2009;40:237-45]. In this paper, we generalize Liu's method to a more general fuzzy quadratic programming problem, where the cost coefficients in objective function, constraint coefficients, and right-hand sides are all fuzzy numbers. A pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the fuzzy quadratic program. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a family of conventional one-level quadratic programs. Solving the pair of quadratic programs produces the fuzzy objective values of the problem. With the ability of calculating the fuzzy objective value developed in this paper, it might help initiate wider applications.
Large-Deviation Results for Discriminant Statistics of Gaussian Locally Stationary Processes
Directory of Open Access Journals (Sweden)
Junichi Hirukawa
2012-01-01
Full Text Available This paper discusses the large-deviation principle of discriminant statistics for Gaussian locally stationary processes. First, large-deviation theorems for quadratic forms and the log-likelihood ratio for a Gaussian locally stationary process with a mean function are proved. Their asymptotics are described by the large deviation rate functions. Second, we consider the situations where processes are misspecified to be stationary. In these misspecified cases, we formally make the log-likelihood ratio discriminant statistics and derive the large deviation theorems of them. Since they are complicated, they are evaluated and illustrated by numerical examples. We realize the misspecification of the process to be stationary seriously affecting our discrimination.
Algorithms for sparse, symmetric, definite quadratic lambda-matrix eigenproblems
International Nuclear Information System (INIS)
Scott, D.S.; Ward, R.C.
1981-01-01
Methods are presented for computing eigenpairs of the quadratic lambda-matrix, M lambda 2 + C lambda + K, where M, C, and K are large and sparse, and have special symmetry-type properties. These properties are sufficient to insure that all the eigenvalues are real and that theory analogous to the standard symmetric eigenproblem exists. The methods employ some standard techniques such as partial tri-diagonalization via the Lanczos Method and subsequent eigenpair calculation, shift-and- invert strategy and subspace iteration. The methods also employ some new techniques such as Rayleigh-Ritz quadratic roots and the inertia of symmetric, definite, quadratic lambda-matrices
Quadratic stabilisability of multi-agent systems under switching topologies
Guan, Yongqiang; Ji, Zhijian; Zhang, Lin; Wang, Long
2014-12-01
This paper addresses the stabilisability of multi-agent systems (MASs) under switching topologies. Necessary and/or sufficient conditions are presented in terms of graph topology. These conditions explicitly reveal how the intrinsic dynamics of the agents, the communication topology and the external control input affect stabilisability jointly. With the appropriate selection of some agents to which the external inputs are applied and the suitable design of neighbour-interaction rules via a switching topology, an MAS is proved to be stabilisable even if so is not for each of uncertain subsystem. In addition, a method is proposed to constructively design a switching rule for MASs with norm-bounded time-varying uncertainties. The switching rules designed via this method do not rely on uncertainties, and the switched MAS is quadratically stabilisable via decentralised external self-feedback for all uncertainties. With respect to applications of the stabilisability results, the formation control and the cooperative tracking control are addressed. Numerical simulations are presented to demonstrate the effectiveness of the proposed results.
A mathematical perspective on flight dynamics and control
L'Afflitto, Andrea
2017-01-01
This brief presents several aspects of flight dynamics, which are usually omitted or briefly mentioned in textbooks, in a concise, self-contained, and rigorous manner. The kinematic and dynamic equations of an aircraft are derived starting from the notion of the derivative of a vector and then thoroughly analysed, interpreting their deep meaning from a mathematical standpoint and without relying on physical intuition. Moreover, some classic and advanced control design techniques are presented and illustrated with meaningful examples. Distinguishing features that characterize this brief include a definition of angular velocity, which leaves no room for ambiguities, an improvement on traditional definitions based on infinitesimal variations. Quaternion algebra, Euler parameters, and their role in capturing the dynamics of an aircraft are discussed in great detail. After having analyzed the longitudinal- and lateral-directional modes of an aircraft, the linear-quadratic regulator, the linear-quadratic Gaussian r...
Detecting periodicities with Gaussian processes
Directory of Open Access Journals (Sweden)
Nicolas Durrande
2016-04-01
Full Text Available We consider the problem of detecting and quantifying the periodic component of a function given noise-corrupted observations of a limited number of input/output tuples. Our approach is based on Gaussian process regression, which provides a flexible non-parametric framework for modelling periodic data. We introduce a novel decomposition of the covariance function as the sum of periodic and aperiodic kernels. This decomposition allows for the creation of sub-models which capture the periodic nature of the signal and its complement. To quantify the periodicity of the signal, we derive a periodicity ratio which reflects the uncertainty in the fitted sub-models. Although the method can be applied to many kernels, we give a special emphasis to the Matérn family, from the expression of the reproducing kernel Hilbert space inner product to the implementation of the associated periodic kernels in a Gaussian process toolkit. The proposed method is illustrated by considering the detection of periodically expressed genes in the arabidopsis genome.
Monogamy inequality for distributed gaussian entanglement.
Hiroshima, Tohya; Adesso, Gerardo; Illuminati, Fabrizio
2007-02-02
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.
Entanglement-assisted quantum feedback control
Yamamoto, Naoki; Mikami, Tomoaki
2017-07-01
The main advantage of quantum metrology relies on the effective use of entanglement, which indeed allows us to achieve strictly better estimation performance over the standard quantum limit. In this paper, we propose an analogous method utilizing entanglement for the purpose of feedback control. The system considered is a general linear dynamical quantum system, where the control goal can be systematically formulated as a linear quadratic Gaussian control problem based on the quantum Kalman filtering method; in this setting, an entangled input probe field is effectively used to reduce the estimation error and accordingly the control cost function. In particular, we show that, in the problem of cooling an opto-mechanical oscillator, the entanglement-assisted feedback control can lower the stationary occupation number of the oscillator below the limit attainable by the controller with a coherent probe field and furthermore beats the controller with an optimized squeezed probe field.
Integrable Hamiltonian systems and interactions through quadratic constraints
International Nuclear Information System (INIS)
Pohlmeyer, K.
1975-08-01
Osub(n)-invariant classical relativistic field theories in one time and one space dimension with interactions that are entirely due to quadratic constraints are shown to be closely related to integrable Hamiltonian systems. (orig.) [de
A perturbative solution for gravitational waves in quadratic gravity
International Nuclear Information System (INIS)
Neto, Edgard C de Rey; Aguiar, Odylio D; Araujo, Jose C N de
2003-01-01
We find a gravitational wave solution to the linearized version of quadratic gravity by adding successive perturbations to Einstein's linearized field equations. We show that only the Ricci-squared quadratic invariant contributes to give a different solution to those found in Einstein's general relativity. The perturbative solution is written as a power series in the β parameter, the coefficient of the Ricci-squared term in the quadratic gravitational action. We also show that, for monochromatic waves of a given angular frequency ω, the perturbative solution can be summed out to give an exact solution to the linearized version of quadratic gravity, for 0 1/2 . This result may lead to implications for the predictions for gravitational wave backgrounds of cosmological origin
Accurate nonlocal theory for cascaded quadratic soliton compression
DEFF Research Database (Denmark)
Bache, Morten; Bang, Ole; Moses, Jeffrey
2007-01-01
We study soliton compression in bulk quadratic nonlinear materials at 800 nm, where group-velocity mismatch dominates. We develop a nonlocal theory showing that efficient compression depends strongly on characteristic nonlocal time scales related to pulse dispersion....
Generation of singular optical beams from fundamental Gaussian beam using Sagnac interferometer
Naik, Dinesh N.; Viswanathan, Nirmal K.
2016-09-01
We propose a simple free-space optics recipe for the controlled generation of optical vortex beams with a vortex dipole or a single charge vortex, using an inherently stable Sagnac interferometer. We investigate the role played by the amplitude and phase differences in generating higher-order Gaussian beams from the fundamental Gaussian mode. Our simulation results reveal how important the control of both the amplitude and the phase difference between superposing beams is to achieving optical vortex beams. The creation of a vortex dipole from null interference is unveiled through the introduction of a lateral shear and a radial phase difference between two out-of-phase Gaussian beams. A stable and high quality optical vortex beam, equivalent to the first-order Laguerre-Gaussian beam, is synthesized by coupling lateral shear with linear phase difference, introduced orthogonal to the shear between two out-of-phase Gaussian beams.
White Gaussian Noise - Models for Engineers
Jondral, Friedrich K.
2018-04-01
This paper assembles some information about white Gaussian noise (WGN) and its applications. It starts from a description of thermal noise, i. e. the irregular motion of free charge carriers in electronic devices. In a second step, mathematical models of WGN processes and their most important parameters, especially autocorrelation functions and power spectrum densities, are introduced. In order to proceed from mathematical models to simulations, we discuss the generation of normally distributed random numbers. The signal-to-noise ratio as the most important quality measure used in communications, control or measurement technology is accurately introduced. As a practical application of WGN, the transmission of quadrature amplitude modulated (QAM) signals over additive WGN channels together with the optimum maximum likelihood (ML) detector is considered in a demonstrative and intuitive way.
Breaking Gaussian incompatibility on continuous variable quantum systems
Energy Technology Data Exchange (ETDEWEB)
Heinosaari, Teiko, E-mail: teiko.heinosaari@utu.fi [Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turku (Finland); Kiukas, Jukka, E-mail: jukka.kiukas@aber.ac.uk [Department of Mathematics, Aberystwyth University, Penglais, Aberystwyth, SY23 3BZ (United Kingdom); Schultz, Jussi, E-mail: jussi.schultz@gmail.com [Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turku (Finland); Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano (Italy)
2015-08-15
We characterise Gaussian quantum channels that are Gaussian incompatibility breaking, that is, transform every set of Gaussian measurements into a set obtainable from a joint Gaussian observable via Gaussian postprocessing. Such channels represent local noise which renders measurements useless for Gaussian EPR-steering, providing the appropriate generalisation of entanglement breaking channels for this scenario. Understanding the structure of Gaussian incompatibility breaking channels contributes to the resource theory of noisy continuous variable quantum information protocols.
Optimal control of LQG problem with an explicit trade-off between mean and variance
Qian, Fucai; Xie, Guo; Liu, Ding; Xie, Wenfang
2011-12-01
For discrete-time linear-quadratic Gaussian (LQG) control problems, a utility function on the expectation and the variance of the conventional performance index is considered. The utility function is viewed as an overall objective of the system and can perform the optimal trade-off between the mean and the variance of performance index. The nonlinear utility function is first converted into an auxiliary parameters optimisation problem about the expectation and the variance. Then an optimal closed-loop feedback controller for the nonseparable mean-variance minimisation problem is designed by nonlinear mathematical programming. Finally, simulation results are given to verify the algorithm's effectiveness obtained in this article.
Scale-Invariant Rotating Black Holes in Quadratic Gravity
Directory of Open Access Journals (Sweden)
Guido Cognola
2015-07-01
Full Text Available Black hole solutions in pure quadratic theories of gravity are interesting since they allow the formulation of 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.
A Trust-region-based Sequential Quadratic Programming Algorithm
DEFF Research Database (Denmark)
Henriksen, Lars Christian; Poulsen, Niels Kjølstad
This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints.......This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints....
Staff turnover in hotels : exploring the quadratic and linear relationships.
Mohsin, A.; Lengler, J.F.B.; Aguzzoli, R.L.
2015-01-01
The aim of this study is to assess whether the relationship between intention to leave the job and its antecedents is quadratic or linear. To explore those relationships a theoretical model (see Fig. 1) and eight hypotheses are proposed. Each linear hypothesis is followed by an alternative quadratic hypothesis. The alternative hypotheses propose that the relationship between the four antecedent constructs and intention to leave the job might not be linear, as the existing literature suggests....
On wave-packet dynamics in a decaying quadratic potential
DEFF Research Database (Denmark)
Møller, Klaus Braagaard; Henriksen, Niels Engholm
1997-01-01
We consider the time-dependent Schrodinger equation for a quadratic potential with an exponentially decaying force constant. General analytical solutions are presented and we highlight in particular, the signatures of classical mechanics in the wave packet dynamics.......We consider the time-dependent Schrodinger equation for a quadratic potential with an exponentially decaying force constant. General analytical solutions are presented and we highlight in particular, the signatures of classical mechanics in the wave packet dynamics....
The stability of quadratic-reciprocal functional equation
Song, Aimin; Song, Minwei
2018-04-01
A new quadratic-reciprocal functional equation f ((k +1 )x +k y )+f ((k +1 )x -k y )=2/f (x )f (y )[(k+1 ) 2f (y )+k2f (x )] [(k+1)2f (y )-k2f (x )] 2 is introduced. The Hyers-Ulam stability for the quadratic-reciprocal functional equations is proved in Banach spaces using the direct method and the fixed point method, respectively.
Burgers' turbulence problem with linear or quadratic external potential
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Leonenko, N.N.
2005-01-01
We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions.......We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions....
Quadratic programming with fuzzy parameters: A membership function approach
International Nuclear Information System (INIS)
Liu, S.-T.
2009-01-01
Quadratic programming has been widely applied to solving real world problems. The conventional quadratic programming model requires the parameters to be known constants. In the real world, however, the parameters are seldom known exactly and have to be estimated. This paper discusses the fuzzy quadratic programming problems where the cost coefficients, constraint coefficients, and right-hand sides are represented by convex fuzzy numbers. Since the parameters in the program are fuzzy numbers, the derived objective value is a fuzzy number as well. Using Zadeh's extension principle, a pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the fuzzy quadratic program. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a family of conventional one-level quadratic programs. Solving the pair of quadratic programs produces the fuzzy objective values of the problem. An example illustrates method proposed in this paper.
Berczynski, Pawel; Bliokh, Konstantin Yu; Kravtsov, Yuri A; Stateczny, Andrzej
2006-06-01
We present an ab initio account of the paraxial complex geometrical optics (CGO) in application to scalar Gaussian beam propagation and diffraction in a 3D smoothly inhomogeneous medium. The paraxial CGO deals with quadratic expansion of the complex eikonal and reduces the wave problem to the solution of ordinary differential equations of the Riccati type. This substantially simplifies the description of Gaussian beam diffraction as compared with full-wave or parabolic (quasi-optics) equations. For a Gaussian beam propagating in a homogeneous medium or along the symmetry axis in a lenslike medium, the CGO equations possess analytical solutions; otherwise, they can be readily solved numerically. As a nontrivial example we consider Gaussian beam propagation and diffraction along a helical ray in an axially symmetric waveguide medium. It is shown that the major axis of the beam's elliptical cross section grows unboundedly; it is oriented predominantly in the azimuthal (binormal) direction and does not obey the parallel-transport law.
International Nuclear Information System (INIS)
McHugh, Derek; Buzek, Vladimir; Ziman, Mario
2006-01-01
We present a class of non-Gaussian two-mode continuous-variable states for which the separability criterion for Gaussian states can be employed to detect whether they are separable or not. These states reduce to the two-mode Gaussian states as a special case
Quantum beamstrahlung from gaussian bunches
International Nuclear Information System (INIS)
Chen, P.
1987-08-01
The method of Baier and Katkov is applied to calculate the correction terms to the Sokolov-Ternov radiation formula due to the variation of the magnetic field strength along the trajectory of a radiating particle. We carry the calculation up to the second order in the power expansion of B tau/B, where tau is the formation time of radiation. The expression is then used to estimate the quantum beamstrahlung average energy loss from e + e - bunches with gaussian distribution in bunch currents. We show that the effect of the field variation is to reduce the average energy loss from previous calculations based on the Sokolov-Ternov formula or its equivalent. Due to the limitation of our method, only an upper bound of the reduction is obtained. 18 refs
Cautious NMPC with Gaussian Process Dynamics for Miniature Race Cars
Hewing, Lukas; Liniger, Alexander; Zeilinger, Melanie N.
2017-01-01
This paper presents an adaptive high performance control method for autonomous miniature race cars. Racing dynamics are notoriously hard to model from first principles, which is addressed by means of a cautious nonlinear model predictive control (NMPC) approach that learns to improve its dynamics model from data and safely increases racing performance. The approach makes use of a Gaussian Process (GP) and takes residual model uncertainty into account through a chance constrained formulation. ...
Limit theorems for functionals of Gaussian vectors
Institute of Scientific and Technical Information of China (English)
Hongshuai DAI; Guangjun SHEN; Lingtao KONG
2017-01-01
Operator self-similar processes,as an extension of self-similar processes,have been studied extensively.In this work,we study limit theorems for functionals of Gaussian vectors.Under some conditions,we determine that the limit of partial sums of functionals of a stationary Gaussian sequence of random vectors is an operator self-similar process.
Palm distributions for log Gaussian Cox processes
DEFF Research Database (Denmark)
Coeurjolly, Jean-Francois; Møller, Jesper; Waagepetersen, Rasmus
This paper reviews useful results related to Palm distributions of spatial point processes and provides a new result regarding the characterization of Palm distributions for the class of log Gaussian Cox processes. This result is used to study functional summary statistics for a log Gaussian Cox...
Gaussian limit of compact spin systems
International Nuclear Information System (INIS)
Bellissard, J.; Angelis, G.F. de
1981-01-01
It is shown that the Wilson and Wilson-Villain U(1) models reproduce, in the low coupling limit, the gaussian lattice approximation of the Euclidean electromagnetic field. By the same methods it is also possible to prove that the plane rotator and the Villain model share a common gaussian behaviour in the low temperature limit. (Auth.)
On the dependence structure of Gaussian queues
Es-Saghouani, A.; Mandjes, M.R.H.
2009-01-01
In this article we study Gaussian queues (that is, queues fed by Gaussian processes, such as fractional Brownian motion (fBm) and the integrated Ornstein-Uhlenbeck (iOU) process), with a focus on the dependence structure of the workload process. The main question is to what extent does the workload
Shedding new light on Gaussian harmonic analysis
Teuwen, J.J.B.
2016-01-01
This dissertation consists out of two rather disjoint parts. One part concerns some results on Gaussian harmonic analysis and the other on an optimization problem in optics. In the first part we study the Ornstein–Uhlenbeck process with respect to the Gaussian measure. We focus on two areas. One is
Quadratic electromechanical strain in silicon investigated by scanning probe microscopy
Yu, Junxi; Esfahani, Ehsan Nasr; Zhu, Qingfeng; Shan, Dongliang; Jia, Tingting; Xie, Shuhong; Li, Jiangyu
2018-04-01
Piezoresponse force microscopy (PFM) is a powerful tool widely used to characterize piezoelectricity and ferroelectricity at the nanoscale. However, it is necessary to distinguish microscopic mechanisms between piezoelectricity and non-piezoelectric contributions measured by PFM. In this work, we systematically investigate the first and second harmonic apparent piezoresponses of a silicon wafer in both vertical and lateral modes, and we show that it exhibits an apparent electromechanical response that is quadratic to the applied electric field, possibly arising from ionic electrochemical dipoles induced by the charged probe. As a result, the electromechanical response measured is dominated by the second harmonic response in the vertical mode, and its polarity can be switched by the DC voltage with the evolving coercive field and maximum amplitude, in sharp contrast to typical ferroelectric materials we used as control. The ionic activity in silicon is also confirmed by the scanning thermo-ionic microscopy measurement, and the work points toward a set of methods to distinguish true piezoelectricity from the apparent ones.
Entanglement in Gaussian matrix-product states
International Nuclear Information System (INIS)
Adesso, Gerardo; Ericsson, Marie
2006-01-01
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
Gaussian vs non-Gaussian turbulence: impact on wind turbine loads
DEFF Research Database (Denmark)
Berg, Jacob; Natarajan, Anand; Mann, Jakob
2016-01-01
taking into account the safety factor for extreme moments. Other extreme load moments as well as the fatigue loads are not affected because of the use of non-Gaussian turbulent inflow. It is suggested that the turbine thus acts like a low-pass filter that averages out the non-Gaussian behaviour, which......From large-eddy simulations of atmospheric turbulence, a representation of Gaussian turbulence is constructed by randomizing the phases of the individual modes of variability. Time series of Gaussian turbulence are constructed and compared with its non-Gaussian counterpart. Time series from the two...
Applying the J-optimal channelized quadratic observer to SPECT myocardial perfusion defect detection
Kupinski, Meredith K.; Clarkson, Eric; Ghaly, Michael; Frey, Eric C.
2016-03-01
To evaluate performance on a perfusion defect detection task from 540 image pairs of myocardial perfusion SPECT image data we apply the J-optimal channelized quadratic observer (J-CQO). We compare AUC values of the linear Hotelling observer and J-CQO when the defect location is fixed and when it occurs in one of two locations. As expected, when the location is fixed a single channels maximizes AUC; location variability requires multiple channels to maximize the AUC. The AUC is estimated from both the projection data and reconstructed images. J-CQO is quadratic since it uses the first- and second- order statistics of the image data from both classes. The linear data reduction by the channels is described by an L x M channel matrix and in prior work we introduced an iterative gradient-based method for calculating the channel matrix. The dimensionality reduction from M measurements to L channels yields better estimates of these sample statistics from smaller sample sizes, and since the channelized covariance matrix is L x L instead of M x M, the matrix inverse is easier to compute. The novelty of our approach is the use of Jeffrey's divergence (J) as the figure of merit (FOM) for optimizing the channel matrix. We previously showed that the J-optimal channels are also the optimum channels for the AUC and the Bhattacharyya distance when the channel outputs are Gaussian distributed with equal means. This work evaluates the use of J as a surrogate FOM (SFOM) for AUC when these statistical conditions are not satisfied.
Optical-response properties in hybrid optomechanical systems with quadratic coupling
Sun, Xue-Jian; Wang, Xin; Liu, Li-Na; Liu, Wen-Xiao; Fang, Ai-Ping; Li, Hong-Rong
2018-02-01
We theoretically investigate the optical-response properties of the four-mode quadratically coupled optomechanical system (OMS), in which two standard OMSs with quadratic coupling are coupled to each other via a common waveguide. In the presence of a strong control field applied to one cavity and a weak probe field applied to the other, we show that by suitably tuning the system parameters, there appears the normal mode splitting, optomechanically induced absorption, and double or triple electromagnetically induced transparency phenomena in the probe absorption spectrum. In particular, the explicit physical explanations for those fantastic phenomena are detailed discussed. Moreover, we also show that our proposal can be exploited to implement the optical switch as well as the slow and fast light effects.
Increasing Entanglement between Gaussian States by Coherent Photon Subtraction
DEFF Research Database (Denmark)
Ourjoumtsev, Alexei; Dantan, Aurelien Romain; Tualle Brouri, Rosa
2007-01-01
We experimentally demonstrate that the entanglement between Gaussian entangled states can be increased by non-Gaussian operations. Coherent subtraction of single photons from Gaussian quadrature-entangled light pulses, created by a nondegenerate parametric amplifier, produces delocalized states...
Representation of Gaussian semimartingales with applications to the covariance function
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas
2010-01-01
stationary Gaussian semimartingales and their canonical decomposition. Thirdly, we give a new characterization of the covariance function of Gaussian semimartingales, which enable us to characterize the class of martingales and the processes of bounded variation among the Gaussian semimartingales. We...
The quadratic reciprocity law a collection of classical proofs
Baumgart, Oswald
2015-01-01
This book is the English translation of Baumgart’s thesis on the early proofs of the quadratic reciprocity law (“Über das quadratische Reciprocitätsgesetz. Eine vergleichende Darstellung der Beweise”), first published in 1885. It is divided into two parts. The first part presents a very brief history of the development of number theory up to Legendre, as well as detailed descriptions of several early proofs of the quadratic reciprocity law. The second part highlights Baumgart’s comparisons of the principles behind these proofs. A current list of all known proofs of the quadratic reciprocity law, with complete references, is provided in the appendix. This book will appeal to all readers interested in elementary number theory and the history of number theory.
Quadratic algebra approach to relativistic quantum Smorodinsky-Winternitz systems
International Nuclear Information System (INIS)
Marquette, Ian
2011-01-01
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 bounds of feasible space on constrained nonconvex quadratic programming
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.
Time-optimal thermalization of single-mode Gaussian states
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.
Some continual integrals from gaussian forms
International Nuclear Information System (INIS)
Mazmanishvili, A.S.
1985-01-01
The result summary of continual integration of gaussian functional type is given. The summary contains 124 continual integrals which are the mathematical expectation of the corresponding gaussian form by the continuum of random trajectories of four types: real-valued Ornstein-Uhlenbeck process, Wiener process, complex-valued Ornstein-Uhlenbeck process and the stochastic harmonic one. The summary includes both the known continual integrals and the unpublished before integrals. Mathematical results of the continual integration carried in the work may be applied in the problem of the theory of stochastic process, approaching to the finding of mean from gaussian forms by measures generated by the pointed stochastic processes
Loop corrections to primordial non-Gaussianity
Boran, Sibel; Kahya, E. O.
2018-02-01
We discuss quantum gravitational loop effects to observable quantities such as curvature power spectrum and primordial non-Gaussianity of cosmic microwave background (CMB) radiation. We first review the previously shown case where one gets a time dependence for zeta-zeta correlator due to loop corrections. Then we investigate the effect of loop corrections to primordial non-Gaussianity of CMB. We conclude that, even with a single scalar inflaton, one might get a huge value for non-Gaussianity which would exceed the observed value by at least 30 orders of magnitude. Finally we discuss the consequences of this result for scalar driven inflationary models.
Gaussian Mixture Model of Heart Rate Variability
Costa, Tommaso; Boccignone, Giuseppe; Ferraro, Mario
2012-01-01
Heart rate variability (HRV) is an important measure of sympathetic and parasympathetic functions of the autonomic nervous system and a key indicator of cardiovascular condition. This paper proposes a novel method to investigate HRV, namely by modelling it as a linear combination of Gaussians. Results show that three Gaussians are enough to describe the stationary statistics of heart variability and to provide a straightforward interpretation of the HRV power spectrum. Comparisons have been made also with synthetic data generated from different physiologically based models showing the plausibility of the Gaussian mixture parameters. PMID:22666386
Non-Gaussianity from isocurvature perturbations
Energy Technology Data Exchange (ETDEWEB)
Kawasaki, Masahiro; Nakayama, Kazunori; Sekiguchi, Toyokazu; Suyama, Teruaki [Institute for Cosmic Ray Research, University of Tokyo, Kashiwa 277-8582 (Japan); Takahashi, Fuminobu, E-mail: kawasaki@icrr.u-tokyo.ac.jp, E-mail: nakayama@icrr.u-tokyo.ac.jp, E-mail: sekiguti@icrr.u-tokyo.ac.jp, E-mail: suyama@icrr.u-tokyo.ac.jp, E-mail: fuminobu.takahashi@ipmu.jp [Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa 277-8568 (Japan)
2008-11-15
We develop a formalism for studying non-Gaussianity in both curvature and isocurvature perturbations. It is shown that non-Gaussianity in the isocurvature perturbation between dark matter and photons leaves distinct signatures in the cosmic microwave background temperature fluctuations, which may be confirmed in future experiments, or possibly even in the currently available observational data. As an explicit example, we consider the quantum chromodynamics axion and show that it can actually induce sizable non-Gaussianity for the inflationary scale, H{sub inf} = O(10{sup 9}-10{sup 11}) GeV.
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.
Energy Technology Data Exchange (ETDEWEB)
Korotkov, S F; Khalitov, N T
1965-01-01
he quadratic method of programming is used to solve the following type of problem. A circular reservoir is subjected to a peripheral waterflood. The reservoir is drained by wells arranged in 3 concentric circles. The objective is to control the operation of producing wells, that a maximum quantity of water-free oil will be produced. The wells are flowed so that bottomhole pressure is above the bubble point. A quadratic equation is used to express the essential features of the problem; a system of linear equations is used to express the boundary conditions. The problem is solved by means of the Wolf algorithm method. The method is demonstrated by an illustrative example.
Gaussian measures of entanglement versus negativities: Ordering of two-mode Gaussian states
International Nuclear Information System (INIS)
Adesso, Gerardo; Illuminati, Fabrizio
2005-01-01
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
Inverse modelling of atmospheric tracers: non-Gaussian methods and second-order sensitivity analysis
Directory of Open Access Journals (Sweden)
M. Bocquet
2008-02-01
Full Text Available For a start, recent techniques devoted to the reconstruction of sources of an atmospheric tracer at continental scale are introduced. A first method is based on the principle of maximum entropy on the mean and is briefly reviewed here. A second approach, which has not been applied in this field yet, is based on an exact Bayesian approach, through a maximum a posteriori estimator. The methods share common grounds, and both perform equally well in practice. When specific prior hypotheses on the sources are taken into account such as positivity, or boundedness, both methods lead to purposefully devised cost-functions. These cost-functions are not necessarily quadratic because the underlying assumptions are not Gaussian. As a consequence, several mathematical tools developed in data assimilation on the basis of quadratic cost-functions in order to establish a posteriori analysis, need to be extended to this non-Gaussian framework. Concomitantly, the second-order sensitivity analysis needs to be adapted, as well as the computations of the averaging kernels of the source and the errors obtained in the reconstruction. All of these developments are applied to a real case of tracer dispersion: the European Tracer Experiment [ETEX]. Comparisons are made between a least squares cost function (similar to the so-called 4D-Var approach and a cost-function which is not based on Gaussian hypotheses. Besides, the information content of the observations which is used in the reconstruction is computed and studied on the application case. A connection with the degrees of freedom for signal is also established. As a by-product of these methodological developments, conclusions are drawn on the information content of the ETEX dataset as seen from the inverse modelling point of view.
Large N saddle formulation of quadratic building block theories
International Nuclear Information System (INIS)
Halpern, M.B.
1980-01-01
I develop a large N saddle point formulation for the broad class of 'theories of quadratic building blocks'. Such theories are those on which the sums over internal indices are contained in quadratic building blocks, e.g. PHI 2 = Σsup(N)sub(a-1)PHi sup(a)sup(a). The formulation applies as well to fermions, derivative coupling and non-polynomial interactions. In a related development, closed Schwinger-Dyson equations for Green functions of the building blocks are derived and solved for large N. (orig.)
Remarks on second-order quadratic systems in algebras
Directory of Open Access Journals (Sweden)
Art Sagle
2017-10-01
Full Text Available This paper is an addendum to our earlier paper [8], where a systematic study of quadratic systems of second order ordinary differential equations defined in commutative algebras was presented. Here we concentrate on special solutions and energy considerations of some quadratic systems defined in algebras which need not be commutative, however, we shall throughout assume the algebra to be associative. We here also give a positive answer to an open question, concerning periodic motions of such systems, posed in our earlier paper.
Dhage Iteration Method for Generalized Quadratic Functional Integral Equations
Directory of Open Access Journals (Sweden)
Bapurao C. Dhage
2015-01-01
Full Text Available In this paper we prove the existence as well as approximations of the solutions for a certain nonlinear generalized quadratic functional integral equation. An algorithm for the solutions is developed and it is shown that the sequence of successive approximations starting at a lower or upper solution converges monotonically to the solutions of related quadratic functional integral equation under some suitable mixed hybrid conditions. We rely our main result on Dhage iteration method embodied in a recent hybrid fixed point theorem of Dhage (2014 in partially ordered normed linear spaces. An example is also provided to illustrate the abstract theory developed in the paper.
Quantum tomography and classical propagator for quadratic quantum systems
International Nuclear Information System (INIS)
Man'ko, O.V.
1999-03-01
The classical propagator for tomographic probability (which describes the quantum state instead of wave function or density matrix) is presented for quadratic quantum systems and its relation to the quantum propagator is considered. The new formalism of quantum mechanics, based on the probability representation of the state, is applied to particular quadratic systems - the harmonic oscillator, particle's free motion, problems of an ion in a Paul trap and in asymmetric Penning trap, and to the process of stimulated Raman scattering. The classical propagator for these systems is written in an explicit form. (author)
Subgroups of class groups of algebraic quadratic function fields
International Nuclear Information System (INIS)
Wang Kunpeng; Zhang Xianke
2001-09-01
Ideal class groups H(K) of algebraic quadratic function fields K are studied, by using mainly the theory of continued fractions of algebraic functions. Properties of such continued fractions are discussed first. Then a necessary and sufficient condition is given for the class group H(K) to contain a cyclic subgroup of any order n, this criterion condition holds true for both real and imaginary fields K. Furthermore, several series of function fields K, including real, inertia imaginary, as well as ramified imaginary quadratic function fields, are given, and their class groups H(K) are proved to contain cyclic subgroups of order n. (author)
Smoothing optimization of supporting quadratic surfaces with Zernike polynomials
Zhang, Hang; Lu, Jiandong; Liu, Rui; Ma, Peifu
2018-03-01
A new optimization method to get a smooth freeform optical surface from an initial surface generated by the supporting quadratic method (SQM) is proposed. To smooth the initial surface, a 9-vertex system from the neighbor quadratic surface and the Zernike polynomials are employed to establish a linear equation system. A local optimized surface to the 9-vertex system can be build by solving the equations. Finally, a continuous smooth optimization surface is constructed by stitching the above algorithm on the whole initial surface. The spot corresponding to the optimized surface is no longer discrete pixels but a continuous distribution.
Extensions of linear-quadratic control, optimization and matrix theory
Jacobson, David H
1977-01-01
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat
Emotion suppression moderates the quadratic association between RSA and executive function.
Spangler, Derek P; Bell, Martha Ann; Deater-Deckard, Kirby
2015-09-01
There is uncertainty about whether respiratory sinus arrhythmia (RSA), a cardiac marker of adaptive emotion regulation, is involved in relatively low or high executive function performance. In the present study, we investigated (a) whether RSA during rest and tasks predict both relatively low and high executive function within a larger quadratic association among the two variables, and (b) the extent to which this quadratic trend was moderated by individual differences in emotion regulation. To achieve these aims, a sample of ethnically and socioeconomically diverse women self-reported reappraisal and emotion suppression. They next experienced a 2-min resting period during which electrocardiogram (ECG) was continually assessed. In the next phase, the women completed an array of executive function and nonexecutive cognitive tasks while ECG was measured throughout. As anticipated, resting RSA showed a quadratic association with executive function that was strongest for high suppression. These results suggest that relatively high resting RSA may predict poor executive function ability when emotion regulation consumes executive control resources needed for ongoing cognitive performance. © 2015 Society for Psychophysiological Research.
Optimal unitary dilation for bosonic Gaussian channels
International Nuclear Information System (INIS)
Caruso, Filippo; Eisert, Jens; Giovannetti, Vittorio; Holevo, Alexander S.
2011-01-01
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.
Phase statistics in non-Gaussian scattering
International Nuclear Information System (INIS)
Watson, Stephen M; Jakeman, Eric; Ridley, Kevin D
2006-01-01
Amplitude weighting can improve the accuracy of frequency measurements in signals corrupted by multiplicative speckle noise. When the speckle field constitutes a circular complex Gaussian process, the optimal function of amplitude weighting is provided by the field intensity, corresponding to the intensity-weighted phase derivative statistic. In this paper, we investigate the phase derivative and intensity-weighted phase derivative returned from a two-dimensional random walk, which constitutes a generic scattering model capable of producing both Gaussian and non-Gaussian fluctuations. Analytical results are developed for the correlation properties of the intensity-weighted phase derivative, as well as limiting probability densities of the scattered field. Numerical simulation is used to generate further probability densities and determine optimal weighting criteria from non-Gaussian fields. The results are relevant to frequency retrieval in radiation scattered from random media
Galaxy bias and primordial non-Gaussianity
Energy Technology Data Exchange (ETDEWEB)
Assassi, Valentin; Baumann, Daniel [DAMTP, Cambridge University, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Schmidt, Fabian, E-mail: assassi@ias.edu, E-mail: D.D.Baumann@uva.nl, E-mail: fabians@MPA-Garching.MPG.DE [Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85748 Garching (Germany)
2015-12-01
We present a systematic study of galaxy biasing in the presence of primordial non-Gaussianity. For a large class of non-Gaussian initial conditions, we define a general bias expansion and prove that it is closed under renormalization, thereby showing that the basis of operators in the expansion is complete. We then study the effects of primordial non-Gaussianity on the statistics of galaxies. We show that the equivalence principle enforces a relation between the scale-dependent bias in the galaxy power spectrum and that in the dipolar part of the bispectrum. This provides a powerful consistency check to confirm the primordial origin of any observed scale-dependent bias. Finally, we also discuss the imprints of anisotropic non-Gaussianity as motivated by recent studies of higher-spin fields during inflation.
Optimal cloning of mixed Gaussian states
International Nuclear Information System (INIS)
Guta, Madalin; Matsumoto, Keiji
2006-01-01
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
Encoding information using laguerre gaussian modes
CSIR Research Space (South Africa)
Trichili, A
2015-08-01
Full Text Available The authors experimentally demonstrate an information encoding protocol using the two degrees of freedom of Laguerre Gaussian modes having different radial and azimuthal components. A novel method, based on digital holography, for information...
Interweave Cognitive Radio with Improper Gaussian Signaling
Hedhly, Wafa; Amin, Osama; Alouini, Mohamed-Slim
2018-01-01
Improper Gaussian signaling (IGS) has proven its ability in improving the performance of underlay and overlay cognitive radio paradigms. In this paper, the interweave cognitive radio paradigm is studied when the cognitive user employs IGS
Galaxy bias and primordial non-Gaussianity
International Nuclear Information System (INIS)
Assassi, Valentin; Baumann, Daniel; Schmidt, Fabian
2015-01-01
We present a systematic study of galaxy biasing in the presence of primordial non-Gaussianity. For a large class of non-Gaussian initial conditions, we define a general bias expansion and prove that it is closed under renormalization, thereby showing that the basis of operators in the expansion is complete. We then study the effects of primordial non-Gaussianity on the statistics of galaxies. We show that the equivalence principle enforces a relation between the scale-dependent bias in the galaxy power spectrum and that in the dipolar part of the bispectrum. This provides a powerful consistency check to confirm the primordial origin of any observed scale-dependent bias. Finally, we also discuss the imprints of anisotropic non-Gaussianity as motivated by recent studies of higher-spin fields during inflation
Statistically tuned Gaussian background subtraction technique for ...
Indian Academy of Sciences (India)
temporal median method and mixture of Gaussian model and performance evaluation ... to process the videos captured by unmanned aerial vehicle (UAV). ..... The output is obtained by simulation using MATLAB 2010 in a standalone PC with ...
A non-Gaussian multivariate distribution with all lower-dimensional Gaussians and related families
Dutta, Subhajit
2014-07-28
Several fascinating examples of non-Gaussian bivariate distributions which have marginal distribution functions to be Gaussian have been proposed in the literature. These examples often clarify several properties associated with the normal distribution. In this paper, we generalize this result in the sense that we construct a pp-dimensional distribution for which any proper subset of its components has the Gaussian distribution. However, the jointpp-dimensional distribution is inconsistent with the distribution of these subsets because it is not Gaussian. We study the probabilistic properties of this non-Gaussian multivariate distribution in detail. Interestingly, several popular tests of multivariate normality fail to identify this pp-dimensional distribution as non-Gaussian. We further extend our construction to a class of elliptically contoured distributions as well as skewed distributions arising from selections, for instance the multivariate skew-normal distribution.
A non-Gaussian multivariate distribution with all lower-dimensional Gaussians and related families
Dutta, Subhajit; Genton, Marc G.
2014-01-01
Several fascinating examples of non-Gaussian bivariate distributions which have marginal distribution functions to be Gaussian have been proposed in the literature. These examples often clarify several properties associated with the normal distribution. In this paper, we generalize this result in the sense that we construct a pp-dimensional distribution for which any proper subset of its components has the Gaussian distribution. However, the jointpp-dimensional distribution is inconsistent with the distribution of these subsets because it is not Gaussian. We study the probabilistic properties of this non-Gaussian multivariate distribution in detail. Interestingly, several popular tests of multivariate normality fail to identify this pp-dimensional distribution as non-Gaussian. We further extend our construction to a class of elliptically contoured distributions as well as skewed distributions arising from selections, for instance the multivariate skew-normal distribution.
Mismatch management for optical and matter-wave quadratic solitons
International Nuclear Information System (INIS)
Driben, R.; Oz, Y.; Malomed, B. A.; Gubeskys, A.; Yurovsky, V. A.
2007-01-01
We propose a way to control solitons in χ (2) (quadratically nonlinear) systems by means of periodic modulation imposed on the phase-mismatch parameter ('mismatch management', MM). It may be realized in the cotransmission of fundamental-frequency (FF) and second-harmonic (SH) waves in a planar optical waveguide via a long-period modulation of the usual quasi-phase-matching pattern of ferroelectric domains. In an altogether different physical setting, the MM may also be implemented by dint of the Feshbach resonance in a harmonically modulated magnetic field in a hybrid atomic-molecular Bose-Einstein condensate (BEC), with the atomic and molecular mean fields (MFs) playing the roles of the FF and SH, respectively. Accordingly, the problem is analyzed in two different ways. First, in the optical model, we identify stability regions for spatial solitons in the MM system, in terms of the MM amplitude and period, using the MF equations for spatially inhomogeneous configurations. In particular, an instability enclave is found inside the stability area. The robustness of the solitons is also tested against variation of the shape of the input pulse, and a threshold for the formation of stable solitons is found in terms of the power. Interactions between stable solitons are virtually unaffected by the MM. The second method (parametric approximation), going beyond the MF description, is developed for spatially homogeneous states in the BEC model. It demonstrates that the MF description is valid for large modulation periods, while, at smaller periods, non-MF components acquire gain, which implies destruction of the MF under the action of the high-frequency MM
Gaussian sum rules for optical functions
International Nuclear Information System (INIS)
Kimel, I.
1981-12-01
A new (Gaussian) type of sum rules (GSR) for several optical functions, is presented. The functions considered are: dielectric permeability, refractive index, energy loss function, rotatory power and ellipticity (circular dichroism). While reducing to the usual type of sum rules in a certain limit, the GSR contain in general, a Gaussian factor that serves to improve convergence. GSR might be useful in analysing experimental data. (Author) [pt
Gaussian maximally multipartite-entangled states
Facchi, Paolo; Florio, Giuseppe; Lupo, Cosmo; Mancini, Stefano; Pascazio, Saverio
2009-12-01
We study maximally multipartite-entangled states in the context of Gaussian continuous variable quantum systems. By considering multimode Gaussian states with constrained energy, we show that perfect maximally multipartite-entangled states, which exhibit the maximum amount of bipartite entanglement for all bipartitions, only exist for systems containing n=2 or 3 modes. We further numerically investigate the structure of these states and their frustration for n≤7 .
Gaussian maximally multipartite-entangled states
International Nuclear Information System (INIS)
Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio; Lupo, Cosmo; Mancini, Stefano
2009-01-01
We study maximally multipartite-entangled states in the context of Gaussian continuous variable quantum systems. By considering multimode Gaussian states with constrained energy, we show that perfect maximally multipartite-entangled states, which exhibit the maximum amount of bipartite entanglement for all bipartitions, only exist for systems containing n=2 or 3 modes. We further numerically investigate the structure of these states and their frustration for n≤7.
Non-Gaussian halo assembly bias
International Nuclear Information System (INIS)
Reid, Beth A.; Verde, Licia; Dolag, Klaus; Matarrese, Sabino; Moscardini, Lauro
2010-01-01
The strong dependence of the large-scale dark matter halo bias on the (local) non-Gaussianity parameter, f 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
Adaptive Laguerre-Gaussian variant of the Gaussian beam expansion method.
Cagniot, Emmanuel; Fromager, Michael; Ait-Ameur, Kamel
2009-11-01
A variant of the Gaussian beam expansion method consists in expanding the Bessel function J0 appearing in the Fresnel-Kirchhoff integral into a finite sum of complex Gaussian functions to derive an analytical expression for a Laguerre-Gaussian beam diffracted through a hard-edge aperture. However, the validity range of the approximation depends on the number of expansion coefficients that are obtained by optimization-computation directly. We propose another solution consisting in expanding J0 onto a set of collimated Laguerre-Gaussian functions whose waist depends on their number and then, depending on its argument, predicting the suitable number of expansion functions to calculate the integral recursively.
Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations
DEFF Research Database (Denmark)
Nam, Phan Thanh; Napiorkowski, Marcin; Solovej, Jan Philip
2016-01-01
We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our...
ON WEIGHTED GENERALIZED FUNCTIONS ASSOCIATED WITH QUADRATIC FORMS
Directory of Open Access Journals (Sweden)
E. L. Shishkina
2016-12-01
Full Text Available In this article we consider certain types of weighted generalized functions associated with nondegenerate quadratic forms. Such functions and their derivatives are used for constructing fundamental solutions of iterated ultra-hyperbolic equations with the Bessel operator and for constructing negative real powers of ultra-hyperbolic operators with the Bessel operator.
Feedback nash equilibria for linear quadratic descriptor differential games
Engwerda, J.C.; Salmah, S.
2012-01-01
In this paper, we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon for descriptor systems of index one. The performance function is assumed to be indefinite. We derive both necessary and sufficient conditions under which this game has a
Initial post dynamic buckling of a quadratic-cubic column ...
African Journals Online (AJOL)
In this investigation, we determine the dynamic buckling load of an imperfect finite column resting on a mixed quadratic-cubic nonlinear elastic foundation trapped by an explicitly time dependent sinusoidally slowly varying dynamic load .The resultant coefficients are dynamically slowly varying and the formulation contains ...
Quadratic algebras in the noncommutative integration method of wave equation
International Nuclear Information System (INIS)
Varaksin, O.L.
1995-01-01
The paper deals with the investigation of applications of the method of noncommutative integration of linear differential equations by partial derivatives. Nontrivial example was taken for integration of three-dimensions wave equation with the use of non-Abelian quadratic algebras
Propagator of a time-dependent unbound quadratic Hamiltonian system
International Nuclear Information System (INIS)
Yeon, K.H.; Kim, H.J.; Um, C.I.; George, T.F.; Pandey, L.N.
1996-01-01
The propagator for a time-dependent unbound quadratic Hamiltonian system is explicitly evaluated using the path integral method. Two time-invariant quantities of the system are found where these invariants determine whether or not the system is bound. Several examples are considered to illustrate that the propagator obtained for the unbound systems is correct
On Fredholm-Stieltjes quadratic integral equation with supremum
International Nuclear Information System (INIS)
Darwish, M.A.
2007-08-01
We prove an existence theorem of monotonic solutions for a quadratic integral equation of Fredholm-Stieltjes type in C[0,1]. The concept of measure of non-compactness and a fixed point theorem due to Darbo are the main tools in carrying out our proof. (author)
Pareto optimality in infinite horizon linear quadratic differential games
Reddy, P.V.; Engwerda, J.C.
2013-01-01
In this article we derive conditions for the existence of Pareto optimal solutions for linear quadratic infinite horizon cooperative differential games. First, we present a necessary and sufficient characterization for Pareto optimality which translates to solving a set of constrained optimal
Special cases of the quadratic shortest path problem
Sotirov, Renata; Hu, Hao
2017-01-01
The quadratic shortest path problem (QSPP) is the problem of finding a path with prespecified start vertex s and end vertex t in a digraph such that the sum of weights of arcs and the sum of interaction costs over all pairs of arcs on the path is minimized. We first consider a variant of the QSPP
Quadratic Poisson brackets compatible with an algebra structure
Balinsky, A. A.; Burman, Yu.
1994-01-01
Quadratic Poisson brackets on a vector space equipped with a bilinear multiplication are studied. A notion of a bracket compatible with the multiplication is introduced and an effective criterion of such compatibility is given. Among compatible brackets, a subclass of coboundary brackets is described, and such brackets are enumerated in a number of examples.
On misclassication probabilities of linear and quadratic classiers ...
African Journals Online (AJOL)
We study the theoretical misclassication probability of linear and quadratic classiers and examine the performance of these classiers under distributional variations in theory and using simulation. We derive expression for Bayes errors for some competing distributions from the same family under location shift. Keywords: ...
Feedback Nash Equilibria for Linear Quadratic Descriptor Differential Games
Engwerda, J.C.; Salmah, Y.
2010-01-01
In this note we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon for descriptor systems of index one. The performance function is assumed to be indefinite. We derive both necessary and sufficient conditions under which this game has a
A Unified Approach to Teaching Quadratic and Cubic Equations.
Ward, A. J. B.
2003-01-01
Presents a simple method for teaching the algebraic solution of cubic equations via completion of the cube. Shows that this method is readily accepted by students already familiar with completion of the square as a method for quadratic equations. (Author/KHR)
Analysis of Quadratic Diophantine Equations with Fibonacci Number Solutions
Leyendekkers, J. V.; Shannon, A. G.
2004-01-01
An analysis is made of the role of Fibonacci numbers in some quadratic Diophantine equations. A general solution is obtained for finding factors in sums of Fibonacci numbers. Interpretation of the results is facilitated by the use of a modular ring which also permits extension of the analysis.
Visualising the Complex Roots of Quadratic Equations with Real Coefficients
Bardell, Nicholas S.
2012-01-01
The roots of the general quadratic equation y = ax[superscript 2] + bx + c (real a, b, c) are known to occur in the following sets: (i) real and distinct; (ii) real and coincident; and (iii) a complex conjugate pair. Case (iii), which provides the focus for this investigation, can only occur when the values of the real coefficients a, b, and c are…
Nonlocal description of X waves in quadratic nonlinear materials
DEFF Research Database (Denmark)
Larsen, Peter Ulrik Vingaard; Sørensen, Mads Peter; Bang, Ole
2006-01-01
We study localized light bullets and X-waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multi-dimensional nonlinear waves. For X-waves we show that a local cascading limit in terms of a nonlinear Schrodinger equation...
Linear and quadratic in temperature resistivity from holography
Energy Technology Data Exchange (ETDEWEB)
Ge, Xian-Hui [Department of Physics, Shanghai University, Shanghai 200444 (China); Shanghai Key Laboratory of High Temperature Superconductors,Shanghai 200444 (China); Shanghai Key Lab for Astrophysics,100 Guilin Road, 200234 Shanghai (China); Tian, Yu [School of Physics, University of Chinese Academy of Sciences,Beijing, 100049 (China); Shanghai Key Laboratory of High Temperature Superconductors,Shanghai 200444 (China); Wu, Shang-Yu [Department of Electrophysics, National Chiao Tung University,Hsinchu 300 (China); Wu, Shao-Feng [Department of Physics, Shanghai University, Shanghai 200444 (China); Shanghai Key Laboratory of High Temperature Superconductors,Shanghai 200444 (China); Shanghai Key Lab for Astrophysics,100 Guilin Road, 200234 Shanghai (China)
2016-11-22
We present a new black hole solution in the asymptotic Lifshitz spacetime with a hyperscaling violating factor. A novel computational method is introduced to compute the DC thermoelectric conductivities analytically. We find that both the linear-T and quadratic-T contributions to the resistivity can be realized, indicating that a more detailed comparison with experimental phenomenology can be performed in this scenario.
A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces
Energy Technology Data Exchange (ETDEWEB)
Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at [University of Innsbruck, Department of Mathematics (Austria); Tuffaha, Amjad, E-mail: atufaha@aus.edu [American University of Sharjah, Department of Mathematics (United Arab Emirates)
2017-06-15
We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solution of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.
Nonlinear and non-Gaussian Bayesian based handwriting beautification
Shi, Cao; Xiao, Jianguo; Xu, Canhui; Jia, Wenhua
2013-03-01
A framework is proposed in this paper to effectively and efficiently beautify handwriting by means of a novel nonlinear and non-Gaussian Bayesian algorithm. In the proposed framework, format and size of handwriting image are firstly normalized, and then typeface in computer system is applied to optimize vision effect of handwriting. The Bayesian statistics is exploited to characterize the handwriting beautification process as a Bayesian dynamic model. The model parameters to translate, rotate and scale typeface in computer system are controlled by state equation, and the matching optimization between handwriting and transformed typeface is employed by measurement equation. Finally, the new typeface, which is transformed from the original one and gains the best nonlinear and non-Gaussian optimization, is the beautification result of handwriting. Experimental results demonstrate the proposed framework provides a creative handwriting beautification methodology to improve visual acceptance.
Predictive Active Set Selection Methods for Gaussian Processes
DEFF Research Database (Denmark)
Henao, Ricardo; Winther, Ole
2012-01-01
We propose an active set selection framework for Gaussian process classification for cases when the dataset is large enough to render its inference prohibitive. Our scheme consists of a two step alternating procedure of active set update rules and hyperparameter optimization based upon marginal...... high impact to the classifier decision process while removing those that are less relevant. We introduce two active set rules based on different criteria, the first one prefers a model with interpretable active set parameters whereas the second puts computational complexity first, thus a model...... with active set parameters that directly control its complexity. We also provide both theoretical and empirical support for our active set selection strategy being a good approximation of a full Gaussian process classifier. Our extensive experiments show that our approach can compete with state...
New gaussian points for the solution of first order ordinary ...
African Journals Online (AJOL)
Numerical experiments carried out using the new Gaussian points revealed there efficiency on stiff differential equations. The results also reveal that methods using the new Gaussian points are more accurate than those using the standard Gaussian points on non-stiff initial value problems. Keywords: Gaussian points ...
International Nuclear Information System (INIS)
Poon, Phoenix S. Y.; Law, C. K.
2007-01-01
We show that the negativity of a general two-mode Gaussian state can be explicitly expressed in terms of an optimal uncertainty product in position-momentum space. Such an uncertainty product is shown to have the greatest violation of a separability criterion based on positive partial transposition. Our analytic formula indicates the observables determining the negativity. For asymmetric Gaussian states, we show that the negativity is controlled by an asymmetric parameter which sets an upper bound for the negativity
Modelling and control of a flotation process
International Nuclear Information System (INIS)
Ding, L.; Gustafsson, T.
1999-01-01
A general description of a flotation process is given. The dynamic model of a MIMO nonlinear subprocess in flotation, i. e. the pulp levels in five compartments in series is developed and the model is verified with real data from a production plant. In order to reject constant disturbances five extra states are introduced and the model is modified. An exact linearization has been made for the non-linear model and a linear quadratic gaussian controller is proposed based on the linearized model. The simulation result shows an improved performance of the pulp level control when the set points are changed or a disturbance occur. In future the controller will be tested in production. (author)
DEFF Research Database (Denmark)
Bennedsen, Mikkel
Using theory on (conditionally) Gaussian processes with stationary increments developed in Barndorff-Nielsen et al. (2009, 2011), this paper presents a general semiparametric approach to conducting inference on the fractal index, α, of a time series. Our setup encompasses a large class of Gaussian...
Huo, Xiaoming; Elad, Michael; Flesia, Ana G.; Muise, Robert R.; Stanfill, S. Robert; Friedman, Jerome; Popescu, Bogdan; Chen, Jihong; Mahalanobis, Abhijit; Donoho, David L.
2003-09-01
In target recognition applications of discriminant of classification analysis, each 'feature' is a result of a convolution of an imagery with a filter, which may be derived from a feature vector. It is important to use relatively few features. We analyze an optimal reduced-rank classifier under the two-class situation. Assuming each population is Gaussian and has zero mean, and the classes differ through the covariance matrices: ∑1 and ∑2. The following matrix is considered: Λ=(∑1+∑2)-1/2∑1(∑1+∑2)-1/2. We show that the k eigenvectors of this matrix whose eigenvalues are most different from 1/2 offer the best rank k approximation to the maximum likelihood classifier. The matrix Λ and its eigenvectors have been introduced by Fukunaga and Koontz; hence this analysis gives a new interpretation of the well known Fukunaga-Koontz transform. The optimality that is promised in this method hold if the two populations are exactly Guassian with the same means. To check the applicability of this approach to real data, an experiment is performed, in which several 'modern' classifiers were used on an Infrared ATR data. In these experiments, a reduced-rank classifier-Tuned Basis Functions-outperforms others. The competitive performance of the optimal reduced-rank quadratic classifier suggests that, at least for classification purposes, the imagery data behaves in a nearly-Gaussian fashion.
Graphical calculus for Gaussian pure states
International Nuclear Information System (INIS)
Menicucci, Nicolas C.; Flammia, Steven T.; Loock, Peter van
2011-01-01
We provide a unified graphical calculus for all Gaussian pure states, including graph transformation rules for all local and semilocal Gaussian unitary operations, as well as local quadrature measurements. We then use this graphical calculus to analyze continuous-variable (CV) cluster states, the essential resource for one-way quantum computing with CV systems. Current graphical approaches to CV cluster states are only valid in the unphysical limit of infinite squeezing, and the associated graph transformation rules only apply when the initial and final states are of this form. Our formalism applies to all Gaussian pure states and subsumes these rules in a natural way. In addition, the term 'CV graph state' currently has several inequivalent definitions in use. Using this formalism we provide a single unifying definition that encompasses all of them. We provide many examples of how the formalism may be used in the context of CV cluster states: defining the 'closest' CV cluster state to a given Gaussian pure state and quantifying the error in the approximation due to finite squeezing; analyzing the optimality of certain methods of generating CV cluster states; drawing connections between this graphical formalism and bosonic Hamiltonians with Gaussian ground states, including those useful for CV one-way quantum computing; and deriving a graphical measure of bipartite entanglement for certain classes of CV cluster states. We mention other possible applications of this formalism and conclude with a brief note on fault tolerance in CV one-way quantum computing.
Variational Gaussian approximation for Poisson data
Arridge, Simon R.; Ito, Kazufumi; Jin, Bangti; Zhang, Chen
2018-02-01
The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.
Mode entanglement of Gaussian fermionic states
Spee, C.; Schwaiger, K.; Giedke, G.; Kraus, B.
2018-04-01
We investigate the entanglement of n -mode n -partite Gaussian fermionic states (GFS). First, we identify a reasonable definition of separability for GFS and derive a standard form for mixed states, to which any state can be mapped via Gaussian local unitaries (GLU). As the standard form is unique, two GFS are equivalent under GLU if and only if their standard forms coincide. Then, we investigate the important class of local operations assisted by classical communication (LOCC). These are central in entanglement theory as they allow one to partially order the entanglement contained in states. We show, however, that there are no nontrivial Gaussian LOCC (GLOCC) among pure n -partite (fully entangled) states. That is, any such GLOCC transformation can also be accomplished via GLU. To obtain further insight into the entanglement properties of such GFS, we investigate the richer class of Gaussian stochastic local operations assisted by classical communication (SLOCC). We characterize Gaussian SLOCC classes of pure n -mode n -partite states and derive them explicitly for few-mode states. Furthermore, we consider certain fermionic LOCC and show how to identify the maximally entangled set of pure n -mode n -partite GFS, i.e., the minimal set of states having the property that any other state can be obtained from one state inside this set via fermionic LOCC. We generalize these findings also to the pure m -mode n -partite (for m >n ) case.
Productive interactions: heavy particles and non-Gaussianity
International Nuclear Information System (INIS)
Flauger, Raphael; Mirbabayi, Mehrdad; Senatore, Leonardo; Silverstein, Eva
2017-01-01
We analyze the shape and amplitude of oscillatory features in the primordial power spectrum and non-Gaussianity induced by periodic production of heavy degrees of freedom coupled to the inflaton φ. We find that non-adiabatic production of particles can contribute effects which are detectable or constrainable using cosmological data even if their time-dependent masses are always heavier than the scale φ̇ 1/2 , much larger than the Hubble scale. This provides a new role for UV completion, consistent with the criteria from effective field theory for when heavy fields cannot be integrated out. This analysis is motivated in part by the structure of axion monodromy, and leads to an additional oscillatory signature in a subset of its parameter space. At the level of a quantum field theory model that we analyze in detail, the effect arises consistently with radiative stability for an interesting window of couplings up to of order ∼< 1. The amplitude of the bispectrum and higher-point functions can be larger than that for Resonant Non-Gaussianity, and its signal/noise may be comparable to that of the corresponding oscillations in the power spectrum (and even somewhat larger within a controlled regime of parameters). Its shape is distinct from previously analyzed templates, but was partly motivated by the oscillatory equilateral searches performed recently by the Planck collaboration. We also make some general comments about the challenges involved in making a systematic study of primordial non-Gaussianity.
Productive interactions: heavy particles and non-Gaussianity
Energy Technology Data Exchange (ETDEWEB)
Flauger, Raphael [Department of Physics, The University of Texas at Austin, Austin, TX, 78712 (United States); Mirbabayi, Mehrdad [Institute for Advanced Study, Princeton, NJ 08540 (United States); Senatore, Leonardo; Silverstein, Eva, E-mail: flauger@physics.ucsd.edu, E-mail: mehrdadm@ias.edu, E-mail: senatore@stanford.edu, E-mail: evas@slac.stanford.edu [Stanford Institute for Theoretical Physics, Stanford University, Stanford, CA 94305 (United States)
2017-10-01
We analyze the shape and amplitude of oscillatory features in the primordial power spectrum and non-Gaussianity induced by periodic production of heavy degrees of freedom coupled to the inflaton φ. We find that non-adiabatic production of particles can contribute effects which are detectable or constrainable using cosmological data even if their time-dependent masses are always heavier than the scale φ̇{sup 1/2}, much larger than the Hubble scale. This provides a new role for UV completion, consistent with the criteria from effective field theory for when heavy fields cannot be integrated out. This analysis is motivated in part by the structure of axion monodromy, and leads to an additional oscillatory signature in a subset of its parameter space. At the level of a quantum field theory model that we analyze in detail, the effect arises consistently with radiative stability for an interesting window of couplings up to of order ∼< 1. The amplitude of the bispectrum and higher-point functions can be larger than that for Resonant Non-Gaussianity, and its signal/noise may be comparable to that of the corresponding oscillations in the power spectrum (and even somewhat larger within a controlled regime of parameters). Its shape is distinct from previously analyzed templates, but was partly motivated by the oscillatory equilateral searches performed recently by the Planck collaboration. We also make some general comments about the challenges involved in making a systematic study of primordial non-Gaussianity.
Transfer of non-Gaussian quantum states of mechanical oscillator to light
Filip, Radim; Rakhubovsky, Andrey A.
2015-11-01
Non-Gaussian quantum states are key resources for quantum optics with continuous-variable oscillators. The non-Gaussian states can be deterministically prepared by a continuous evolution of the mechanical oscillator isolated in a nonlinear potential. We propose feasible and deterministic transfer of non-Gaussian quantum states of mechanical oscillators to a traveling light beam, using purely all-optical methods. The method relies on only basic feasible and high-quality elements of quantum optics: squeezed states of light, linear optics, homodyne detection, and electro-optical feedforward control of light. By this method, a wide range of novel non-Gaussian states of light can be produced in the future from the mechanical states of levitating particles in optical tweezers, including states necessary for the implementation of an important cubic phase gate.
Khan, Tariq Mahmood; Bailey, Donald G; Khan, Mohammad A U; Kong, Yinan
2017-05-01
A real-time image filtering technique is proposed which could result in faster implementation for fingerprint image enhancement. One major hurdle associated with fingerprint filtering techniques is the expensive nature of their hardware implementations. To circumvent this, a modified anisotropic Gaussian filter is efficiently adopted in hardware by decomposing the filter into two orthogonal Gaussians and an oriented line Gaussian. An architecture is developed for dynamically controlling the orientation of the line Gaussian filter. To further improve the performance of the filter, the input image is homogenized by a local image normalization. In the proposed structure, for a middle-range reconfigurable FPGA, both parallel compute-intensive and real-time demands were achieved. We manage to efficiently speed up the image-processing time and improve the resource utilization of the FPGA. Test results show an improved speed for its hardware architecture while maintaining reasonable enhancement benchmarks.
The cyclicity of period annulus of a quadratic reversible Lotka–Volterra system
International Nuclear Information System (INIS)
Li, Chengzhi; Llibre, Jaume
2009-01-01
We prove that by perturbing the periodic annulus of the quadratic polynomial reversible Lotka–Volterra differential system, inside the class of all quadratic polynomial differential systems we can obtain at most two limit cycles
International Nuclear Information System (INIS)
Desjacques, Vincent; Jeong, Donghui; Schmidt, Fabian
2011-01-01
Recent results of N-body simulations have shown that current theoretical models are not able to correctly predict the amplitude of the scale-dependent halo bias induced by primordial non-Gaussianity, for models going beyond the simplest, local quadratic case. Motivated by these discrepancies, we carefully examine three theoretical approaches based on (1) the statistics of thresholded regions, (2) a peak-background split method based on separation of scales, and (3) a peak-background split method using the conditional mass function. We first demonstrate that the statistics of thresholded regions, which is shown to be equivalent at leading order to a local bias expansion, cannot explain the mass-dependent deviation between theory and N-body simulations. In the two formulations of the peak-background split on the other hand, we identify an important, but previously overlooked, correction to the non-Gaussian bias that strongly depends on halo mass. This new term is in general significant for any primordial non-Gaussianity going beyond the simplest local f NL model. In a separate paper (to be published in PRD rapid communication), the authors compare these new theoretical predictions with N-body simulations, showing good agreement for all simulated types of non-Gaussianity.
Chen, Zheng; Mi, Chris Chunting; Xiong, Rui; Xu, Jun; You, Chenwen
2014-02-01
This paper introduces an online and intelligent energy management controller to improve the fuel economy of a power-split plug-in hybrid electric vehicle (PHEV). Based on analytic analysis between fuel-rate and battery current at different driveline power and vehicle speed, quadratic equations are applied to simulate the relationship between battery current and vehicle fuel-rate. The power threshold at which engine is turned on is optimized by genetic algorithm (GA) based on vehicle fuel-rate, battery state of charge (SOC) and driveline power demand. The optimal battery current when the engine is on is calculated using quadratic programming (QP) method. The proposed algorithm can control the battery current effectively, which makes the engine work more efficiently and thus reduce the fuel-consumption. Moreover, the controller is still applicable when the battery is unhealthy. Numerical simulations validated the feasibility of the proposed controller.
New results for time reversed symplectic dynamic systems and quadratic functionals
Directory of Open Access Journals (Sweden)
Roman Simon Hilscher
2012-05-01
Full Text Available In this paper, we examine time scale symplectic (or Hamiltonian systems and the associated quadratic functionals which contain a forward shift in the time variable. Such systems and functionals have a close connection to Jacobi systems for calculus of variations and optimal control problems on time scales. Our results, among which we consider the Reid roundabout theorem, generalize the corresponding classical theory for time reversed discrete symplectic systems, as well as they complete the recently developed theory of time scale symplectic systems.
Vaidyanathan, S.; Sambas, A.; Sukono; Mamat, M.; Gundara, G.; Mada Sanjaya, W. S.; Subiyanto
2018-03-01
A 3-D new chaotic attractor with two quadratic nonlinearities is proposed in this paper. The dynamical properties of the new chaotic system are described in terms of phase portraits, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, etc. We show that the new chaotic system has three unstable equilibrium points. The new chaotic attractor is dissipative in nature. As an engineering application, adaptive synchronization of identical new chaotic attractors is designed via nonlinear control and Lyapunov stability theory. Furthermore, an electronic circuit realization of the new chaotic attractor is presented in detail to confirm the feasibility of the theoretical chaotic attractor model.
Projection of curves on B-spline surfaces using quadratic reparameterization
Yang, Yijun
2010-09-01
Curves on surfaces play an important role in computer aided geometric design. In this paper, we present a hyperbola approximation method based on the quadratic reparameterization of Bézier surfaces, which generates reasonable low degree curves lying completely on the surfaces by using iso-parameter curves of the reparameterized surfaces. The Hausdorff distance between the projected curve and the original curve is controlled under the user-specified distance tolerance. The projected curve is T-G 1 continuous, where T is the user-specified angle tolerance. Examples are given to show the performance of our algorithm. © 2010 Elsevier Inc. All rights reserved.
Non-Gaussianity in island cosmology
International Nuclear Information System (INIS)
Piao Yunsong
2009-01-01
In this paper we fully calculate the non-Gaussianity of primordial curvature perturbation of the island universe by using the second order perturbation equation. We find that for the spectral index n s ≅0.96, which is favored by current observations, the non-Gaussianity level f NL seen in an island will generally lie between 30 and 60, which may be tested by the coming observations. In the landscape, the island universe is one of anthropically acceptable cosmological histories. Thus the results obtained in some sense mean the coming observations, especially the measurement of non-Gaussianity, will be significant to clarify how our position in the landscape is populated.
Entanglement negativity bounds for fermionic Gaussian states
Eisert, Jens; Eisler, Viktor; Zimborás, Zoltán
2018-04-01
The entanglement negativity is a versatile measure of entanglement that has numerous applications in quantum information and in condensed matter theory. It can not only efficiently be computed in the Hilbert space dimension, but for noninteracting bosonic systems, one can compute the negativity efficiently in the number of modes. However, such an efficient computation does not carry over to the fermionic realm, the ultimate reason for this being that the partial transpose of a fermionic Gaussian state is no longer Gaussian. To provide a remedy for this state of affairs, in this work, we introduce efficiently computable and rigorous upper and lower bounds to the negativity, making use of techniques of semidefinite programming, building upon the Lagrangian formulation of fermionic linear optics, and exploiting suitable products of Gaussian operators. We discuss examples in quantum many-body theory and hint at applications in the study of topological properties at finite temperature.
Induced motion of domain walls in multiferroics with quadratic interaction
Energy Technology Data Exchange (ETDEWEB)
Gerasimchuk, Victor S., E-mail: viktor.gera@gmail.com [National Technical University of Ukraine “Kyiv Polytechnic Institute”, Peremohy Avenue 37, 03056 Kiev (Ukraine); Shitov, Anatoliy A., E-mail: shitov@mail.ru [Donbass National Academy of Civil Engineering, Derzhavina Street 2, 86123 Makeevka, Donetsk Region (Ukraine)
2013-10-15
We theoretically study the dynamics of 180-degree domain wall of the ab-type in magnetic materials with quadratic magnetoelectric interaction in external alternating magnetic and electric fields. The features of the oscillatory and translational motions of the domain walls and stripe structures depending on the parameters of external fields and characteristics of the multiferroics are discussed. The possibility of the domain walls drift in a purely electric field is established. - Highlights: • We study DW and stripe DS in multiferroics with quadratic magnetoelectric interaction. • We build up the theory of oscillatory and translational (drift) DW and DS motion. • DW motion can be caused by crossed alternating electric and magnetic fields. • DW motion can be caused by alternating “pure” electric field. • DW drift velocity is formed by the AFM and Dzyaloshinskii interaction terms.
Symmetric coupling of angular momenta, quadratic algebras and discrete polynomials
International Nuclear Information System (INIS)
Aquilanti, V; Marinelli, D; Marzuoli, A
2014-01-01
Eigenvalues and eigenfunctions of the volume operator, associated with the symmetric coupling of three SU(2) angular momentum operators, can be analyzed on the basis of a discrete Schrödinger–like equation which provides a semiclassical Hamiltonian picture of the evolution of a 'quantum of space', as shown by the authors in [1]. Emphasis is given here to the formalization in terms of a quadratic symmetry algebra and its automorphism group. This view is related to the Askey scheme, the hierarchical structure which includes all hypergeometric polynomials of one (discrete or continuous) variable. Key tool for this comparative analysis is the duality operation defined on the generators of the quadratic algebra and suitably extended to the various families of overlap functions (generalized recoupling coefficients). These families, recognized as lying at the top level of the Askey scheme, are classified and a few limiting cases are addressed
Quadratic grating apodized photon sieves for simultaneous multiplane microscopy
Cheng, Yiguang; Zhu, Jiangping; He, Yu; Tang, Yan; Hu, Song; Zhao, Lixin
2017-10-01
We present a new type of imaging device, named quadratic grating apodized photon sieve (QGPS), used as the objective for simultaneous multiplane imaging in X-rays. The proposed QGPS is structured based on the combination of two concepts: photon sieves and quadratic gratings. Its design principles are also expounded in detail. Analysis of imaging properties of QGPS in terms of point-spread function shows that QGPS can image multiple layers within an object field onto a single image plane. Simulated and experimental results in visible light both demonstrate the feasibility of QGPS for simultaneous multiplane imaging, which is extremely promising to detect dynamic specimens by X-ray microscopy in the physical and life sciences.
QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.
Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit
2014-01-01
We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n -gon, our construction produces 2 n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n ( n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called 'serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed.
Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality
Acikmese, Ahmet Behcet; Corless, Martin
2004-01-01
We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.
Information sets as permutation cycles for quadratic residue codes
Directory of Open Access Journals (Sweden)
Richard A. Jenson
1982-01-01
Full Text Available The two cases p=7 and p=23 are the only known cases where the automorphism group of the [p+1, (p+1/2] extended binary quadratic residue code, O(p, properly contains PSL(2,p. These codes have some of their information sets represented as permutation cycles from Aut(Q(p. Analysis proves that all information sets of Q(7 are so represented but those of Q(23 are not.
Stationary walking solitons in bulk quadratic nonlinear media
Mihalache, Dumitru; Mazilu, D; Crasonavn, L C; Torner Sabata, Lluís
1997-01-01
We study the mutual trapping of fundamental and second-harmonic light beams propagating in bulk quadratic nonlinear media in the presence of Poynting vector beam walk-off. We show numerically the existence of a two-parameter family of (2 + 1)-dimensional stationary, spatial walking solitons. We have found that the solitons exist at various values of material parameters with different wave intensities and soliton velocities. We discuss the differences between (2 + 1) and (1 + 1)-dimensional wa...
Bifurcation in Z2-symmetry quadratic polynomial systems with delay
International Nuclear Information System (INIS)
Zhang Chunrui; Zheng Baodong
2009-01-01
Z 2 -symmetry systems are considered. Firstly the general forms of Z 2 -symmetry quadratic polynomial system are given, and then a three-dimensional Z 2 equivariant system is considered, which describes the relations of two predator species for a single prey species. Finally, the explicit formulas for determining the Fold and Hopf bifurcations are obtained by using the normal form theory and center manifold argument.
A Note on 5-bit Quadratic Permutations’ Classification
Božilov, Dušan; Bilgin, Begül; Sahin, Hacı Ali
2017-01-01
Classification of vectorial Boolean functions up to affine equivalence is used widely to analyze various cryptographic and implementation properties of symmetric-key algorithms. We show that there exist 75 affine equivalence classes of 5-bit quadratic permutations. Furthermore, we explore important cryptographic properties of these classes, such as linear and differential properties and degrees of their inverses, together with multiplicative complexity and existence of uniform threshold reali...
Integrable systems with quadratic nonlinearity in Fourier space
International Nuclear Information System (INIS)
Marikhin, V.G.
2003-01-01
The Lax pair representation in Fourier space is used to obtain a list of integrable scalar evolutionary equations with quadratic nonlinearity. The known systems of this type such as KdV, intermediate long-wave equation (ILW), Camassa-Holm and Degasperis-Procesi systems are represented in this list. Some new systems are obtained as well. Two-dimensional and discrete generalizations are discussed
Complex eigenvalues for neutron transport equation with quadratically anisotropic scattering
International Nuclear Information System (INIS)
Sjoestrand, N.G.
1981-01-01
Complex eigenvalues for the monoenergetic neutron transport equation in the buckling approximation have been calculated for various combinations of linearly and quadratically anisotropic scattering. The results are discussed in terms of the time-dependent case. Tables are given of complex bucklings for real decay constants and of complex decay constants for real bucklings. The results fit nicely into the pattern of real and purely imaginary eigenvalues obtained earlier. (author)
Invariant measures on multimode quantum Gaussian states
Lupo, C.; Mancini, S.; De Pasquale, A.; Facchi, P.; Florio, G.; Pascazio, S.
2012-12-01
We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom—the symplectic eigenvalues—which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.
Invariant measures on multimode quantum Gaussian states
International Nuclear Information System (INIS)
Lupo, C.; Mancini, S.; De Pasquale, A.; Facchi, P.; Florio, G.; Pascazio, S.
2012-01-01
We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom—the symplectic eigenvalues—which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.
Invariant measures on multimode quantum Gaussian states
Energy Technology Data Exchange (ETDEWEB)
Lupo, C. [School of Science and Technology, Universita di Camerino, I-62032 Camerino (Italy); Mancini, S. [School of Science and Technology, Universita di Camerino, I-62032 Camerino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, I-06123 Perugia (Italy); De Pasquale, A. [NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa (Italy); Facchi, P. [Dipartimento di Matematica and MECENAS, Universita di Bari, I-70125 Bari (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Florio, G. [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi, Piazza del Viminale 1, I-00184 Roma (Italy); Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy); Pascazio, S. [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy)
2012-12-15
We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom-the symplectic eigenvalues-which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.
Construction of Capacity Achieving Lattice Gaussian Codes
Alghamdi, Wael
2016-04-01
We propose a new approach to proving results regarding channel coding schemes based on construction-A lattices for the Additive White Gaussian Noise (AWGN) channel that yields new characterizations of the code construction parameters, i.e., the primes and dimensions of the codes, as functions of the block-length. The approach we take introduces an averaging argument that explicitly involves the considered parameters. This averaging argument is applied to a generalized Loeliger ensemble [1] to provide a more practical proof of the existence of AWGN-good lattices, and to characterize suitable parameters for the lattice Gaussian coding scheme proposed by Ling and Belfiore [3].
Gaussian processes and constructive scalar field theory
International Nuclear Information System (INIS)
Benfatto, G.; Nicolo, F.
1981-01-01
The last years have seen a very deep progress of constructive euclidean field theory, with many implications in the area of the random fields theory. The authors discuss an approach to super-renormalizable scalar field theories, which puts in particular evidence the connections with the theory of the Gaussian processes associated to the elliptic operators. The paper consists of two parts. Part I treats some problems in the theory of Gaussian processes which arise in the approach to the PHI 3 4 theory. Part II is devoted to the discussion of the ultraviolet stability in the PHI 3 4 theory. (Auth.)
Integration of non-Gaussian fields
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager; Mohr, Gunnar; Hoffmeyer, Pernille
1996-01-01
The limitations of the validity of the central limit theorem argument as applied to definite integrals of non-Gaussian random fields are empirically explored by way of examples. The purpose is to investigate in specific cases whether the asymptotic convergence to the Gaussian distribution is fast....... and Randrup-Thomsen, S. Reliability of silo ring under lognormal stochastic pressure using stochastic interpolation. Proc. IUTAM Symp., Probabilistic Structural Mechanics: Advances in Structural Reliability Methods, San Antonio, TX, USA, June 1993 (eds.: P. D. Spanos & Y.-T. Wu) pp. 134-162. Springer, Berlin...
Quantum information theory with Gaussian systems
Energy Technology Data Exchange (ETDEWEB)
Krueger, O.
2006-04-06
This thesis applies ideas and concepts from quantum information theory to systems of continuous-variables such as the quantum harmonic oscillator. The focus is on three topics: the cloning of coherent states, Gaussian quantum cellular automata and Gaussian private channels. Cloning was investigated both for finite-dimensional and for continuous-variable systems. We construct a private quantum channel for the sequential encryption of coherent states with a classical key, where the key elements have finite precision. For the case of independent one-mode input states, we explicitly estimate this precision, i.e. the number of key bits needed per input state, in terms of these parameters. (orig.)
Quantum information theory with Gaussian systems
International Nuclear Information System (INIS)
Krueger, O.
2006-01-01
This thesis applies ideas and concepts from quantum information theory to systems of continuous-variables such as the quantum harmonic oscillator. The focus is on three topics: the cloning of coherent states, Gaussian quantum cellular automata and Gaussian private channels. Cloning was investigated both for finite-dimensional and for continuous-variable systems. We construct a private quantum channel for the sequential encryption of coherent states with a classical key, where the key elements have finite precision. For the case of independent one-mode input states, we explicitly estimate this precision, i.e. the number of key bits needed per input state, in terms of these parameters. (orig.)
Model selection for Gaussian kernel PCA denoising
DEFF Research Database (Denmark)
Jørgensen, Kasper Winther; Hansen, Lars Kai
2012-01-01
We propose kernel Parallel Analysis (kPA) for automatic kernel scale and model order selection in Gaussian kernel PCA. Parallel Analysis [1] is based on a permutation test for covariance and has previously been applied for model order selection in linear PCA, we here augment the procedure to also...... tune the Gaussian kernel scale of radial basis function based kernel PCA.We evaluate kPA for denoising of simulated data and the US Postal data set of handwritten digits. We find that kPA outperforms other heuristics to choose the model order and kernel scale in terms of signal-to-noise ratio (SNR...
General quadratic gauge theory: constraint structure, symmetries and physical functions
Energy Technology Data Exchange (ETDEWEB)
Gitman, D M [Institute of Physics, University of Sao Paulo (Brazil); Tyutin, I V [Lebedev Physics Institute, Moscow (Russian Federation)
2005-06-17
How can we relate the constraint structure and constraint dynamics of the general gauge theory in the Hamiltonian formulation to specific features of the theory in the Lagrangian formulation, especially relate the constraint structure to the gauge transformation structure of the Lagrangian action? How can we construct the general expression for the gauge charge if the constraint structure in the Hamiltonian formulation is known? Whether we can identify the physical functions defined as commuting with first-class constraints in the Hamiltonian formulation and the physical functions defined as gauge invariant functions in the Lagrangian formulation? The aim of the present paper is to consider the general quadratic gauge theory and to answer the above questions for such a theory in terms of strict assertions. To fulfil such a programme, we demonstrate the existence of the so-called superspecial phase-space variables in terms of which the quadratic Hamiltonian action takes a simple canonical form. On the basis of such a representation, we analyse a functional arbitrariness in the solutions of the equations of motion of the quadratic gauge theory and derive the general structure of symmetries by analysing a symmetry equation. We then use these results to identify the two definitions of physical functions and thus prove the Dirac conjecture.
Design of reinforced areas of concrete column using quadratic polynomials
Arif Gunadi, Tjiang; Parung, Herman; Rachman Djamaluddin, Abd; Arwin Amiruddin, A.
2017-11-01
Designing of reinforced concrete columns mostly carried out by a simple planning method which uses column interaction diagram. However, the application of this method is limited because it valids only for certain compressive strenght of the concrete and yield strength of the reinforcement. Thus, a more applicable method is still in need. Another method is the use of quadratic polynomials as a basis for the approach in designing reinforced concrete columns, where the ratio of neutral lines to the effective height of a cross section (ξ) if associated with ξ in the same cross-section with different reinforcement ratios is assumed to form a quadratic polynomial. This is identical to the basic principle used in the Simpson rule for numerical integral using quadratic polynomials and had a sufficiently accurate level of accuracy. The basis of this approach to be used both the normal force equilibrium and the moment equilibrium. The abscissa of the intersection of the two curves is the ratio that had been mentioned, since it fulfill both of the equilibrium. The application of this method is relatively more complicated than the existing method but provided with tables and graphs (N vs ξN ) and (M vs ξM ) so that its used could be simplified. The uniqueness of these tables are only distinguished based on the compresssive strength of the concrete, so in application it could be combined with various yield strenght of the reinforcement available in the market. This method could be solved by using programming languages such as Fortran.
Fast, multiple optimizations of quadratic dose objective functions in IMRT
International Nuclear Information System (INIS)
Breedveld, Sebastiaan; Storchi, Pascal R M; Keijzer, Marleen; Heijmen, Ben J M
2006-01-01
Inverse treatment planning for intensity-modulated radiotherapy may include time consuming, multiple minimizations of an objective function. In this paper, methods are presented to speed up the process of (repeated) minimization of the well-known quadratic dose objective function, extended with a smoothing term that ensures generation of clinically acceptable beam profiles. In between two subsequent optimizations, the voxel-dependent importance factors of the quadratic terms will generally be adjusted, based on an intermediate plan evaluation. The objective function has been written in matrix-vector format, facilitating the use of a recently published, fast quadratic minimization algorithm, instead of commonly applied gradient-based methods. This format also reduces the calculation time in between subsequent minimizations, related to adjustment of the voxel-dependent importance factors. Sparse matrices are used to limit the required amount of computer memory. For three patients, comparisons have been made with a gradient method. Mean speed improvements of up to a factor of 37 have been achieved
Measurement of quadratic electrogyration effect in castor oil
Izdebski, Marek; Ledzion, Rafał; Górski, Piotr
2015-07-01
This work presents a detailed analysis of electrogyration measurement in liquids with the usage of an optical polarimetric technique. Theoretical analysis of the optical response to an applied electric field is illustrated by experimental data for castor oil which exhibits natural optical activity, quadratic electro-optic effect and quadratic electrogyration effect. Moreover, the experimental data show that interaction of the oil with a pair of flat electrodes induces a significant dichroism and natural linear birefringence. The combination of these effects occurring at the same time complicates the procedure of measurements. It has been found that a single measurement is insufficient to separate the contribution of the electrogyration effect, but it is possible on the basis of several measurements performed with various orientations of the polarizer and the analyser. The obtained average values of the quadratic electrogyration coefficient β13 in castor oil at room temperature are from - 0.92 ×10-22 to - 1.44 ×10-22m2V-2 depending on the origin of the oil. Although this study is focused on measurements in castor oil, the presented analysis is much more general.
International Nuclear Information System (INIS)
Ji, Se-Wan; Nha, Hyunchul; Kim, M S
2015-01-01
It is a topic of fundamental and practical importance how a quantum correlated state can be reliably distributed through a noisy channel for quantum information processing. The concept of quantum steering recently defined in a rigorous manner is relevant to study it under certain circumstances and here we address quantum steerability of Gaussian states to this aim. In particular, we attempt to reformulate the criterion for Gaussian steering in terms of local and global purities and show that it is sufficient and necessary for the case of steering a 1-mode system by an N-mode system. It subsequently enables us to reinforce a strong monogamy relation under which only one party can steer a local system of 1-mode. Moreover, we show that only a negative partial-transpose state can manifest quantum steerability by Gaussian measurements in relation to the Peres conjecture. We also discuss our formulation for the case of distributing a two-mode squeezed state via one-way quantum channels making dissipation and amplification effects, respectively. Finally, we extend our approach to include non-Gaussian measurements, more precisely, all orders of higher-order squeezing measurements, and find that this broad set of non-Gaussian measurements is not useful to demonstrate steering for Gaussian states beyond Gaussian measurements. (paper)
Application of IFT and SPSA to servo system control.
Rădac, Mircea-Bogdan; Precup, Radu-Emil; Petriu, Emil M; Preitl, Stefan
2011-12-01
This paper treats the application of two data-based model-free gradient-based stochastic optimization techniques, i.e., iterative feedback tuning (IFT) and simultaneous perturbation stochastic approximation (SPSA), to servo system control. The representative case of controlled processes modeled by second-order systems with an integral component is discussed. New IFT and SPSA algorithms are suggested to tune the parameters of the state feedback controllers with an integrator in the linear-quadratic-Gaussian (LQG) problem formulation. An implementation case study concerning the LQG-based design of an angular position controller for a direct current servo system laboratory equipment is included to highlight the pros and cons of IFT and SPSA from an application's point of view. The comparison of IFT and SPSA algorithms is focused on an insight into their implementation.
Lesmana, E.; Chaerani, D.; Khansa, H. N.
2018-03-01
Energy-Saving Generation Dispatch (ESGD) is a scheme made by Chinese Government in attempt to minimize CO2 emission produced by power plant. This scheme is made related to global warming which is primarily caused by too much CO2 in earth’s atmosphere, and while the need of electricity is something absolute, the power plants producing it are mostly thermal-power plant which produced many CO2. Many approach to fulfill this scheme has been made, one of them came through Minimum Cost Flow in which resulted in a Quadratically Constrained Quadratic Programming (QCQP) form. In this paper, ESGD problem with Minimum Cost Flow in QCQP form will be solved using Lagrange’s Multiplier Method
Evaluation of Gaussian approximations for data assimilation in reservoir models
Iglesias, Marco A.
2013-07-14
implementation of the MCMC method provides the gold standard against which the aforementioned Gaussian approximations are assessed. We present numerical synthetic experiments where we quantify the capability of each of the ad hoc Gaussian approximation in reproducing the mean and the variance of the posterior distribution (characterized via MCMC) associated to a data assimilation problem. Both single-phase and two-phase (oil-water) reservoir models are considered so that fundamental differences in the resulting forward operators are highlighted. The main objective of our controlled experiments was to exhibit the substantial discrepancies of the approximation properties of standard ad hoc Gaussian approximations. Numerical investigations of the type we present here will lead to the greater understanding of the cost-efficient, but ad hoc, Bayesian techniques used for data assimilation in petroleum reservoirs and hence ultimately to improved techniques with more accurate uncertainty quantification. © 2013 Springer Science+Business Media Dordrecht.
Gaussian vector fields on triangulated surfaces
DEFF Research Database (Denmark)
Ipsen, John H
2016-01-01
proven to be very useful to resolve the complex interplay between in-plane ordering of membranes and membrane conformations. In the present work we have developed a procedure for realistic representations of Gaussian models with in-plane vector degrees of freedoms on a triangulated surface. The method...
The Wehrl entropy has Gaussian optimizers
DEFF Research Database (Denmark)
De Palma, Giacomo
2018-01-01
We determine the minimum Wehrl entropy among the quantum states with a given von Neumann entropy and prove that it is achieved by thermal Gaussian states. This result determines the relation between the von Neumann and the Wehrl entropies. The key idea is proving that the quantum-classical channel...
Gaussian shaping filter for nuclear spectrometry
International Nuclear Information System (INIS)
Menezes, A.S.C. de.
1980-01-01
A theorical study of a gaussian shaping filter, using Pade approximation, for using in gamma spectroscopy is presented. This approximation has proved superior to the classical cascade RC integrators approximation in therms of signal-to-noise ratio and pulse simmetry. An experimental filter was designed, simulated in computer, constructed, and tested in the laboratory. (author) [pt
Asymptotic expansions for the Gaussian unitary ensemble
DEFF Research Database (Denmark)
Haagerup, Uffe; Thorbjørnsen, Steen
2012-01-01
Let g : R ¿ C be a C8-function with all derivatives bounded and let trn denote the normalized trace on the n × n matrices. In Ref. 3 Ercolani and McLaughlin established asymptotic expansions of the mean value ¿{trn(g(Xn))} for a rather general class of random matrices Xn, including the Gaussian U...
Gaussian curvature on hyperelliptic Riemann surfaces
Indian Academy of Sciences (India)
Indian Acad. Sci. (Math. Sci.) Vol. 124, No. 2, May 2014, pp. 155–167. c Indian Academy of Sciences. Gaussian curvature on hyperelliptic Riemann surfaces. ABEL CASTORENA. Centro de Ciencias Matemáticas (Universidad Nacional Autónoma de México,. Campus Morelia) Apdo. Postal 61-3 Xangari, C.P. 58089 Morelia,.
Additivity properties of a Gaussian channel
International Nuclear Information System (INIS)
Giovannetti, Vittorio; Lloyd, Seth
2004-01-01
The Amosov-Holevo-Werner conjecture implies the additivity of the minimum Renyi entropies at the output of a channel. The conjecture is proven true for all Renyi entropies of integer order greater than two in a class of Gaussian bosonic channel where the input signal is randomly displaced or where it is coupled linearly to an external environment
Modeling text with generalizable Gaussian mixtures
DEFF Research Database (Denmark)
Hansen, Lars Kai; Sigurdsson, Sigurdur; Kolenda, Thomas
2000-01-01
We apply and discuss generalizable Gaussian mixture (GGM) models for text mining. The model automatically adapts model complexity for a given text representation. We show that the generalizability of these models depends on the dimensionality of the representation and the sample size. We discuss...
Improving the gaussian effective potential: quantum mechanics
International Nuclear Information System (INIS)
Eboli, O.J.P.; Thomaz, M.T.; Lemos, N.A.
1990-08-01
In order to gain intuition for variational problems in field theory, we analyze variationally the quantum-mechanical anharmonic oscillator [(V(x)sup(k) - sub(2) x sup(2) + sup(λ) - sub(4) λ sup(4)]. Special attention is paid to improvements to the Gaussian effective potential. (author)
Open problems in Gaussian fluid queueing theory
Dȩbicki, K.; Mandjes, M.
2011-01-01
We present three challenging open problems that originate from the analysis of the asymptotic behavior of Gaussian fluid queueing models. In particular, we address the problem of characterizing the correlation structure of the stationary buffer content process, the speed of convergence to
Oracle Wiener filtering of a Gaussian signal
Babenko, A.; Belitser, E.
2011-01-01
We study the problem of filtering a Gaussian process whose trajectories, in some sense, have an unknown smoothness ß0 from the white noise of small intensity e. If we knew the parameter ß0, we would use the Wiener filter which has the meaning of oracle. Our goal is now to mimic the oracle, i.e.,
Oracle Wiener filtering of a Gaussian signal
Babenko, A.; Belitser, E.N.
2011-01-01
We study the problem of filtering a Gaussian process whose trajectories, in some sense, have an unknown smoothness β0 from the white noise of small intensity . If we knew the parameter β0, we would use the Wiener filter which has the meaning of oracle. Our goal is now to mimic the oracle, i.e.,
Perfusion Quantification Using Gaussian Process Deconvolution
DEFF Research Database (Denmark)
Andersen, Irene Klærke; Have, Anna Szynkowiak; Rasmussen, Carl Edward
2002-01-01
The quantification of perfusion using dynamic susceptibility contrast MRI (DSC-MRI) requires deconvolution to obtain the residual impulse response function (IRF). In this work, a method using the Gaussian process for deconvolution (GPD) is proposed. The fact that the IRF is smooth is incorporated...
International Nuclear Information System (INIS)
Lopez de la Cruz, J.; Gutierrez, M.A.
2008-01-01
This paper presents a stochastic analysis of spatial point patterns as effect of localized pitting corrosion. The Quadrat Counts method is studied with two empirical pit patterns. The results are dependent on the quadrat size and bias is introduced when empty quadrats are accounted for the analysis. The spatially inhomogeneous Poisson process is used to improve the performance of the Quadrat Counts method. The latter combines Quadrat Counts with distance-based statistics in the analysis of pit patterns. The Inter-Event and the Nearest-Neighbour statistics are here implemented in order to compare their results. Further, the treatment of patterns in irregular domains is discussed
Optimal estimation and scheduling in aquifer management using the rapid feedback control method
Ghorbanidehno, Hojat; Kokkinaki, Amalia; Kitanidis, Peter K.; Darve, Eric
2017-12-01
Management of water resources systems often involves a large number of parameters, as in the case of large, spatially heterogeneous aquifers, and a large number of "noisy" observations, as in the case of pressure observation in wells. Optimizing the operation of such systems requires both searching among many possible solutions and utilizing new information as it becomes available. However, the computational cost of this task increases rapidly with the size of the problem to the extent that textbook optimization methods are practically impossible to apply. In this paper, we present a new computationally efficient technique as a practical alternative for optimally operating large-scale dynamical systems. The proposed method, which we term Rapid Feedback Controller (RFC), provides a practical approach for combined monitoring, parameter estimation, uncertainty quantification, and optimal control for linear and nonlinear systems with a quadratic cost function. For illustration, we consider the case of a weakly nonlinear uncertain dynamical system with a quadratic objective function, specifically a two-dimensional heterogeneous aquifer management problem. To validate our method, we compare our results with the linear quadratic Gaussian (LQG) method, which is the basic approach for feedback control. We show that the computational cost of the RFC scales only linearly with the number of unknowns, a great improvement compared to the basic LQG control with a computational cost that scales quadratically. We demonstrate that the RFC method can obtain the optimal control values at a greatly reduced computational cost compared to the conventional LQG algorithm with small and controllable losses in the accuracy of the state and parameter estimation.
Attitude Control of a Satellite by using Digital Signal Processing
Directory of Open Access Journals (Sweden)
Adirelle C. Santana
2012-03-01
Full Text Available This article has discussed the development of a three-axis attitude digital controller for an artificial satellite using a digital signal processor. The main motivation of this study is the attitude control system of the satellite Multi-Mission Platform, developed by the Brazilian National Institute for Space Research for application in different sort of missions. The controller design was based on the theory of the Linear Quadratic Gaussian Regulator, synthesized from the linearized model of the motion of the satellite, i.e., the kinematics and dynamics of attitude. The attitude actuators considered in this study are pairs of cold gas jets powered by a pulse width/pulse frequency modulator. In the first stage of the project development, a system controller for continuous time was studied with the aim of testing the adequacy of the adopted control. The next steps had included an analysis of discretization techniques, the setting time of sampling rate, and the testing of the digital version of the Linear Quadratic Gaussian Regulator controller in the MATLAB/SIMULINK. To fulfill the study, the controller was implemented in a digital signal processor, specifically the Blackfin BF537 from Analog Devices, along with the pulse width/pulse frequency modulator. The validation tests used a scheme of co-simulation, where the model of the satellite was simulated in MATLAB/SIMULINK, while the controller and modulator were processed in the digital signal processor with a tool called Processor-In-the-Loop, which acted as a data communication link between both environments.function and required time to achieve a given mission accuracy are determined, and results are provided as illustration.
Estimators for local non-Gaussianities
International Nuclear Information System (INIS)
Creminelli, P.; Senatore, L.; Zaldarriaga, M.
2006-05-01
We study the Likelihood function of data given f NL for the so-called local type of non-Gaussianity. In this case the curvature perturbation is a non-linear function, local in real space, of a Gaussian random field. We compute the Cramer-Rao bound for f NL and show that for small values of f NL the 3- point function estimator saturates the bound and is equivalent to calculating the full Likelihood of the data. However, for sufficiently large f NL , the naive 3-point function estimator has a much larger variance than previously thought. In the limit in which the departure from Gaussianity is detected with high confidence, error bars on f NL only decrease as 1/ln N pix rather than N pix -1/2 as the size of the data set increases. We identify the physical origin of this behavior and explain why it only affects the local type of non- Gaussianity, where the contribution of the first multipoles is always relevant. We find a simple improvement to the 3-point function estimator that makes the square root of its variance decrease as N pix -1/2 even for large f NL , asymptotically approaching the Cramer-Rao bound. We show that using the modified estimator is practically equivalent to computing the full Likelihood of f NL given the data. Thus other statistics of the data, such as the 4-point function and Minkowski functionals, contain no additional information on f NL . In particular, we explicitly show that the recent claims about the relevance of the 4-point function are not correct. By direct inspection of the Likelihood, we show that the data do not contain enough information for any statistic to be able to constrain higher order terms in the relation between the Gaussian field and the curvature perturbation, unless these are orders of magnitude larger than the size suggested by the current limits on f NL . (author)
Cosmological information in Gaussianized weak lensing signals
Joachimi, B.; Taylor, A. N.; Kiessling, A.
2011-11-01
Gaussianizing the one-point distribution of the weak gravitational lensing convergence has recently been shown to increase the signal-to-noise ratio contained in two-point statistics. We investigate the information on cosmology that can be extracted from the transformed convergence fields. Employing Box-Cox transformations to determine optimal transformations to Gaussianity, we develop analytical models for the transformed power spectrum, including effects of noise and smoothing. We find that optimized Box-Cox transformations perform substantially better than an offset logarithmic transformation in Gaussianizing the convergence, but both yield very similar results for the signal-to-noise ratio. None of the transformations is capable of eliminating correlations of the power spectra between different angular frequencies, which we demonstrate to have a significant impact on the errors in cosmology. Analytic models of the Gaussianized power spectrum yield good fits to the simulations and produce unbiased parameter estimates in the majority of cases, where the exceptions can be traced back to the limitations in modelling the higher order correlations of the original convergence. In the ideal case, without galaxy shape noise, we find an increase in the cumulative signal-to-noise ratio by a factor of 2.6 for angular frequencies up to ℓ= 1500, and a decrease in the area of the confidence region in the Ωm-σ8 plane, measured in terms of q-values, by a factor of 4.4 for the best performing transformation. When adding a realistic level of shape noise, all transformations perform poorly with little decorrelation of angular frequencies, a maximum increase in signal-to-noise ratio of 34 per cent, and even slightly degraded errors on cosmological parameters. We argue that to find Gaussianizing transformations of practical use, it will be necessary to go beyond transformations of the one-point distribution of the convergence, extend the analysis deeper into the non
Gradient-based adaptation of general gaussian kernels.
Glasmachers, Tobias; Igel, Christian
2005-10-01
Gradient-based optimizing of gaussian kernel functions is considered. The gradient for the adaptation of scaling and rotation of the input space is computed to achieve invariance against linear transformations. This is done by using the exponential map as a parameterization of the kernel parameter manifold. By restricting the optimization to a constant trace subspace, the kernel size can be controlled. This is, for example, useful to prevent overfitting when minimizing radius-margin generalization performance measures. The concepts are demonstrated by training hard margin support vector machines on toy data.
Active vibration control of smart hull structure using piezoelectric composite actuators
International Nuclear Information System (INIS)
Sohn, Jung Woo; Choi, Seung-Bok; Lee, Chul-Hee
2009-01-01
In this paper, active vibration control performance of the smart hull structure with macro-fiber composite (MFC) is evaluated. MFC is an advanced piezoelectric composite which has great flexibility and increased actuating performance compared to a monolithic piezoelectric ceramic patch. The governing equations of motion of the hull structure with MFC actuators are derived based on the classical Donnell–Mushtari shell theory. The actuating model for the interaction between hull structure and MFC is included in the governing equations. Subsequently, modal characteristics are investigated and compared with the results obtained from experiment. The governing equations of the vibration control system are then established and expressed in the state space form. A linear quadratic Gaussian (LQG) control algorithm is designed in order to effectively and actively control the imposed vibration. The controller is experimentally realized and vibration control performances are evaluated
International Nuclear Information System (INIS)
Berkan, R.C.
1990-06-01
After several successful applications to aerospace industry, the modern control theory methods have recently attracted many control engineers from other engineering disciplines. For advanced nuclear reactors, the modern control theory may provide major advantages in safety, availability, and economic aspects. This report is intended to illustrate the feasibility of applying the linear quadratic Gaussian (LQG) compensator in nuclear reactor applications. The LQG design is compared with the existing classical control schemes. Both approaches are tested using the Experimental Breeder Reactor 2 (EBR-2) as the system. The experiments are performed using a mathematical model of the EBR-2 plant. Despite the fact that the controller and plant models do not include all known physical constraints, the results are encouraging. This preliminary study provides an informative, introductory picture for future considerations of using modern control theory methods in nuclear industry. 10 refs., 25 figs
Feedback tracking control for dynamic morphing of piezocomposite actuated flexible wings
Wang, Xiaoming; Zhou, Wenya; Wu, Zhigang
2018-03-01
Aerodynamic properties of flexible wings can be improved via shape morphing using piezocomposite materials. Dynamic shape control of flexible wings is investigated in this study by considering the interactions between structural dynamics, unsteady aerodynamics and piezo-actuations. A novel antisymmetric angle-ply bimorph configuration of piezocomposite actuators is presented to realize coupled bending-torsional shape control. The active aeroelastic model is derived using finite element method and Theodorsen unsteady aerodynamic loads. A time-varying linear quadratic Gaussian (LQG) tracking control system is designed to enhance aerodynamic lift with pre-defined trajectories. Proof-of-concept simulations of static and dynamic shape control are presented for a scaled high-aspect-ratio wing model. Vibrations of the wing and fluctuations in aerodynamic forces are caused by using the static voltages directly in dynamic shape control. The lift response has tracked the trajectories well with favorable dynamic morphing performance via feedback tracking control.
Learning non-Gaussian Time Series using the Box-Cox Gaussian Process
Rios, Gonzalo; Tobar, Felipe
2018-01-01
Gaussian processes (GPs) are Bayesian nonparametric generative models that provide interpretability of hyperparameters, admit closed-form expressions for training and inference, and are able to accurately represent uncertainty. To model general non-Gaussian data with complex correlation structure, GPs can be paired with an expressive covariance kernel and then fed into a nonlinear transformation (or warping). However, overparametrising the kernel and the warping is known to, respectively, hin...
Linear and quadratic models of point process systems: contributions of patterned input to output.
Lindsay, K A; Rosenberg, J R
2012-08-01
In the 1880's Volterra characterised a nonlinear system using a functional series connecting continuous input and continuous output. Norbert Wiener, in the 1940's, circumvented problems associated with the application of Volterra series to physical problems by deriving from it a new series of terms that are mutually uncorrelated with respect to Gaussian processes. Subsequently, Brillinger, in the 1970's, introduced a point-process analogue of Volterra's series connecting point-process inputs to the instantaneous rate of point-process output. We derive here a new series from this analogue in which its terms are mutually uncorrelated with respect to Poisson processes. This new series expresses how patterned input in a spike train, represented by third-order cross-cumulants, is converted into the instantaneous rate of an output point-process. Given experimental records of suitable duration, the contribution of arbitrary patterned input to an output process can, in principle, be determined. Solutions for linear and quadratic point-process models with one and two inputs and a single output are investigated. Our theoretical results are applied to isolated muscle spindle data in which the spike trains from the primary and secondary endings from the same muscle spindle are recorded in response to stimulation of one and then two static fusimotor axons in the absence and presence of a random length change imposed on the parent muscle. For a fixed mean rate of input spikes, the analysis of the experimental data makes explicit which patterns of two input spikes contribute to an output spike. Copyright © 2012 Elsevier Ltd. All rights reserved.
Fast uncertainty reduction strategies relying on Gaussian process models
International Nuclear Information System (INIS)
Chevalier, Clement
2013-01-01
This work deals with sequential and batch-sequential evaluation strategies of real-valued functions under limited evaluation budget, using Gaussian process models. Optimal Stepwise Uncertainty Reduction (SUR) strategies are investigated for two different problems, motivated by real test cases in nuclear safety. First we consider the problem of identifying the excursion set above a given threshold T of a real-valued function f. Then we study the question of finding the set of 'safe controlled configurations', i.e. the set of controlled inputs where the function remains below T, whatever the value of some others non-controlled inputs. New SUR strategies are presented, together with efficient procedures and formulas to compute and use them in real world applications. The use of fast formulas to recalculate quickly the posterior mean or covariance function of a Gaussian process (referred to as the 'kriging update formulas') does not only provide substantial computational savings. It is also one of the key tools to derive closed form formulas enabling a practical use of computationally-intensive sampling strategies. A contribution in batch-sequential optimization (with the multi-points Expected Improvement) is also presented. (author)
Vacuum solutions of Bianchi cosmologies in quadratic gravity
International Nuclear Information System (INIS)
Deus, Juliano Alves de; Muller, Daniel
2011-01-01
Full text: In this work we solve numerically the vacuum solutions of field equations of Bianchi homogeneous universes in the context of Semiclassical theory. Our interest is to study the quadratic theory of gravity with regard in the cosmological description of our universe in periods of intense fields. Bianchi cosmologies are anisotropic homogeneous cosmological models, but can include the isotropic models as particular cases (Bianchi I, VII and IX include homogeneous and isotropic Friedmann models plane, hyperbolic and spherical, respectively). Homogeneous models are good cosmological representations of our universe. With focus in solutions for intense fields, like the early universe, where isotropy is not necessarily required, the adopted scenario is the vacuum solutions, where the geometry is dominant in determining the gravitation. Still following in this way, the Semiclassical theory, which considers quantum matter fields propagating in classical geometrical background, is addressed to give the field equations. This formalism leads to fourth-order ordinary differential equations, in contrast to second-order equations from General Relativity. The Lagrangian of the theory is quadratic in the Ricci scalar and in the Ricci tensor. The equations system is highly non-linear and can be only numerically solved, except perhaps for few particular cases. We obtained numerical solutions for Bianchi V II A evolving to Minkowski and to de Sitter solutions, and also to singularities. The both first and second solutions were obtained choosing initial conditions near from respective exact vacuum solutions from Einstein theory, which are also exact solutions of the quadratic theory. Other Bianchi types are still under study. (author)
MCEM algorithm for the log-Gaussian Cox process
Delmas, Celine; Dubois-Peyrard, Nathalie; Sabbadin, Regis
2014-01-01
Log-Gaussian Cox processes are an important class of models for aggregated point patterns. They have been largely used in spatial epidemiology (Diggle et al., 2005), in agronomy (Bourgeois et al., 2012), in forestry (Moller et al.), in ecology (sightings of wild animals) or in environmental sciences (radioactivity counts). A log-Gaussian Cox process is a Poisson process with a stochastic intensity depending on a Gaussian random eld. We consider the case where this Gaussian random eld is ...
Piecewise quadratic Lyapunov functions for stability verification of approximate explicit MPC
Directory of Open Access Journals (Sweden)
Morten Hovd
2010-04-01
Full Text Available Explicit MPC of constrained linear systems is known to result in a piecewise affine controller and therefore also piecewise affine closed loop dynamics. The complexity of such analytic formulations of the control law can grow exponentially with the prediction horizon. The suboptimal solutions offer a trade-off in terms of complexity and several approaches can be found in the literature for the construction of approximate MPC laws. In the present paper a piecewise quadratic (PWQ Lyapunov function is used for the stability verification of an of approximate explicit Model Predictive Control (MPC. A novel relaxation method is proposed for the LMI criteria on the Lyapunov function design. This relaxation is applicable to the design of PWQ Lyapunov functions for discrete-time piecewise affine systems in general.
Spectral analysis of the SN approximations in a slab with quadratically anisotropic scattering
International Nuclear Information System (INIS)
Ourique, L.E.; Pazos, R.P.; Vilhena, M.T.; Barros, R.C.
2003-01-01
The spectral analysis of the S N approximations to the one-dimensional transport equation began with 3 and 4, following the studies of 1 and 2 about the discrete eigenvalues of the transport equation. In previous work about the influence of a parameter in the solutions of S N approximations, it was considered the total macroscopic cross section as a control parameter and was analyzed how its variation changes the nature of the eigenvalues of the S N transport matrix, in problems with linearly anisotropic scattering. It was showed the existence of bifurcations points, i.e., there exist some values of control parameters for which the S N transport matrix has only real eigenvalues while for other values the S N relation between the eigenvalues of S N transport matrix and control parameter, supposing quadratically anisotropic scattering. Numerical results are reported. (author)
Spectral analysis of the S{sub N} approximations in a slab with quadratically anisotropic scattering
Energy Technology Data Exchange (ETDEWEB)
Ourique, L.E.; Pazos, R.P. [Pontificia Univ. Catolica do Rio Grande do Sul, Porto Alegre, RS (Brazil)]. E-mail: ourique@pucrs.br; rpp@pucrs.br; Vilhena, M.T. [Rio Grande do Sul Univ., Porto Alegre, RS (Brazil). Escola de Engenharia); vilhena@cesup.ufrgs.br; Barros, R.C. [Universidade do Estado, Nova Friburgo, RJ (Brazil). Instituto Politecnico]. E-mail: dickbarros@uol.com.br
2003-07-01
The spectral analysis of the S{sub N} approximations to the one-dimensional transport equation began with 3 and 4, following the studies of 1 and 2 about the discrete eigenvalues of the transport equation. In previous work about the influence of a parameter in the solutions of S{sub N} approximations, it was considered the total macroscopic cross section as a control parameter and was analyzed how its variation changes the nature of the eigenvalues of the S{sub N} transport matrix, in problems with linearly anisotropic scattering. It was showed the existence of bifurcations points, i.e., there exist some values of control parameters for which the S{sub N} transport matrix has only real eigenvalues while for other values the S{sub N} relation between the eigenvalues of S{sub N} transport matrix and control parameter, supposing quadratically anisotropic scattering. Numerical results are reported. (author)
Lipschitz stability of the K-quadratic functional equation | Chahbi ...
African Journals Online (AJOL)
Let N be the set of all positive integers, G an Abelian group with a metric d and E a normed space. For any f : G → E we define the k-quadratic difference of the function f by the formula Qk ƒ(x; y) := 2ƒ(x) + 2k2ƒ(y) - f(x + ky) - f(x - ky) for x; y ∈ G and k ∈ N. Under some assumptions about f and Qkƒ we prove that if Qkƒ is ...
Uniform sparse bounds for discrete quadratic phase Hilbert transforms
Kesler, Robert; Arias, Darío Mena
2017-09-01
For each α \\in T consider the discrete quadratic phase Hilbert transform acting on finitely supported functions f : Z → C according to H^{α }f(n):= \\sum _{m ≠ 0} e^{iα m^2} f(n - m)/m. We prove that, uniformly in α \\in T , there is a sparse bound for the bilinear form for every pair of finitely supported functions f,g : Z→ C . The sparse bound implies several mapping properties such as weighted inequalities in an intersection of Muckenhoupt and reverse Hölder classes.
BRST operator for superconformal algebras with quadratic nonlinearity
International Nuclear Information System (INIS)
Khviengia, Z.; Sezgin, E.
1993-07-01
We construct the quantum BRST operators for a large class of superconformal and quasi-superconformal algebras with quadratic nonlinearity. The only free parameter in these algebras is the level of the (super) Kac-Moody sector. The nilpotency of the quantum BRST operator imposes a condition on the level. We find this condition for (quasi) superconformal algebras with a Kac-Moody sector based on a simple Lie algebra and for the Z 2 x Z 2 -graded superconformal algebras with a Kac-Moody sector based on the superalgebra osp(N modul 2M) or sl (N + 2 modul N). (author). 22 refs, 3 tabs
Quadratic integrand double-hybrid made spin-component-scaled
Energy Technology Data Exchange (ETDEWEB)
Brémond, Éric, E-mail: eric.bremond@iit.it; Savarese, Marika [CompuNet, Istituto Italiano di Tecnologia, via Morego 30, I-16163 Genoa (Italy); Sancho-García, Juan C.; Pérez-Jiménez, Ángel J. [Departamento de Química Física, Universidad de Alicante, E-03080 Alicante (Spain); Adamo, Carlo [CompuNet, Istituto Italiano di Tecnologia, via Morego 30, I-16163 Genoa (Italy); Chimie ParisTech, PSL Research University, CNRS, Institut de Recherche de Chimie Paris IRCP, F-75005 Paris (France); Institut Universitaire de France, 103 Boulevard Saint Michel, F-75005 Paris (France)
2016-03-28
We propose two analytical expressions aiming to rationalize the spin-component-scaled (SCS) and spin-opposite-scaled (SOS) schemes for double-hybrid exchange-correlation density-functionals. Their performances are extensively tested within the framework of the nonempirical quadratic integrand double-hybrid (QIDH) model on energetic properties included into the very large GMTKN30 benchmark database, and on structural properties of semirigid medium-sized organic compounds. The SOS variant is revealed as a less computationally demanding alternative to reach the accuracy of the original QIDH model without losing any theoretical background.
SPEECH EMOTION RECOGNITION USING MODIFIED QUADRATIC DISCRIMINATION FUNCTION
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Quadratic Discrimination Function(QDF)is commonly used in speech emotion recognition,which proceeds on the premise that the input data is normal distribution.In this Paper,we propose a transformation to normalize the emotional features,then derivate a Modified QDF(MQDF) to speech emotion recognition.Features based on prosody and voice quality are extracted and Principal Component Analysis Neural Network (PCANN) is used to reduce dimension of the feature vectors.The results show that voice quality features are effective supplement for recognition.and the method in this paper could improve the recognition ratio effectively.
Quadratic Forms and Semiclassical Eigenfunction Hypothesis for Flat Tori
T. Sardari, Naser
2018-03-01
Let Q( X) be any integral primitive positive definite quadratic form in k variables, where {k≥4}, and discriminant D. For any integer n, we give an upper bound on the number of integral solutions of Q( X) = n in terms of n, k, and D. As a corollary, we prove a conjecture of Lester and Rudnick on the small scale equidistribution of almost all functions belonging to any orthonormal basis of a given eigenspace of the Laplacian on the flat torus {T^d} for {d≥ 5}. This conjecture is motivated by the work of Berry [2,3] on the semiclassical eigenfunction hypothesis.
Abelian groups and quadratic residues in weak arithmetic
Czech Academy of Sciences Publication Activity Database
Jeřábek, Emil
2010-01-01
Roč. 56, č. 3 (2010), s. 262-278 ISSN 0942-5616 R&D Projects: GA AV ČR IAA1019401; GA MŠk(CZ) 1M0545 Institutional research plan: CEZ:AV0Z10190503 Keywords : bounded arithmetic * abelian group * Fermat's little theorem * quadratic reciprocity Subject RIV: BA - General Mathematics Impact factor: 0.361, year: 2010 http://onlinelibrary.wiley.com/doi/10.1002/malq.200910009/abstract;jsessionid=9F636FFACB84C025FD90C7E6880350DD.f03t03
Analysis of electroperforated materials using the quadrat counts method
Energy Technology Data Exchange (ETDEWEB)
Miranda, E; Garzon, C; Garcia-Garcia, J [Departament d' Enginyeria Electronica, Universitat Autonoma de Barcelona, 08193 Bellaterra, Barcelona (Spain); MartInez-Cisneros, C; Alonso, J, E-mail: enrique.miranda@uab.cat [Departament de Quimica AnalItica, Universitat Autonoma de Barcelona, 08193 Bellaterra, Barcelona (Spain)
2011-06-23
The electroperforation distribution in thin porous materials is investigated using the quadrat counts method (QCM), a classical statistical technique aimed to evaluate the deviation from complete spatial randomness (CSR). Perforations are created by means of electrical discharges generated by needle-like tungsten electrodes. The objective of perforating a thin porous material is to enhance its air permeability, a critical issue in many industrial applications involving paper, plastics, textiles, etc. Using image analysis techniques and specialized statistical software it is shown that the perforation locations follow, beyond a certain length scale, a homogeneous 2D Poisson distribution.
Soliton interaction in quadratic and cubic bulk media
DEFF Research Database (Denmark)
Johansen, Steffen Kjær; Bang, Ole
2000-01-01
Summary form only given. The understanding of how and to what extend the cubic nonlinearity affects beam propagation and spatial soliton formation in quadratic media is of vital importance in fundamental and applied nonlinear physics. We consider beam propagation under type-I SHG conditions...... in lossless bulk second order nonlinear optical materials with a nonvanishing third order nonlinearity. It is known that in pure second order systems a single soliton can never collapse whereas in systems with both nonlinearities and that stable single soliton propagation can only in some circumstances...
Sub-quadratic decoding of one-point hermitian codes
DEFF Research Database (Denmark)
Nielsen, Johan Sebastian Rosenkilde; Beelen, Peter
2015-01-01
We present the first two sub-quadratic complexity decoding algorithms for one-point Hermitian codes. The first is based on a fast realization of the Guruswami-Sudan algorithm using state-of-the-art algorithms from computer algebra for polynomial-ring matrix minimization. The second is a power...... decoding algorithm: an extension of classical key equation decoding which gives a probabilistic decoding algorithm up to the Sudan radius. We show how the resulting key equations can be solved by the matrix minimization algorithms from computer algebra, yielding similar asymptotic complexities....
Field equations for gravity quadratic in the curvature
International Nuclear Information System (INIS)
Rose, B.
1992-01-01
Vacuum field equations for gravity are studied having their origin in a Lagrangian quadratic in the curvature. The motivation for this choice of the Lagrangian-namely the treating of gravity in a strict analogy to gauge theories of Yang-Mills type-is criticized, especially the implied view of connections as gauge potentials with no dynamical relation to the metric. The correct field equations with respect to variation of the connections and the metric independently are given. We deduce field equations which differs from previous ones by variation of the metric, the torsion, and the nonmetricity from which the connections are built. 6 refs
Quadratic Hamiltonians on non-symmetric Poisson structures
International Nuclear Information System (INIS)
Arribas, M.; Blesa, F.; Elipe, A.
2007-01-01
Many dynamical systems may be represented in a set of non-canonical coordinates that generate an su(2) algebraic structure. The topology of the phase space is the one of the S 2 sphere, the Poisson structure is the one of the rigid body, and the Hamiltonian is a parametric quadratic form in these 'spherical' coordinates. However, there are other problems in which the Poisson structure losses its symmetry. In this paper we analyze this case and, we show how the loss of the spherical symmetry affects the phase flow and parametric bifurcations for the bi-parametric cases
A novel multitarget model of radiation-induced cell killing based on the Gaussian distribution.
Zhao, Lei; Mi, Dong; Sun, Yeqing
2017-05-07
The multitarget version of the traditional target theory based on the Poisson distribution is still used to describe the dose-survival curves of cells after ionizing radiation in radiobiology and radiotherapy. However, noting that the usual ionizing radiation damage is the result of two sequential stochastic processes, the probability distribution of the damage number per cell should follow a compound Poisson distribution, like e.g. Neyman's distribution of type A (N. A.). In consideration of that the Gaussian distribution can be considered as the approximation of the N. A. in the case of high flux, a multitarget model based on the Gaussian distribution is proposed to describe the cell inactivation effects in low linear energy transfer (LET) radiation with high dose-rate. Theoretical analysis and experimental data fitting indicate that the present theory is superior to the traditional multitarget model and similar to the Linear - Quadratic (LQ) model in describing the biological effects of low-LET radiation with high dose-rate, and the parameter ratio in the present model can be used as an alternative indicator to reflect the radiation damage and radiosensitivity of the cells. Copyright © 2017 Elsevier Ltd. All rights reserved.
Large deviations for Gaussian processes in Hoelder norm
International Nuclear Information System (INIS)
Fatalov, V R
2003-01-01
Some results are proved on the exact asymptotic representation of large deviation probabilities for Gaussian processes in the Hoeder norm. The following classes of processes are considered: the Wiener process, the Brownian bridge, fractional Brownian motion, and stationary Gaussian processes with power-law covariance function. The investigation uses the method of double sums for Gaussian fields
Phase space structure of generalized Gaussian cat states
International Nuclear Information System (INIS)
Nicacio, Fernando; Maia, Raphael N.P.; Toscano, Fabricio; Vallejos, Raul O.
2010-01-01
We analyze generalized Gaussian cat states obtained by superposing arbitrary Gaussian states. The structure of the interference term of the Wigner function is always hyperbolic, surviving the action of a thermal reservoir. We also consider certain superpositions of mixed Gaussian states. An application to semiclassical dynamics is discussed.
Linking network usage patterns to traffic Gaussianity fit
de Oliveira Schmidt, R.; Sadre, R.; Melnikov, Nikolay; Schönwälder, Jürgen; Pras, Aiko
Gaussian traffic models are widely used in the domain of network traffic modeling. The central assumption is that traffic aggregates are Gaussian distributed. Due to its importance, the Gaussian character of network traffic has been extensively assessed by researchers in the past years. In 2001,
Directory of Open Access Journals (Sweden)
Esteban Pérez-López
2014-11-01
Full Text Available Because of the importance of quantitative chemical analysis in research, quality control, sales of services and other areas of interest , and the limiting of some instrumental analysis methods for quantification with linear calibration curve, sometimes because the short linear dynamic ranges of the analyte, and sometimes by limiting the technique itself, is that there is a need to investigate a little more about the convenience of using quadratic curves for analytical quantification, which seeks demonstrate that it is a valid calculation model for chemical analysis instruments. To this was taken as an analysis method based on the technique and atomic absorption spectroscopy in particular a determination of magnesium in a sample of drinking water Tacares sector Northern Grecia, employing a nonlinear calibration curve and a curve specific quadratic behavior, which was compared with the test results obtained for the same analysis with a linear calibration curve. The results show that the methodology is valid for the determination referred to, with all confidence, since the concentrations are very similar, and as used hypothesis testing can be considered equal.
Linear–Quadratic Mean-Field-Type Games: A Direct Method
Directory of Open Access Journals (Sweden)
Tyrone E. Duncan
2018-02-01
Full Text Available In this work, a multi-person mean-field-type game is formulated and solved that is described by a linear jump-diffusion system of mean-field type and a quadratic cost functional involving the second moments, the square of the expected value of the state, and the control actions of all decision-makers. We propose a direct method to solve the game, team, and bargaining problems. This solution approach does not require solving the Bellman–Kolmogorov equations or backward–forward stochastic differential equations of Pontryagin’s type. The proposed method can be easily implemented by beginners and engineers who are new to the emerging field of mean-field-type game theory. The optimal strategies for decision-makers are shown to be in a state-and-mean-field feedback form. The optimal strategies are given explicitly as a sum of the well-known linear state-feedback strategy for the associated deterministic linear–quadratic game problem and a mean-field feedback term. The equilibrium cost of the decision-makers are explicitly derived using a simple direct method. Moreover, the equilibrium cost is a weighted sum of the initial variance and an integral of a weighted variance of the diffusion and the jump process. Finally, the method is used to compute global optimum strategies as well as saddle point strategies and Nash bargaining solution in state-and-mean-field feedback form.
On Alternate Relaying with Improper Gaussian Signaling
Gaafar, Mohamed
2016-06-06
In this letter, we investigate the potential benefits of adopting improper Gaussian signaling (IGS) in a two-hop alternate relaying (AR) system. Given the known benefits of using IGS in interference-limited networks, we propose to use IGS to relieve the inter-relay interference (IRI) impact on the AR system assuming no channel state information is available at the source. In this regard, we assume that the two relays use IGS and the source uses proper Gaussian signaling (PGS). Then, we optimize the degree of impropriety of the relays signal, measured by the circularity coefficient, to maximize the total achievable rate. Simulation results show that using IGS yields a significant performance improvement over PGS, especially when the first hop is a bottleneck due to weak source-relay channel gains and/or strong IRI.
On Alternate Relaying with Improper Gaussian Signaling
Gaafar, Mohamed; Amin, Osama; Ikhlef, Aissa; Chaaban, Anas; Alouini, Mohamed-Slim
2016-01-01
In this letter, we investigate the potential benefits of adopting improper Gaussian signaling (IGS) in a two-hop alternate relaying (AR) system. Given the known benefits of using IGS in interference-limited networks, we propose to use IGS to relieve the inter-relay interference (IRI) impact on the AR system assuming no channel state information is available at the source. In this regard, we assume that the two relays use IGS and the source uses proper Gaussian signaling (PGS). Then, we optimize the degree of impropriety of the relays signal, measured by the circularity coefficient, to maximize the total achievable rate. Simulation results show that using IGS yields a significant performance improvement over PGS, especially when the first hop is a bottleneck due to weak source-relay channel gains and/or strong IRI.
Direct Importance Estimation with Gaussian Mixture Models
Yamada, Makoto; Sugiyama, Masashi
The ratio of two probability densities is called the importance and its estimation has gathered a great deal of attention these days since the importance can be used for various data processing purposes. In this paper, we propose a new importance estimation method using Gaussian mixture models (GMMs). Our method is an extention of the Kullback-Leibler importance estimation procedure (KLIEP), an importance estimation method using linear or kernel models. An advantage of GMMs is that covariance matrices can also be learned through an expectation-maximization procedure, so the proposed method — which we call the Gaussian mixture KLIEP (GM-KLIEP) — is expected to work well when the true importance function has high correlation. Through experiments, we show the validity of the proposed approach.
Fractional Diffusion in Gaussian Noisy Environment
Directory of Open Access Journals (Sweden)
Guannan Hu
2015-03-01
Full Text Available We study the fractional diffusion in a Gaussian noisy environment as described by the fractional order stochastic heat equations of the following form: \\(D_t^{(\\alpha} u(t, x=\\textit{B}u+u\\cdot \\dot W^H\\, where \\(D_t^{(\\alpha}\\ is the Caputo fractional derivative of order \\(\\alpha\\in (0,1\\ with respect to the time variable \\(t\\, \\(\\textit{B}\\ is a second order elliptic operator with respect to the space variable \\(x\\in\\mathbb{R}^d\\ and \\(\\dot W^H\\ a time homogeneous fractional Gaussian noise of Hurst parameter \\(H=(H_1, \\cdots, H_d\\. We obtain conditions satisfied by \\(\\alpha\\ and \\(H\\, so that the square integrable solution \\(u\\ exists uniquely.
Extended Linear Models with Gaussian Priors
DEFF Research Database (Denmark)
Quinonero, Joaquin
2002-01-01
In extended linear models the input space is projected onto a feature space by means of an arbitrary non-linear transformation. A linear model is then applied to the feature space to construct the model output. The dimension of the feature space can be very large, or even infinite, giving the model...... a very big flexibility. Support Vector Machines (SVM's) and Gaussian processes are two examples of such models. In this technical report I present a model in which the dimension of the feature space remains finite, and where a Bayesian approach is used to train the model with Gaussian priors...... on the parameters. The Relevance Vector Machine, introduced by Tipping, is a particular case of such a model. I give the detailed derivations of the expectation-maximisation (EM) algorithm used in the training. These derivations are not found in the literature, and might be helpful for newcomers....
Interweave Cognitive Radio with Improper Gaussian Signaling
Hedhly, Wafa
2018-01-15
Improper Gaussian signaling (IGS) has proven its ability in improving the performance of underlay and overlay cognitive radio paradigms. In this paper, the interweave cognitive radio paradigm is studied when the cognitive user employs IGS. The instantaneous achievable rate performance of both the primary and secondary users are analyzed for specific secondary user sensing and detection capabilities. Next, the IGS scheme is optimized to maximize the achievable rate secondary user while satisfying a target minimum rate requirement for the primary user. Proper Gaussian signaling (PGS) scheme design is also derived to be used as benchmark of the IGS scheme design. Finally, different numerical results are introduced to show the gain reaped from adopting IGS over PGS under different system parameters. The main advantage of employing IGS is observed at low sensing and detection capabilities of the SU, lower PU direct link and higher SU interference on the PU side.
Image reconstruction under non-Gaussian noise
DEFF Research Database (Denmark)
Sciacchitano, Federica
During acquisition and transmission, images are often blurred and corrupted by noise. One of the fundamental tasks of image processing is to reconstruct the clean image from a degraded version. The process of recovering the original image from the data is an example of inverse problem. Due...... to the ill-posedness of the problem, the simple inversion of the degradation model does not give any good reconstructions. Therefore, to deal with the ill-posedness it is necessary to use some prior information on the solution or the model and the Bayesian approach. Additive Gaussian noise has been......D thesis intends to solve some of the many open questions for image restoration under non-Gaussian noise. The two main kinds of noise studied in this PhD project are the impulse noise and the Cauchy noise. Impulse noise is due to for instance the malfunctioning pixel elements in the camera sensors, errors...
Controllable outrigger damping system for high rise building with MR dampers
Wang, Zhihao; Chang, Chia-Ming; Spencer, Billie F., Jr.; Chen, Zhengqing
2010-04-01
A novel energy dissipation system that can achieve the amplified damping ratio for a frame-core tube structures is explored, where vertical dampers are equipped between the outrigger and perimeter columns. The modal characteristics of the structural system with linear viscous dampers are theoretically analyzed from the simplified finite element model by parametric analysis. The result shows that modal damping ratios of the first several modes can increase a lot with this novel damping system. To improve the control performance of system, the semi-active control devices, magnetorheological (MR) dampers, are adopted to develop a controllable outrigger damping system. The clipped optimal control with the linear-quadratic Gaussian (LQG) acceleration feedback is adopted in this paper. The effectiveness of both passive and semi-active control outrigger damping systems is evaluated through the numerical simulation of a representative tall building subjected to two typical earthquake records.
Non-Markovianity of Gaussian Channels.
Torre, G; Roga, W; Illuminati, F
2015-08-14
We introduce a necessary and sufficient criterion for the non-Markovianity of Gaussian quantum dynamical maps based on the violation of divisibility. The criterion is derived by defining a general vectorial representation of the covariance matrix which is then exploited to determine the condition for the complete positivity of partial maps associated with arbitrary time intervals. Such construction does not rely on the Choi-Jamiolkowski representation and does not require optimization over states.
Log Gaussian Cox processes on the sphere
DEFF Research Database (Denmark)
Pacheco, Francisco Andrés Cuevas; Møller, Jesper
We define and study the existence of log Gaussian Cox processes (LGCPs) for the description of inhomogeneous and aggregated/clustered point patterns on the d-dimensional sphere, with d = 2 of primary interest. Useful theoretical properties of LGCPs are studied and applied for the description of sky...... positions of galaxies, in comparison with previous analysis using a Thomas process. We focus on simple estimation procedures and model checking based on functional summary statistics and the global envelope test....