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1

Steering of Frequency Standards by the Use of Linear Quadratic Gaussian Control Theory.  

National Technical Information Service (NTIS)

Linear quadratic Gaussian control is a technique that uses Kalman filtering to estimate a state vector used for input into a control calculation. A control correction is calculated by minimizing a quadratic cost function that is dependent on both the stat...

P. Koppang R. Leland

1995-01-01

2

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

Microsoft Academic Search

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

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

2005-01-01

3

LQG\\/LTR (linear quadratic Gaussian with loop transfer recovery) robust control system design for a low-pressure feedwater heater train  

Microsoft Academic Search

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

G. V. Murphy; J. M. Bailey

1990-01-01

4

Linear quadratic Gaussian differential games with different information patterns  

NASA Astrophysics Data System (ADS)

A discrete-time linear-quadratic-Gaussian (LQG) differential game is considered where the players have access to unshared control- and measurement-histories. The particular problem that is solved is where one adversary has access to only noisy partial information of the state while the other makes a perfect measurement of the state vector. The system dynamics are assumed linear with additive process noise. The solutions show a significant departure from previously published results. First, process noise is included in the dynamical system and a quadratic weighting in the state is included in the cost criterion. Secondly, no prior assumption is made about the structure of the strategies. Specifically, the equilibrium strategies of both players are shown to be finite-dimensional, not infinite-dimensional as was originally thought. Thirdly, it is assumed that the perfect-measurement adversary's control matrix is in the range space of the other adversary's measurement matrix. Then, by a limit of the linear-exponential-Gaussian game solution to the LQG game solution, it is seen that the partial information player avoids reproducing an estimated version of his adversary's strategy. A key feature of this problem solution is the filter structure of the player with partial measurements. In particular, the error of the filter is a Gaussian random variable whose statistics are independent of the opponent's control history. This filter also allows the partial measurement player to estimate the entire state without having to guess/estimate his opponent's strategy. It is noted that for this class of stochastic games, for all possible pure control strategy pairs, there always exist correlations using which each player can improve his performance. Since the error variance of the filter derived here is independent of the opponent's strategy and his control action, the improvements in cost for each player appears minimal. This property is used to extend the notion of a saddle point for deterministic games to that of a saddle interval in pure strategies for games with uncertainty.

Swarup, Ashitosh

5

Optimal and suboptimal quadratic forms for noncentered Gaussian processes  

NASA Astrophysics Data System (ADS)

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

Grebenkov, Denis S.

2013-09-01

6

Adaptive filter and linear quadratic Gaussian/loop transfer recovery compensator combination control of a non-linear tip-tilt mirror  

NASA Astrophysics Data System (ADS)

Adaptive control of a tip-tilt mirror requires precise model estimation, which is difficult for the nonlinear features of piezoelectric actuators such as creep, hysteresis and resonance. A linear quadratic Gaussian control/loop transfer recovery (LQG/LTR) based compensation of the non-linearity is used, which employs a high sampling frequency position sensor to measure the displacements of the tip-tilt mirror and feedbacks the modified command needed to make the actuator response linearly to input command. A normalized LMS adaptive filter whose gains are adjusted by weight updating algorithm to minimize the mean square error of the output is used in order to reduce the jitter introduced by kinds of broadband and narrowband disturbance. The principle of an adaptive filter and LQG/LTR compensator combination control of a nonlinear tip-tilt mirror is introduced. The method is compared with the integrator and LQG/LTR combination control by numerical simulation. Results reveal that the adaptive filter and LQG/LTR compensator combination control is more effective and has less tracking residual error.

Guo, Youming; Ma, Xiaoyu; Rao, Changhui

7

Time-averaged quadratic functionals of a Gaussian process  

NASA Astrophysics Data System (ADS)

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

Grebenkov, Denis S.

2011-06-01

8

Analytic, Computational, and Approximate Forms for Ratios of Noncentral and Central Gaussian Quadratic Forms  

PubMed Central

Many useful statistics equal the ratio of a possibly noncentral chi-square to a quadratic form in Gaussian variables with all positive weights. Expressing the density and distribution function as positively weighted sums of corresponding F functions has many advantages. The mixture forms have analytic value when embedded within a more complex problem. The mixture forms also have computational value. The expansions work well with quadratic forms having few components and small degrees of freedom. A more general algorithm from earlier literature can take longer or fail to converge in the same setting. Many approximations have been suggested for the problem. a positively weighted noncentral quadratic form can always have two moments matched to a noncentral chi-square. For a single quadratic form, the noncentral form performs neither uniformly more or less accurately than older approximations. The approach also gives a noncentral F approximation for any ratio of a positively weighted noncentral form to a positively weighted central quadratic form. The method provides better accuracy for noncentral ratios than approximations based on a single chi-square. The accuracy suffices for many practical applications, such as power analysis, even with few degrees of freedom. Naturally the approximation proves much faster and simpler to compute than any exact method. Embedding the approximation in analytic expressions provides simple forms which correctly guarantee only positive values have nonzero probabilities, and also automatically reduce to partially or fully exact results when either quadratic form has only one term.

Kim, Hae-Young; Gribbin, Matthew J.; Muller, Keith E.; Taylor, Douglas J.

2013-01-01

9

Adaptive linear quadratic control using policy iteration  

Microsoft Academic Search

In this paper we present the stability and convergence results for dynamic programming-based reinforcement learning applied to linear quadratic regulation (LQR). The specific algorithm we analyze is based on Q-learning and it is proven to converge to an optimal controller provided that the underlying system is controllable and a particular signal vector is persistently excited. This is the first convergence

Steven J. Bradtke; B. Erik Ydstie; A. G. Barto

1994-01-01

10

Linear quadratic stochastic control of atomic hydrogen masers.  

PubMed

Data are given showing the results of using the linear quadratic Gaussian (LQG) technique to steer remote hydrogen masers to Coordinated Universal Time (UTC) as given by the United States Naval Observatory (USNO) via two-way satellite time transfer and the Global Positioning System (GPS). Data also are shown from the results of steering a hydrogen maser to the real-time USNO mean. A general overview of the theory behind the LQG technique also is given. The LQG control is a technique that uses Kalman filtering to estimate time and frequency errors used as input into a control calculation. A discrete frequency steer is calculated by minimizing a quadratic cost function that is dependent on both the time and frequency errors and the control effort. Different penalties, chosen by the designer, are assessed by the controller as the time and frequency errors and control effort vary from zero. With this feature, controllers can be designed to force the time and frequency differences between two standards to zero, either more or less aggressively depending on the application. PMID:18238452

Koppang, P; Leland, R

1999-01-01

11

Quadratic  

NSDL National Science Digital Library

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

12

Linear quadratic stochastic control of atomic hydrogen masers  

Microsoft Academic Search

Data are given showing the results of using the linear quadratic Gaussian (LQG) technique to steer remote hydrogen masers to Coordinated Universal Time (UTC) as given by the United States Naval Observatory (USNO) via two-way satellite time transfer and the Global Positioning System (GPS). Data also are shown from the results of steering a hydrogen maser to the real-time USNO

Paul Koppang; Robert Leland

1999-01-01

13

Linear quadratic optimal control for an experimental OHS aircraft  

Microsoft Academic Search

This paper describes the computer simulation and experimentation of a remotely controlled model aircraft under linear quadratic control. The aircraft is first modelled mathematically using Newton's laws and coordinate transformations which form a set of nonlinear differential equations. The mathematical model is linearized and used as the basis for the linear quadratic problem. The control system is simulated and then

J. S. Mukherjee; J. K. Pieper

2000-01-01

14

On constrained infinite-time linear quadratic optimal control  

Microsoft Academic Search

This work presents a solution to the infinite-time linear quadratic optimal control (ITLQOC) problem with state and control constraints. It is shown that a single, finite dimensional, convex program of known size can yield this solution. Properties of the resulting value function, with respect to initial conditions, are also established and are shoen to be useful in determining the aforementioned

D. Chmielewski; V. Manousiouthakis

1996-01-01

15

Decentralized robust control via quadratically invariant model projection  

Microsoft Academic Search

We propose a computational approach to systematically find decentralized H? suboptimal controllers for general unstructured models. Exploiting the quadratically invariant model projection and the classical robust control synthesis techniques, we show that the original nonconvex problem can be conservatively solved by a series of convex optimization problems.

Jong-Han Kim; Sanjay Lall; Walter Merrill; Alireza Behbahani

2011-01-01

16

Distortion sum-rate performance of successive coding strategy in quadratic gaussian CEO problem  

Microsoft Academic Search

We consider a distributed sensor network, modeled by the CEO problem, in which each sensor communicates its observation to the fusion center (FC) using limited transmission rate. Based on the successive coding strategy, we obtain the optimal rate allocation strategy for the Gaussian CEO problem which minimizes the average distortion in the source estimate produced by the FC. This strategy

Hamid Behroozi; M. Reza Soleymani

2007-01-01

17

Control charts for non-Gaussian distributions  

NASA Astrophysics Data System (ADS)

Traditional statistical process control (SPC) techniques applied in the industrial processes field consider often that the distribution ofdata is Gaussian. The estimation ofparameters, the detection ofthe out oforder situations and the control of the followed characteristics are easy to achieve for the normal populations. In reality, whatever the origin of a characteristic (large series productions for components, mechanical parts of OE communication systems, etc. ) the curve of distributions of the measured values is generally far from being normal. The simple approximation to the Gauss distribution and the use of the classical control methods sometimes induces serious errors. In this paper, a study on the statistical control of non Gaussian populations is presented. Particularly we discuss the Rayleigh and the Weibull distribution as being representatives in (SPC for some category of data. The X control charts with variable limits are tested. Experimental simulations are presented for different parameters of the two distributions. The results confirm the methodology and encourage the research in the field of non Gaussian processes.

Babus, Florina; Kobi, Abdessamad; Tiplica, Th.; Bacivarov, Ioan; Bacivarov, Angelica

2007-06-01

18

Extremum seeking loops with quadratic functions: Estimation and control  

Microsoft Academic Search

Extremum-seeking (also peak-seeking ) controllers are designed to operate at an a priori unknown set-point that extremizes the value of a performance function. Traditional approaches to the problem assume a time-scale separation between the gradient computation and function minimization and the system dynamics. The work here, in contrast, assumes that the performance function can be approximated by a quadratic function

R. N. Banavar

2003-01-01

19

Optimal Control and Geodesics on Quadratic Matrix Lie Groups  

Microsoft Academic Search

The purpose of this paper is to extend the symmetric representation of the rigid body equations from the group SO(n) to other groups. These groups are matrix subgroups of the general linear group that are defined by a quadratic ma- trix identity. Their corresponding Lie algebras include several classical semisim- ple matrix Lie algebras. The approach is to start with

Anthony M. Bloch; Peter E. Crouch; Jerrold E. Marsden; Amit K. Sanyal

2008-01-01

20

Quadratic Methodology. Volume I. A Short Course on the Application of Optimical Control Theory to the Design of Practical Control Systems.  

National Technical Information Service (NTIS)

This report is the class notes on a course on Quadratic Methodology - The art of applying Quadratic Optimal Control Theory to Design Practical Control Systems. The subjects discussed are: formulation of the problem, modeling, optimal control for the time ...

A. J. Van Dierendonck G. D. Hartman

1973-01-01

21

Optimal control development for chilled water plants using a quadratic representation  

Microsoft Academic Search

Optimal supervisory control strategy for the set points of controlled variables in the cooling plants has been studied by computer simulation. A quadratic linear regression equation for predicting the total cooling system power in terms of the controlled and uncontrolled variables was developed using simulated data collected under different values of controlled and uncontrolled variables. The optimal set temperatures such

B. C. Ahn; J. W. Mitchell

2001-01-01

22

Intelligent Linear-Quadratic Optimal Output Feedback Regulator for a Deregulated Automatic Generation Control System  

Microsoft Academic Search

One of the main observed problems in the control of automatic generation control systems is the limitation to access and measurement of state variables in the real world. In order to solve this problem, an optimal output feedback method, the linear-quadratic regulator controller, is used. In the output feedback method, only measurable state variables within each control area are required

Elyas Rakhshani

2012-01-01

23

An FPGA implementation of a sparse quadratic programming solver for constrained predictive control  

Microsoft Academic Search

Model predictive control (MPC) is an advanced industrial control technique that relies on the solution of a quadratic programming (QP) problem at every sampling instant to determine the input action required to control the current and future behaviour of a physical system. Its ability in handling large multiple input multiple output (MIMO) systems with physical constraints has led to very

Juan Luis Jerez; George Anthony Constantinides; Eric C. Kerrigan

2011-01-01

24

Gaussian Networks for Direct Adaptive Control  

Microsoft Academic Search

A direct adaptive tracking control architecture is proposed and evaluated for a class of continuous-time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible. The architecture employs a network of gausian radial basis functions to adaptively compensate for the plant nonlinearities. Under mild assumptions about the degree of smoothness

Robert M. Sanner; Jean-Jacques E. Slotine

1991-01-01

25

New approaches to relaxed quadratic stability condition of fuzzy control systems  

Microsoft Academic Search

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

Euntai Kim; Heejin Lee

2000-01-01

26

Laser Control of Chemical Dynamics. I. Control of Electronic Transitions by Quadratic Chirping  

NASA Astrophysics Data System (ADS)

An effective scheme for the laser control of wavepacket dynamics applicable to systems with many degrees of freedom is discussed. It is demonstrated that specially designed quadratically chirped pulses can be used to achieve fast and near-complete excitation of the wavepacket without significantly distorting its shape. The parameters of the laser pulse can be estimated analytically from the Zhu-Nakamura (ZN) theory of nonadiabatic transitions. The scheme is applicable to various processes, such as simple electronic excitations, pump-dumps, and selective bond-breaking, and, taking diatomic and triatomic molecules as examples, it is actually shown to work well.

Zou, S.; Kondorskiy, A.; Mil'nikov, G.; Nakamura, H.

27

Robust control of a flexible robot arm using the quadratic d-stability approach  

Microsoft Academic Search

This paper shows how the quadratic d-stability design method provides a solution to a flexible robot arm control problem. The experimental process exhibits time delay, nonminimum phase behavior and lightly damped modes. The method is based on pole placement considerations and involves the resolution of two parameter dependent Riccati equations with an extra condition. Performances achieved numerically by the designed

Jamal Daafouz; Germain Garcia; Jacques Bernussou

1998-01-01

28

Optimal supervisory control of a central chilled water plant with heuristic search sequential quadratic programming  

Microsoft Academic Search

A new methodology for adapting rigorous simulation programs to optimal supervisory control of a central chilled water plant is proposed in this article, which solves plant operation mode optimization and set points optimization by combining heuristic search with sequential quadratic programming. The mathematical basis of this algorithm is developed. A new derivative calculation strategy is introduced in set points optimization.

Jian Sun

2010-01-01

29

The Robustness and Design of Constrained Cross-Directional Control Via Integral Quadratic Constraints  

Microsoft Academic Search

A robust stability test for a class of constrained cross-directional controllers is found. Under special circum- stances, the stability test is executed on a mode-by-mode basis and greatly simplified to a frequency-domain criterion. The test is also exploited to develop tuning algorithms. The control system involves a quadratic program embedded within an internal model control antiwindup structure and achieves optimal

Rafael M. Morales; William P. Heath

2011-01-01

30

Intelligent longitudinal cruise control by quadratic minimization and robust synthesis  

Microsoft Academic Search

In the last four decades, many efforts have been made to improve the factors of safety and comfort in the area of vehicular traffic. In future intelligent transportation systems, one important aspect of automation components is the design of intelligent control systems that enables the system to behave autonomously, thus ensuring safety, comfort and best usage of available infrastructure. In

K. M. Junaid; Wang Shuning; K. Usman; Tao Wencheng

2005-01-01

31

Fuzzy neural network quadratic stabilization output feedback control for biped robots via H/sub /spl infin// approach.  

PubMed

A novel fuzzy neural network (FNN) quadratic stabilization output feedback control scheme is proposed for the trajectory tracking problems of biped robots with an FNN nonlinear observer. First, a robust quadratic stabilization FNN nonlinear observer is presented to estimate the joint velocities of a biped robot, in which an H/sub /spl infin// approach and variable structure control (VSC) are embedded to attenuate the effect of external disturbances and parametric uncertainties. After the construction of the FNN nonlinear observer, a quadratic stabilization FNN controller is developed with a robust hybrid control scheme. As the employment of a quadratic stability approach, not only does it afford the possibility of trading off the design between FNN, H/sub /spl infin// optimal control, and VSC, but conservative estimation of the FNN reconstruction error bound is also avoided by considering the system matrix uncertainty separately. It is shown that all signals in the closed-loop control system are bounded. PMID:18238158

Liu, Zhi; Li, Chunwen

2003-01-01

32

Sequencing batch-reactor control using Gaussian-process models.  

PubMed

This paper presents a Gaussian-process (GP) model for the design of sequencing batch-reactor (SBR) control for wastewater treatment. The GP model is a probabilistic, nonparametric model with uncertainty predictions. In the case of SBR control, it is used for the on-line optimisation of the batch-phases duration. The control algorithm follows the course of the indirect process variables (pH, redox potential and dissolved oxygen concentration) and recognises the characteristic patterns in their time profile. The control algorithm uses GP-based regression to smooth the signals and GP-based classification for the pattern recognition. When tested on the signals from an SBR laboratory pilot plant, the control algorithm provided a satisfactory agreement between the proposed completion times and the actual termination times of the biodegradation processes. In a set of tested batches the final ammonia and nitrate concentrations were below 1 and 0.5 mg L(-1), respectively, while the aeration time was shortened considerably. PMID:23597762

Kocijan, Juš; Hvala, Nadja

2013-03-28

33

Laser control of electronic transitions of wave packet by using quadratically chirped pulses  

SciTech Connect

An effective scheme is proposed for the laser control of wave packet dynamics. It is demonstrated that by using specially designed quadratically chirped pulses, fast and nearly complete excitation of wave packet can be achieved without significant distortion of its shape. The parameters of the laser pulse can be estimated analytically from the Zhu-Nakamura theory of nonadiabatic transition. If the wave packet is not too narrow or not too broad, then the scheme is expected to be utilizable for multidimensional systems. The scheme is applicable to various processes such as simple electronic excitation, pump-dump, and selective bond breaking, and it is actually numerically demonstrated to work well by taking diatomic and triatomic molecules (LiH, NaK, H{sub 2}O) as examples.

Zou Shiyang; Kondorskiy, Alexey; Mil'nikov, Gennady; Nakamura, Hiroki [Department of Theoretical Studies, Institute for Molecular Science, Modioli, Okazaki 444-8585 (Japan)

2005-02-22

34

Quadratic formula  

NSDL National Science Digital Library

The quadratic formula is easy to solve, yet sufficiently sophisticated that it provides insight into oscillations of masses connected by springs, as well as insight into chemical bonds between atoms. The purpose of this video is to illustrate what it means to find the "zeros" or "roots" of the quadratic equation, both using a graphical description, as well as by analytically completing the square to obtain the famous quadratic formula.

Liao, David

35

Robust stabilization of uncertain linear systems: quadratic stabilizability and H? control theory  

Microsoft Academic Search

The problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time-domain results on the quadratic stabilization of uncertain systems and the frequency-domain results on H? optimization. A complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given. Relations

PRAMOD P. KHARGONEKAR; IAN R. PETERSEN; KEMIN ZHOU

1990-01-01

36

Quadratic Damping  

ERIC Educational Resources Information Center

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…

Fay, Temple H.

2012-01-01

37

Quadratic Damping  

ERIC Educational Resources Information Center

|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…

Fay, Temple H.

2012-01-01

38

Gaussian relative entropy of entanglement  

SciTech Connect

We calculate the relative entropy between two quantum Gaussian states with given correlation matrices by demonstrating a practical method of transforming one of the correlation matrices into an exponential quadratic operator matrix. We show that the closest Gaussian separable state achieving the Gaussian relative entropy of entanglement is at the border between separable and inseparable Gaussian state sets. For a two-mode Gaussian state, the calculation of the Gaussian relative entropy of entanglement is greatly simplified by deducing a matrix with ten undetermined parameters to one with only three. The two-mode Gaussian states are classified into four types. Numerical calculations strongly suggest that the Gaussian relative entropy of entanglement for each type is realized by a Gaussian separable state within the same type. For a symmetric Gaussian state it is strictly proven that the Gaussian relative entropy of entanglement is achieved by a symmetric Gaussian separable sta0008.

Chen Xiaoyu [School of Science, China Institute of Metrology, 310018, Hangzhou (China)

2005-06-15

39

Intelligent model reference adaptive distribution control for non-Gaussian stochastic systems  

Microsoft Academic Search

This paper presents model reference adaptive control (MRAC) approach to control the shape of output distribution in non-Gaussian stochastic systems. The method is based on Iterative Learning Control (ILC) and employs a neural network framework for controller design. The output probability density function (PDF) tracking problem is first reduced to dynamic neural network (NN) weight control. It is assumed that

P. Afshar

2009-01-01

40

A search-free method for calculating the tunings of PID controllers for the minimum of a quadratic criterion  

NASA Astrophysics Data System (ADS)

A new method for calculating the tunings of PID controllers for linear plants with a time delay minimizing the quadratic criterion I 2 is considered. The idea of the proposed method consists in obtaining the complex frequency response of the optimal linear controller followed by approaching to it the complex frequency response of a PID controller in the essential frequency band using the least squares method.

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

2012-10-01

41

Quantum Optimal Control of Single Harmonic Oscillator under Quadratic Controls together with Linear Dipole Polarizability: A Fluctuation Free Expectation Value Dynamical Perspective  

SciTech Connect

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.

Ayvaz, Muzaffer; Demiralp, Metin [Istanbul Technical University, Informatics Institute, Maslak, 34469, Istanbul (Turkey)

2011-09-14

42

Model validation for robust control of uncertain systems with an integral quadratic constraint  

Microsoft Academic Search

This paper presents a new approach to the model validation problem for a class of uncertain systems in which the uncertainty is described by an integral quadratic constraint. The proposed model validation algorithm is based on the solution to a game-type Riccati differential equation and a set of state equations closely related to a robust Kalman filtering problem.

Andrey V. Savkin; Ian R. Petersen

1996-01-01

43

Identification of Local Minimizers in Inertia-Controlling Methods for Quadratic Programming.  

National Technical Information Service (NTIS)

The verification of a local minimizer of a general (i.e., nonconvex) quadratic program is in general an NP-hard problem. The difficulty concerns the optimality of certain points (which we call dead points) at which the first-order necessary conditions for...

A. L. Forsgren P. E. Gill W. Murray

1989-01-01

44

Design and synchronization of Gaussian particle filter using distributed controller scheme  

Microsoft Academic Search

This paper presents design and synchronization method for Gaussian particle filter (GPF) using distributed controller scheme. The GPF has many processing blocks where each processing block computes very complex arithmetic operations. Data dependency among processing blocks in the GPF creates an opportunity for efficient distributed controller, which guarantees correct operation. We verify its correctness using Verilog and SystemC. Each processing

Sangjiii Hong; Xiaoyao Liang; Miodrag Bolic; P. M. Djuric

2004-01-01

45

Active Flutter Control for Flexible Vehicles, Volume 1.  

National Technical Information Service (NTIS)

An active flutter control methodology based on linear quadratic gaussian theory and its application to the control of a super critical wing is presented. Results of control surface and sensor position optimization are discussed. Both frequency response ma...

J. K. Mahesh W. L. Garrard C. R. Stones P. D. Hausman

1979-01-01

46

Real Time Control of Reservoir Systems.  

National Technical Information Service (NTIS)

The development of a new method for the real time operation of reservoir systems is described. The method, called Extended Linear Quadratic Gaussian (ELQG) controller, draws on and extends stochastic control theory results, and is well suited for the opti...

A. P. Georgakakos D. H. Marks

1985-01-01

47

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

NASA Astrophysics Data System (ADS)

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

Ranjita Chanu, Sapam; Natarajan, Vasant

2013-05-01

48

Active vibration control of smart piezoelectric beams: Comparison of classical and optimal feedback control strategies  

Microsoft Academic Search

This paper presents a numerical study concerning the active vibration control of smart piezoelectric beams. A comparison between the classical control strategies, constant gain and amplitude velocity feedback, and optimal control strategies, linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG) controller, is performed in order to investigate their effectiveness to suppress vibrations in beams with piezoelectric patches acting as

C. M. A. Vasques; J. Dias Rodrigues

2006-01-01

49

Gaussian equilibration.  

PubMed

A finite quantum system evolving unitarily equilibrates in a probabilistic fashion. In the general many-body setting the time fluctuations of an observable A are typically exponentially small in the system size. We consider here quasifree Fermi systems where the Hamiltonian and observables are quadratic in the Fermi operators. We first prove a bound on the temporal fluctuations ?A(2) and then map the equilibration dynamics to a generalized classical XY model in the infinite temperature limit. Using this insight, we conjecture that, in most cases, a central limit theorem can be formulated, leading to what we call Gaussian equilibration: observables display a Gaussian distribution with relative error ?A/A[over ¯]=O(L(-1/2)), where L is the dimension of the single-particle space. The conjecture, corroborated by numerical evidence, is proven analytically under mild assumptions for the magnetization in the quantum XY model and for a class of observables in a tight-binding model. We also show that the variance is discontinuous at the transition between a quasifree model and a nonintegrable one. PMID:23410282

Venuti, Lorenzo Campos; Zanardi, Paolo

2013-01-07

50

Numerical Methods Based on Gaussian Quadrature and Continuous Runge-Kutta Integration for Optimal Control Problems  

Microsoft Academic Search

\\u000a This paper provides a numerical approach for solving optimal control problems governed by ordinary differential equations.\\u000a Continuous extension of an explicit, fixed step-size Runge-Kutta scheme is used in order to approximate state variables; moreover,\\u000a the objective function is discretized by means of Gaussian quadrature rules. The resulting scheme represents a nonlinear programming\\u000a problem, which can be solved by optimization algorithms.

Fasma Diele; Carmela Marangi; Stefania Ragni

2004-01-01

51

Reducing the model-data misfit in a marine ecosystem model using periodic parameters and Linear Quadratic Optimal Control  

NASA Astrophysics Data System (ADS)

This paper presents the application of the Linear Quadratic Optimal Control (LQOC) method for a parameter optimization problem in a marine ecosystem model. The ecosystem model simulates the distribution of nitrogen, phytoplankton, zooplankton and detritus in a water column with temperature and turbulent diffusivity profiles taken from a three-dimensional ocean circulation model. We present the linearization method which is based on the available observations. The linearization is necessary to apply the LQOC method on the nonlinear system of state equations. We show the form of the linearized time-variant problems and the resulting two algebraic Riccati Equations. By using the LQOC method, we are able to introduce temporally varying periodic model parameters and to significantly improve - compared to the use of constant parameters - the fit of the model output to given observational data.

El Jarbi, M.; Rückelt, J.; Slawig, T.; Oschlies, A.

2012-08-01

52

Linear-Quadratic Optimal Control of Periodic-Review Perishable Inventory Systems  

Microsoft Academic Search

In this brief, the problem of inventory control in systems with perishable goods is addressed from the control-theoretic perspective. In the analyzed setting, the deteriorating stock used to fulfill unknown, time-varying demand is replenished with delay from a remote supply source. In order to eliminate the threat of the bullwhip effect (amplified demand variations translated to the ordering signal), we

P. Ignaciuk; A. Bartoszewicz

2012-01-01

53

Support method for solving a linear-quadratic problem with polythedral with polyhedral constraints on control  

Microsoft Academic Search

T his paper deals with min imizat ion of a qu ad rat ic co nvex term inal co st function al on the t raject ories of a linear dynamic system subject to polyhedral constraints on control and linear constraints on terminal state. The proposed a lgorithm is direct . accurate, relaxa tional. and in it th e support

M. O. Bibi

1996-01-01

54

Direct dynamics using variational Gaussian wavepackets. Application to the intelligent control of benzene photochemistry  

NASA Astrophysics Data System (ADS)

The direct dynamics variational multi-configuration Gaussian wavepacket (DD-vMCG) method is based on the multi-configuration time-dependent Hartree (MCTDH) algorithm. It uses a time-dependent basis set of parameterised Gaussian functions, which are coupled so as to variationally provide the best possible representation of the wavepacket. This approach is designed to treat quantum effects in large molecules with on-the-fly calculation of the potential energy surface performed by an interfaced quantum chemistry program. Here, we apply this method to the study of the non-adiabatic photochemistry of benzene. Our aim is to rationalise how the way the wavepacket crosses the S1/S0 seam may modify the branching ratio Dewar benzene : benzvalene and enhance their production rather than non-radiative decay back to benzene. This study is intended to identify realistic non-radiative decay pathways that lead to alternative photochemical reactivity and to find corresponding targets that can be reached by optimal control experiments.

Lasorne, Benjamin; Bearpark, Michael J.; Robb, Michael A.; Worth, Graham A.

2007-03-01

55

Reducing the model-data misfit in a marine ecosystem model using periodic parameters and linear quadratic optimal control  

NASA Astrophysics Data System (ADS)

This paper presents the application of the Linear Quadratic Optimal Control (LQOC) method to a parameter optimization problem for a one-dimensional marine ecosystem model of NPZD (N for dissolved inorganic nitrogen, P for phytoplankton, Z for zooplankton and D for detritus) type. This ecosystem model, developed by Oschlies and Garcon, simulates the distribution of nitrogen, phytoplankton, zooplankton and detritus in a water column and is driven by ocean circulation data. The LQOC method is used to introduce annually periodic model parameters in a linearized version of the model. We show that the obtained version of the model gives a significant reduction of the model-data misfit, compared to the one obtained for the original model with optimized constant parameters. The found inner-annual variability of the optimized parameters provides hints for improvement of the original model. We use the obtained optimal periodic parameters also in validation and prediction experiments with the original non-linear version of the model. In both cases, the results are significantly better than those obtained with optimized constant parameters.

El Jarbi, M.; Rückelt, J.; Slawig, T.; Oschlies, A.

2013-02-01

56

Design and laser fabrication of controllable non-Gaussian roughness surfaces at microscale  

NASA Astrophysics Data System (ADS)

Surface structures at micro-/nano-scale have been studied in many fields for their wide range of applications. To understand the interdependences between surface structures and functional performances accurately, fabrication methods of complex structures with controllable surface parameters are crucial to be investigated. Toward this purpose, 3D non-Gaussian surfaces were designed and fabricated here. Two typical design methods were compared, which are based on Johnson translator and Pearson translator respectively. Several suggestions were provided to improve the design accuracy and efficiency. Primary roughness surfaces have been fabricated by laser direct writing. Different scanning paths and designed structures were compared to optimize the fabrication accuracy. The statistical and spectral characteristics of the fabricated roughness surfaces were demonstrated to be in accord with the designed values.

Luo, Tingting; Liu, Xiaoning; Chen, Yuhang; Huang, Wenhao; Liu, Zhe

2013-07-01

57

Self-Replicating Quadratics  

ERIC Educational Resources Information Center

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

Withers, Christopher S.; Nadarajah, Saralees

2012-01-01

58

Lesson 14: Quadratic Formula  

NSDL National Science Digital Library

Completing the square is applied to the general quadratic to derive the quadratic formula. Before an area application example is given there is a quick review of the four methods that have been presented for solving quadratic equations. Complex numbers are introduced before the discriminant is presented.

2011-01-01

59

On centralized optimal control  

Microsoft Academic Search

It can be argued that the Holy Grail of control theory is the determination of the optimal feedback control law or simply the feedback control law. This is understandable given the huge success of the linear quadratic Gaussian (LQG) theory and applications for the past half-century. It is not an exaggeration to say that the entire aerospace industry, from the

Yu-Chi Ho

2005-01-01

60

Communication rate allocation in quantized control  

Microsoft Academic Search

A linear-quadratic-Gaussian (LQG) delocalized control problem is formulated to require both specification of a control law and communication of measurements to controller and controls to plant. Efficient communication requires quantization of both measurement and control signals. The basic design problem is to allocate in an optimum fashion a fixed total communication rate to the measurement and control communication systems. A

Thomas R. Fischer; Charles J. Meadow

1983-01-01

61

Quadratic eigenvalue problems.  

SciTech Connect

In this report we will describe some nonlinear eigenvalue problems that arise in the areas of solid mechanics, acoustics, and coupled structural acoustics. We will focus mostly on quadratic eigenvalue problems, which are a special case of nonlinear eigenvalue problems. Algorithms for solving the quadratic eigenvalue problem will be presented, along with some example calculations.

Walsh, Timothy Francis; Day, David Minot

2007-04-01

62

Optimal control and estimation for terminal guidance of tactical missiles  

NASA Astrophysics Data System (ADS)

Good results in developing advanced guidance laws and estimation techniques for application in future tactical weapons were obtained using the linear quadratic, the linear quadratic Gaussian, singular perturbation, reachable set, and f differential game theories. Of the thirty algorithms developed the most simplistic was derived using the linear quadratic Gaussian theory. The derivation of this guidance law is discussed and its performance is compared to proportional navigation. Results show that the use of optimal control and estimation theory can be done without increasing the hardware requirements of the missile system. These concepts also offer the potential for decreasing sensor accuracy specifications without degrading the total system performance.

Riggs, T. L., Jr.

1980-10-01

63

A Gaussian mixture model based classification scheme for myoelectric control of powered upper limb prostheses  

Microsoft Academic Search

This paper introduces and evaluates the use of Gaussian mixture models (GMMs) for multiple limb motion classification using continuous myoelectric signals. The focus of this work is to optimize the configuration of this classification scheme. To that end, a complete experimental evaluation of this system is conducted on a 12 subject database. The experiments examine the GMMs algorithmic issues including

Yonghong Huang; Kevin B. Englehart; Bernard Hudgins; Adrian D. C. Chan

2005-01-01

64

Application of l1 optimal control to the engine idle speed control problem  

Microsoft Academic Search

In this paper, the engine idle speed control (ISC) problem is revisited with the l1 optimization design methodology. A controller configuration consisting of a feedback linear quadratic Gaussian (LQG) optimal controller and a feedforward l1 optimal controller is chosen to satisfy the design objectives. The main goal of this work is to demonstrate the application of the l1 optimal control

Kenneth R. Butts; N. Sivashankar; Jing Sun

1999-01-01

65

A Special Quadratic Program.  

National Technical Information Service (NTIS)

This paper presents a characterization of the solutions of a special quadratic program. This characterization is then used in the development of an efficient algorithm for this class of problems. (Author)

R. Helgason J. Kennington H. Lall

1978-01-01

66

Generation of Hermite-Gaussian modes and vortex arrays based on two-dimensional gain distribution controlled microchip laser.  

PubMed

We have demonstrated high-order Hermite-Gaussian (HG) mode generation based on 2D gain distribution control edge-pumped, composite all-ceramic Yb:YAG/YAG microchip lasers using a V-type cavity. Several hundred milliwatts to several watts HG(mn) modes are achieved. We also generated different kinds of vortex arrays directly from the oscillator with the same power level. In addition, a more than 7 W doughnut-shape mode can be generated in the same cavity. PMID:22743487

Kong, Weipeng; Sugita, Atsushi; Taira, Takunori

2012-07-01

67

Perturbations of quadratic centers of genus one  

Microsoft Academic Search

We propose a program for finding the cyclicity of period annuli of quadratic\\u000asystems with centers of genus one. As a first step, we classify all such\\u000asystems and determine the essential one-parameter quadratic perturbations which\\u000aproduce the maximal number of limit cycles. We compute the associated\\u000aPoincare-Pontryagin-Melnikov functions whose zeros control the number of limit\\u000acycles. To illustrate our

Sébastien Gautier; Lubomir Gavrilov; Iliya D. Iliev

2009-01-01

68

Quadratic spline subroutine package  

USGS Publications Warehouse

A continuous piecewise quadratic function with continuous first derivative is devised for approximating a single-valued, but unknown, function represented by a set of discrete points. The quadratic is proposed as a treatment intermediate between using the angular (but reliable, easily constructed and manipulated) piecewise linear function and using the smoother (but occasionally erratic) cubic spline. Neither iteration nor the solution of a system of simultaneous equations is necessary to determining the coefficients. Several properties of the quadratic function are given. A set of five short FORTRAN subroutines is provided for generating the coefficients (QSC), finding function value and derivatives (QSY), integrating (QSI), finding extrema (QSE), and computing arc length and the curvature-squared integral (QSK). (USGS)

Rasmussen, L. A.

1982-01-01

69

Quadratic exponential vectors  

SciTech Connect

We give a necessary and sufficient condition for the existence of a quadratic exponential vector with test function in L{sup 2}(R{sup d}) intersection L{sup {infinity}}(R{sup d}). We prove the linear independence and totality, in the quadratic Fock space, of these vectors. Using a technique different from the one used by Accardi et al. [Quantum Probability and Infinite Dimensional Analysis, Vol. 25, p. 262, (2009)], we also extend, to a more general class of test functions, the explicit form of the scalar product between two such vectors.

Accardi, Luigi; Dhahri, Ameur [Volterra Center, University of Roma Tor Vergata, Via Columbia 2, 00133 Roma (Italy)

2009-12-15

70

Generation of doughnutlike vortex beam with tunable orbital angular momentum from lasers with controlled Hermite-Gaussian modes.  

PubMed

This study demonstrates successive higher-order Hermite-Gaussian (HG(0,m)) mode operations in a microchip solid-state laser with a controlled off-axis laser diode (LD) pumping and generation of the corresponding doughnutlike laser beam of tunable ring diameter and orbital angular momentum, by experimentally focusing a Hermite-Gaussian mode (HGM) lasing beam into an astigmatic mode converter (AMC) with a mode-matching lens. Based on the successful generation of stable doughnutlike vortex beams by combining the LD off-axis pumping of microchip lasers and an AMC, this study proposes a design for a compact, solid doughnutlike vortex laser beam generator that combines three elements (i.e., laser cavity, mode-matching lens, and AMC) into one practical device. The desired doughnutlike vortex beam with different orbital angular momentum is easily generated by simply controlling the lateral off-axis pump position and pump beam shape on the laser crystal by numerical simulation. PMID:18470253

Chu, Shu-Chun; Ohtomo, Takayuki; Otsuka, Kenju

2008-05-10

71

Improved temperature control of a PWR nuclear reactor using an LQG\\/LTR based controller  

Microsoft Academic Search

State feedback assisted classical (SFAC) control has been developed to improve the temperature response performance of nuclear reactors via modifying the embedded classical controller reference signal. This is done by means of an outermost state feedback controller. A linear quadratic Gaussian with loop transfer recovery (LQG\\/LTR) at the plant output seems a good candidate for the state feedback loop of

Hussein Arab-Alibeik; Saeed Setayeshi

2003-01-01

72

A Quadratic Spring Equation  

ERIC Educational Resources Information Center

|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]…

Fay, Temple H.

2010-01-01

73

Networked Control System Design over a Wireless LAN  

Microsoft Academic Search

We analyze and implement a networked control system where the communication between the sensors, the controller, and the actuator takes place over a wireless LAN (802.11b) ad hoc system. The wireless LAN system introduces random delays and packet loss in the feedback loop. We present an extended version of the separation principle of Linear Quadratic Gaussian (LQG) control with both

Michael Drew; Xiangheng Liu; Andrea Goldsmith; Karl Hedrick

2005-01-01

74

Quadratic knapsack problems  

Microsoft Academic Search

The quadratic knapsack (QK) model naturally arises in a variety of problems in operations research, statistics and combinatorics.\\u000a Some “upper planes” for the QK problem are derived, and their different uses in a branch-and-bound scheme for solving such\\u000a a problem are discussed. Some theoretical results concerning the class of all upper planes, as well as extensive computational\\u000a experience, are reported.

G. Gallo; P. L. Hammer; B. Simeone

75

Quadratic component analysis.  

PubMed

I present a method for analyzing multichannel recordings in response to repeated stimulus presentation. Quadratic Component Analysis (QCA) extracts responses that are stimulus-induced (triggered by the stimulus but not precisely locked in time), as opposed to stimulus-evoked (time-locked to the stimulus). Induced responses are often found in neural response data from magnetoencephalography (MEG), electroencephalography (EEG), or multichannel electrophysiological and optical recordings. The instantaneous power of a linear combination of channels can be expressed as a weighted sum of instantaneous cross-products between channel waveforms. Based on this fact, a technique known as Denoising Source Separation (DSS) is used to find the most reproducible "quadratic component" (linear combination of cross-products). The linear component with a square most similar to this quadratic component is taken to approximate the most reproducible evoked activity. Projecting out the component and repeating the analysis allows multiple induced components to be extracted by deflation. The method is illustrated with synthetic data, as well as real MEG data. At unfavorable signal-to-noise ratios, it can reveal stimulus-induced activity that is invisible to other approaches such as time-frequency analysis. PMID:22079456

de Cheveigné, Alain

2011-11-04

76

Direct adaptive control of wind energy conversion systems using Gaussian networks.  

PubMed

Grid connected wind energy conversion systems (WECS) present interesting control demands, due to the intrinsic nonlinear characteristics of windmills and electric generators. In this paper a direct adaptive control strategy for WECS control is proposed. It is based on the combination of two control actions: a radial basis zfunction network-based adaptive controller, which drives the tracking error to zero with user specified dynamics, and a supervisory controller, based on crude bounds of the system's nonlinearities. The supervisory controller fires when the finite neural-network approximation properties cannot be guaranteed. The form of the supervisor control and the adaptation law for the neural controller are derived from a Lyapunov analysis of stability. The results are applied to a typical turbine/generator pair, showing the feasibility of the proposed solution. PMID:18252585

Mayosky, M A; Cancelo, I E

1999-01-01

77

Gain scheduling control of variable speed WTG under widely varying turbulence loading  

Microsoft Academic Search

Probabilistic paradigms for wind turbine controller design have been gaining attention. Motivation derives from the need to replace outdated empirical-based designs with more physically relevant models. This paper proposes an adaptive controller in the form of a linear quadratic Gaussian (LQG) for control of a stall-regulated, variable speed wind turbine generator (WTG). In the control scheme, the strategy is twofold:

Endusa Billy Muhando; Tomonobu Senjyu; Naomitsu Urasaki; Atsushi Yona; Hiroshi Kinjo; Toshihisa Funabashi

2007-01-01

78

A Gaussian copula approach for the analysis of secondary phenotypes in case-control genetic association studies.  

PubMed

In many case-control genetic association studies, a set of correlated secondary phenotypes that may share common genetic factors with disease status are collected. Examination of these secondary phenotypes can yield valuable insights about the disease etiology and supplement the main studies. However, due to unequal sampling probabilities between cases and controls, standard regression analysis that assesses the effect of SNPs (single nucleotide polymorphisms) on secondary phenotypes using cases only, controls only, or combined samples of cases and controls can yield inflated type I error rates when the test SNP is associated with the disease. To solve this issue, we propose a Gaussian copula-based approach that efficiently models the dependence between disease status and secondary phenotypes. Through simulations, we show that our method yields correct type I error rates for the analysis of secondary phenotypes under a wide range of situations. To illustrate the effectiveness of our method in the analysis of real data, we applied our method to a genome-wide association study on high-density lipoprotein cholesterol (HDL-C), where "cases" are defined as individuals with extremely high HDL-C level and "controls" are defined as those with low HDL-C level. We treated 4 quantitative traits with varying degrees of correlation with HDL-C as secondary phenotypes and tested for association with SNPs in LIPG, a gene that is well known to be associated with HDL-C. We show that when the correlation between the primary and secondary phenotypes is >0.2, the P values from case-control combined unadjusted analysis are much more significant than methods that aim to correct for ascertainment bias. Our results suggest that to avoid false-positive associations, it is important to appropriately model secondary phenotypes in case-control genetic association studies. PMID:21933777

He, Jing; Li, Hongzhe; Edmondson, Andrew C; Rader, Daniel J; Li, Mingyao

2011-09-19

79

Lesson 17: Quadratic Inequalities  

NSDL National Science Digital Library

The lesson begins with using graphs to solve quadratic inequalities. AN equation modeling the height of a rocket is graphed along with a second equation that represents the minimum height at which the rocket can legally and safely be exploded. The intersections of the graphs provide the solution interval. A second method is then presented where the inequality is put into standard form and then solved for its x-intercepts. Interval notation and union of sets is reviewed before a purely algebraic procedure for solving the inequalities is presented. The lesson concludes with an application problem.

2011-01-01

80

Robust dynamic inversion controller design and analysis (using the X-38 vehicle as a case study)  

Microsoft Academic Search

A new way to approach robust Dynamic Inversion controller synthesis is addressed in this paper. A Linear Quadratic Gaussian outer-loop controller improves the robustness of a Dynamic Inversion inner-loop controller in the presence of uncertainties. Desired dynamics are given by the dynamic compensator, which shapes the loop. The selected dynamics are based on both performance and stability robustness requirements. These

Daigoro Ito

2001-01-01

81

Decentralized LQG control with online set-point adaptation for parallel power converter systems  

Microsoft Academic Search

This paper proposes a new approach to the control of a power network with parallel power converters. A decentralized linear quadratic Gaussian (LQG) control approach based on local models without full knowledge of the overall network is proposed. Through integrating a virtual disturbance source model the local LQG controllers can individually learn online information about the dynamics of the others.

Junqi Liu; Dragan Obradovic; Antonello Monti

2010-01-01

82

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

Microsoft Academic Search

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

G. V. Murphy; J. M. Bailey

1990-01-01

83

On Efficient Semidefinite Relaxations for Quadratically Constrained Quadratic Programming  

Microsoft Academic Search

Abstract Two important topics in the study of Quadratically Constrained Quadratic Programming (QCQP) are how to exactly solve a QCQP with few constraints in polynomial time and how to find an inexpensive and strong relaxation bound for a QCQP with many constraints. In this thesis, we first review some important results on QCQP, like the S-Procedure, and the strength of

Yichuan Ding

2007-01-01

84

Quadratic Lagrangians and horizons  

SciTech Connect

It has been known for some time that the standard isotropic cosmological model with an {ital R}{sup 2} Lagrangian has horizon-breaking solutions in the {ital t}{r arrow}0 singularity limit. We search for horizonless power-law solutions in the vacuum Bianchi type-I and orthogonal type-V cosmological models. We find that type V with an {ital R}{sup 2} Lagrangian does contain such solutions. At first glance this would suggest that quadratic theories might provide an alternative resolution to the horizon problem. However, for both the horizonless isotropic and type-V solutions we show that the eigenvalues of the linear vector field near the stationary points in phase space have opposite signs, demonstrating that such solutions are not Lyapunov stable. The addition of free quantum fields may stabilize the solutions.

Rothman, T.; Anninos, P. (Department of Physics and Center for Relativity, The University of Texas at Austin, Austin, Texas (USA))

1991-11-15

85

Lead with closed-loop system compensation of a radically rotating elastic rod attached to a rigid body part I: A unified approach to the design of Llnear control system  

Microsoft Academic Search

Due to difficulties in modeling and poor knowledge of parameters, the behavior of flexible structures is subject to significant uncertainty. Hence it is essential that the control system provide an absolutely stable property in the presence of large variations. Over the years, many control laws—proportion and derivative (PD) control, nonlinear, linear-quadratic, adaptive, and linear quadratic Gaussian (LQG)—have been synthesized for

Chung-Feng Jeffrey Kuo; Lin Shu-Chyuarn

1998-01-01

86

Improved coding and control of HF systems in a non-Gaussian noise environment  

NASA Astrophysics Data System (ADS)

A HF communication system which is capable of adapting various parameters, such as frequency and coding scheme, to provide the user with the most reliable HF path is described. Each transceiver/ATU is of amateur-grade, and is capable of delivering approximately 150 W over the range 2 to 30 MHz. The transceivers are fully computer-controllable, and this enables automatic channel selection to be achieved. When used with 10m whip antennas, a cheap and portable HF system results; however, for some channels, the 10m antenna will not present an ideal match to the system, and thus the automatic tuning facility of the ATU is used to achieve a match, which may take up to 3 seconds. Due to this constraint, broadband antennas for the probing channel become desirable, at the expense of making the system less portable. The coding/control software runs on two 8085 systems. Each 8085 system is equipped of 8 Kbytes of ROM and 8 Kbytes of RAM, and therefore reasonably complex algorithms may be accommodated. Additional memory cards may be added to the system at a later date as required. Presently, Golay (23,12) and other half-rate codes (the Golay (23,12) code is in fact implemented as a (24,12) code for ease of system timing), are supported by the system, but it is intended to utilize other coding schemes, such as the embedded-array code (Darnell, Honary and Zolghadr, 1986) at a later date by modifying the software.

Hague, J.

1988-12-01

87

Robust convex quadratically constrained programs  

Microsoft Academic Search

In this paper we study robust convex quadratically constrained programs, a subset of the class of robust convex programs introduced by Ben-Tal and Nemirovski (4). Unlike (4), our focus in this paper is to identify uncertainty structures that allow the corresponding robust quadratically constrained programs to be reformulated as second-order cone programs. We propose three classes of uncertainty sets that

Donald Goldfarb; Garud Iyengar

2003-01-01

88

Strong self-focusing of laser beam in a medium with quadratic nonlinear response  

NASA Astrophysics Data System (ADS)

We compare self-focusing of laser beam with Gaussian, super-Gaussian and ring profile in a medium with quadratic nonlinear response due to cascading SHG. The duration of the light pulse under consideration is about microsecond. Nevertheless, the dispersion of group velocity is also taken into account. We demonstrate a possibility of strong growth for intensity of the laser radiation without changing the pulse shape and Gaussian profile of the beam. For initial super- Gaussian and ring profile the Gaussian profile appears due to the diffraction of laser beam at certain section of nonlinear medium. Then, the optical radiation undergoes self-focusing without changing the Gaussian intensity distribution till appearance of the first nonlinear focus. This phenomenon has various practical applications. For example, it can be used for developing the laser system in microsecond range of pulse duration which operates in the regime similar to KLM regime for femtosecond laser system.

Trofimov, Vyacheslav A.; Lysak, Tatiana M.

2012-10-01

89

The select of a permanent magnet brushed DC motor with optimal controller for providing propellant of @Home Mobile Robot  

Microsoft Academic Search

This paper first will describe @Home Mobile Robot and DC motors. In continuous, is designed a Direct current (DC) motor for special task due to specific speed diagram for considered robot. This robot wants to work in intermittent operation condition. Finally is done a speed control on a selected permanent magnet brushed DC motor using of Linear-Quadratic-Regulator (LQR), Linear-Quadratic-Gaussian (LQG)

Seiyed Hamid Zareh; Maryam Khosroshahi; Meysam Abbasi; Kambiz Ghaemi Osgouie

2010-01-01

90

A QUADRATIC PROGRAMMING APPROACH TO THE DESIGN OF ACTIVE–PASSIVE VIBRATION ISOLATION SYSTEMS  

Microsoft Academic Search

A quadratic programming algorithm is presented for studying the design tradeoffs of active–passive vibration isolation systems. The novelty of the technique is that the optimal control problem is posed as a quadratic optimization with linear constraints. The quadratic cost function represents the mean square response of the payload acceleration and isolator stroke, and the linear constraints represent asymptotic tracking requirements

D. J. Leo; D. J. Inman

1999-01-01

91

a Quadratic Programming Approach to the Design of Active-Passive Vibration Isolation Systems  

Microsoft Academic Search

A quadratic programming algorithm is presented for studying the design tradeoffs of active-passive vibration isolation systems. The novelty of the technique is that the optimal control problem is posed as a quadratic optimization with linear constraints. The quadratic cost function represents the mean square response of the payload acceleration and isolator stroke, and the linear constraints represent asymptotic tracking requirements

D. J. Leo; D. J. Inman

1999-01-01

92

A Sequential Quadratically Constrained Quadratic Programming Method of Feasible Directions  

SciTech Connect

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

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

2007-12-15

93

Power-Distortion Performance of Successive Coding Strategy in Gaussian Ceo Problem  

Microsoft Academic Search

In this paper, we investigate the power-distortion performance of the successive coding strategy in the so-called quadratic Gaussian CEO problem. In the CEO problem, L sensors will be deployed to observe independently corrupted versions of the source. They communicate information about their observations to the CEO through a Gaussian multiple access channel (MAC) without cooperating with each other. Two types

Hamid Behroozi; M. Reza Soleymani

2006-01-01

94

MultiTask Learning of Gaussian Graphical Models  

Microsoft Academic Search

We present multi-task structure learning for Gaussian graphical models. We discuss uniqueness and boundedness of the optimal solution of the maximization problem. A block coordinate descent method leads to a provably convergent algorithm that gen- erates a sequence of positive deflnite solu- tions. Thus, we reduce the original prob- lem into a sequence of strictly convex '1 regularized quadratic minimization

Jean Honorio; Dimitris Samaras

2010-01-01

95

Quadratic and Cubic Transition Elements.  

National Technical Information Service (NTIS)

Based on the investigation of Barsoum, Henshell and Shaw, quarterpoint quadratic elements have been successfully used as crack tip elements in fracture mechanics. This concept of singular element was extended to cubic isoparametric elements. Recently it w...

M. A. Hussain J. D. Vasilakis S. L. Pu

1980-01-01

96

Quadratic brackets from symplectic forms  

NASA Astrophysics Data System (ADS)

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. On leave from the Institute for Nuclear Research, Bulgarian Academy of Sciences, Tsarigradsko Chaussee 72, BG-1784 Sofia, Bulgaria.

Alekseev, Anton Yu.; Todorov, Ivan T.

1994-06-01

97

Gaussian cloning of coherent states with known phases  

SciTech Connect

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.

Alexanian, Moorad [Department of Physics and Physical Oceanography, University of North Carolina at Wilmington, Wilmington, North Carolina 28403 (United States)

2006-04-15

98

Interface solitons in quadratic nonlinear photonic lattices  

SciTech Connect

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

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

2009-07-15

99

Reactive-power dispatch by successive quadratic programming  

Microsoft Academic Search

The reactive-power dispatch is formulated as the minimization of real-power losses in the system, utilizing a full set of control variables: generator voltages, switchable shunt susceptances, and transformer taps. The solution of the loss problem is obtained by successively solving quadratic programming problems. First- and second-order loss sensitivity coefficients are derived for the quadratic problem formulation. The derivations are based

V. H. Quintana; M. Santos-Nieto

1989-01-01

100

Generalized Ince Gaussian beams  

NASA Astrophysics Data System (ADS)

In this work we present a detailed analysis of the tree families of generalized Gaussian beams, which are the generalized Hermite, Laguerre, and Ince Gaussian beams. The generalized Gaussian beams are not the solution of a Hermitian operator at an arbitrary z plane. We derived the adjoint operator and the adjoint eigenfunctions. Each family of generalized Gaussian beams forms a complete biorthonormal set with their adjoint eigenfunctions, therefore, any paraxial field can be described as a superposition of a generalized family with the appropriate weighting and phase factors. Each family of generalized Gaussian beams includes the standard and elegant corresponding families as particular cases when the parameters of the generalized families are chosen properly. The generalized Hermite Gaussian and Laguerre Gaussian beams correspond to limiting cases of the generalized Ince Gaussian beams when the ellipticity parameter of the latter tends to infinity or to zero, respectively. The expansion formulas among the three generalized families and their Fourier transforms are also presented.

Bandres, Miguel A.; Gutiérrez-Vega, Julio C.

2006-08-01

101

LQG\\/LTR robust control of nuclear reactors with improved temperature performance  

Microsoft Academic Search

The authors present the design of a robust controller using the linear quadratic Gaussian with loop transfer recovery (LQG\\/LTR) for nuclear reactors with the objective of maintaining a desirable performance for reactor fuel temperature and the temperature of the coolant leaving the reactor for a wide range of reactor powers. The results obtained are compared to those for an observer-based

Adel Ben-Abdennour; Robert M. Edwards; Kwang Y. Lee

1992-01-01

102

Gaussian perceptron: experimental results  

Microsoft Academic Search

A new neural model which has a Gaussian activation function is presented. This model is referred to as the Gaussian perceptron. For the training of single-layered Gaussian perceptrons, the Gaussian perceptron learning algorithm, which is a variant of the conventional perceptron learning algorithm, is presented. The winner-take-all algorithm is proposed as a multilayer training algorithm. A number of examples are

Taek Mu Kwon

1991-01-01

103

Gaussian Markov Triplets  

NASA Astrophysics Data System (ADS)

The Markov property of states of algebras of the canonical commutation relation is studied and in the case of Gaussian states several equivalent properties are obtained. The detailed description is given in terms of a block matrix. The relation to classical multivariate Gaussian Markov triplets is also described. The minimizer of relative entropy with respect to a Gaussian markov state has the Markov property.

Petz, Dénes; Pitrik, József

2010-01-01

104

Gaussian particle filtering  

Microsoft Academic Search

Sequential Bayesian estimation for dynamic state space models involves recursive estimation of hidden states based on noisy observations. The update of filtering and predictive densities for nonlinear models with non-Gaussian noise using Monte Carlo particle filtering methods is considered. The Gaussian particle filter (GPF) is introduced, where densities are approximated as a single Gaussian, an assumption which is also made

Jayesh H. Kotecha; Petar M. Djuric

2001-01-01

105

Control systems synthesis for a large flexible space antenna  

Microsoft Academic Search

The problem of control systems synthesis is considered for controlling the rigid-body attitude and elastic motion of a large deployable space-based antenna. Two methods for control systems synthesis are considered. The first method utilizes the stability and robustness properties of the controller consisting of torque actuators and collocated attitude and rate sensors. The second method is based on the linear-quadratic-Gaussian

S. M. Joshi

1982-01-01

106

A Quadratic Closure for Compressible Turbulence  

SciTech Connect

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

Futterman, J A

2008-09-16

107

Concretising Factorisation of Quadratic Expressions  

ERIC Educational Resources Information Center

|The way quadratic factorisation was usually taught to students in Bukit View Secondary was through the familiar "cross-method." However, some teachers felt that a significant number of students could not use the method effectively even after careful demonstration through repeated examples. In addition, many secondary mathematics teachers find it…

Hoong, Leong Yew; Fwe, Yap Sook; Yvonne, Teo Mei Lin; Subramaniam, Thilagam d/o; Zaini, Irni Karen Bte Mohd; Chiew, Quek Eng; Karen, Tan Kang Ling

2010-01-01

108

ON CONDITIONALLY DEFINITE QUADRATIC FORMS  

Microsoft Academic Search

Second order optimality conditions may require the verification of a conditional definiteness condition of the formwhere Q(·) is a quadratic form on R and A is an m x n matrix. The prototype case, apart from that of positive definiteness, is that in which A is the n x n identity matrix—in this case the conditionally definite forms are called

D H Martin; D H Jacobson

1982-01-01

109

Solving Quadratic Equations by Factoring  

NSDL National Science Digital Library

This video explains how to solve quadratic equations with the factoring method. In 4 minutes 23 seconds, the two narrators explain in detail the steps required. Additionally, how these equations relate to objects and events in the real world such as roller coasters is covered.

2012-08-06

110

Helical apodizers for tunable hyper Gaussian masks  

NASA Astrophysics Data System (ADS)

We discuss an optical method for controlling the half-width of Gaussian like transmittance windows, by using a pair of absorption masks that have both radial and helical amplitude variations. For describing the radial part of the proposed masks, we employ amplitude transmittance profiles of the form T(?) = exp(- ? s ). For s = 2, one has an amplitude transmittance that is proportional to a Gaussian function. A sub Gaussian mask is defined by a value of s < 2. And if s > 2, one has super Gaussian masks. Our discussion considers that any of these radially varying masks has also helical modulations. We show that by using a suitable pair of this type of masks, one can control the halfwidth of Gaussian like windows.

Ojeda-Castañeda, J.; Ledesma, Sergio; Gómez-Sarabia, Cristina M.

2013-09-01

111

Linear and Quadratic Time-Frequency Representations.  

National Technical Information Service (NTIS)

This report is reviewing both linear and quadratic time-frequency representations. The linear representations discussed are Short-Time Fourier Transform and S-transform. The quadratic representation discussed is Wigner distribution. We outline the motivat...

T. Thayaparan

2000-01-01

112

Geometrical Solutions of Quadratic Equations.  

ERIC Educational Resources Information Center

|Demonstrates that the equation of a circle (x-h)2 + (y-k)2 = r2 with center (h; k) and radius r reduces to a quadratic equation x2-2xh + (h2 + k2 -r2) = O at the intersection with the x-axis. Illustrates how to determine the center of a circle as well as a point on a circle. (Author/ASK)|

Grewal, A. S.; Godloza, L.

1999-01-01

113

Generalized Quadratic Stabilization for Perturbated Discrete-time Singular Systems with Delayed State  

Microsoft Academic Search

This paper discusses a generalized quadratic stabilization problem for a class of discrete-time singular system with time-delay and nonlinear perturbation (DSSDP) which satisfies Lipschitz condition. By means of Sprocedure approach, necessary and sufficient condition is presented via matrix inequality such that the control system is generalized quadratically stabilizable. An explicit expression of static state feedback controllers is obtained via some

Guoping Lu; Daniel W. C. Ho

2003-01-01

114

On the LQG problem with correlated noise and its relation to minimum variance control  

Microsoft Academic Search

The linear quadratic Gaussian (LQG) stochastic control problem with correlated dynamic and observation noise and no information delay is studied. An explicit feedback solution is given for finite as well as infinite time problems. These results are then applied to minimum variance control of single-input single-output ARMAX systems. The LQG controller and the minimum variance controller obtained using input-output methods

R. H. Kwong

1987-01-01

115

An H Controller With Wind Disturbance Rejection Properties for the DSS13 Antenna  

Microsoft Academic Search

The feed-forward and linear quadratic Gaussian (LQG) controllers signiflcantly reduced the servo error at higher rate tracking. However, the servo error due to wind disturbances acting on the antenna structure is still signiflcant. This error cannot be reduced by the feed-forward controller and is only moderately reduced by the LQG controller. The H1 controller design approach gives the possibility of

W. Gawronski

1996-01-01

116

Learning Mixtures of Gaussians  

Microsoft Academic Search

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

Sanjoy Dasgupta

1999-01-01

117

Efficient high-energy femtosecond pulse compression in quadratic media with flattop beams.  

PubMed

Using a Gaussian-to-flattop beam reshaper and a frequency-doubling crystal, we demonstrate highly efficient and spatially uniform pulse compression of 1mJ, ~100fs pulses from a regenerative Ti:sapphire amplifier. The technique has general applicability to all-bulk self-defocusing-type cascaded-quadratic compressors, providing a way to increase peak power and intensity for a wide range of amplified femtosecond pulsed lasers. PMID:17767274

Moses, Jeffrey; Alhammali, Eihab; Eichenholz, Jason M; Wise, Frank W

2007-09-01

118

Application of reduced-order controller to turbulent flows for drag reduction  

Microsoft Academic Search

A reduced-order linear feedback controller is designed and applied to turbulent channel flow for drag reduction. From the linearized two-dimensional Navier-Stokes equations a distributed feedback controller, which produces blowing\\/suction at the wall based on the measured turbulent streamwise wall-shear stress, is derived using model reduction techniques and linearquadratic-Gaussian\\/loop-transfer-recovery control synthesis. The quadratic cost criterion used for synthesis is composed of

Keun H. Lee; Luca Cortelezzi; John Kim; Jason Speyer

2001-01-01

119

Reactive power optimization using successive quadratic programming method  

Microsoft Academic Search

This paper presents a reactive power optimization model that is based on successive quadratic programming (SQP) methods. Mathematical formulation and unified algorithm suppose different objective functions (OF) of reactive power optimization, depending on type and purposes of current reactive power control or planning problem. A bicriterion reactive power optimization model, that represents compromise between economical and security objective functions, is

N. Grudinin

1998-01-01

120

Gaussian Multipole Model (GMM)  

PubMed Central

An electrostatic model based on charge density is proposed as a model for future force fields. The model is composed of a nucleus and a single Slater-type contracted Gaussian multipole charge density on each atom. The Gaussian multipoles are fit to the electrostatic potential (ESP) calculated at the B3LYP/6-31G* and HF/aug-cc-pVTZ levels of theory and tested by comparing electrostatic dimer energies, inter-molecular density overlap integrals, and permanent molecular multipole moments with their respective ab initio values. For the case of water, the atomic Gaussian multipole moments Qlm are shown to be a smooth function of internal geometry (bond length and bond angle), which can be approximated by a truncated linear Taylor series. In addition, results are given when the Gaussian multipole charge density is applied to a model for exchange-repulsion energy based on the inter-molecular density overlap.

Elking, Dennis M.; Cisneros, G. Andres; Piquemal, Jean-Philip; Darden, Thomas A.; Pedersen, Lee G.

2009-01-01

121

Free Gaussian Wave Packet  

NSDL National Science Digital Library

The Free Gaussian Wave Packet model simulates the time evolution of a free-particle Gaussian wave packet in position and k (momentum) space.  The position-space and k-space (momentum-space) wave functions are depicted using three colors on the graph to depict the absolute square of the wave function, the real part of the wave function, and the imaginary part of the wave function. The user may change the wave packet's initial width, its initial average position, and its initial average k value (momentum). The Free Gaussian Wave Packet model was created using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_qm_free_gaussian.jar file will run the program if Java is installed.

Palop, Jose I.

2010-07-16

122

Transverse mode properties of lasers with Gaussian gain  

NASA Astrophysics Data System (ADS)

The modes and beam characteristics of a Gaussian gain laser resonator are analyzed. Such a gain is typically associated with an end pumped solid state laser. The beam propagation method is used to find the eigenmodes. The eigenmodes are non Gaussian in appearance and differ greatly from the modes of the same cavity with a quadratic gain. It is found that the cavity geometry strongly influences mode formation around degenerate cavity geometries throughout a broad range of operational parameters. The beam propagation method is used to evolve the field through the resonator, resulting in computation of the nonorthogonal eigenmodes. This permits evaluation of the excess noise dependence on geometric cavity parameters such as length and focal length. It is shown that the beam quality M 2 and Petermann K factor are related and are anticorrelated at degeneracies. An explanation is given based on the self Fourier transforming properties of degenerate cavity locations. It is shown how the empty cavity properties of transverse mode degeneracies are not revealed with a quadratic gain, but are strikingly present with a Gaussian gain. A confocal cavity is studied in detail and found to have the property that forces K to unity even in the presence of strong gains and narrow pump widths. The interplay between the diffraction effects of a geometrically stable cavity and the Gaussian gain will be studied to reveal the nature and implications of the non-normal modes encountered.

Maes, Carl Francis

123

Gaussian operations and privacy  

SciTech Connect

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

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

2005-07-15

124

Multiobjective Gaussian Particle Swarm Approach Applied to Multiloop PI Controller Tuning of a Quadruple-Tank System  

Microsoft Academic Search

The use of PI (Proportional-Integral), PD (Proportional-Derivative) and PID (Proportional-Integral-Derivative)controllers\\u000a have a long history in control engineering and are acceptable for most of real applications because of their simplicity in\\u000a architecture and their performances are quite robust for a wide range of operating conditions. Unfortunately, it has been\\u000a quite difficult to tune properly the gains of PI, PD, and PID

Leandro Dos Santos Coelho; Helon Vicente Hultmann Ayala; Nadia Nedjah; Luiza De Macedo Mourelle

2010-01-01

125

Gaussian quantum information  

NASA Astrophysics Data System (ADS)

The science of quantum information has arisen over the last two decades centered on the manipulation of individual quanta of information, known as quantum bits or qubits. Quantum computers, quantum cryptography, and quantum teleportation are among the most celebrated ideas that have emerged from this new field. It was realized later on that using continuous-variable quantum information carriers, instead of qubits, constitutes an extremely powerful alternative approach to quantum information processing. This review focuses on continuous-variable quantum information processes that rely on any combination of Gaussian states, Gaussian operations, and Gaussian measurements. Interestingly, such a restriction to the Gaussian realm comes with various benefits, since on the theoretical side, simple analytical tools are available and, on the experimental side, optical components effecting Gaussian processes are readily available in the laboratory. Yet, Gaussian quantum information processing opens the way to a wide variety of tasks and applications, including quantum communication, quantum cryptography, quantum computation, quantum teleportation, and quantum state and channel discrimination. This review reports on the state of the art in this field, ranging from the basic theoretical tools and landmark experimental realizations to the most recent successful developments.

Weedbrook, Christian; Pirandola, Stefano; García-Patrón, Raúl; Cerf, Nicolas J.; Ralph, Timothy C.; Shapiro, Jeffrey H.; Lloyd, Seth

2012-04-01

126

Measuring Primordial Non-Gaussianity in the Cosmic Microwave Background  

NASA Astrophysics Data System (ADS)

We derive a fast way for measuring primordial non-Gaussianity in a nearly full-sky map of the cosmic microwave background. We find a cubic combination of sky maps combining bispectrum configurations to capture a quadratic term in primordial fluctuations. Our method takes only N3/2 operations rather than N5/2, as taken by the bispectrum analysis (1000 times faster for l=512), retaining the same sensitivity. A key component is a map of the underlying primordial fluctuations, which can be more sensitive to the primordial non-Gaussianity than a temperature map. We also derive a fast and accurate statistic for measuring non-Gaussian signals from foreground point sources. The statistic is 106 times faster than the full bispectrum analysis and can be used to estimate contamination from the sources. Our algorithm has been successfully applied to the Wilkinson Microwave Anisotropy Probe sky maps by Komatsu and coworkers.

Komatsu, E.; Spergel, D. N.; Wandelt, B. D.

2005-11-01

127

Large non-Gaussianity in multiple-field inflation  

SciTech Connect

We investigate non-Gaussianity in general multiple-field inflation using the formalism we developed in earlier papers. We use a perturbative expansion of the nonlinear equations to calculate the three-point correlator of the curvature perturbation analytically. We derive a general expression that involves only a time integral over background and linear perturbation quantities. We work out this expression explicitly for the two-field slow-roll case, and find that non-Gaussianity can be orders of magnitude larger than in the single-field case. In particular, the bispectrum divided by the square of the power spectrum can easily be of O(1-10), depending on the model. Our result also shows the explicit momentum dependence of the bispectrum. This conclusion of large non-Gaussianity is confirmed in a semianalytic investigation of a simple quadratic two-field model.

Rigopoulos, G.I. [Institute for Theoretical Physics, Utrecht University, Postbus 80.195, 3508 TD Utrecht (Netherlands); Shellard, E.P.S.; Tent, B.J.W. van [Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA (United Kingdom)

2006-04-15

128

Binary Quadratic Forms: A Historical View  

ERIC Educational Resources Information Center

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

Khosravani, Azar N.; Beintema, Mark B.

2006-01-01

129

Binary Quadratic Forms: A Historical View  

ERIC Educational Resources Information Center

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

Khosravani, Azar N.; Beintema, Mark B.

2006-01-01

130

How to solve a Quadratic Equation  

Microsoft Academic Search

One of the author's favorite experiences in high school mathematics was learning how to solve quadratic equations. As is usual with life, things are not as simple as they were in high school. There are several problems with the quadratic formula. In this article, the author talks about these problems and various solutions to them.

James F. Blinn

2005-01-01

131

Another Look at the Quadratic Formula.  

ERIC Educational Resources Information Center

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

Obermeyer, Dean D.

1982-01-01

132

Sensitivity analysis in Gaussian Bayesian networks using a symbolic-numerical technique  

Microsoft Academic Search

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

Enrique Castillo; Uffe Kjærulff

2003-01-01

133

Distortion sum-rate performance of successive coding strategy in Gaussian wireless sensor networks  

Microsoft Academic Search

In this paper, we investigate the distortion sum-rate performance of the successive coding strategy in the so-called quadratic Gaussian CEO problem. In the CEO problem, the central unit or the CEO desires to obtain an optimal estimate of the source signal. Since the source cannot be observed directly, L sensors will be deployed to observe independently corrupted versions of the

Hamid Behroozi; M. Reza Soleymani

2005-01-01

134

First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Tests of Gaussianity  

Microsoft Academic Search

We present limits to the amplitude of non-Gaussian primordial fluctuations in the WMAP 1 yr cosmic microwave background sky maps. A nonlinear coupling parameter, fNL, characterizes the amplitude of a quadratic term in the primordial potential. We use two statistics: one is a cubic statistic which measures phase correlations of temperature fluctuations after combining all configurations of the angular bispectrum.

E. Komatsu; A. Kogut; M. R. Nolta; C. L. Bennett; M. Halpern; G. Hinshaw; N. Jarosik; M. Limon; S. S. Meyer; L. Page; D. N. Spergel; G. S. Tucker; L. Verde; E. Wollack; E. L. Wright

2003-01-01

135

LQG\\/LTR controller design using a reduced order model  

Microsoft Academic Search

A specific robust controller design procedure, linear quadratic Gaussian with loop transfer recovery (LQG\\/LTR), is studied. LQG\\/LTR design using a reduced-order model is performed. The error due to the use of the reduced model is accounted for by computing multiplicative error. All closed right half plane modes of the given system are included in the reduced-order model. The reduced-order LQG\\/LTR

Rajiva Prakash; S. V. Rao

1989-01-01

136

A quadratically convergent VBSCF method  

NASA Astrophysics Data System (ADS)

A quadratically convergent valence bond self-consistent field method is described where the simultaneous optimisation of orbitals and the coefficients of the configurations (VB structures) is based on a Newton-Raphson scheme. The applicability of the method is demonstrated in actual calculations. The convergence and efficiency are compared with the Super-CI method. A necessary condition to achieve convergence in the Newton-Raphson method is that the Hessian is positive definite. When this is not the case, a combination of the Super-CI and Newton-Raphson methods is shown to be an optimal choice instead of shifting the eigenvalues of the Hessian to make it positive definite. In the combined method, the first few iterations are performed with the Super-CI method and then the Newton-Raphson scheme is switched on based on an internal indicator. This approach is found computationally a more economical choice than using either the Newton-Raphson or Super-CI method alone to perform a full optimisation of the nonorthogonal orbitals.

Rashid, Zahid; van Lenthe, Joop H.

2013-02-01

137

Fuzzy Gaussian Potential Neural Networks Using a Functional Reasoning  

Microsoft Academic Search

This paper presents the principal design of a fuzzy gaussian potential neural network (FGPNN) to achieve high capability to learn expert control rules of the fuzzy controller. In this construction, each membership function consists of a gaussian potential function (GPF) which causes the utilization of a reduced number of labels, and eventually the complexity of structural design becomes simple, specially

Mohammad Teshnehlab; Keigo Watanabe

1994-01-01

138

Bioluminescence tomography with Gaussian prior  

PubMed Central

Parameterizing the bioluminescent source globally in Gaussians provides several advantages over voxel representation in bioluminescence tomography. It is mathematically unique to recover Gaussians [Med. Phys. 31(8), 2289 (2004)] and practically sufficient to approximate various shapes by Gaussians in diffusive medium. The computational burden is significantly reduced since much fewer unknowns are required. Besides, there are physiological evidences that the source can be modeled by Gaussians. The simulations show that the proposed model and algorithm significantly improves accuracy and stability in the presence of Gaussian or non- Gaussian sources, noisy data or the optical background mismatch. It is also validated through in vivo experimental data.

Gao, Hao; Zhao, Hongkai; Cong, Wenxiang; Wang, Ge

2010-01-01

139

Quadratic prediction problems in multivariate linear models  

Microsoft Academic Search

Linear and quadratic prediction problems in finite populations have become of great interest to many authors recently. In the present paper, we mainly aim to extend the problem of quadratic prediction from a general linear model, of form y=X?+e,e?N(0,?2V), to a multivariate linear model, denoted by Y=XB+E,V ec(E)?N(0,??V) with Y=(yij)n×q=(y1,…,yq). Firstly, the optimal invariant quadratic unbiased (OIQU) predictor and the

Xu-Qing Liu; Dong-Dong Wang; Jian-Ying Rong

2009-01-01

140

Combining Gaussian Mixture Models  

Microsoft Academic Search

A Gaussian mixture model (GMM) estimates a probability density function using the expectation-maximization algorithm. However, it may lead to a poor performance or inconsistency. This paper analytically shows that per- formance of a GMM can be improved in terms of Kullback-Leibler divergence with a committee of GMMs with different initial parameters. Simulations on synthetic datasets demonstrate that a committee of

Hyoung-joo Lee; Sungzoon Cho

2004-01-01

141

Gaussian fields and Gaussian sheets with generalized Cauchy covariance structure  

Microsoft Academic Search

Two types of Gaussian processes, namely the Gaussian field with generalized Cauchy covariance (GFGCC) and the Gaussian sheet with generalized Cauchy covariance (GSGCC) are considered. Some of the basic properties and the asymptotic properties of the spectral densities of these random fields are studied. The associated self-similar random fields obtained by applying the Lamperti transformation to GFGCC and GSGCC are

S. C. Lim; L. P. Teo

2009-01-01

142

Scintillations of Laguerre Gaussian beams  

NASA Astrophysics Data System (ADS)

By using the Rytov method, we formulate and numerically evaluate the scintillations of Laguerre Gaussian beams in weak atmospheric turbulence. Our results indicate that at on-axis positions, Laguerre Gaussian beams with zero angular mode number will have less scintillations than fundamental Gaussian beams, where the amount of scintillations will further decrease with rising radial mode number. When off-axis positions are considered, this situation reverses however, and the scintillations of Laguerre Gaussian beams become generally higher than the fundamental Gaussian beam. Plotted against the source size, the on-axis scintillations of Laguerre Gaussian beams fall below the fundamental Gaussian beam, following the same trend as the fundamental Gaussian beam all throughout the source size range examined.

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

2010-03-01

143

Quasi-Gaussian Particle Filtering  

Microsoft Academic Search

\\u000a The recently-raised Gaussian particle filtering (GPF) introduced the idea of Bayesian sampling into Gaussian filters. This\\u000a note proposes to generalize the GPF by further relaxing the Gaussian restriction on the prior probability. Allowing the non-Gaussianity\\u000a of the prior probability, the generalized GPF is provably superior to the original one. Numerical results show that better\\u000a performance is obtained with considerably reduced

Yuanxin Wu; Dewen Hu; Meiping Wu; Xiaoping Hu

2006-01-01

144

Elegant Ince-Gaussian beams  

NASA Astrophysics Data System (ADS)

The existence of elegant Ince-Gaussian beams that constitute a third complete family of exact and biorthogonal elegant solutions of the paraxial wave equation is demonstrated. Their transverse structure is described by Ince polynomials with a complex argument. Elegant Ince-Gaussian beams constitute exact and continuous transition modes between elegant Laguerre-Gaussian and elegant Hermite-Gaussian beams. The expansion formulas among the three elegant families are derived.

Bandres, Miguel A.

2004-08-01

145

Size matters more than method: Visual quadrats vs photography in measuring human impact on Mediterranean rocky reef communities  

Microsoft Academic Search

The performances of two commonly used non-destructive sampling procedures for rocky benthic assemblages (i.e. photography and visually assessed quadrats) were compared. A damaging human activity, date mussel (Lithophaga lithophaga) harvesting (DMH), was chosen. Directly impacted sites were compared with reference conditions (controls). Both visual quadrats and photography were equally able to detect differences between impacted situations and controls. However, visual

Valeriano Parravicini; Carla Morri; Giada Ciribilli; Monica Montefalcone; Giancarlo Albertelli; Carlo Nike Bianchi

2009-01-01

146

Strict sensitivity analysis in fuzzy quadratic programming  

Microsoft Academic Search

Quadratic programming can be seen both as a general approach to linear programming and a special class of non-linear programming. Moreover, quadratic programming problems are of utmost importance in an increasing variety of practical fields, such as, regression, efficient production and portfolio selection. As ambiguity and vagueness are natural and ever-present in real-life situations requiring solutions, it makes perfect sense

B. Kheirfam; J. L. Verdegay

147

A central limit theorem for quadratic forms in strongly dependent linear variables and its application to asymptotical normality of Whittle's estimate  

Microsoft Academic Search

Summary A central limit theorem for quadratic forms in strongly dependent linear (or moving average) variables is proved, generalizing the results of Avram [1] and Fox and Taqqu [3] for Gaussian variables. The theorem is applied to prove asymptotical normality of Whittle's estimate of the parameter of strongly dependent linear sequences.

L. Giraitis; D. Surgailis

1990-01-01

148

Optimal power flow using sequential quadratic programming  

NASA Astrophysics Data System (ADS)

Optimal power flow (OPF) is an operational as well as a planning tool used by electric utilities to help them operate their network in the most economic and secure mode of operation. Various algorithms to solve the OPF problem evolved over the past three decades; linear programming (LP) techniques were among the major mathematical programming methods utilized. The linear models of the objective function and the linearization of the constraints are the main features of these techniques. The main advantages of the LP approach are simplicity and speed. Nonlinear programming techniques have been applied to OPF solution. The major drawback is the expensive solution of large sparse systems of equations. This research is concerned with the development of a new OPF solution algorithm using sequential quadratic programming (SQP). In this formulation, a small dense system the size of which is equal to the number of control variables is solved in an inner loop. The Jacobian and Hessian terms are calculated in an outer loop. The total number of outer loop iterations is comparable to those in an ordinary load flow in contrast to 20--30 iterations in other nonlinear methods. In addition, the total number of floating point operations is less than that encountered in direct methods by two orders of magnitude. We also model dispatch over a twenty four-hour time horizon in a transmission constrained power network that includes price-responsive loads where large energy customers can operate their loads in time intervals with lowest spot prices.

Nejdawi, Imad M.

1999-11-01

149

Turbofan Engine Control System Design Using the LQG\\/LTR Methodology  

Microsoft Academic Search

Application of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery methodology to design of a control system for a simplified turbofan engine model is considered. The importance of properly scaling the plant to achieve the desired Target-Feedback-Loop is emphasized. The steps involved in the application of the methodology are discussed via an example, and evaluation results a presented for a reduced-order compensator. The effect

Sanjay Garg

1989-01-01

150

Exact quantum states of a general time-dependent quadratic system from classical action  

NASA Astrophysics Data System (ADS)

A generalization of a driven harmonic oscillator with time-dependent mass and frequency, by adding total time-derivative terms to the Lagrangian, is considered. The generalization, which gives a general quadratic Hamiltonian system, does not change the classical equation of motion. Based on the observation by Feynman and Hibbs, the propagators (kernels) of the systems are calculated from the classical action, in terms of solutions of the classical equation of motion: two homogeneous solutions and one particular solution. The kernels are then used to find wave functions that satisfy the Schrödinger equation. One of the wave functions is shown to be that of a Gaussian pure state. In every case considered, we prove that the kernel does not depend on the way of choosing the classical solutions, while the wave functions depend on the choice. The generalization, which gives a rather complicated quadratic Hamiltonian, is simply interpreted as applying unitary transformation to the driven harmonic oscillator system in the Hamiltonian formulation.

Song, Dae-Yup

1999-04-01

151

On decoding (31, 16, 7) quadratic residue code up to its error correcting capacity with bit-error probability estimates  

NASA Astrophysics Data System (ADS)

The quadratic residue codes are a class of the error correcting codes with interesting mathematics. Among them, the (31, 16, 7) quadratic residue code is the code with reducible generator polynomial and three-error-correcting capacity. The algebraic decoding algorithm for the (32, 16, 8) quadratic residue code is developed by Reed et al. (1990). In this paper, a simplified decoding algorithm is proposed. The algorithm uses bit-error probability estimates, which is first developed by Reed MIT Lincoln Laboratory Report (1959), to cancel the third error and then uses the algebraic decoding algorithm mentioned above to correct the remaining two errors. Simulation results show that this modified decoding algorithm slightly reduces the decoding complexity for correcting the third error while maintaining the same BER performance in additive white Gaussian noise (AWGN). Also, the flowchart of the above decoding algorithm is illustrated with Fig. 1.

Lin, Tsung-Ching; Shih, Pei-Yu; Su, Wen-Ku; Truong, Trieu-Kien

2010-08-01

152

GENERALIZED QUADRATIC STABILIZATION FOR DISCRETE-TIME SINGULAR SYSTEMS WITH TIME-DELAY AND NONLINEAR PERTURBATION  

Microsoft Academic Search

This paper discusses a generalized quadratic stabilization problem for a class of discrete-time singular systems with time-delay and nonlinear per- turbation (DSSDP), which the satisfies Lipschitz condition. By means of the S-procedure approach, necessary and sufficient conditions are presented via a matrix inequality such that the control system is generalized quadratically stabilizable. An explicit expression of the static state feedback

Guoping Lu; Daniel W. C. Ho

2005-01-01

153

Driving non-Gaussian to Gaussian states with linear optics  

SciTech Connect

We introduce a protocol that maps finite-dimensional pure input states onto approximately Gaussian states in an iterative procedure. This protocol can be used to distill highly entangled bipartite Gaussian states from a supply of weakly entangled pure Gaussian states. The entire procedure requires only the use of passive optical elements and photon detectors, which solely distinguish between the presence and absence of photons.

Browne, Daniel E.; Scheel, Stefan; Plenio, Martin B. [QOLS, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW (United Kingdom); Eisert, Jens [QOLS, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW (United Kingdom); Institut fuer Physik, Universitaet Potsdam, Am Neuen Palais 10, D-14469 Potsdam (Germany)

2003-06-01

154

Gaussian matrix-product states for coding in bosonic communication channels  

NASA Astrophysics Data System (ADS)

The communication capacity of Gaussian bosonic channels with memory has recently attracted much interest. Here, we investigate a method to prepare the multimode entangled input symbol states for encoding classical information into these channels. In particular, we study the usefulness of a Gaussian matrix-product state (GMPS) as an input symbol state, which can be sequentially generated although it remains heavily entangled for an arbitrary number of modes. We show that the GMPS can achieve more than 99.9% of the Gaussian capacity for Gaussian bosonic memory channels with a Markovian or non-Markovian correlated noise model in a large range of noise correlation strengths. Furthermore, we present a noise class for which the GMPS is the exact optimal input symbol state of the corresponding channel. Since GMPS are ground states of particular quadratic Hamiltonians, our results suggest a possible link between the theory of quantum communication channels and quantum many-body physics.

Schäfer, Joachim; Karpov, Evgueni; Cerf, Nicolas J.

2012-01-01

155

Sharp Quadratic Majorization in One Dimension  

PubMed Central

Majorization methods solve minimization problems by replacing a complicated problem by a sequence of simpler problems. Solving the sequence of simple optimization problems guarantees convergence to a solution of the complicated original problem. Convergence is guaranteed by requiring that the approximating functions majorize the original function at the current solution. The leading examples of majorization are the EM algorithm and the SMACOF algorithm used in Multidimensional Scaling. The simplest possible majorizing subproblems are quadratic, because minimizing a quadratic is easy to do. In this paper quadratic majorizations for real-valued functions of a real variable are analyzed, and the concept of sharp majorization is introduced and studied. Applications to logit, probit, and robust loss functions are discussed.

de Leeuw, Jan; Lange, Kenneth

2009-01-01

156

The Quadratic-Chi Histogram Distance Family  

Microsoft Academic Search

\\u000a We present a new histogram distance family, the Quadratic-Chi (QC). QC members are Quadratic-Form distances with a cross-bin\\u000a ?\\u000a 2-like normalization. The cross-bin ?\\u000a 2-like normalization reduces the effect of large bins having undo influence. Normalization was shown to be helpful in many\\u000a cases, where the ?\\u000a 2 histogram distance outperformed the L\\u000a 2 norm. However, ?\\u000a 2 is sensitive

Ofir Pele; Michael Werman

2010-01-01

157

Nonlinear dynamics of quadratically cubic systems  

NASA Astrophysics Data System (ADS)

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.

Rudenko, O. V.

2013-07-01

158

Mating Non-Renormalizable Quadratic Polynomials  

NASA Astrophysics Data System (ADS)

In this paper we prove the existence and uniqueness of matings of the basilica with any quadratic polynomial which lies outside of the 1/2-limb of {mathcal {M}} , is non- renormalizable, and does not have any non-repelling periodic orbits.

Aspenberg, Magnus; Yampolsky, Michael

2009-04-01

159

An r-Dimensional Quadratic Placement Algorithm  

Microsoft Academic Search

In this paper the solution to the problem of placing n connected points (or nodes) in r-dimensional Euclidean space is given. The criterion for optimality is minimizing a weighted sum of squared distances between the points subject to quadratic constraints of the form X'X - 1, for each of the r unknown coordinate vectors. It is proved that the problem

Kenneth M. Hall

1970-01-01

160

Curious Consequences of a Miscopied Quadratic  

ERIC Educational Resources Information Center

The starting point of this article is a search for pairs of quadratic polynomials x[superscript 2] + bx plus or minus c with the property that they both factor over the integers. The search leads quickly to some number theory in the form of primitive Pythagorean triples, and this paper develops the connection between these two topics.

Poet, Jeffrey L.; Vestal, Donald L., Jr.

2005-01-01

161

Applications of Multivariate Quadratic Public Key Systems  

Microsoft Academic Search

In this article, we investigate the class of multivariate quadratic (MQ) public key systems. These systems are becoming a serious alternative to RSA or ECC based systems. After introducing the main ideas and sketching some relevant systems, we deal with the advantages and disadvantages of these kinds of schemes. Based on our observations, we determine application domains in which MQ-schemes

Christopher Wolf; Bart Preneel

2005-01-01

162

Factorization Using the Quadratic Sieve Algorithm  

Microsoft Academic Search

Since the cryptosecurity of the RSA two key cryptoalgorithm is no greater than the difficulty of factoring the modulus (product of two secret primes), a code that implements the Quadratic Sieve factorization algorithm on the CRAY I computer has been developed at the Sandia National Laboratories to determine as sharply as possible the current state-of-the-art in factoring. Because all viable

James A. Davis; Diane B. Holdridge

1983-01-01

163

Factorization Using the Quadratic Sieve Algorithm.  

National Technical Information Service (NTIS)

Since the cryptosecurity of the RSA two key cryptoalgorithm is no greater than the difficulty of factoring the modulus (product of two secret primes), a code that implements the Quadratic Sieve factorization algorithm on the CRAY I computer has been devel...

J. A. Davis D. B. Holdridge

1983-01-01

164

Integration of the Quadratic Function and Generalization  

ERIC Educational Resources Information Center

|We will first recall useful formulas in integration that simplify the calculation of certain definite integrals with the quadratic function. A main formula relies only on the coefficients of the function. We will then explore a geometric proof of one of these formulas. Finally, we will extend the formulas to more general cases. (Contains 3…

Mitsuma, Kunio

2011-01-01

165

The period function of quadratic centers  

Microsoft Academic Search

In this paper we investigate the bifurcation diagram of the period function associated to a family of quadratic centers, namely the dehomogenized Loud's systems. The local bifurcation diagram of the period function at the center is fully understood using the results of Chicone and Jacobs (4). Most of the present paper deals with the local bifurcation diagram at the polycycle

P. Marde; J. Villadelprat

166

Quadratic forms involving Green's and Robin functions  

SciTech Connect

General inequalities for quadratic forms with coefficients depending on the values of Green's and Robin functions are obtained. These inequalities cover also the reduced moduli of strips and half-strips. Some applications of the results obtained to extremal partitioning problems and related questions of geometric function theory are discussed. Bibliography: 29 titles.

Dubinin, Vladimir N [Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences, Vladivostok (Russian Federation)

2009-10-31

167

Experiments with successive quadratic programming algorithms  

Microsoft Academic Search

There are many variants of successive quadratic programming (SQP) algorithms. Important issues include: the choice of either line search or trust region strategies; the QP formulation to be used; and how the QP is to be solved. Here, we consider the QP's proposed by Fletcher and Powell and discuss a specialized reduced-gradient procedure for solving them. A computer implementation is

Y. Fan; S. Sarkar; L. Lasdon

1988-01-01

168

ChemXSeer Digital Library Gaussian Search  

Microsoft Academic Search

We report on the Gaussian file search system designed as part of the ChemXSeer digital library. Gaussian files are produced by the Gaussian software [4], a software package used for calculating molecular electronic structure and properties. The output files are semi-structured, allowing relatively easy access to the Gaussian attributes and metadata. Our system is currently capable of searching Gaussian documents

Shibamouli Lahiri; Juan Pablo Fernández Ramírez; Shikha Nangia; Prasenjit Mitra; C. Lee Giles; Karl T. Mueller

2011-01-01

169

Gaussian Processes in Machine Learning  

Microsoft Academic Search

We give a basic introduction to Gaussian Process regression models. We focus on understanding the role of the stochastic process and how it is used to define a distribution over functions. We present the simple equations for incorporating training data and examine how to learn the hyperparameters using the marginal likelihood. We explain the practical advantages of Gaussian Process and

Carl Edward Rasmussen; Max Planck

2003-01-01

170

On Exponential Hedging and Related Quadratic Backward Stochastic Differential Equations  

SciTech Connect

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.

Sekine, Jun [Institute of Economic Research, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501 (Japan)], E-mail: sekine@kier.kyoto-u.ac.jp

2006-09-15

171

Wind turbine power tracking using an improved multimodel quadratic approach.  

PubMed

In this paper, an improved multimodel optimal quadratic control structure for variable speed, pitch regulated wind turbines (operating at high wind speeds) is proposed in order to integrate high levels of wind power to actively provide a primary reserve for frequency control. On the basis of the nonlinear model of the studied plant, and taking into account the wind speed fluctuations, and the electrical power variation, a multimodel linear description is derived for the wind turbine, and is used for the synthesis of an optimal control law involving a state feedback, an integral action and an output reference model. This new control structure allows a rapid transition of the wind turbine generated power between different desired set values. This electrical power tracking is ensured with a high-performance behavior for all other state variables: turbine and generator rotational speeds and mechanical shaft torque; and smooth and adequate evolution of the control variables. PMID:20434153

Khezami, Nadhira; Benhadj Braiek, Naceur; Guillaud, Xavier

2010-07-01

172

The Symmetric Formulation of the Simplex Method for Quadratic Programming.  

National Technical Information Service (NTIS)

For the solution of convex quadratic programming problem, a number of efficient methods have been developed. The most well-known methods are the Simplex method for quadratic programming, discovered by Dantzig and, together with the closely related dual me...

C. van de Panne A. Whinston

1966-01-01

173

On the Linear and Quadratic Discriminators for Pattern Recognition.  

National Technical Information Service (NTIS)

In this report, two problems in pattern recognition are considered: (1) when the likelihood ratio criterion results in a quadratic discriminant function, it may be possible to factor the quadratic form into two linear discriminant functions. It is shown t...

P. S. R. S. Rao

1967-01-01

174

A SEQUENTIAL QUADRATIC PROGRAMMING ALGORITHM UTILIZING QR MATRIX FACTORIZATION  

Microsoft Academic Search

Some recent studies indicate that the sequential quadratic programming (SQP) approach has a sound theoretical basis and promising empirical results for solving general constrained optimization problems. This paper presents a variant of the SQP method which utilizes QR matrix factorization to solve the quadratic programming subproblem which result from taking a quadratic approximation of the original problem. Theoretically, the QR

CHIANG KAO; SHIH PEN CHEN

1994-01-01

175

Two-phase Method to Solve Fuzzy Quadratic Programming Problems  

Microsoft Academic Search

Quadratic programming problems are of up most importance in a variety of relevant practical fields, as e.g., portfolio selection. This work presents and develops an original and novel fuzzy sets based method that solves a class of quadratic programming problems with vagueness in the set of constraints. The method uses two phases to solve fuzzy quadratic programming problems, which eventually

Ricardo C. Silva; José L. Verdegay; Akebo Yamakami

2007-01-01

176

Non-Gaussian spin dephasing  

SciTech Connect

We address spin dephasing induced by stochastic transitions between different precession frequencies. A very famous analytical approximation is the Gaussian approximation presented by [Anderson and Weiss, Rev. Mod. Phys. 25, 269 (1953)]. It states that independent from the transition dynamics, a Gaussian frequency distribution implies a Gaussian distribution of the phase angles, which provides a simple analytical result for the transverse magnetization decay. In contrast we find that (i) the assumption of Gaussian dephasing restricts the stochastic dynamics to a very limited class (ii) the Anderson-Weiss model is applicable only in a special case of fluctuations, i.e., if and only if the Green's function G({omega}{sub 2},{omega}{sub 1},{delta}t) describing the transition probability between two frequencies {omega}{sub 1}{yields}{omega}{sub 2} is Gaussian, and (iii) the exact time course of magnetization decay is dependent on the relaxation time in the motional narrowing limit and the correlation time describing the correlation function of the local frequencies. In contrast to previous publications, we conclude that a Gaussian equilibrium distribution of local frequencies does not imply a Gaussian-distributed phase angle. The general theory is illustrated by calculating the Green's function of the transition dynamics for a stochastic process in the strong collision approximation. The result is highly relevant for describing relaxation processes in the presence of local field inhomogeneities.

Bauer, W.R. [Medizinische Universitaetsklinik, Bayerische Julius-Maximilians-Universitaet Wuerzburg, Josef-Schneider-Strasse 2, 97080 Wuerzburg (Germany); Ziener, C.H.; Jakob, P.M. [Institut fuer Experimentelle Physik 5, Bayerische Julius-Maximilians-Universitaet Wuerzburg, Am Hubland, 97074 Wuerzburg (Germany)

2005-05-15

177

Factorization using the quadratic sieve algorithm  

SciTech Connect

Since the cryptosecurity of the RSA two key cryptoalgorithm is no greater than the difficulty of factoring the modulus (product of two secret primes), a code that implements the Quadratic Sieve factorization algorithm on the CRAY I computer has been developed at the Sandia National Laboratories to determine as sharply as possible the current state-of-the-art in factoring. Because all viable attacks on RSA thus far proposed are equivalent to factorization of the modulus, sharper bounds on the computational difficulty of factoring permit improved estimates for the size of RSA parameters needed for given levels of cryptosecurity. Analysis of the Quadratic Sieve indicates that it may be faster than any previously published general purpose algorithm for factoring large integers. The high speed of the CRAY I coupled with the capability of the CRAY to pipeline certain vectorized operations make this algorithm (and code) the front runner in current factoring techniques.

Davis, J.A.; Holdridge, D.B.

1983-12-01

178

Factorization using the quadratic sieve algorithm  

SciTech Connect

Since the cryptosecurity of the RSA two key cryptoalgorithm is no greater than the difficulty of factoring the modulus (product of two secret primes), a code that implements the Quadratic Sieve factorization algorithm on the CRAY I computer has been developed at the Sandia National Laboratories to determine as sharply as possible the current state-of-the-art in factoring. Because all viable attacks on RSA thus far proposed are equivalent to factorization of the modulus, sharper bounds on the computational difficulty of factoring permit improved estimates for the size of RSA parameters needed for given levels of cryptosecurity. Analysis of the Quadratic Sieve indicates that it may be faster than any previously published general purpose algorithm for factoring large integers. The high speed of the CRAY I coupled with the capability of the CRAY to pipeline certain vectorized operations make this algorithm (and code) the front runner in current factoring techniques.

Davis, J.A.; Holdridge, D.B.

1983-01-01

179

A parameterized hessian quadratic programming problem  

Microsoft Academic Search

We present a general active set algorithm for the solution of a convex quadratic programming problem having a parametrized\\u000a Hessian matrix. The parametric Hessian matrix is a positive semidefinite Hessian matrix plus a real parameter multiplying\\u000a a symmetric matrix of rank one or two. The algorithm solves the problem for all parameter values in the open interval upon\\u000a which the

M. J. Best; R. J. Caron

1986-01-01

180

Testing for Cointegration in Linear Quadratic Models  

Microsoft Academic Search

This article evaluates the finite-sample performance of various tests for cointegration by Monte Carlo methods. The evaluation takes place within the linear quadratic model. The results indicate sharp differences in the ability of the tests to detect cointegrating relations, especially when the cost-of-adjustment term and the number of regressors are large. Although no single test dominates for all the parameter

Allan W. Gregory

1994-01-01

181

Tracking Algorithm Base on Quadratic BOC  

Microsoft Academic Search

Binary Offset Carrier (BOC) modulated signal has multi-correlation peaks, whose S curve of Phase Detector (PD) having several cross-zero points, this can lead to do error judge on receiver tracking. So, a new tracking algorithm is proposed in this paper, it using the quadratic BOC to removing the effect of several cross-zero points on S curve. The comparing analysis and

Li Yang; ChengSheng Pan; YanChun Wang; HaiYan Liu

2010-01-01

182

Electron clusters in a quadratic potential  

NASA Astrophysics Data System (ADS)

Clusters of electrons in a quadratic external potential are studied. By expanding in inverse powers of the space dimensionality the ground state energy of the N-electron cluster is found in the whole range of variation of the problem's parameter. The rearrangement of electron orbitals in the crossover region is investigated. On leave from the Institute of Cybernetics, Mathematics and Physics (ICIMAF), Calle O No. 8, Havana, Cuba.

Belov, A. A.; Lozovik, Yu. E.; Gonzalez, A.

1989-12-01

183

Isocurvature, non-Gaussianity, and the curvaton model  

SciTech Connect

Recent analyses of the statistical distribution of the temperature anisotropies in the cosmic microwave background do not rule out the possibility that there is a large non-Gaussian contribution to the primordial power spectrum. This fact motivates the reanalysis of the curvaton scenario, paying special attention to the compatibility of large non-Gaussianity of the local type with the current detection limits on the isocurvature amplitude in the cosmic microwave background. We find that if the curvaton mechanism generates a primordial power spectrum with an important non-Gaussian component, any residual isocurvature imprint originated by the curvaton, would have an amplitude too big to be compatible with the current bounds. This implies that the isocurvature mode should be equal to zero in this scenario and we explore the consequences of this inference. In order to prevent the generation of a such a signal, the cold dark matter (CDM) must be created at a late stage, after the curvaton decays completely. This is used to constrain the nature of the CDM, arriving at a general relation between the temperature of the universe at CDM creation and the scale of inflation. It is possible to find an absolute maximum for the temperature at CDM creation, which is dependent on the particular inflationary potential. For a quadratic potential, we find T{sub cdm}<1.7x10{sup 6} GeV.

Beltran, Maria [Department of Astronomy and Astrophysics, The University of Chicago, 5460 S. Ellis, Chicago, Illinois 60637 (United States)

2008-07-15

184

Explicit Solution to a Certain Non-ELQG Risk-sensitive Stochastic Control Problem  

SciTech Connect

A risk-sensitive stochastic control problem with finite/infinite horizon is studied with a 1-dimensional controlled process defined by a linear SDE with a linear control-term in the drift. In the criterion function, a non-linear/quadratic term is introduced by using the solution to a Riccati differential equation, and hence, the problem is not ELQG (Exponential Linear Quadratic Gaussian) in general. For the problem, optimal value and control are calculated in explicit forms and the set of admissible risk-sensitive parameters is given in a concrete form. As applications, two types of large deviations control problems, i.e., maximizing an upside large deviations probability and minimizing a downside large deviations probability, are mentioned.

Hata, Hiroaki, E-mail: hata@math.sinica.edu.t [Academia Sinica, Institute of Mathematics (China); Sekine, Jun, E-mail: sekine@kier.kyoto-u.ac.j [Kyoto University, Institute of Economic Research (Japan)

2010-12-15

185

Quadratic neural unit is a good compromise between linear models and neural networks for industrial applications  

Microsoft Academic Search

The paper discusses the quadratic neural unit (QNU) and highlights its attractiveness for industrial applications such as for plant modeling, control, and time series prediction. Linear systems are still often preferred in industrial control applications for their solvable and single solution nature and for the clarity to the most application engineers. Artificial neural networks are powerful cognitive nonlinear tools, but

Ivo Bukovsky; Noriyasu Homma; Ladislav Smetana; Ricardo Rodriguez; Martina Mironovova; Stanislav Vrana

2010-01-01

186

INTERFERENCE DETECTION IN GAUSSIAN NOISE  

SciTech Connect

Interference detection in Gaussian noise is proposed. It can be applied for easy detection and editing of interference lines in radio spectral line observations. One does not need to know the position of occurrence or keep track of interference in the band. By using statistical properties of N-channel Gaussian noise it is possible to differentiate interference from normal Gaussian noise. These statistical properties are three quantities which are calculated on the subject spectrum. The first is the expected absolute maximum from the mean level across the spectrum. The second is the expected absolute difference maximum (array of adjacent differences of channel values taken across the spectrum), and the third is the expected absolute added difference maximum. For N-channel Gaussian noise, these quantities have a well-defined value. Any deviation across the spectrum that violates an upper limit formed by these expected maxima is attributed to interference. Results obtained on real data by applying this technique have been displayed.

Baddi, Raju [Raman Research Institute, C.V. Raman Avenue., Bangalore 560 080 (India)

2011-06-15

187

Vestibular integrator neurons have quadratic functions due to voltage dependent conductances.  

PubMed

The nonlinear properties of the dendrites of the prepositus hypoglossi nucleus (PHN) neurons are essential for the operation of the vestibular neural integrator that converts a head velocity signal to one that controls eye position. A novel system of frequency probing, namely quadratic sinusoidal analysis (QSA), was used to decode the intrinsic nonlinear behavior of these neurons under voltage clamp conditions. Voltage clamp currents were measured at harmonic and interactive frequencies using specific nonoverlapping stimulation frequencies. Eigenanalysis of the QSA matrix reduces it to a remarkably compact processing unit, composed of just one or two dominant components (eigenvalues). The QSA matrix of rat PHN neurons provides signatures of the voltage dependent conductances for their particular dendritic and somatic distributions. An important part of the nonlinear response is due to the persistent sodium conductance (gNaP), which is likely to be essential for sustained effects needed for a neural integrator. It was found that responses in the range of 10 mV peak to peak could be well described by quadratic nonlinearities suggesting that effects of higher degree nonlinearities would add only marginal improvement. Therefore, the quadratic response is likely to sufficiently capture most of the nonlinear behavior of neuronal systems except for extremely large synaptic inputs. Thus, neurons have two distinct linear and quadratic functions, which shows that piecewise linear?+?quadratic analysis is much more complete than just piecewise linear analysis; in addition quadratic analysis can be done at a single holding potential. Furthermore, the nonlinear neuronal responses contain more frequencies over a wider frequency band than the input signal. As a consequence, they convert limited amplitude and bandwidth input signals to wider bandwidth and more complex output responses. Finally, simulations at subthreshold membrane potentials with realistic PHN neuron models suggest that the quadratic functions are fundamentally dominated by active dendritic structures and persistent sodium conductances. PMID:23519443

Magnani, Christophe; Eugène, Daniel; Idoux, Erwin; Moore, Lee E

2013-03-22

188

Moments for general quadratic densities in n dimensions  

SciTech Connect

We present the calculation of the generating functions and the rth-order correlations for densities of the form {rho}(x) {proportional_to} where g(s) is a non-negative function of the quadratic ''action'' s(x)={summation}{sub i,j}H{sub ij}x{sub i}x{sub j}, where x = (x{sub 1},x{sub 2}...,x{sub n}) is a real n-dimensional vector and H is a real, symmetric n x n matrix whose eigenvalues are strictly positive. In particular, we find the connection between the (r+2)th-order and rth-order correlations, which constitutes a generalization of the Gaussian moment theorem, which corresponds to the particular choice g(s)=e{sup -s/2}. We present several examples for specific choices for g(s), including the explicit expression for the generating function for each case and the subspace projection of {rho}(x) in a few cases. We also provide the straightforward generalizations to: (1) the case where g=g(s(x)+a {center_dot} x), where a=(a{sub 1},a{sub 2},...,a{sub n}) is an arbitrary real n-dimensional vector, and (2) the complex case, in which the action is of the form s(z) = {summation}{sub i,j}H{sub ij}z{sup *}{sub i} z{sub j} where z=(z{sub 1},z{sub 2}...z{sub n}) is an n-dimensional complex vector and H is a Hermitian n x n matrix whose eigenvalues are strictly positive.

Furman, Miguel A.

2002-03-20

189

Quadratic finite elements and incompressible viscous flows.  

SciTech Connect

Pressure stabilization methods are applied to higher-order velocity finite elements for application to viscous incompressible flows. Both a standard pressure stabilizing Petrov-Galerkin (PSPG) method and a new polynomial pressure projection stabilization (PPPS) method have been implemented and tested for various quadratic elements in two dimensions. A preconditioner based on relaxing the incompressibility constraint is also tested for the iterative solution of saddle point problems arising from mixed Galerkin finite element approximations to the Navier-Stokes equations. The preconditioner is demonstrated for BB stable elements with discontinuous pressure approximations in two and three dimensions.

Dohrmann, Clark R.; Gartling, David K.

2005-01-01

190

Oscillations of a quadratically damped pendulum  

NASA Astrophysics Data System (ADS)

A physical pendulum consisting of a circular disk at the end of a thin metal rod is connected to a low-friction rotary motion sensor, so that its angular position and velocity can be accurately measured. The disk can be oriented either perpendicular or parallel to the plane of swing to give significant or negligible air drag, respectively. The motion is analytically modeled in phase space. A quadratic dependence of the damping torque on the angular velocity fits the results. This laboratory experiment is suitable for undergraduate physics majors taking a first or second course in classical mechanics.

Mungan, Carl E.; Lipscombe, Trevor C.

2013-09-01

191

Efficient quadratic regularization for expression arrays.  

PubMed

Gene expression arrays typically have 50 to 100 samples and 1000 to 20,000 variables (genes). There have been many attempts to adapt statistical models for regression and classification to these data, and in many cases these attempts have challenged the computational resources. In this article we expose a class of techniques based on quadratic regularization of linear models, including regularized (ridge) regression, logistic and multinomial regression, linear and mixture discriminant analysis, the Cox model and neural networks. For all of these models, we show that dramatic computational savings are possible over naive implementations, using standard transformations in numerical linear algebra. PMID:15208198

Hastie, Trevor; Tibshirani, Robert

2004-07-01

192

Anisotropy of quadratic magneto-optic effects in reflection  

NASA Astrophysics Data System (ADS)

Quadratic or second-order magneto-optic effects in reflection significantly effect in-plane magnetization measurements. While the magneto-optic effects linear in magnetization are independent of orientation of cubic crystal axes, the amplitude and sign of the quadratic effects change significantly under crystal rotation. Theoretical formulas for the magneto-optic effects have been derived using a permittivity tensor including terms quadratic in magnetization. A method for separation of the diagonal and off-diagonal quadratic magneto-optic tensor components (G11-G12) and 2G44 is proposed. The theory was completed by an experimental observation of the quadratic effect anisotropy in an epitaxial Fe layer prepared on a MgO substrate. The influence of the magnetization components on the magneto-optic vector magnetometry is discussed for an interface, a single layer, and exchange coupled bilayer system for a general magnetization direction including the quadratic magneto-optic effect anisotropy.

Postava, K.; Hrabovský, D.; Pištora, J.; Fert, A. R.; Viš?ovský, Š.; Yamaguchi, T.

2002-05-01

193

Welfare Impacts of Rising Food Prices in Rural Ethiopia: a Quadratic Almost Ideal Demand System Approach  

Microsoft Academic Search

Ethiopia has experienced high food prices, especially since 2005. This paper examines the welfare impacts of rising food prices in rural Ethiopia using Quadratic Almost Ideal Demand System (QUAIDS) approach controlled for expenditure endogeniety and zero consumption expenditure. The elasticity coefficients from QUAIDS are used to estimate Compensated Variations (CV), which explicitly accounts for profit function and substitution effects. The

Nigussie Tefera Uregia; Mulat Demeke Desta; Shahidur Rashid

2012-01-01

194

Welfare Impacts of Rising Food Prices in Rural Ethiopia: a Quadratic Almost Ideal Demand System Approach  

Microsoft Academic Search

Ethiopia has experienced high food prices since early 2004. This paper examines the welfare impacts of rising food prices in rural Ethiopia using Quadratic Almost Ideal Demand System (QUAIDS) approach controlled for expenditure endogeniety and zero consumption expenditure. The elasticity coefficients from QUAIDS are used to estimate Compensated Variations (CV), which explicitly accounts for profit function and substitution effects. The

Nigussie Tefera Uregia; Mulat Demeke Desta; Shahidur Rashid

2012-01-01

195

Stable, effective fuzzy DMC algorithms with on-line quadratic optimization  

Microsoft Academic Search

Stable fuzzy DMC (FDMC) algorithms are presented in the paper. The algorithms consist in solving only quadratic optimization problems at each time instant. Therefore, they are effective and relatively little complicated. The stabilization mechanisms introduced are simple and easy to implement. These mechanisms can be used in conjunction with any variant of FDMC (fuzzy dynamic matrix control) algorithm. Exemplary simulation

P. Marusak; P. Tatjewski

2003-01-01

196

Plane and Guided Wave Effects and Devices Via Quadratic Cascading  

Microsoft Academic Search

\\u000a Quadratic cascading, i. e. the sequence of two second-order nonlinear processes, has assumed an important role in recent years\\u000a as one of the possibilities for a low power, lossless, ultrafast approach to all-optical processing of signals. [1–5] The foundation of quadratic cascading is as old as quadratic nonlinear optics itself, but its implications were brought\\u000a up later on in several

Gaetano Assanto; Katia Gallo; Claudio Conti

197

Quadratic immersed finite element spaces and their approximation capabilities  

Microsoft Academic Search

This paper discusses a class of quadratic immersed finite element (IFE) spaces developed for solving second order elliptic\\u000a interface problems. Unlike the linear IFE basis functions, the quadratic IFE local nodal basis functions cannot be uniquely\\u000a defined by nodal values and interface jump conditions. Three types of one dimensional quadratic IFE basis functions are presented\\u000a together with their extensions for

Brian Camp; Tao Lin; Yanping Lin; Weiwei Sun

2006-01-01

198

On generalized averaged Gaussian formulas  

NASA Astrophysics Data System (ADS)

We present a simple numerical method for constructing the optimal (generalized) averaged Gaussian quadrature formulas which are the optimal stratified extensions of Gauss quadrature formulas. These extensions exist in many cases in which real positive Kronrod formulas do not exist. For the Jacobi weight functions w(x)equiv w^{(alpha,beta)}(x)D(1-x)^alpha(1+x)^beta ( alpha,beta>-1 ) we give a necessary and sufficient condition on the parameters alpha and beta such that the optimal averaged Gaussian quadrature formulas are internal.

Spalevic, Miodrag M.

2007-09-01

199

Tachyon mediated non-Gaussianity  

SciTech Connect

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.

Dutta, Bhaskar; Leblond, Louis; Kumar, Jason [Department of Physics, Texas A and M University, College Station, Texas 77843 (United States); Department of Physics and Astronomy, University of California, Irvine, California 92697 (United States)

2008-10-15

200

Steller Structure Treatment of Quadratic Gravity  

NASA Astrophysics Data System (ADS)

A scheme for considering stellar structure by taking advantage of the quadratic theory of gravitation in four-dimensions is proposed, citing the fact that the possible deviation of gravity in astrophysical systems from the Newtonian inverse square law can be explained through the use of this theory. A modified Lane-Emden equation is derived by making use of the linearized static field equation of quadratic gravity and the polytropic equation of state for a fluid. The influence on stellar structure of the additional force included in quadratic gravity is investigated. It is shown that the additional force can be treated as a perturbation of a bound system by solutions of the modified Lane-Emden equation and an order-of-magnitude analysis. %ZY. Fujii, Nature (London) 234 (1971), 5; Phys. Rev. D9 (1974), 874. D. R. Long, Phys. Rev. D 9 (1974), 850. J. O'Hanlon, Phys. Rev. Lett. 29 (1972), 137. D. R. Mikkelson and M. J. Newman, Phys. Rev. D 16 (1977), 919. R. V. Wagoner, Phys. Rev. D 1 (1970), 3209. J. Z. Xu and Y. H. Chen, Gen. Relat. Gravit. J. 23 (1991), 169. K. S. Stelle, Gen. Relat. Gravit. J. 8 (1978), 631. C. Xu and G. F. R. Ellis, Class. Quant. Grav. 8 (1991), 1747. A. Eddington, The Mathematical Theory of Relativity, 2nd ed. (Cambridge University Press, Cambridge, 1924). W. Pauli, Theory of Relativity (Pergamon Press, New York, 1921). H. A. Buchdahl, Proc. Edinburgh Math. Soc. 8 (1948), 89. J. D. Barrow and A. C. Ottewill, J. of Phys. A 16 (1983), 2757. M. B. Mijic, M. S. Morris and W. M. Suen, Phys. Rev. D 34 (1986), 2934. A. L. Berkin, Phys. Rev. D 42 (1990), 1017. N. D. Birrell and P. C. W. Davies, Quantum Field in Curved Space (Cambridge University Press, 1982). E. T. Tomboulis, Quantum Theory of Gravity, ed. S. M. Christensen (Bristol: Adam Hilger 1984). H. J. Treder, Ann. der Phys. 32 (1975), 383. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley, New York 1972). E. N. Glass and G. Szamosi, Phys. Rev. D 35 (1987), 1205.

Chen, Y.; Shao, C.; Chen, X.

2001-07-01

201

A quadratic programming framework for constrained and robust jet engine health monitoring  

NASA Astrophysics Data System (ADS)

Kalman filters are largely used in the jet engine community for condition monitoring purpose. This algorithm gives a good estimate of the engine condition provided that the residuals between the model prediction and the measurements are zero-mean, Gaussian random variables. In the case of sensor faults, this assumption does not hold anymore and consequently, the diagnosis is spoiled. This contribution presents a recursive estimation algorithm based on a Quadratic Programming (QP) formulation which provides robustness against sensor faults and allows constraints on the health parameters to be specified. The improvements in estimation accuracy brought by this new algorithm are illustrated on a series of typical test-cases that may be encountered on current turbofan engines.

Borguet, S.; Léonard, O.

2009-09-01

202

Photon blockade in quadratically coupled optomechanical systems  

NASA Astrophysics Data System (ADS)

We study the steady-state photon statistics of a quadratically coupled optomechanical cavity, which is weakly driven by a monochromatic laser field. We examine the photon blockade by evaluating the second-order correlation function of the cavity photons. By restricting the system within the zero-, one-, and two-photon subspace, we obtain an approximate analytical expression for the correlation function. We also numerically investigate the correlation function by solving the quantum master equation including both optical and mechanical dissipations. The results show that, in the deep-resolved-sideband and single-photon strong-coupling regimes, the single-photon resonant driving will induce a photon blockade, which is limited by the thermal noise of the mechanical environment.

Liao, Jie-Qiao; Nori, Franco

2013-08-01

203

Linear-quadratic games of resource depletion  

SciTech Connect

In this paper we describe some methods for quantitatively analyzing dynamic, multiple agent models in which at least one agent takes into account his influence on the aggregate environment such as the degree of competitiveness in the petroleum industry. We confine our attention to models in which the agents solve stochastic, quadratic optimization problems subject to linear constraints. Discussion is presented in the context of a resource depletion example. The players are resource suppliers; the task is to compare their behavior when they play alternative dynamic games. Our approach to solving these models of dynamic games is first to deduce the stochastic Euler equations for each of the agents and then to simultaneously solve these stochastic Euler equations subject to the respective transversality conditions. The solution strategy involves factoring the characteristic polynomial of the system of stochastic difference equations. 22 refs.

Epple, D.; Hansen, L.P.; Roberds, W.

1983-01-01

204

Quasimultipartite entanglement measure based on quadratic functions  

SciTech Connect

We develop an entanglement measure by extending Jaeger's Minkowskian norm entanglement measure. This measure can be applied to a much wider class of multipartite mixed states, although still 'quasi' in the sense that it is still incapable of dividing precisely the sets of all separable and entangled states. As a quadratic scalar function of the system density matrix, the quasimeasure can be easily expressed in terms of the so-called coherence vector of the system density matrix, by which we show the basic properties of the quasimeasure including (1) zero entanglement for all separable states, (2) invariance under local unitary operations, and (3) nonincreasing under local positive operator-valued measure measurements. These results open up perspectives in further studies of dynamical problems in open systems, especially the dynamic evolution of entanglement, and the entanglement preservation against the environment-induced decoherence effects.

Zhang Jing; Li Chunwen; Wu Jianwu; Wu Rebing; Tarn Tzyhjong [Department of Automation, Tsinghua University, Beijing 100084 (China); Department of Chemistry, Princeton University, Princeton, New Jersey 08544 (United States); Department of Electrical and Systems Engineering, Washington University, St. Louis, Missouri 63130 (United States)

2006-02-15

205

Quadratic dynamical decoupling with nonuniform error suppression  

SciTech Connect

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

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

2011-10-15

206

Non-gaussian shape recognition  

NASA Astrophysics Data System (ADS)

A detection of primordial non-Gaussianity could transform our understanding of the fundamental theory of inflation. The precision promised by upcoming cosmic microwave background (CMB) and large-scale structure (LSS) surveys raises a natural question: if a detection given a particular template is made, what does this truly tell us about the underlying theory? Even in the case of non-detections and upper bounds on deviations from Gaussianity, what can we then infer about the viable theories that remain? In this paper we present a systematic way to constrain a wide range of non-Gaussian shapes, including general single and multi-field models and models with excited initial states. We present a separable, divergent basis able to recreate many shapes in the literature to high accuracy with between three and seven basis functions. The basis allows shapes to be grouped into broad ''template classes'', satisfying theoretically-relevant priors on their divergence properties in the squeezed limit. We forecast how well a Planck-like CMB survey could not only detect a general non-Gaussian signal but discern more about its shape, using existing templates and new ones we propose. This approach offers an opportunity to tie together minimal theoretical priors with observational constraints on the shape in general, and in the squeezed limit, to gain a deeper insight into what drove inflation.

Byun, Joyce; Bean, Rachel

2013-09-01

207

Gaussian Wave Packet: Step Scattering  

NSDL National Science Digital Library

The Gaussian Wave Packet: Step Scattering model simulates the time evolution of a free Gaussian wave packet in position space when it is incident on a potential energy step.  The position-space wave functions are depicted using three colors on the graph: black which depicts the absolute square of the wave function, blue which depicts the real part of the wave function, and red which depicts the imaginary part of the wave function. The user may change the height of the potential step or the wave packet energy by dragging circles on the energy graph. The initial width of the packet may also be changed. Also shown are the theoretical and calculated transmission and reflection coefficients. The Gaussian Wave Packet: Step Scattering model was created using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_qm_gaussian_step.jar file will run the program if Java is installed.

Palop, Jose I.

2010-12-13

208

Gaussian Velocity Distributions in Avalanches  

NASA Astrophysics Data System (ADS)

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

Shattuck, Mark

2004-03-01

209

Inseparability of photon-added Gaussian states  

NASA Astrophysics Data System (ADS)

The inseparability of photon-added Gaussian states which are generated from two-mode Gaussian states by adding photons is investigated. According to the established inseparability conditions [New J. Phys. 7, 211 (2005); Phys. Rev. Lett. 96, 050503 (2006)], we find that even if a two-mode Gaussian state is separable, the photon-added Gaussian state becomes entangled when the purity of the Gaussian state is larger than a certain value. The lower bound of entanglement of symmetric photon-added Gaussian states is derived. The result shows that entanglement of the photon-added Gaussian states is involved with high-order moment correlations. We find that fidelity of teleporting coherent states cannot be raised by employing the photon-added Gaussian states as a quantum channel of teleportation.

Li, Hong-Rong; Li, Fu-Li; Zhu, Shi-Yao

2007-06-01

210

Inseparability of photon-added Gaussian states  

SciTech Connect

The inseparability of photon-added Gaussian states which are generated from two-mode Gaussian states by adding photons is investigated. According to the established inseparability conditions [New J. Phys. 7, 211 (2005); Phys. Rev. Lett. 96, 050503 (2006)], we find that even if a two-mode Gaussian state is separable, the photon-added Gaussian state becomes entangled when the purity of the Gaussian state is larger than a certain value. The lower bound of entanglement of symmetric photon-added Gaussian states is derived. The result shows that entanglement of the photon-added Gaussian states is involved with high-order moment correlations. We find that fidelity of teleporting coherent states cannot be raised by employing the photon-added Gaussian states as a quantum channel of teleportation.

Li Hongrong [Department of Applied Physics, Xian Jiaotong University, Xian 710049 (China); Department of Physics, Hong Kong Baptist University, Hong Kong (China); Institute of Theoretical Physics, Chinese University of Hong Kong, Hong Kong (China); Li Fuli [Department of Applied Physics, Xian Jiaotong University, Xian 710049 (China); Zhu Shiyao [Department of Physics, Hong Kong Baptist University, Hong Kong (China)

2007-06-15

211

Tangent Lines without Derivatives for Quadratic and Cubic Equations  

ERIC Educational Resources Information Center

|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.)|

Carroll, William J.

2009-01-01

212

Quadratic Assignment Problem Algorithms and the Location of Indivisible Facilities  

Microsoft Academic Search

This paper discusses the problem of assigning locations to indivisible facilities and its relation to the quadratic assignment problem. It also develops two suboptimal algorithms, one dealing with the general quadratic assignment problem and the other with an interesting special case. Qualitative and quantitative comparisons with existing suboptimal algorithms are presented.

Frederick S. Hillier; Michael M. Connors

1966-01-01

213

Sketching the General Quadratic Equation Using Dynamic Geometry Software  

ERIC Educational Resources Information Center

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

Stols, G. H.

2005-01-01

214

Quadratic elongation: A quantitative measure of distortion in coordination polyhedra  

USGS Publications Warehouse

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

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

1971-01-01

215

Analytical placement: A linear or a quadratic objective function?  

Microsoft Academic Search

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

Georg Sigl; Konrad Doll; Frank M. Johannes

1991-01-01

216

The quadratic programming problem with fuzzy relation inequality constraints  

Microsoft Academic Search

The quadratic programming has been widely applied to solve real world problems. The quadratic functions are often applied in the inventory management, portfolio selection, engineering design, molecular study, and economics, etc. Fuzzy relation inequalities (FRI) are important elements of fuzzy mathematics, and they have recently been widely applied in the fuzzy comprehensive evaluation and cybernetics. In view of the importance

Ali Abbasi Molai

217

Real irreducible sesquilinear-quadratic tensor concomitants of complex bivectors  

Microsoft Academic Search

Irreducible tensor concomitants of an arbitrary complex antisymmetric second rank tensor, or bivector, in a Minkowski space-time are presented. These tensors are quadratic in the complex bivector and invariant under an overall multiplicative phase change of the bivector; in other words, they are sesquilinear-quadratic tensor concomitants of the complex bivector. The tensors are real and irreducible under the full real

T. D. Carozzi; J. E. S. Bergman

2006-01-01

218

Quadratic finite element methods for unilateral contact problems  

Microsoft Academic Search

The present paper is concerned with the frictionless unilateral contact problem between two elastic bodies in a bidimensional context. We consider a mixed formulation in which the unknowns are the displacement field and the contact pressure. We introduce a finite element method using quadratic elements and continuous piecewise quadratic multipliers on the contact zone. The discrete unilateral non-interpenetration condition is

Patrick Hild; Patrick Laborde

2002-01-01

219

Quadratic phase coupling of the maturing hippocampal EEG  

Microsoft Academic Search

Bispectral analysis is used in this paper to examine the status of quadratic phase couplings in developing neuronal interactions of two hippocampal subfields, CA1 and the dentate gyrus. It was found that the frequency bands where active quadratic phase coupling occurs gradually shift from a low theta range (5-7 Hz) for animals of 15 days of age to a high

Taikaug Ning; J. V. Tranquillo; J. D. Bronzino

1996-01-01

220

Finding Quadratic Schedules for Affine Recurrence Equations Via Nonsmooth Optimization  

Microsoft Academic Search

Frequently, affine recurrence equations can be scheduled more efficiently by quadratic scheduling functions than by linear scheduling functions. In this paper, the problem of finding optimal quadratic schedules for affine recurrence equations is formulated as a convex nonsmooth programming problem. In particular, sufficient constraints for causality are used generalizing Lamport's condition. In this way, the presented problem formulation becomes independent

Wolfgang Achtziger; Karl-heinz Zimmermann

2000-01-01

221

Some Paradoxical Results for the Quadratically Weighted Kappa  

ERIC Educational Resources Information Center

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

Warrens, Matthijs J.

2012-01-01

222

Sensitivity Analysis of Parameters in Linear-Quadratic Radiobiologic Modeling  

SciTech Connect

Purpose: Radiobiologic modeling is increasingly used to estimate the effects of altered treatment plans, especially for dose escalation. The present article shows how much the linear-quadratic (LQ) (calculated biologically equivalent dose [BED] varies when individual parameters of the LQ formula are varied by {+-}20% and by 1%. Methods: Equivalent total doses (EQD2 = normalized total doses (NTD) in 2-Gy fractions for tumor control, acute mucosal reactions, and late complications were calculated using the linear- quadratic formula with overall time: BED = nd (1 + d/ [{alpha}/{beta}]) - log{sub e}2 (T - Tk) / {alpha}Tp, where BED is BED = total dose x relative effectiveness (RE = nd (1 + d/ [{alpha}/{beta}]). Each of the five biologic parameters in turn was altered by {+-}10%, and the altered EQD2s tabulated; the difference was finally divided by 20. EQD2 or NTD is obtained by dividing BED by the RE for 2-Gy fractions, using the appropriate {alpha}/{beta} ratio. Results: Variations in tumor and acute mucosal EQD ranged from 0.1% to 0.45% per 1% change in each parameter for conventional schedules, the largest variation being caused by overall time. Variations in 'late' EQD were 0.4% to 0.6% per 1% change in the only biologic parameter, the {alpha}/{beta} ratio. For stereotactic body radiotherapy schedules, variations were larger, up to 0.6 to 0.9 for tumor and 1.6% to 1.9% for late, per 1% change in parameter. Conclusions: Robustness occurs similar to that of equivalent uniform dose (EUD), for the same reasons. Total dose, dose per fraction, and dose-rate cause their major effects, as well known.

Fowler, Jack F. [Departments of Human Oncology and Medical Physics, School of Medicine, University of Wisconsin, Madison, WI (United States)], E-mail: jackfowlersbox@gmail.com

2009-04-01

223

Scintillations of multiwavelength Gaussian, cos, cosh and annular Gaussian beams  

NASA Astrophysics Data System (ADS)

We provide the scintillation formulation for a multiwavelength source. Within this context, the scintillation aspects of Gaussian, cos, cosh and annular Gaussian beams are investigated. For all situations examined, it is found that for a source comprising many wavelengths, there will be less scintillations as compared to a single wavelength source of the lowest wavelength and but the reverse will be true if the comparison is with respect to the single wavelength source of the highest wavelength. The same is observed at all propagation distances, source sizes, on-axis and off-axis positions considered. Additionally, it is seen that the scintillation characteristics of multiwavelength sources will follow similar trends of single wavelength sources. The analysis is based on the Rytov approximation, therefore our results are valid for conditions of weak atmospheric turbulence.

Eyyubo?lu, Halil T.

2012-01-01

224

Quadratic algebras for three-dimensional superintegrable systems  

SciTech Connect

The three-dimensional superintegrable systems with quadratic integrals of motion have five functionally independent integrals, one among them is the Hamiltonian. Kalnins, Kress, and Miller have proved that in the case of nondegenerate potentials with quadratic integrals of motion there is a sixth quadratic integral, which is linearly independent of the other integrals. The existence of this sixth integral implies that the integrals of motion form a ternary parafermionic-like quadratic Poisson algebra with five generators. In this contribution we investigate the structure of this algebra. We show that in all the nondegenerate cases there is at least one subalgebra of three integrals having a Poisson quadratic algebra structure, which is similar to the two-dimensional case.

Daskaloyannis, C., E-mail: daskalo@math.auth.gr; Tanoudis, Y. [Aristotle University of Thessaloniki, Mathematics Department (Greece)

2010-02-15

225

Quadratic divergences and quantum gravitational contributions to gauge coupling constants  

SciTech Connect

The calculation of quadratic divergences in Einstein-Maxwell theory with a possible cosmological constant is considered. We describe a method of calculation, using the background-field method, that is sensitive to quadratic divergences, is respectful of gauge invariance, and is independent of gauge conditions. A standard renormalization group analysis is applied to the result where it is shown that the quadratic divergences do lead to asymptotic freedom as found in the original paper of Robinson and Wilczek. The role and nature of these quadratic divergences is critically evaluated in light of recent criticism. Within the context of the background-field method, it is shown that it is possible to define the charge in a physically motivated way in which the quadratic divergences do not play a role. This latter view is studied in more depth in a toy model described in an appendix.

Toms, David J. [School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne, NE1 7RU (United Kingdom)

2011-10-15

226

How many eigenvalues of a Gaussian random matrix are positive?  

SciTech Connect

We study the probability distribution of the index N{sub +}, i.e., the number of positive eigenvalues of an NxN Gaussian random matrix. We show analytically that, for large N and large N{sub +} with the fraction 0{<=}c=N{sub +}/N{<=}1 of positive eigenvalues fixed, the index distribution P(N{sub +}=cN,N){approx}exp[-{beta}N{sup 2}{Phi}(c)] where {beta} is the Dyson index characterizing the Gaussian ensemble. The associated large deviation rate function {Phi}(c) is computed explicitly for all 0{<=}c{<=}1. It is independent of {beta} and displays a quadratic form modulated by a logarithmic singularity around c=1/2. As a consequence, the distribution of the index has a Gaussian form near the peak, but with a variance {Delta}(N) of index fluctuations growing as {Delta}(N){approx}lnN/{beta}{pi}{sup 2} for large N. For {beta}=2, this result is independently confirmed against an exact finite-N formula, yielding {Delta}(N)=lnN/2{pi}{sup 2}+C+O(N{sup -1}) for large N, where the constant C for even N has the nontrivial value C=({gamma}+1+3ln2)/2{pi}{sup 2}{approx_equal}0.185 248... and {gamma}=0.5772... is the Euler constant. We also determine for large N the probability that the interval [{zeta}{sub 1},{zeta}{sub 2}] is free of eigenvalues. Some of these results have been announced in a recent letter [Phys. Rev. Lett. 103, 220603 (2009)].

Majumdar, Satya N.; Nadal, Celine [Laboratoire de Physique Theorique et Modeles Statistiques (UMR 8626 du CNRS), Universite Paris-Sud, Batiment 100, 91405 Orsay Cedex (France); Scardicchio, Antonello [Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste (Italy); INFN, Sezione di Trieste, Strada Costiera 11, 34151 Trieste (Italy); Vivo, Pierpaolo [Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste (Italy)

2011-04-15

227

A note on generalized averaged Gaussian formulas  

NASA Astrophysics Data System (ADS)

We have recently proposed a very simple numerical method for constructing the averaged Gaussian quadrature formulas. These formulas exist in many more cases than the real positive Gauss?Kronrod formulas. In this note we try to answer whether the averaged Gaussian formulas are an adequate alternative to the corresponding Gauss?Kronrod quadrature formulas, to estimate the remainder term of a Gaussian rule.

Spalevic, Miodrag

2007-11-01

228

Gaussian statistics for palaeomagnetic vectors  

USGS Publications Warehouse

With the aim of treating the statistics of palaeomagnetic directions and intensities jointly and consistently, we represent the mean and the variance of palaeomagnetic vectors, at a particular site and of a particular polarity, by a probability density function in a Cartesian three-space of orthogonal magnetic-field components consisting of a single (unimoda) non-zero mean, spherically-symmetrical (isotropic) Gaussian function. For palaeomagnetic data of mixed polarities, we consider a bimodal distribution consisting of a pair of such symmetrical Gaussian functions, with equal, but opposite, means and equal variances. For both the Gaussian and bi-Gaussian distributions, and in the spherical three-space of intensity, inclination, and declination, we obtain analytical expressions for the marginal density functions, the cumulative distributions, and the expected values and variances for each spherical coordinate (including the angle with respect to the axis of symmetry of the distributions). The mathematical expressions for the intensity and off-axis angle are closed-form and especially manageable, with the intensity distribution being Rayleigh-Rician. In the limit of small relative vectorial dispersion, the Gaussian (bi-Gaussian) directional distribution approaches a Fisher (Bingham) distribution and the intensity distribution approaches a normal distribution. In the opposite limit of large relative vectorial dispersion, the directional distributions approach a spherically-uniform distribution and the intensity distribution approaches a Maxwell distribution. We quantify biases in estimating the properties of the vector field resulting from the use of simple arithmetic averages, such as estimates of the intensity or the inclination of the mean vector, or the variances of these quantities. With the statistical framework developed here and using the maximum-likelihood method, which gives unbiased estimates in the limit of large data numbers, we demonstrate how to formulate the inverse problem, and how to estimate the mean and variance of the magnetic vector field, even when the data consist of mixed combinations of directions and intensities. We examine palaeomagnetic secular-variation data from Hawaii and Re??union, and although these two sites are on almost opposite latitudes, we find significant differences in the mean vector and differences in the local vectorial variances, with the Hawaiian data being particularly anisotropic. These observations are inconsistent with a description of the mean field as being a simple geocentric axial dipole and with secular variation being statistically symmetrical with respect to reflection through the equatorial plane. Finally, our analysis of palaeomagnetic acquisition data from the 1960 Kilauea flow in Hawaii and the Holocene Xitle flow in Mexico, is consistent with the widely held suspicion that directional data are more accurate than intensity data.

Love, J. J.; Constable, C. G.

2003-01-01

229

Cooling and squeezing via quadratic optomechanical coupling  

SciTech Connect

We explore the physics of optomechanical systems in which an optical cavity mode is coupled parametrically to the square of the position of a mechanical oscillator. We derive an effective master equation describing two-phonon cooling of the mechanical oscillator. We show that for high temperatures and weak coupling, the steady-state phonon number distribution is nonthermal (Gaussian) and that even for strong cooling the mean phonon number remains finite. Moreover, we demonstrate how to achieve mechanical squeezing by driving the cavity with two beams. Finally, we calculate the optical output and squeezing spectra. Implications for optomechanics experiments with the membrane-in-the-middle geometry or ultracold atoms in optical resonators are discussed.

Nunnenkamp, A.; Boerkje, K.; Harris, J. G. E.; Girvin, S. M. [Departments of Physics and Applied Physics, Yale University, New Haven, Connecticut 06520 (United States)

2010-08-15

230

TWO-PERSON ZERO-SUM LINEAR QUADRATIC STOCHASTIC DIFFERENTIAL GAMES BY A HILBERT SPACE METHOD  

Microsoft Academic Search

An open-loop two-person zero-sum linear quadratic (LQ for short) stochastic difierential game is considered. The controls for both players are al- lowed to appear in both the drift and difiusion of the state equation, the weight- ing matrices in the payofi\\/cost functional are not assumed to be deflnite\\/non- singular, and the cross-terms between two controls are allowed to appear. A

Libin Mou; Jiongmin Yong

2006-01-01

231

Regular black holes in quadratic gravity  

NASA Astrophysics Data System (ADS)

The first-order correction of the perturbative solution of the coupled equations of the quadratic gravity and nonlinear electrodynamics is constructed, with the zeroth-order solution coinciding with the ones given by Ayón-Beato and Garcí a and by Bronnikov. It is shown that a simple generalization of the Bronnikov's electromagnetic Lagrangian leads to the solution expressible in terms of the polylogarithm functions. The solution is parametrized by two integration constants and depends on two free parameters. By the boundary conditions the integration constants are related to the charge and total mass of the system as seen by a distant observer, whereas the free parameters are adjusted to make the resultant line element regular at the center. It is argued that various curvature invariants are also regular there that strongly suggests the regularity of the spacetime. Despite the complexity of the problem the obtained solution can be studied analytically. The location of the event horizon of the black hole, its asymptotics and temperature are calculated. Special emphasis is put on the extremal configuration.

Berej, Waldemar; Matyjasek, Jerzy; Tryniecki, Dariusz; Woronowicz, Mariusz

2006-05-01

232

A non-Gaussian landscape  

NASA Astrophysics Data System (ADS)

Primordial perturbations with wavelengths greater than the observable universe shift the effective background fields in our observable patch from their global averages over the inflating space. This leads to a landscape picture where the properties of our observable patch depend on its location and may significantly differ from the expectation values predicted by the underlying fundamental inflationary model. We show that if multiple fields are present during inflation, this may happen even if our horizon exit would be preceded by only a few e-foldings of inflation. Non-Gaussian statistics are especially affected: for example models of local non-Gaussianity predicting |fNL0| >> 10 over the entire inflating volume can have a probability up to a few tens of percent to generate a non-detectable bispectrum in our observable patch |fNLobs.|lesssim10. In this work we establish systematic connections between the observable local properties of primordial perturbations and the global properties of the inflating space which reflect the underlying high energy physics. We study in detail the implications of both a detection and non-detection of primordial non-Gaussianity by Planck, and discover novel ways of characterising the naturalness of different observational configurations.

Nurmi, Sami; Byrnes, Christian T.; Tasinato, Gianmassimo

2013-06-01

233

Development and modification of a Gaussian and non-Gaussian noise exposure system  

NASA Astrophysics Data System (ADS)

Millions of people across the world currently have noise induced hearing loss, and many are working in conditions with both continuous Gaussian and non-Gaussian noises that could affect their hearing. It was hypothesized that the energy of the noise was the cause of the hearing loss and did not depend on temporal pattern of a noise. This was referred to as the equal energy hypothesis. This hypothesis has been shown to have limitations though. This means that there is a difference in the types of noise a person receives to induce hearing loss and it is necessary to build a system that can easily mimic various conditions to conduct research. This study builds a system that can produce both non-Gaussian impulse/impact noises and continuous Gaussian noise. It was found that the peak sound pressure level of the system could reach well above the needed 120 dB level to represent acoustic trauma and could replicate well above the 85 dB A-weighted sound pressure level to produce conditions of gradual developing hearing loss. The system reached a maximum of 150 dB sound peak pressure level and a maximum of 133 dB A-weighted sound pressure level. Various parameters could easily be adjusted to control the sound, such as the high and low cutoff frequency to center the sound at 4 kHz. The system build can easily be adjusted to create numerous sound conditions and will hopefully be modified and improved in hopes of eventually being used for animal studies to lead to the creation of a method to treat or prevent noise induced hearing loss.

Schlag, Adam W.

234

A Predictable Robust Fully Programmable Analog Gaussian Noise Source for Mixed-Signal\\/Digital ATE  

Microsoft Academic Search

A robust programmable analog Gaussian noise generator suitable for mixed-signal\\/digital ATEs is presented. Unlike conventional methods (LFSR based noise generators or resistor thermal noise amplification techniques), the user has full control of the characteristics of the Gaussian signal. Indeed, the frequency band, the mean, and variance of the distribution are fully programmable over the voltage range within the supply rails.

Sadok Aouini; Gordon W. Roberts

2006-01-01

235

Entanglement distillation from Gaussian input states  

NASA Astrophysics Data System (ADS)

Entanglement distillation is an essential protocol for long-distance quantum communications, typically for extending the range of quantum key distribution. In the field of continuous variable quantum information processing, quantum as well as classical information is encoded in the light field quadratures, often in the form of Gaussian states. However, distillation from Gaussian input states has not yet been accomplished. It is made difficult by a prominent no-go theorem stating that no Gaussian operation can distill Gaussian states. Here we demonstrate, for the first time, such distillation from Gaussian input states, realized by the implementation of non-Gaussian operations. By subtracting one or two photons, a large gain of entanglement was observed. For two photons, Gaussian-like entanglement was also improved. Other than quantum key distribution, this distilled entanglement can also be used for downstream applications such as high-fidelity quantum teleportation and a loophole-free Bell test.

Takahashi, Hiroki; Neergaard-Nielsen, Jonas S.; Takeuchi, Makoto; Takeoka, Masahiro; Hayasaka, Kazuhiro; Furusawa, Akira; Sasaki, Masahide

2010-03-01

236

Nonlinear clustering in models with primordial non-Gaussianity: The halo model approach  

SciTech Connect

We develop the halo model of large-scale structure as an accurate tool for probing primordial non-Gaussianity. In this study we focus on understanding the matter clustering at several redshifts in the context of primordial non-Gaussianity that is a quadratic correction to the local Gaussian potential, characterized by the parameter f{sub NL}. In our formulation of the halo model we pay special attention to the effect of halo exclusion and show that this can potentially solve the long-standing problem of excess power on large scales in this model. The halo model depends on the mass function, clustering of halo centers, and the density profiles. We test these ingredients using a large ensemble of high-resolution Gaussian and non-Gaussian numerical simulations, covering f{sub NL}={l_brace}0,+100,-100{r_brace}. In particular, we provide a first exploration of how halo density profiles change in the presence of primordial non-Gaussianity. We find that for f{sub NL} positive (negative) high-mass haloes have an increased (decreased) core density, so being more (less) concentrated than in the Gaussian case. We also examine the halo bias and show that, if the halo model is correct, then there is a small asymmetry in the scale dependence of the bias on very large scales, which arises because the Gaussian bias must be renormalized. We show that the matter power spectrum is modified by {approx}2.5% and {approx}3.5% on scales k{approx}1.0 h Mpc{sup -1} at z=0 and z=1, respectively. Our halo model calculation reproduces the absolute amplitude to within < or approx. 10% and the ratio of non-Gaussian to Gaussian spectra to within < or approx. 1%. We also measure the matter correlation function and find similarly good levels of agreement between the halo model and the data. We anticipate that this modeling will be useful for constraining f{sub NL} from measurements of the shear correlation function in future weak lensing surveys such as Euclid.

Smith, Robert E. [Institute for Theoretical Physics, University of Zurich, Zurich CH 8037 (Switzerland); Argelander-Institute for Astronomy, Auf dem Huegel 71, D-53121 Bonn (Germany); Desjacques, Vincent [Institute for Theoretical Physics, University of Zurich, Zurich CH 8037 (Switzerland); Marian, Laura [Argelander-Institute for Astronomy, Auf dem Huegel 71, D-53121 Bonn (Germany)

2011-02-15

237

Gaussianity of LISA's confusion backgrounds  

SciTech Connect

Data analysis for the proposed Laser Interferometer Space Antenna (LISA) will be complicated by the huge number of sources in the LISA band. In the frequency band {approx}10{sup -4}-2x10{sup -3} Hz, galactic white dwarf binaries (GWDBs) are sufficiently dense in frequency space that it will be impossible to resolve most of them, and ''confusion noise'' from the unresolved Galactic binaries will dominate over instrumental noise in determining LISA's sensitivity to other sources in that band. Confusion noise from unresolved extreme-mass-ratio inspirals (EMRIs) could also contribute significantly to LISA's total noise curve. To date, estimates of the effect of LISA's confusion noise on matched-filter searches and their detection thresholds have generally approximated the noise as Gaussian, based on the central limit theorem. However in matched-filter searches, the appropriate detection threshold for a given class of signals may be located rather far out on the tail of the signal-to-noise probability distribution, where a priori it is unclear whether the Gaussian approximation is reliable. Using the Edgeworth expansion and the theory of large deviations, we investigate the probability distribution of the usual matched-filter detection statistic, far out on the tail of the distribution. We apply these tools to four somewhat idealized versions of LISA data searches: searches for EMRI signals buried in GWDB confusion noise, and searches for massive black hole binary signals buried in (i) GWDB noise, (ii) EMRI noise, and (iii) a sum of EMRI noise and Gaussian noise. Assuming reasonable short-distance cutoffs in the populations of confusion sources (since the very closest and hence strongest sources will be individually resolvable), modifications to the appropriate detection threshold, due to the non-Gaussianity of the confusion noise, turn out to be quite small for realistic cases. The smallness of the correction is partly due to the fact that these three types of sources evolve on quite different time scales, so no single background source closely resembles any search template. We also briefly discuss other types of LISA searches where the non-Gaussianity of LISA's confusion backgrounds could perhaps have a much greater impact on search reliability and efficacy.

Racine, Etienne [Department of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, California 91125 (United States); Cutler, Curt [Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109 (United States)

2007-12-15

238

Generalized symmetry transformation with Gaussian phase weight function  

NASA Astrophysics Data System (ADS)

The generalized symmetry transformation (GST) is a symmetry operator detecting objects by using edge gradient directions. Conventional GST uses the cosine function to define the phase weight function (PWF), which represents the symmetry of two gradient directions. The cosine function of PWF leads to a good performance in detecting symmetrical objects. However, the weights of gradient pairs, which are considered to be asymmetrical, are relatively high, so side effects appear near the symmetry pick regions. (Note that side effects disturb the multiple object detection.) In this paper, we use the Gaussian function in calculating the symmetric weights of gradient pairs. The Gaussian function can suppress the weights of less symmetric gradient pairs. In addition, the symmetry for elliptically shaped objects can be more emphasized by controlling the width of the Gaussian function. The proposed GST is evaluated through experiments on synthetic images, which include various bright and dark plane figures, and on real images, which requires the detection of elliptical shapes.

Lee, Hee-Yul; Kim, Tae-Hun; Jeon, Joon-Hyung; Choi, Il; Park, Kil-Houm

2012-03-01

239

Phase-only shaping algorithm for Gaussian-apodized Bessel beams.  

PubMed

Gaussian-apodized Bessel beams can be used to create a Bessel-like axial line focus at a distance from the focusing lens. For many applications it is desirable to create an axial intensity profile that is uniform along the Bessel zone. In this article, we show that this can be accomplished through phase-only shaping of the wavefront in the far field where the beam has an annular ring structure with a Gaussian cross section. We use a one-dimensional transform to map the radial input field to the axial Bessel field and then optimized the axial intensity with a Gerchberg-Saxton algorithm. By separating out the quadratic portion of the shaping phase the algorithm converges more rapidly. PMID:23842364

Durfee, Charles G; Gemmer, John; Moloney, Jerome V

2013-07-01

240

Vibrations of the nonlinear oscillator with quadratic nonlinearity  

NASA Astrophysics Data System (ADS)

In this paper the vibration of a mass-spring oscillator with strong quadratic nonlinearity and one degree of freedom is analyzed. The both, strong and hard, springs are considered. The restoring force in the spring which is the function of the quadratic deformation has to satisfy the condition of antisymmetry. The mathematical model is an ordinary second order differential equation where the quadratic nonlinear term changes the sign. The quantitative and the qualitative analysis of the equation is done. The exact analytical solution is obtained. It depends on the Jacobi elliptic function.

Cveticanin, L.

2004-10-01

241

Models for the 3D singular isotropic oscillator quadratic algebra  

SciTech Connect

We give the first explicit construction of the quadratic algebra for a 3D quantum superintegrable system with nondegenerate (4-parameter) potential together with realizations of irreducible representations of the quadratic algebra in terms of differential-differential or differential-difference and difference-difference operators in two variables. The example is the singular isotropic oscillator. We point out that the quantum models arise naturally from models of the Poisson algebras for the corresponding classical superintegrable system. These techniques extend to quadratic algebras for superintegrable systems in n dimensions and are closely related to Hecke algebras and multivariable orthogonal polynomials.

Kalnins, E. G., E-mail: math0236@waikato.ac.n [University of Waikato, Department of Mathematics (New Zealand); Miller, W.; Post, S. [University of Minnesota, School of Mathematics (United States)

2010-02-15

242

Intensity fluctuations of partially coherent cos Gaussian and cosh Gaussian beams in atmospheric turbulence  

NASA Astrophysics Data System (ADS)

On-axis and off-axis scintillation indices of partially coherent collimated cos Gaussian and cosh Gaussian beams are evaluated on their propagation in a weakly turbulent atmosphere. In the coherent limits, our results are in quite good agreement with those for the existing Rytov scintillation index of coherent cos Gaussian and cosh Gaussian beams, especially for very small and very large sized beams and at weaker turbulence levels. The on-axis scintillation index becomes lower as the degree of source coherence decreases for both cos Gaussian and cosh Gaussian beams. Comparing to the partially coherent Gaussian beam on-axis scintillations, partially coherent cos Gaussian beam scintillations are generally lower and partially coherent cosh Gaussian beam scintillations are higher. Scintillations of Gaussian beams are very close to the scintillations of equal-power cos Gaussian and are quite similar to the scintillations of equal-power cosh Gaussian beams. Off-axis evaluations yield that the scintillations of both cos Gaussian and cosh Gaussian beams increase as the diagonal distance from the origin increases, being valid for all degrees of partial coherence.

Baykal, Yahya; Eyyubo?lu, Halil T.; Çil, Celal Z.; Cai, Yangjian; Korotkova, Olga

2011-05-01

243

Quadratic-Exponential Moment Error Bounds for Digital Communication Systems.  

National Technical Information Service (NTIS)

By utilizing the theory of moment spaces, upper and lower bounds to error probability of digital communication systems, based on the use of quadratic-exponential moments of the intersymbol interference random variables, are obtained. Some bounds can be ev...

K. Yao

1976-01-01

244

Duality and Sensitivity in Quadratic Optimization over a Sphere.  

National Technical Information Service (NTIS)

Duality is introduced for the problem of optimizing a quadratic form over an ellipsoid. Based on the duality results, some existing solution procedures are interpreted as in fact solving the dual. The duality relations also provide a natural framework for...

O. E. Flippo B. Jansen

1992-01-01

245

Influence of turbulence on the spectrum of diffracted chirped Gaussian pulsed beams  

NASA Astrophysics Data System (ADS)

The influence of turbulence on the spectrum of diffracted chirped Gaussian pulsed beams is studied in detail. By using the quadratic approximation of the Rytov’s phase structure function and the finite expansion of the aperture function, the analytical expression for the spectrum of diffracted chirped Gaussian pulsed beams propagating through atmospheric turbulence is derived. It is shown that in free space there exist the on-axis and off-axis multi-spectral switch for diffracted chirped Gaussian pulsed beams. However, the turbulence results in a decrease of the spectral transition height, and the spectral switch even disappears when the turbulence is strong enough, which is very different from the behavior of undiffracted chirped Gaussian pulsed beams. Specially, with increasing the strength of turbulence, the higher-order spectral switch disappears firstly for on-axis case, while the lower-order spectral switch disappears firstly for off-axis case. In free space the on-axis spectrum is blue-shifted after a certain propagation distance, but the on-axis spectrum is red-shifted after a shorter propagation distance when the turbulence is strong enough. The spectral transition height increases with increasing the chirp parameter and decreasing the pulse duration, and the odd number order position without spectral shift is independent of the chirp parameter and pulse duration.

Ji, Xiaoling

2008-07-01

246

A transient, quadratic nodal method for triangular-Z geometry  

Microsoft Academic Search

Many systematically-derived nodal methods have been developed for Cartesian geometry due to the extensive interest in Light Water Reactors. These methods typically model the transverse-integrated flux as either an analytic or low order polynomial function of position within the node. Recently, quadratic nodal methods have been developed for R-Z and hexagonal geometry. A static and transient quadratic nodal method is

DeLorey

1993-01-01

247

Digital filter bank design quadratic-constrained formulation  

Microsoft Academic Search

Formulate the filter bank design problem as an quadratic-constrained least-squares minimization problem. The solution of the minimization problem converges very quickly since the cost function as well as the constraints are quadratic functions with respect to the unknown parameters. The formulations of the perfect-reconstruction cosine-modulated filter bank, of the near-perfect-reconstruction pseudo-QMF bank, and of the two-channel biorthogonal linear-phase filter bank

Truong Q. Nguyen

1995-01-01

248

On the Convergence of Successive Linear-Quadratic Programming Algorithms  

Microsoft Academic Search

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

Richard H. Byrd; Nicholas I. M. Gould; Jorge Nocedal; Richard A. Waltz

2005-01-01

249

Highly degenerate quadratic forms over finite fields of characteristic 2  

Microsoft Academic Search

Let K\\/F be an extension of finite fields of characteristic two. We consider quadratic forms written as the trace of xR(x), where R(x) is a linearized polynomial. We show all quadratic forms can be so written, in an essentially unique way. We classify those R, with coefficients 0 or 1, where the form has a codimension 2 radical. This is

Robert W. Fitzgerald

2005-01-01

250

Degradability of Bosonic Gaussian channels  

SciTech Connect

The notion of weak-degradability of quantum channels is introduced by generalizing the degradability definition given by Devetak and Shor. Exploiting the unitary equivalence with beam-splitter/amplifier channels we then prove that a large class of one-mode Bosonic Gaussian channels are either weakly degradable or anti-degradable. In the latter case this implies that their quantum capacity Q is null. In the former case instead, this allows us to establish the additivity of the coherent information for those maps which admit unitary representation with single-mode pure environment.

Caruso, Filippo; Giovannetti, Vittorio [NEST CNR-INFM and Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa (Italy)

2006-12-15

251

Bayesian Variables Acceptance-Sampling Plans: Quadratic Loss Function and Step-Loss Function  

Microsoft Academic Search

In developing quality-control procedures, a step-loss function has been used implicitly or explicitly to describe consumer perceptions about product quality. A quadratic loss function has been suggested by Taguchi as an alternative to the step-loss function in measuring the loss due to imperfect product quality (cost of acceptance). In this article, Bayesian analyses of the known-standard-deviation acceptance-sampling problem are described

Herbert Moskowitz; Kwei Tang

1992-01-01

252

Modelling geomagnetic reversals as a Gaussian Cox Process  

NASA Astrophysics Data System (ADS)

The mean rate of reversal of the geomagnetic field, as recorded in the Geomagnetic Polarity Time Scale (GPTS), has long been an object of study. The significance of the apparent long-term variations in the mean rate of reversals - including the occurrence of superchrons - has been debated, as has the possible origins of these variations in external control of the geodynamo (e.g. by the time-varying boundary conditions imposed by mantle convection). Here we model the long-term variations in the reversal rate nonparametrically, in terms of an inhomogeneous Poisson process. Specifically, we consider a Gaussian Cox process, a type of doubly-stochastic Poisson process where the mean rate (or intensity) is modelled in terms of a Gaussian process. Such processes are amenable to likelihood-based inference using Bayesian Markov Chain Monte-Carlo (MCMC) methods, which we employ to provide posterior distributions of the model parameters. The specification of a Gaussian process requires a covariance function, relating the intensity at nearby times; crucially, however, the timescale of the covariance function is not prescribed, but appears as a model hyperparameter, whose posterior distribution is an important output of the analysis. For the geodynamo, this hyperparameter should robustly characterise the timescale of long-term variations. Two different types of Gaussian Cox process are considered: a Log Gaussian Cox Process, applied to binned reversal data; and a Sigmoidal Gaussian Cox Process, applied to the discrete reversal data using a technique involving latent variables. Different MCMC algorithms for sampling the posterior distribution of the model parameters are investigated for both types of process, to check (and to optimise) the convergence of the MCMC chains. This analysis is applied to different records of the GPTS, including those of Cande & Kent (1995) and Gradstein & Ogg (1996). The implications of this analysis for the geodynamo, and the possibility of comparable analysis of the output of numerical geodynamo simulations, are discussed.

Sarson, Graeme; Boys, Richard; Golightly, Andrew; Henderson, Daniel

2013-04-01

253

Local model network identification with Gaussian processes.  

PubMed

A Bayesian Gaussian process (GP) modeling approach has recently been introduced to model-based control strategies. The estimate of the variance of the predicted output is the most useful advantage of GPs in comparison to neural networks (NNs) and fuzzy models. However, the GP model is computationally demanding and nontransparent. To reduce the computation load and increase transparency, a local linear GP model network is proposed in this paper. The proposed methodology combines the local model network principle with the GP prior approach. A novel algorithm for structure determination and optimization is introduced, which is widely applicable to the training of local model networks. The modeling procedure of the local linear GP (LGP) model network is demonstrated on an example of a nonlinear laboratory scale process rig. PMID:18220189

Gregorcic, Gregor; Lightbody, Gordon

2007-09-01

254

Optofluidic generation of Laguerre-Gaussian beams  

PubMed Central

Laguerre-Gaussian (LG) beams have been extensively studied due to their unique structure, characterized by a phase singularity at the center of the beam. Common methods for generating such beams include the use of diffractive optical elements and spatial light modulators, which although offering excellent versatility, suffers from several drawbacks, including in many cases a low power damage threshold as well as complexity and expense. This paper presents a simple, low cost method for the generation of high-fidelity LG beams using rapid prototyping techniques. Our approach is based on a fluidic-hologram concept, whereby the properties of the LG beam can be finely controlled by varying the refractive-index of the fluid that flows through the hologram. This simple approach, while optimized here for LG beam generation, is also expected to find applications in the production of tunable fluidic optical trains.

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

2010-01-01

255

Optofluidic generation of Laguerre-Gaussian beams.  

PubMed

Laguerre-Gaussian (LG) beams have been extensively studied due to their unique structure, characterized by a phase singularity at the center of the beam. Common methods for generating such beams include the use of diffractive optical elements and spatial light modulators, which although offering excellent versatility, suffers from several drawbacks, including in many cases a low power damage threshold as well as complexity and expense. This paper presents a simple, low cost method for the generation of high-fidelity LG beams using rapid prototyping techniques. Our approach is based on a fluidic-hologram concept, whereby the properties of the LG beam can be finely controlled by varying the refractive-index of the fluid that flows through the hologram. This simple approach, while optimized here for LG beam generation, is also expected to find applications in the production of tunable fluidic optical trains. PMID:19907539

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

2009-09-28

256

Strongly scale-dependent non-Gaussianity  

SciTech Connect

We discuss models of primordial density perturbations where the non-Gaussianity is strongly scale dependent. In particular, the non-Gaussianity may have a sharp cutoff and be very suppressed on large cosmological scales, but sizable on small scales. This may have an impact on probes of non-Gaussianity in the large-scale structure and in the cosmic microwave background radiation anisotropies.

Riotto, Antonio [INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padua (Italy); CERN, PH-TH Division, CH-1211, Geneve 23 (Switzerland); Sloth, Martin S. [CERN, PH-TH Division, CH-1211, Geneve 23 (Switzerland)

2011-02-15

257

Two-photon optics of Bessel-Gaussian modes  

NASA Astrophysics Data System (ADS)

In this paper we consider geometrical two-photon optics of Bessel-Gaussian modes generated in spontaneous parametric down-conversion of a Gaussian pump beam. We provide a general theoretical expression for the orbital angular momentum (OAM) spectrum and Schmidt number in this basis and show how this may be varied by control over the radial degree of freedom, a continuous parameter in Bessel-Gaussian modes. As a test we first implement a back-projection technique to classically predict, by experiment, the quantum correlations for Bessel-Gaussian modes produced by three holographic masks: a blazed axicon, a binary axicon, and a binary Bessel function. We then proceed to test the theory on the down-converted photons using the binary Bessel mask. We experimentally quantify the number of usable OAM modes and confirm the theoretical prediction of a flattening in the OAM spectrum and a concomitant increase in the OAM bandwidth. The results have implications for the control of dimensionality in quantum states.

McLaren, Melanie; Romero, Jacquiline; Padgett, Miles J.; Roux, Filippus S.; Forbes, Andrew

2013-09-01

258

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

PubMed Central

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

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

2012-01-01

259

A transient, quadratic nodal method for triangular-Z geometry  

SciTech Connect

Many systematically-derived nodal methods have been developed for Cartesian geometry due to the extensive interest in Light Water Reactors. These methods typically model the transverse-integrated flux as either an analytic or low order polynomial function of position within the node. Recently, quadratic nodal methods have been developed for R-Z and hexagonal geometry. A static and transient quadratic nodal method is developed for triangular-Z geometry. This development is particularly challenging because the quadratic expansion in each node must be performed between the node faces and the triangular points. As a consequence, in the 2-D plane, the flux and current at the points of the triangles must be treated. Quadratic nodal equations are solved using a non-linear iteration scheme, which utilizes the corrected, mesh-centered finite difference equations, and forces these equations to match the quadratic equations by computing discontinuity factors during the solution. Transient nodal equations are solved using the improved quasi-static method, which has been shown to be a very efficient solution method for transient problems. Several static problems are used to compare the quadratic nodal method to the Coarse Mesh Finite Difference (CMFD) method. The quadratic method is shown to give more accurate node-averaged fluxes. However, it appears that the method has difficulty predicting node leakages near reactor boundaries and severe material interfaces. The consequence is that the eigenvalue may be poorly predicted for certain reactor configurations. The transient methods are tested using a simple analytic test problem, a heterogeneous heavy water reactor benchmark problem, and three thermal hydraulic test problems. Results indicate that the transient methods have been implemented correctly.

DeLorey, T.F.

1993-06-01

260

Robust control of smart structures using neural network hardware  

NASA Astrophysics Data System (ADS)

In this paper, the use of Intel's Electronically Trainable Analog Neural Network (ETANN) chipi80170NX for implementing single-chip robust controllers for smart structures is successfully demonstrated. Robust controllers like the linear quadratic regulator (LQR) and linear quadratic Gaussian with loop transfer recovery (LQG/LTR) are implemented in various configurations using the ETANN chip on the smart structure test article. The test article is a cantilevered plate with PZTs as actuators and shaded PVDF film as sensors. The spatially distributed sensors allow direct measurement of the states of the system enabling the implementation of the LQR controller. A two step connectionist approach is used to design and implement the neural network based controllers. First a robust controller is designed using conventional design techniques to meet the required closed loop performance. The controller dynamics are copied into the ETANN chip and the trained chip is used to control the test structure. A custom interface board and external signal conditioning circuits are developed to interface the neural network chip with the sensors and actuators on the smart structure test article. The steps involved in training and implementing the robust controllers on a smart structure are detailed. Some of the practical considerations of implementing the controller using the ETANN chip are pointed out and some suggestions made to deal with the limitations. Simulation and experimental results of the closed loop system with all the controller implementation models are presented.

Damle, Rajendra; Rao, Vittal; Kern, Frank

1997-06-01

261

Polyspectral Techniques for Detection and Estimation in Gaussian and Non-Gaussian Noise  

Microsoft Academic Search

We consider methods for detection and estimation using higher order statistics. At first we focus on signals in Gaussian noise. The projection relationship between lower and higher order cumulants is exploited to estimate signal energy, and detection tests for non-Gaussian linear processes are developed. Comparison with conventional energy detection shows the potential for enhancement by exploiting the non-Gaussian property of

Brian Marshall Sadler

1993-01-01

262

Robust synchronization of a class of uncertain chaotic systems based on quadratic optimal theory and adaptive strategy  

NASA Astrophysics Data System (ADS)

This paper presents a chaos synchronization method for a class of uncertain chaotic systems using the combination of an optimal control theory and an adaptive strategy. A quadratic optimal regulator and an adaptive control are used to represent the controller's structure. The asymptotic stability of the corresponding error dynamical system is guaranteed through Lyapunov stability analysis. The proposed controller is employed in two uncertain chaotic Lu systems, and their promising performances are illustrated.

Ataei, Mohammad; Iromloozadeh, Armin; Karimi, Bahram

2010-12-01

263

Winding of planar Gaussian processes  

NASA Astrophysics Data System (ADS)

We consider a smooth, rotationally invariant, centered Gaussian process in the plane, with arbitrary correlation matrix Ctt'. We study the winding angle phit, around its center. We obtain a closed formula for the variance of the winding angle as a function of the matrix Ctt'. For most stationary processes Ctt' = C(t-t') the winding angle exhibits diffusion at large time with diffusion coefficient D=\\int _0^\\infty \\rmd s\\, C'(s)^2/(C(0)^2-C(s)^2) . Correlations of exp(inphit) with integer n, the distribution of the angular velocity \\dot \\phi_t , and the variance of the algebraic area are also obtained. For smooth processes with stationary increments (random walks) the variance of the winding angle grows as \\frac {1}{2} (\\ln t)^2 , with proper generalizations to the various classes of fractional Brownian motion. These results are tested numerically. Non-integer n is studied numerically.

LeDoussal, Pierre; Etzioni, Yoav; Horovitz, Baruch

2009-07-01

264

Voice Conversion using structrued Gaussian Mixture Model  

Microsoft Academic Search

Gaussian Mixture Model (GMM) is commonly used in voice conversion. However, traditional GMM based voice conversion usually extracts a conversion function from parallel corpus, which greatly limits the application of the technology. In an attempt to overcome this drawback, structured Gaussian Mixture Model (SGMM) is applied to model the speaker's acoustic feature distribution. In particular, two speakers' isolated SGMMs are

Daojian Zeng; Yibiao Yu

2010-01-01

265

Deep Structure of Gaussian Scale Space  

Microsoft Academic Search

The deep structure of scale space is essential to the further processing of an image at different resolutions to extract certain features or to carry out other requirements such as image denosing. In this paper we study the deep structure of Gaussian scale space by virtue of singularity theory. Five normal forms of Gaussian scale space are provided, which is

Yang Zhihui; Cui Wenjuan; Zhang Mengmeng

2008-01-01

266

Neural Networks: A Replacement for Gaussian Processes?  

Microsoft Academic Search

Gaussian processes have been favourably compared to back- propagation neural networks as a tool for regression. We show that a recurrent neural network can implement exact Gaussian process infer- ence using only linear neurons that integrate their inputs over time, inhibitory recurrent connections, and one-shot Hebbian learning. The network amounts to a dynamical system which relaxes to the correct so-

Matthew Lilley; Marcus R. Frean

2005-01-01

267

Twin Gaussian Processes for Structured Prediction  

Microsoft Academic Search

We describe twin Gaussian processes (TGP), a generic structured prediction method that uses Gaussian process (GP) priors on both covariates and responses, both multivariate, and estimates outputs by minimizing the Kullback-Leibler divergence between two GP modeled as normal distributions over finite index sets of training and testing examples, emphasizing the goal that similar inputs should produce similar percepts and this

Liefeng Bo; Cristian Sminchisescu

2010-01-01

268

Iterative Gaussianization: From ICA to Random Rotations  

Microsoft Academic Search

Most signal processing problems involve the chal- lenging task of multidimensional probability density function (PDF) estimation. In this paper, we propose a solution to this problem by using a family of rotation-based iterative Gaussian- ization (RBIG) transforms. The general framework consists of the sequential application of a univariate marginal Gaussianization transform followed by an orthonormal transform. The proposed procedure looks

Valero Laparra; Gustavo Camps-Valls; Jesus Malo

2011-01-01

269

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

Microsoft Academic Search

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

Chang Shu; James R. Perkins

2001-01-01

270

Integrated optimization of actuator placement and vibration control for piezoelectric adaptive trusses  

NASA Astrophysics Data System (ADS)

In this paper, the integrated optimization of actuator placement and vibration control for piezoelectric adaptive truss is studied. Based on the dynamic finite element (FE) model and a linear-quadratic-Gaussian (LQG) model of vibration control for an adaptive truss, an integrated optimization model is built in which an improved quadratic performance index is adopted as the objective function and the mode closed-loop damping ratio, modal controllability and actuator number are selected as the constraints. A layered optimization strategy is implemented to address this optimization problem with discrete-continuous design variable. To prevent the optimization process from converging to the local optimal solution, the genetic algorithm (GA) for outside-layer optimization is extended with an improved penalty function. Numerical examples and the vibration control experiments for piezoelectric adaptive truss were used to validate the efficiency of the proposed method. The following conclusions were drawn from the results. (1) The improved penalty function can orient the optimization process to the global optimal solution. (2) Although the number of struts on the truss is large, the optimization computation time is short because of the high efficiency of the proposed method. (3) In the experiment, the quadratic performance index, modal response and sensor signals for the present paper's optimal actuator placement scheme are better than those described in the literature, but the placement requires more energy, which is consistent with the numerical results.

Li, W. P.; Huang, H.

2013-01-01

271

Quadratic Integrate-and-Fire Neuron Network Model  

NSDL National Science Digital Library

The Quadratic Integrate-and-Fire Neuron Network Model uses a network of Quadratic Integrate-and-Fire neurons to demonstrate how connectivity influences network synchrony. The user selects the number of neurons and the degree of connectivity, and can see how the neurons synchronize over time. In addition, the user can watch the potential of a single neuron. Although the dynamics of a single neuron do not change, the network architecture has a dramatic effect on how quickly the neurons will synchronize. The Quadratic Integrate-and-Fire Neuron Network Model was developed using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the jar file will run the program if Java is installed. You can modify this simulation if you have EJS installed by right-clicking within the map and selecting "Open Ejs Model" from the pop-up menu item.

Thomson, Colin F.

2012-12-22

272

Application of quadratic neural networks to seismic signal classification  

NASA Astrophysics Data System (ADS)

This paper solves the seismic signal classification problem using the quadratic neural networks with closed-boundary discriminating surfaces. In this study, we have demonstrated the quadratic neural network (QNN) potential capabilities in application to the seismic signal classification problems and show that the efficiency achieved here, is much better to what obtained with conventional multilayer neural networks. Firstly, we have performed some pre-processing on the long period recordings to cancel out the instrumental and attenuation side effects. Secondly, we have extracted the ARMA filter coefficients of the windowed P-wave phase through some matrix manipulations using the conventional Prony ARMA modeling scheme. The derived coefficients are then applied to QNN for training and classification. The results have shown that a quadratic neuron is likely to have a performance similar to that of a multilayer perceptron when the target is to discriminate distribution of points in clusters within the input space.

Allameh Zadeh, M.; Nassery, P.

1999-06-01

273

Quadratic algebra approach to relativistic quantum Smorodinsky-Winternitz systems  

SciTech Connect

There exists a relation between the Klein-Gordon and the Dirac equations with scalar and vector potentials of equal magnitude and the Schroedinger equation. We obtain the relativistic energy spectrum for the four relativistic quantum Smorodinsky-Winternitz systems from their quasi-Hamiltonian and the quadratic algebras studied by Daskaloyannis in the nonrelativistic context. We also apply the quadratic algebra approach directly to the initial Dirac equation for these four systems and show that the quadratic algebras obtained are the same than those obtained from the quasi-Hamiltonians. We point out how results obtained in context of quantum superintegrable systems and their polynomial algebras can be applied to the quantum relativistic case.

Marquette, Ian [Department of Mathematics, University of York, Heslington, York YO10 5DD (United Kingdom)

2011-04-15

274

A New Method for Obtaining Stellar Velocity Distributions from Absorption-Line Spectra - Unresolved Gaussian Decomposition  

NASA Astrophysics Data System (ADS)

We have developed a new algorithm for extracting the line-of-sight velocity distributions (LOSVDs) of galaxies from the broadening of absorption lines in their spectra relative to those of a stellar `template'. This method models the LOSVD as the sum of a set of Gaussian distributions uniformly spaced in velocity. By choosing the dispersion, {DELTA}v, of these Gaussians so that the separate components are unresolved according to the Rayleigh criterion, such a sum can model any LOSVD that is smooth on scales smaller than {DELTA}v. The velocity scale on which the LOSVD is forced to be smooth is thus set explicitly by the user. The algorithm then involves solving for the amplitudes of the individual components to produce the LOSVD that, when convolved with the stellar template, best reproduces the observed galaxy spectrum in a least-squares sense. This procedure is an example of quadratic programming for which efficient algorithms exist, and, since all of the convolutions in the analysis involve similar Gaussians, the computational expense in calculating the model is also small. The physical constraint that the LOSVD must be non-negative can be readily included in the quadratic programming, and the method allows an explicit treatment of the errors in the derived LOSVD. Monte Carlo tests show that this algorithm can, indeed, efficiently extract a wide range of LOSVDs from absorption- line spectra with attainable signal-to-noise ratios. Application to the early-type disc galaxy UGC 12591 illustrates the potential of this approach for constraining dynamical models of galaxies.

Kuijken, K.; Merrifield, M. R.

1993-10-01

275

Mismatch management for optical and matter-wave quadratic solitons  

SciTech Connect

We propose a way to control solitons in {chi}{sup (2)} (quadratically nonlinear) systems by means of periodic modulation imposed on the phase-mismatch parameter ('mismatch management', MM). It may be realized in the cotransmission of fundamental-frequency (FF) and second-harmonic (SH) waves in a planar optical waveguide via a long-period modulation of the usual quasi-phase-matching pattern of ferroelectric domains. In an altogether different physical setting, the MM may also be implemented by dint of the Feshbach resonance in a harmonically modulated magnetic field in a hybrid atomic-molecular Bose-Einstein condensate (BEC), with the atomic and molecular mean fields (MFs) playing the roles of the FF and SH, respectively. Accordingly, the problem is analyzed in two different ways. First, in the optical model, we identify stability regions for spatial solitons in the MM system, in terms of the MM amplitude and period, using the MF equations for spatially inhomogeneous configurations. In particular, an instability enclave is found inside the stability area. The robustness of the solitons is also tested against variation of the shape of the input pulse, and a threshold for the formation of stable solitons is found in terms of the power. Interactions between stable solitons are virtually unaffected by the MM. The second method (parametric approximation), going beyond the MF description, is developed for spatially homogeneous states in the BEC model. It demonstrates that the MF description is valid for large modulation periods, while, at smaller periods, non-MF components acquire gain, which implies destruction of the MF under the action of the high-frequency MM.

Driben, R.; Oz, Y.; Malomed, B. A.; Gubeskys, A.; Yurovsky, V. A. [Department of Interdisciplinary Studies, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel); School of Chemistry, Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978 (Israel)

2007-02-15

276

Constrained Load Flow Using Recursive Quadratic Programming  

Microsoft Academic Search

The present paper will discuss the efficient, practical and definitive algorithm for dealing with constrained load flow problems. Algorithms based on mathematical programming and algorithms based on the load flow calculation methods have been studied since earlier days. However, on account of numerous control variables to be determined and of inadequate calculating efficiency, the guarantee of unfailing solution is yet

K. Aoki; A. Nishikori; R. Yokoyama

1987-01-01

277

Quasi-Gaussian electromagnetic beams  

NASA Astrophysics Data System (ADS)

A class of Maxwellian beams, which is an exact solution of the vector wave equation (Helmholtz equation) and Maxwell's equations, is introduced. The solution, termed a quasi-Gaussian electromagnetic (EM) beam, is formed from a superposition of sources and sinks with complex coordinates, and is characterized by an arbitrary waist w0 and a diffraction convergence length known as the Rayleigh range zR. An attractive feature of this beam is the description of strongly focused (or strongly divergent) EM-optical wave fields for kw0?1, where k is the wave number. A vector wave analysis is developed to determine and compute the spatial Cartesian components of the electric and magnetic fields (valid in the near field and the far field) stemming from Maxwell's vector equations and the Lorenz gauge condition, with particular emphasis on the parameter kw0 and the polarization states of the vector potentials used to derive the EM field's components. The results are potentially useful in the study of the axial and/or arbitrary wave scattering, radiation force, and torque in lasers operating with strongly focused (or strongly divergent) beams for particle manipulation in optical tweezers and imaging applications.

Mitri, F. G.

2013-03-01

278

Gaussian Multiplicative Chaos and KPZ Duality  

NASA Astrophysics Data System (ADS)

This paper is concerned with the construction of atomic Gaussian multiplicative chaos and the KPZ formula in Liouville quantum gravity. On the first hand, we construct purely atomic random measures corresponding to values of the parameter ? 2 beyond the transition phase (i.e. ? 2 > 2 d) and check the duality relation with sub-critical Gaussian multiplicative chaos. On the other hand, we give a simplified proof of the classical KPZ formula as well as the dual KPZ formula for atomic Gaussian multiplicative chaos. In particular, this framework allows to construct singular Liouville measures and to understand the duality relation in Liouville quantum gravity.

Barral, Julien; Jin, Xiong; Rhodes, Rémi; Vargas, Vincent

2013-10-01

279

Characterization of bipartite Gaussian states from OPO  

NASA Astrophysics Data System (ADS)

In a recent paper by D'Auria et al (2009 Phys. Rev. Lett. 102 020502) we reported the full experimental reconstruction of Gaussian entangled states generated by a type-II optical parametric oscillator (OPO) below threshold using a single homodyne detector. Here we investigate more deeply the Gaussian character of the OPO output addressing the homodyne traces. More precisely, we apply a suitable normality test to check the actual Gaussian distribution of the homodyne data and then we perform the full reconstruction of the signal.

D'Auria, V.; Fornaro, S.; Porzio, A.; Solimeno, S.; Olivares, S.; Paris, M. G. A.

2010-09-01

280

Gaussian Mixture Model of Heart Rate Variability  

PubMed Central

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.

Costa, Tommaso; Boccignone, Giuseppe; Ferraro, Mario

2012-01-01

281

A Dynamical Systems Analysis of Semidefinite Programming with Application to Quadratic Optimization with Pure Quadratic Equality Constraints  

SciTech Connect

This paper considers the problem of minimizing a quadratic cost subject to purely quadratic equality constraints. This problem is tackled by first relating it to a standard semidefinite programming problem. The approach taken leads to a dynamical systems analysis of semidefinite programming and the formulation of a gradient descent flow which can be used to solve semidefinite programming problems. Though the reformulation of the initial problem as a semidefinite pro- gramming problem does not in general lead directly to a solution of the original problem, the initial problem is solved by using a modified flow incorporating a penalty function.

Orsi, R. J. [Department of Electrical and Electronic Engineering, University of Melbourne, Parkville, VIC 3052 (Australia); Mahony, R. E. [Heudiasyc - UTC UMR 6599, Centre de Recherche de Royallieu, BP 20529, 60205 Compiegne Cedex (France); Moore, J. B. [Department of Systems Engineering, RSISE, Australian National University, Canberra, ACT 0200 (Australia)

1999-09-15

282

Near-optimal placement using a quadratic objective function  

Microsoft Academic Search

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

John P. Blanks

1985-01-01

283

Quadratic stabilization of sampled-data systems with quantization  

Microsoft Academic Search

A design method of memoryless quantizers in sampled-data systems is proposed. The design objective is quadratic stability in the continuous-time domain, and thus the decay rate between sampling times is guaranteed. Our general treatment enables us to look for quantizers efficient in terms of data rate.

Hideaki Ishii; Bruce A. Francis

2003-01-01

284

The decimal scale for releves of permanent quadrats  

Microsoft Academic Search

For vegetation analyses of permanent quadrats the author formerly used a modified scale of Braun-Blanquet with smaller intervals than in the original. For calculations of difference- and change quotients etc., on the basis of coverage, the symbols of this scale have to be converted to values proportional to the real coverage percentages. A conversion in simple terms is not possible;

G. Londo

1976-01-01

285

Finding the Best Quadratic Approximation of a Function  

ERIC Educational Resources Information Center

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

Yang, Yajun; Gordon, Sheldon P.

2011-01-01

286

Distribution of Quadratic Forms in the Multivariate Singular Normal Distribution.  

National Technical Information Service (NTIS)

The purpose of this paper is to investigate the distribution and independence properties of quadratic forms of the type X'AX where X, a pxl random vector, has the multivariate normal distribution with the corresponding mean vector mu and the pxp variance ...

P. C. Davis C. H. Kapadia J. T. Webster

1969-01-01

287

Stanley decomposition of the joint covariants of three quadratics  

NASA Astrophysics Data System (ADS)

The Stanley decomposition of the joint covariants of three quadratics is computed using a new transvectant algorithm and computer algebra. This is sufficient to compute the general form of the normal form with respect to a nilpotent with three 3-dimensional irreducible blocks.

Sanders, Jan A.

2007-12-01

288

Detection of quadratic phase coupling in shallow underwater channel  

Microsoft Academic Search

This paper addresses the problem of detection of quadratic phase coupling (QPC) at the receiver when the source signal has traversed through an underwater channel. The channel has been numerically modeled using normal mode theory In a bounded underwater channel, the phase associated with each frequency varies with range as well as due to the characteristics of the channel. We

Tanmay Roy; Arun Kumar; Rajendar Bahl

2002-01-01

289

Unravelling Student Challenges with Quadratics: A Cognitive Approach  

ERIC Educational Resources Information Center

The author's secondary school mathematics students have often reported to her that quadratic relations are one of the most conceptually challenging aspects of the high school curriculum. From her own classroom experiences there seemed to be several aspects to the students' challenges. Many students, even in their early secondary education, have…

Kotsopoulos, Donna

2007-01-01

290

Defining Classes of Quadratic Systems in the Plane.  

National Technical Information Service (NTIS)

The definition of classes of quadratic systems in the plane is studied. Taking into account their index and multiplicity, possible combinations of singular points, both in the finite part of the plane and at infinity, lead to the definition of 173 classes...

J. W. Reyn

1991-01-01

291

Analysis of Quadratic Diophantine Equations with Fibonacci Number Solutions  

ERIC Educational Resources Information Center

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

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

2004-01-01

292

Zero-sum linear quadratic stochastic integral games and BSVIEs  

Microsoft Academic Search

This paper formulates and studies a linear quadratic (LQ for short) game problem governed by linear stochastic Volterra integral equation. Sufficient and necessary condition of the existence of saddle points for this problem are derived. As a consequence we solve the problems left by Chen and Yong in [3]. Firstly, in our framework, the term GX^2(T) is allowed to be

Tianxiao Wang; Yufeng Shi

2010-01-01

293

An extension of Karmarkar's projective algorithm for convex quadratic programming  

Microsoft Academic Search

We present an extension of Karmarkar's linear programming algorithm for solving a more general group of optimization problems: convex quadratic programs. This extension is based on the iterated application of the objective augmentation and the projective transformation, followed by optimization over an inscribing ellipsoid centered at the current solution. It creates a sequence of interior feasible points that converge to

Yinyu Ye; Edison Tse

1989-01-01

294

A Quadratic Programming Model for Political Districting Problem  

Microsoft Academic Search

Political Districting Problem is one of the critical issues in political elections, it can be expressed as: how to partition a state into reasonable districts for parliament election and presiden- tial election. In this paper, the political districting problem for parliament election is modelled as a doubly weighted graph partition problem and it is formulated into quadratic programming model. Using

Zhenping Li; Rui-Sheng Wang; Yong Wang

295

Quadrat Sampling: A Computer-Generated Laboratory Exercise  

NSDL National Science Digital Library

Obtaining spatial distributions by quadrat sampling can be difficult because field work tends to yield inconclusive data. This article describes a computer program that generates different spatial patterns for two species. It produces meaningful comparisons between two or more different habitats and uses cluster points which determine the interactions within and between species.

Boyer, John F.

2010-02-16

296

Solving quadratic lambda-matrix problems without factorization  

Microsoft Academic Search

An algorithm is presented for computing the eigenvalues of smallest magnitude and their associated eigenvectors of the quadratic lambda-matrix M lambda² + C lambda + K. M, C, and K are assumed to be symmetric matrices with K positive definite and M negative definite. The algorithm is based on a generalization of the Rayleigh quotient and the Lanczos method for

D. S. Scott; R. C. Ward

1981-01-01

297

Dual support method for solving convex quadratic programs  

Microsoft Academic Search

In this article, we present a new dual method for solving convex (but not strictly convex) quadratic programs (QPs). Our method is the generalization of the dual support method, developed by Gabasov and co-workers in 1981, for solving convex QPs. It proceeds in two phases: the first is to construct the initial support, called coordinator support, for the problem and

Belkacem Brahmi; Mohand Ouamer Bibi

2010-01-01

298

A dual method for solving general convex quadratic programs  

Microsoft Academic Search

In this paper, we present a new method for solving quadratic programming problems, not strictly convex. Constraints of the problem are linear equalities and inequalities, with bounded variables. The suggested method combines the active-set strategies and support methods. The algorithm of the method and numerical experiments are presented, while comparing our approach with the active set method on randomly generated

Belkacem BRAHMI; Mohand Ouamer BIBI

2009-01-01

299

The Quadratic Spinor Lagrangian, Axial Torsion Current and Generalizations  

Microsoft Academic Search

We show that the Einstein-Hilbert, the Einstein-Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), when the three classes of Dirac spinor fields, under Lounesto spinor field classification, are considered. To each one of these classes, there corresponds an unique kind of action for a covariant gravity theory. In other words, it is shown to

R. Da Rocha; J. G. Pereira

2007-01-01

300

Dynamics of quadratic polynomials, III: Parapuzzle and SBR measures  

Microsoft Academic Search

This is a continuation of notes on dynamics of quadratic polynomials. In this part we transfer the our prior geometric result to the parameter plane. To any parameter value c in the Mandelbrot set (which lies outside of the main cardioid and little Mandelbrot sets attached to it) we associate a ``principal nest of parapuzzle pieces'' and show that the

Mikhail Lyubich

1996-01-01

301

Moving localized structures in quadratic media with a saturable absorber  

Microsoft Academic Search

Spatial moving pulses are found in an optical resonator with a quadratic medium coupled to an intra-cavity saturable absorber. In the context of frequency degenerate optical parametric oscillators, the saturable absorber is shown to be able to generate large amplitude asymmetric pulses in the transverse section of the signal beam. They arise in a regime where the lasing solution undergoes

A. Barsella; C. Lepers; M. Taki; M. Tlidi

2004-01-01

302

A greedy genetic algorithm for the quadratic assignment problem  

Microsoft Academic Search

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

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

2000-01-01

303

A Greedy Genetic Algorithm for the Quadratic Assignment Problem  

Microsoft Academic Search

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

Ravindra K. Ahuja; James B. Orlin

1997-01-01

304

Pseudorandom Number Assignment in Quadratic Response Surface Designs  

Microsoft Academic Search

This paper examines three general strategies for the assignment of pseudorandom number streams to simulation experiments in quadratic response surface designs. Comparisons of these variance-reduction schemes are presented for four design criteria that collectively address the two goals of response surface methodology: prediction and optimization.

James R. Hussey; Raymond H. Myers; Ernest C. Houck

1987-01-01

305

ECONOMIC ACCEPTANCE SAMPLING BY VARIABLES WITH QUADRATIC QUALITY COSTS  

Microsoft Academic Search

An economic model is developed, to assist in the selection of minimum cost acceptance sampling plans by variables. The quadratic Taguchi loss function is adopted to model the cost of accepting items, with quality characteristics deviating from the target value. The case of a normally distributed quality characteristic with known variance is examined, and a simple and efficient optimization algorithm

GEORGE TAGARAS

1994-01-01

306

Fast Fourier Transform Solvers and Preconditioners for Quadratic Spline Collocation  

Microsoft Academic Search

Quadratic Spline Collocation (QSC) methods of optimal order of convergence have been recently developed for the solution of elliptic Partial Differentia l Equations (PDEs). In this paper, linear solvers based on Fast Fourier Transforms (FFT) are developed for the solution of the QSC equations. The complexity of the FFT solvers is , where is the gridsize in one dimension. These

Christina C. Christara; Kit Sun Ng

2000-01-01

307

Perturbative metric of charged black holes in quadratic gravity  

Microsoft Academic Search

We consider perturbative solutions to the classical field equations coming from a quadratic gravitational Lagrangian in four dimensions. We study the charged, spherically symmetric black hole, and explicitly give corrections up to third order (in the coupling constant beta multiplying the RmunuRmunu term) to the Reissner-Nordström metric. We discuss the thermodynamics of such black holes; in particular, we compute explicitly

M. Campanelli; C. O. Lousto; J. Audretsch

1995-01-01

308

Comparative benthic plant ecology by SCUBA-monitored quadrats  

Microsoft Academic Search

The feasibility of permanent benthic quadrats checked by SCUBA divers was tested. Stations were set up on the bottom of six representative aquatic habitats, both marine and inland, including oligotrophic and eutrophic ponds, river, coastal lagoon, estuary, and open marine coast. Data include physical-chemical factors, species composition, number and height of shoots, and general observations. From volume\\/length constants, the standing

R. D. Wood; Paul E. Hargraves

1969-01-01

309

On Quadratic Bottom Drag, Geostrophic Turbulence, and Oceanic Mesoscale Eddies  

Microsoft Academic Search

Many investigators have idealized the oceanic mesoscale eddy field with numerical simulations of geo- strophic turbulence forced by a horizontally homogeneous, baroclinically unstable mean flow. To date such studies have employed linear bottom Ekman friction (hereinafter, linear drag). This paper presents simu- lations of two-layer baroclinically unstable geostrophic turbulence damped by quadratic bottom drag, which is generally thought to be

Brian K. Arbic; Robert B. Scott

2008-01-01

310

Quadratic: manipulating algebraic expressions on an interactive tabletop  

Microsoft Academic Search

This paper introduces Quadratic---a virtual manipulative for two people to explore algebraic expressions on an interactive tabletop. Users assemble rectangles out of fundamental components: 1, x, and x2. As the area of a rectangle is both the product of its sides and the sum of its components, users can explore how the product of two linear expressions (the rectangle's sides)

Jochen Rick

2010-01-01

311

Interior-point methods for reduced Hessian successive quadratic programming  

Microsoft Academic Search

Typical chemical process optimization problems have a large number of equations, but relatively few degrees of freedom. A reduced Hessian successive quadratic programming (rSQP) algorithm has been shown to be successful in solving these types of models efficiently. While the rSQP algorithm reduces the dimension of the QP subproblem solved at each iteration, the number of inequality constraints could still

David J. Ternet; Lorenz T. Biegler

1999-01-01

312

NQG/H?/LTR Control for a Hard Nonlinear Servo System  

NASA Astrophysics Data System (ADS)

In this paper we propose a new nonlinear controller design method, called nonlinear quadratic Gaussian/H-infinity/loop transfer recovery (NQG/H?/LTR), for nonlinear servo systems with hard nonlinearities such as Coulomb friction, dead-zone. We consider a H? performance constraint for the optimization of statistically linearized systems, by replacing a covariance Lyapunov equation into a modified Riccati equation of which solution leads to an upper bound of the nonlinear quadratic Gaussian (NQG) performance. As a result, the nonlinear correction term is included in coupled Riccati equation, which is generally very difficult to have a numerical solution. To solve this problem, we use the modified loop shaping technique and show some analytic proofs on LTR condition. Finally, the NQG/H?/LTR controller is synthesized by inverse random input describing function techniques (IRIDF). It is shown that the proposed design method has a better performance robustness to the hard nonlinearity than the LQG/H?/LTR method via simulations and experiments for the timing-belt driving servo system that contains the Coulomb friction and dead-zone.

Han, Seong Ik; Kim, Byong Sam

313

RANDOM CLUSTERING BASED ON THE CONDITIONAL INVERSE GAUSSIAN-POISSON DISTRIBUTION  

Microsoft Academic Search

The present article describes a Conditional Inverse Gaussian-Poisson (CIGP) distribution, obtained by conditioning an inverse Gaussian-Poisson population model on its total frequency.This CIGP distribution is equivalent to random partitioning of positive integers, with the possibility for a number of applications in statistical ecology, linguistics and statistical disclosure control to name a few.After showing the marginal moments of the distribution, parameter

Nobuaki Hoshino

2003-01-01

314

Gaussian Multiplicative Chaos for Symmetric Isotropic Matrices  

NASA Astrophysics Data System (ADS)

Motivated by isotropic fully developed turbulence, we define a theory of symmetric matrix valued isotropic Gaussian multiplicative chaos. Our construction extends the scalar theory developed by J.P. Kahane in 1985.

Chevillard, Laurent; Rhodes, Rémi; Vargas, Vincent

2013-02-01

315

Phase statistics in non-Gaussian scattering  

NASA Astrophysics Data System (ADS)

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.

Watson, Stephen M.; Jakeman, Eric; Ridley, Kevin D.

2006-06-01

316

Gaussian Sum Rules for Optical Functions.  

National Technical Information Service (NTIS)

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...

I. Kimel

1981-01-01

317

Evaluation of Derivatives of Gaussian Integrals.  

National Technical Information Service (NTIS)

We show that by a suitable change of variables, the derivatives of molecular integrals over Gaussian-type functions required for analytic energy derivatives can be evaluated with significantly less computational effort than current formulations. The reduc...

T. Helgaker P. R. Taylor

1992-01-01

318

Optimal unitary dilation for bosonic Gaussian channels  

SciTech Connect

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

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

2011-08-15

319

Gaussian-state analysis of biphoton imaging  

Microsoft Academic Search

Previous work on biphoton imaging configurations is recast in the more inclusive framework of Gaussian-state quantum fields. This formulation shows that biphoton image formation is classical, but not its image-to-background ratio.

Baris I. Erkmen; Jeffrey H. Shapiro

2008-01-01

320

Nonnegative Matrix Factorization with Gaussian Process Priors  

PubMed Central

We present a general method for including prior knowledge in a nonnegative matrix factorization (NMF), based on Gaussian process priors. We assume that the nonnegative factors in the NMF are linked by a strictly increasing function to an underlying Gaussian process specified by its covariance function. This allows us to find NMF decompositions that agree with our prior knowledge of the distribution of the factors, such as sparseness, smoothness, and symmetries. The method is demonstrated with an example from chemical shift brain imaging.

Schmidt, Mikkel N.; Laurberg, Hans

2008-01-01

321

Information rates of non-Gaussian processes  

Microsoft Academic Search

The rate distortion functionR(D)of an information source was introduced by Shannon to specify the channel capacity required in transmitting information from the source with an average distortion not exceedingD. Exact rates have been calculated for Gaussian sources under a mean-square error criterion. For non-Gaussian continuous sources, Shannon has given upper and lower bounds onR(D). In specific cases, the difference between

A. M. GERRISH; P. Schultheiss

1964-01-01

322

Gaussian beams in inhomogeneous media: A review  

Microsoft Academic Search

The paper outlines the most important results of the paraxial complex geometrical optics (CGO) in respect to Gaussian beams\\u000a diffraction in the smooth inhomogeneous media and discusses interrelations between CGO and other asymptotic methods, which\\u000a reduce the problem of Gaussian beam diffraction to the solution of ordinary differential equations, namely: (i) Babich’s method,\\u000a which deals with the abridged parabolic equation

Yu. A. Kravtsov; P. Berczynski

2007-01-01

323

The Gaussian rank correlation estimator: robustness properties  

Microsoft Academic Search

The Gaussian rank correlation equals the usual correlation coefficient computed from the normal scores of the data. Although\\u000a its influence function is unbounded, it still has attractive robustness properties. In particular, its breakdown point is\\u000a above 12%. Moreover, the estimator is consistent and asymptotically efficient at the normal distribution. The correlation\\u000a matrix obtained from pairwise Gaussian rank correlations is always

Kris Boudt; Jonathan Cornelissen; Christophe Croux

2010-01-01

324

Gaussian sum rules for optical functions  

NASA Astrophysics Data System (ADS)

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 analyzing experimental data.

Kimel, Isidoro

1982-06-01

325

Gaussian surfaces and nullcone dual surfaces of null curves in a three-dimensional nullcone with index 2  

NASA Astrophysics Data System (ADS)

In this paper, we consider the null curves in the 3-nullcone with index 2 and we investigate these curves in the framework of the theory of Legendrian dualities between nullcones. The sufficient and necessary conditions for the classifications of the singularities of both Gaussian surfaces and those nullcone dual surfaces that are associated with a null curve are given; these conditions are closely related to several new geometric invariants. In addition, we reveal the relationships between these geometric invariants and the order of contact for the 2nd principal normal curve n(s) of a null curve ?(s) with quadratic surfaces. Finally, two examples, namely, a Gaussian surface and a nullcone dual surface, are used to demonstrate our theoretical results.

Wang, Zhigang; Pei, Donghe; Kong, Lingling

2013-11-01

326

Utilizing gaussian-schell model beams to mitigate atmospheric turbulence in free space optical communications  

NASA Astrophysics Data System (ADS)

Turbulence affects traditional free space optical communication by causing speckle to appear in the received beam profile. This occurs due to changes in the refractive index of the atmosphere that are caused by fluctuations in temperature and pressure, resulting in an inhomogeneous medium. The Gaussian-Schell model of partial coherence has been suggested as a means of mitigating these atmospheric inhomogeneities on the transmission side. This dissertation analyzed the Gaussian-Schell model of partial coherence by verifying the Gaussian-Schell model in the far-field, investigated the number of independent phase control screens necessary to approach the ideal Gaussian-Schell model, and showed experimentally that the Gaussian-Schell model of partial coherence is achievable in the far-field using a liquid crystal spatial light modulator. A method for optimizing the statistical properties of the Gaussian-Schell model was developed to maximize the coherence of the field while ensuring that it does not exhibit the same statistics as a fully coherent source. Finally a technique to estimate the minimum spatial resolution necessary in a spatial light modulator was developed to effectively propagate the Gaussian-Schell model through a range of atmospheric turbulence strengths. This work showed that regardless of turbulence strength or receiver aperture, transmitting the Gaussian-Schell model of partial coherence instead of a fully coherent source will yield a reduction in the intensity fluctuations of the received field. By measuring the variance of the intensity fluctuations and the received mean, it is shown through the scintillation index that using the Gaussian-Schell model of partial coherence is a simple and straight forward method to mitigate atmospheric turbulence instead of traditional adaptive optics in free space optical communications.

Drexler, Kyle R.

327

Ultrabroadband generation of multiple concurrent nonlinear coherent interactions in random quadratic media  

NASA Astrophysics Data System (ADS)

Triply coincident nonlinear second harmonic interactions continuously tunable in an extremely large spectral range (800-1400 nm) are demonstrated in strontium barium niobate random quadratic crystal. The spectral dependence of the triple process is in agreement with a first order quasi-phase-matching collinear interaction. The analysis of the polarization states of the generated beams reveals mutually coherent interactions between different processes simultaneously contributing to the total intensity. The results constitute a necessary step in the implementation of ultra-broadband entangled photon pairs from randomly poled structures and are relevant to a wide range of applications, for which broadband polarization controlled light is required.

Mateos, Luis; Molina, Pablo; Galisteo-López, Juan F.; López, Cefe; Bausá, Luisa E.; Ramírez, Mariola O.

2013-09-01

328

Gaussian Finite Element Method for Description of Underwater Sound Diffraction  

Microsoft Academic Search

A new method for solving diffraction problems is presented in this dissertation. It is based on the use of Gaussian diffraction theory. The Rayleigh integral is used to prove the core of Gaussian theory: the diffraction field of a Gaussian is described by a Gaussian function. The parabolic approximation used by previous authors is not necessary to this proof. Comparison

Dehua Huang

1992-01-01

329

A Unified Study on the Cyclicity of Period Annulus of the Reversible Quadratic Hamiltonian Systems  

Microsoft Academic Search

The cyclicity of the period annulus of reversible quadratic Hamiltonian systems under quadratic perturbations was studied by several authors for different cases by using different methods. In this paper, we study this problem in a unified way.

Chengzhi Li; Jaume Llibre

2004-01-01

330

FIBER OPTIC POINT QUADRAT SYSTEM FOR IMPROVED ACCURACY IN VEGETATION SAMPLING  

EPA Science Inventory

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

331

Statistically linearized optimal control of an electromagnetic vibratory energy harvester  

NASA Astrophysics Data System (ADS)

In this paper, an extension of linear-quadratic-Gaussian (LQG) control theory is used to determine the optimal state feedback controller for a vibratory energy harvesting system with Coulomb friction. Specifically, the energy harvester is a base-excited single-degree-of-freedom (SDOF) resonant oscillator with an electromagnetic transducer attached between the base and the moving mass. The development of the optimal controller for this system is based on statistical linearization, whereby the Coulomb friction force is replaced by an equivalent linear viscous damping term, which is calculated from the stationary covariance of the closed-loop system. It is shown that the covariance matrix and optimal feedback gain matrix can be computed by implementing an iterative algorithm involving linear matrix inequalities (LMIs). Furthermore, this theory is augmented to account for a non-quadratic dissipation in the electronics used to control the energy conversion. Simulation results are presented for the SDOF energy harvester in which the performance of the optimal state feedback control law is compared to the performance of the optimal static admittance over a range of disturbance bandwidths.

Cassidy, Ian L.; Scruggs, Jeffrey T.

2012-08-01

332

A Parametric Approach to Solve Quadratic Programming Problems with Fuzzy Environment in the Set of Constraints  

Microsoft Academic Search

Quadratic programming can be seen both as a gen- eral approach to linear programming and a special class of nonlin- ear programming. Moreover, Quadratic Programming problems are of utmost importance in a variety of relevant practical fields, such as, portfolio selection. This work presents and develops a novel fuzzy-sets-based method that solves a class of quadratic program- ming problems with

Carlos Cruz; Ricardo C. Silva; José L. Verdegay; Akebo Yamakami

2009-01-01

333

Applicability of quadratic and threshold models to motion discrimination in the rabbit retina  

Microsoft Academic Search

Computational and behavioral studies suggest that visual motion discrimination is based on quadratic nonlinearities. This raises the question of whether the behavior of motion sensitive neurons early in the visual system is actually quadratic. Theoretical studies show that mechanisms proposed for retinal directional selectivity do not behave quadratically at high stimulus contrast. However, for low contrast stimuli, models for these

Norberto M. Grzywacz; F. R. Amthor; L. A. Mistler

1990-01-01

334

Existence, attractiveness and stability of solutions for quadratic Urysohn fractional integral equations  

NASA Astrophysics Data System (ADS)

Two nonlinear quadratic Urysohn fractional integral equations are studied. Existence and locally attractive results of solutions for a nonlinear quadratic Urysohn fractional integral equation on an unbounded interval are proved. Some interesting stability results of solutions for another quadratic Urysohn fractional integral equation in three certain sets are presented.

Wang, Jinrong; Dong, Xiwang; Zhou, Yong

2012-02-01

335

The Hua Loo-Keng problem on prime numbers representable by given quadratic forms  

NASA Astrophysics Data System (ADS)

In this paper, we solve the Hua Loo-Keng problem with prime numbers representable by given primitive positive-definite binary quadratic forms whose discriminants coincide with those of the imaginary quadratic fields in which the quadratic forms decompose into linear factors.

Gritsenko, Sergey A.

2007-06-01

336

Quadratic nonlinear Klein-Gordon equation in one dimension  

NASA Astrophysics Data System (ADS)

We study the initial value problem for the quadratic nonlinear Klein-Gordon equation vtt + v - vxx = ?v2, t ? R, x ? R, with initial conditions v(0, x) = v0(x), vt(0, x) = v1(x), x ? R, where v0 and v1 are real-valued functions, ? ? R. Using the method of normal forms of Shatah [``Normal forms and quadratic nonlinear Klein-Gordon equations,'' Commun. Pure Appl. Math. 38, 685-696 (1985)], we obtain a sharp asymptotic behavior of small solutions without the condition of a compact support on the initial data, which was assumed in the previous work of J.-M. Delort [``Existence globale et comportement asymptotique pour l'équation de Klein-Gordon quasi-linéaire á données petites en dimension 1,'' Ann. Sci. Ec. Normale Super. 34(4), 1-61 (2001)].

Hayashi, Nakao; Naumkin, Pavel I.

2012-10-01

337

A simplified general design procedure for beam shaper converting Gaussian to super-Gaussian profile  

Microsoft Academic Search

This paper introduces a simplified general design procedure for designing laser beam shapers capable of redistributing an arbitrary beam profile into any desired output profile. Both geometrical and diffractive optical modelings are performed on a practical single lens shaper converting Gaussian to super-Gaussian profile that shows significant reduction of destructive effects on the beam uniformity over the sharp edge shapers.

Chuyu Liu; Shukui Zhang

2008-01-01

338

A simplified general design procedure for beam shaper converting Gaussian to super-Gaussian profile  

SciTech Connect

This paper introduces a simplified general design procedure for designing laser beam shapers capable of redistributing an arbitrary beam profile into any desired output profile. Both geometrical and diffractive optical modelings are performed on a practical single lens shaper converting Gaussian to super-Gaussian profile that shows significant reduction of destructive effects on the beam uniformity over the sharp edge shapers.

Liu, Chuyu; Zhang, Shukui

2008-08-01

339

Quadratic fluctuation-dissipation theorem for multilayer plasmas  

SciTech Connect

The author establishes the dynamical and static quadratic fluctuation-dissipation theorems (QFDTs) for multilayer classical one-component plasmas in the absence of external magnetic fields. Areal densities and spacings between layers need not be equal. The static QFDT is used to derive the lowest-order (in coupling parameter) Mayer cluster expansion for the layer-space matrix elements of the equilibrium three-point correlation function. {copyright} {ital 1999} {ital The American Physical Society}

Golden, K.I. [Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont 05401-1455 (United States)

1999-01-01

340

The quadratic spinor Lagrangian, axial torsion current, and generalizations  

Microsoft Academic Search

We show that the Einstein-Hilbert, the Einstein-Palatini, and the Holst\\u000aactions can be derived from the Quadratic Spinor Lagrangian (QSL), when the\\u000athree classes of Dirac spinor fields, under Lounesto spinor field\\u000aclassification, are considered. To each one of these classes, there corresponds\\u000aa unique kind of action for a covariant gravity theory. In other words, it is\\u000ashown to

Roldao da Rocha; J. G. Pereira

2007-01-01

341

A quadratic motion-based object-oriented video codec  

Microsoft Academic Search

A novel motion-based object-oriented codec for video transmission at very low bit-rates is proposed. The object motion is modeled by quadratic transform with coefficients estimated via a nonlinear quasi-Newton method. The segmentation problem is put forward as a constrained optimization problem which interacts with the motion estimation process in the course of region growing. A context-based shape coding method which

Y. Yemez; B. Sankur; E. Anar?m

2000-01-01

342

Bi-impulse response design of isotropic quadratic filters  

Microsoft Academic Search

The bi-impulse response of a 1-D or 2-D quadratic Volterra filter is introduced as a mathematical tool able to completely describe the nonlinear operator. The conditions that must be satisfied in order to obtain isotropic input\\/output relations are studied. The result is a formal framework that allows simple but effective operators (particularly for image enhancement and preprocessing) to be designed

G. Ramponi

1990-01-01

343

Symmetry-breaking instability of quadratic soliton bound states  

SciTech Connect

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

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

2011-01-15

344

Quantum integrals of motion for variable quadratic Hamiltonians  

SciTech Connect

We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic Hamiltonians. An extension of the Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy-related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application.

Cordero-Soto, Ricardo, E-mail: ricardojavier81@gmail.co [Mathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, AZ 85287-1804 (United States); Suazo, Erwin, E-mail: erwin.suazo@upr.ed [Department of Mathematical Sciences, University of Puerto Rico, Mayaquez, call box 9000, PR 00681-9000 (Puerto Rico); Suslov, Sergei K., E-mail: sks@asu.ed [School of Mathematical and Statistical Sciences and Mathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, AZ 85287-1804 (United States)

2010-09-15

345

Approximation algorithms for homogeneous polynomial optimization with quadratic constraints  

Microsoft Academic Search

In this paper, we consider approximation algorithms for optimizing a generic multi-variate homogeneous polynomial function, subject to homogeneous quadratic constraints. Such optimiza- tion models have wide applications, e.g., in signal processing, magnetic resonance imaging (MRI), data training, approximation theory, and portfolio selection. Since polynomial functions are non- convex in general, the problems under consideration are all NP-hard. In this paper

Simai He; Zhening Li; Shuzhong Zhang

2010-01-01

346

Induced motion of domain walls in multiferroics with quadratic interaction  

NASA Astrophysics Data System (ADS)

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.

Gerasimchuk, Victor S.; Shitov, Anatoliy A.

2013-10-01

347

Discrete quadratic solitons with competing second-harmonic components  

SciTech Connect

We describe families of discrete solitons in quadratic waveguide arrays supported by competing cascaded nonlinear interactions between one fundamental and two second-harmonic modes. We characterize the existence, stability, and excitation dynamics of these solitons and show that their features may resemble those of solitons in saturable media. Our results also demonstrate that a power threshold may appear for soliton formation, leading to a suppression of beam self-focusing which explains recent experimental observations.

Setzpfandt, Frank; Pertsch, Thomas [Institute of Applied Physics, Abbe Center of Photonics, Friedrich-Schiller-Universitaet Jena, Max-Wien-Platz 1, D-07743 Jena (Germany); Sukhorukov, Andrey A. [Nonlinear Physics Center, Research School of Physics and Engineering, Australian National University, Canberra, 0200 ACT (Australia)

2011-11-15

348

Noncommutative classical and quantum mechanics for quadratic Lagrangians (Hamiltonians)  

Microsoft Academic Search

Classical and quantum mechanics based on an extended Heisenberg algebra with additional canonical commutation relations for\\u000a position and momentum coordinates are considered. In this approach additional noncommutativity is removed from the algebra\\u000a by a linear transformation of coordinates and transferred to the Hamiltonian (Lagrangian). This linear transformation does\\u000a not change the quadratic form of the Hamiltonian (Lagrangian), and Feynman’s path

Branko Dragovich; Zoran Raki?

2009-01-01

349

Solving Large Quadratic Assignment Problems on Computational Grids  

Microsoft Academic Search

The quadratic assignment problem (QAP) is among the hardest combinatorial optimization prob- lems. Some instances of size 30 have remained unsolved for decades. The solution of these problems requires both improvements in mathematical programming algorithms and the utilization of powerful com- putational platforms. In this article we describe a novel ap proach to solve QAPs using a state-of-the-art branch-and-bound algorithm

Kurt Anstreicher; Nathan Brixius; Jean-Pierre Goux; Jeff Linderoth

2000-01-01

350

Cumulants as non-Gaussian qualifiers  

NASA Astrophysics Data System (ADS)

We discuss the requirements of good statistics for quantifying non-Gaussianity in the cosmic microwave background. The importance of rotational invariance and statistical independence is stressed, but we show that these are sometimes incompatible. It is shown that the first of these requirements prefers a real space (or wavelet) formulation, whereas the latter favors quantities defined in Fourier space. Bearing this in mind we decide to be eclectic and define two new sets of statistics to quantify the level of non-Gaussianity. Both sets make use of the concept of cumulants of a distribution. However, one set is defined in real space, with reference to the wavelet transform, whereas the other is defined in Fourier space. We derive a series of properties concerning these statistics for a Gaussian random field and show how one can relate these quantities to the higher order moments of temperature maps. Although our frameworks lead to an infinite hierarchy of quantities we show how cosmic variance and experimental constraints give a natural truncation of this hierarchy. We then focus on the real space statistics and analyze the non-Gaussian signal generated by point sources obscured by large scale Gaussian fluctuations. We conclude by discussing the practical implementations of these techniques.

Ferreira, Pedro G.; Magueijo, João; Silk, Joseph

1997-10-01

351

Iterative Gaussianization: from ICA to random rotations.  

PubMed

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

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

2011-02-24

352

Graphical calculus for Gaussian pure states  

SciTech Connect

We provide a unified graphical calculus for all Gaussian pure states, including graph transformation rules for all local and semilocal Gaussian unitary operations, as well as local quadrature measurements. We then use this graphical calculus to analyze continuous-variable (CV) cluster states, the essential resource for one-way quantum computing with CV systems. Current graphical approaches to CV cluster states are only valid in the unphysical limit of infinite squeezing, and the associated graph transformation rules only apply when the initial and final states are of this form. Our formalism applies to all Gaussian pure states and subsumes these rules in a natural way. In addition, the term 'CV graph state' currently has several inequivalent definitions in use. Using this formalism we provide a single unifying definition that encompasses all of them. We provide many examples of how the formalism may be used in the context of CV cluster states: defining the 'closest' CV cluster state to a given Gaussian pure state and quantifying the error in the approximation due to finite squeezing; analyzing the optimality of certain methods of generating CV cluster states; drawing connections between this graphical formalism and bosonic Hamiltonians with Gaussian ground states, including those useful for CV one-way quantum computing; and deriving a graphical measure of bipartite entanglement for certain classes of CV cluster states. We mention other possible applications of this formalism and conclude with a brief note on fault tolerance in CV one-way quantum computing.

Menicucci, Nicolas C.; Flammia, Steven T. [Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5 (Canada); Loock, Peter van [Optical Quantum Information Theory Group, Max Planck Institute for the Science of Light, Guenther-Scharowsky-Str. 1, Building 26, D-91058 Erlangen (Germany); Institute of Theoretical Physics I, Universitaet Erlangen-Nuernberg, Staudtstr. 7/B2, D-91058 Erlangen (Germany)

2011-04-15

353

The propagation of a polarized gaussian beam in a smoothly inhomogeneous isotropic medium  

NASA Astrophysics Data System (ADS)

In the frame of the eikonal-based complex geometrical optics, which describes the phase front and cross section of a light beam using the quadratic expansion of a complex-valued eikonal, we investigate the transverse deflections of a polarized Gaussian beam (GB) in a smoothly inhomogeneous isotropic medium, which is called the spin Hall effect of the beam. The linear complex-valued eikonal terms are introduced firstly to describe the polarization-dependent transverse shifts of the beam in the inhomogeneous medium. We find that the polarization-dependent transverse shifts of the beams include two parts: one originates from the coupling between the spin angular momentum and the extrinsic orbital angular momentum due to the curve trajectory of the center of gravity of the polarized GB, and the other from the coupling between the spin angular momentum and the intrinsic orbital angular momentum due to the rotation of the beam with respect to the central ray.

Li, Hehe; Ji, Peiyong

2012-11-01

354

Analysis of non-Gaussian surge response of tension leg platforms under wind loads  

SciTech Connect

The nonlinearity in the wind loading expression for a complaint offshore structure, e.g., a tension leg platform (TLP), results in response statistics that deviate from the Gaussian distribution. This paper focuses on the statistical analysis of the response of these structures to random wind loads. The analysis presented here involves a nonlinear system with memory. As an improvement over the commonly used linearization approach, an equivalent statistical quadratization method is presented. The higher-order response cumulants are based on Volterra series. A direct integration scheme and Kac-Siegert technique is utilized to evaluate the response cumulants. Based on the first four cumulants, the response probability density function, crossing rates, and peak value distribution are derived. The results provide a good comparison with simulation. A nonlinear wind gust loading factor based on the derived extreme value distribution of nonlinear wind effects is formulated.

Kareem, A. (Univ. of Notre Dame, IN (United States). Dept. of Civil Engineering and Geological Sciences); Zhao, J. (Barnett Casbarian Inc., Houston, TX (United States))

1994-08-01

355

Applications of Nonlinear Control Using the State-Dependent Riccati Equation.  

National Technical Information Service (NTIS)

This thesis examines the relatively new theory of nonlinear control using state dependent coefficient factorizations to mimic linear state space systems. The control theory is a nonlinear quadratic approach, analagous to linear quadratic regulation. All i...

D. K. Parrish

1995-01-01

356

On the Gaussian Approximation for Master Equations  

NASA Astrophysics Data System (ADS)

We analyze the Gaussian approximation as a method to obtain the first and second moments of a stochastic process described by a master equation. We justify the use of this approximation with ideas coming from van Kampen's expansion approach (the fact that the probability distribution is Gaussian at first order). We analyze the scaling of the error with a large parameter of the system and compare it with van Kampen's method. Our theoretical analysis and the study of several examples shows that the Gaussian approximation turns out to be more accurate than van Kampen's expansion at first order. This could be specially important for problems involving stochastic processes in systems with a small number of particles.

Lafuerza, Luis F.; Toral, Raul

2010-09-01

357

Second order Pseudo-gaussian shaper  

SciTech Connect

The purpose of this document is to provide a calculus spreadsheet for the design of second-order pseudo-gaussian shapers. A very interesting reference is given by C.H. Mosher ''Pseudo-Gaussian Transfer Functions with Superlative Recovery'', IEEE TNS Volume 23, p. 226-228 (1976). Fred Goulding and Don Landis have studied the structure of those filters and their implementation and this document will outline the calculation leading to the relation between the coefficients of the filter. The general equation of the second order pseudo-gaussian filter is: f(t) = P{sub 0} {center_dot} e{sup -3kt} {center_dot} sin{sup 2}(kt). The parameter k is a normalization factor.

Beche, Jean-Francois

2002-11-22

358

Non-gaussian velocity correlations in fluids  

NASA Astrophysics Data System (ADS)

Several molecular dynamics experiments in monoatomic fluids indicate that the velocity v of a tagged particle has a clear non-Gaussian behaviour: here we present typical simulation data obtained for < v 2(0) v 2( t)>. We have previously found that at long times these non-Gaussian features can be explained in terms of a non-linear Langevin equation developed by Mori, Fujisaka and Shigematsu. Here we show that the latter approach can be the long-time version of the reduced model known as the non-linear itinerant oscillator. In principle, such a model can also reproduce the non-Gaussian behaviour at short times, as found in the simulations and confirmed by the proper sum rules. The reduced model is numerically solved in a particular one-dimensional overdamped case and the main features present in the computer experiment are found to be qualitatively reproduced.

Balucani, U.; Tognetti, V.; Vallauri, R.; Grigolini, P.; Marin, P.

1982-09-01

359

Index Distribution of Gaussian Random Matrices  

SciTech Connect

We compute analytically, for large N, the probability distribution of the number of positive eigenvalues (the index N{sub +}) of a random NxN matrix belonging to Gaussian orthogonal (beta=1), unitary (beta=2) or symplectic (beta=4) ensembles. The distribution of the fraction of positive eigenvalues c=N{sub +}/N scales, for large N, as P(c,N){approx_equal}exp[-betaN{sup 2}PHI(c)] where the rate function PHI(c), symmetric around c=1/2 and universal (independent of beta), is calculated exactly. The distribution has non-Gaussian tails, but even near its peak at c=1/2 it is not strictly Gaussian due to an unusual logarithmic singularity in the rate function.

Majumdar, Satya N.; Nadal, Celine [Laboratoire de Physique Theorique et Modeles Statistiques (UMR 8626 du CNRS), Universite Paris-Sud, Batiment 100, 91405 Orsay Cedex (France); Scardicchio, Antonello; Vivo, Pierpaolo [Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34014 Trieste (Italy)

2009-11-27

360

Novel coordinate system for Gaussian beam reflection.  

PubMed

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

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

2012-06-01

361

Gaussian mode selection with intracavity diffractive optics.  

PubMed

We outline a resonator design that allows for the selection of a Gaussian mode by diffractive optical elements. This is made possible by the metamorphosis of a Gaussian beam into a flat-top beam during propagation from one end of the resonator to the other. By placing the gain medium at the flat-top beam end, it is possible to extract high energy in a low-loss cavity. A further feature of this resonator is the ability to select the field properties at either end of the cavity almost independently, thus opening the way to minimize the output divergence while simultaneously maximizing the output energy. PMID:19794792

Litvin, Igor A; Forbes, Andrew

2009-10-01

362

Entropic characterization of separability in Gaussian states  

SciTech Connect

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

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

2010-02-15

363

Gaussian-state description of squeezed light  

SciTech Connect

We present a Gaussian-state description of squeezed light generated in an optical parametric oscillator. Using the Gaussian-state description we describe the dynamics of the system conditioned on homodyne detection on the output field. Our theory shows that the output field is squeezed only if observed for long enough times or by a detector with finite bandwidth. As an application of the present approach we consider the use of finite bandwidth squeezed light together with a sample of spin-polarized atoms to estimate a magnetic field.

Petersen, Vivi; Moelmer, Klaus [QUANTOP-Danish National Research Foundation Center for Quantum Optics, University of Aarhus, DK-8000 Aarhus C (Denmark); Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C (Denmark); Madsen, Lars Bojer [Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C (Denmark)

2005-11-15

364

Absorbing filter to flatten gaussian beams.  

PubMed

An absorbing filter that flattens the Gaussian intensity profile of a laser beam has been developed. The filter was fabricated by dc magnetron sputtering a thin tantalum film, by using a combination of substrate masking and motion. A model of the filter production has been developed that successfully predicts the film profile and performance. A typical filter produced by using these techniques results in a flat output to within +/-3% over a 2.2 mm with a transmission of 60% of the peak intensity of the Gaussian beam. PMID:20725305

Dew, S K; Parsons, R R

1992-06-20

365

Invariant measures on multimode quantum Gaussian states  

SciTech Connect

We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom-the symplectic eigenvalues-which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.

Lupo, C. [School of Science and Technology, Universita di Camerino, I-62032 Camerino (Italy); Mancini, S. [School of Science and Technology, Universita di Camerino, I-62032 Camerino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, I-06123 Perugia (Italy); De Pasquale, A. [NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa (Italy); Facchi, P. [Dipartimento di Matematica and MECENAS, Universita di Bari, I-70125 Bari (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Florio, G. [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi, Piazza del Viminale 1, I-00184 Roma (Italy); Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy); Pascazio, S. [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy)

2012-12-15

366

Application of k-means and Gaussian mixture model for classification of seismic activities in Istanbul  

NASA Astrophysics Data System (ADS)

Two unsupervised pattern recognition algorithms, k-means, and Gaussian mixture model (GMM) analyses have been applied to classify seismic events in the vicinity of Istanbul. Earthquakes, which are occurring at different seismicity rates and extensions of the Thrace-Eskisehir Fault Zone and the North Anatolian Fault (NAF), Turkey, are being contaminated by quarries operated around Istanbul. We have used two time variant parameters, complexity, the ratio of integrated powers of the velocity seismogram, and S/P amplitude ratio as classifiers by using waveforms of 179 events (1.8 < M < 3.0). We have compared two algorithms with classical multivariate linear/quadratic discriminant analyses. The total accuracies of the models for GMM, k-means, linear discriminant function (LDF), and quadratic discriminant function (QDF) are 96.1%, 95.0%, 96.1%, 96.6%, respectively. The performances of models are discussed for earthquakes and quarry blasts separately. All methods clustered the seismic events acceptably where QDF slightly gave better improvements compared to others. We have found that unsupervised clustering algorithms, for which no a-prior target information is available, display a similar discriminatory power as supervised methods of discriminant analysis.

Kuyuk, H. S.; Yildirim, E.; Dogan, E.; Horasan, G.

2012-08-01

367

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

NASA Astrophysics Data System (ADS)

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

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

2012-04-01

368

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

SciTech Connect

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

Chandola, Varun [ORNL; Vatsavai, Raju [ORNL

2010-01-01

369

Gas distribution, metal enrichment and baryon fraction in Gaussian and non-Gaussian universes  

NASA Astrophysics Data System (ADS)

We study the cosmological evolution of baryons in universes with and without primordial non-Gaussianities via N-body/hydrodynamical simulations, including gas cooling, star formation, stellar evolution, chemical enrichment from both population III and population II regimes, and feedback effects. We find that large fNL values for non-Gaussianities can alter the gas probability distribution functions, the metal pollution history, the halo baryon, gas and stellar fractions, mostly at early times. More precisely, (i) non-Gaussianities lead to an earlier evolution of primordial gas, structures and star formation; (ii) metal enrichment starts earlier (with respect to the Gaussian scenario) in non-Gaussian models with larger fNL; (iii) gas fractions within the haloes are not significantly affected by the different values of fNL, with deviations of ˜1-10% (iv) the stellar fraction is quite sensitive to non-Gaussianities at early times, with discrepancies reaching up to a factor of ˜10 at very high z, and rapidly converging at low z; (v) the trends at low redshift are independent from fNL: they are mostly led by the ongoing baryonic evolution and by the feedback mechanisms, which determine a ˜25-30% discrepancy in the baryon fraction of galaxy groups/clusters with respect to the cosmic values; (vi) non-Gaussianity impacts on the cluster x-ray emission or on the Sunyaev-Zeldovic effect(s) are expected to be not very large and dominated by feedback mechanisms, whereas some effects on the 21 cm emission can be expected at early times; (vii) in order to address non-Gaussianities in the cosmological structure contest, high-redshift (z ˜ 10) investigations are required: first stars, galaxies, quasars and gamma-ray bursts may be potential cosmological probes of non-Gaussianities.

Maio, Umberto

2011-11-01

370

Analytical relationship between Gaussian and transformed-Gaussian spatially distributed fields  

NASA Astrophysics Data System (ADS)

A transformation of a Gaussian random field results in a change of the spatial dependence. In simple terms, the range and the shape of a variogram are different between an underlying Gaussian and a transformed Gaussian field. There is a relationship between the underlying and the transformed spatial dependence. This paper shows how this relationship can be expressed analytically. Rather than generating multidimensional random fields and conducting spatial statistical analysis, we develop an accurate and efficient approach based on a unique mapping of the correlation coefficients of the original multi-Gaussian fields to the transformed correlation coefficients to evaluate the spatial correlation of transformed non-Gaussian random fields for any type of geostatistical parameterization. Such a mapping can also yield accurate estimation of the spatial correlation of the underlying Gaussian field given the spatial correlation of the transformed field. Results indicate that (1) a nonlinear transformation of spatially distributed fields usually changes the spatial dependence structure; and (2) the relationship between the dependence structures of the underlying and the transformed field can be expressed analytically, and it is sufficient to do this in one dimension. We use the developed approach to investigate the change of correlations of connected random fields generated by the absolute-value transformation. Results show (1) the correlation lengths of the underlying Gaussian fields are 1.67 and 2.64 times of those of transformed non-Gaussian fields for Gaussian and exponential covariance models, respectively; (2) the anisotropic ratio does not change; and (3) the anticorrelation in hole-effect correlation models disappear.

Gong, Rulan; Haslauer, Claus P.; Chen, Yiming; Luo, Jian

2013-03-01

371

Topics in Statistical Process Control.  

National Technical Information Service (NTIS)

The inverse gaussian distribution can be used to model processes with skewed output. In this thesis, several Shewhard and CUSUM control schemes are developed for the inverse gaussian distribution. The behavior of these schemes is described. A new type of ...

D. H. Olwell

1996-01-01

372

Generating the Gaussian Basis Functions for Multi-Gaussian Beam Models  

NASA Astrophysics Data System (ADS)

A new K-space Prony's method is developed to determine the amplitude and phase terms of the Gaussians used in a multi-Gaussian beam model. Unlike the previous uses of Prony's method this new K-space approach allows the fitting of the Gaussian beams directly at the face of the transducer. The ability of the K-space Prony's method to model the transducer wave field of planar and focused piston transducers is demonstrated. It is shown that while this method is very fast there are also some stability and sensitivity issues associated with this approach.

Schmerr, Lester W.; Lopez-Sanchez, Ana; Sedov, Alexander

2007-03-01

373

Non-Gaussian states from continuous-wave Gaussian light sources  

SciTech Connect

We present a general analysis of the state obtained by subjecting a continuous-wave (cw) Gaussian field to non-Gaussian measurements. The generic multimode state of a cw Gaussian field is fully characterized by the time dependent mean values and variances and the two-time covariances of the field quadrature variables. We present a general theory to extract from this information the results of detection and quantum state reduction within specific temporal output modes. The formalism is applied to schemes for heralded production of propagating light pulses with single photon and Schroedinger kitten states from a cw squeezed beam of light.

Moelmer, Klaus [Danish National Research Foundation Center for Quantum Optics, Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C (Denmark)

2006-06-15

374

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

PubMed

A unified operator approach is described for deriving Hermite-Gaussian and Laguerre-Gaussian laser beams by using as a starting point a plane-wave-spectrum representation of the electromagnetic field. We show that by using the plane-wave representation of the fundamental Gaussian mode as a seed function, all higher-order beam modes can be derived by acting with differential operators on this fundamental solution. The approach presented can be easily generalized to nonparaxial situations and to include vector effects of the electromagnetic field. PMID:15330483

Enderlein, Jörg; Pampaloni, Francesco

2004-08-01

375

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

PubMed

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

Lindsay, K A; Rosenberg, J R

2012-06-18

376

Detecting drug promiscuity using Gaussian ensemble screening.  

PubMed

Polypharmacology describes the binding of a ligand to multiple protein targets (a promiscuous ligand) or multiple diverse ligands binding to a given target (a promiscuous target). Pharmaceutical companies are discovering increasing numbers of both promiscuous drugs and drug targets. Hence, polypharmacology is now recognized as an important aspect of drug design. Here, we describe a new and fast way to predict polypharmacological relationships between drug classes quantitatively, which we call Gaussian Ensemble Screening (GES). This approach represents a cluster of molecules with similar spherical harmonic surface shapes as a Gaussian distribution with respect to a selected center molecule. Calculating the Gaussian overlap between pairs of such clusters allows the similarity between drug classes to be calculated analytically without requiring thousands of bootstrap comparisons, as in current promiscuity prediction approaches. We find that such cluster similarity scores also follow a Gaussian distribution. Hence, a cluster similarity score may be transformed into a probability value, or "p-value", in order to quantify the relationships between drug classes. We present results obtained when using the GES approach to predict relationships between drug classes in a subset of the MDL Drug Data Report (MDDR) database. Our results indicate that GES is a useful way to study polypharmacology relationships, and it could provide a novel way to propose new targets for drug repositioning. PMID:22747187

Pérez-Nueno, Violeta I; Venkatraman, Vishwesh; Mavridis, Lazaros; Ritchie, David W

2012-07-19

377

Coalitional Games in Gaussian Interference Channels  

Microsoft Academic Search

The formation of coalitions in a Gaussian interference channel where the receivers are allowed to cooperate is studied under the framework of coalitional game theory. Allowing any arbitrary sharing of the total rate achieved by a coalition between its member links, it is shown that the grand coalition (coalition of all links) maximizes spectrum utilization and is also stable, that

Suhas Mathur; Lalitha Sankaranarayanan; Narayan B. Mandayam

2006-01-01

378

Gaussian particle filtering for tracking maneuvering targets  

Microsoft Academic Search

Tracking for maneuvering targets in the presence of clutter is a challenging problem. In this paper, we present an algorithm for reliable tracking of maneuvering targets based on Gaussian particle filtering (GPF) techniques. It has been shown that sequential Monte Carlo (SMC) methods outperform the various Kalman filter based algorithms for nonlinear tracking models. The SMC, also known as particle

Tadesse Ghirmai

2007-01-01

379

Distributed Gaussian particle filtering using likelihood consensus  

Microsoft Academic Search

We propose a distributed implementation of the Gaussian particle filter (GPF) for use in a wireless sensor network. Each sensor runs a local GPF that computes a global state estimate. The updating of the particle weights at each sensor uses the joint likelihood function, which is calculated in a distributed way, using only local communications, via the recently proposed likelihood

Ondrej Hlinka; Ondrej Sluciak; Franz Hlawatsch; Petar M. Djuric; Markus Rupp

2011-01-01

380

Rockburst Prediction Using Gaussian Process Machine Learning  

Microsoft Academic Search

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

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

2009-01-01

381

Coding Capacity of Mismatched Gaussian Channels.  

National Technical Information Service (NTIS)

Bounds on the coding capacity of Gaussian channels are obtained when the power constraint on the signal is mismatched to the channel noise. In the case of some feedback channels in which the noise has a Cramer-Hida representation of finite multiplicity, a...

I. W. McKeague C. R. Baker

1986-01-01

382

Automatic accent identification using Gaussian mixture models  

Microsoft Academic Search

It is well known that speaker variability caused by accent is an important factor in speech recognition. Some major accents in China are so different as to make this problem very severe. In this paper, we propose a Gaussian mixture model (GMM) based Mandarin accent identification method. In this method, a number of GMMs are trained to identify the most

Too Chen; Chao Huang; Eric Chang; Jingehan Wang

2001-01-01

383

Subspace Gaussian Mixture Models for speech recognition  

Microsoft Academic Search

This technical report contains the details of an acoustic modeling approach based on subspace adaptation of a shared Gaussian Mix- ture Model. This refers to adaptation to a particular speech state; it is not a speaker adaptation technique, although we do later in- troduce a speaker adaptation technique that it tied to this p articular framework. Our model is a

Daniel Povey; Lukas Burget; Mohit Agarwal; Pinar Akyazi; Kai Feng; Arnab Ghoshal; Ondrej Glembek; Nagendra Kumar Goel; Martin Karafiát; Ariya Rastrow; Richard C. Rose; Petr Schwarz; Samuel Thomas

2010-01-01

384

Vector quantization based on Gaussian mixture models  

Microsoft Academic Search

We model the underlying probability density function of vectors in a database as a Gaussian mixture (GM) model. The model is employed for high rate vector quantization analysis and for design of vector quantizers. It is shown that the high rate formulas accurately predict the performance of model-based quantizers. We propose a novel method for optimizing GM model parameters for

P. Hedelin; J. Skoglund

2000-01-01

385

Radon-Nikodym Derivatives of Gaussian Measures  

Microsoft Academic Search

We give simple necessary and sufficient conditions on the mean and covariance for a Gaussian measure to be equivalent to Wiener measure. This was formerly an unsolved problem [26]. An unsolved problem is to obtain the Radom-Nikodym derivative $d\\\\mu\\/d\\\

L. A. Shepp

1966-01-01

386

Adaptive Radar Detection of Extended Gaussian Targets.  

National Technical Information Service (NTIS)

We have addressed the derivation and the analysis of an adaptive decision scheme to detect possible extended targets modeled as Gaussian vectors known to belong to a given subspace; noise returns from the cells under test are modeled as independent and id...

G. Ricci L. L. Scharf

2004-01-01

387

On Manifolds in Gaussian Scale Space  

Microsoft Academic Search

In an ordinary 2D image the critical points and the isophotes through the saddle points provide sufficient information for classifying the image into distinct regions belonging to the extrema (i.e. a collection of bright and dark blobs), together with their nesting due to the saddle isophotes. For scale space images, obtained by convolution of the image with a Gaussian filter

Arjan Kuijper

2003-01-01

388

Nonlinear Bayesian estimation using Gaussian sum approximations  

Microsoft Academic Search

Knowledge of the probability density function of the state conditioned on all available measurement data provides the most complete possible description of the state, and from this density any of the common types of estimates (e.g., minimum variance or maximum a posteriori) can be determined. Except in the linear Gaussian case, it is extremely difficult to determine this density function.

D. L. Alspach; H. W. Sorenson

1972-01-01

389

Phase Space Tranformations of Gaussian Diffusions.  

National Technical Information Service (NTIS)

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

A. Brandao T. Kolsrud

1996-01-01

390

Gaussian processes for canonical correlation analysis  

Microsoft Academic Search

We consider several stochastic process methods for performing canonical correlation analysis (CCA). The first uses a Gaussian process formulation of regression in which we use the current projection of one data set as the target for the other and then repeat with the second projection as the target for adapting the parameters of the first. The second uses a method

Colin Fyfe; Gayle Leen; Pei Ling Lai

2008-01-01

391

Transitional behavior of quantum Gaussian memory channels  

SciTech Connect

We address the question of optimality of entangled input states in quantum Gaussian memory channels. For a class of such channels, which can be traced back to the memoryless setting, we state a criterion which relates the optimality of entangled inputs to the symmetry properties of the channels' action. Several examples of channel models belonging to this class are discussed.

Lupo, C. [School of Science and Technology, University of Camerino, I-62032 Camerino (Italy); Mancini, S. [School of Science and Technology, University of Camerino, I-62032 Camerino (Italy); INFN-Sezione di Perugia, I-06123 Perugia (Italy)

2010-05-15

392

Diffusion of Super-Gaussian Profiles  

ERIC Educational Resources Information Center

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

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

2007-01-01

393

Non-Gaussianity effects in petrophysical quantities  

NASA Astrophysics Data System (ADS)

It has been proved that there are many indicators (petrophysical quantities) for the estimation of petroleum reservoirs. The value of information contained in each indicator is yet to be addressed. In this work, the most famous and applicable petrophysical quantities for a reservoir, which are the gamma emission (GR), sonic transient time (DT), neutron porosity (NPHI), bulk density (RHOB), and deep induced resistivity (ILD), have been analyzed in order to characterize a reservoir. The implemented technique is the well-logging method. Based on the log-normal model defined in random multiplicative processes, the probability distribution function (PDF) for the data sets is described. The shape of the PDF depends on the parameter ?2 which determines the efficiency of non-Gaussianity. When non-Gaussianity appears, it is a sign of uncertainty and phase transition in the critical regime. The large value and scale-invariant behavior of the non-Gaussian parameter ?2 is an indication of a new phase which proves adequate for the existence of petroleum reservoirs. Our results show that one of the indicators (GR) is more non-Gaussian than the other indicators, scale wise. This means that GR is a continuously critical indicator. But by moving windows with various scales, the estimated ?2 shows that the most appropriate indicator for distinguishing the critical regime is ILD, which shows an increase at the end of the measured region of the well.

Koohi Lai, Z.; Jafari, G. R.

2013-10-01

394

A Linear Quadratic Guidance law for solid fuel, space-based interceptors  

NASA Astrophysics Data System (ADS)

The paper discusses the use of Linear Quadratic Guidance to design acceleration profiles for interceptors launched from a space platform against an accelerating threat. It is assumed that the interceptor has a solid propellant which burns continuously from ignition, but that the graining is segmented so that different levels of acceleration are available over different portions of the trajectory. Simulation results are given which show that the acceleration profiles generated, when using Augmented Pronav as a guidance law, are highly dependent on the Intercept Point Prediction error vector. The key difference between the guidance law presented in this paper and other optimal control laws is that Linear Quadratic Guidance is used in a pure regulator mode (no terminal constraint enforced) for most of the homing period. Since one is not enforcing a terminal constraint, pure regulators have not been regarded as a viable class of guidance laws in the past. However, if the homing period is lengthy it is quite advantageous to use a pure regulator for most of the homing period and enforce a terminal constraint only over the latter portion. Overall divert velocity requirements are reduced and uniform acceleration profiles are generated which make it easy to design solid fuel engines.

Schmidt, G. C.; Hardtla, J. W.

395

Creepers: Real quadratic orders with large class number  

NASA Astrophysics Data System (ADS)

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

Patterson, Roger

2007-03-01

396

Fluctuation-dissipation inequality for quadratic open systems  

NASA Astrophysics Data System (ADS)

For open systems derived from quadratic total Hamiltonians, we derive a dynamic fluctuation-dissipation (FD) inequality valid for any total initial state and without regard to the sign of the dissipation. With the added constraint that this state be factorized with the reservoir in thermal equilibrium, an uncertainty relation arises naturally from the FD inequality that can be stronger than the usual uncertainty principle in the form ??2/4. We discuss some of the properties of the uncertainty relation relevant to decoherence.

Tameshtit, Allan

2013-11-01

397

Relativistic Stellar Model Admitting a Quadratic Equation of State  

NASA Astrophysics Data System (ADS)

A class of solutions describing the interior of a static spherically symmetric compact anisotropic star is reported. The analytic solution has been obtained by utilizing the Finch and Skea [Class. Quantum Grav.6 (1989) 467] ansatz for the metric potential grr which has a clear geometric interpretation for the associated background spacetime. Based on physical grounds, appropriate bounds on the model parameters have been obtained and it has been shown that the model admits an equation of state (EOS) which is quadratic in nature.

Sharma, R.; Ratanpal, B. S.

2013-11-01

398

Nios II hardware acceleration of the epsilon quadratic sieve algorithm  

NASA Astrophysics Data System (ADS)

The quadratic sieve (QS) algorithm is one of the most powerful algorithms to factor large composite primes used to break RSA cryptographic systems. The hardware structure of the QS algorithm seems to be a good fit for FPGA acceleration. Our new ?-QS algorithm further simplifies the hardware architecture making it an even better candidate for C2H acceleration. This paper shows our design results in FPGA resource and performance when implementing very long arithmetic on the Nios microprocessor platform with C2H acceleration for different libraries (GMP, LIP, FLINT, NRMP) and QS architecture choices for factoring 32-2048 bit RSA numbers.

Meyer-Bäse, Uwe; Botella, Guillermo; Castillo, Encarnacion; García, Antonio

2010-04-01

399

Multipole-mode interface solitons in quadratic nonlinear photonic lattices  

NASA Astrophysics Data System (ADS)

We address the properties of nonlinear multipole modes supported by an interface between two distinct optical lattices imprinted in two-dimensional nonlinear quadratic media. Such multipole-mode solitons feature out of phase between neighboring lobes, which may be located in two different sides of the lattices. We analyze the impact of guiding parameters of lattices on the existence and stability of multipole-mode interface solitons in different phase mismatching conditions. Remarkably, our results show that multipole-mode interface solitons have the highly asymmetric shape and they are stable in the broad range of system parameters.

Xu, Zhiyong

2009-11-01

400

Rigorous performance bounds for quadratic and nested dynamical decoupling  

SciTech Connect

We present rigorous performance bounds for the quadratic dynamical decoupling pulse sequence which protects a qubit from general decoherence, and for its nested generalization to an arbitrary number of qubits. Our bounds apply under the assumptions of instantaneous pulses and of bounded perturbing environment and qubit-environment Hamiltonians such as those realized by baths of nuclear spins in quantum dots. We prove that if the total sequence time is fixed then the trace-norm distance between the unperturbed and protected system states can be made arbitrarily small by increasing the number of applied pulses.

Xia, Yuhou; Uhrig, Goetz S.; Lidar, Daniel A. [Department of Mathematics and Department of Physics, Haverford College, Haverford, Pennsylvania 19041 (United States); Lehrstuhl fuer Theoretische Physik I, Technische Universitaet Dortmund, Otto-Hahn Strasse 4, D-44221 Dortmund (Germany); Department of Electrical Engineering, Department of Chemistry, and Department of Physics, Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089 (United States)

2011-12-15

401

Growth of the Ideal Generated by a Quadratic Boolean Function  

Microsoft Academic Search

\\u000a We give exact formulas for the growth of the ideal A? for ? a quadratic element of the algebra of Boolean functions over the Galois field GF(2). That is, we calculate dimAk l<\\/font\\u000a>\\\\dim A_k \\\\lambda where A\\u000a \\u000a k\\u000a is the subspace of elements of degree less than or equal to k. These results clarify some of the assertions made

Jintai Ding; Timothy J. Hodges; Victoria Kruglov

2010-01-01

402

Ergodic Type Bellman Equations of First Order with Quadratic Hamiltonian  

SciTech Connect

We consider Bellman equations of ergodic type in first order. The Hamiltonian is quadratic on the first derivative of the solution. We study the structure of viscosity solutions and show that there exists a critical value among the solutions. It is proved that the critical value has the representation by the long time average of the kernel of the max-plus Schroedinger type semigroup. We also characterize the critical value in terms of an invariant density in max-plus sense, which can be understood as a counterpart of the characterization of the principal eigenvalue of the Schroedinger operator by an invariant measure.

Kaise, Hidehiro [Nagoya University, Graduate School of Information Science (Japan)], E-mail: kaise@is.nagoya-u.ac.jp; Sheu, S.-J. [Academia Sinica, Institute of Mathematics (China)], E-mail: sheusj@math.sinica.edu.tw

2009-02-15

403

Adaptive, quadratic preprocessing of document images for binarization.  

PubMed

This paper presents an adaptive algorithm for preprocessing document images prior to binarization in character recognition problems. Our method is similar in its approach to the blind adaptive equalization of binary communication channels. The adaptive filter utilizes a quadratic system model to provide edge enhancement for input images that have been corrupted by noise and other types of distortions during the scanning process. Experimental results demonstrating significant improvement in the quality of the binarized images over both direct binarization and a previously available preprocessing technique are also included. PMID:18276315

Mo, S; Mathews, J

1998-01-01

404

Quantifying non-Gaussianity for quantum information  

SciTech Connect

We address the quantification of non-Gaussianity (nG) of states and operations in continuous-variable systems and its use in quantum information. We start by illustrating in detail the properties and the relationships of two recently proposed measures of nG based on the Hilbert-Schmidt distance and the quantum relative entropy (QRE) between the state under examination and a reference Gaussian state. We then evaluate the non-Gaussianities of several families of non-Gaussian quantum states and show that the two measures have the same basic properties and also share the same qualitative behavior in most of the examples taken into account. However, we also show that they introduce a different relation of order; that is, they are not strictly monotone to each other. We exploit the nG measures for states in order to introduce a measure of nG for quantum operations, to assess Gaussification and de-Gaussification protocols, and to investigate in detail the role played by nG in entanglement-distillation protocols. Besides, we exploit the QRE-based nG measure to provide different insight on the extremality of Gaussian states for some entropic quantities such as conditional entropy, mutual information, and the Holevo bound. We also deal with parameter estimation and present a theorem connecting the QRE nG to the quantum Fisher information. Finally, since evaluation of the QRE nG measure requires the knowledge of the full density matrix, we derive some experimentally friendly lower bounds to nG for some classes of states and by considering the possibility of performing on the states only certain efficient or inefficient measurements.

Genoni, Marco G.; Paris, Matteo G. A. [Consorzio Nazionale Interuniversitario per le Scienze Fisiche della Materia, UdR Milano, I-20133 Milano (Italy); Dipartimento di Fisica, Universita degli Studi di Milano, I-20133 Milano (Italy)

2010-11-15

405

a Distributed Gaussian Discrete Variable Representation  

NASA Astrophysics Data System (ADS)

In this work a discrete variable representation (DVR) is constructed from a distributed Gaussian basis (DGB). A DGB is a finite or infinite chain of uniformly distributed Gaussians g_{n}(x) = e^{-c^2(x/d-n)^2} where n takes integer values. There are three main parts of this thesis. In the first part (Chapter III) the finite chain distributed Gaussian DVR (Finite Chain DG-DVR) is derived. In order to accomplish this, the distributed Gaussian orthogonal polynomials are introduced. The connection of these polynomials to Stieltjes-Wigert polynomials is shown. The recurrence relation for these orthogonal polynomials is derived. Tested recipes are given to calculate the quadrature points and weights and to construct the corresponding Lagrange functions which are analogs of Lagrange interpolation polynomials. The symmetries of quadrature points, weights, and Lagrange functions are derived. Limit cases ctoinfty and cto 0 are studied. In the second part (Chapter IV)the infinite chain limit DG-DVR is derived from a limit of the finite chain DG-DVR. The quadrature points and weights and the Lagrange functions are found in this limit and kinetic energy operator is constructed. It is shown that in the limit c to 0 the infinite chain DG-DVR reduces to Colbert and Miller's DVR. A discussion of ability of a distributed Gaussian basis to represent an arbitrary function is given. The results of this treatment yield a possible explanation of surprising accuracy of Colbert-Miller DVR. In the third part construction of the DG-DVR is given when one point is chosen arbitrarily. Some interesting identities and integral representations for the b _{n} and sigma_ {n} coefficients that are introduced in the second part are found.

Karabulut, Hasan

406

Quantifying non-Gaussianity for quantum information  

NASA Astrophysics Data System (ADS)

We address the quantification of non-Gaussianity (nG) of states and operations in continuous-variable systems and its use in quantum information. We start by illustrating in detail the properties and the relationships of two recently proposed measures of nG based on the Hilbert-Schmidt distance and the quantum relative entropy (QRE) between the state under examination and a reference Gaussian state. We then evaluate the non-Gaussianities of several families of non-Gaussian quantum states and show that the two measures have the same basic properties and also share the same qualitative behavior in most of the examples taken into account. However, we also show that they introduce a different relation of order; that is, they are not strictly monotone to each other. We exploit the nG measures for states in order to introduce a measure of nG for quantum operations, to assess Gaussification and de-Gaussification protocols, and to investigate in detail the role played by nG in entanglement-distillation protocols. Besides, we exploit the QRE-based nG measure to provide different insight on the extremality of Gaussian states for some entropic quantities such as conditional entropy, mutual information, and the Holevo bound. We also deal with parameter estimation and present a theorem connecting the QRE nG to the quantum Fisher information. Finally, since evaluation of the QRE nG measure requires the knowledge of the full density matrix, we derive some experimentally friendly lower bounds to nG for some classes of states and by considering the possibility of performing on the states only certain efficient or inefficient measurements.

Genoni, Marco G.; Paris, Matteo G. A.

2010-11-01

407

Radiation pressure acceleration of corrugated thin foils by Gaussian and super-Gaussian beams  

SciTech Connect

Rayleigh-Taylor instability of radiation pressure accelerated ultrathin foils by laser having Gaussian and super-Gaussian intensity distribution is investigated using a single fluid code. The foil is allowed to have ring shaped surface ripples. The radiation pressure force on such a foil is non-uniform with finite transverse component F{sub r}; F{sub r} varies periodically with r. Subsequently, the ripple grows as the foil moves ahead along z. With a Gaussian beam, the foil acquires an overall curvature due to non-uniformity in radiation pressure and gets thinner. In the process, the ripple perturbation is considerably washed off. With super-Gaussian beam, the ripple is found to be more strongly washed out. In order to avoid transmission of the laser through the thinning foil, a criterion on the foil thickness is obtained.

Adusumilli, K.; Goyal, D.; Tripathi, V. K. [Department of Physics, Indian Institute of Technology - Delhi, New Delhi - 110016 (India)

2012-01-15

408

Evaluation of a photovoltaic energy mechatronics system with a built-in quadratic maximum power point tracking algorithm  

SciTech Connect

The historically high cost of crude oil price is stimulating research into solar (green) energy as an alternative energy source. In general, applications with large solar energy output require a maximum power point tracking (MPPT) algorithm to optimize the power generated by the photovoltaic effect. This work aims to provide a stand-alone solution for solar energy applications by integrating a DC/DC buck converter to a newly developed quadratic MPPT algorithm along with its appropriate software and hardware. The quadratic MPPT method utilizes three previously used duty cycles with their corresponding power outputs. It approaches the maximum value by using a second order polynomial formula, which converges faster than the existing MPPT algorithm. The hardware implementation takes advantage of the real-time controller system from National Instruments, USA. Experimental results have shown that the proposed solar mechatronics system can correctly and effectively track the maximum power point without any difficulties. (author)

Chao, R.M.; Ko, S.H.; Lin, I.H. [Department of Systems and Naval Mechatronics Engineering, National Cheng Kung University, Tainan, Taiwan 701 (China); Pai, F.S. [Department of Electronic Engineering, National University of Tainan (China); Chang, C.C. [Department of Environment and Energy, National University of Tainan (China)

2009-12-15

409

Transmitting multiple correlated gaussian sources over a Gaussian MAC using delay-free mappings  

Microsoft Academic Search

In this paper, we study the problem of communicating multiple correlated Gaussian memoryless sources over a Gaussian Multiple Access Channel (GMAC). We focus on distributed delay-free, low complexity, joint source-channel coding (JSCC) solutions to the problem. Theoretical performance bounds are derived and linear and nonlinear JSCC schemes are evaluated. The main contribution is a nonlinear hybrid discrete-analog mapping based on

Pål Anders Floor; Anna N. Kim; Tor A. Ramstad; Ilangko Balasingham; Niklas Wernersson; Mikael Skoglund

2011-01-01

410

The heuristics of cepstrum analysis of a stationary complex echoed Gaussian signal in stationary Gaussian noise  

Microsoft Academic Search

We consider cepstrum analysis of a model consisting of a detector receiving a Gaussian single complex echoed signal in Gaussian noise of the formx(t) + beta[cos theta x(t- tau) + sin theta x_{H}(t- tau)] + n(t),wherebetais the echo amplitude,thetaan arbitrary constant, andx_{H}(t - tau)is the Hilbert transform ofx(t - tau). We assume no a priori knowledge of the spectra of

B. Bogert; J. Ossanna

1966-01-01

411

Hybrid model based on SVM with Gaussian loss function and adaptive Gaussian PSO  

Microsoft Academic Search

In view of the bad capability of the standard support vector machine (SVM) in field of white noise of input series, a new v-SVM with Gaussian loss function which is call g-SVM is put forward to handle white noises. To seek the unknown parameters of g-SVM, an adaptive normal Gaussian particle swarm optimization (ANPSO) is also proposed. The results of

Qi Wu; Shuyan Wu; Jing Liu

2010-01-01

412

MLP and RBFN for Detecting White Gaussian Signals in White Gaussian Interference  

Microsoft Academic Search

This paper deals with the application of Neural Networks to binary detection based on multiple observations. The problem of\\u000a detecting a desired signal in Additive-White-Gaussian-Noise is considered, assuming that the desired signal samples are also\\u000a gaussian, independent and identically distributed random variables. The test statistic is then the squared magnitude of the\\u000a observation vector and the optimum boundary is a

Pilar Jarabo Amores; Roberto Gil-pita; Manuel Rosa-zurera; Francisco López-ferreras

2003-01-01

413

Handling non-Gaussianity of state and observations in Ensemble Kalman Filters with refined Gaussian anamorphosis  

NASA Astrophysics Data System (ADS)

Sequential data assimilation schemes based on the Ensemble Kalman Filter are optimal in the sense of yielding the best linear unbiased estimate (BLUE) and the maximum a posteriori estimate (MAP) only if the involved error distributions are Gaussian. Nevertheless non-Gaussian error distributions are commonly encountered in geoscience. Gaussian anamorphosis is one method to cope with non-Gaussianity in ensemble filters. It transforms the variables involved such that the distributions of the resulting variables are Gaussian and usually involves a back transformation after the filter has been applied. If only state variables are transformed, the inverse of the anamorphosis function applied to the posterior ensemble is sufficient as a back transformation and if only observations are transformed a back transformation might not be needed at all. If, however, state variables and observations are transformed, the posterior ensemble has to be corrected to yield the correct distribution of the original state variables. Otherwise a systematic error dependent on the derivative of the anamorphosis function is introduced. We demonstrate this effect with illustrative examples based on distributions on the bounded interval [0, 1] and a simplified case of assimilating albedo observations into a land surface model. In both cases direct observations are used and both, state variables and observations, are transformed to have Gaussian distributions on [-?, ?]. The posterior ensembles are compared to the result of a Bayesian update of the bounded distributions for the toy examples and to a synthetically generated truth for the albedo example.

Geppert, Gernot; Loew, Alexander; Ament, Felix

2013-04-01

414

Total decoupling of general quadratic pencils, Part I: Theory  

NASA Astrophysics Data System (ADS)

The notion of quadratic pencils, ?M+?C+K, where M, C, and K are n×n real matrices with or without some additional properties such as symmetry or positive definiteness, plays critical roles in many important applications. It has been long desirable, yet with very limited success, to reduce a complicated high-degree-of-freedom system to some simpler low-degree-of-freedom subsystems. Recently, Garvey, Friswell and Prells proposed a promising approach by which, under some mild assumptions, a general quadratic pencils can be converted by real-valued isospectral transformations into a totally decoupled system. This approach, if numerically feasible, would reduce the original n-degree-of-freedom second-order system to n totally independent single-degree-of-freedom second-order subsystems. Such a claim would be a striking breakthrough in the common knowledge that generally no three matrices M, C, and K can be diagonalized simultaneously. This paper intends to serve three purposes: to clarify some of the ambiguities in the original proposition, to simplify some of the computational details and, most importantly, to complete the theory of existence by matrix polynomial factorization tactics.

Chu, Moody T.; Del Buono, Nicoletta

2008-01-01

415

Learning quadratic receptive fields from neural responses to natural stimuli.  

PubMed

Models of neural responses to stimuli with complex spatiotemporal correlation structure often assume that neurons are selective for only a small number of linear projections of a potentially high-dimensional input. In this review, we explore recent modeling approaches where the neural response depends on the quadratic form of the input rather than on its linear projection, that is, the neuron is sensitive to the local covariance structure of the signal preceding the spike. To infer this quadratic dependence in the presence of arbitrary (e.g., naturalistic) stimulus distribution, we review several inference methods, focusing in particular on two information theory-based approaches (maximization of stimulus energy and of noise entropy) and two likelihood-based approaches (Bayesian spike-triggered covariance and extensions of generalized linear models). We analyze the formal relationship between the likelihood-based and information-based approaches to demonstrate how they lead to consistent inference. We demonstrate the practical feasibility of these procedures by using model neurons responding to a flickering variance stimulus. PMID:23607557

Rajan, Kanaka; Marre, Olivier; Tka?ik, Gašper

2013-04-22

416

Half-quadratic based Iterative Minimization for Robust Sparse Representation.  

PubMed

Robust sparse representation has shown significant potential in solving challenging problems in computer vision such as biometrics and visual surveillance. Although several robust sparse models have been proposed and promising results have been obtained, they are either for error correction or for error detection, and learning a general framework that systematically unifies these two aspects and explore their relation is still an open problem. In this paper, we develop a half-quadratic (HQ) framework to solve the robust sparse representation problem. By defining different kinds of half-quadratic functions, the proposed HQ framework is applicable to performing both error correction and error detection. More specifically, by using the additive form of HQ, we propose an L1-regularized error correction method by iteratively recovering corrupted data from errors incurred by noises and outliers; by using the multiplicative form of HQ, we propose an L1-regularized error detection method by learning from uncorrupted data iteratively. We also show that the L1-regularization solved by soft-thresholding function has a dual relationship to Huber M-estimator, which theoretically guarantees the performance of robust sparse representation in terms of M-estimation. Experiments on robust face recognition under severe occlusion and corruption validate our framework and findings. PMID:23712994

He, Ran; Zheng, Wei-Shi; Tan, Tieniu; Sun, Zhenan

2013-05-21

417

Single-molecule orientation measurements with a quadrated pupil.  

PubMed

This Letter presents a means of measuring the dipole orientation of a fluorescent, orientationally fixed single molecule, which uses a specially designed phase mask, termed a "quadrated pupil," conjugate to the back focal plane of a conventional wide-field microscope. The method leverages the spatial anisotropy of the far-field emission pattern of a dipole emitter and makes this anisotropy amenable to quantitative analysis at the image plane. In comparison to older image-fitting techniques that infer orientation by matching simulations to defocused or excessively magnified images, the quadrated pupil approach is more robust to minor modeling discrepancies and optical aberrations. Precision of 1°-5° is achieved in proof-of-concept experiments for both azimuthal (?) and polar (?) angles without defocusing. Since the phase mask is implemented on a liquid-crystal spatial light modulator that may be deactivated without any mechanical perturbation of the sample or imaging system, the technique may be readily integrated into clear aperture imaging studies. PMID:23632538

Backer, Adam S; Backlund, Mikael P; Lew, Matthew D; Moerner, W E

2013-05-01

418

Implementation of Multivariate Quadratic Quasigroup for Wireless Sensor Network  

NASA Astrophysics Data System (ADS)

Wireless sensor networks (WSN) consists of sensor nodes with limited energy, processing, communication and memory. Security in WSN is becoming critical with the emergence of applications that require mechanisms for authenticity, integrity and confidentiality. Due to resource constraints in WSN, matching public key cryptosystems (PKC) for these networks is an open research problem. Recently a new PKC based on quasigroups multivariate quadratic. Experiments performed show that MQQ performed in less time than existing major PKC, so that some articles claim that has MQQ speed of a typical symmetric block cipher. Considering features promising to take a new path in the difficult task of providing wireless sensor networks in public key cryptosystems. This paper implements in nesC a new class of public key algorithm called Multivariate Quadratic Quasigroup. This implementation focuses on modules for encryption and decryption of 160-bit MQQ, the modules have been implemented on platforms TelosB and MICAz. We measured execution time and space occupied in the ROM and RAM of the sensors.

Maia, Ricardo José Menezes; Barreto, Paulo Sérgio Licciardi Messeder; de Oliveira, Bruno Trevizan

419

Electric current quadratic in an applied electric field  

NASA Astrophysics Data System (ADS)

The theory of the photogalvanic effect in a low frequency electric field is developed. We complete the semiclassical theory of the effect in bulk samples lacking inversion symmetry, taking into account contributions from the asymmetry of scattering, the shift current, and the effect of Berry's phase. We consider the effect in such samples both in the presence and absence of a constant magnetic field. It is found that by experimentally measuring this effect, that Berry's curvature and the average shift of the center of mass of an electron during a scattering event can be extracted. We also investigate the magnetic field dependence of the part of the electrical current which is quadratic in voltage in mesoscopic conductors. We find that the part of the current which is quadratic in bias voltage, and linear in an applied magnetic field can be related to the effective electron-electron interaction strength. We also find that in the case when the magnetic field is oriented parallel to the plane of a two dimensional sample, that the spin-orbit scattering rate can be measured.

Deyo, Eric

420

Adaptive filtering for non-Gaussian stable processes  

Microsoft Academic Search

A large class of physical phenomena observed in practice exhibit non-Gaussian behavior. In the letter ?-stable distributions, which have heavier tails than Gaussian distributions, are considered to model non-Gaussian signals. Adaptive signal processing in the presence of such a noise is a requirement of many practical problems. Since direct application of commonly used adaptation techniques fail in these applications, new

Orhan Arikan; A. Enis Cetin; Engin Erzin

1994-01-01

421

Efficient representation of purity-preserving Gaussian quantum filters  

NASA Astrophysics Data System (ADS)

We discuss representation of single-mode purity-preserving conditional Gaussian quantum operations by complex symplectic matrices. This formalism allows us to efficiently determine the result of concatenation of several probabilistic purity-preserving Gaussian operations. We present several examples of application of this formalism and discuss canonical forms of the considered single-mode conditional Gaussian operations.

Fiurášek, Jaromír

2013-05-01

422

Local Gaussian operations can enhance continuous-variable entanglement distillation  

Microsoft Academic Search

Entanglement distillation is a fundamental building block in long-distance quantum communication. Though known to be useless on their own for distilling Gaussian entangled states, local Gaussian operations may still help to improve non-Gaussian entanglement distillation schemes. Here we show that by applying local squeezing operations, both the performance and the efficiency of existing distillation protocols can be enhanced. We derive

ShengLi Zhang; Peter van Loock

2011-01-01

423

Unsupervised spoken keyword spotting via segmental DTW on Gaussian posteriorgrams  

Microsoft Academic Search

In this paper, we present an unsupervised learning framework to address the problem of detecting spoken keywords. Without any transcription information, a Gaussian Mixture Model is trained to label speech frames with a Gaussian posteriorgram. Given one or more spoken examples of a keyword, we use segmental dynamic time warping to compare the Gaussian posteriorgrams between keyword samples and test

Yaodong Zhang; James R. Glass

2009-01-01

424

A "Gaussian" for diffusion on the sphere  

NASA Astrophysics Data System (ADS)

We present an analytical closed form expression, which gives a good approximate propagator for diffusion on the sphere. Our formula is the spherical counterpart of the Gaussian propagator for diffusion on the plane. While the analytical formula is derived using saddle point methods for short times, it works well even for intermediate times. Our formula goes beyond conventional "short time heat kernel expansions" in that it is nonperturbative in the spatial coordinate, a feature that is ideal for studying large deviations. Our work suggests a new and efficient algorithm for numerical integration of the diffusion equation on a sphere. We perform Monte Carlo simulations to compare the numerical efficiency of the new algorithm with the older Gaussian one.

Ghosh, Abhijit; Samuel, Joseph; Sinha, Supurna

2012-05-01

425

Soft ellipsoid model for Gaussian polymer chains  

NASA Astrophysics Data System (ADS)

A soft ellipsoid model for Gaussian polymer chains is studied, following an idea proposed by Murat and Kremer [J. Chem. Phys. 108, 4340 (1998)]. In this model chain molecules are mapped onto ellipsoids with certain shapes, and to each shape a monomer density is assigned. In the first part of the work, the probabilities for the shapes and the associated monomer densities are studied in detail for Gaussian chains. Both quantities are expressed in terms of simple approximate formulas. The free energy of a system composed of many ellipsoids is given by an intramolecular part accounting for the internal degrees of freedom and an intermolecular part following from pair interactions between the monomer densities. Structural and kinetic properties of both homogeneous systems and binary mixtures are subsequently studied by Monte Carlo simulations. It is shown that the model provides a powerful phenomenological approach for investigating polymeric systems on semimacroscopic time and length scales.

Eurich, Frank; Maass, Philipp

2001-05-01

426

Geometrical approach to gaussian beam propagation.  

PubMed

The curvature of the wavefront and the spot size of a propagating Gaussian beam may be determined from simple geometrical transformations of the lateral foci. The analysis starts from the construction of the lateral foci in the case of a spherical Fabry-Perot. Then the cases of Gaussian beam propagation through media with different refractive indices, lenses, and simple optical systems are treated. Constructions show how propagation in the image space is readily determined in each case. This analysis is the generalization of the technique outlined by Deschamps and Mast. The geometrical constructions developed for simple cases are applied to the design of some special cases of interest in laser optics: cavities by a lens, laser zoom telescope, and ring cavity. PMID:20057839

Laures, P

1967-04-01

427

Resolution of unity for fermionic Gaussian operators  

NASA Astrophysics Data System (ADS)

The fermionic Gaussian operator basis provides a representation for treating strongly correlated fermion systems, as well as playing an important role in random matrix theory. We prove that a resolution of unity exists for any even distribution of eigenvalues over Hermitian fermionic Gaussian operators in the nonstandard symmetry classes. This has some important consequences. It demonstrates a useful technique for constructing fundamental mathematical identities in an exponentially complex Hilbert space. It also shows that, to obtain nontrivial results for random matrix canonical ensembles in the nonstandard symmetry classes, it is necessary to consider ensembles that are not even functions of the eigenvalues. We show that the same restriction does not apply to the standard Wigner-Dyson symmetry classes of random matrices.

Rosales-Zárate, Laura E. C.; Drummond, P. D.

2013-07-01

428

Integrated structural control design of large space structures  

SciTech Connect

Active control of structures has been under intensive development for the last ten years. Reference 2 reviews much of the identification and control technology for structural control developed during this time. The technology was initially focused on space structure and weapon applications; however, recently the technology is also being directed toward applications in manufacturing and transportation. Much of this technology focused on multiple-input/multiple-output (MIMO) identification and control methodology because many of the applications require a coordinated control involving multiple disturbances and control objectives where multiple actuators and sensors are necessary for high performance. There have been many optimal robust control methods developed for the design of MIMO robust control laws; however, there appears to be a significant gap between the theoretical development and experimental evaluation of control and identification methods to address structural control applications. Many methods have been developed for MIMO identification and control of structures, such as the Eigensystem Realization Algorithm (ERA), Q-Markov Covariance Equivalent Realization (Q-Markov COVER) for identification; and, Linear Quadratic Gaussian (LQG), Frequency Weighted LQG and H-/ii-synthesis methods for control. Upon implementation, many of the identification and control methods have shown limitations such as the excitation of unmodelled dynamics and sensitivity to system parameter variations. As a result, research on methods which address these problems have been conducted.

Allen, J.J.; Lauffer, J.P.

1995-01-01

429

Local Gaussian operations can enhance continuous-variable entanglement distillation  

SciTech Connect

Entanglement distillation is a fundamental building block in long-distance quantum communication. Though known to be useless on their own for distilling Gaussian entangled states, local Gaussian operations may still help to improve non-Gaussian entanglement distillation schemes. Here we show that by applying local squeezing operations both the performance and the efficiency of existing distillation protocols can be enhanced. We find that such an enhancement through local Gaussian unitaries can be obtained even when the initially shared Gaussian entangled states are mixed, as, for instance, after their distribution through a lossy-fiber communication channel.

Zhang Shengli; Loock, Peter van [Optical Quantum Information Theory Group, Max Planck Institute for the Science of Light, Guenther-Scharowsky-Strasse 1/Bau 26, DE-91058 Erlangen (Germany); Institute of Theoretical Physics I, Universitaet Erlangen-Nuernberg, Staudtstrasse 7/B2, DE-91058 Erlangen (Germany)

2011-12-15

430

Migration by the Kirchhoff, slant stack, and Gaussian beam methods  

SciTech Connect

Gaussian beam migration offers features that are unmatched by any other single depth migration method. Unfortunately, computer algorithms for Gaussian beam migration are more complicated and difficult to understand that those for most other methods. One way to simplify Gaussian beam migration is to understand how it is related to other methods that may be more familiar. In particular, Gaussian beam migration is similar to Kirchhoff integral migration. It is also similar to the phase-shift (or slant stack) migration method. In a sense, the Gaussian beam approach to depth migration is to combine the best of these more familiar methods to obtain an efficient, robust, and flexible method for seismic imaging.

Hale, D.

1992-08-01

431

Migration by the Kirchhoff, slant stack, and Gaussian beam methods  

SciTech Connect

Gaussian beam migration offers features that are unmatched by any other single depth migration method. Unfortunately, computer algorithms for Gaussian beam migration are more complicated and difficult to understand that those for most other methods. One way to simplify Gaussian beam migration is to understand how it is related to other methods that may be more familiar. In particular, Gaussian beam migration is similar to Kirchhoff integral migration. It is also similar to the phase-shift (or slant stack) migration method. In a sense, the Gaussian beam approach to depth migration is to combine the best of these more familiar methods to obtain an efficient, robust, and flexible method for seismic imaging.

Hale, D.

1992-01-01

432

On Gaussian Marginals of Uniformly Convex Bodies  

Microsoft Academic Search

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

Emanuel Milman

2009-01-01

433

The Gaussian Multiple Access WireTap  

Microsoft Academic Search

We consider the Gaussian Multiple Access Wire-Tap Channel (GMAC-WT). In this scenario, multiple users communicate with an intended receiver in the presence of an intelligent and informed wire-tapper who receives a degraded version of the signal at the receiver. We define suitable security measures for this multi-access environment. Using codebooks generated randomly according to a Gaus- sian distribution, achievable secrecy

Aylin Yener

434

GaPP: Gaussian Processes in Python  

NASA Astrophysics Data System (ADS)

The algorithm Gaussian processes can reconstruct a function from a sample of data without assuming a parameterization of the function. The GaPP code can be used on any dataset to reconstruct a function. It handles individual error bars on the data and can be used to determine the derivatives of the reconstructed function. The data sample can consist of observations of the function and of its first derivative.

Seikel, Marina; Clarkson, Chris; Smith, Mathew

2013-03-01

435

Computational aspects of Gaussian beam migration  

SciTech Connect

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

Hale, D.

1992-01-01

436

Computational aspects of Gaussian beam migration  

SciTech Connect

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

Hale, D.

1992-08-01

437

Shell model on a random Gaussian basis  

SciTech Connect

Pauli-projected random Gaussians are used as a representation to solve the shell model equations. The elements of the representation are chosen by a variational procedure. This scheme is particularly suited to describe cluster formation and cluster decay in nuclei. It overcomes the basis-size problem of the ordinary shell model and the technical difficulties of the cluster-configuration shell model. The model reproduces the [alpha]-decay width of [sup 212]Po satisfactorily.

Varga, K. (Institute of Nuclear Research of the Hungarian Academy of Sciences (MTA ATOMKI), Debrecen, Hungary and RIKEN, Hirosawa, Wako, Saitama 351-01 (Japan)); Liotta, R.J. (Royal Institute of Technology, S-10405 Stockholm (Sweden))

1994-09-01

438

Talbot effect in Gaussian optical systems  

SciTech Connect

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

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

2001-11-30

439

Active curve axis Gaussian mixture models  

Microsoft Academic Search

Gaussian Mixture Models (GMM) have been broadly applied for the fitting of probability density function. However,due to the intrinsic linearity of GMM,usually many components are needed to appropriately fit the data distribution,when there are curve manifolds in the data cloud. In order to solve this problem and represent data with curve manifolds better,in this paper we propose a new nonlinear

Baibo Zhang; Changshui Zhang; Xing Yi

2005-01-01

440

Fracture prediction using Gaussian curvature analysis  

SciTech Connect

Gaussian curvature analysis (GCA) is a technique for identifying those portions of a geological structure that, on the basis of their geometrical attributes, are likely to be more fractured than surrounding regions. As simple paper folding experiments show, a layer which does not stretch or contract can be folded into a huge variety of shapes but these do not include those with double curvature, such as domes or saddles. The occurrence of geometries of the latter type, which have non-zero Gaussian curvature values, implies the presence of folding-related strains which could be expressed as fracturing. The new method involves the computation and display of Gaussian curvature values across a mapped structure, and serves to highlight those parts which are more likely to show a greater intensity of fracturing. Current developments of the GCA method concentrate on the quantification of local strains within a folded layer. A theoretical model of three-dimensional buckling is presented which allows the calculation of strain magnitudes from principal curvature values. Several examples of GCA will be discussed, including applications to structures associated with salt diapirs.

Lisle, R.J.; Robinson, J.M. (Univ. of Wales, Cardiff (United Kingdom))

1996-01-01

441

Annular Gaussian beams in turbulent media  

NASA Astrophysics Data System (ADS)

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

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

2004-01-01

442

Integrability of Quadratic Non-autonomous Quantum Linear Systems  

NASA Astrophysics Data System (ADS)

The Quantum Harmonic Oscillator is one of the most important models in Quantum Mechanics. Analogous to the classical mass vibrating back and forth on a spring, the quantum oscillator system has attracted substantial attention over the years because of its importance in many advanced and difficult quantum problems. This dissertation deals with solving generalized models of the time-dependent Schrodinger equation which are called generalized quantum harmonic oscillators, and these are characterized by an arbitrary quadratic Hamiltonian of linear momentum and position operators. The primary challenge in this work is that most quantum models with timedependence are not solvable explicitly, yet this challenge became the driving motivation for this work. In this dissertation, the methods used to solve the time-dependent Schrodinger equation are the fundamental singularity (or Green's function) and the Fourier (eigenfunction expansion) methods. Certain Riccati- and Ermakov-type systems arise, and these systems are highlighted and investigated. The overall aims of this dissertation are to show that quadratic Hamiltonian systems are completely integrable systems, and to provide explicit approaches to solving the time-dependent Schr¨odinger equation governed by an arbitrary quadratic Hamiltonian operator. The methods and results established in the dissertation are not yet well recognized in the literature, yet hold for high promise for further future research. Finally, the most recent results in the dissertation correspond to the harmonic oscillator group and its symmetries. A simple derivation of the maximum kinematical invariance groups of the free particle and quantum harmonic oscillator is constructed from the view point of the Riccati- and Ermakov-type systems, which shows an alternative to the traditional Lie Algebra approach. To conclude, a missing class of solutions of the time-dependent Schrodinger equation for the simple harmonic oscillator in one dimension is constructed. Probability distributions of the particle linear position and momentum, are emphasized with Mathematica animations. The eigenfunctions qualitatively differ from the traditional standing waves of the one-dimensional Schrodinger equation. The physical relevance of these dynamic states is still questionable, and in order to investigate their physical meaning, animations could also be created for the squeezed coherent states. This will be addressed in future work.

Lopez, Raquel

443

Rays of Small Integer Solutions of Homogeneous Ternary Quadratic Equations  

NASA Astrophysics Data System (ADS)

We have dealt with the general ternary quadratic equation: ax2 + by^ {2} + cz2 + dxy + exz + fyz = 0 with integer coefficients. After giving a matrix-reduction formula for a quadratic equation in any number of variables, of which the reduction of the above ternary equation is an easy consequence, we have devoted our attention to the reduced equation: ax^ {2} + by2 + cz^{2 } = 0. We have devised an algorithm for reducing Dirichlet's possibly larger solutions to this prescribed range of Holzer's. Then we have generalized Holzer's theorem to the case of the ternary equation: ax^{2 } + by2 + cz2 + dxy + exz + fyz = 0, giving in this context a new range called the CM-range, of which the Holzer's range is a particular case when d = e = f = 0. We have described an algorithm for getting a solution of the general ternary within this CM-range. After that we have devised an algorithm for getting all the solutions of the Legendre's equation ax 2 + by2 + cz^ {2} = 0 within the Holzer's range--and have shown that if we regard this Legendre's equation as a double cone, these solutions within the Holzer's range lie along some definite rays, here called the CM-rays, which are completely determined by the prime factors of the coefficients a, b and c. After giving an algorithm for detecting these CM-rays of the reduced equation: ax^2 + by^2 + cz^2 = 0, we have shown how one can produce some similar rays of solutions of the above general ternary quadratic equation: ax2 + by2 + cz2 + dxy + exz + fyz = 0. Note that apart from the method of exhausting all the possibilities, so far there has been no precisely stated algorithm to find the minimum solutions of the above ternary equations. Towards the end, observing in the context of our main result an inequality involving two functions, namely C and PCM from doubz_sp{*} {3} to doubz_+, and simultaneously presenting some tables of these positive CM-rays or PCM-rays lying in the positive octant, we have concluded this work with a number of hints for some possible future investigations. (Abstract shortened with permission of author.).

Mishra, Sudhakara

1991-02-01

444

Design and optimization of photo bioreactor for O2 regulation and control by system dynamics and computer simulation.  

PubMed

In this paper, a valid kinetic model of photo bioreactor (PBR) used for highly-effective cultivation of blue algae, Spirulina platensis, was developed for fully describing the dynamic characteristics of O(2) concentration, then a closed-loop PBR with Linear-Quadratic Gaussian (LQG) servo controller was established and optimized via digital simulation and dynamic response optimization, and the effectiveness of the closed-loop PBR was further tested and accredited by real-time simulation. The result showed that the closed-loop PBR could regulate and control the O(2) concentration in its gas phase according to the reference with desired dynamic response performance, hence microalgae with unique characteristic could be selected as a powerful tool for O(2) regulation and control whenever O(2) concentration in Bioregenerative Life Support System (BLSS) deviates from the nominal level in emergencies, and greatly enhance safety and reliability of BLSS on space and ground missions. PMID:22153599

Hu, Dawei; Li, Ming; Zhou, Rui; Sun, Yi

2011-11-22

445

Quadratic Forms for the Fermionic Unitary Gas Model  

NASA Astrophysics Data System (ADS)

We consider a quantum system in dimension three composed by a group of N identical fermions, with mass 1/2, interacting via zero-range interaction with a group of M identical fermions of a different type, with mass m/2. Exploiting a renormalization procedure, we construct the corresponding quadratic form and define the so-called Skornyakov-Ter-Martirosyan extension H?, which is the natural candidate as a possible Hamiltonian of the system. It is shown that if the form is unbounded from below then H? is not a self-adjoint and bounded from below operator, and this in particular suggests that the so-called Thomas effect could occur. In the special case N = 2, M = 1 we prove that this is in fact the case when a suitable condition on the parameter m is satisfied.

Finco, Domenico; Teta, Alessandro

2012-04-01

446

Kaluza-Klein reduction of a quadratic curvature model  

NASA Astrophysics Data System (ADS)

Palatini variational principle is implemented on a five dimensional quadratic curvature gravity model, rendering two sets of equations, which can be interpreted as the field equations and the stress-energy tensor. Unification of gravity with electromagnetism and the scalar dilaton field is achieved through the Kaluza-Klein dimensional reduction mechanism. The reduced curvature invariant, field equations and the stress-energy tensor are obtained in the actual four dimensional spacetime. The structure of the interactions among the constituent fields is exhibited in detail. It is shown that the Lorentz force density naturally emerges from the reduced field equations and the equations of the standard Kaluza-Klein theory are demonstrated to be intrinsically contained in this model.

Ba?kal, Sibel; Kuyrukcu, Halil

2013-02-01

447

Constrained multiple indicator kriging using sequential quadratic programming  

NASA Astrophysics Data System (ADS)

Multiple indicator kriging (MIK) is a nonparametric method used to estimate conditional cumulative distribution functions (CCDF). Indicator estimates produced by MIK may not satisfy the order relations of a valid CCDF which is ordered and bounded between 0 and 1. In this paper a new method has been presented that guarantees the order relations of the cumulative distribution functions estimated by multiple indicator kriging. The method is based on minimizing the sum of kriging variances for each cutoff under unbiasedness and order relations constraints and solving constrained indicator kriging system by sequential quadratic programming. A computer code is written in the Matlab environment to implement the developed algorithm and the method is applied to the thickness data.

Soltani-Mohammadi, Saeed; Erhan Tercan, A.

2012-11-01

448

Repopulation Kinetics and the Linear-Quadratic Model  

NASA Astrophysics Data System (ADS)

The standard Linear-Quadratic (LQ) survival model for radiotherapy is used to investigate different schedules of radiation treatment planning for advanced head and neck cancer. We explore how these treament protocols may be affected by different tumour repopulation kinetics between treatments. The laws for tumour cell repopulation include the logistic and Gompertz models and this extends the work of Wheldon et al. [1], which was concerned with the case of exponential repopulation between treatments. Treatment schedules investigated include standarized and accelerated fractionation. Calculations based on the present work show, that even with growth laws scaled to ensure that the repopulation kinetics for advanced head and neck cancer are comparable, considerable variation in the survival fraction to orders of magnitude emerged. Calculations show that application of the Gompertz model results in a significantly poorer prognosis for tumour eradication. Gaps in treatment also highlight the differences in the LQ model with the effect of repopulation kinetics included.

O'Rourke, S. F. C.; McAneney, H.; Starrett, C.; O'Sullivan, J. M.

2009-08-01

449

Consultant-Guided Search Algorithms for the Quadratic Assignment Problem  

NASA Astrophysics Data System (ADS)

Consultant-Guided Search (CGS) is a recent swarm intelligence metaheuristic for combinatorial optimization problems, inspired by the way real people make decisions based on advice received from consultants. Until now, CGS has been successfully applied to the Traveling Salesman Problem. Because a good metaheuristic should be able to tackle efficiently a large variety of problems, it is important to see how CGS behaves when applied to other classes of problems. In this paper, we propose an algorithm for the Quadratic Assignment Problem (QAP), which hybridizes CGS with a local search procedure. Our experimental results show that CGS is able to compete in terms of solution quality with one of the best Ant Colony Optimization algorithms, the MAX-MIN Ant System.

Iordache, Serban

450

Impact of a global quadratic potential on galactic rotation curves.  

PubMed

We present a conformal gravity fit to the 20 largest of a sample of 110 spiral galaxies. We identify the presence of a universal quadratic potential V(?)(r)=-?c²r²/2 with ?=9.54×10??? cm?² induced by cosmic inhomogeneities. When V(?)(r) is taken in conjunction with both a universal linear potential V(??)(r)=??c²r/2 with ??=3.06×10?³? cm?¹ generated by the homogeneous cosmic background and the contribution generated by the local luminous matter in galaxies, the theory then accounts for the rotation curve systematics observed in the entire 110 galaxies, without the need for any dark matter whatsoever. Our study suggests that using dark matter may be nothing more than an attempt to describe global effects in purely local galactic terms. With V(?)(r) being negative, galaxies can only support bound orbits up to distances of order ??/?=100kpc, with global physics imposing a limit on the size of galaxies. PMID:21517292

Mannheim, Philip D; O'Brien, James G

2011-03-23

451

On quadratic stochastic processes and related differential equations  

NASA Astrophysics Data System (ADS)

It is known that the theory of Markov process is a rapidly developing field with numerous applications to many branches of mathematics and physics, biology and so on. But there are some physical models which cannot be described by such processes. One of such models is related to population genetics. These processes are called quadratic stochastic processes (q.s.p.). In this theory it is important to construct nontrivial examples of such processes. In the present paper we are going to provide a construction of q.s.p. by means of two given processes. We should stress that such a construction allows us to produce lots of nontrivial examples of q.s.o. We also associate to given q.s.p. two kind of processes. Note that one of such processes is Markov. It is proved that such kind of processes uniquely define q.s.p. Moreover, we also derive some differential equations for q.s.p.

Mukhamedov, Farrukh; Akma Supar, Nurul; Hee, Pah Chin

2013-04-01

452

Half-optical-cycle damped solitons in quadratic nonlinear media  

NASA Astrophysics Data System (ADS)

In this paper, Using a classical model of the radiation-matter interaction, we show that the propagation of (1+1) dimensional few-optical-cycle pulses in quadratic nonlinear media, taking moderate absorption into account, can be described by the Korteweg-de Vries-Burgers’ (KdVB) equation without using the slowly varying envelope approximation. To fulfill this purpose we use the reductive perturbation method and consider the long-wave approximation, assuming that the characteristic frequency of the pulse is much lower than the resonance frequency of the atoms. We also study both analytical and numerical solution of the KdVB equation describing damped few-optical-cycle soliton propagation.

Kimiaee Asadi, Faezeh; Shokri, Babak; Leblond, Hervé

2013-05-01

453

Lensless imaging by entangled photons from quadratic nonlinear photonic crystals  

NASA Astrophysics Data System (ADS)

Lenses play a key role in quantum imaging but inevitably constrain the spatial resolution and working wavelength. In this work we develop and demonstrate a lensless quantum ghost imaging by engineering quadratic nonlinear photonic crystals. With a transverse parabolic domain modulation introduced into the lithium tantalate crystal, the entangled photon pairs generated from parametric down-conversion will self-focus. Therefore we can dispense with additional lenses to construct imaging in a nonlocal way. The lensless imaging is found to follow a specific imaging formula where the effective focal length is determined by the domain modulation and pump wavelength. Additionally, two nonlocal images can be retrieved when the entangled photon pair is generated under two concurrent noncollinear phase-matching geometries. Our work provides a principle and method to realize lensless ghost imaging, which may be extended to other wavelengths and stimulate new types of practical quantum technologies.

Xu, P.; Leng, H. Y.; Zhu, Z. H.; Bai, Y. F.; Jin, H.; Gong, Y. X.; Yu, X. Q.; Xie, Z. D.; Mu, S. Y.; Zhu, S. N.

2012-07-01

454

The correlation properties of gamma and other non-Gaussian processes generated by memoryless nonlinear transformation  

NASA Astrophysics Data System (ADS)

The autocorrelation function (ACF) of a non-Gaussian random process, obtained by the memoryless nonlinear transformation of a Gaussian process with a known ACF, is calculated as a power series with coefficients expressed as one-dimensional integrals. In general these must be evaluated numerically; two analytically tractable special cases are also considered. In cases of practical interest the series has been found to converge rapidly. These results are then used in the simulation of a non-Gaussian process with a specified ACF, which can take values less than the square of its mean. Our approach is compared with other methods in the open literature. Examples are given of time series and random fields with gamma single-point statistics that provide controlled models of high-resolution radar clutter.

Tough, R. J. A.; Ward, K. D.

1999-12-01

455

Gaussian mixtures versus MLP for terrain classification in Landsat TM images  

NASA Astrophysics Data System (ADS)

In this paper we introduce a new technique to build a Gaussian mixture classifier. It is based on the selection of the number and location of nodes dedicated to every class by means of discriminative rules. This feature allows us to make a fair comparison with MLP networks for terrain classification in remote sense applications, a field where non-parametric techniques usually outperform classical ML Gaussian classifiers. The main characteristic of the architecture proposed is the ability to select the proper number of Gaussian nodes per class attending to discriminative rules. The growth control is imposed by the use of an information theoretic criterion that prevents the network from becoming extremely complex, thus loosing generalization capabilities. After the growing phase is finished, a mutual information criterion is maximized to bias the parameters to a more discriminative configuration. We report a comparative study on terrain classification over a Landsat-TM image, using this technique and MLP classifiers with one hidden layer.

Alba, Jose L.; Docio, Laura; Docampo, Domingo

1997-04-01

456

Hemispherical asymmetry and local non-Gaussianity: A consistency condition  

NASA Astrophysics Data System (ADS)

In this paper we provide a consistency relation between the amplitude of the hemispherical bipolar asymmetry, A, and the amplitude of the primordial non-Gaussianity in the squeezed limit, fNL, as |A|?10-1fNL. We demonstrate that this consistency condition is at work for any model of inflation in which the curvature perturbations are sourced by a single light field with the Bunch–Davies initial condition, irrespective of the number of inflation fields that contribute to the background inflationary expansion. As a nontrivial example, we show that observable hemispherical asymmetry can be generated in single-field nonattractor inflationary models. We also study hemispherical asymmetry generated in the models of multiple fields inflation. We show that A is controlled by the weighted sum of non-Gaussianity contribution from each field. In particular, we show that observable hemispherical asymmetry can be generated in models in which inhomogeneities are generated from a light scalar field modulating the surface of the end of inflation.

Namjoo, Mohammad Hossein; Baghram, Shant; Firouzjahi, Hassan

2013-10-01

457

Confidence set inference with a prior quadratic bound  

NASA Astrophysics Data System (ADS)

In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z = (z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y(0)=(y sub 1(0),...,y sub D(0)) knowledge of the statistical distribution of the random errors in y(0). The data space Y containing y(0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x (e.g., energy or dissipation rate), Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. CSI is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface. Neither the heat flow nor the energy bound is strong enough to permit estimation of B(r) at single points on the CMB, but the heat flow bound permits estimation of uniform averages of B(r) over discs on the CMB, and both bounds permit weighted disc-averages with continous weighting kernels. Both bounds also permit estimation of low-degree Gauss coefficients at the CMB. The heat flow bound resolves them up to degree 8 if the crustal field at satellite altitudes must be treated as a systematic error, but can resolve to degree 11 under the most favorable statistical treatment of the crust. These two limits produce circles of confusion on the CMB with diameters of 25 deg and 19 deg respectively.

Backus, George E.

1988-09-01

458

Propagation of Laguerre–Gaussian and Bessel–Gaussian Schell-model beams through paraxial optical systems in turbulent atmosphere  

NASA Astrophysics Data System (ADS)

Based on the extended Huygens–Fresnel diffraction integral, the expressions for the average intensity and the effective size of Laguerre–Gaussian and Bessel–Gaussian Schell-model beams propagating through a paraxial ABCD optical system are obtained in the turbulent atmosphere. The influences of the source coherence and atmospheric turbulence on the propagation of Laguerre–Gaussian and Bessel–Gaussian Schell-model beams in the turbulent atmosphere are investigated in detail. It is found that the beam profile will eventually evolve into a Gaussian-like distribution through turbulence in contrast to ring-shaped far-field pattern in free space. The effective size of Laguerre–Gaussian and Bessel–Gaussian Schell-model beams with lower source coherence is less affected by turbulence. The parameter ? and index n of the sources have some effects on intensity distribution and beam spreading through atmospheric turbulence.

Cang, Ji; Xiu, Peng; Liu, Xu

2013-12-01

459

Gaussian capacity of the quantum bosonic memory channel with additive correlated Gaussian noise  

NASA Astrophysics Data System (ADS)

We present an algorithm for calculation of the Gaussian classical capacity of a quantum bosonic memory channel with additive Gaussian noise. The algorithm, restricted to Gaussian input states, is applicable to all channels with noise correlations obeying certain conditions and works in the full input energy domain, beyond previous treatments of this problem. As an illustration, we study the optimal input states and capacity of a quantum memory channel with Gauss-Markov noise [J. Schäfer, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.80.062313 80, 062313 (2009)]. We evaluate the enhancement of the transmission rate when using these optimal entangled input states by comparison with a product coherent-state encoding and find out that such a simple coherent-state encoding achieves not less than 90% of the capacity.

Schäfer, Joachim; Karpov, Evgueni; Cerf, Nicolas J.

2011-09-01

460

Control of linear smart structural systems using neural networks  

NASA Astrophysics Data System (ADS)

In recent studies, neural network based controllers for vibration suppression of smart structures have been reported. Many of these controller have been successfully implemented in simulation as well as using PC based data acquisition hardware. These studies have shown that in addition to conventional controller design methodologies, neural networks offer an effective basis for design and implementation of controllers. With the introduction of the Electronically Trainable Analog Neural Network (ETANN) chip i80170NX by Intel and a digital neural network chip Ni1000 by Nestor Corp., hardware implementation of neural network based controllers has been made possible. These neural network chips have also found applications in other areas such as signal processing and character recognition. In this paper, the capabilities of the ETANN based robust controllers for smart structural systems have been investigated. Robust controllers like the Liner Quadratic Regulator (LQR) and Linear Quadratic Gaussian with Loop Transfer Recovery (LQG/LTR) are implemented on a cantilevered plate system using the ETANN chip. Specially shaped PVDF film is used as sensors and PZTs as actuators. The LQG/LTR controller is implemented in two neural network configurations for dynamical systems suggested by Narendra and Parathasarathy. Analog hardware components used in the interface between the ETANN chip and the actuators/sensors on the smart structure test article have been developed. Practical considerations and limitations of the fully analog implementation of the controllers which are not considered in simulations have been discussed in the paper. Practical consideration in training the analog neural network chip for optimal performance has also been described. Experimental results of the closed loop performance of the smart structural system are presented.

Damle, Rajendra R.; Rao, Vittal S.

1996-05-01

461

Approximating the Best Linear Unbiased Estimator of Non-Gaussian Signals with Gaussian Noise  

NASA Astrophysics Data System (ADS)

Obtaining the best linear unbiased estimator (BLUE) of noisy signals is a traditional but powerful approach to noise reduction. Explicitly computing the BLUE usually requires the prior knowledge of the noise covariance matrix and the subspace to which the true signal belongs. However, such prior knowledge is often unavailable in reality, which prevents us from applying the BLUE to real-world problems. To cope with this problem, we give a practical procedure for approximating the BLUE without such prior knowledge. Our additional assumption is that the true signal follows a non-Gaussian distribution while the noise is Gaussian.

Sugiyama, Masashi; Kawanabe, Motoaki; Blanchard, Gilles; Müller, Klaus-Robert

462

The meta-Gaussian Bayesian Processor of forecasts and associated preliminary experiments  

NASA Astrophysics Data System (ADS)

Public weather services are trending toward providing users with probabilistic weather forecasts, in place of traditional deterministic forecasts. Probabilistic forecasting techniques are continually being improved to optimize available forecasting information. The Bayesian Processor of Forecast (BPF), a new statistical method for probabilistic forecast, can transform a deterministic forecast into a probabilistic forecast according to the historical statistical relationship between observations and forecasts generated by that forecasting system. This technique accounts for the typical forecasting performance of a deterministic forecasting system in quantifying the forecast uncertainty. The meta-Gaussian likelihood model is suitable for a variety of stochastic dependence structures with monotone likelihood ratios. The meta-Gaussian BPF adopting this kind of likelihood model can therefore be applied across many fields, including meteorology and hydrology. The Bayes theorem with two continuous random variables and the normal-linear BPF are briefly introduced. The meta-Gaussian BPF for a continuous predictand using a single predictor is then presented and discussed. The performance of the meta-Gaussian BPF is tested in a preliminary experiment. Control forecasts of daily surface temperature at 0000 UTC at Changsha and Wuhan stations are used as the deterministic forecast data. These control forecasts are taken from ensemble predictions with a 96-h lead time generated by the National Meteorological Center of the China Meteorological Administration, the European Centre for Medium-Range Weather Forecasts, and the US National Centers for Environmental Prediction during January 2008. The results of the experiment show that the meta-Gaussian BPF can transform a deterministic control forecast of surface temperature from any one of the three ensemble predictions into a useful probabilistic forecast of surface temperature. These probabilistic forecasts quantify the uncertainty of the control forecast; accordingly, the performance of the probabilistic forecasts differs based on the source of the underlying deterministic control forecasts.

Chen, Fajing; Jiao, Meiyan; Chen, Jing

2013-04-01

463

Provably fast integer factoring with quasi-uniform small quadratic residues  

Microsoft Academic Search

Finding small quadratic residues modulo n, when n is a large composite number of unknown factorisation is almost certainly a computationally hard problem. This problem arises in a natural way when factoring n by the use of congruences of squares. We construct here a polynomial-time algorithm based on the use of lattices, which finds in a near uniform way quadratic

Brigitte Vallée

1989-01-01

464

Hidden Lessons: How a Focus on Slope-Like Properties of Quadratic Functions Encouraged Unexpected Generalizations  

ERIC Educational Resources Information Center

|This article presents secondary students' generalizations about the connections between algebraic and graphical representations of quadratic functions, focusing specifically on the roles of the parameters a, b, and c in the general form of a quadratic function, y = ax[superscript 2] + bx + c. Students' generalizations about these connections led…

Ellis, Amy B.; Grinstead, Paul

2008-01-01

465

Global Models for the Orientation Field of Fingerprints: An Approach Based on Quadratic Differentials  

Microsoft Academic Search

Quadratic differentials naturally define analytic orientation fields on planar surfaces. We propose to model orientation fields of fingerprints by specifying quadratic differentials. Models for all fingerprint classes such as arches, loops and whorls are laid out. These models are parametrised by few, geometrically interpretable parameters which are invariant under Euclidean motions. We demonstrate their ability in adapting to given, observed

Stephan Huckemann; Thomas Hotz; Axel Munk

2008-01-01

466

Modified Quadratic Discriminant Functions and the Application to Chinese Character Recognition  

Microsoft Academic Search

Issues in the quadratic discriminant functions (QDF) are discussed and two types of modified quadratic disriminant functions (MQDF1, MQDF2) which are less sensitive to the estimation error of the covariance matrices are proposed. The MQDF1 is a function which employs a kind of a (pseudo) Bayesian estimate of the covariance matrix instead of the maximum likelihood estimate ordinarily used in

Fumitaka Kimura; Kenji Takashina; Shinji Tsuruoka; Yasuji Miyake

1987-01-01

467

Inelastic scattering in a local polaron model with quadratic coupling to bosons  

Microsoft Academic Search

We calculate the inelastic scattering probabilities in the wide band limit of a local polaron model with quadratic coupling to bosons. The central object is a two-particle Green's function which is calculated exactly using a purely algebraic approach. Compared with the usual linear interaction term a quadratic interaction term gives higher probabilities for inelastic scattering involving a large number of

Thomas Olsen

2009-01-01

468

An analytic solution of projectile motion with the quadratic resistance law using the homotopy analysis method  

Microsoft Academic Search

We consider the problem of two-dimensional projectile motion in which the resistance acting on an object moving in air is proportional to the square of the velocity of the object (quadratic resistance law). It is well known that the quadratic resistance law is valid in the range of the Reynolds number: 1 × 103 ~ 2 × 105 (for instance,

Kazuki Yabushita; Mariko Yamashita; Kazuhiro Tsuboi

2007-01-01

469

Fast Parallel DNA-Based Algorithms for Molecular Computation: Quadratic Congruence and Factoring Integers  

Microsoft Academic Search

Assume that $n$ is a positive integer. If there is an integer $0< M < n$ such that $M ^{2}\\\\equiv C~({\\\\rm mod} ~n)$, i.e., the congruence has a solution, then $C$ is said to be a quadratic congruence $({\\\\rm mod}~ n)$. If the congruence does not have a solution, then $C$ is said to be a quadratic noncongruence $({\\\\rm mod}~

2012-01-01

470

The cyclicity of period annuli of some classes of reversible quadratic systems  

Microsoft Academic Search

The cyclicity of period annuli of some classes of reversible and non-Hamiltonian quadratic systems under quadratic perturbations are studied. The argument principle method and the centroid curve method are combined to prove that the related Abelian integral has at most two zeros.

G. Chen; C. LI; C. Liu; J. Llibre

2006-01-01

471

The cyclicity of period annulus of a quadratic reversible Lotka-Volterra system  

NASA Astrophysics Data System (ADS)

We prove that by perturbing the periodic annulus of the quadratic polynomial reversible Lotka-Volterra differential system \\dot x=y+\\case{3}{2}(x^2-y^2) , \\dot y=-x(1-y) , inside the class of all quadratic polynomial differential systems we can obtain at most two limit cycles.

Li, Chengzhi; Llibre, Jaume

2009-12-01

472

The cyclicity of period annulus of a quadratic reversible Lotka-Volterra system  

Microsoft Academic Search

We prove that by perturbing the periodic annulus of the quadratic polynomial reversible Lotka-Volterra differential system \\\\dot x=y+\\\\case{3}{2}(x^2-y^2) , \\\\dot y=-x(1-y) , inside the class of all quadratic polynomial differential systems we can obtain at most two limit cycles.

Chengzhi Li; Jaume Llibre

2009-01-01

473

The evaluation of completely general quadratic force fields using theory and experimental data  

Microsoft Academic Search

A semiempirical method was developed to calculate completely general quadratic potential functions using a combination of molecular orbital calculations and limited vibrational data. In the molecular orbital constraint using interaction coordinates (MOSCIC) method symmetry interaction displacement coordinates are constrained in nonlinear least squares determination of quadratic compliance constants. The only experimental data required in the MOCIC method are the frequencies

T. H. Arnold

1979-01-01

474

An efficient interior point method for sequential quadratic programming based optimal power flow  

Microsoft Academic Search

This paper presents a new sequential quadratic programming algorithm for solving the optimal power flow problem. The algorithm is structured with an outer linearization loop and an inner optimization loop. The inner loop solves a relaxed reduced quadratic programming problem. Because constraint relaxation keeps the inner loop problem of small dimension, the algorithm is quite efficient. Its outer loop iteration

Imad M. Nejdawi; Kevin A. Clements; Paul W. Davis

2000-01-01

475

Diffraction of a Gaussian beam in a three-dimensional smoothly inhomogeneous medium: an eikonal-based complex geometrical-optics approach.  

PubMed

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. PMID:16715163

Berczynski, Pawel; Bliokh, Konstantin Yu; Kravtsov, Yuri A; Stateczny, Andrzej

2006-06-01

476

An introduction to Gaussian Bayesian networks.  

PubMed

The extraction of regulatory networks and pathways from postgenomic data is important for drug -discovery and development, as the extracted pathways reveal how genes or proteins regulate each other. Following up on the seminal paper of Friedman et al. (J Comput Biol 7:601-620, 2000), Bayesian networks have been widely applied as a popular tool to this end in systems biology research. Their popularity stems from the tractability of the marginal likelihood of the network structure, which is a consistent scoring scheme in the Bayesian context. This score is based on an integration over the entire parameter space, for which highly expensive computational procedures have to be applied when using more complex -models based on differential equations; for example, see (Bioinformatics 24:833-839, 2008). This chapter gives an introduction to reverse engineering regulatory networks and pathways with Gaussian Bayesian networks, that is Bayesian networks with the probabilistic BGe scoring metric [see (Geiger and Heckerman 235-243, 1995)]. In the BGe model, the data are assumed to stem from a Gaussian distribution and a normal-Wishart prior is assigned to the unknown parameters. Gaussian Bayesian network methodology for analysing static observational, static interventional as well as dynamic (observational) time series data will be described in detail in this chapter. Finally, we apply these Bayesian network inference methods (1) to observational and interventional flow cytometry (protein) data from the well-known RAF pathway to evaluate the global network reconstruction accuracy of Bayesian network inference and (2) to dynamic gene expression time series data of nine circadian genes in Arabidopsis thaliana to reverse engineer the unknown regulatory network topology for this domain. PMID:20824469

Grzegorczyk, Marco

2010-01-01

477

Non-gaussianity from broken symmetries  

SciTech Connect

Recently we studied inflation models in which the inflation potential is characterized by an underlying approximate global symmetry. In the first work we pointed out that in such a model curvature perturbations are generated after the end of the slow-roll phase of inflation. In this work we develop further the observational implications of the model and compute the degree of non-Gaussianity predicted in the scenario. We find that the corresponding nonlinearity parameter, F{sub NL}, can be as large as 10{sup 2}.

Kolb, Edward W.; /Fermilab /Chicago U., Astron. Astrophys. Ctr. /Chicago U., EFI; Riotto, Antonio; /CERN; Vallinotto, Alberto; /Chicago U. /Fermilab

2005-11-01

478

Infrared image segmentation with Gaussian mixture modeling  

NASA Astrophysics Data System (ADS)

Infrared imaging allows surveillance during the night, thus it has been widely used for military and security applications. However, infrared images are generally characterized by low resolution, low contrast, and an unclear texture with no color information. Moreover, various types of noises and background clutters can degrade the image quality. This paper discusses multi-level segmentation for infrared images. The expectation-maximization algorithm is adopted to cluster pixels on the basis of Gaussian mixture models. The use of the multi-level segmentation method enables the extraction of human target regions from the background of the image. Several infrared images are processed to demonstrate the effectiveness of the presented method.

Lee, Dong-Su; Yeom, Seokwon

2012-05-01

479

Fractional Fourier transform for elliptical Gaussian beams  

NASA Astrophysics Data System (ADS)

Based on the definition of fractional Fourier transform (FRT), an analytical formula is derived for the FRT of elliptical Gaussian beam (EGB) by using a tensor method. The corresponding tensor ABCD law for performing the FRT of EGB is obtained. The connection between the FRT formula and the generalized Collins formula is discussed. By using the derived formula, the influences of the fractional order on the properties of EGB in the fractional Fourier plane are studied in detail. The derived formulae provide a powerful tool for analyzing and calculating the FRT of EGB.

Cai, Yangjian; Lin, Qiang

2003-03-01

480

Non-Gaussianity from broken symmetries  

SciTech Connect

Recently we studied inflation models in which the inflaton potential is characterized by an underlying approximate global symmetry. In the first work we pointed out that in such a model curvature perturbations are generated after the end of the slow-roll phase of inflation. In this work we develop further the observational implications of the model and compute the degree of non-Gaussianity predicted in the scenario. We find that the corresponding nonlinearity parameter, f{sub NL}, can be as large as 10{sup 2}.

Kolb, Edward W.; Riotto, Antonio; Vallinotto, Alberto [Particle Astrophysics Center, Fermi National Accelerator Laboratory, Batavia, Illinois 60510-0500 (United States); and Department of Astronomy and Astrophysics, Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637-1433 (United States); CERN Theory Division CH-1211, Geneva 23 (Switzerland); Physics Department, The University of Chicago, Chicago, Illinois 60637-1433 (United States); and Particle Astrophysics Center, Fermi National Accelerator Laboratory, Batavia, Illinois 60510-0500 (United States)

2006-01-15

481

2DPUF: A sequential gaussian puff model  

SciTech Connect

This report documents the Environmental Transport Section's (ETS) two-dimensional, sequential gaussian puff transport and dispersion model for emergency response. The sequential puff scheme is described, and the dispersion equations are presented. The advantages of this model over the ETS's PUFF/PLUME model are discussed. Options are calculating a two-dimensional wind field, interpolation procedures, and the wind field grid are described. The various grid systems for puff transport calculations and dose estimates are also described. A flow diagram for the modules comprising the 2DPUF code and a description of each module is presented.

Addis, R.P.; O'Steen, B.L.

1990-01-01

482

2DPUF: A sequential gaussian puff model  

SciTech Connect

This report documents the Environmental Transport Section`s (ETS) two-dimensional, sequential gaussian puff transport and dispersion model for emergency response. The sequential puff scheme is described, and the dispersion equations are presented. The advantages of this model over the ETS`s PUFF/PLUME model are discussed. Options are calculating a two-dimensional wind field, interpolation procedures, and the wind field grid are described. The various grid systems for puff transport calculations and dose estimates are also described. A flow diagram for the modules comprising the 2DPUF code and a description of each module is presented.

Addis, R.P.; O`Steen, B.L.

1990-12-31

483

Super-Gaussian Solitons in Optical Fibers  

NASA Astrophysics Data System (ADS)

The variational principle is employed to obtain the evolution of the parameters of a super-Gaussian chirped soliton that propagates through an optical fiber and is governed by the dispersion-managed nonlinear Schrödinger's equation. These pulses have better features compared to a classical soliton and reduced timing jitter due to the Gordon-Haus effect. The waveform deviates from that of a classical soliton. The periodically-changing strong chirp of such a soliton reduces the effective nonlinearity that is necessary for balancing the local dispersion. This study is extended to obtain the adiabatic evolution of the parameters of such a soliton in the presence of perturbation terms.

Biswas, Anjan

484

Gaussian beam decomposition of high frequency wave fields  

SciTech Connect

In this paper, we present a method of decomposing a highly oscillatory wave field into a sparse superposition of Gaussian beams. The goal is to extract the necessary parameters for a Gaussian beam superposition from this wave field, so that further evolution of the high frequency waves can be computed by the method of Gaussian beams. The methodology is described for R{sup d} with numerical examples for d=2. In the first example, a field generated by an interface reflection of Gaussian beams is decomposed into a superposition of Gaussian beams. The beam parameters are reconstructed to a very high accuracy. The data in the second example is not a superposition of a finite number of Gaussian beams. The wave field to be approximated is generated by a finite difference method for a geometry with two slits. The accuracy in the decomposition increases monotonically with the number of beams.

Tanushev, Nicolay M. [Department of Mathematics, University of Texas at Austin, 1 University Station C1200, Austin, TX 78712-0257 (United States)], E-mail: nicktan@math.utexas.edu; Engquist, Bjoern; Tsai, Richard [Department of Mathematics, University of Texas at Austin, 1 University Station C1200, Austin, TX 78712-0257 (United States)

2009-12-10

485

Linear dependence and energy conservation in Gaussian wavepacket basis sets  

NASA Astrophysics Data System (ADS)

We propose a method for dealing with the problem of linear dependence in quantum dynamics simulations employing over-complete Gaussian wavepacket (GWP) basis sets. In particular, by periodically projecting out redundant basis functions using the matching pursuit algorithm whilst simultaneously introducing GWPs which avoid linear dependence with the current basis set, we find that numerical conditioning of the equations-of-motion can be readily controlled. In applications to particle tunnelling in one- and two-dimensional potentials, this method allows us to reproduce the exact quantum-mechanical results with fewer GWP basis functions than similar calculations with non-adaptive basis sets, a result which we trace back to the improved energy conservation of our adaptive approach.

Habershon, Scott

2012-01-01

486

Linear dependence and energy conservation in Gaussian wavepacket basis sets.  

PubMed

We propose a method for dealing with the problem of linear dependence in quantum dynamics simulations employing over-complete Gaussian wavepacket (GWP) basis sets. In particular, by periodically projecting out redundant basis functions using the matching pursuit algorithm whilst simultaneously introducing GWPs which avoid linear dependence with the current basis set, we find that numerical conditioning of the equations-of-motion can be readily controlled. In applications to particle tunnelling in one- and two-dimensional potentials, this method allows us to reproduce the exact quantum-mechanical results with fewer GWP basis functions than similar calculations with non-adaptive basis sets, a result which we trace back to the improved energy conservation of our adaptive approach. PMID:22239771

Habershon, Scott

2012-01-01

487

Fast Gaussian Process Regression using KD-Trees  

Microsoft Academic Search

The computation required for Gaussian process regression with n train- ing examples is about O(n3) during training and O(n) for each predic- tion. This makes Gaussian process regression too slow for large datasets. In this paper, we present a fast approximation method, based on kd-trees, that signicantly reduces both the prediction and the training times of Gaussian process regression.

Yirong Shen; Andrew Y. Ng; Matthias Seeger

2005-01-01

488

Convergence Analysis of the Gaussian Mixture PHD Filter  

Microsoft Academic Search

The Gaussian mixture Probability Hypothesis Den- sity (PHD) filter was proposed recently for jointly estimating the time-varying number of targets and their states from a sequence of sets of observations without the need for measurement-to- track data association. It was shown that, under linear-