Learning graph matching.

PubMed

Caetano, Tibério S; McAuley, Julian J; Cheng, Li; Le, Quoc V; Smola, Alex J

2009-06-01

As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to finding a correspondence between the nodes of different graphs. Many formulations of this problem can be cast in general as a quadratic assignment problem, where a linear term in the objective function encodes node compatibility and a quadratic term encodes edge compatibility. The main research focus in this theme is about designing efficient algorithms for approximately solving the quadratic assignment problem, since it is NP-hard. In this paper we turn our attention to a different question: how to estimate compatibility functions such that the solution of the resulting graph matching problem best matches the expected solution that a human would manually provide. We present a method for learning graph matching: the training examples are pairs of graphs and the 'labels' are matches between them. Our experimental results reveal that learning can substantially improve the performance of standard graph matching algorithms. In particular, we find that simple linear assignment with such a learning scheme outperforms Graduated Assignment with bistochastic normalisation, a state-of-the-art quadratic assignment relaxation algorithm.

Nonlinear Associations between Plasma Cholesterol Levels and Neuropsychological Function

PubMed Central

Wendell, Carrington R.; Zonderman, Alan B.; Katzel, Leslie I.; Rosenberger, William F.; Plamadeala, Victoria V.; Hosey, Megan M.; Waldstein, Shari R.

2016-01-01

Objective Although both high and low levels of total and low-density lipoprotein (LDL) cholesterol have been associated with poor neuropsychological function, little research has examined nonlinear effects. We examined quadratic relations of cholesterol to performance on a comprehensive neuropsychological battery. Method Participants were 190 older adults (53% men, ages 54–83) free of major medical, neurologic, and psychiatric disease. Measures of fasting plasma total and high-density lipoprotein (HDL) cholesterol were assayed, and LDL cholesterol was calculated. Participants completed neuropsychological measures of attention, executive function, memory, visuospatial judgment, and manual speed/dexterity. Multiple regression analyses examined cholesterol levels as quadratic predictors of each measure of cognitive performance, with age (dichotomized as <70 vs. 70+) as an effect modifier. Results A significant quadratic effect of total cholesterol2 × age was identified for Logical Memory II (b=−.0013, p=.039), such that the 70+ group performed best at high and low levels of total cholesterol than at mid-range total cholesterol (U-shaped), and the <70 group performed worse at high and low levels of total cholesterol than at mid-range total cholesterol (inverted U-shape). Similarly, significant U- and J-shaped effects of LDL cholesterol2 × age were identified for Visual Reproduction II (b=−.0020, p=.026) and log of Trails B (b=.0001, p=.044). Quadratic associations between HDL cholesterol and cognitive performance were nonsignificant. Conclusions Results indicate differential associations between cholesterol and neuropsychological function across different ages and domains of function. High and low total and LDL cholesterol may confer both risk and benefit for suboptimal cognitive function at different ages. PMID:27280580

Plate/shell structure topology optimization of orthotropic material for buckling problem based on independent continuous topological variables

NASA Astrophysics Data System (ADS)

Ye, Hong-Ling; Wang, Wei-Wei; Chen, Ning; Sui, Yun-Kang

2017-10-01

The purpose of the present work is to study the buckling problem with plate/shell topology optimization of orthotropic material. A model of buckling topology optimization is established based on the independent, continuous, and mapping method, which considers structural mass as objective and buckling critical loads as constraints. Firstly, composite exponential function (CEF) and power function (PF) as filter functions are introduced to recognize the element mass, the element stiffness matrix, and the element geometric stiffness matrix. The filter functions of the orthotropic material stiffness are deduced. Then these filter functions are put into buckling topology optimization of a differential equation to analyze the design sensitivity. Furthermore, the buckling constraints are approximately expressed as explicit functions with respect to the design variables based on the first-order Taylor expansion. The objective function is standardized based on the second-order Taylor expansion. Therefore, the optimization model is translated into a quadratic program. Finally, the dual sequence quadratic programming (DSQP) algorithm and the global convergence method of moving asymptotes algorithm with two different filter functions (CEF and PF) are applied to solve the optimal model. Three numerical results show that DSQP&CEF has the best performance in the view of structural mass and discretion.

Linear and quadratic static response functions and structure functions in Yukawa liquids.

PubMed

Magyar, Péter; Donkó, Zoltán; Kalman, Gabor J; Golden, Kenneth I

2014-08-01

We compute linear and quadratic static density response functions of three-dimensional Yukawa liquids by applying an external perturbation potential in molecular dynamics simulations. The response functions are also obtained from the equilibrium fluctuations (static structure factors) in the system via the fluctuation-dissipation theorems. The good agreement of the quadratic response functions, obtained in the two different ways, confirms the quadratic fluctuation-dissipation theorem. We also find that the three-point structure function may be factorizable into two-point structure functions, leading to a cluster representation of the equilibrium triplet correlation function.

Improved Evolutionary Programming with Various Crossover Techniques for Optimal Power Flow Problem

NASA Astrophysics Data System (ADS)

Tangpatiphan, Kritsana; Yokoyama, Akihiko

This paper presents an Improved Evolutionary Programming (IEP) for solving the Optimal Power Flow (OPF) problem, which is considered as a non-linear, non-smooth, and multimodal optimization problem in power system operation. The total generator fuel cost is regarded as an objective function to be minimized. The proposed method is an Evolutionary Programming (EP)-based algorithm with making use of various crossover techniques, normally applied in Real Coded Genetic Algorithm (RCGA). The effectiveness of the proposed approach is investigated on the IEEE 30-bus system with three different types of fuel cost functions; namely the quadratic cost curve, the piecewise quadratic cost curve, and the quadratic cost curve superimposed by sine component. These three cost curves represent the generator fuel cost functions with a simplified model and more accurate models of a combined-cycle generating unit and a thermal unit with value-point loading effect respectively. The OPF solutions by the proposed method and Pure Evolutionary Programming (PEP) are observed and compared. The simulation results indicate that IEP requires less computing time than PEP with better solutions in some cases. Moreover, the influences of important IEP parameters on the OPF solution are described in details.

The cortisol reactivity threshold model: Direction of trait rumination and cortisol reactivity association varies with stressor severity.

PubMed

Vrshek-Schallhorn, Suzanne; Avery, Bradley M; Ditcheva, Maria; Sapuram, Vaibhav R

2018-06-01

Various internalizing risk factors predict, in separate studies, both augmented and reduced cortisol responding to lab-induced stress. Stressor severity appears key: We tested whether heightened trait-like internalizing risk (here, trait rumination) predicts heightened cortisol reactivity under modest objective stress, but conversely predicts reduced reactivity under more robust objective stress. Thus, we hypothesized that trait rumination would interact with a curvilinear (quadratic) function of stress severity to predict cortisol reactivity. Evidence comes from 85 currently non-depressed emerging adults who completed either a non-stressful control protocol (n = 29), an intermediate difficulty Trier Social Stress Test (TSST; n = 26), or a robustly stressful negative evaluative TSST (n = 30). Latent growth curve models evaluated relationships between trait rumination and linear and quadratic effects of stressor severity on the change in cortisol and negative affect over time. Among other findings, a significant Trait Rumination x Quadratic Stress Severity interaction effect for cortisol's Quadratic Trend of Time (i.e., reactivity, B = .125, p = .017) supported the hypothesis. Rumination predicted greater cortisol reactivity to intermediate stress (r p  = .400, p = .043), but blunted reactivity to more robust negative evaluative stress (r p  = -0.379, p = 0.039). Contrasting hypotheses, negative affective reactivity increased independently of rumination as stressor severity increased (B = .453, p = 0.044). The direction of the relationship between an internalizing risk factor (trait rumination) and cortisol reactivity varies as a function of stressor severity. We propose the Cortisol Reactivity Threshold Model, which may help reconcile several divergent reactivity literatures and has implications for internalizing psychopathology, particularly depression. Copyright © 2017 Elsevier Ltd. All rights reserved.

Students' Understanding of Quadratic Equations

ERIC Educational Resources Information Center

López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

2016-01-01

Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…

Functional Data Approximation on Bounded Domains using Polygonal Finite Elements.

PubMed

Cao, Juan; Xiao, Yanyang; Chen, Zhonggui; Wang, Wenping; Bajaj, Chandrajit

2018-07-01

We construct and analyze piecewise approximations of functional data on arbitrary 2D bounded domains using generalized barycentric finite elements, and particularly quadratic serendipity elements for planar polygons. We compare approximation qualities (precision/convergence) of these partition-of-unity finite elements through numerical experiments, using Wachspress coordinates, natural neighbor coordinates, Poisson coordinates, mean value coordinates, and quadratic serendipity bases over polygonal meshes on the domain. For a convex n -sided polygon, the quadratic serendipity elements have 2 n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, rather than the usual n ( n + 1)/2 basis functions to achieve quadratic convergence. Two greedy algorithms are proposed to generate Voronoi meshes for adaptive functional/scattered data approximations. Experimental results show space/accuracy advantages for these quadratic serendipity finite elements on polygonal domains versus traditional finite elements over simplicial meshes. Polygonal meshes and parameter coefficients of the quadratic serendipity finite elements obtained by our greedy algorithms can be further refined using an L 2 -optimization to improve the piecewise functional approximation. We conduct several experiments to demonstrate the efficacy of our algorithm for modeling features/discontinuities in functional data/image approximation.

Differences between quadratic equations and functions: Indonesian pre-service secondary mathematics teachers’ views

NASA Astrophysics Data System (ADS)

Aziz, T. A.; Pramudiani, P.; Purnomo, Y. W.

2018-01-01

Difference between quadratic equation and quadratic function as perceived by Indonesian pre-service secondary mathematics teachers (N = 55) who enrolled at one private university in Jakarta City was investigated. Analysis of participants’ written responses and interviews were conducted consecutively. Participants’ written responses highlighted differences between quadratic equation and function by referring to their general terms, main characteristics, processes, and geometrical aspects. However, they showed several obstacles in describing the differences such as inappropriate constraints and improper interpretations. Implications of the study are discussed.

Quadratic spline subroutine package

USGS Publications Warehouse

Rasmussen, Lowell A.

1982-01-01

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

Application of the sequential quadratic programming algorithm for reconstructing the distribution of optical parameters based on the time-domain radiative transfer equation.

PubMed

Qi, Hong; Qiao, Yao-Bin; Ren, Ya-Tao; Shi, Jing-Wen; Zhang, Ze-Yu; Ruan, Li-Ming

2016-10-17

Sequential quadratic programming (SQP) is used as an optimization algorithm to reconstruct the optical parameters based on the time-domain radiative transfer equation (TD-RTE). Numerous time-resolved measurement signals are obtained using the TD-RTE as forward model. For a high computational efficiency, the gradient of objective function is calculated using an adjoint equation technique. SQP algorithm is employed to solve the inverse problem and the regularization term based on the generalized Gaussian Markov random field (GGMRF) model is used to overcome the ill-posed problem. Simulated results show that the proposed reconstruction scheme performs efficiently and accurately.

IFSM fractal image compression with entropy and sparsity constraints: A sequential quadratic programming approach

NASA Astrophysics Data System (ADS)

Kunze, Herb; La Torre, Davide; Lin, Jianyi

2017-01-01

We consider the inverse problem associated with IFSM: Given a target function f , find an IFSM, such that its fixed point f ¯ is sufficiently close to f in the Lp distance. Forte and Vrscay [1] showed how to reduce this problem to a quadratic optimization model. In this paper, we extend the collage-based method developed by Kunze, La Torre and Vrscay ([2][3][4]), by proposing the minimization of the 1-norm instead of the 0-norm. In fact, optimization problems involving the 0-norm are combinatorial in nature, and hence in general NP-hard. To overcome these difficulties, we introduce the 1-norm and propose a Sequential Quadratic Programming algorithm to solve the corresponding inverse problem. As in Kunze, La Torre and Vrscay [3] in our formulation, the minimization of collage error is treated as a multi-criteria problem that includes three different and conflicting criteria i.e., collage error, entropy and sparsity. This multi-criteria program is solved by means of a scalarization technique which reduces the model to a single-criterion program by combining all objective functions with different trade-off weights. The results of some numerical computations are presented.

Revealing Ozgur's Thoughts of a Quadratic Function with a Clinical Interview: Concepts and Their Underlying Reasons

ERIC Educational Resources Information Center

Ozaltun Celik, Aytug; Bukova Guzel, Esra

2017-01-01

The quadratic function is an important concept for calculus but the students at high school have many difficulties related to this concept. It is important that the teaching of the quadratic function is realized considering the students' thinking. In this context, the aim of this study conducted through a qualitative case study is to reveal the…

The stability of quadratic-reciprocal functional equation

NASA Astrophysics Data System (ADS)

Song, Aimin; Song, Minwei

2018-04-01

A new quadratic-reciprocal functional equation f ((k +1 )x +k y )+f ((k +1 )x -k y )=2/f (x )f (y )[(k+1 ) 2f (y )+k2f (x )] [(k+1)2f (y )-k2f (x )] 2 is introduced. The Hyers-Ulam stability for the quadratic-reciprocal functional equations is proved in Banach spaces using the direct method and the fixed point method, respectively.

Closed-loop, pilot/vehicle analysis of the approach and landing task

NASA Technical Reports Server (NTRS)

Anderson, M. R.; Schmidt, D. K.

1986-01-01

In the case of approach and landing, it is universally accepted that the pilot uses more than one vehicle response, or output, to close his control loops. Therefore, to model this task, a multi-loop analysis technique is required. The analysis problem has been in obtaining reasonable analytic estimates of the describing functions representing the pilot's loop compensation. Once these pilot describing functions are obtained, appropriate performance and workload metrics must then be developed for the landing task. The optimal control approach provides a powerful technique for obtaining the necessary describing functions, once the appropriate task objective is defined in terms of a quadratic objective function. An approach is presented through the use of a simple, reasonable objective function and model-based metrics to evaluate loop performance and pilot workload. The results of an analysis of the LAHOS (Landing and Approach of Higher Order Systems) study performed by R.E. Smith is also presented.

Computing the Partial Fraction Decomposition of Rational Functions with Irreducible Quadratic Factors in the Denominators

ERIC Educational Resources Information Center

Man, Yiu-Kwong

2012-01-01

In this note, a new method for computing the partial fraction decomposition of rational functions with irreducible quadratic factors in the denominators is presented. This method involves polynomial divisions and substitutions only, without having to solve for the complex roots of the irreducible quadratic polynomial or to solve a system of linear…

On Vieta's Formulas and the Determination of a Set of Positive Integers by Their Sum and Product

ERIC Educational Resources Information Center

Valahas, Theodoros; Boukas, Andreas

2011-01-01

In Years 9 and 10 of secondary schooling students are typically introduced to quadratic expressions and functions and related modelling, algebra, and graphing. This includes work on the expansion and factorisation of quadratic expressions (typically with integer values of coefficients), graphing quadratic functions, finding the roots of quadratic…

Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems

NASA Astrophysics Data System (ADS)

Szederkényi, Gábor; Hangos, Katalin M.

2004-04-01

We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities.

On the time-weighted quadratic sum of linear discrete systems

NASA Technical Reports Server (NTRS)

Jury, E. I.; Gutman, S.

1975-01-01

A method is proposed for obtaining the time-weighted quadratic sum for linear discrete systems. The formula of the weighted quadratic sum is obtained from matrix z-transform formulation. In addition, it is shown that this quadratic sum can be derived in a recursive form for several useful weighted functions. The discussion presented parallels that of MacFarlane (1963) for weighted quadratic integral for linear continuous systems.

Newton on Objects Moving in a Fluid--The Penetration Length

ERIC Educational Resources Information Center

Saslow, Wayne M.; Lu, Hong

2008-01-01

We solve for the motion of an object with initial velocity v[subscript 0] and subject only to the combined drag of forces linear and quadratic in the velocity. This problem was treated briefly by Newton, after he developed a theoretical argument for the quadratic term, which we now know is characteristic of turbulent flow. Linear drag introduces a…

Using Linear and Quadratic Functions to Teach Number Patterns in Secondary School

ERIC Educational Resources Information Center

Kenan, Kok Xiao-Feng

2017-01-01

This paper outlines an approach to definitively find the general term in a number pattern, of either a linear or quadratic form, by using the general equation of a linear or quadratic function. This approach is governed by four principles: (1) identifying the position of the term (input) and the term itself (output); (2) recognising that each…

Optimization on Paddy Crops in Central Java (with Solver, SVD on Least Square and ACO (Ant Colony Algorithm))

NASA Astrophysics Data System (ADS)

Parhusip, H. A.; Trihandaru, S.; Susanto, B.; Prasetyo, S. Y. J.; Agus, Y. H.; Simanjuntak, B. H.

2017-03-01

Several algorithms and objective functions on paddy crops have been studied to get optimal paddy crops in Central Java based on the data given from Surakarta and Boyolali. The algorithms are linear solver, least square and Ant Colony Algorithms (ACO) to develop optimization procedures on paddy crops modelled with Modified GSTAR (Generalized Space-Time Autoregressive) and nonlinear models where the nonlinear models are quadratic and power functions. The studied data contain paddy crops from Surakarta and Boyolali determining the best period of planting in the year 1992-2012 for Surakarta where 3 periods for planting are known and the optimal amount of paddy crops in Boyolali in the year 2008-2013. Having these analyses may guide the local agriculture government to give a decision on rice sustainability in its region. The best period for planting in Surakarta is observed, i.e. the best period is in September-December based on the data 1992-2012 by considering the planting area, the cropping area, and the paddy crops are the most important factors to be taken into account. As a result, we can refer the paddy crops in this best period (about 60.4 thousand tons per year) as the optimal results in 1992-2012 where the used objective function is quadratic. According to the research, the optimal paddy crops in Boyolali about 280 thousand tons per year where the studied factors are the amount of rainfalls, the harvested area and the paddy crops in 2008-2013. In this case, linear and power functions are studied to be the objective functions. Compared to all studied algorithms, the linear solver is still recommended to be an optimization tool for a local agriculture government to predict paddy crops in future.

An iterative method for tri-level quadratic fractional programming problems using fuzzy goal programming approach

NASA Astrophysics Data System (ADS)

Kassa, Semu Mitiku; Tsegay, Teklay Hailay

2017-08-01

Tri-level optimization problems are optimization problems with three nested hierarchical structures, where in most cases conflicting objectives are set at each level of hierarchy. Such problems are common in management, engineering designs and in decision making situations in general, and are known to be strongly NP-hard. Existing solution methods lack universality in solving these types of problems. In this paper, we investigate a tri-level programming problem with quadratic fractional objective functions at each of the three levels. A solution algorithm has been proposed by applying fuzzy goal programming approach and by reformulating the fractional constraints to equivalent but non-fractional non-linear constraints. Based on the transformed formulation, an iterative procedure is developed that can yield a satisfactory solution to the tri-level problem. The numerical results on various illustrative examples demonstrated that the proposed algorithm is very much promising and it can also be used to solve larger-sized as well as n-level problems of similar structure.

Optimal estimation and scheduling in aquifer management using the rapid feedback control method

NASA Astrophysics Data System (ADS)

Ghorbanidehno, Hojat; Kokkinaki, Amalia; Kitanidis, Peter K.; Darve, Eric

2017-12-01

Management of water resources systems often involves a large number of parameters, as in the case of large, spatially heterogeneous aquifers, and a large number of "noisy" observations, as in the case of pressure observation in wells. Optimizing the operation of such systems requires both searching among many possible solutions and utilizing new information as it becomes available. However, the computational cost of this task increases rapidly with the size of the problem to the extent that textbook optimization methods are practically impossible to apply. In this paper, we present a new computationally efficient technique as a practical alternative for optimally operating large-scale dynamical systems. The proposed method, which we term Rapid Feedback Controller (RFC), provides a practical approach for combined monitoring, parameter estimation, uncertainty quantification, and optimal control for linear and nonlinear systems with a quadratic cost function. For illustration, we consider the case of a weakly nonlinear uncertain dynamical system with a quadratic objective function, specifically a two-dimensional heterogeneous aquifer management problem. To validate our method, we compare our results with the linear quadratic Gaussian (LQG) method, which is the basic approach for feedback control. We show that the computational cost of the RFC scales only linearly with the number of unknowns, a great improvement compared to the basic LQG control with a computational cost that scales quadratically. We demonstrate that the RFC method can obtain the optimal control values at a greatly reduced computational cost compared to the conventional LQG algorithm with small and controllable losses in the accuracy of the state and parameter estimation.

The non-avian theropod quadrate I: standardized terminology with an overview of the anatomy and function

PubMed Central

Araújo, Ricardo; Mateus, Octávio

2015-01-01

The quadrate of reptiles and most other tetrapods plays an important morphofunctional role by allowing the articulation of the mandible with the cranium. In Theropoda, the morphology of the quadrate is particularly complex and varies importantly among different clades of non-avian theropods, therefore conferring a strong taxonomic potential. Inconsistencies in the notation and terminology used in discussions of the theropod quadrate anatomy have been noticed, including at least one instance when no less than eight different terms were given to the same structure. A standardized list of terms and notations for each quadrate anatomical entity is proposed here, with the goal of facilitating future descriptions of this important cranial bone. In addition, an overview of the literature on quadrate function and pneumaticity in non-avian theropods is presented, along with a discussion of the inferences that could be made from this research. Specifically, the quadrate of the large majority of non-avian theropods is akinetic but the diagonally oriented intercondylar sulcus of the mandibular articulation allowed both rami of the mandible to move laterally when opening the mouth in many of theropods. Pneumaticity of the quadrate is also present in most averostran clades and the pneumatic chamber—invaded by the quadrate diverticulum of the mandibular arch pneumatic system—was connected to one or several pneumatic foramina on the medial, lateral, posterior, anterior or ventral sides of the quadrate. PMID:26401455

Polarimetric image reconstruction algorithms

NASA Astrophysics Data System (ADS)

Valenzuela, John R.

In the field of imaging polarimetry Stokes parameters are sought and must be inferred from noisy and blurred intensity measurements. Using a penalized-likelihood estimation framework we investigate reconstruction quality when estimating intensity images and then transforming to Stokes parameters (traditional estimator), and when estimating Stokes parameters directly (Stokes estimator). We define our cost function for reconstruction by a weighted least squares data fit term and a regularization penalty. It is shown that under quadratic regularization, the traditional and Stokes estimators can be made equal by appropriate choice of regularization parameters. It is empirically shown that, when using edge preserving regularization, estimating the Stokes parameters directly leads to lower RMS error in reconstruction. Also, the addition of a cross channel regularization term further lowers the RMS error for both methods especially in the case of low SNR. The technique of phase diversity has been used in traditional incoherent imaging systems to jointly estimate an object and optical system aberrations. We extend the technique of phase diversity to polarimetric imaging systems. Specifically, we describe penalized-likelihood methods for jointly estimating Stokes images and optical system aberrations from measurements that contain phase diversity. Jointly estimating Stokes images and optical system aberrations involves a large parameter space. A closed-form expression for the estimate of the Stokes images in terms of the aberration parameters is derived and used in a formulation that reduces the dimensionality of the search space to the number of aberration parameters only. We compare the performance of the joint estimator under both quadratic and edge-preserving regularization. The joint estimator with edge-preserving regularization yields higher fidelity polarization estimates than with quadratic regularization. Under quadratic regularization, using the reduced-parameter search strategy, accurate aberration estimates can be obtained without recourse to regularization "tuning". Phase-diverse wavefront sensing is emerging as a viable candidate wavefront sensor for adaptive-optics systems. In a quadratically penalized weighted least squares estimation framework a closed form expression for the object being imaged in terms of the aberrations in the system is available. This expression offers a dramatic reduction of the dimensionality of the estimation problem and thus is of great interest for practical applications. We have derived an expression for an approximate joint covariance matrix for object and aberrations in the phase diversity context. Our expression for the approximate joint covariance is compared with the "known-object" Cramer-Rao lower bound that is typically used for system parameter optimization. Estimates of the optimal amount of defocus in a phase-diverse wavefront sensor derived from the joint-covariance matrix, the known-object Cramer-Rao bound, and Monte Carlo simulations are compared for an extended scene and a point object. It is found that our variance approximation, that incorporates the uncertainty of the object, leads to an improvement in predicting the optimal amount of defocus to use in a phase-diverse wavefront sensor.

Emotion suppression moderates the quadratic association between RSA and executive function

PubMed Central

Spangler, Derek P.; Bell, Martha Ann; Deater-Deckard, Kirby

2016-01-01

There is uncertainty about whether respiratory sinus arrhythmia (RSA), a cardiac marker of adaptive emotion regulation, is involved in relatively low or high executive function performance. In the present study, we investigated: (1) whether RSA during rest and tasks predict both relatively low and high executive function within a larger quadratic association among the two variables, and (2) the extent to which this quadratic trend was moderated by individual differences in emotion regulation. To achieve these aims, a sample of ethnically and socioeconomically diverse women self-reported reappraisal and emotion suppression. They next experienced a two-minute resting period during which ECG was continually assessed. In the next phase, the women completed an array of executive function and non-executive cognitive tasks while ECG was measured throughout. As anticipated, resting RSA showed a quadratic association with executive function that was strongest for high suppression. These results suggest that relatively high resting RSA may predict poor executive function ability when emotion regulation consumes executive control resources needed for ongoing cognitive performance. PMID:26018941

Random regression analyses using B-splines functions to model growth from birth to adult age in Canchim cattle.

PubMed

Baldi, F; Alencar, M M; Albuquerque, L G

2010-12-01

The objective of this work was to estimate covariance functions using random regression models on B-splines functions of animal age, for weights from birth to adult age in Canchim cattle. Data comprised 49,011 records on 2435 females. The model of analysis included fixed effects of contemporary groups, age of dam as quadratic covariable and the population mean trend taken into account by a cubic regression on orthogonal polynomials of animal age. Residual variances were modelled through a step function with four classes. The direct and maternal additive genetic effects, and animal and maternal permanent environmental effects were included as random effects in the model. A total of seventeen analyses, considering linear, quadratic and cubic B-splines functions and up to seven knots, were carried out. B-spline functions of the same order were considered for all random effects. Random regression models on B-splines functions were compared to a random regression model on Legendre polynomials and with a multitrait model. Results from different models of analyses were compared using the REML form of the Akaike Information criterion and Schwarz' Bayesian Information criterion. In addition, the variance components and genetic parameters estimated for each random regression model were also used as criteria to choose the most adequate model to describe the covariance structure of the data. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most adequate to describe the covariance structure of the data. Random regression models using B-spline functions as base functions fitted the data better than Legendre polynomials, especially at mature ages, but higher number of parameters need to be estimated with B-splines functions. © 2010 Blackwell Verlag GmbH.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tom, Nathan; Yu, Yi-Hsiang; Wright, Alan

The focus of this paper is to balance power absorption against structural loading for a novel fixed-bottom oscillating surge wave energy converter in both regular and irregular wave environments. The power-to-load ratio will be evaluated using pseudospectral control (PSC) to determine the optimum power-takeoff (PTO) torque based on a multiterm objective function. This paper extends the pseudospectral optimal control problem to not just maximize the time-averaged absorbed power but also include measures for the surge-foundation force and PTO torque in the optimization. The objective function may now potentially include three competing terms that the optimizer must balance. Separate weighting factorsmore » are attached to the surge-foundation force and PTO control torque that can be used to tune the optimizer performance to emphasize either power absorption or load shedding. To correct the pitch equation of motion, derived from linear hydrodynamic theory, a quadratic-viscous-drag torque has been included in the system dynamics; however, to continue the use of quadratic programming solvers, an iteratively obtained linearized drag coefficient was utilized that provided good accuracy in the predicted pitch motion. Furthermore, the analysis considers the use of a nonideal PTO unit to more accurately evaluate controller performance. The PTO efficiency is not directly included in the objective function but rather the weighting factors are utilized to limit the PTO torque amplitudes, thereby reducing the losses resulting from the bidirectional energy flow through a nonideal PTO. Results from PSC show that shedding a portion of the available wave energy can lead to greater reductions in structural loads, peak-to-average power ratio, and reactive power requirement.« less

Finding the Best Quadratic Approximation of a Function

ERIC Educational Resources Information Center

Yang, Yajun; Gordon, Sheldon P.

2011-01-01

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

Minimizing distortion and internal forces in truss structures by simulated annealing

NASA Technical Reports Server (NTRS)

Kincaid, Rex K.

1989-01-01

Inaccuracies in the length of members and the diameters of joints of large truss reflector backup structures may produce unacceptable levels of surface distortion and member forces. However, if the member lengths and joint diameters can be measured accurately it is possible to configure the members and joints so that root-mean-square (rms) surface error and/or rms member forces is minimized. Following Greene and Haftka (1989) it is assumed that the force vector f is linearly proportional to the member length errors e(sub M) of dimension NMEMB (the number of members) and joint errors e(sub J) of dimension NJOINT (the number of joints), and that the best-fit displacement vector d is a linear function of f. Let NNODES denote the number of positions on the surface of the truss where error influences are measured. The solution of the problem is discussed. To classify, this problem was compared to a similar combinatorial optimization problem. In particular, when only the member length errors are considered, minimizing d(sup 2)(sub rms) is equivalent to the quadratic assignment problem. The quadratic assignment problem is a well known NP-complete problem in operations research literature. Hence minimizing d(sup 2)(sub rms) is is also an NP-complete problem. The focus of the research is the development of a simulated annealing algorithm to reduce d(sup 2)(sub rms). The plausibility of this technique is its recent success on a variety of NP-complete combinatorial optimization problems including the quadratic assignment problem. A physical analogy for simulated annealing is the way liquids freeze and crystallize. All computational experiments were done on a MicroVAX. The two interchange heuristic is very fast but produces widely varying results. The two and three interchange heuristic provides less variability in the final objective function values but runs much more slowly. Simulated annealing produced the best objective function values for every starting configuration and was faster than the two and three interchange heuristic.

Cooperative Solutions in Multi-Person Quadratic Decision Problems: Finite-Horizon and State-Feedback Cost-Cumulant Control Paradigm

DTIC Science & Technology

2007-01-01

CONTRACT NUMBER Problems: Finite -Horizon and State-Feedback Cost-Cumulant Control Paradigm (PREPRINT) 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER...cooperative cost-cumulant control regime for the class of multi-person single-objective decision problems characterized by quadratic random costs and... finite -horizon integral quadratic cost associated with a linear stochastic system . Since this problem formation is parameterized by the number of cost

Concurrent topology optimization for minimization of total mass considering load-carrying capabilities and thermal insulation simultaneously

NASA Astrophysics Data System (ADS)

Long, Kai; Wang, Xuan; Gu, Xianguang

2017-09-01

The present work introduces a novel concurrent optimization formulation to meet the requirements of lightweight design and various constraints simultaneously. Nodal displacement of macrostructure and effective thermal conductivity of microstructure are regarded as the constraint functions, which means taking into account both the load-carrying capabilities and the thermal insulation properties. The effective properties of porous material derived from numerical homogenization are used for macrostructural analysis. Meanwhile, displacement vectors of macrostructures from original and adjoint load cases are used for sensitivity analysis of the microstructure. Design variables in the form of reciprocal functions of relative densities are introduced and used for linearization of the constraint function. The objective function of total mass is approximately expressed by the second order Taylor series expansion. Then, the proposed concurrent optimization problem is solved using a sequential quadratic programming algorithm, by splitting into a series of sub-problems in the form of the quadratic program. Finally, several numerical examples are presented to validate the effectiveness of the proposed optimization method. The various effects including initial designs, prescribed limits of nodal displacement, and effective thermal conductivity on optimized designs are also investigated. An amount of optimized macrostructures and their corresponding microstructures are achieved.

Quadratic forms involving Green's and Robin functions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dubinin, Vladimir N

2009-10-31

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.

Students' Conceptions Supporting Their Symbolization and Meaning of Function Rules

ERIC Educational Resources Information Center

Fonger, Nicole L.; Ellis, Amy; Dogan, Muhammed F.

2016-01-01

This paper explores the nature of students' quantitative reasoning and conceptions of functions supporting their ability to symbolize quadratic function rules, and the meanings students make of these rules. We analyzed middle school students' problem solving activity during a small group teaching experiment (n = 6) emphasizing quadratic growth…

On Asymptotic Behaviour and W 2, p Regularity of Potentials in Optimal Transportation

NASA Astrophysics Data System (ADS)

Liu, Jiakun; Trudinger, Neil S.; Wang, Xu-Jia

2015-03-01

In this paper we study local properties of cost and potential functions in optimal transportation. We prove that in a proper normalization process, the cost function is uniformly smooth and converges locally smoothly to a quadratic cost x · y, while the potential function converges to a quadratic function. As applications we obtain the interior W 2, p estimates and sharp C 1, α estimates for the potentials, which satisfy a Monge-Ampère type equation. The W 2, p estimate was previously proved by Caffarelli for the quadratic transport cost and the associated standard Monge-Ampère equation.

An optimal consumption and investment problem with quadratic utility and negative wealth constraints.

PubMed

Roh, Kum-Hwan; Kim, Ji Yeoun; Shin, Yong Hyun

2017-01-01

In this paper, we investigate the optimal consumption and portfolio selection problem with negative wealth constraints for an economic agent who has a quadratic utility function of consumption and receives a constant labor income. Due to the property of the quadratic utility function, we separate our problem into two cases and derive the closed-form solutions for each case. We also illustrate some numerical implications of the optimal consumption and portfolio.

Sex differences of anthropometric indices of obesity by age among Iranian adults in northern Iran: A predictive regression model.

PubMed

Hajian-Tilaki, Karimollah; Heidari, Behzad

2015-01-01

The biological variation of body mass index (BMI) and waist circumference (WC) with age may vary by gender. The objective of this study was to investigate the functional relationship of anthropometric measures with age and sex. The data were collected from a population-based cross-sectional study of 1800 men and 1800 women aged 20-70 years in northern Iran. The linear and quadratic pattern of age on weight, height, BMI and WC and WHR were tested statistically and the interaction effect of age and gender was also formally tested. The quadratic model (age(2)) provided a significantly better fit than simple linear model for weight, BMI and WC. BMI, WC and weight explained a greater variance using quadratic form for women compared with men (for BMI, R(2)=0.18, p<0.001 vs R(2)=0.059, p<0.001 and for WC, R(2)=0.17, p<0.001 vs R(2)=0.047, p<0.001). For height, there is an inverse linear relationship while for WHR, a positive linear association was apparent by aging, the quadratic form did not add to better fit. These findings indicate the different patterns of weight gain, fat accumulation for visceral adiposity and loss of muscle mass between men and women in the early and middle adulthood.

A tutorial on the LQG/LTR method. [Linear Quadratic Gaussian/Loop Transfer Recovery

NASA Technical Reports Server (NTRS)

Athans, M.

1986-01-01

In this paper the so-called Linear-Quadratic-Gaussian method with Loop-Transfer-Recovery is surveyed. The objective is to provide a pragmatic exposition, with special emphasis on the step-by-step characteristics for designing multivariable feedback control systems.

Hyers-Ulam stability of a generalized Apollonius type quadratic mapping

NASA Astrophysics Data System (ADS)

Park, Chun-Gil; Rassias, Themistocles M.

2006-10-01

Let X,Y be linear spaces. It is shown that if a mapping satisfies the following functional equation: then the mapping is quadratic. We moreover prove the Hyers-Ulam stability of the functional equation (0.1) in Banach spaces.

Optimal control theory (OWEM) applied to a helicopter in the hover and approach phase

NASA Technical Reports Server (NTRS)

Born, G. J.; Kai, T.

1975-01-01

A major difficulty in the practical application of linear-quadratic regulator theory is how to choose the weighting matrices in quadratic cost functions. The control system design with optimal weighting matrices was applied to a helicopter in the hover and approach phase. The weighting matrices were calculated to extremize the closed loop total system damping subject to constraints on the determinants. The extremization is really a minimization of the effects of disturbances, and interpreted as a compromise between the generalized system accuracy and the generalized system response speed. The trade-off between the accuracy and the response speed is adjusted by a single parameter, the ratio of determinants. By this approach an objective measure can be obtained for the design of a control system. The measure is to be determined by the system requirements.

Integration of the Quadratic Function and Generalization

ERIC Educational Resources Information Center

Mitsuma, Kunio

2011-01-01

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

Emotion suppression moderates the quadratic association between RSA and executive function.

PubMed

Spangler, Derek P; Bell, Martha Ann; Deater-Deckard, Kirby

2015-09-01

There is uncertainty about whether respiratory sinus arrhythmia (RSA), a cardiac marker of adaptive emotion regulation, is involved in relatively low or high executive function performance. In the present study, we investigated (a) whether RSA during rest and tasks predict both relatively low and high executive function within a larger quadratic association among the two variables, and (b) the extent to which this quadratic trend was moderated by individual differences in emotion regulation. To achieve these aims, a sample of ethnically and socioeconomically diverse women self-reported reappraisal and emotion suppression. They next experienced a 2-min resting period during which electrocardiogram (ECG) was continually assessed. In the next phase, the women completed an array of executive function and nonexecutive cognitive tasks while ECG was measured throughout. As anticipated, resting RSA showed a quadratic association with executive function that was strongest for high suppression. These results suggest that relatively high resting RSA may predict poor executive function ability when emotion regulation consumes executive control resources needed for ongoing cognitive performance. © 2015 Society for Psychophysiological Research.

An Unexpected Influence on a Quadratic

ERIC Educational Resources Information Center

Davis, Jon D.

2013-01-01

Using technology to explore the coefficients of a quadratic equation can lead to an unexpected result. This article describes an investigation that involves sliders and dynamically linked representations. It guides students to notice the effect that the parameter "a" has on the graphical representation of a quadratic function in the form…

Convexity Conditions and the Legendre-Fenchel Transform for the Product of Finitely Many Positive Definite Quadratic Forms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao Yunbin, E-mail: zhaoyy@maths.bham.ac.u

2010-12-15

While the product of finitely many convex functions has been investigated in the field of global optimization, some fundamental issues such as the convexity condition and the Legendre-Fenchel transform for the product function remain unresolved. Focusing on quadratic forms, this paper is aimed at addressing the question: When is the product of finitely many positive definite quadratic forms convex, and what is the Legendre-Fenchel transform for it? First, we show that the convexity of the product is determined intrinsically by the condition number of so-called 'scaled matrices' associated with quadratic forms involved. The main result claims that if the conditionmore » number of these scaled matrices are bounded above by an explicit constant (which depends only on the number of quadratic forms involved), then the product function is convex. Second, we prove that the Legendre-Fenchel transform for the product of positive definite quadratic forms can be expressed, and the computation of the transform amounts to finding the solution to a system of equations (or equally, finding a Brouwer's fixed point of a mapping) with a special structure. Thus, a broader question than the open 'Question 11' in Hiriart-Urruty (SIAM Rev. 49, 225-273, 2007) is addressed in this paper.« less

Quadratic Frequency Modulation Signals Parameter Estimation Based on Two-Dimensional Product Modified Parameterized Chirp Rate-Quadratic Chirp Rate Distribution.

PubMed

Qu, Zhiyu; Qu, Fuxin; Hou, Changbo; Jing, Fulong

2018-05-19

In an inverse synthetic aperture radar (ISAR) imaging system for targets with complex motion, the azimuth echo signals of the target are always modeled as multicomponent quadratic frequency modulation (QFM) signals. The chirp rate (CR) and quadratic chirp rate (QCR) estimation of QFM signals is very important to solve the ISAR image defocus problem. For multicomponent QFM (multi-QFM) signals, the conventional QR and QCR estimation algorithms suffer from the cross-term and poor anti-noise ability. This paper proposes a novel estimation algorithm called a two-dimensional product modified parameterized chirp rate-quadratic chirp rate distribution (2D-PMPCRD) for QFM signals parameter estimation. The 2D-PMPCRD employs a multi-scale parametric symmetric self-correlation function and modified nonuniform fast Fourier transform-Fast Fourier transform to transform the signals into the chirp rate-quadratic chirp rate (CR-QCR) domains. It can greatly suppress the cross-terms while strengthening the auto-terms by multiplying different CR-QCR domains with different scale factors. Compared with high order ambiguity function-integrated cubic phase function and modified Lv's distribution, the simulation results verify that the 2D-PMPCRD acquires higher anti-noise performance and obtains better cross-terms suppression performance for multi-QFM signals with reasonable computation cost.

A reliable algorithm for optimal control synthesis

NASA Technical Reports Server (NTRS)

Vansteenwyk, Brett; Ly, Uy-Loi

1992-01-01

In recent years, powerful design tools for linear time-invariant multivariable control systems have been developed based on direct parameter optimization. In this report, an algorithm for reliable optimal control synthesis using parameter optimization is presented. Specifically, a robust numerical algorithm is developed for the evaluation of the H(sup 2)-like cost functional and its gradients with respect to the controller design parameters. The method is specifically designed to handle defective degenerate systems and is based on the well-known Pade series approximation of the matrix exponential. Numerical test problems in control synthesis for simple mechanical systems and for a flexible structure with densely packed modes illustrate positively the reliability of this method when compared to a method based on diagonalization. Several types of cost functions have been considered: a cost function for robust control consisting of a linear combination of quadratic objectives for deterministic and random disturbances, and one representing an upper bound on the quadratic objective for worst case initial conditions. Finally, a framework for multivariable control synthesis has been developed combining the concept of closed-loop transfer recovery with numerical parameter optimization. The procedure enables designers to synthesize not only observer-based controllers but also controllers of arbitrary order and structure. Numerical design solutions rely heavily on the robust algorithm due to the high order of the synthesis model and the presence of near-overlapping modes. The design approach is successfully applied to the design of a high-bandwidth control system for a rotorcraft.

The Effects of an Undergraduate Algebra Course on Prospective Middle School Teachers' Understanding of Functions, Especially Quadratic Functions

ERIC Educational Resources Information Center

Duarte, Jonathan T.

2010-01-01

Although current reform movements have stressed the importance of developing prospective middle school mathematics teachers' subject matter knowledge and understandings, there is a dearth of research studies with regard to prospective middle school teachers' confidence and knowledge with respect to quadratic functions. This study was intended to…

Balancing Power Absorption Against Structural Loads With Viscous Drag and Power-Takeoff Efficiency Considerations

DOE PAGES

Tom, Nathan; Yu, Yi-Hsiang; Wright, Alan; ...

2017-11-17

The focus of this paper is to balance power absorption against structural loading for a novel fixed-bottom oscillating surge wave energy converter in both regular and irregular wave environments. The power-to-load ratio will be evaluated using pseudospectral control (PSC) to determine the optimum power-takeoff (PTO) torque based on a multiterm objective function. This paper extends the pseudospectral optimal control problem to not just maximize the time-averaged absorbed power but also include measures for the surge-foundation force and PTO torque in the optimization. The objective function may now potentially include three competing terms that the optimizer must balance. Separate weighting factorsmore » are attached to the surge-foundation force and PTO control torque that can be used to tune the optimizer performance to emphasize either power absorption or load shedding. To correct the pitch equation of motion, derived from linear hydrodynamic theory, a quadratic-viscous-drag torque has been included in the system dynamics; however, to continue the use of quadratic programming solvers, an iteratively obtained linearized drag coefficient was utilized that provided good accuracy in the predicted pitch motion. Furthermore, the analysis considers the use of a nonideal PTO unit to more accurately evaluate controller performance. The PTO efficiency is not directly included in the objective function but rather the weighting factors are utilized to limit the PTO torque amplitudes, thereby reducing the losses resulting from the bidirectional energy flow through a nonideal PTO. Results from PSC show that shedding a portion of the available wave energy can lead to greater reductions in structural loads, peak-to-average power ratio, and reactive power requirement.« less

A parametric LQ approach to multiobjective control system design

NASA Technical Reports Server (NTRS)

Kyr, Douglas E.; Buchner, Marc

1988-01-01

The synthesis of a constant parameter output feedback control law of constrained structure is set in a multiple objective linear quadratic regulator (MOLQR) framework. The use of intuitive objective functions such as model-following ability and closed-loop trajectory sensitivity, allow multiple objective decision making techniques, such as the surrogate worth tradeoff method, to be applied. For the continuous-time deterministic problem with an infinite time horizon, dynamic compensators as well as static output feedback controllers can be synthesized using a descent Anderson-Moore algorithm modified to impose linear equality constraints on the feedback gains by moving in feasible directions. Results of three different examples are presented, including a unique reformulation of the sensitivity reduction problem.

Excited-state absorption in tetrapyridyl porphyrins: comparing real-time and quadratic-response time-dependent density functional theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bowman, David N.; Asher, Jason C.; Fischer, Sean A.

2017-01-01

Threemeso-substituted tetrapyridyl porphyrins (free base, Ni(ii), and Cu(ii)) were investigated for their optical limiting (OL) capabilities using real-time (RT-), linear-response (LR-), and quadratic-response (QR-) time-dependent density functional theory (TDDFT) methods.

AQMAN; linear and quadratic programming matrix generator using two-dimensional ground-water flow simulation for aquifer management modeling

USGS Publications Warehouse

Lefkoff, L.J.; Gorelick, S.M.

1987-01-01

A FORTRAN-77 computer program code that helps solve a variety of aquifer management problems involving the control of groundwater hydraulics. It is intended for use with any standard mathematical programming package that uses Mathematical Programming System input format. The computer program creates the input files to be used by the optimization program. These files contain all the hydrologic information and management objectives needed to solve the management problem. Used in conjunction with a mathematical programming code, the computer program identifies the pumping or recharge strategy that achieves a user 's management objective while maintaining groundwater hydraulic conditions within desired limits. The objective may be linear or quadratic, and may involve the minimization of pumping and recharge rates or of variable pumping costs. The problem may contain constraints on groundwater heads, gradients, and velocities for a complex, transient hydrologic system. Linear superposition of solutions to the transient, two-dimensional groundwater flow equation is used by the computer program in conjunction with the response matrix optimization method. A unit stress is applied at each decision well and transient responses at all control locations are computed using a modified version of the U.S. Geological Survey two dimensional aquifer simulation model. The program also computes discounted cost coefficients for the objective function and accounts for transient aquifer conditions. (Author 's abstract)

Optimization of Spinal Muscular Atrophy subject's muscle activity during gait

NASA Astrophysics Data System (ADS)

Umat, Gazlia; Rambely, Azmin Sham

2014-06-01

Spinal Muscular Atrophy (SMA) is a hereditary disease related muscle nerve disorder caused by degeneration of the anterior cells of the spinal cord. SMA is divided into four types according to the degree of seriousness. SMA patients show different gait with normal people. Therefore, this study focused on the effects of SMA patient muscle actions and the difference that exists between SMA subjects and normal subjects. Therefore, the electromyography (EMG) test will be used to track the behavior of muscle during walking and optimization methods are used to get the muscle stress that is capable of doing the work while walking. Involved objective function is non-linear function of the quadratic and cubic functions. The study concludes with a comparison of the objective function using the force that sought to use the moment of previous studies and the objective function using the data obtained from EMG. The results shows that the same muscles, peroneus longus and bisepsfemoris, were used during walking activity by SMA subjects and control subjects. Muscle stress force best solution achieved from part D in simulation carried out.

An Algebraic Approach for Solving Quadratic Inequalities

ERIC Educational Resources Information Center

Mahmood, Munir; Al-Mirbati, Rudaina

2017-01-01

In recent years most text books utilise either the sign chart or graphing functions in order to solve a quadratic inequality of the form ax[superscript 2] + bx + c < 0 This article demonstrates an algebraic approach to solve the above inequality. To solve a quadratic inequality in the form of ax[superscript 2] + bx + c < 0 or in the…

Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning.

PubMed

Gorban, A N; Mirkes, E M; Zinovyev, A

2016-12-01

Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including high sensitivity to contaminating factors and dimensionality curse. Therefore, a lot of recent applications in machine learning exploited properties of non-quadratic error functionals based on L 1 norm or even sub-linear potentials corresponding to quasinorms L p (0

The application of nonlinear programming and collocation to optimal aeroassisted orbital transfers

NASA Astrophysics Data System (ADS)

Shi, Y. Y.; Nelson, R. L.; Young, D. H.; Gill, P. E.; Murray, W.; Saunders, M. A.

1992-01-01

Sequential quadratic programming (SQP) and collocation of the differential equations of motion were applied to optimal aeroassisted orbital transfers. The Optimal Trajectory by Implicit Simulation (OTIS) computer program codes with updated nonlinear programming code (NZSOL) were used as a testbed for the SQP nonlinear programming (NLP) algorithms. The state-of-the-art sparse SQP method is considered to be effective for solving large problems with a sparse matrix. Sparse optimizers are characterized in terms of memory requirements and computational efficiency. For the OTIS problems, less than 10 percent of the Jacobian matrix elements are nonzero. The SQP method encompasses two phases: finding an initial feasible point by minimizing the sum of infeasibilities and minimizing the quadratic objective function within the feasible region. The orbital transfer problem under consideration involves the transfer from a high energy orbit to a low energy orbit.

A duality theorem-based algorithm for inexact quadratic programming problems: Application to waste management under uncertainty

NASA Astrophysics Data System (ADS)

Kong, X. M.; Huang, G. H.; Fan, Y. R.; Li, Y. P.

2016-04-01

In this study, a duality theorem-based algorithm (DTA) for inexact quadratic programming (IQP) is developed for municipal solid waste (MSW) management under uncertainty. It improves upon the existing numerical solution method for IQP problems. The comparison between DTA and derivative algorithm (DAM) shows that the DTA method provides better solutions than DAM with lower computational complexity. It is not necessary to identify the uncertain relationship between the objective function and decision variables, which is required for the solution process of DAM. The developed method is applied to a case study of MSW management and planning. The results indicate that reasonable solutions have been generated for supporting long-term MSW management and planning. They could provide more information as well as enable managers to make better decisions to identify desired MSW management policies in association with minimized cost under uncertainty.

Sinogram restoration in computed tomography with an edge-preserving penalty

PubMed Central

Little, Kevin J.; La Rivière, Patrick J.

2015-01-01

Purpose: With the goal of producing a less computationally intensive alternative to fully iterative penalized-likelihood image reconstruction, our group has explored the use of penalized-likelihood sinogram restoration for transmission tomography. Previously, we have exclusively used a quadratic penalty in our restoration objective function. However, a quadratic penalty does not excel at preserving edges while reducing noise. Here, we derive a restoration update equation for nonquadratic penalties. Additionally, we perform a feasibility study to extend our sinogram restoration method to a helical cone-beam geometry and clinical data. Methods: A restoration update equation for nonquadratic penalties is derived using separable parabolic surrogates (SPS). A method for calculating sinogram degradation coefficients for a helical cone-beam geometry is proposed. Using simulated data, sinogram restorations are performed using both a quadratic penalty and the edge-preserving Huber penalty. After sinogram restoration, Fourier-based analytical methods are used to obtain reconstructions, and resolution-noise trade-offs are investigated. For the fan-beam geometry, a comparison is made to image-domain SPS reconstruction using the Huber penalty. The effects of varying object size and contrast are also investigated. For the helical cone-beam geometry, we investigate the effect of helical pitch (axial movement/rotation). Huber-penalty sinogram restoration is performed on 3D clinical data, and the reconstructed images are compared to those generated with no restoration. Results: We find that by applying the edge-preserving Huber penalty to our sinogram restoration methods, the reconstructed image has a better resolution-noise relationship than an image produced using a quadratic penalty in the sinogram restoration. However, we find that this relatively straightforward approach to edge preservation in the sinogram domain is affected by the physical size of imaged objects in addition to the contrast across the edge. This presents some disadvantages of this method relative to image-domain edge-preserving methods, although the computational burden of the sinogram-domain approach is much lower. For a helical cone-beam geometry, we found applying sinogram restoration in 3D was reasonable and that pitch did not make a significant difference in the general effect of sinogram restoration. The application of Huber-penalty sinogram restoration to clinical data resulted in a reconstruction with less noise while retaining resolution. Conclusions: Sinogram restoration with the Huber penalty is able to provide better resolution-noise performance than restoration with a quadratic penalty. Additionally, sinogram restoration with the Huber penalty is feasible for helical cone-beam CT and can be applied to clinical data. PMID:25735286

Sinogram restoration in computed tomography with an edge-preserving penalty

DOE Office of Scientific and Technical Information (OSTI.GOV)

Little, Kevin J., E-mail: little@uchicago.edu; La Rivière, Patrick J.

2015-03-15

Purpose: With the goal of producing a less computationally intensive alternative to fully iterative penalized-likelihood image reconstruction, our group has explored the use of penalized-likelihood sinogram restoration for transmission tomography. Previously, we have exclusively used a quadratic penalty in our restoration objective function. However, a quadratic penalty does not excel at preserving edges while reducing noise. Here, we derive a restoration update equation for nonquadratic penalties. Additionally, we perform a feasibility study to extend our sinogram restoration method to a helical cone-beam geometry and clinical data. Methods: A restoration update equation for nonquadratic penalties is derived using separable parabolic surrogatesmore » (SPS). A method for calculating sinogram degradation coefficients for a helical cone-beam geometry is proposed. Using simulated data, sinogram restorations are performed using both a quadratic penalty and the edge-preserving Huber penalty. After sinogram restoration, Fourier-based analytical methods are used to obtain reconstructions, and resolution-noise trade-offs are investigated. For the fan-beam geometry, a comparison is made to image-domain SPS reconstruction using the Huber penalty. The effects of varying object size and contrast are also investigated. For the helical cone-beam geometry, we investigate the effect of helical pitch (axial movement/rotation). Huber-penalty sinogram restoration is performed on 3D clinical data, and the reconstructed images are compared to those generated with no restoration. Results: We find that by applying the edge-preserving Huber penalty to our sinogram restoration methods, the reconstructed image has a better resolution-noise relationship than an image produced using a quadratic penalty in the sinogram restoration. However, we find that this relatively straightforward approach to edge preservation in the sinogram domain is affected by the physical size of imaged objects in addition to the contrast across the edge. This presents some disadvantages of this method relative to image-domain edge-preserving methods, although the computational burden of the sinogram-domain approach is much lower. For a helical cone-beam geometry, we found applying sinogram restoration in 3D was reasonable and that pitch did not make a significant difference in the general effect of sinogram restoration. The application of Huber-penalty sinogram restoration to clinical data resulted in a reconstruction with less noise while retaining resolution. Conclusions: Sinogram restoration with the Huber penalty is able to provide better resolution-noise performance than restoration with a quadratic penalty. Additionally, sinogram restoration with the Huber penalty is feasible for helical cone-beam CT and can be applied to clinical data.« less

This is SPIRAL-TAP: Sparse Poisson Intensity Reconstruction ALgorithms--theory and practice.

PubMed

Harmany, Zachary T; Marcia, Roummel F; Willett, Rebecca M

2012-03-01

Observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise model. As a result, accurate reconstruction of a spatially or temporally distributed phenomenon (f*) from Poisson data (y) cannot be effectively accomplished by minimizing a conventional penalized least-squares objective function. The problem addressed in this paper is the estimation of f* from y in an inverse problem setting, where the number of unknowns may potentially be larger than the number of observations and f* admits sparse approximation. The optimization formulation considered in this paper uses a penalized negative Poisson log-likelihood objective function with nonnegativity constraints (since Poisson intensities are naturally nonnegative). In particular, the proposed approach incorporates key ideas of using separable quadratic approximations to the objective function at each iteration and penalization terms related to l1 norms of coefficient vectors, total variation seminorms, and partition-based multiscale estimation methods.

A methodology to find the elementary landscape decomposition of combinatorial optimization problems.

PubMed

Chicano, Francisco; Whitley, L Darrell; Alba, Enrique

2011-01-01

A small number of combinatorial optimization problems have search spaces that correspond to elementary landscapes, where the objective function f is an eigenfunction of the Laplacian that describes the neighborhood structure of the search space. Many problems are not elementary; however, the objective function of a combinatorial optimization problem can always be expressed as a superposition of multiple elementary landscapes if the underlying neighborhood used is symmetric. This paper presents theoretical results that provide the foundation for algebraic methods that can be used to decompose the objective function of an arbitrary combinatorial optimization problem into a sum of subfunctions, where each subfunction is an elementary landscape. Many steps of this process can be automated, and indeed a software tool could be developed that assists the researcher in finding a landscape decomposition. This methodology is then used to show that the subset sum problem is a superposition of two elementary landscapes, and to show that the quadratic assignment problem is a superposition of three elementary landscapes.

The eigenfrequency spectrum of linear magnetohydrodynamic perturbations in stationary equilibria: A variational principle

NASA Astrophysics Data System (ADS)

Andries, Jesse

2010-11-01

The frequencies of the normal modes of oscillation of linear magnetohydrodynamic perturbations of a stationary equilibrium are related to the stationary points of a quadratic functional over the Hilbert space of Lagrangian displacement vectors, which is subject to a constraint. In the absence of a background flow (or of a uniform flow), the relation reduces to the well-known Rayleigh-Ritz variational principle. In contrast to the existing variational principles for perturbations of stationary equilibria, the present treatment does neither impose additional symmetry restrictions on the equilibrium, nor does it involve the generalization to bilinear functionals instead of quadratic forms. This allows a more natural interpretation of the quadratic forms as energy functionals.

Permutation flow-shop scheduling problem to optimize a quadratic objective function

NASA Astrophysics Data System (ADS)

Ren, Tao; Zhao, Peng; Zhang, Da; Liu, Bingqian; Yuan, Huawei; Bai, Danyu

2017-09-01

A flow-shop scheduling model enables appropriate sequencing for each job and for processing on a set of machines in compliance with identical processing orders. The objective is to achieve a feasible schedule for optimizing a given criterion. Permutation is a special setting of the model in which the processing order of the jobs on the machines is identical for each subsequent step of processing. This article addresses the permutation flow-shop scheduling problem to minimize the criterion of total weighted quadratic completion time. With a probability hypothesis, the asymptotic optimality of the weighted shortest processing time schedule under a consistency condition (WSPT-CC) is proven for sufficiently large-scale problems. However, the worst case performance ratio of the WSPT-CC schedule is the square of the number of machines in certain situations. A discrete differential evolution algorithm, where a new crossover method with multiple-point insertion is used to improve the final outcome, is presented to obtain high-quality solutions for moderate-scale problems. A sequence-independent lower bound is designed for pruning in a branch-and-bound algorithm for small-scale problems. A set of random experiments demonstrates the performance of the lower bound and the effectiveness of the proposed algorithms.

The wave function and minimum uncertainty function of the bound quadratic Hamiltonian system

NASA Technical Reports Server (NTRS)

Yeon, Kyu Hwang; Um, Chung IN; George, T. F.

1994-01-01

The bound quadratic Hamiltonian system is analyzed explicitly on the basis of quantum mechanics. We have derived the invariant quantity with an auxiliary equation as the classical equation of motion. With the use of this invariant it can be determined whether or not the system is bound. In bound system we have evaluated the exact eigenfunction and minimum uncertainty function through unitary transformation.

A Pair of Resonance Stripe Solitons and Lump Solutions to a Reduced (3+1)-Dimensional Nonlinear Evolution Equation

NASA Astrophysics Data System (ADS)

Chen, Mei-Dan; Li, Xian; Wang, Yao; Li, Biao

2017-06-01

With symbolic computation, some lump solutions are presented to a (3+1)-dimensional nonlinear evolution equation by searching the positive quadratic function from the Hirota bilinear form of equation. The quadratic function contains six free parameters, four of which satisfy two determinant conditions guaranteeing analyticity and rational localization of the solutions, while the others are free. Then, by combining positive quadratic function with exponential function, the interaction solutions between lump solutions and the stripe solitons are presented on the basis of some conditions. Furthermore, we extend this method to obtain more general solutions by combining of positive quadratic function and hyperbolic cosine function. Thus the interaction solutions between lump solutions and a pair of resonance stripe solitons are derived and asymptotic property of the interaction solutions are analyzed under some specific conditions. Finally, the dynamic properties of these solutions are shown in figures by choosing the values of the parameters. Supported by National Natural Science Foundation of China under Grant Nos. 11271211, 11275072, and 11435005, Ningbo Natural Science Foundation under Grant No. 2015A610159 and the Opening Project of Zhejiang Provincial Top Key Discipline of Physics Sciences in Ningbo University under Grant No. xkzw11502 and K.C. Wong Magna Fund in Ningbo University

Failures and Inabilities of High School Students about Quadratic Equations and Functions

ERIC Educational Resources Information Center

Memnun, Dilek Sezgin; Aydin, Bünyamin; Dinç, Emre; Çoban, Merve; Sevindik, Fatma

2015-01-01

In this research study, it was aimed to examine failures and inabilities of eleventh grade students about quadratic equations and functions. For this purpose, these students were asked ten open-ended questions. The analysis of the answers given by the students to these questions indicated that a significant part of these students had failures and…

Differentiated Learning Environment--A Classroom for Quadratic Equation, Function and Graphs

ERIC Educational Resources Information Center

Dinç, Emre

2017-01-01

This paper will cover the design of a learning environment as a classroom regarding the Quadratic Equations, Functions and Graphs. The goal of the learning environment offered in the paper is to design a classroom where students will enjoy the process, use their skills they already have during the learning process, control and plan their learning…

Optimal control of LQG problem with an explicit trade-off between mean and variance

NASA Astrophysics Data System (ADS)

Qian, Fucai; Xie, Guo; Liu, Ding; Xie, Wenfang

2011-12-01

For discrete-time linear-quadratic Gaussian (LQG) control problems, a utility function on the expectation and the variance of the conventional performance index is considered. The utility function is viewed as an overall objective of the system and can perform the optimal trade-off between the mean and the variance of performance index. The nonlinear utility function is first converted into an auxiliary parameters optimisation problem about the expectation and the variance. Then an optimal closed-loop feedback controller for the nonseparable mean-variance minimisation problem is designed by nonlinear mathematical programming. Finally, simulation results are given to verify the algorithm's effectiveness obtained in this article.

Polynomials to model the growth of young bulls in performance tests.

PubMed

Scalez, D C B; Fragomeni, B O; Passafaro, T L; Pereira, I G; Toral, F L B

2014-03-01

The use of polynomial functions to describe the average growth trajectory and covariance functions of Nellore and MA (21/32 Charolais+11/32 Nellore) young bulls in performance tests was studied. The average growth trajectories and additive genetic and permanent environmental covariance functions were fit with Legendre (linear through quintic) and quadratic B-spline (with two to four intervals) polynomials. In general, the Legendre and quadratic B-spline models that included more covariance parameters provided a better fit with the data. When comparing models with the same number of parameters, the quadratic B-spline provided a better fit than the Legendre polynomials. The quadratic B-spline with four intervals provided the best fit for the Nellore and MA groups. The fitting of random regression models with different types of polynomials (Legendre polynomials or B-spline) affected neither the genetic parameters estimates nor the ranking of the Nellore young bulls. However, fitting different type of polynomials affected the genetic parameters estimates and the ranking of the MA young bulls. Parsimonious Legendre or quadratic B-spline models could be used for genetic evaluation of body weight of Nellore young bulls in performance tests, whereas these parsimonious models were less efficient for animals of the MA genetic group owing to limited data at the extreme ages.

Development of C++ Application Program for Solving Quadratic Equation in Elementary School in Nigeria

ERIC Educational Resources Information Center

Bandele, Samuel Oye; Adekunle, Adeyemi Suraju

2015-01-01

The study was conducted to design, develop and test a c++ application program CAP-QUAD for solving quadratic equation in elementary school in Nigeria. The package was developed in c++ using object-oriented programming language, other computer program that were also utilized during the development process is DevC++ compiler, it was used for…

Design of an all-optical fractional-order differentiator with terahertz bandwidth based on a fiber Bragg grating in transmission.

PubMed

Liu, Xin; Shu, Xuewen

2017-08-20

All-optical fractional-order temporal differentiators with bandwidths reaching terahertz (THz) values are demonstrated with transmissive fiber Bragg gratings. Since the designed fractional-order differentiator is a minimum phase function, the reflective phase of the designed function can be chosen arbitrarily. As examples, we first design several 0.5th-order differentiators with bandwidths reaching the THz range for comparison. The reflective phases of the 0.5th-order differentiators are chosen to be linear phase, quadratic phase, cubic phase, and biquadratic phase, respectively. We find that both the maximum coupling coefficient and the spatial resolution of the designed grating increase when the reflective phase varies from quadratic function to cubic function to biquadratic function. Furthermore, when the reflective phase is chosen to be a quadratic function, the obtained grating coupling coefficient and period are more likely to be achieved in practice. Then we design fractional-order differentiators with different orders when the reflective phase is chosen to be a quadratic function. We see that when the designed order of the differentiator increases, the obtained maximum coupling coefficient also increases while the oscillation of the coupling coefficient decreases. Finally, we give the numerical performance of the designed 0.5th-order differentiator by showing its temporal response and calculating its cross-correlation coefficient.

Chaotic simulated annealing by a neural network with a variable delay: design and application.

PubMed

Chen, Shyan-Shiou

2011-10-01

In this paper, we have three goals: the first is to delineate the advantages of a variably delayed system, the second is to find a more intuitive Lyapunov function for a delayed neural network, and the third is to design a delayed neural network for a quadratic cost function. For delayed neural networks, most researchers construct a Lyapunov function based on the linear matrix inequality (LMI) approach. However, that approach is not intuitive. We provide a alternative candidate Lyapunov function for a delayed neural network. On the other hand, if we are first given a quadratic cost function, we can construct a delayed neural network by suitably dividing the second-order term into two parts: a self-feedback connection weight and a delayed connection weight. To demonstrate the advantage of a variably delayed neural network, we propose a transiently chaotic neural network with variable delay and show numerically that the model should possess a better searching ability than Chen-Aihara's model, Wang's model, and Zhao's model. We discuss both the chaotic and the convergent phases. During the chaotic phase, we simply present bifurcation diagrams for a single neuron with a constant delay and with a variable delay. We show that the variably delayed model possesses the stochastic property and chaotic wandering. During the convergent phase, we not only provide a novel Lyapunov function for neural networks with a delay (the Lyapunov function is independent of the LMI approach) but also establish a correlation between the Lyapunov function for a delayed neural network and an objective function for the traveling salesman problem. © 2011 IEEE

Nonlinear response from transport theory and quantum field theory at finite temperature

NASA Astrophysics Data System (ADS)

Carrington, M. E.; Defu, Hou; Kobes, R.

2001-07-01

We study the nonlinear response in weakly coupled hot φ4 theory. We obtain an expression for a quadratic shear viscous response coefficient using two different formalisms: transport theory and response theory. The transport theory calculation is done by assuming a local equilibrium form for the distribution function and expanding in the gradient of the local four dimensional velocity field. By performing a Chapman-Enskog expansion on the Boltzmann equation we obtain a hierarchy of equations for the coefficients of the expanded distribution function. To do the response theory calculation we use Zubarev's techniques in nonequilibrium statistical mechanics to derive a generalized Kubo formula. Using this formula allows us to obtain the quadratic shear viscous response from the three-point retarded Green function of the viscous shear stress tensor. We use the closed time path formalism of real time finite temperature field theory to show that this three-point function can be calculated by writing it as an integral equation involving a four-point vertex. This four-point vertex can in turn be obtained from an integral equation which represents the resummation of an infinite series of ladder and extended-ladder diagrams. The connection between transport theory and response theory is made when we show that the integral equation for this four-point vertex has exactly the same form as the equation obtained from the Boltzmann equation for the coefficient of the quadratic term of the gradient expansion of the distribution function. We conclude that calculating the quadratic shear viscous response using transport theory and keeping terms that are quadratic in the gradient of the velocity field in the Chapman-Enskog expansion of the Boltzmann equation is equivalent to calculating the quadratic shear viscous response from response theory using the next-to-linear response Kubo formula, with a vertex given by an infinite resummation of ladder and extended-ladder diagrams.

Exploring Quadratic Functions with Logger "Pro"

ERIC Educational Resources Information Center

Pope, Derek

2018-01-01

The author shares the lesson that he used to introduce the quadratic unit to students in an extended second-year algebra class, demonstrate why it was appropriate for his struggling learners, and discuss possible future modifications to this lesson.

A class of finite-time dual neural networks for solving quadratic programming problems and its k-winners-take-all application.

PubMed

Li, Shuai; Li, Yangming; Wang, Zheng

2013-03-01

This paper presents a class of recurrent neural networks to solve quadratic programming problems. Different from most existing recurrent neural networks for solving quadratic programming problems, the proposed neural network model converges in finite time and the activation function is not required to be a hard-limiting function for finite convergence time. The stability, finite-time convergence property and the optimality of the proposed neural network for solving the original quadratic programming problem are proven in theory. Extensive simulations are performed to evaluate the performance of the neural network with different parameters. In addition, the proposed neural network is applied to solving the k-winner-take-all (k-WTA) problem. Both theoretical analysis and numerical simulations validate the effectiveness of our method for solving the k-WTA problem. Copyright © 2012 Elsevier Ltd. All rights reserved.

Characterization of a Quadratic Function in Rn

ERIC Educational Resources Information Center

Xu, Conway

2010-01-01

It is proved that a scalar-valued function "f"(x) defined in "n"-dimensional space must be quadratic, if the intersection of tangent planes at x[subscript 1] and x[subscript 2] always contains the midpoint of the line joining x[subscript 1] and x[subscript 2]. This is the converse of a result of Stenlund proved in this JOURNAL in 2001.

Minitrack tracking function description, volume 2

NASA Technical Reports Server (NTRS)

Englar, T. S.; Mango, S. A.; Roettcher, C. A.; Watters, D. L.

1973-01-01

The minitrack tracking function is described and specific operations are identified. The subjects discussed are: (1) preprocessor listing, (2) minitrack hardware, (3) system calibration, (4) quadratic listing, and (5) quadratic flow diagram. Detailed information is provided on the construction of the tracking system and its operation. The calibration procedures are supported by mathematical models to show the application of the computer programs.

Convergence analysis of evolutionary algorithms that are based on the paradigm of information geometry.

PubMed

Beyer, Hans-Georg

2014-01-01

The convergence behaviors of so-called natural evolution strategies (NES) and of the information-geometric optimization (IGO) approach are considered. After a review of the NES/IGO ideas, which are based on information geometry, the implications of this philosophy w.r.t. optimization dynamics are investigated considering the optimization performance on the class of positive quadratic objective functions (the ellipsoid model). Exact differential equations describing the approach to the optimizer are derived and solved. It is rigorously shown that the original NES philosophy optimizing the expected value of the objective functions leads to very slow (i.e., sublinear) convergence toward the optimizer. This is the real reason why state of the art implementations of IGO algorithms optimize the expected value of transformed objective functions, for example, by utility functions based on ranking. It is shown that these utility functions are localized fitness functions that change during the IGO flow. The governing differential equations describing this flow are derived. In the case of convergence, the solutions to these equations exhibit an exponentially fast approach to the optimizer (i.e., linear convergence order). Furthermore, it is proven that the IGO philosophy leads to an adaptation of the covariance matrix that equals in the asymptotic limit-up to a scalar factor-the inverse of the Hessian of the objective function considered.

Structure-adaptive CBCT reconstruction using weighted total variation and Hessian penalties

PubMed Central

Shi, Qi; Sun, Nanbo; Sun, Tao; Wang, Jing; Tan, Shan

2016-01-01

The exposure of normal tissues to high radiation during cone-beam CT (CBCT) imaging increases the risk of cancer and genetic defects. Statistical iterative algorithms with the total variation (TV) penalty have been widely used for low dose CBCT reconstruction, with state-of-the-art performance in suppressing noise and preserving edges. However, TV is a first-order penalty and sometimes leads to the so-called staircase effect, particularly over regions with smooth intensity transition in the reconstruction images. A second-order penalty known as the Hessian penalty was recently used to replace TV to suppress the staircase effect in CBCT reconstruction at the cost of slightly blurring object edges. In this study, we proposed a new penalty, the TV-H, which combines TV and Hessian penalties for CBCT reconstruction in a structure-adaptive way. The TV-H penalty automatically differentiates the edges, gradual transition and uniform local regions within an image using the voxel gradient, and adaptively weights TV and Hessian according to the local image structures in the reconstruction process. Our proposed penalty retains the benefits of TV, including noise suppression and edge preservation. It also maintains the structures in regions with gradual intensity transition more successfully. A majorization-minimization (MM) approach was designed to optimize the objective energy function constructed with the TV-H penalty. The MM approach employed a quadratic upper bound of the original objective function, and the original optimization problem was changed to a series of quadratic optimization problems, which could be efficiently solved using the Gauss-Seidel update strategy. We tested the reconstruction algorithm on two simulated digital phantoms and two physical phantoms. Our experiments indicated that the TV-H penalty visually and quantitatively outperformed both TV and Hessian penalties. PMID:27699100

Structure-adaptive CBCT reconstruction using weighted total variation and Hessian penalties.

PubMed

Shi, Qi; Sun, Nanbo; Sun, Tao; Wang, Jing; Tan, Shan

2016-09-01

The exposure of normal tissues to high radiation during cone-beam CT (CBCT) imaging increases the risk of cancer and genetic defects. Statistical iterative algorithms with the total variation (TV) penalty have been widely used for low dose CBCT reconstruction, with state-of-the-art performance in suppressing noise and preserving edges. However, TV is a first-order penalty and sometimes leads to the so-called staircase effect, particularly over regions with smooth intensity transition in the reconstruction images. A second-order penalty known as the Hessian penalty was recently used to replace TV to suppress the staircase effect in CBCT reconstruction at the cost of slightly blurring object edges. In this study, we proposed a new penalty, the TV-H, which combines TV and Hessian penalties for CBCT reconstruction in a structure-adaptive way. The TV-H penalty automatically differentiates the edges, gradual transition and uniform local regions within an image using the voxel gradient, and adaptively weights TV and Hessian according to the local image structures in the reconstruction process. Our proposed penalty retains the benefits of TV, including noise suppression and edge preservation. It also maintains the structures in regions with gradual intensity transition more successfully. A majorization-minimization (MM) approach was designed to optimize the objective energy function constructed with the TV-H penalty. The MM approach employed a quadratic upper bound of the original objective function, and the original optimization problem was changed to a series of quadratic optimization problems, which could be efficiently solved using the Gauss-Seidel update strategy. We tested the reconstruction algorithm on two simulated digital phantoms and two physical phantoms. Our experiments indicated that the TV-H penalty visually and quantitatively outperformed both TV and Hessian penalties.

Understanding squeezing of quantum states with the Wigner function

NASA Technical Reports Server (NTRS)

Royer, Antoine

1994-01-01

The Wigner function is argued to be the only natural phase space function evolving classically under quadratic Hamiltonians with time-dependent bilinear part. This is used to understand graphically how certain quadratic time-dependent Hamiltonians induce squeezing of quantum states. The Wigner representation is also used to generalize Ehrenfest's theorem to the quantum uncertainties. This makes it possible to deduce features of the quantum evolution, such as squeezing, from the classical evolution, whatever the Hamiltonian.

Phonation threshold pressure across the pitch range: preliminary test of a model.

PubMed

Solomon, Nancy Pearl; Ramanathan, Pradeep; Makashay, Matthew J

2007-09-01

This study sought to examine the specific relationship between phonation threshold pressure (PTP) and voice fundamental frequency (F(0)) across the pitch range. A published theoretical model of this relationship described a quadratic equation, with PTP increasing exponentially with F(0). Prospective data from eight adults with normal, untrained voices were collected. Subjects produced their quietest phonation at 10 randomly ordered pitches from 5% to 95% of their semitone pitch range at 10% intervals. Analysis included curve fitting for individual and group data, as well as comparisons to the previous model. The group data fit a quadratic function similar to that proposed previously, but the specific quadratic coefficient and constant values differed. Four of the individual subjects' data were best fit by quartic functions, two by quadratic functions, and one by a linear function. This preliminary study indicates that PTP may be minimal at a "comfortable" pitch rather than the lowest pitch tested, and that, for some individuals, PTP may be slightly elevated during the passaggio between modal and falsetto vocal registers. These data support the general form of the theoretical PTP-F(0) function for these speakers, and indicate the possibility of potential refinements to the model. Future studies with larger groups of male and female subjects across a wider age range may eventually reveal the specific nature of the function.

Removal of jitter noise in 3D shape recovery from image focus by using Kalman filter.

PubMed

Jang, Hoon-Seok; Muhammad, Mannan Saeed; Choi, Tae-Sun

2018-02-01

In regard to Shape from Focus, one critical factor impacting system application is mechanical vibration of the translational stage causing jitter noise along the optical axis. This noise is not detectable by simply observing the image. However, when focus measures are applied, inaccuracies in the depth occur. In this article, jitter noise and focus curves are modeled by Gaussian distribution and quadratic function, respectively. Then Kalman filter is designed and applied to eliminate this noise in the focus curves, as a post-processing step after the focus measure application. Experiments are implemented with simulated objects and real objects to show usefulness of proposed algorithm. © 2017 Wiley Periodicals, Inc.

Effect of dietary supplementation of Lactobacillus-fermented Artemisia princeps on growth performance, meat lipid peroxidation, and intestinal microflora in Hy-line Brown male chickens.

PubMed

Kim, C H; Kim, G-B; Chang, M B; Bae, G S; Paik, I K; Kil, D Y

2012-11-01

The objective of this experiment was to investigate the effect of dietary supplementation of Lactobacillus-fermented Artemisia princeps (LFA) on growth performance, meat lipid peroxidation, and intestinal microflora in Hy-line Brown male chickens. A total of six hundred twenty-four 1-d-old Hy-Line Brown male chicks were randomly allotted to 3 dietary treatments with 4 replicated pens consisting of 52 chicks. The control diet was formulated to be adequate in energy and nutrients. Two additional diets were prepared by adding 2.5 or 5.0 g/kg of LFA to the control diet. The experimental diets were fed on an ad libitum basis to the birds during 7 wk. Body weight gain and feed intake were recorded at 2 and 7 wk. At the end of the experiment, 2 birds from each treatment were killed by cervical dislocation and the samples for ileal content, breast, and thigh meat were collected for the determination of meat lipid peroxidation and microbial population. Results indicated that increasing inclusion level of LFA in diets improved BW gain (linear and quadratic, P < 0.05) and tended to improve feed efficiency (linear and quadratic, P < 0.10) of birds during 0 to 7 wk. Feeding the diets containing increasing amounts of LFA to birds reduced (quadratic, P < 0.05) thiobarbituric acid-reactive substance (TBARS) values in breast and thigh meat during 15 d of storage. The concentrations of Lactobacillus spp. in the ileal content of birds increased (linear and quadratic, P < 0.05), but those of Salmonella spp. tended to be decreased (quadratic, P < 0.10) as inclusion level of LFA in diets increased. These results suggest that dietary LFA may be used as a functional ingredient to improve growth performance, meat lipid stability, and intestinal health of birds.

Multi-task feature selection in microarray data by binary integer programming.

PubMed

Lan, Liang; Vucetic, Slobodan

2013-12-20

A major challenge in microarray classification is that the number of features is typically orders of magnitude larger than the number of examples. In this paper, we propose a novel feature filter algorithm to select the feature subset with maximal discriminative power and minimal redundancy by solving a quadratic objective function with binary integer constraints. To improve the computational efficiency, the binary integer constraints are relaxed and a low-rank approximation to the quadratic term is applied. The proposed feature selection algorithm was extended to solve multi-task microarray classification problems. We compared the single-task version of the proposed feature selection algorithm with 9 existing feature selection methods on 4 benchmark microarray data sets. The empirical results show that the proposed method achieved the most accurate predictions overall. We also evaluated the multi-task version of the proposed algorithm on 8 multi-task microarray datasets. The multi-task feature selection algorithm resulted in significantly higher accuracy than when using the single-task feature selection methods.

Interaction phenomenon to dimensionally reduced p-gBKP equation

NASA Astrophysics Data System (ADS)

Zhang, Runfa; Bilige, Sudao; Bai, Yuexing; Lü, Jianqing; Gao, Xiaoqing

2018-02-01

Based on searching the combining of quadratic function and exponential (or hyperbolic cosine) function from the Hirota bilinear form of the dimensionally reduced p-gBKP equation, eight class of interaction solutions are derived via symbolic computation with Mathematica. The submergence phenomenon, presented to illustrate the dynamical features concerning these obtained solutions, is observed by three-dimensional plots and density plots with particular choices of the involved parameters between the exponential (or hyperbolic cosine) function and the quadratic function. It is proved that the interference between the two solitary waves is inelastic.

Application of Statistic Experimental Design to Assess the Effect of Gammairradiation Pre-Treatment on the Drying Characteristics and Qualities of Wheat

NASA Astrophysics Data System (ADS)

Yu, Yong; Wang, Jun

Wheat, pretreated by 60Co gamma irradiation, was dried by hot-air with irradiation dosage 0-3 kGy, drying temperature 40-60 °C, and initial moisture contents 19-25% (drying basis). The drying characteristics and dried qualities of wheat were evaluated based on drying time, average dehydration rate, wet gluten content (WGC), moisture content of wet gluten (MCWG)and titratable acidity (TA). A quadratic rotation-orthogonal composite experimental design, with three variables (at five levels) and five response functions, and analysis method were employed to study the effect of three variables on the individual response functions. The five response functions (drying time, average dehydration rate, WGC, MCWG, TA) correlated with these variables by second order polynomials consisting of linear, quadratic and interaction terms. A high correlation coefficient indicated the suitability of the second order polynomial to predict these response functions. The linear, interaction and quadratic effects of three variables on the five response functions were all studied.

A bivariate rational interpolation with a bi-quadratic denominator

NASA Astrophysics Data System (ADS)

Duan, Qi; Zhang, Huanling; Liu, Aikui; Li, Huaigu

2006-10-01

In this paper a new rational interpolation with a bi-quadratic denominator is developed to create a space surface using only values of the function being interpolated. The interpolation function has a simple and explicit rational mathematical representation. When the knots are equally spaced, the interpolating function can be expressed in matrix form, and this form has a symmetric property. The concept of integral weights coefficients of the interpolation is given, which describes the "weight" of the interpolation points in the local interpolating region.

Time evolution of a Gaussian class of quasi-distribution functions under quadratic Hamiltonian.

PubMed

Ginzburg, D; Mann, A

2014-03-10

A Lie algebraic method for propagation of the Wigner quasi-distribution function (QDF) under quadratic Hamiltonian was presented by Zoubi and Ben-Aryeh. We show that the same method can be used in order to propagate a rather general class of QDFs, which we call the "Gaussian class." This class contains as special cases the well-known Wigner, Husimi, Glauber, and Kirkwood-Rihaczek QDFs. We present some examples of the calculation of the time evolution of those functions.

Analyzing Quadratic Unconstrained Binary Optimization Problems Via Multicommodity Flows

PubMed Central

Wang, Di; Kleinberg, Robert D.

2009-01-01

Quadratic Unconstrained Binary Optimization (QUBO) problems concern the minimization of quadratic polynomials in n {0, 1}-valued variables. These problems are NP-complete, but prior work has identified a sequence of polynomial-time computable lower bounds on the minimum value, denoted by C2, C3, C4,…. It is known that C2 can be computed by solving a maximum-flow problem, whereas the only previously known algorithms for computing Ck (k > 2) require solving a linear program. In this paper we prove that C3 can be computed by solving a maximum multicommodity flow problem in a graph constructed from the quadratic function. In addition to providing a lower bound on the minimum value of the quadratic function on {0, 1}n, this multicommodity flow problem also provides some information about the coordinates of the point where this minimum is achieved. By looking at the edges that are never saturated in any maximum multicommodity flow, we can identify relational persistencies: pairs of variables that must have the same or different values in any minimizing assignment. We furthermore show that all of these persistencies can be detected by solving single-commodity flow problems in the same network. PMID:20161596

Analyzing Quadratic Unconstrained Binary Optimization Problems Via Multicommodity Flows.

PubMed

Wang, Di; Kleinberg, Robert D

2009-11-28

Quadratic Unconstrained Binary Optimization (QUBO) problems concern the minimization of quadratic polynomials in n {0, 1}-valued variables. These problems are NP-complete, but prior work has identified a sequence of polynomial-time computable lower bounds on the minimum value, denoted by C(2), C(3), C(4),…. It is known that C(2) can be computed by solving a maximum-flow problem, whereas the only previously known algorithms for computing C(k) (k > 2) require solving a linear program. In this paper we prove that C(3) can be computed by solving a maximum multicommodity flow problem in a graph constructed from the quadratic function. In addition to providing a lower bound on the minimum value of the quadratic function on {0, 1}(n), this multicommodity flow problem also provides some information about the coordinates of the point where this minimum is achieved. By looking at the edges that are never saturated in any maximum multicommodity flow, we can identify relational persistencies: pairs of variables that must have the same or different values in any minimizing assignment. We furthermore show that all of these persistencies can be detected by solving single-commodity flow problems in the same network.

Minimization of the root of a quadratic functional under a system of affine equality constraints with application to portfolio management

NASA Astrophysics Data System (ADS)

Landsman, Zinoviy

2008-10-01

We present an explicit closed form solution of the problem of minimizing the root of a quadratic functional subject to a system of affine constraints. The result generalizes Z. Landsman, Minimization of the root of a quadratic functional under an affine equality constraint, J. Comput. Appl. Math. 2007, to appear, see , articles in press, where the optimization problem was solved under only one linear constraint. This is of interest for solving significant problems pertaining to financial economics as well as some classes of feasibility and optimization problems which frequently occur in tomography and other fields. The results are illustrated in the problem of optimal portfolio selection and the particular case when the expected return of finance portfolio is certain is discussed.

Estimating the quadratic mean diameters of fine woody debris in forests of the United States

Treesearch

Christopher W. Woodall; Vicente J. Monleon

2010-01-01

Most fine woody debris (FWD) line-intersect sampling protocols and associated estimators require an approximation of the quadratic mean diameter (QMD) of each individual FWD size class. There is a lack of empirically derived QMDs by FWD size class and species/forest type across the U.S. The objective of this study is to evaluate a technique known as the graphical...

Non-destructive testing of ceramic materials using mid-infrared ultrashort-pulse laser

NASA Astrophysics Data System (ADS)

Sun, S. C.; Qi, Hong; An, X. Y.; Ren, Y. T.; Qiao, Y. B.; Ruan, Liming M.

2018-04-01

The non-destructive testing (NDT) of ceramic materials using mid-infrared ultrashort-pulse laser is investigated in this study. The discrete ordinate method is applied to solve the transient radiative transfer equation in 2D semitransparent medium and the emerging radiative intensity on boundary serves as input for the inverse analysis. The sequential quadratic programming algorithm is employed as the inverse technique to optimize objective function, in which the gradient of objective function with respect to reconstruction parameters is calculated using the adjoint model. Two reticulated porous ceramics including partially stabilized zirconia and oxide-bonded silicon carbide are tested. The retrieval results show that the main characteristics of defects such as optical properties, geometric shapes and positions can be accurately reconstructed by the present model. The proposed technique is effective and robust in NDT of ceramics even with measurement errors.

Exact solutions for an oscillator with anti-symmetric quadratic nonlinearity

NASA Astrophysics Data System (ADS)

Beléndez, A.; Martínez, F. J.; Beléndez, T.; Pascual, C.; Alvarez, M. L.; Gimeno, E.; Arribas, E.

2018-04-01

Closed-form exact solutions for an oscillator with anti-symmetric quadratic nonlinearity are derived from the first integral of the nonlinear differential equation governing the behaviour of this oscillator. The mathematical model is an ordinary second order differential equation in which the sign of the quadratic nonlinear term changes. Two parameters characterize this oscillator: the coefficient of the linear term and the coefficient of the quadratic term. Not only the common case in which both coefficients are positive but also all possible combinations of positive and negative signs of these coefficients which provide periodic motions are considered, giving rise to four different cases. Three different periods and solutions are obtained, since the same result is valid in two of these cases. An interesting feature is that oscillatory motions whose equilibrium points are not at x = 0 are also considered. The periods are given in terms of an incomplete or complete elliptic integral of the first kind, and the exact solutions are expressed as functions including Jacobi elliptic cosine or sine functions.

Quadratic Programming for Allocating Control Effort

NASA Technical Reports Server (NTRS)

Singh, Gurkirpal

2005-01-01

A computer program calculates an optimal allocation of control effort in a system that includes redundant control actuators. The program implements an iterative (but otherwise single-stage) algorithm of the quadratic-programming type. In general, in the quadratic-programming problem, one seeks the values of a set of variables that minimize a quadratic cost function, subject to a set of linear equality and inequality constraints. In this program, the cost function combines control effort (typically quantified in terms of energy or fuel consumed) and control residuals (differences between commanded and sensed values of variables to be controlled). In comparison with prior control-allocation software, this program offers approximately equal accuracy but much greater computational efficiency. In addition, this program offers flexibility, robustness to actuation failures, and a capability for selective enforcement of control requirements. The computational efficiency of this program makes it suitable for such complex, real-time applications as controlling redundant aircraft actuators or redundant spacecraft thrusters. The program is written in the C language for execution in a UNIX operating system.

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

NASA Technical Reports Server (NTRS)

Koppang, Paul; Leland, Robert

1996-01-01

Linear quadratic Gaussian control is a technique that uses Kalman filtering to estimate a state vector used for input into a control calculation. A control correction is calculated by minimizing a quadratic cost function that is dependent on both the state vector and the control amount. Different penalties, chosen by the designer, are assessed by the controller as the state vector and control amount vary from given optimal values. With this feature controllers can be designed to force the phase and frequency differences between two standards to zero either more or less aggressively depending on the application. Data will be used to show how using different parameters in the cost function analysis affects the steering and the stability of the frequency standards.

Deploying a quantum annealing processor to detect tree cover in aerial imagery of California

PubMed Central

Basu, Saikat; Ganguly, Sangram; Michaelis, Andrew; Mukhopadhyay, Supratik; Nemani, Ramakrishna R.

2017-01-01

Quantum annealing is an experimental and potentially breakthrough computational technology for handling hard optimization problems, including problems of computer vision. We present a case study in training a production-scale classifier of tree cover in remote sensing imagery, using early-generation quantum annealing hardware built by D-wave Systems, Inc. Beginning within a known boosting framework, we train decision stumps on texture features and vegetation indices extracted from four-band, one-meter-resolution aerial imagery from the state of California. We then impose a regulated quadratic training objective to select an optimal voting subset from among these stumps. The votes of the subset define the classifier. For optimization, the logical variables in the objective function map to quantum bits in the hardware device, while quadratic couplings encode as the strength of physical interactions between the quantum bits. Hardware design limits the number of couplings between these basic physical entities to five or six. To account for this limitation in mapping large problems to the hardware architecture, we propose a truncation and rescaling of the training objective through a trainable metaparameter. The boosting process on our basic 108- and 508-variable problems, thus constituted, returns classifiers that incorporate a diverse range of color- and texture-based metrics and discriminate tree cover with accuracies as high as 92% in validation and 90% on a test scene encompassing the open space preserves and dense suburban build of Mill Valley, CA. PMID:28241028

Development of a probabilistic analysis methodology for structural reliability estimation

NASA Technical Reports Server (NTRS)

Torng, T. Y.; Wu, Y.-T.

1991-01-01

The novel probabilistic analysis method for assessment of structural reliability presented, which combines fast-convolution with an efficient structural reliability analysis, can after identifying the most important point of a limit state proceed to establish a quadratic-performance function. It then transforms the quadratic function into a linear one, and applies fast convolution. The method is applicable to problems requiring computer-intensive structural analysis. Five illustrative examples of the method's application are given.

An empirical analysis of the quantitative effect of data when fitting quadratic and cubic polynomials

NASA Technical Reports Server (NTRS)

Canavos, G. C.

1974-01-01

A study is made of the extent to which the size of the sample affects the accuracy of a quadratic or a cubic polynomial approximation of an experimentally observed quantity, and the trend with regard to improvement in the accuracy of the approximation as a function of sample size is established. The task is made possible through a simulated analysis carried out by the Monte Carlo method in which data are simulated by using several transcendental or algebraic functions as models. Contaminated data of varying amounts are fitted to either quadratic or cubic polynomials, and the behavior of the mean-squared error of the residual variance is determined as a function of sample size. Results indicate that the effect of the size of the sample is significant only for relatively small sizes and diminishes drastically for moderate and large amounts of experimental data.

Quantum superintegrable system with a novel chain structure of quadratic algebras

NASA Astrophysics Data System (ADS)

Liao, Yidong; Marquette, Ian; Zhang, Yao-Zhong

2018-06-01

We analyse the n-dimensional superintegrable Kepler–Coulomb system with non-central terms. We find a novel underlying chain structure of quadratic algebras formed by the integrals of motion. We identify the elements for each sub-structure and obtain the algebra relations satisfied by them and the corresponding Casimir operators. These quadratic sub-algebras are realized in terms of a chain of deformed oscillators with factorized structure functions. We construct the finite-dimensional unitary representations of the deformed oscillators, and give an algebraic derivation of the energy spectrum of the superintegrable system.

Lump solutions and interaction phenomenon to the third-order nonlinear evolution equation

NASA Astrophysics Data System (ADS)

Kofane, T. C.; Fokou, M.; Mohamadou, A.; Yomba, E.

2017-11-01

In this work, the lump solution and the kink solitary wave solution from the (2 + 1) -dimensional third-order evolution equation, using the Hirota bilinear method are obtained through symbolic computation with Maple. We have assumed that the lump solution is centered at the origin, when t = 0 . By considering a mixing positive quadratic function with exponential function, as well as a mixing positive quadratic function with hyperbolic cosine function, interaction solutions like lump-exponential and lump-hyperbolic cosine are presented. A completely non-elastic interaction between a lump and kink soliton is observed, showing that a lump solution can be swallowed by a kink soliton.

An Alternative Method to the Classical Partial Fraction Decomposition

ERIC Educational Resources Information Center

Cherif, Chokri

2007-01-01

PreCalculus students can use the Completing the Square Method to solve quadratic equations without the need to memorize the quadratic formula since this method naturally leads them to that formula. Calculus students, when studying integration, use various standard methods to compute integrals depending on the type of function to be integrated.…

[The Visual Association Test to study episodic memory in clinical geriatric psychology].

PubMed

Diesfeldt, Han; Prins, Marleen; Lauret, Gijs

2018-04-01

The Visual Association Test (VAT) is a brief learning task that consists of six line drawings of pairs of interacting objects (association cards). Subjects are asked to name or identify each object and later are presented with one object from the pair (the cue) and asked to name the other (the target). The VAT was administered in a consecutive sample of 174 psychogeriatric day care participants with mild to major neurocognitive disorder. Comparison of test performance with normative data from non-demented subjects revealed that 69% scored within the range of a major deficit (0-8 over two recall trials), 14% a minor, and 17% no deficit (9-10, and ≥10 respectively).VAT-scores correlated with another test of memory function, the Cognitive Screening Test (CST), based on the Short Portable Mental Status Questionnaire (r = 0.53). Tests of executive functioning (Expanded Mental Control Test, Category Fluency, Clock Drawing) did not add significantly to the explanation of variance in VAT-scores.Fifty-five participants (31.6%) were faced with initial problems in naming or identifying one or more objects on the cue cards or association cards. If necessary, naming was aided by the investigator. Initial difficulties in identifying cue objects were associated with lower VAT-scores, but this did not hold for difficulties in identifying target objects.A hierarchical multiple regression analysis was used to examine whether linear or quadratic trends best fitted VAT performance across the range of CST scores. The regression model revealed a linear but not a quadratic trend. The best fitting linear model implied that VAT scores differentiated between CST scores in the lower, as well as in the upper range, indicating the absence of floor and ceiling effects, respectively. Moreover, the VAT compares favourably to word list-learning tasks being more attractive in its presentation of interacting visual objects and cued recall based on incidental learning of the association between cues and targets.For practical purposes and based on documented sensitivity and specificity, Bayesian probability tables give predictive power of age-specific VAT cutoff scores for the presence or absence of a major neurocognitive disorder across a range of a priori probabilities or base rates.

Nonlinear model for an optical read-only-memory disk readout channel based on an edge-spread function.

PubMed

Kobayashi, Seiji

2002-05-10

A point-spread function (PSF) is commonly used as a model of an optical disk readout channel. However, the model given by the PSF does not contain the quadratic distortion generated by the photo-detection process. We introduce a model for calculating an approximation of the quadratic component of a signal. We show that this model can be further simplified when a read-only-memory (ROM) disk is assumed. We introduce an edge-spread function by which a simple nonlinear model of an optical ROM disk readout channel is created.

Quadratic RK shooting solution for a environmental parameter prediction boundary value problem

NASA Astrophysics Data System (ADS)

Famelis, Ioannis Th.; Tsitouras, Ch.

2014-10-01

Using tools of Information Geometry, the minimum distance between two elements of a statistical manifold is defined by the corresponding geodesic, e.g. the minimum length curve that connects them. Such a curve, where the probability distribution functions in the case of our meteorological data are two parameter Weibull distributions, satisfies a 2nd order Boundary Value (BV) system. We study the numerical treatment of the resulting special quadratic form system using Shooting method. We compare the solutions of the problem when we employ a classical Singly Diagonally Implicit Runge Kutta (SDIRK) 4(3) pair of methods and a quadratic SDIRK 5(3) pair . Both pairs have the same computational costs whereas the second one attains higher order as it is specially constructed for quadratic problems.

Bi-Objective Optimal Control Modification Adaptive Control for Systems with Input Uncertainty

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.

2012-01-01

This paper presents a new model-reference adaptive control method based on a bi-objective optimal control formulation for systems with input uncertainty. A parallel predictor model is constructed to relate the predictor error to the estimation error of the control effectiveness matrix. In this work, we develop an optimal control modification adaptive control approach that seeks to minimize a bi-objective linear quadratic cost function of both the tracking error norm and predictor error norm simultaneously. The resulting adaptive laws for the parametric uncertainty and control effectiveness uncertainty are dependent on both the tracking error and predictor error, while the adaptive laws for the feedback gain and command feedforward gain are only dependent on the tracking error. The optimal control modification term provides robustness to the adaptive laws naturally from the optimal control framework. Simulations demonstrate the effectiveness of the proposed adaptive control approach.

Clinical-Functional Vulnerability Index-20 (IVCF-20): rapid recognition of frail older adults

PubMed Central

de Moraes, Edgar Nunes; do Carmo, Juliana Alves; de Moraes, Flávia Lanna; Azevedo, Raquel Souza; Machado, Carla Jorge; Montilla, Dalia Elena Romero

2016-01-01

ABSTRACT OBJECTIVE To evaluate the adequacy of the Clinical-Functional Vulnerability Index-20, a rapid triage instrument to test vulnerability in Brazilian older adults, for the use in primary health care. METHODS The study included convenience sample of 397 patients aged older than or equal to 60 years attended at Centro de Referência para o Idoso (Reference Center for Older Adults) and of 52 older adults the same age attended at the community. The results of the questionnaire, consisting of 20 questions, were compared with those of the Comprehensive Geriatric Assessment, considered a reference for identifying frail older adults. Spearman’s correlation was evaluated in the Clinical-Functional Vulnerability Index-20 with the Comprehensive Geriatric Assessment; the validity was verified by the area under the ROC curve; reliability was estimated by the percentage of agreement among evaluators and by the kappa coefficient, both with quadratic weighted. The cut-off point was obtained based on the higher accuracy criterion. Cronbach’s alpha, a measure of internal consistency, was estimated. RESULTS The Spearman’s correlation coefficient was high and positive for both groups (0.792 for older adults attended at the Reference Center and 0.305 for older adults from the community [p < 0.001]). The area under the ROC curve for older adults attended at the Reference Center was substantial (0.903). The cut-off point obtained was six, and older adults with scores in Clinical-Functional Vulnerability Index-20 above that value had strong possibility of being frail. For older adults from the community, the quadratic weighted agreement among evaluators was 99.5%, and the global quadratic weighted kappa coefficient was 0.94. Cronbach’s alpha was high for older adults attended at the Reference Center (0.861) and those attended at the community (0.740). CONCLUSIONS The Clinical-Functional Vulnerability Index-20 questionnaire, in the sample examined, turned out to be positively correlated with the Comprehensive Geriatric Assessment, in addition to the results indicating a high degree of validity and reliability. Thus, the Clinical-Functional Vulnerability Index-20 proves to be viable as a triage instrument in the primary health care that identifies frail older adults (older adults at risk of weakening and frail older adults). PMID:28099667

EUD-based biological optimization for carbon ion therapy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brüningk, Sarah C., E-mail: sarah.brueningk@icr.ac.uk; Kamp, Florian; Wilkens, Jan J.

2015-11-15

Purpose: Treatment planning for carbon ion therapy requires an accurate modeling of the biological response of each tissue to estimate the clinical outcome of a treatment. The relative biological effectiveness (RBE) accounts for this biological response on a cellular level but does not refer to the actual impact on the organ as a whole. For photon therapy, the concept of equivalent uniform dose (EUD) represents a simple model to take the organ response into account, yet so far no formulation of EUD has been reported that is suitable to carbon ion therapy. The authors introduce the concept of an equivalentmore » uniform effect (EUE) that is directly applicable to both ion and photon therapies and exemplarily implemented it as a basis for biological treatment plan optimization for carbon ion therapy. Methods: In addition to a classical EUD concept, which calculates a generalized mean over the RBE-weighted dose distribution, the authors propose the EUE to simplify the optimization process of carbon ion therapy plans. The EUE is defined as the biologically equivalent uniform effect that yields the same probability of injury as the inhomogeneous effect distribution in an organ. Its mathematical formulation is based on the generalized mean effect using an effect-volume parameter to account for different organ architectures and is thus independent of a reference radiation. For both EUD concepts, quadratic and logistic objective functions are implemented into a research treatment planning system. A flexible implementation allows choosing for each structure between biological effect constraints per voxel and EUD constraints per structure. Exemplary treatment plans are calculated for a head-and-neck patient for multiple combinations of objective functions and optimization parameters. Results: Treatment plans optimized using an EUE-based objective function were comparable to those optimized with an RBE-weighted EUD-based approach. In agreement with previous results from photon therapy, the optimization by biological objective functions resulted in slightly superior treatment plans in terms of final EUD for the organs at risk (OARs) compared to voxel-based optimization approaches. This observation was made independent of the underlying objective function metric. An absolute gain in OAR sparing was observed for quadratic objective functions, whereas intersecting DVHs were found for logistic approaches. Even for considerable under- or overestimations of the used effect- or dose–volume parameters during the optimization, treatment plans were obtained that were of similar quality as the results of a voxel-based optimization. Conclusions: EUD-based optimization with either of the presented concepts can successfully be applied to treatment plan optimization. This makes EUE-based optimization for carbon ion therapy a useful tool to optimize more specifically in the sense of biological outcome while voxel-to-voxel variations of the biological effectiveness are still properly accounted for. This may be advantageous in terms of computational cost during treatment plan optimization but also enables a straight forward comparison of different fractionation schemes or treatment modalities.« less

A reduced successive quadratic programming strategy for errors-in-variables estimation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tjoa, I.-B.; Biegler, L. T.; Carnegie-Mellon Univ.

Parameter estimation problems in process engineering represent a special class of nonlinear optimization problems, because the maximum likelihood structure of the objective function can be exploited. Within this class, the errors in variables method (EVM) is particularly interesting. Here we seek a weighted least-squares fit to the measurements with an underdetermined process model. Thus, both the number of variables and degrees of freedom available for optimization increase linearly with the number of data sets. Large optimization problems of this type can be particularly challenging and expensive to solve because, for general-purpose nonlinear programming (NLP) algorithms, the computational effort increases atmore » least quadratically with problem size. In this study we develop a tailored NLP strategy for EVM problems. The method is based on a reduced Hessian approach to successive quadratic programming (SQP), but with the decomposition performed separately for each data set. This leads to the elimination of all variables but the model parameters, which are determined by a QP coordination step. In this way the computational effort remains linear in the number of data sets. Moreover, unlike previous approaches to the EVM problem, global and superlinear properties of the SQP algorithm apply naturally. Also, the method directly incorporates inequality constraints on the model parameters (although not on the fitted variables). This approach is demonstrated on five example problems with up to 102 degrees of freedom. Compared to general-purpose NLP algorithms, large improvements in computational performance are observed.« less

Optimization of the structural and control system for LSS with reduced-order model

NASA Technical Reports Server (NTRS)

Khot, N. S.

1989-01-01

The objective is the simultaneous design of the structural and control system for space structures. The minimum weight of the structure is the objective function, and the constraints are placed on the closed loop distribution of the frequencies and the damping parameters. The controls approach used is linear quadratic regulator with constant feedback. A reduced-order control system is used. The effect of uncontrolled modes is taken into consideration by the model error sensitivity suppression (MESS) technique which modified the weighting parameters for the control forces. For illustration, an ACOSS-FOUR structure is designed for a different number of controlled modes with specified values for the closed loop damping parameters and frequencies. The dynamic response of the optimum designs for an initial disturbance is compared.

Quadratic formula for determining the drop size in pressure-atomized sprays with and without swirl

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, T.-W, E-mail: attwl@asu.edu; An, Keju

2016-06-15

We use a theoretical framework based on the integral form of the conservation equations, along with a heuristic model of the viscous dissipation, to find a closed-form solution to the liquid atomization problem. The energy balance for the spray renders to a quadratic formula for the drop size as a function, primarily of the liquid velocity. The Sauter mean diameter found using the quadratic formula shows good agreements and physical trends, when compared with experimental observations. This approach is shown to be applicable toward specifying initial drop size in computational fluid dynamics of spray flows.

A trust region-based approach to optimize triple response systems

NASA Astrophysics Data System (ADS)

Fan, Shu-Kai S.; Fan, Chihhao; Huang, Chia-Fen

2014-05-01

This article presents a new computing procedure for the global optimization of the triple response system (TRS) where the response functions are non-convex quadratics and the input factors satisfy a radial constrained region of interest. The TRS arising from response surface modelling can be approximated using a nonlinear mathematical program that considers one primary objective function and two secondary constraint functions. An optimization algorithm named the triple response surface algorithm (TRSALG) is proposed to determine the global optimum for the non-degenerate TRS. In TRSALG, the Lagrange multipliers of the secondary functions are determined using the Hooke-Jeeves search method and the Lagrange multiplier of the radial constraint is located using the trust region method within the global optimality space. The proposed algorithm is illustrated in terms of three examples appearing in the quality-control literature. The results of TRSALG compared to a gradient-based method are also presented.

Nonlinear associations between plasma cholesterol levels and neuropsychological function.

PubMed

Wendell, Carrington R; Zonderman, Alan B; Katzel, Leslie I; Rosenberger, William F; Plamadeala, Victoria V; Hosey, Megan M; Waldstein, Shari R

2016-11-01

Although both high and low levels of total and low-density lipoprotein (LDL) cholesterol have been associated with poor neuropsychological function, little research has examined nonlinear effects. We examined quadratic relations of cholesterol to performance on a comprehensive neuropsychological battery. Participants were 190 older adults (53% men, ages 54-83) free of major medical, neurologic, and psychiatric disease. Measures of fasting plasma total and high-density lipoprotein (HDL) cholesterol were assayed, and LDL cholesterol was calculated. Participants completed neuropsychological measures of attention, executive function, memory, visuospatial judgment, and manual speed and dexterity. Multiple regression analyses examined cholesterol levels as quadratic predictors of each measure of cognitive performance, with age (dichotomized as <70 vs. 70+) as an effect modifier. A significant quadratic effect of Total Cholesterol² × Age was identified for Logical Memory II ( b = -.0013, p = .039), such that the 70+ group performed best at high and low levels of total cholesterol than at midrange total cholesterol (U-shaped) and the <70 group performed worse at high and low levels of total cholesterol than at midrange total cholesterol (inverted U shape). Similarly, significant U- and J-shaped effects of LDL Cholesterol² × Age were identified for Visual Reproduction II ( b = -.0020, p = .026) and log of the Trail Making Test, Part B (b = .0001, p = .044). Quadratic associations between HDL cholesterol and cognitive performance were nonsignificant. Results indicate differential associations between cholesterol and neuropsychological function across different ages and domains of function. High and low total and LDL cholesterol may confer both risk and benefit for suboptimal cognitive function at different ages. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Comparison of optimization algorithms in intensity-modulated radiation therapy planning

NASA Astrophysics Data System (ADS)

Kendrick, Rachel

Intensity-modulated radiation therapy is used to better conform the radiation dose to the target, which includes avoiding healthy tissue. Planning programs employ optimization methods to search for the best fluence of each photon beam, and therefore to create the best treatment plan. The Computational Environment for Radiotherapy Research (CERR), a program written in MATLAB, was used to examine some commonly-used algorithms for one 5-beam plan. Algorithms include the genetic algorithm, quadratic programming, pattern search, constrained nonlinear optimization, simulated annealing, the optimization method used in Varian EclipseTM, and some hybrids of these. Quadratic programing, simulated annealing, and a quadratic/simulated annealing hybrid were also separately compared using different prescription doses. The results of each dose-volume histogram as well as the visual dose color wash were used to compare the plans. CERR's built-in quadratic programming provided the best overall plan, but avoidance of the organ-at-risk was rivaled by other programs. Hybrids of quadratic programming with some of these algorithms seems to suggest the possibility of better planning programs, as shown by the improved quadratic/simulated annealing plan when compared to the simulated annealing algorithm alone. Further experimentation will be done to improve cost functions and computational time.

Statistical distribution sampling

NASA Technical Reports Server (NTRS)

Johnson, E. S.

1975-01-01

Determining the distribution of statistics by sampling was investigated. Characteristic functions, the quadratic regression problem, and the differential equations for the characteristic functions are analyzed.

Local hyperspectral data multisharpening based on linear/linear-quadratic nonnegative matrix factorization by integrating lidar data

NASA Astrophysics Data System (ADS)

Benhalouche, Fatima Zohra; Karoui, Moussa Sofiane; Deville, Yannick; Ouamri, Abdelaziz

2015-10-01

In this paper, a new Spectral-Unmixing-based approach, using Nonnegative Matrix Factorization (NMF), is proposed to locally multi-sharpen hyperspectral data by integrating a Digital Surface Model (DSM) obtained from LIDAR data. In this new approach, the nature of the local mixing model is detected by using the local variance of the object elevations. The hyper/multispectral images are explored using small zones. In each zone, the variance of the object elevations is calculated from the DSM data in this zone. This variance is compared to a threshold value and the adequate linear/linearquadratic spectral unmixing technique is used in the considered zone to independently unmix hyperspectral and multispectral data, using an adequate linear/linear-quadratic NMF-based approach. The obtained spectral and spatial information thus respectively extracted from the hyper/multispectral images are then recombined in the considered zone, according to the selected mixing model. Experiments based on synthetic hyper/multispectral data are carried out to evaluate the performance of the proposed multi-sharpening approach and literature linear/linear-quadratic approaches used on the whole hyper/multispectral data. In these experiments, real DSM data are used to generate synthetic data containing linear and linear-quadratic mixed pixel zones. The DSM data are also used for locally detecting the nature of the mixing model in the proposed approach. Globally, the proposed approach yields good spatial and spectral fidelities for the multi-sharpened data and significantly outperforms the used literature methods.

Quadratic function between arterial partial oxygen pressure and mortality risk in sepsis patients: an interaction with simplified acute physiology score.

PubMed

Zhang, Zhongheng; Ji, Xuqing

2016-10-13

Oxygen therapy is widely used in emergency and critical care settings, while there is little evidence on its real therapeutic effect. The study aimed to explore the impact of arterial oxygen partial pressure (PaO 2 ) on clinical outcomes in patients with sepsis. A large clinical database was employed for the study. Subjects meeting the diagnostic criteria of sepsis were eligible for the study. All measurements of PaO 2 were extracted. The primary endpoint was death from any causes during hospital stay. Survey data analysis was performed by using individual ICU admission as the primary sampling unit. Quadratic function was assumed for PaO 2 and its interaction with other covariates were explored. A total of 199,125 PaO 2 samples were identified for 11,002 ICU admissions. Each ICU stay comprised 18 PaO 2 samples in average. The fitted multivariable model supported our hypothesis that the effect of PaO 2 on mortality risk was in quadratic form. There was significant interaction between PaO 2 and SAPS-I (p = 0.007). Furthermore, the main effect of PaO 2 on SOFA score was nonlinear. The study shows that the effect of PaO 2 on mortality risk is in quadratic function form, and there is significant interaction between PaO 2 and severity of illness.

A General Method for Solving Systems of Non-Linear Equations

NASA Technical Reports Server (NTRS)

Nachtsheim, Philip R.; Deiss, Ron (Technical Monitor)

1995-01-01

The method of steepest descent is modified so that accelerated convergence is achieved near a root. It is assumed that the function of interest can be approximated near a root by a quadratic form. An eigenvector of the quadratic form is found by evaluating the function and its gradient at an arbitrary point and another suitably selected point. The terminal point of the eigenvector is chosen to lie on the line segment joining the two points. The terminal point found lies on an axis of the quadratic form. The selection of a suitable step size at this point leads directly to the root in the direction of steepest descent in a single step. Newton's root finding method not infrequently diverges if the starting point is far from the root. However, the current method in these regions merely reverts to the method of steepest descent with an adaptive step size. The current method's performance should match that of the Levenberg-Marquardt root finding method since they both share the ability to converge from a starting point far from the root and both exhibit quadratic convergence near a root. The Levenberg-Marquardt method requires storage for coefficients of linear equations. The current method which does not require the solution of linear equations requires more time for additional function and gradient evaluations. The classic trade off of time for space separates the two methods.

Algebras Generated by Geometric Scalar Forms and their Applications in Physics and Social Sciences

DOE Office of Scientific and Technical Information (OSTI.GOV)

Keller, Jaime

2008-09-17

The present paper analyzes the consequences of defining that the geometric scalar form is not necessarily quadratic, but in general K-atic, that is obtained from the K{sup th} power of the linear form, requiring {l_brace}e{sub i};i = 1,...,N;(e{sub i}){sup K} = 1{r_brace} and d-vector {sigma}{sub i}x{sub i}e{sub i}. We consider the algebras which are thus generated, for positive integer K, a generalization of the geometric algebras we know under the names of Clifford or Grassmann algebras. We then obtain a set of geometric K-algebras. We also consider the generalization of special functions of geometry which corresponds to the K-order scalarmore » forms (as trigonometric functions and other related geometric functions which are based on the use of quadratic forms). We present an overview of the use of quadratic forms in physics as in our general theory, we have called START. And, in order to give an introduction to the use of the more general K-algebras and to the possible application to sciences other than physics, the application to social sciences is considered.For the applications to physics we show that quadratic spaces are a fundamental clue to understand the structure of theoretical physics (see, for example, Keller in ICNAAM 2005 and 2006)« less

Uniform sparse bounds for discrete quadratic phase Hilbert transforms

NASA Astrophysics Data System (ADS)

Kesler, Robert; Arias, Darío Mena

2017-09-01

For each α \\in T consider the discrete quadratic phase Hilbert transform acting on finitely supported functions f : Z → C according to H^{α }f(n):= \\sum _{m ≠ 0} e^{iα m^2} f(n - m)/m. We prove that, uniformly in α \\in T , there is a sparse bound for the bilinear form < H^{α } f , g > for every pair of finitely supported functions f,g : Z→ C . The sparse bound implies several mapping properties such as weighted inequalities in an intersection of Muckenhoupt and reverse Hölder classes.

Inertially Stabilized Platforms for SATCOM On-The-Move Applications: A Hybrid Open/Closed-Loop Antenna Pointing Strategy

DTIC Science & Technology

2008-06-01

Photo courtesy of www.mathworks.com. Next, Equation (3.16) translates the aircraft disturbance rates through the de - sired local azimuth and elevation...Hessian matrix of the assumed quadratic cost function [34–36]. Equation (4.11) exactly de - termines the minimum of a quadratic function in a single...according to: Bkpk = −gk (4.21) Bk+1 = Bk +Qk (4.22) where Bk in some way approximates Gk from (4.12), and Qk is an update matrix de - pendent upon xk

Genetic evaluation and selection response for growth in meat-type quail through random regression models using B-spline functions and Legendre polynomials.

PubMed

Mota, L F M; Martins, P G M A; Littiere, T O; Abreu, L R A; Silva, M A; Bonafé, C M

2018-04-01

The objective was to estimate (co)variance functions using random regression models (RRM) with Legendre polynomials, B-spline function and multi-trait models aimed at evaluating genetic parameters of growth traits in meat-type quail. A database containing the complete pedigree information of 7000 meat-type quail was utilized. The models included the fixed effects of contemporary group and generation. Direct additive genetic and permanent environmental effects, considered as random, were modeled using B-spline functions considering quadratic and cubic polynomials for each individual segment, and Legendre polynomials for age. Residual variances were grouped in four age classes. Direct additive genetic and permanent environmental effects were modeled using 2 to 4 segments and were modeled by Legendre polynomial with orders of fit ranging from 2 to 4. The model with quadratic B-spline adjustment, using four segments for direct additive genetic and permanent environmental effects, was the most appropriate and parsimonious to describe the covariance structure of the data. The RRM using Legendre polynomials presented an underestimation of the residual variance. Lesser heritability estimates were observed for multi-trait models in comparison with RRM for the evaluated ages. In general, the genetic correlations between measures of BW from hatching to 35 days of age decreased as the range between the evaluated ages increased. Genetic trend for BW was positive and significant along the selection generations. The genetic response to selection for BW in the evaluated ages presented greater values for RRM compared with multi-trait models. In summary, RRM using B-spline functions with four residual variance classes and segments were the best fit for genetic evaluation of growth traits in meat-type quail. In conclusion, RRM should be considered in genetic evaluation of breeding programs.

Determination of Strength Exercise Intensities Based on the Load-Power-Velocity Relationship

PubMed Central

Jandačka, Daniel; Beremlijski, Petr

2011-01-01

The velocity of movement and applied load affect the production of mechanical power output and subsequently the extent of the adaptation stimulus in strength exercises. We do not know of any known function describing the relationship of power and velocity and load in the bench press exercise. The objective of the study is to find a function modeling of the relationship of relative velocity, relative load and mechanical power output for the bench press exercise and to determine the intensity zones of the exercise for specifically focused strength training of soccer players. Fifteen highly trained soccer players at the start of a competition period were studied. The subjects of study performed bench presses with the load of 0, 10, 30, 50, 70 and 90% of the predetermined one repetition maximum with maximum possible speed of movement. The mean measured power and velocity for each load (kg) were used to develop a multiple linear regression function which describes the quadratic relationship between the ratio of power (W) to maximum power (W) and the ratios of the load (kg) to one repetition maximum (kg) and the velocity (m•s−1) to maximal velocity (m•s−1). The quadratic function of two variables that modeled the searched relationship explained 74% of measured values in the acceleration phase and 75% of measured values from the entire extent of the positive power movement in the lift. The optimal load for reaching maximum power output suitable for the dynamics effort strength training was 40% of one repetition maximum, while the optimal mean velocity would be 75% of maximal velocity. Moreover, four zones: maximum power, maximum velocity, velocity-power and strength-power were determined on the basis of the regression function. PMID:23486484

Determination of strength exercise intensities based on the load-power-velocity relationship.

PubMed

Jandačka, Daniel; Beremlijski, Petr

2011-06-01

The velocity of movement and applied load affect the production of mechanical power output and subsequently the extent of the adaptation stimulus in strength exercises. We do not know of any known function describing the relationship of power and velocity and load in the bench press exercise. The objective of the study is to find a function modeling of the relationship of relative velocity, relative load and mechanical power output for the bench press exercise and to determine the intensity zones of the exercise for specifically focused strength training of soccer players. Fifteen highly trained soccer players at the start of a competition period were studied. The subjects of study performed bench presses with the load of 0, 10, 30, 50, 70 and 90% of the predetermined one repetition maximum with maximum possible speed of movement. The mean measured power and velocity for each load (kg) were used to develop a multiple linear regression function which describes the quadratic relationship between the ratio of power (W) to maximum power (W) and the ratios of the load (kg) to one repetition maximum (kg) and the velocity (m•s(-1)) to maximal velocity (m•s(-1)). The quadratic function of two variables that modeled the searched relationship explained 74% of measured values in the acceleration phase and 75% of measured values from the entire extent of the positive power movement in the lift. The optimal load for reaching maximum power output suitable for the dynamics effort strength training was 40% of one repetition maximum, while the optimal mean velocity would be 75% of maximal velocity. Moreover, four zones: maximum power, maximum velocity, velocity-power and strength-power were determined on the basis of the regression function.

QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.

PubMed

Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit

2014-01-01

We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n -gon, our construction produces 2 n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n ( n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called 'serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed.

Extending the accuracy of the SNAP interatomic potential form

NASA Astrophysics Data System (ADS)

Wood, Mitchell A.; Thompson, Aidan P.

2018-06-01

The Spectral Neighbor Analysis Potential (SNAP) is a classical interatomic potential that expresses the energy of each atom as a linear function of selected bispectrum components of the neighbor atoms. An extension of the SNAP form is proposed that includes quadratic terms in the bispectrum components. The extension is shown to provide a large increase in accuracy relative to the linear form, while incurring only a modest increase in computational cost. The mathematical structure of the quadratic SNAP form is similar to the embedded atom method (EAM), with the SNAP bispectrum components serving as counterparts to the two-body density functions in EAM. The effectiveness of the new form is demonstrated using an extensive set of training data for tantalum structures. Similar to artificial neural network potentials, the quadratic SNAP form requires substantially more training data in order to prevent overfitting. The quality of this new potential form is measured through a robust cross-validation analysis.

MO-FG-CAMPUS-TeP2-01: A Graph Form ADMM Algorithm for Constrained Quadratic Radiation Treatment Planning

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, X; Belcher, AH; Wiersma, R

Purpose: In radiation therapy optimization the constraints can be either hard constraints which must be satisfied or soft constraints which are included but do not need to be satisfied exactly. Currently the voxel dose constraints are viewed as soft constraints and included as a part of the objective function and approximated as an unconstrained problem. However in some treatment planning cases the constraints should be specified as hard constraints and solved by constrained optimization. The goal of this work is to present a computation efficiency graph form alternating direction method of multipliers (ADMM) algorithm for constrained quadratic treatment planning optimizationmore » and compare it with several commonly used algorithms/toolbox. Method: ADMM can be viewed as an attempt to blend the benefits of dual decomposition and augmented Lagrangian methods for constrained optimization. Various proximal operators were first constructed as applicable to quadratic IMRT constrained optimization and the problem was formulated in a graph form of ADMM. A pre-iteration operation for the projection of a point to a graph was also proposed to further accelerate the computation. Result: The graph form ADMM algorithm was tested by the Common Optimization for Radiation Therapy (CORT) dataset including TG119, prostate, liver, and head & neck cases. Both unconstrained and constrained optimization problems were formulated for comparison purposes. All optimizations were solved by LBFGS, IPOPT, Matlab built-in toolbox, CVX (implementing SeDuMi) and Mosek solvers. For unconstrained optimization, it was found that LBFGS performs the best, and it was 3–5 times faster than graph form ADMM. However, for constrained optimization, graph form ADMM was 8 – 100 times faster than the other solvers. Conclusion: A graph form ADMM can be applied to constrained quadratic IMRT optimization. It is more computationally efficient than several other commercial and noncommercial optimizers and it also used significantly less computer memory.« less

Application of the fractional Fourier transform to image reconstruction in MRI.

PubMed

Parot, Vicente; Sing-Long, Carlos; Lizama, Carlos; Tejos, Cristian; Uribe, Sergio; Irarrazaval, Pablo

2012-07-01

The classic paradigm for MRI requires a homogeneous B(0) field in combination with linear encoding gradients. Distortions are produced when the B(0) is not homogeneous, and several postprocessing techniques have been developed to correct them. Field homogeneity is difficult to achieve, particularly for short-bore magnets and higher B(0) fields. Nonlinear magnetic components can also arise from concomitant fields, particularly in low-field imaging, or intentionally used for nonlinear encoding. In any of these situations, the second-order component is key, because it constitutes the first step to approximate higher-order fields. We propose to use the fractional Fourier transform for analyzing and reconstructing the object's magnetization under the presence of quadratic fields. The fractional fourier transform provides a precise theoretical framework for this. We show how it can be used for reconstruction and for gaining a better understanding of the quadratic field-induced distortions, including examples of reconstruction for simulated and in vivo data. The obtained images have improved quality compared with standard Fourier reconstructions. The fractional fourier transform opens a new paradigm for understanding the MR signal generated by an object under a quadratic main field or nonlinear encoding. Copyright © 2011 Wiley Periodicals, Inc.

PSQP: Puzzle Solving by Quadratic Programming.

PubMed

Andalo, Fernanda A; Taubin, Gabriel; Goldenstein, Siome

2017-02-01

In this article we present the first effective method based on global optimization for the reconstruction of image puzzles comprising rectangle pieces-Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.

Model test on the relationship feed energy and protein ratio to the production and quality of milk protein

NASA Astrophysics Data System (ADS)

Hartanto, R.; Jantra, M. A. C.; Santosa, S. A. B.; Purnomoadi, A.

2018-01-01

The purpose of this research was to find an appropriate relationship model between the feed energy and protein ratio with the amount of production and quality of milk proteins. This research was conducted at Getasan Sub-district, Semarang Regency, Central Java Province, Indonesia using 40 samples (Holstein Friesian cattle, lactation period II-III and lactation month 3-4). Data were analyzed using linear and quadratic regressions, to predict the production and quality of milk protein from feed energy and protein ratio that describe the diet. The significance of model was tested using analysis of variance. Coefficient of determination (R2), residual variance (RV) and root mean square prediction error (RMSPE) were reported for the developed equations as an indicator of the goodness of model fit. The results showed no relationship in milk protein (kg), milk casein (%), milk casein (kg) and milk urea N (mg/dl) as function of CP/TDN. The significant relationship was observed in milk production (L or kg) and milk protein (%) as function of CP/TDN, both in linear and quadratic models. In addition, a quadratic change in milk production (L) (P = 0.003), milk production (kg) (P = 0.003) and milk protein concentration (%) (P = 0.026) were observed with increase of CP/TDN. It can be concluded that quadratic equation was the good fitting model for this research, because quadratic equation has larger R2, smaller RV and smaller RMSPE than those of linear equation.

Wormholes in R^2-gravity within the f( R, T) formalism

NASA Astrophysics Data System (ADS)

Sahoo, P. K.; Moraes, P. H. R. S.; Sahoo, Parbati

2018-01-01

We propose, as a novelty in the literature, the modeling of wormholes within a particular case of f( R, T) gravity, namely f(R,T)=R+α R2+λ T, with R and T being the Ricci scalar and trace of the energy-momentum tensor, respectively, while α and λ are constants. Although such a functional form application can be found in the literature, those concern compact astrophysical objects, such that no wormhole analysis has been done so far. The quadratic geometric and linear material corrections of this theory render the matter content of the wormhole remarkably able to obey the energy conditions.

An exponential decay model for mediation.

PubMed

Fritz, Matthew S

2014-10-01

Mediation analysis is often used to investigate mechanisms of change in prevention research. Results finding mediation are strengthened when longitudinal data are used because of the need for temporal precedence. Current longitudinal mediation models have focused mainly on linear change, but many variables in prevention change nonlinearly across time. The most common solution to nonlinearity is to add a quadratic term to the linear model, but this can lead to the use of the quadratic function to explain all nonlinearity, regardless of theory and the characteristics of the variables in the model. The current study describes the problems that arise when quadratic functions are used to describe all nonlinearity and how the use of nonlinear functions, such as exponential decay, address many of these problems. In addition, nonlinear models provide several advantages over polynomial models including usefulness of parameters, parsimony, and generalizability. The effects of using nonlinear functions for mediation analysis are then discussed and a nonlinear growth curve model for mediation is presented. An empirical example using data from a randomized intervention study is then provided to illustrate the estimation and interpretation of the model. Implications, limitations, and future directions are also discussed.

An Exponential Decay Model for Mediation

PubMed Central

Fritz, Matthew S.

2013-01-01

Mediation analysis is often used to investigate mechanisms of change in prevention research. Results finding mediation are strengthened when longitudinal data are used because of the need for temporal precedence. Current longitudinal mediation models have focused mainly on linear change, but many variables in prevention change nonlinearly across time. The most common solution to nonlinearity is to add a quadratic term to the linear model, but this can lead to the use of the quadratic function to explain all nonlinearity, regardless of theory and the characteristics of the variables in the model. The current study describes the problems that arise when quadratic functions are used to describe all nonlinearity and how the use of nonlinear functions, such as exponential decay, addresses many of these problems. In addition, nonlinear models provide several advantages over polynomial models including usefulness of parameters, parsimony, and generalizability. The effects of using nonlinear functions for mediation analysis are then discussed and a nonlinear growth curve model for mediation is presented. An empirical example using data from a randomized intervention study is then provided to illustrate the estimation and interpretation of the model. Implications, limitations, and future directions are also discussed. PMID:23625557

Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar

2016-06-15

We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit. -- Highlights: •Symmetric quadratic operators aremore » useful models for many physical applications. •Any such operator exhibits a pseudo-Hermitian matrix representation. •Its eigenvalues are the natural frequencies of the Hamiltonian operator. •The eigenvalues may be real or complex and describe a phase transition.« less

Synchronization of Coupled Dynamical Systems: Tolerance to Weak Connectivity and Arbitrarily Bounded Time-Varying Delays

DOE Office of Scientific and Technical Information (OSTI.GOV)

Meng, Ziyang; Yang, Tao; Li, Guoqi

Here, we study synchronization of coupled linear systems over networks with weak connectivity and nonuniform time-varying delays. We focus on the case where the internal dynamics are time-varying but non-expansive (stable dynamics with a quadratic Lyapunov function). Both uniformly jointly connected and infinitely jointly connected communication topologies are considered. A new concept of quadratic synchronization is introduced. We first show that global asymptotic quadratic synchronization can be achieved over directed networks with uniform joint connectivity and arbitrarily bounded delays. We then study the case of infinitely jointly connected communication topology. In particular, for the undirected communication topologies, it turns outmore » that the existence of a uniform time interval for the jointly connected communication topology is not necessary and quadratic synchronization can be achieved when the time-varying nonuniform delays are arbitrarily bounded. Finally, simulation results are provided to validate the theoretical results.« less

On Volterra quadratic stochastic operators with continual state space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar

2015-05-15

Let (X,F) be a measurable space, and S(X,F) be the set of all probability measures on (X,F) where X is a state space and F is σ - algebraon X. We consider a nonlinear transformation (quadratic stochastic operator) defined by (Vλ)(A) = ∫{sub X}∫{sub X}P(x,y,A)dλ(x)dλ(y), where P(x, y, A) is regarded as a function of two variables x and y with fixed A ∈ F . A quadratic stochastic operator V is called a regular, if for any initial measure the strong limit lim{sub n→∞} V{sup n }(λ) is exists. In this paper, we construct a family of quadratic stochastic operators defined on themore » segment X = [0,1] with Borel σ - algebra F on X , prove their regularity and show that the limit measure is a Dirac measure.« less

Towards a unifying approach to diversity measures: bridging the gap between the Shannon entropy and Rao's quadratic index.

PubMed

Ricotta, Carlo; Szeidl, Laszlo

2006-11-01

The diversity of a species assemblage has been studied extensively for many decades in relation to its possible connection with ecosystem functioning and organization. In this view most diversity measures, such as Shannon's entropy, rely upon information theory as a basis for the quantification of diversity. Also, traditional diversity measures are computed using species relative abundances and cannot account for the ecological differences between species. Rao first proposed a diversity index, termed quadratic diversity (Q) that incorporates both species relative abundances and pairwise distances between species. Quadratic diversity is traditionally defined as the expected distance between two randomly selected individuals. In this paper, we show that quadratic diversity can be interpreted as the expected conflict among the species of a given assemblage. From this unusual interpretation, it naturally follows that Rao's Q can be related to the Shannon entropy through a generalized version of the Tsallis parametric entropy.

Synchronization of Coupled Dynamical Systems: Tolerance to Weak Connectivity and Arbitrarily Bounded Time-Varying Delays

DOE PAGES

Meng, Ziyang; Yang, Tao; Li, Guoqi; ...

2017-09-18

Here, we study synchronization of coupled linear systems over networks with weak connectivity and nonuniform time-varying delays. We focus on the case where the internal dynamics are time-varying but non-expansive (stable dynamics with a quadratic Lyapunov function). Both uniformly jointly connected and infinitely jointly connected communication topologies are considered. A new concept of quadratic synchronization is introduced. We first show that global asymptotic quadratic synchronization can be achieved over directed networks with uniform joint connectivity and arbitrarily bounded delays. We then study the case of infinitely jointly connected communication topology. In particular, for the undirected communication topologies, it turns outmore » that the existence of a uniform time interval for the jointly connected communication topology is not necessary and quadratic synchronization can be achieved when the time-varying nonuniform delays are arbitrarily bounded. Finally, simulation results are provided to validate the theoretical results.« less

Two healing lengths in a two-band GL-model with quadratic terms: Numerical results

NASA Astrophysics Data System (ADS)

Macias-Medri, A. E.; Rodríguez-Núñez, J. J.

2018-05-01

A two-band and quartic interaction order Ginzburg-Landau model in the presence of a single vortex is studied in this work. Interactions of second (quadratic, with coupling parameter γ) and fourth (quartic, with coupling parameter γ˜) order between the two superconducting order parameters (fi with i = 1,2) are incorporated in a functional. Terms beyond quadratic gradient contributions are neglected in the corresponding minimized free energy. The solution of the system of coupled equations is solved by numerical methods to obtain the fi-profiles, where our starting point was the calculation of the superconducting critical temperature Tc. With this at hand, we evaluate fi and the magnetic field along the z-axis, B0, as function of γ, γ˜, the radial distance r/λ1(0) and the temperature T, for T ≈ Tc. The self-consistent equations allow us to compute λ (penetration depth) and the healing lengths of fi (Lhi with i = 1,2) as functions of T, γ and γ˜. At the end, relevant discussions about type-1.5 superconductivity in the compounds we have studied are presented.

Random regression analyses using B-spline functions to model growth of Nellore cattle.

PubMed

Boligon, A A; Mercadante, M E Z; Lôbo, R B; Baldi, F; Albuquerque, L G

2012-02-01

The objective of this study was to estimate (co)variance components using random regression on B-spline functions to weight records obtained from birth to adulthood. A total of 82 064 weight records of 8145 females obtained from the data bank of the Nellore Breeding Program (PMGRN/Nellore Brazil) which started in 1987, were used. The models included direct additive and maternal genetic effects and animal and maternal permanent environmental effects as random. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of age (cubic regression) were considered as random covariate. The random effects were modeled using B-spline functions considering linear, quadratic and cubic polynomials for each individual segment. Residual variances were grouped in five age classes. Direct additive genetic and animal permanent environmental effects were modeled using up to seven knots (six segments). A single segment with two knots at the end points of the curve was used for the estimation of maternal genetic and maternal permanent environmental effects. A total of 15 models were studied, with the number of parameters ranging from 17 to 81. The models that used B-splines were compared with multi-trait analyses with nine weight traits and to a random regression model that used orthogonal Legendre polynomials. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most appropriate and parsimonious model to describe the covariance structure of the data. Selection for higher weight, such as at young ages, should be performed taking into account an increase in mature cow weight. Particularly, this is important in most of Nellore beef cattle production systems, where the cow herd is maintained on range conditions. There is limited modification of the growth curve of Nellore cattle with respect to the aim of selecting them for rapid growth at young ages while maintaining constant adult weight.

Lump solutions with interaction phenomena in the (2+1)-dimensional Ito equation

NASA Astrophysics Data System (ADS)

Zou, Li; Yu, Zong-Bing; Tian, Shou-Fu; Feng, Lian-Li; Li, Jin

2018-03-01

In this paper, we consider the (2+1)-dimensional Ito equation, which was introduced by Ito. By considering the Hirota’s bilinear method, and using the positive quadratic function, we obtain some lump solutions of the Ito equation. In order to ensure rational localization and analyticity of these lump solutions, some sufficient and necessary conditions are provided on the parameters that appeared in the solutions. Furthermore, the interaction solutions between lump solutions and the stripe solitons are discussed by combining positive quadratic function with exponential function. Finally, the dynamic properties of these solutions are shown via the way of graphical analysis by selecting appropriate values of the parameters.

An international age- and gender-controlled model for the Spinal Cord Injury Ability Realization Measurement Index (SCI-ARMI).

PubMed

Scivoletto, Giorgio; Glass, Clive; Anderson, Kim D; Galili, Tal; Benjamin, Yoav; Front, Lilach; Aidinoff, Elena; Bluvshtein, Vadim; Itzkovich, Malka; Aito, Sergio; Baroncini, Ilaria; Benito-Penalva, Jesùs; Castellano, Simona; Osman, Aheed; Silva, Pedro; Catz, Amiram

2015-01-01

Background. A quadratic formula of the Spinal Cord Injury Ability Realization Measurement Index (SCI-ARMI) has previously been published. This formula was based on a model of Spinal Cord Independence Measure (SCIM95), the 95th percentile of the SCIM III values, which correspond with the American Spinal Injury Association Motor Scores (AMS) of SCI patients. Objective. To further develop the original formula. Setting. Spinal cord injury centers from 6 countries and the Statistical Laboratory, Tel-Aviv University, Israel. Methods. SCIM95 of 661 SCI patients was modeled, using a quantile regression with or without adjustment for age and gender, to calculate SCI-ARMI values. SCI-ARMI gain during rehabilitation and its correlations were examined. Results. A new quadratic SCIM95 model was created. This resembled the previously published model, which yielded similar SCIM95 values in all the countries, after adjustment for age and gender. Without this adjustment, however, only 86% of the non-Israeli SCIM III observations were lower than those SCIM95 values (P < .0001). Adding the variables age and gender to the new model affected the SCIM95 value significantly (P < .04). Adding country information did not add a significant effect (P > .1). SCI-ARMI gain was positive (38.8 ± 22 points, P < .0001) and correlated weakly with admission age and AMS. Conclusions. The original quadratic SCI-ARMI formula is valid for an international population after adjustment for age and gender. The new formula considers more factors that affect functional ability following SCI. © The Author(s) 2014.

Order-Constrained Solutions in K-Means Clustering: Even Better than Being Globally Optimal

ERIC Educational Resources Information Center

Steinley, Douglas; Hubert, Lawrence

2008-01-01

This paper proposes an order-constrained K-means cluster analysis strategy, and implements that strategy through an auxiliary quadratic assignment optimization heuristic that identifies an initial object order. A subsequent dynamic programming recursion is applied to optimally subdivide the object set subject to the order constraint. We show that…

Reconstruction of the unknown optimization cost functions from experimental recordings during static multi-finger prehension

PubMed Central

Niu, Xun; Terekhov, Alexander V.; Latash, Mark L.; Zatsiorsky, Vladimir M.

2013-01-01

The goal of the research is to reconstruct the unknown cost (objective) function(s) presumably used by the neural controller for sharing the total force among individual fingers in multi-finger prehension. The cost function was determined from experimental data by applying the recently developed Analytical Inverse Optimization (ANIO) method (Terekhov et al 2010). The core of the ANIO method is the Theorem of Uniqueness that specifies conditions for unique (with some restrictions) estimation of the objective functions. In the experiment, subjects (n=8) grasped an instrumented handle and maintained it at rest in the air with various external torques, loads, and target grasping forces applied to the object. The experimental data recorded from 80 trials showed a tendency to lie on a 2-dimensional hyperplane in the 4-dimensional finger-force space. Because the constraints in each trial were different, such a propensity is a manifestation of a neural mechanism (not the task mechanics). In agreement with the Lagrange principle for the inverse optimization, the plane of experimental observations was close to the plane resulting from the direct optimization. The latter plane was determined using the ANIO method. The unknown cost function was reconstructed successfully for each performer, as well as for the group data. The cost functions were found to be quadratic with non-zero linear terms. The cost functions obtained with the ANIO method yielded more accurate results than other optimization methods. The ANIO method has an evident potential for addressing the problem of optimization in motor control. PMID:22104742

The GUP and quantum Raychaudhuri equation

NASA Astrophysics Data System (ADS)

Vagenas, Elias C.; Alasfar, Lina; Alsaleh, Salwa M.; Ali, Ahmed Farag

2018-06-01

In this paper, we compare the quantum corrections to the Schwarzschild black hole temperature due to quadratic and linear-quadratic generalised uncertainty principle, with the corrections from the quantum Raychaudhuri equation. The reason for this comparison is to connect the deformation parameters β0 and α0 with η which is the parameter that characterises the quantum Raychaudhuri equation. The derived relation between the parameters appears to depend on the relative scale of the system (black hole), which could be read as a beta function equation for the quadratic deformation parameter β0. This study shows a correspondence between the two phenomenological approaches and indicates that quantum Raychaudhuri equation implies the existence of a crystal-like structure of spacetime.

Reconstruction of quadratic curves in 3D using two or more perspective views: simulation studies

NASA Astrophysics Data System (ADS)

Kumar, Sanjeev; Sukavanam, N.; Balasubramanian, R.

2006-01-01

The shapes of many natural and man-made objects have planar and curvilinear surfaces. The images of such curves usually do not have sufficient distinctive features to apply conventional feature-based reconstruction algorithms. In this paper, we describe a method of reconstruction of a quadratic curve in 3-D space as an intersection of two cones containing the respective projected curve images. The correspondence between this pair of projections of the curve is assumed to be established in this work. Using least-square curve fitting, the parameters of a curve in 2-D space are found. From this we are reconstructing the 3-D quadratic curve. Relevant mathematical formulations and analytical solutions for obtaining the equation of reconstructed curve are given. The result of the described reconstruction methodology are studied by simulation studies. This reconstruction methodology is applicable to LBW decision in cricket, path of the missile, Robotic Vision, path lanning etc.

Power law asymptotics in the creation of strange attractors in the quasi-periodically forced quadratic family

NASA Astrophysics Data System (ADS)

Ohlson Timoudas, Thomas

2017-12-01

Let Φ be a quasi-periodically forced quadratic map, where the rotation constant ω is a Diophantine irrational. A strange non-chaotic attractor (SNA) is an invariant (under Φ) attracting graph of a nowhere continuous measurable function ψ from the circle {T} to [0, 1] . This paper investigates how a smooth attractor degenerates into a strange one, as a parameter \

Elegant Ince-Gaussian beams in a quadratic-index medium

NASA Astrophysics Data System (ADS)

Bai, Zhi-Yong; Deng, Dong-Mei; Guo, Qi

2011-09-01

Elegant Ince—Gaussian beams, which are the exact solutions of the paraxial wave equation in a quadratic-index medium, are derived in elliptical coordinates. These kinds of beams are the alternative form of standard Ince—Gaussian beams and they display better symmetry between the Ince-polynomials and the Gaussian function in mathematics. The transverse intensity distribution and the phase of the elegant Ince—Gaussian beams are discussed.

A quadratic-tensor model algorithm for nonlinear least-squares problems with linear constraints

NASA Technical Reports Server (NTRS)

Hanson, R. J.; Krogh, Fred T.

1992-01-01

A new algorithm for solving nonlinear least-squares and nonlinear equation problems is proposed which is based on approximating the nonlinear functions using the quadratic-tensor model by Schnabel and Frank. The algorithm uses a trust region defined by a box containing the current values of the unknowns. The algorithm is found to be effective for problems with linear constraints and dense Jacobian matrices.

Quantum Quench of the Sachdev-Ye-Kitaev Model

NASA Astrophysics Data System (ADS)

Steinberg, Julia; Eberlein, Andreas; Sachdev, Subir

The Sachdev-Ye-Kitaev model is a single site model containing N flavors of fermions with random infinite range interactions. It is exactly solvable in the large N limit and has an emergent reparameterization symmetry in time at low temperatures and strong coupling. This leads to many interesting properties such as locally critical behavior in correlation functions and the saturation of the chaos bound proposed .We start with the generalized Sachdev-Ye-Kitaev with quadratic and quartic interactions. This Hamiltonian has the form of a 0+1d Fermi liquid and contains long-lived quasiparticles at all values of the quadratic coupling. We quench the system into a locally critical state without quasiparticles by turning off the quadratic coupling at some initial time. We numerically study the spectral function at intermediate and long times and determine the timescale in which the system loses memory of the quasiparticles. J.S. is supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE1144152.

QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES

PubMed Central

RAND, ALEXANDER; GILLETTE, ANDREW; BAJAJ, CHANDRAJIT

2013-01-01

We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called ‘serendipity’ elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed. PMID:25301974

Repair-dependent cell radiation survival and transformation: an integrated theory.

PubMed

Sutherland, John C

2014-09-07

The repair-dependent model of cell radiation survival is extended to include radiation-induced transformations. The probability of transformation is presumed to scale with the number of potentially lethal damages that are repaired in a surviving cell or the interactions of such damages. The theory predicts that at doses corresponding to high survival, the transformation frequency is the sum of simple polynomial functions of dose; linear, quadratic, etc, essentially as described in widely used linear-quadratic expressions. At high doses, corresponding to low survival, the ratio of transformed to surviving cells asymptotically approaches an upper limit. The low dose fundamental- and high dose plateau domains are separated by a downwardly concave transition region. Published transformation data for mammalian cells show the high-dose plateaus predicted by the repair-dependent model for both ultraviolet and ionizing radiation. For the neoplastic transformation experiments that were analyzed, the data can be fit with only the repair-dependent quadratic function. At low doses, the transformation frequency is strictly quadratic, but becomes sigmodial over a wider range of doses. Inclusion of data from the transition region in a traditional linear-quadratic analysis of neoplastic transformation frequency data can exaggerate the magnitude of, or create the appearance of, a linear component. Quantitative analysis of survival and transformation data shows good agreement for ultraviolet radiation; the shapes of the transformation components can be predicted from survival data. For ionizing radiations, both neutrons and x-rays, survival data overestimate the transforming ability for low to moderate doses. The presumed cause of this difference is that, unlike UV photons, a single x-ray or neutron may generate more than one lethal damage in a cell, so the distribution of such damages in the population is not accurately described by Poisson statistics. However, the complete sigmodial dose-response data for neoplastic transformations can be fit using the repair-dependent functions with all parameters determined only from transformation frequency data.

Effect of dietary supplementation with Moringa Oleifera leaf on performance, meat quality, and oxidative stability of meat in broilers.

PubMed

Cui, Yao-Ming; Wang, Jing; Lu, Wei; Zhang, Hai-Jun; Wu, Shu-Geng; Qi, Guang-Hai

2018-04-11

The objective of this study was to evaluate the effects of dietary supplementation with Moringa oleifera leaf (MOL) on performance, carcass characteristics, meat quality, and oxidative stability of breast muscle in broilers. A total of 720 1-d-old male Arbor Acres birds were randomly divided into 6 dietary groups, which were fed a basal diet supplemented with 0, 1, 2, 5, 10, and 15% MOL, respectively. Each group had 6 replicates of 20 birds each. The feeding trial lasted for 42 d. The results showed dietary MOL supplementation linearly and quadratically decreased body weight and average daily gain (P < 0.01), and increased feed conversion ratio (P < 0.001). Abdominal fat decreased linearly and quadratically in response to the supplementation of MOL in diets, both on d 21 and 42 (P < 0.001). In breast muscle, dietary supplementation with MOL quadratically increased the contents of C18:2, C18:3n-3, C20:4, polyunsaturated fatty acids (PUFA), n-3 PUFA, n-6 PUFA (P < 0.01), and decreased thrombogenic index (TI; P = 0.019). Dietary inclusion of MOL improved meat color, evidenced by quadratically reduced b* (yellowness) values (45 min postmortem, P = 0.001; 24 h postmortem, P = 0.018) and increased a* (redness) values (24 h postmortem, P < 0.001). Besides, diets supplemented with MOL quadratically decreased malondialdehyde (MDA) levels in breast muscle during storage (P < 0.001). Plasma total anti-oxidative capacity, total superoxide dismutase, glutathione peroxidase activities increased quadratically (P < 0.01), whereas MDA decreased quadratically (P < 0.001), in response to dietary MOL supplementation. In summary, MOL could be used as a feed ingredient for broilers to improve PUFA contents, oxidative stability, color of breast muscle, and abdominal fat without adverse effects on growth performance, with an inclusion of 1.56% in the diets.

Top-down deactivation of interference from irrelevant spatial or verbal stimulus features.

PubMed

Frings, Christian; Wühr, Peter

2014-11-01

The selective-attention model of Houghton and Tipper (1994) assumes top-down deactivation of (conflicting) distractor representations as a mechanism of visual attention. Deactivation should produce an inverted-U-shaped activation function for distractor representations. In a recent study, Frings, Wentura, and Wühr (2012) tested this prediction in a variant of the flanker task in which a cue sometimes required participants to respond to the distractors rather than to the target. When reaction times and error rates were plotted as a function of the target-cue stimulus onset asynchrony, a quadratic trend emerged, consistent with the notion of distractor deactivation. However, in the flanker task, an alternative explanation for the quadratic trend in terms of attentional zooming is possible. The present experiments tested the deactivation account against the attentional-zooming account with the Stroop and the Simon task, in which attentional zooming should have minimal effects on distractor processing, because the target and distractor are presented at the same spatial location. Both experiments replicated the quadratic trend in the performance functions for responses to incongruent distractors, and additionally showed linear trends in the performance functions for responses to congruent distractors. These results provide additional support for the notion of top-down deactivation of distractor representations as a mechanism of visual selective attention.

Robust Control of Uncertain Systems via Dissipative LQG-Type Controllers

NASA Technical Reports Server (NTRS)

Joshi, Suresh M.

2000-01-01

Optimal controller design is addressed for a class of linear, time-invariant systems which are dissipative with respect to a quadratic power function. The system matrices are assumed to be affine functions of uncertain parameters confined to a convex polytopic region in the parameter space. For such systems, a method is developed for designing a controller which is dissipative with respect to a given power function, and is simultaneously optimal in the linear-quadratic-Gaussian (LQG) sense. The resulting controller provides robust stability as well as optimal performance. Three important special cases, namely, passive, norm-bounded, and sector-bounded controllers, which are also LQG-optimal, are presented. The results give new methods for robust controller design in the presence of parametric uncertainties.

Development of Analysis Tools for Certification of Flight Control Laws

DTIC Science & Technology

2009-03-31

In Proc. Conf. on Decision and Control, pages 881-886, Bahamas, 2004. [7] G. Chesi, A. Garulli, A. Tesi , and A. Vicino. LMI-based computation of...Minneapolis, MN, 2006, pp. 117-122. [10] G. Chesi, A. Garulli, A. Tesi . and A. Vicino, "LMI-based computation of optimal quadratic Lyapunov functions...Convex Optimization. Cambridge Univ. Press. Chesi, G., A. Garulli, A. Tesi and A. Vicino (2005). LMI-based computation of optimal quadratic Lyapunov

Online gaming for learning optimal team strategies in real time

NASA Astrophysics Data System (ADS)

Hudas, Gregory; Lewis, F. L.; Vamvoudakis, K. G.

2010-04-01

This paper first presents an overall view for dynamical decision-making in teams, both cooperative and competitive. Strategies for team decision problems, including optimal control, zero-sum 2-player games (H-infinity control) and so on are normally solved for off-line by solving associated matrix equations such as the Riccati equation. However, using that approach, players cannot change their objectives online in real time without calling for a completely new off-line solution for the new strategies. Therefore, in this paper we give a method for learning optimal team strategies online in real time as team dynamical play unfolds. In the linear quadratic regulator case, for instance, the method learns the Riccati equation solution online without ever solving the Riccati equation. This allows for truly dynamical team decisions where objective functions can change in real time and the system dynamics can be time-varying.

Physical Watermarking for Securing Cyber-Physical Systems via Packet Drop Injections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ozel, Omur; Weekrakkody, Sean; Sinopoli, Bruno

Physical watermarking is a well known solution for detecting integrity attacks on Cyber-Physical Systems (CPSs) such as the smart grid. Here, a random control input is injected into the system in order to authenticate physical dynamics and sensors which may have been corrupted by adversaries. Packet drops may naturally occur in a CPS due to network imperfections. To our knowledge, previous work has not considered the role of packet drops in detecting integrity attacks. In this paper, we investigate the merit of injecting Bernoulli packet drops into the control inputs sent to actuators as a new physical watermarking scheme. Withmore » the classical linear quadratic objective function and an independent and identically distributed packet drop injection sequence, we study the effect of packet drops on meeting security and control objectives. Our results indicate that the packet drops could act as a potential physical watermark for attack detection in CPSs.« less

Algorithm For Optimal Control Of Large Structures

NASA Technical Reports Server (NTRS)

Salama, Moktar A.; Garba, John A..; Utku, Senol

1989-01-01

Cost of computation appears competitive with other methods. Problem to compute optimal control of forced response of structure with n degrees of freedom identified in terms of smaller number, r, of vibrational modes. Article begins with Hamilton-Jacobi formulation of mechanics and use of quadratic cost functional. Complexity reduced by alternative approach in which quadratic cost functional expressed in terms of control variables only. Leads to iterative solution of second-order time-integral matrix Volterra equation of second kind containing optimal control vector. Cost of algorithm, measured in terms of number of computations required, is of order of, or less than, cost of prior algoritms applied to similar problems.

Cost decomposition of linear systems with application to model reduction

NASA Technical Reports Server (NTRS)

Skelton, R. E.

1980-01-01

A means is provided to assess the value or 'cst' of each component of a large scale system, when the total cost is a quadratic function. Such a 'cost decomposition' of the system has several important uses. When the components represent physical subsystems which can fail, the 'component cost' is useful in failure mode analysis. When the components represent mathematical equations which may be truncated, the 'component cost' becomes a criterion for model truncation. In this latter event component costs provide a mechanism by which the specific control objectives dictate which components should be retained in the model reduction process. This information can be valuable in model reduction and decentralized control problems.

On the cost of approximating and recognizing a noise perturbed straight line or a quadratic curve segment in the plane. [central processing units

NASA Technical Reports Server (NTRS)

Cooper, D. B.; Yalabik, N.

1975-01-01

Approximation of noisy data in the plane by straight lines or elliptic or single-branch hyperbolic curve segments arises in pattern recognition, data compaction, and other problems. The efficient search for and approximation of data by such curves were examined. Recursive least-squares linear curve-fitting was used, and ellipses and hyperbolas are parameterized as quadratic functions in x and y. The error minimized by the algorithm is interpreted, and central processing unit (CPU) times for estimating parameters for fitting straight lines and quadratic curves were determined and compared. CPU time for data search was also determined for the case of straight line fitting. Quadratic curve fitting is shown to require about six times as much CPU time as does straight line fitting, and curves relating CPU time and fitting error were determined for straight line fitting. Results are derived on early sequential determination of whether or not the underlying curve is a straight line.

Extending the accuracy of the SNAP interatomic potential form

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wood, Mitchell A.; Thompson, Aidan P.

The Spectral Neighbor Analysis Potential (SNAP) is a classical interatomic potential that expresses the energy of each atom as a linear function of selected bispectrum components of the neighbor atoms. An extension of the SNAP form is proposed that includes quadratic terms in the bispectrum components. The extension is shown to provide a large increase in accuracy relative to the linear form, while incurring only a modest increase in computational cost. The mathematical structure of the quadratic SNAP form is similar to the embedded atom method (EAM), with the SNAP bispectrum components serving as counterparts to the two-body density functionsmore » in EAM. It is also argued that the quadratic SNAP form is a special case of an artificial neural network (ANN). The effectiveness of the new form is demonstrated using an extensive set of training data for tantalum structures. Similarly to ANN potentials, the quadratic SNAP form requires substantially more training data in order to prevent overfitting, as measured by cross-validation analysis.« less

Extending the accuracy of the SNAP interatomic potential form

DOE PAGES

Wood, Mitchell A.; Thompson, Aidan P.

2018-03-28

The Spectral Neighbor Analysis Potential (SNAP) is a classical interatomic potential that expresses the energy of each atom as a linear function of selected bispectrum components of the neighbor atoms. An extension of the SNAP form is proposed that includes quadratic terms in the bispectrum components. The extension is shown to provide a large increase in accuracy relative to the linear form, while incurring only a modest increase in computational cost. The mathematical structure of the quadratic SNAP form is similar to the embedded atom method (EAM), with the SNAP bispectrum components serving as counterparts to the two-body density functionsmore » in EAM. It is also argued that the quadratic SNAP form is a special case of an artificial neural network (ANN). The effectiveness of the new form is demonstrated using an extensive set of training data for tantalum structures. Similarly to ANN potentials, the quadratic SNAP form requires substantially more training data in order to prevent overfitting, as measured by cross-validation analysis.« less

The numerical study and comparison of radial basis functions in applications of the dual reciprocity boundary element method to convection-diffusion problems

NASA Astrophysics Data System (ADS)

Chanthawara, Krittidej; Kaennakham, Sayan; Toutip, Wattana

2016-02-01

The methodology of Dual Reciprocity Boundary Element Method (DRBEM) is applied to the convection-diffusion problems and investigating its performance is our first objective of the work. Seven types of Radial Basis Functions (RBF); Linear, Thin-plate Spline, Cubic, Compactly Supported, Inverse Multiquadric, Quadratic, and that proposed by [12], were closely investigated in order to numerically compare their effectiveness drawbacks etc. and this is taken as our second objective. A sufficient number of simulations were performed covering as many aspects as possible. Varidated against both exacts and other numerical works, the final results imply strongly that the Thin-Plate Spline and Linear type of RBF are superior to others in terms of both solutions' quality and CPU-time spent while the Inverse Multiquadric seems to poorly yield the results. It is also found that DRBEM can perform relatively well at moderate level of convective force and as anticipated becomes unstable when the problem becomes more convective-dominated, as normally found in all classical mesh-dependence methods.

Contact-force distribution optimization and control for quadruped robots using both gradient and adaptive neural networks.

PubMed

Li, Zhijun; Ge, Shuzhi Sam; Liu, Sibang

2014-08-01

This paper investigates optimal feet forces' distribution and control of quadruped robots under external disturbance forces. First, we formulate a constrained dynamics of quadruped robots and derive a reduced-order dynamical model of motion/force. Consider an external wrench on quadruped robots; the distribution of required forces and moments on the supporting legs of a quadruped robot is handled as a tip-point force distribution and used to equilibrate the external wrench. Then, a gradient neural network is adopted to deal with the optimized objective function formulated as to minimize this quadratic objective function subjected to linear equality and inequality constraints. For the obtained optimized tip-point force and the motion of legs, we propose the hybrid motion/force control based on an adaptive neural network to compensate for the perturbations in the environment and approximate feedforward force and impedance of the leg joints. The proposed control can confront the uncertainties including approximation error and external perturbation. The verification of the proposed control is conducted using a simulation.

Data Assimilation on a Quantum Annealing Computer: Feasibility and Scalability

NASA Astrophysics Data System (ADS)

Nearing, G. S.; Halem, M.; Chapman, D. R.; Pelissier, C. S.

2014-12-01

Data assimilation is one of the ubiquitous and computationally hard problems in the Earth Sciences. In particular, ensemble-based methods require a large number of model evaluations to estimate the prior probability density over system states, and variational methods require adjoint calculations and iteration to locate the maximum a posteriori solution in the presence of nonlinear models and observation operators. Quantum annealing computers (QAC) like the new D-Wave housed at the NASA Ames Research Center can be used for optimization and sampling, and therefore offers a new possibility for efficiently solving hard data assimilation problems. Coding on the QAC is not straightforward: a problem must be posed as a Quadratic Unconstrained Binary Optimization (QUBO) and mapped to a spherical Chimera graph. We have developed a method for compiling nonlinear 4D-Var problems on the D-Wave that consists of five steps: Emulating the nonlinear model and/or observation function using radial basis functions (RBF) or Chebyshev polynomials. Truncating a Taylor series around each RBF kernel. Reducing the Taylor polynomial to a quadratic using ancilla gadgets. Mapping the real-valued quadratic to a fixed-precision binary quadratic. Mapping the fully coupled binary quadratic to a partially coupled spherical Chimera graph using ancilla gadgets. At present the D-Wave contains 512 qbits (with 1024 and 2048 qbit machines due in the next two years); this machine size allows us to estimate only 3 state variables at each satellite overpass. However, QAC's solve optimization problems using a physical (quantum) system, and therefore do not require iterations or calculation of model adjoints. This has the potential to revolutionize our ability to efficiently perform variational data assimilation, as the size of these computers grows in the coming years.

Direct Reconstruction of CT-Based Attenuation Correction Images for PET With Cluster-Based Penalties

NASA Astrophysics Data System (ADS)

Kim, Soo Mee; Alessio, Adam M.; De Man, Bruno; Kinahan, Paul E.

2017-03-01

Extremely low-dose (LD) CT acquisitions used for PET attenuation correction have high levels of noise and potential bias artifacts due to photon starvation. This paper explores the use of a priori knowledge for iterative image reconstruction of the CT-based attenuation map. We investigate a maximum a posteriori framework with cluster-based multinomial penalty for direct iterative coordinate decent (dICD) reconstruction of the PET attenuation map. The objective function for direct iterative attenuation map reconstruction used a Poisson log-likelihood data fit term and evaluated two image penalty terms of spatial and mixture distributions. The spatial regularization is based on a quadratic penalty. For the mixture penalty, we assumed that the attenuation map may consist of four material clusters: air + background, lung, soft tissue, and bone. Using simulated noisy sinogram data, dICD reconstruction was performed with different strengths of the spatial and mixture penalties. The combined spatial and mixture penalties reduced the root mean squared error (RMSE) by roughly two times compared with a weighted least square and filtered backprojection reconstruction of CT images. The combined spatial and mixture penalties resulted in only slightly lower RMSE compared with a spatial quadratic penalty alone. For direct PET attenuation map reconstruction from ultra-LD CT acquisitions, the combination of spatial and mixture penalties offers regularization of both variance and bias and is a potential method to reconstruct attenuation maps with negligible patient dose. The presented results, using a best-case histogram suggest that the mixture penalty does not offer a substantive benefit over conventional quadratic regularization and diminishes enthusiasm for exploring future application of the mixture penalty.

Application’s Method of Quadratic Programming for Optimization of Portfolio Selection

NASA Astrophysics Data System (ADS)

Kawamoto, Shigeru; Takamoto, Masanori; Kobayashi, Yasuhiro

Investors or fund-managers face with optimization of portfolio selection, which means that determine the kind and the quantity of investment among several brands. We have developed a method to obtain optimal stock’s portfolio more rapidly from twice to three times than conventional method with efficient universal optimization. The method is characterized by quadratic matrix of utility function and constrained matrices divided into several sub-matrices by focusing on structure of these matrices.

Legendre-tau approximation for functional differential equations. Part 2: The linear quadratic optimal control problem

NASA Technical Reports Server (NTRS)

Ito, K.; Teglas, R.

1984-01-01

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Legendre-tau approximation for functional differential equations. II - The linear quadratic optimal control problem

NASA Technical Reports Server (NTRS)

Ito, Kazufumi; Teglas, Russell

1987-01-01

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Finite difference schemes for long-time integration

NASA Technical Reports Server (NTRS)

Haras, Zigo; Taasan, Shlomo

1993-01-01

Finite difference schemes for the evaluation of first and second derivatives are presented. These second order compact schemes were designed for long-time integration of evolution equations by solving a quadratic constrained minimization problem. The quadratic cost function measures the global truncation error while taking into account the initial data. The resulting schemes are applicable for integration times fourfold, or more, longer than similar previously studied schemes. A similar approach was used to obtain improved integration schemes.

Two-Dimensional Signal Processing and Storage and Theory and Applications of Electromagnetic Measurements.

DTIC Science & Technology

1987-01-01

the results of that problem to be applied to deblurring . Four procedures for finding the maximum entropy solution have been developed and have becn...distortion operator h, converges quadratically to an impulse and, as a result, the restoration x, converges quadratically to x. Therefore, when the standard...is concerned with the modeling of a * signal as the sum of sinusoids in white noise where the sinusoidal frequencies are varying as a function of time

Half-quadratic variational regularization methods for speckle-suppression and edge-enhancement in SAR complex image

NASA Astrophysics Data System (ADS)

Zhao, Xia; Wang, Guang-xin

2008-12-01

Synthetic aperture radar (SAR) is an active remote sensing sensor. It is a coherent imaging system, the speckle is its inherent default, which affects badly the interpretation and recognition of the SAR targets. Conventional methods of removing the speckle is studied usually in real SAR image, which reduce the edges of the images at the same time as depressing the speckle. Morever, Conventional methods lost the information about images phase. Removing the speckle and enhancing the target and edge simultaneously are still a puzzle. To suppress the spckle and enhance the targets and the edges simultaneously, a half-quadratic variational regularization method in complex SAR image is presented, which is based on the prior knowledge of the targets and the edge. Due to the non-quadratic and non- convex quality and the complexity of the cost function, a half-quadratic variational regularization variation is used to construct a new cost function,which is solved by alternate optimization. In the proposed scheme, the construction of the model, the solution of the model and the selection of the model peremeters are studied carefully. In the end, we validate the method using the real SAR data.Theoretic analysis and the experimental results illustrate the the feasibility of the proposed method. Further more, the proposed method can preserve the information about images phase.

A New Control Paradigm for Stochastic Differential Equations

NASA Astrophysics Data System (ADS)

Schmid, Matthias J. A.

This study presents a novel comprehensive approach to the control of dynamic systems under uncertainty governed by stochastic differential equations (SDEs). Large Deviations (LD) techniques are employed to arrive at a control law for a large class of nonlinear systems minimizing sample path deviations. Thereby, a paradigm shift is suggested from point-in-time to sample path statistics on function spaces. A suitable formal control framework which leverages embedded Freidlin-Wentzell theory is proposed and described in detail. This includes the precise definition of the control objective and comprises an accurate discussion of the adaptation of the Freidlin-Wentzell theorem to the particular situation. The new control design is enabled by the transformation of an ill-posed control objective into a well-conditioned sequential optimization problem. A direct numerical solution process is presented using quadratic programming, but the emphasis is on the development of a closed-form expression reflecting the asymptotic deviation probability of a particular nominal path. This is identified as the key factor in the success of the new paradigm. An approach employing the second variation and the differential curvature of the effective action is suggested for small deviation channels leading to the Jacobi field of the rate function and the subsequently introduced Jacobi field performance measure. This closed-form solution is utilized in combination with the supplied parametrization of the objective space. For the first time, this allows for an LD based control design applicable to a large class of nonlinear systems. Thus, Minimum Large Deviations (MLD) control is effectively established in a comprehensive structured framework. The construction of the new paradigm is completed by an optimality proof for the Jacobi field performance measure, an interpretive discussion, and a suggestion for efficient implementation. The potential of the new approach is exhibited by its extension to scalar systems subject to state-dependent noise and to systems of higher order. The suggested control paradigm is further advanced when a sequential application of MLD control is considered. This technique yields a nominal path corresponding to the minimum total deviation probability on the entire time domain. It is demonstrated that this sequential optimization concept can be unified in a single objective function which is revealed to be the Jacobi field performance index on the entire domain subject to an endpoint deviation. The emerging closed-form term replaces the previously required nested optimization and, thus, results in a highly efficient application-ready control design. This effectively substantiates Minimum Path Deviation (MPD) control. The proposed control paradigm allows the specific problem of stochastic cost control to be addressed as a special case. This new technique is employed within this study for the stochastic cost problem giving rise to Cost Constrained MPD (CCMPD) as well as to Minimum Quadratic Cost Deviation (MQCD) control. An exemplary treatment of a generic scalar nonlinear system subject to quadratic costs is performed for MQCD control to demonstrate the elementary expandability of the new control paradigm. This work concludes with a numerical evaluation of both MPD and CCMPD control for three exemplary benchmark problems. Numerical issues associated with the simulation of SDEs are briefly discussed and illustrated. The numerical examples furnish proof of the successful design. This study is complemented by a thorough review of statistical control methods, stochastic processes, Large Deviations techniques and the Freidlin-Wentzell theory, providing a comprehensive, self-contained account. The presentation of the mathematical tools and concepts is of a unique character, specifically addressing an engineering audience.

On the asymptotic optimality and improved strategies of SPTB heuristic for open-shop scheduling problem

NASA Astrophysics Data System (ADS)

Bai, Danyu; Zhang, Zhihai

2014-08-01

This article investigates the open-shop scheduling problem with the optimal criterion of minimising the sum of quadratic completion times. For this NP-hard problem, the asymptotic optimality of the shortest processing time block (SPTB) heuristic is proven in the sense of limit. Moreover, three different improvements, namely, the job-insert scheme, tabu search and genetic algorithm, are introduced to enhance the quality of the original solution generated by the SPTB heuristic. At the end of the article, a series of numerical experiments demonstrate the convergence of the heuristic, the performance of the improvements and the effectiveness of the quadratic objective.

Heterochromatic Flicker Photometry for Objective Lens Density Quantification.

PubMed

Najjar, Raymond P; Teikari, Petteri; Cornut, Pierre-Loïc; Knoblauch, Kenneth; Cooper, Howard M; Gronfier, Claude

2016-03-01

Although several methods have been proposed to evaluate lens transmittance, to date there is no consensual in vivo approach in clinical practice. The aim of this study was to compare ocular lens density and transmittance measurements obtained by an improved psychophysical scotopic heterochromatic flicker photometry (sHFP) technique to the results obtained by three other measures: a psychophysical threshold technique, a Scheimpflug imaging technique, and a clinical assessment using a validated subjective scale. Forty-three subjects (18 young, 9 middle aged, and 16 older) were included in the study. Individual lens densities were measured and transmittance curves were derived from sHFP indexes. Ocular lens densities were compared across methods by using linear regression analysis. The four approaches showed a quadratic increase in lens opacification with age. The sHFP technique revealed that transmittance decreased with age over the entire visual spectrum. This decrease was particularly pronounced between young and older participants in the short (53.03% decrease in the 400-500 nm range) wavelength regions of the light spectrum. Lens density derived from sHFP highly correlated with the values obtained with the other approaches. Compared to other objective measures, sHFP also showed the lowest variability and the best fit with a quadratic trend (r2 = 0.71) of lens density increase as a function of age. The sHFP technique offers a practical, reliable, and accurate method to measure lens density in vivo and predict lens transmittance over the visible spectrum. An accurate quantification of lens transmittance should be obtained in clinical practice, but also in research in visual and nonvisual photoreception.

Quadratic response functions in the relativistic four-component Kohn-Sham approximation

NASA Astrophysics Data System (ADS)

Henriksson, Johan; Saue, Trond; Norman, Patrick

2008-01-01

A formulation and implementation of the quadratic response function in the adiabatic four-component Kohn-Sham approximation is presented. The noninteracting reference state is time-reversal symmetric and formed from Kramers pair spinors, and the energy density is gradient corrected. Example calculations are presented for the optical properties of disubstituted halobenzenes in their meta and ortho conformations. It is demonstrated that correlation and relativistic effects are not additive, and it is shown that relativity alone reduces the μβ¯-response signal by 62% and 75% for meta- and ortho-bromobenzene, respectively, and enhances the same response by 17% and 21% for meta- and ortho-iodobenzene, respectively. Of the employed functionals, CAM-B3LYP shows the best performance and gives hyperpolarizabilities β distinctly different from B3LYP.

Fluence map optimization (FMO) with dose-volume constraints in IMRT using the geometric distance sorting method.

PubMed

Lan, Yihua; Li, Cunhua; Ren, Haozheng; Zhang, Yong; Min, Zhifang

2012-10-21

A new heuristic algorithm based on the so-called geometric distance sorting technique is proposed for solving the fluence map optimization with dose-volume constraints which is one of the most essential tasks for inverse planning in IMRT. The framework of the proposed method is basically an iterative process which begins with a simple linear constrained quadratic optimization model without considering any dose-volume constraints, and then the dose constraints for the voxels violating the dose-volume constraints are gradually added into the quadratic optimization model step by step until all the dose-volume constraints are satisfied. In each iteration step, an interior point method is adopted to solve each new linear constrained quadratic programming. For choosing the proper candidate voxels for the current dose constraint adding, a so-called geometric distance defined in the transformed standard quadratic form of the fluence map optimization model was used to guide the selection of the voxels. The new geometric distance sorting technique can mostly reduce the unexpected increase of the objective function value caused inevitably by the constraint adding. It can be regarded as an upgrading to the traditional dose sorting technique. The geometry explanation for the proposed method is also given and a proposition is proved to support our heuristic idea. In addition, a smart constraint adding/deleting strategy is designed to ensure a stable iteration convergence. The new algorithm is tested on four cases including head-neck, a prostate, a lung and an oropharyngeal, and compared with the algorithm based on the traditional dose sorting technique. Experimental results showed that the proposed method is more suitable for guiding the selection of new constraints than the traditional dose sorting method, especially for the cases whose target regions are in non-convex shapes. It is a more efficient optimization technique to some extent for choosing constraints than the dose sorting method. By integrating a smart constraint adding/deleting scheme within the iteration framework, the new technique builds up an improved algorithm for solving the fluence map optimization with dose-volume constraints.

Verb bias and verb-specific competition effects on sentence production

PubMed Central

Thothathiri, Malathi; Evans, Daniel G.; Poudel, Sonali

2017-01-01

How do speakers choose between structural options for expressing a given meaning? Overall preference for some structures over others as well as prior statistical association between specific verbs and sentence structures (“verb bias”) are known to broadly influence language use. However, the effects of prior statistical experience on the planning and execution of utterances and the mechanisms that facilitate structural choice for verbs with different biases have not been fully explored. In this study, we manipulated verb bias for English double-object (DO) and prepositional-object (PO) dative structures: some verbs appeared solely in the DO structure (DO-only), others solely in PO (PO-only) and yet others equally in both (Equi). Structural choices during subsequent free-choice sentence production revealed the expected dispreference for DO overall but critically also a reliable linear trend in DO production that was consistent with verb bias (DO-only > Equi > PO-only). Going beyond the general verb bias effect, three results suggested that Equi verbs, which were associated equally with the two structures, engendered verb-specific competition and required additional resources for choosing the dispreferred DO structure. First, DO production with Equi verbs but not the other verbs correlated with participants’ inhibition ability. Second, utterance duration prior to the choice of a DO structure showed a quadratic trend (DO-only < Equi > PO-only) with the longest durations for Equi verbs. Third, eye movements consistent with reimagining the event also showed a quadratic trend (DO-only < Equi > PO-only) prior to choosing DO, suggesting that participants used such recall particularly for Equi verbs. Together, these analyses of structural choices, utterance durations, eye movements and individual differences in executive functions shed light on the effects of verb bias and verb-specific competition on sentence production and the role of different executive functions in choosing between sentence structures. PMID:28672009

Sharing Teaching Ideas.

ERIC Educational Resources Information Center

Touval, Ayana

1992-01-01

Introduces the concept of maximum and minimum function values as turning points on the function's graphic representation and presents a method for finding these values without using calculus. The process of utilizing transformations to find the turning point of a quadratic function is extended to find the turning points of cubic functions. (MDH)

Peroxidised dietary lipids impair intestinal function and morphology of the small intestine villi of nursery pigs in a dose-dependent manner.

PubMed

Rosero, David S; Odle, Jack; Moeser, Adam J; Boyd, R Dean; van Heugten, Eric

2015-12-28

The objective of this study was to investigate the effect of increasing degrees of lipid peroxidation on structure and function of the small intestine of nursery pigs. A total of 216 pigs (mean body weight was 6·5 kg) were randomly allotted within weight blocks and sex and fed one of five experimental diets for 35 d (eleven pens per treatment with three to four pigs per pen). Treatments included a control diet without added lipid, and diets supplemented with 6 % soyabean oil that was exposed to heat (80°C) and constant oxygen flow (1 litre/min) for 0, 6, 9 and 12 d. Increasing lipid peroxidation linearly reduced feed intake (P<0·001) and weight gain (P=0·024). Apparent faecal digestibility of gross energy (P=0·001) and fat (P<0·001) decreased linearly as the degree of peroxidation increased. Absorption of mannitol (linear, P=0·097) and d-xylose (linear, P=0·089), measured in serum 2 h post gavage with a solution containing 0·2 g/ml of d-xylose and 0·3 g/ml of mannitol, tended to decrease progressively as the peroxidation level increased. Increasing peroxidation also resulted in increased villi height (linear, P<0·001) and crypt depth (quadratic, P=0·005) in the jejunum. Increasing peroxidation increased malondialdehyde concentrations (quadratic, P=0·035) and reduced the total antioxidant capacity (linear, P=0·044) in the jejunal mucosa. In conclusion, lipid peroxidation progressively diminished animal performance and modified the function and morphology of the small intestine of nursery pigs. Detrimental effects were related with the disruption of redox environment of the intestinal mucosa.

Uni- and multi-variable modelling of flood losses: experiences gained from the Secchia river inundation event.

NASA Astrophysics Data System (ADS)

Carisi, Francesca; Domeneghetti, Alessio; Kreibich, Heidi; Schröter, Kai; Castellarin, Attilio

2017-04-01

Flood risk is function of flood hazard and vulnerability, therefore its accurate assessment depends on a reliable quantification of both factors. The scientific literature proposes a number of objective and reliable methods for assessing flood hazard, yet it highlights a limited understanding of the fundamental damage processes. Loss modelling is associated with large uncertainty which is, among other factors, due to a lack of standard procedures; for instance, flood losses are often estimated based on damage models derived in completely different contexts (i.e. different countries or geographical regions) without checking its applicability, or by considering only one explanatory variable (i.e. typically water depth). We consider the Secchia river flood event of January 2014, when a sudden levee-breach caused the inundation of nearly 200 km2 in Northern Italy. In the aftermath of this event, local authorities collected flood loss data, together with additional information on affected private households and industrial activities (e.g. buildings surface and economic value, number of company's employees and others). Based on these data we implemented and compared a quadratic-regression damage function, with water depth as the only explanatory variable, and a multi-variable model that combines multiple regression trees and considers several explanatory variables (i.e. bagging decision trees). Our results show the importance of data collection revealing that (1) a simple quadratic regression damage function based on empirical data from the study area can be significantly more accurate than literature damage-models derived for a different context and (2) multi-variable modelling may outperform the uni-variable approach, yet it is more difficult to develop and apply due to a much higher demand of detailed data.

Constrained multiple indicator kriging using sequential quadratic programming

NASA Astrophysics Data System (ADS)

Soltani-Mohammadi, Saeed; Erhan Tercan, A.

2012-11-01

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.

High-Speed Numeric Function Generator Using Piecewise Quadratic Approximations

DTIC Science & Technology

2007-09-01

application; User specifies the fuction to approxiamte. % % This programs turns the function provided into an inline function... PRIMARY = < primary file 1> < primary file 2> #SECONDARY = <secondary file 1> <secondary file 2> #CHIP2 = <file to compile to user chip

A new approach to approximating the linear quadratic optimal control law for hereditary systems with control delays

NASA Technical Reports Server (NTRS)

Milman, M. H.

1985-01-01

A factorization approach is presented for deriving approximations to the optimal feedback gain for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the feedback kernels.

Factorization method of quadratic template

NASA Astrophysics Data System (ADS)

Kotyrba, Martin

2017-07-01

Multiplication of two numbers is a one-way function in mathematics. Any attempt to distribute the outcome to its roots is called factorization. There are many methods such as Fermat's factorization, Dixońs method or quadratic sieve and GNFS, which use sophisticated techniques fast factorization. All the above methods use the same basic formula differing only in its use. This article discusses a newly designed factorization method. Effective implementation of this method in programs is not important, it only represents and clearly defines its properties.

Interpersonal Problems and Developmental Trajectories of Binge Eating Disorder

PubMed Central

Blomquist, Kerstin K.; Ansell, Emily B.; White, Marney A.; Masheb, Robin M.; Grilo, Carlos M.

2012-01-01

Objective To explore associations between specific interpersonal constructs and the developmental progression of behaviors leading to binge eating disorder (BED). Method Eighty-four consecutively evaluated, treatment-seeking obese (BMI ≥ 30) men and women with BED were assessed with structured diagnostic and clinical interviews and completed a battery of established measures to assess the current and developmental eating- and weight-related variables as well as interpersonal functioning. Results Using the interpersonal circumplex structural summary method, amplitude, elevation, the affiliation dimension, and the quadratic coefficient for the dominance dimension were associated with eating and weight-related developmental variables. The amplitude coefficient and more extreme interpersonal problems on the dominance dimension (quadratic)—i.e., problems with being extremely high (domineering) or low in dominance (submissive)—were significantly associated with ayounger age at onset of binge eating, BED, and overweight as well as accounted for significant variance in age at binge eating, BED, and overweight onset. Greater interpersonal problems with having an overly affiliative interpersonal style were significantly associated with, and accounted for significant variance in, ayounger age at diet onset. Discussion Findings provide further support for the importance of interpersonal problems among adults with BED and converge with recent work highlighting the importance of specific types of interpersonal problems for understanding heterogeneity and different developmental trajectories of individuals with BED. PMID:22727087

Local classifier weighting by quadratic programming.

PubMed

Cevikalp, Hakan; Polikar, Robi

2008-10-01

It has been widely accepted that the classification accuracy can be improved by combining outputs of multiple classifiers. However, how to combine multiple classifiers with various (potentially conflicting) decisions is still an open problem. A rich collection of classifier combination procedures -- many of which are heuristic in nature -- have been developed for this goal. In this brief, we describe a dynamic approach to combine classifiers that have expertise in different regions of the input space. To this end, we use local classifier accuracy estimates to weight classifier outputs. Specifically, we estimate local recognition accuracies of classifiers near a query sample by utilizing its nearest neighbors, and then use these estimates to find the best weights of classifiers to label the query. The problem is formulated as a convex quadratic optimization problem, which returns optimal nonnegative classifier weights with respect to the chosen objective function, and the weights ensure that locally most accurate classifiers are weighted more heavily for labeling the query sample. Experimental results on several data sets indicate that the proposed weighting scheme outperforms other popular classifier combination schemes, particularly on problems with complex decision boundaries. Hence, the results indicate that local classification-accuracy-based combination techniques are well suited for decision making when the classifiers are trained by focusing on different regions of the input space.

A new anisotropic compact star model having Matese & Whitman mass function

NASA Astrophysics Data System (ADS)

Bhar, Piyali; Ratanpal, B. S.

2016-07-01

Present paper proposed a new singularity free model of anisotropic compact star. The Einstein field equations are solved in closed form by utilizing Matese & Whitman mass function. The model parameters ρ, pr and pt all are well behaved inside the stellar interior and our model satisfies all the required conditions to be physically acceptable. The model given in the present work is compatible with observational data of compact objects like SAX J 1808.4-3658 (SS1), SAX J 1808.4-3658 (SS2) and 4U 1820-30. A particular model of 4U 1820-30 is studied in detail and found that it satisfies all the condition needed for physically acceptable model. The present work is the generalization of Sharma and Ratanpal (Int. J. Mod. Phys. D 22:1350074, 2013) model for compact stars admitting quadratic equation of state.

Sparse Covariance Matrix Estimation by DCA-Based Algorithms.

PubMed

Phan, Duy Nhat; Le Thi, Hoai An; Dinh, Tao Pham

2017-11-01

This letter proposes a novel approach using the [Formula: see text]-norm regularization for the sparse covariance matrix estimation (SCME) problem. The objective function of SCME problem is composed of a nonconvex part and the [Formula: see text] term, which is discontinuous and difficult to tackle. Appropriate DC (difference of convex functions) approximations of [Formula: see text]-norm are used that result in approximation SCME problems that are still nonconvex. DC programming and DCA (DC algorithm), powerful tools in nonconvex programming framework, are investigated. Two DC formulations are proposed and corresponding DCA schemes developed. Two applications of the SCME problem that are considered are classification via sparse quadratic discriminant analysis and portfolio optimization. A careful empirical experiment is performed through simulated and real data sets to study the performance of the proposed algorithms. Numerical results showed their efficiency and their superiority compared with seven state-of-the-art methods.

Non-Gaussian lineshapes and dynamics of time-resolved linear and nonlinear (correlation) spectra.

PubMed

Dinpajooh, Mohammadhasan; Matyushov, Dmitry V

2014-07-17

Signatures of nonlinear and non-Gaussian dynamics in time-resolved linear and nonlinear (correlation) 2D spectra are analyzed in a model considering a linear plus quadratic dependence of the spectroscopic transition frequency on a Gaussian nuclear coordinate of the thermal bath (quadratic coupling). This new model is contrasted to the commonly assumed linear dependence of the transition frequency on the medium nuclear coordinates (linear coupling). The linear coupling model predicts equality between the Stokes shift and equilibrium correlation functions of the transition frequency and time-independent spectral width. Both predictions are often violated, and we are asking here the question of whether a nonlinear solvent response and/or non-Gaussian dynamics are required to explain these observations. We find that correlation functions of spectroscopic observables calculated in the quadratic coupling model depend on the chromophore's electronic state and the spectral width gains time dependence, all in violation of the predictions of the linear coupling models. Lineshape functions of 2D spectra are derived assuming Ornstein-Uhlenbeck dynamics of the bath nuclear modes. The model predicts asymmetry of 2D correlation plots and bending of the center line. The latter is often used to extract two-point correlation functions from 2D spectra. The dynamics of the transition frequency are non-Gaussian. However, the effect of non-Gaussian dynamics is limited to the third-order (skewness) time correlation function, without affecting the time correlation functions of higher order. The theory is tested against molecular dynamics simulations of a model polar-polarizable chromophore dissolved in a force field water.

A new family of N dimensional superintegrable double singular oscillators and quadratic algebra Q(3) ⨁ so(n) ⨁ so(N-n)

NASA Astrophysics Data System (ADS)

Fazlul Hoque, Md; Marquette, Ian; Zhang, Yao-Zhong

2015-11-01

We introduce a new family of N dimensional quantum superintegrable models consisting of double singular oscillators of type (n, N-n). The special cases (2,2) and (4,4) have previously been identified as the duals of 3- and 5-dimensional deformed Kepler-Coulomb systems with u(1) and su(2) monopoles, respectively. The models are multiseparable and their wave functions are obtained in (n, N-n) double-hyperspherical coordinates. We obtain the integrals of motion and construct the finitely generated polynomial algebra that is the direct sum of a quadratic algebra Q(3) involving three generators, so(n), so(N-n) (i.e. Q(3) ⨁ so(n) ⨁ so(N-n)). The structure constants of the quadratic algebra itself involve the Casimir operators of the two Lie algebras so(n) and so(N-n). Moreover, we obtain the finite dimensional unitary representations (unirreps) of the quadratic algebra and present an algebraic derivation of the degenerate energy spectrum of the superintegrable model.

The effects of five-order nonlinear on the dynamics of dark solitons in optical fiber.

PubMed

He, Feng-Tao; Wang, Xiao-Lin; Duan, Zuo-Liang

2013-01-01

We study the influence of five-order nonlinear on the dynamic of dark soliton. Starting from the cubic-quintic nonlinear Schrodinger equation with the quadratic phase chirp term, by using a similarity transformation technique, we give the exact solution of dark soliton and calculate the precise expressions of dark soliton's width, amplitude, wave central position, and wave velocity which can describe the dynamic behavior of soliton's evolution. From two different kinds of quadratic phase chirps, we mainly analyze the effect on dark soliton's dynamics which different fiver-order nonlinear term generates. The results show the following two points with quintic nonlinearities coefficient increasing: (1) if the coefficients of the quadratic phase chirp term relate to the propagation distance, the solitary wave displays a periodic change and the soliton's width increases, while its amplitude and wave velocity reduce. (2) If the coefficients of the quadratic phase chirp term do not depend on propagation distance, the wave function only emerges in a fixed area. The soliton's width increases, while its amplitude and the wave velocity reduce.

The Effects of Five-Order Nonlinear on the Dynamics of Dark Solitons in Optical Fiber

PubMed Central

Wang, Xiao-Lin; Duan, Zuo-Liang

2013-01-01

We study the influence of five-order nonlinear on the dynamic of dark soliton. Starting from the cubic-quintic nonlinear Schrodinger equation with the quadratic phase chirp term, by using a similarity transformation technique, we give the exact solution of dark soliton and calculate the precise expressions of dark soliton's width, amplitude, wave central position, and wave velocity which can describe the dynamic behavior of soliton's evolution. From two different kinds of quadratic phase chirps, we mainly analyze the effect on dark soliton's dynamics which different fiver-order nonlinear term generates. The results show the following two points with quintic nonlinearities coefficient increasing: (1) if the coefficients of the quadratic phase chirp term relate to the propagation distance, the solitary wave displays a periodic change and the soliton's width increases, while its amplitude and wave velocity reduce. (2) If the coefficients of the quadratic phase chirp term do not depend on propagation distance, the wave function only emerges in a fixed area. The soliton's width increases, while its amplitude and the wave velocity reduce. PMID:23818814

Quadratic canonical transformation theory and higher order density matrices.

PubMed

Neuscamman, Eric; Yanai, Takeshi; Chan, Garnet Kin-Lic

2009-03-28

Canonical transformation (CT) theory provides a rigorously size-extensive description of dynamic correlation in multireference systems, with an accuracy superior to and cost scaling lower than complete active space second order perturbation theory. Here we expand our previous theory by investigating (i) a commutator approximation that is applied at quadratic, as opposed to linear, order in the effective Hamiltonian, and (ii) incorporation of the three-body reduced density matrix in the operator and density matrix decompositions. The quadratic commutator approximation improves CT's accuracy when used with a single-determinant reference, repairing the previous formal disadvantage of the single-reference linear CT theory relative to singles and doubles coupled cluster theory. Calculations on the BH and HF binding curves confirm this improvement. In multireference systems, the three-body reduced density matrix increases the overall accuracy of the CT theory. Tests on the H(2)O and N(2) binding curves yield results highly competitive with expensive state-of-the-art multireference methods, such as the multireference Davidson-corrected configuration interaction (MRCI+Q), averaged coupled pair functional, and averaged quadratic coupled cluster theories.

Associations between the degree of early lactation inflammation and performance, metabolism, and immune function in dairy cows.

PubMed

McCarthy, M M; Yasui, T; Felippe, M J B; Overton, T R

2016-01-01

The objective of the current study was to determine associations between the severity of systemic inflammation during the early postpartum period and performance, energy metabolism, and immune function in dairy cows. Cows were assigned to categorical quartiles (Q; Q1=0.18-0.59, Q2=0.60-1.14, Q3=1.15-2.05, and Q4=2.06-2.50 g of haptoglobin/L) based on the highest plasma haptoglobin (Hp) concentration measured during wk 1 postpartum. Although cows were assigned to different categories of inflammation during the postpartum period, we detected a quadratic relationship of inflammation on prepartum dry matter intake (DMI) and body weight (BW) such that cows in Q2 had lower prepartum DMI and cows in Q2 and Q3 had lower prepartum BW compared with cows in the other quartiles. We also detected a quadratic association of inflammation with postpartum DMI and BW such that cows in Q2 and Q3 also had generally lower postpartum DMI and BW compared with cows in Q1. There was a tendency for a Q × time interaction for milk yield and Q × time interactions for 3.5% fat-corrected milk and energy-corrected milk yields; quadratic relationships suggested decreased milk yield for Q2 and Q3 cows. We also found Q × parity and Q × time interactions for plasma glucose and insulin concentrations, suggesting alterations with differing degrees of inflammation. There was also a Q × time interaction for plasma nonesterified fatty acids concentration. In addition, alterations in liver triglyceride and glycogen contents for cows with inflammation as well as alterations in [1-(14)C]propionate oxidation in vitro were observed. Although we observed limited effects of inflammation on neutrophil and monocyte phagocytosis at d 7 postpartum, inflammation appeared to alter neutrophil and monocyte oxidative burst. Overall, cows with any degree of elevated haptoglobin in the first week after calving had alterations in both pre- and postpartum intake and postpartum metabolism. Copyright © 2016 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Evaluation of linearly solvable Markov decision process with dynamic model learning in a mobile robot navigation task.

PubMed

Kinjo, Ken; Uchibe, Eiji; Doya, Kenji

2013-01-01

Linearly solvable Markov Decision Process (LMDP) is a class of optimal control problem in which the Bellman's equation can be converted into a linear equation by an exponential transformation of the state value function (Todorov, 2009b). In an LMDP, the optimal value function and the corresponding control policy are obtained by solving an eigenvalue problem in a discrete state space or an eigenfunction problem in a continuous state using the knowledge of the system dynamics and the action, state, and terminal cost functions. In this study, we evaluate the effectiveness of the LMDP framework in real robot control, in which the dynamics of the body and the environment have to be learned from experience. We first perform a simulation study of a pole swing-up task to evaluate the effect of the accuracy of the learned dynamics model on the derived the action policy. The result shows that a crude linear approximation of the non-linear dynamics can still allow solution of the task, despite with a higher total cost. We then perform real robot experiments of a battery-catching task using our Spring Dog mobile robot platform. The state is given by the position and the size of a battery in its camera view and two neck joint angles. The action is the velocities of two wheels, while the neck joints were controlled by a visual servo controller. We test linear and bilinear dynamic models in tasks with quadratic and Guassian state cost functions. In the quadratic cost task, the LMDP controller derived from a learned linear dynamics model performed equivalently with the optimal linear quadratic regulator (LQR). In the non-quadratic task, the LMDP controller with a linear dynamics model showed the best performance. The results demonstrate the usefulness of the LMDP framework in real robot control even when simple linear models are used for dynamics learning.

Nonlinear dynamics and cavity cooling of levitated nanoparticles

NASA Astrophysics Data System (ADS)

Fonseca, P. Z. G.; Aranas, E. B.; Millen, J.; Monteiro, T. S.; Barker, P. F.

2016-09-01

We investigate a dynamic nonlinear optomechanical system, comprising a nanosphere levitated in a hybrid electro-optical trap. An optical cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, whilst simultaneously cooling the nanosphere, for indefinite periods of time and in high vacuum. Through the rich sideband structure displayed by the cavity output we can observe cooling of the linear and non-linear particle's motion. Here we present an experimental setup which allows full control over the cavity resonant frequencies, and shows cooling of the particle's motion as a function of the detuning. This work paves the way to strong-coupled quantum dynamics between a cavity and a mesoscopic object largely decoupled from its environment.

Pattern of Change in Prolonged Exposure and Cognitive-Processing Therapy for Female Rape Victims With Posttraumatic Stress Disorder

PubMed Central

Nishith, Pallavi; Resick, Patricia A.; Griffin, Michael G.

2010-01-01

Curve estimation techniques were used to identify the pattern of therapeutic change in female rape victims with posttraumatic stress disorder (PTSD). Within-session data on the Posttraumatic Stress Disorder Symptom Scale were obtained, in alternate therapy sessions, on 171 women. The final sample of treatment completers included 54 prolonged exposure (PE) and 54 cognitive-processing therapy (CPT) completers. For both PE and CPT, a quadratic function provided the best fit for the total PTSD, reexperiencing, and arousal scores. However, a difference in the line of best fit was observed for the avoidance symptoms. Although a quadratic function still provided a better fit for the PE avoidance, a linear function was more parsimonious in explaining the CPT avoidance variance. Implications of the findings are discussed. PMID:12182271

Acousto-exciton interaction in a gas of 2D indirect dipolar excitons in the presence of disorder

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kovalev, V. M.; Chaplik, A. V., E-mail: chaplik@isp.nsc.ru

2016-03-15

A theory for the linear and quadratic responses of a 2D gas of indirect dipolar excitons to an external surface acoustic wave perturbation in the presence of a static random potential is considered. The theory is constructed both for high temperatures, definitely greater than the exciton gas condensation temperature, and at zero temperature by taking into account the Bose–Einstein condensation effects. The particle Green functions, the density–density correlation function, and the quadratic response function are calculated by the “cross” diagram technique. The results obtained are used to calculate the absorption of Rayleigh surface waves and the acoustic exciton gas dragmore » by a Rayleigh wave. The damping of Bogoliubov excitations in an exciton condensate due to theirs scattering by a random potential has also been determined.« less

A Relationship Between Visual Complexity and Aesthetic Appraisal of Car Front Images: An Eye-Tracker Study.

PubMed

Chassy, Philippe; Lindell, Trym A E; Jones, Jessica A; Paramei, Galina V

2015-01-01

Image aesthetic pleasure (AP) is conjectured to be related to image visual complexity (VC). The aim of the present study was to investigate whether (a) two image attributes, AP and VC, are reflected in eye-movement parameters; and (b) subjective measures of AP and VC are related. Participants (N=26) explored car front images (M=50) while their eye movements were recorded. Following image exposure (10 seconds), its VC and AP were rated. Fixation count was found to positively correlate with the subjective VC and its objective proxy, JPEG compression size, suggesting that this eye-movement parameter can be considered an objective behavioral measure of VC. AP, in comparison, positively correlated with average dwelling time. Subjective measures of AP and VC were related too, following an inverted U-shape function best-fit by a quadratic equation. In addition, AP was found to be modulated by car prestige. Our findings reveal a close relationship between subjective and objective measures of complexity and aesthetic appraisal, which is interpreted within a prototype-based theory framework. © The Author(s) 2015.

Stochastic resonance in a fractional oscillator driven by multiplicative quadratic noise

NASA Astrophysics Data System (ADS)

Ren, Ruibin; Luo, Maokang; Deng, Ke

2017-02-01

Stochastic resonance of a fractional oscillator subject to an external periodic field as well as to multiplicative and additive noise is investigated. The fluctuations of the eigenfrequency are modeled as the quadratic function of the trichotomous noise. Applying the moment equation method and Shapiro-Loginov formula, we obtain the exact expression of the complex susceptibility and related stability criteria. Theoretical analysis and numerical simulations indicate that the spectral amplification (SPA) depends non-monotonicly both on the external driving frequency and the parameters of the quadratic noise. In addition, the investigations into fractional stochastic systems have suggested that both the noise parameters and the memory effect can induce the phenomenon of stochastic multi-resonance (SMR), which is previously reported and believed to be absent in the case of the multiplicative noise with only a linear term.

Determinant representation of the domain-wall boundary condition partition function of a Richardson-Gaudin model containing one arbitrary spin

NASA Astrophysics Data System (ADS)

Faribault, Alexandre; Tschirhart, Hugo; Muller, Nicolas

2016-05-01

In this work we present a determinant expression for the domain-wall boundary condition partition function of rational (XXX) Richardson-Gaudin models which, in addition to N-1 spins \\frac{1}{2}, contains one arbitrarily large spin S. The proposed determinant representation is written in terms of a set of variables which, from previous work, are known to define eigenstates of the quantum integrable models belonging to this class as solutions to quadratic Bethe equations. Such a determinant can be useful numerically since systems of quadratic equations are much simpler to solve than the usual highly nonlinear Bethe equations. It can therefore offer significant gains in stability and computation speed.

Highly accurate analytic formulae for projectile motion subjected to quadratic drag

NASA Astrophysics Data System (ADS)

Turkyilmazoglu, Mustafa

2016-05-01

The classical phenomenon of motion of a projectile fired (thrown) into the horizon through resistive air charging a quadratic drag onto the object is revisited in this paper. No exact solution is known that describes the full physical event under such an exerted resistance force. Finding elegant analytical approximations for the most interesting engineering features of dynamical behavior of the projectile is the principal target. Within this purpose, some analytical explicit expressions are derived that accurately predict the maximum height, its arrival time as well as the flight range of the projectile at the highest ascent. The most significant property of the proposed formulas is that they are not restricted to the initial speed and firing angle of the object, nor to the drag coefficient of the medium. In combination with the available approximations in the literature, it is possible to gain information about the flight and complete the picture of a trajectory with high precision, without having to numerically simulate the full governing equations of motion.

Stochastic multiresonance for a fractional linear oscillator with time-delayed kernel and quadratic noise

NASA Astrophysics Data System (ADS)

Guo, Feng; Wang, Xue-Yuan; Zhu, Cheng-Yin; Cheng, Xiao-Feng; Zhang, Zheng-Yu; Huang, Xu-Hui

2017-12-01

The stochastic resonance for a fractional oscillator with time-delayed kernel and quadratic trichotomous noise is investigated. Applying linear system theory and Laplace transform, the system output amplitude (SPA) for the fractional oscillator is obtained. It is found that the SPA is a periodical function of the kernel delayed-time. Stochastic multiplicative phenomenon appears on the SPA versus the driving frequency, versus the noise amplitude, and versus the fractional exponent. The non-monotonous dependence of the SPA on the system parameters is also discussed.

Quadratic integrand double-hybrid made spin-component-scaled

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brémond, Éric, E-mail: eric.bremond@iit.it; Savarese, Marika; Sancho-García, Juan C.

2016-03-28

We propose two analytical expressions aiming to rationalize the spin-component-scaled (SCS) and spin-opposite-scaled (SOS) schemes for double-hybrid exchange-correlation density-functionals. Their performances are extensively tested within the framework of the nonempirical quadratic integrand double-hybrid (QIDH) model on energetic properties included into the very large GMTKN30 benchmark database, and on structural properties of semirigid medium-sized organic compounds. The SOS variant is revealed as a less computationally demanding alternative to reach the accuracy of the original QIDH model without losing any theoretical background.

Rotor design optimization using a free wake analysis

NASA Technical Reports Server (NTRS)

Quackenbush, Todd R.; Boschitsch, Alexander H.; Wachspress, Daniel A.; Chua, Kiat

1993-01-01

The aim of this effort was to develop a comprehensive performance optimization capability for tiltrotor and helicopter blades. The analysis incorporates the validated EHPIC (Evaluation of Hover Performance using Influence Coefficients) model of helicopter rotor aerodynamics within a general linear/quadratic programming algorithm that allows optimization using a variety of objective functions involving the performance. The resulting computer code, EHPIC/HERO (HElicopter Rotor Optimization), improves upon several features of the previous EHPIC performance model and allows optimization utilizing a wide spectrum of design variables, including twist, chord, anhedral, and sweep. The new analysis supports optimization of a variety of objective functions, including weighted measures of rotor thrust, power, and propulsive efficiency. The fundamental strength of the approach is that an efficient search for improved versions of the baseline design can be carried out while retaining the demonstrated accuracy inherent in the EHPIC free wake/vortex lattice performance analysis. Sample problems are described that demonstrate the success of this approach for several representative rotor configurations in hover and axial flight. Features that were introduced to convert earlier demonstration versions of this analysis into a generally applicable tool for researchers and designers is also discussed.

Multi-objective design optimization and control of magnetorheological fluid brakes for automotive applications

NASA Astrophysics Data System (ADS)

Shamieh, Hadi; Sedaghati, Ramin

2017-12-01

The magnetorheological brake (MRB) is an electromechanical device that generates a retarding torque through employing magnetorheological (MR) fluids. The objective of this paper is to design, optimize and control an MRB for automotive applications considering. The dynamic range of a disk-type MRB expressing the ratio of generated toque at on and off states has been formulated as a function of the rotational speed, geometrical and material properties, and applied electrical current. Analytical magnetic circuit analysis has been conducted to derive the relation between magnetic field intensity and the applied electrical current as a function of the MRB geometrical and material properties. A multidisciplinary design optimization problem has then been formulated to identify the optimal brake geometrical parameters to maximize the dynamic range and minimize the response time and weight of the MRB under weight, size and magnetic flux density constraints. The optimization problem has been solved using combined genetic and sequential quadratic programming algorithms. Finally, the performance of the optimally designed MRB has been investigated in a quarter vehicle model. A PID controller has been designed to regulate the applied current required by the MRB in order to improve vehicle’s slipping on different road conditions.

AESOP: An interactive computer program for the design of linear quadratic regulators and Kalman filters

NASA Technical Reports Server (NTRS)

Lehtinen, B.; Geyser, L. C.

1984-01-01

AESOP is a computer program for use in designing feedback controls and state estimators for linear multivariable systems. AESOP is meant to be used in an interactive manner. Each design task that the program performs is assigned a "function" number. The user accesses these functions either (1) by inputting a list of desired function numbers or (2) by inputting a single function number. In the latter case the choice of the function will in general depend on the results obtained by the previously executed function. The most important of the AESOP functions are those that design,linear quadratic regulators and Kalman filters. The user interacts with the program when using these design functions by inputting design weighting parameters and by viewing graphic displays of designed system responses. Supporting functions are provided that obtain system transient and frequency responses, transfer functions, and covariance matrices. The program can also compute open-loop system information such as stability (eigenvalues), eigenvectors, controllability, and observability. The program is written in ANSI-66 FORTRAN for use on an IBM 3033 using TSS 370. Descriptions of all subroutines and results of two test cases are included in the appendixes.

A Study of Penalty Function Methods for Constraint Handling with Genetic Algorithm

NASA Technical Reports Server (NTRS)

Ortiz, Francisco

2004-01-01

COMETBOARDS (Comparative Evaluation Testbed of Optimization and Analysis Routines for Design of Structures) is a design optimization test bed that can evaluate the performance of several different optimization algorithms. A few of these optimization algorithms are the sequence of unconstrained minimization techniques (SUMT), sequential linear programming (SLP) and the sequential quadratic programming techniques (SQP). A genetic algorithm (GA) is a search technique that is based on the principles of natural selection or "survival of the fittest". Instead of using gradient information, the GA uses the objective function directly in the search. The GA searches the solution space by maintaining a population of potential solutions. Then, using evolving operations such as recombination, mutation and selection, the GA creates successive generations of solutions that will evolve and take on the positive characteristics of their parents and thus gradually approach optimal or near-optimal solutions. By using the objective function directly in the search, genetic algorithms can be effectively applied in non-convex, highly nonlinear, complex problems. The genetic algorithm is not guaranteed to find the global optimum, but it is less likely to get trapped at a local optimum than traditional gradient-based search methods when the objective function is not smooth and generally well behaved. The purpose of this research is to assist in the integration of genetic algorithm (GA) into COMETBOARDS. COMETBOARDS cast the design of structures as a constrained nonlinear optimization problem. One method used to solve constrained optimization problem with a GA to convert the constrained optimization problem into an unconstrained optimization problem by developing a penalty function that penalizes infeasible solutions. There have been several suggested penalty function in the literature each with there own strengths and weaknesses. A statistical analysis of some suggested penalty functions is performed in this study. Also, a response surface approach to robust design is used to develop a new penalty function approach. This new penalty function approach is then compared with the other existing penalty functions.

Ingestive Behavior of Ovine Fed with Marandu Grass Silage Added with Naturally Dehydrated Brewery Residue

PubMed Central

Lima de Souza, Alexandre; Divino Ribeiro, Marinaldo; Mattos Negrão, Fagton; Castro, Wanderson José Rodrigues; Valério Geron, Luiz Juliano; de Azevedo Câmara, Larissa Rodrigues

2016-01-01

The objective was to evaluate the ingestive behavior of ovine fed Marandu grass silage with dehydrated brewery residue added. The experiment had a completely randomized design with five treatments and four repetitions, with the treatments levels of inclusion being of 0, 10, 20, 30, and 40% natural matter of naturally dehydrated brewery residue for 36 hours to the marandu grass silage. 20 ovines were used and the experimental period was 21 days, 15 being for adaptation to diets. The use of brewery byproduct promoted quadratic effect (P < 0.05) for the consumption of dry matter with maximum point value estimated at adding 23.25% additive. Ingestion efficiency and rumination efficiency of dry matter (g DM/hour) were significant (P < 0.05), by quadratic behavior, and NDF ingestion and rumination efficiency showed crescent linear behavior. The DM and NDF consumption expressed in kg/meal and in minutes/kg were also significant (P < 0.05), showing quadratic behavior. Rumination activity expressed in g DM and NDF/piece was influenced (P < 0.05) by the adding of brewery residue in marandu grass silage in quadratic way, with maximum value estimated of 1.57 g DM/bolus chewed in inclusion of 24.72% additive in grass silage. The conclusion is that intermediary levels adding of 20 to 25% dehydrated brewery residue affects certain parameters of ingestive behavior. PMID:27547811

Parameterisation of rainfall-runoff models for forecasting low and average flows, I: Conceptual modelling

NASA Astrophysics Data System (ADS)

Castiglioni, S.; Toth, E.

2009-04-01

In the calibration procedure of continuously-simulating models, the hydrologist has to choose which part of the observed hydrograph is most important to fit, either implicitly, through the visual agreement in manual calibration, or explicitly, through the choice of the objective function(s). Changing the objective functions it is in fact possible to emphasise different kind of errors, giving them more weight in the calibration phase. The objective functions used for calibrating hydrological models are generally of the quadratic type (mean squared error, correlation coefficient, coefficient of determination, etc) and are therefore oversensitive to high and extreme error values, that typically correspond to high and extreme streamflow values. This is appropriate when, like in the majority of streamflow forecasting applications, the focus is on the ability to reproduce potentially dangerous flood events; on the contrary, if the aim of the modelling is the reproduction of low and average flows, as it is the case in water resource management problems, this may result in a deterioration of the forecasting performance. This contribution presents the results of a series of automatic calibration experiments of a continuously-simulating rainfall-runoff model applied over several real-world case-studies, where the objective function is chosen so to highlight the fit of average and low flows. In this work a simple conceptual model will be used, of the lumped type, with a relatively low number of parameters to be calibrated. The experiments will be carried out for a set of case-study watersheds in Central Italy, covering an extremely wide range of geo-morphologic conditions and for whom at least five years of contemporary daily series of streamflow, precipitation and evapotranspiration estimates are available. Different objective functions will be tested in calibration and the results will be compared, over validation data, against those obtained with traditional squared functions. A companion work presents the results, over the same case-study watersheds and observation periods, of a system-theoretic model, again calibrated for reproducing average and low streamflows.

Quadrat Data for Fermilab Prairie Plant Survey

Science.gov Websites

Quadrat Data 2012 Quadrat Data 2013 Quadrat Data None taken by volunteers in 2014 due to weather problems . 2015 Quadrat Data 2016 Quadrat Data None taken by volunteers in 2017 due to weather and other problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Kuo -Ling; Mehrotra, Sanjay

We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition (SLC) is satisfied. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation in iOptimize maintains global linear and polynomial time convergence properties, while achieving practical performance. It either successfully solves the problem, or concludes that the SLC is not satisfied. When compared with the mature software package MOSEK (barrier solver version 6.0.0.106), iOptimize solves convex quadraticmore » programming problems, convex quadratically constrained quadratic programming problems, and general convex programming problems in fewer iterations. Moreover, several problems for which MOSEK fails are solved to optimality. In addition, we also find that iOptimize detects infeasibility more reliably than the general nonlinear solvers Ipopt (version 3.9.2) and Knitro (version 8.0).« less

Three Lessons on Parabolas--What, Where, Why

ERIC Educational Resources Information Center

Ceyanes, Ben; Lockwood, Pamela; Gill, Kristina

2014-01-01

In this article, Ceyanes, Lockwood, and Gill use "The Geometer's Sketchpad" in a sequence of algebra lessons to introduce quadratic functions as the product of two linear functions. The lessons provide an enriched look at the creation of parabolas and allow students to experience the foundational idea that all functions are…

Optimization of Cubic Polynomial Functions without Calculus

ERIC Educational Resources Information Center

Taylor, Ronald D., Jr.; Hansen, Ryan

2008-01-01

In algebra and precalculus courses, students are often asked to find extreme values of polynomial functions in the context of solving an applied problem; but without the notion of derivative, something is lost. Either the functions are reduced to quadratics, since students know the formula for the vertex of a parabola, or solutions are…

Circulant Matrices and Affine Equivalence of Monomial Rotation Symmetric Boolean Functions

DTIC Science & Technology

2015-01-01

definitions , including monomial rotation symmetric (MRS) Boolean functions and affine equivalence, and a known result for such quadratic functions...degree of the MRS is, we have a similar result as [40, Theorem 1.1] for n = 4p (p prime), or squarefree integers n, which along with our Theorem 5.2

Confidence set inference with a prior quadratic bound

NASA Technical Reports Server (NTRS)

Backus, George E.

1989-01-01

In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z=(z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y (sup 0) = (y (sub 1) (sup 0), ..., y (sub D (sup 0)), using full or partial knowledge of the statistical distribution of the random errors in y (sup 0). The data space Y containing y(sup 0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x, Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. Confidence set inference is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface.

Cosmic structures and gravitational waves in ghost-free scalar-tensor theories of gravity

NASA Astrophysics Data System (ADS)

Bartolo, Nicola; Karmakar, Purnendu; Matarrese, Sabino; Scomparin, Mattia

2018-05-01

We study cosmic structures in the quadratic Degenerate Higher Order Scalar Tensor (qDHOST) model, which has been proposed as the most general scalar-tensor theory (up to quadratic dependence on the covariant derivatives of the scalar field), which is not plagued by the presence of ghost instabilities. We then study a static, spherically symmetric object embedded in de Sitter space-time for the qDHOST model. This model exhibits breaking of the Vainshtein mechanism inside the cosmic structure and Schwarzschild-de Sitter space-time outside, where General Relativity (GR) can be recovered within the Vainshtein radius. We constrained the parameters of the qDHOST model by requiring the validity of the Vainshtein screening mechanism inside the cosmic structures and the consistency with the recently established bounds on gravitational wave speed from GW170817/GRB170817A event. We find that these two constraints rule out the same set of parameters, corresponding to the Lagrangians that are quadratic in second-order derivatives of the scalar field, for the shift symmetric qDHOST.

Application of Lagrangian blending functions for grid generation around airplane geometries

NASA Technical Reports Server (NTRS)

Abolhassani, Jamshid S.; Sadrehaghighi, Ideen; Tiwari, Surendra N.

1990-01-01

A simple procedure was developed and applied for the grid generation around an airplane geometry. This approach is based on a transfinite interpolation with Lagrangian interpolation for the blending functions. A monotonic rational quadratic spline interpolation was employed for the grid distributions.

Stimulus-response correspondence effect as a function of temporal overlap between relevant and irrelevant information processing.

PubMed

Wang, Dong-Yuan Debbie; Richard, F Dan; Ray, Brittany

2016-01-01

The stimulus-response correspondence (SRC) effect refers to advantages in performance when stimulus and response correspond in dimensions or features, even if the common features are irrelevant to the task. Previous research indicated that the SRC effect depends on the temporal course of stimulus information processing. The current study investigated how the temporal overlap between relevant and irrelevant stimulus processing influences the SRC effect. In this experiment, the irrelevant stimulus (a previously associated tone) preceded the relevant stimulus (a coloured rectangle). The irrelevant and relevant stimuli onset asynchrony was varied to manipulate the temporal overlap between the irrelevant and relevant stimuli processing. Results indicated that the SRC effect size varied as a quadratic function of the temporal overlap between the relevant stimulus and irrelevant stimulus. This finding extends previous experimental observations that the SRC effect size varies in an increasing or decreasing function with reaction time. The current study demonstrated a quadratic function between effect size and the temporal overlap.

Sex-specific nonlinear associations between serum lipids and different domains of cognitive function in middle to older age individuals.

PubMed

Lu, Yanhui; An, Yu; Yu, Huanling; Che, Fengyuan; Zhang, Xiaona; Rong, Hongguo; Xi, Yuandi; Xiao, Rong

2017-08-01

To examine how serum lipids relates to specific cognitive ability domains between the men and women in Chinese middle to older age individuals. A complete lipid panel was obtained from 1444 individuals, ages 50-65, who also underwent a selection of cognitive tests. Participants were 584 men and 860 women from Linyi city, Shandong province. Multiple linear regression analyses examined serum lipids level as quadratic predictors of sex-specific measure of performance in different cognitive domains, which were adjusted for sociodemographic and lifestyle characteristics. In men, a significant quadratic effect of total cholesterol (TC) was identified for Digit Symbol (B = -0.081, P = 0.044) and also quadratic effect of low density lipoprotein-cholesterol (LDL-C) was identified for Trail Making Test B (B = -0.082, P = 0.045). Differently in women, there were significant quadratic associations between high density lipoprotein-cholesterol (HDL-C) and multiple neuropsychological tests. The nonlinear lipid-cognition associations differed between men and women and were specific to certain cognitive domains and might be of potential relevance for prevention and therapy of cognitive decline.

Quadratic electroabsorption studies of molecular motion in dye-doped polymers

NASA Astrophysics Data System (ADS)

Poga, Constantina; Kuzyk, Mark G.; Dirk, Carl W.

1993-02-01

This paper reports on quadratic electroabsorption studies of thin-film solid solutions of squarylium dye molecules in poly(methylmethacrylate) polymer with the aim of understanding the role of electronic and reorientational mechanisms in the third-order nonlinear-optical susceptibility. We present a generalized theory of the quadratic electrooptic response that includes both electronic mechanisms and molecular reorientation and show that the ratio of two independent third-order susceptibility tensor components, namely (chi) (3)3333/(chi) (3)1133, determines the relative contribution of each mechanism. Based on these theoretical results, we have designed and built an experiment that determines this ratio as a function of temperature and wavelength. Results show that at room temperature and near the first electronic transition wavelength, the response is dominated by the electronic mechanism, and that the reorientational contribution dominates when the sample is heated above its glass transition temperature. Furthermore, results show that, off-resonance, the sign of the imaginary part of the third-order susceptibility is positive. Quadratic electroabsorption is thus shown to be a versatile tool for measuring the imaginary part of the third-order nonlinear-optical susceptibility which yields information about the interaction of polymer and dopant molecule.

A Sequential Linear Quadratic Approach for Constrained Nonlinear Optimal Control with Adaptive Time Discretization and Application to Higher Elevation Mars Landing Problem

NASA Astrophysics Data System (ADS)

Sandhu, Amit

A sequential quadratic programming method is proposed for solving nonlinear optimal control problems subject to general path constraints including mixed state-control and state only constraints. The proposed algorithm further develops on the approach proposed in [1] with objective to eliminate the use of a high number of time intervals for arriving at an optimal solution. This is done by introducing an adaptive time discretization to allow formation of a desirable control profile without utilizing a lot of intervals. The use of fewer time intervals reduces the computation time considerably. This algorithm is further used in this thesis to solve a trajectory planning problem for higher elevation Mars landing.

A Converse of a Result about the Floor Function by Hermite

ERIC Educational Resources Information Center

Mortici, Cristinel

2012-01-01

The floor function maps a real number to the largest previous integer. More precisely, floor(x)=[x] is the largest integer not greater than x. The square bracket notation [x] for the floor function was introduced by Gauss in his third proof of quadratic reciprocity in 1808. The floor function is also called the greatest integer or entier (French…

Terminal Velocity of a Shuttlecock in Vertical Fall.

ERIC Educational Resources Information Center

Peastrel, Mark; And Others

1980-01-01

Describes a straightforward vertical fall experiment using a badminton shuttlecock, a tape measure, and a millisecond timer. The effects of air resistance are important and directly measurable. The experimental data best fit a predictive model which assumes a resistive force quadratic in the instantaneous speed of the falling object. (GS)

Quadratic semiparametric Von Mises calculus

PubMed Central

Robins, James; Li, Lingling; Tchetgen, Eric

2009-01-01

We discuss a new method of estimation of parameters in semiparametric and nonparametric models. The method is based on U-statistics constructed from quadratic influence functions. The latter extend ordinary linear influence functions of the parameter of interest as defined in semiparametric theory, and represent second order derivatives of this parameter. For parameters for which the matching cannot be perfect the method leads to a bias-variance trade-off, and results in estimators that converge at a slower than n–1/2-rate. In a number of examples the resulting rate can be shown to be optimal. We are particularly interested in estimating parameters in models with a nuisance parameter of high dimension or low regularity, where the parameter of interest cannot be estimated at n–1/2-rate. PMID:23087487

An approach of traffic signal control based on NLRSQP algorithm

NASA Astrophysics Data System (ADS)

Zou, Yuan-Yang; Hu, Yu

2017-11-01

This paper presents a linear program model with linear complementarity constraints (LPLCC) to solve traffic signal optimization problem. The objective function of the model is to obtain the minimization of total queue length with weight factors at the end of each cycle. Then, a combination algorithm based on the nonlinear least regression and sequence quadratic program (NLRSQP) is proposed, by which the local optimal solution can be obtained. Furthermore, four numerical experiments are proposed to study how to set the initial solution of the algorithm that can get a better local optimal solution more quickly. In particular, the results of numerical experiments show that: The model is effective for different arrival rates and weight factors; and the lower bound of the initial solution is, the better optimal solution can be obtained.

Dyadic contrast function and quadratic forward model for radio frequency tomography

NASA Astrophysics Data System (ADS)

Picco, Vittorio

Radio Frequency Tomography is an underground imaging technology that aims to reconstruct extended, deeply buried objects such as tunnels or Underground Facilities (UGF). A network of sensors collects scattered electromagnetic field samples, which are processed to obtain 2D or 3D images of the complex dielectric permittivity profile of the volume under investigation. Unlike systems such as Synthetic Aperture Radar (SAR) or Ground Penetrating Radar (GPR) which normally employ wide-band pulses, RF Tomography uses Continuous Wave (CW) signals to illuminate the scene. The information about the target is not retrieved by relying on bandwidth but by exploiting spatial, frequency and/or polarization diversity. Interestingly, RF Tomography can be readily adapted to obtain images of targets in free space. In this context, in the Andrew Electromagnetics Laboratory of the University of Illinois at Chicago, a measurement system aimed to validate experimentally the performance of RF Tomography has been designed and built. Experimental data have been used to validate its forward model, different inversion algorithms, its performance in terms of resolution and the ability of the system to distinguish between metallic and non-metallic targets. In the specific case of imaging of metallic targets, this thesis proposes to extend the capabilities of RF Tomography by introducing a dyadic permittivity contrast. Electromagnetic scattering from a thin, wire-like object placed in free space with its main axis at an angle with respect to the incident electric field is studied. It is possible to show that for this configuration a fundamental difference exists between a metallic and a dielectric object. This phenomenon can be modeled into Maxwell's equations by using a dyadic permittivity contrast, as it is commonly done when studying crystals. As a result a new formulation of the RF Tomography forward model is obtained, based on a dyadic contrast function. Reconstruction of this dyad allows to estimate not only the location and shape, but also the spatial orientation of the target. In addition, this dissertation proposes an alternative modification of the forward model which removes some limitations caused by the Born approximation. Traditionally, the Born approximation is used to linearize the inherently non-linear forward model. This approximation is valid if the scatterer is small and does not interact strongly with other objects. A quadratic forward model represents a more correct formulation of the scattering phenomenon, and it allows to attempt quantitative reconstruction. Numerical results are presented to highlight the advantages that such a formulation provides over the Born approximation.

Baker-Akhiezer Spinor Kernel and Tau-functions on Moduli Spaces of Meromorphic Differentials

NASA Astrophysics Data System (ADS)

Kalla, C.; Korotkin, D.

2014-11-01

In this paper we study the Baker-Akhiezer spinor kernel on moduli spaces of meromorphic differentials on Riemann surfaces. We introduce the Baker-Akhiezer tau-function which is related to both the Bergman tau-function (which was studied before in the context of Hurwitz spaces and spaces of holomorphic Abelian and quadratic differentials) and the KP tau-function on such spaces. In particular, we derive variational formulas of Rauch-Ahlfors type on moduli spaces of meromorphic differentials with prescribed singularities: we use the system of homological coordinates, consisting of absolute and relative periods of the meromorphic differential, and show how to vary the fundamental objects associated to a Riemann surface (the matrix of b-periods, normalized Abelian differentials, the Bergman bidifferential, the Szegö kernel and the Baker-Akhiezer spinor kernel) with respect to these coordinates. The variational formulas encode dependence both on the moduli of the Riemann surface and on the choice of meromorphic differential (variation of the meromorphic differential while keeping the Riemann surface fixed corresponds to flows of KP type). Analyzing the global properties of the Bergman and Baker-Akhiezer tau-functions, we establish relationships between various divisor classes on the moduli spaces.

Applications of Lagrangian blending functions for grid generation around airplane geometries

NASA Technical Reports Server (NTRS)

Abolhassani, Jamshid S.; Sadrehaghighi, Ideen; Tiwari, Surendra N.; Smith, Robert E.

1990-01-01

A simple procedure has been developed and applied for the grid generation around an airplane geometry. This approach is based on a transfinite interpolation with Lagrangian interpolation for the blending functions. A monotonic rational quadratic spline interpolation has been employed for the grid distributions.

Feature to prototype transition in neural networks

NASA Astrophysics Data System (ADS)

Krotov, Dmitry; Hopfield, John

Models of associative memory with higher order (higher than quadratic) interactions, and their relationship to neural networks used in deep learning are discussed. Associative memory is conventionally described by recurrent neural networks with dynamical convergence to stable points. Deep learning typically uses feedforward neural nets without dynamics. However, a simple duality relates these two different views when applied to problems of pattern classification. From the perspective of associative memory such models deserve attention because they make it possible to store a much larger number of memories, compared to the quadratic case. In the dual description, these models correspond to feedforward neural networks with one hidden layer and unusual activation functions transmitting the activities of the visible neurons to the hidden layer. These activation functions are rectified polynomials of a higher degree rather than the rectified linear functions used in deep learning. The network learns representations of the data in terms of features for rectified linear functions, but as the power in the activation function is increased there is a gradual shift to a prototype-based representation, the two extreme regimes of pattern recognition known in cognitive psychology. Simons Center for Systems Biology.

Soil microbial community structure and function responses to successive planting of Eucalyptus.

PubMed

Chen, Falin; Zheng, Hua; Zhang, Kai; Ouyang, Zhiyun; Li, Huailin; Wu, Bing; Shi, Qian

2013-10-01

Many studies have shown soil degradation after the conversion of native forests to exotic Eucalyptus plantations. However, few studies have investigated the long-term impacts of short-rotation forestry practices on soil microorganisms. The impacts of Eucalyptus successive rotations on soil microbial communities were evaluated by comparing phospholipid fatty acid (PLFA) abundances, compositions, and enzyme activities of native Pinus massoniana plantations and adjacent 1st, 2nd, 3rd, 4th generation Eucalyptus plantations. The conversion from P. massoniana to Eucalyptus plantations significantly decreased soil microbial community size and enzyme activities, and increased microbial physiological stress. However, the PLFA abundances formed "u" shaped quadratic functions with Eucalyptus plantation age. Alternatively, physiological stress biomarkers, the ratios of monounsaturated to saturated fatty acid and Gram+ to Gram- bacteria, formed "n"' shaped quadratic functions, and the ratio of cy17:0 to 16:1omega7c decreased with plantation age. The activities of phenol oxidase, peroxidase, and acid phosphatase increased with Eucalyptus plantation age, while the cellobiohydrolase activity formed "u" shaped quadratic functions. Soil N:P, alkaline hydrolytic nitrogen, soil organic carbon, and understory cover largely explained the variation in PLFA profiles while soil N:P, alkaline hydrolytic nitrogen, and understory cover explained most of the variability in enzyme activity. In conclusion, soil microbial structure and function under Eucalyptus plantations were strongly impacted by plantation age. Most of the changes could be explained by altered soil resource availability and understory cover associated with successive planting of Eucalyptus. Our results highlight the importance of plantation age for assessing the impacts of plantation conversion as well as the importance of reducing disturbance for plantation management.

Bianchi type-I universe in Lyra manifold with quadratic equation of state

NASA Astrophysics Data System (ADS)

Şen, R.; Aygün, S.

2017-02-01

In this study, we have solved Einstein field equations for Bianchi type I universe model in Lyra manifold with quadratic equation of state (EoS) p = ap(t)2 - ρ(t). Where α ≠0 is an important constant. Cosmic pressure, density and displacement vector (β2) are related with α constant. In this study β2 is a decreasing function of time and behaves like a cosmological constant. These solutions agree with the studies of Halford, Pradhan and Singh, Aygün et al., Agarwal et al., Yadav and Haque as well as SN Ia observations.

Discrete Element Method Simulation of a Boulder Extraction From an Asteroid

NASA Technical Reports Server (NTRS)

Kulchitsky, Anton K.; Johnson, Jerome B.; Reeves, David M.; Wilkinson, Allen

2014-01-01

The force required to pull 7t and 40t polyhedral boulders from the surface of an asteroid is simulated using the discrete element method considering the effects of microgravity, regolith cohesion and boulder acceleration. The connection between particle surface energy and regolith cohesion is estimated by simulating a cohesion sample tearing test. An optimal constant acceleration is found where the peak net force from inertia and cohesion is a minimum. Peak pulling forces can be further reduced by using linear and quadratic acceleration functions with up to a 40% reduction in force for quadratic acceleration.

Learning curves in highly skilled chess players: a test of the generality of the power law of practice.

PubMed

Howard, Robert W

2014-09-01

The power law of practice holds that a power function best interrelates skill performance and amount of practice. However, the law's validity and generality are moot. Some researchers argue that it is an artifact of averaging individual exponential curves while others question whether the law generalizes to complex skills and to performance measures other than response time. The present study tested the power law's generality to development over many years of a very complex cognitive skill, chess playing, with 387 skilled participants, most of whom were grandmasters. A power or logarithmic function best fit grouped data but individuals showed much variability. An exponential function usually was the worst fit to individual data. Groups differing in chess talent were compared and a power function best fit the group curve for the more talented players while a quadratic function best fit that for the less talented. After extreme amounts of practice, a logarithmic function best fit grouped data but a quadratic function best fit most individual curves. Individual variability is great and the power law or an exponential law are not the best descriptions of individual chess skill development. Copyright © 2014 Elsevier B.V. All rights reserved.

An algorithm for the solution of dynamic linear programs

NASA Technical Reports Server (NTRS)

Psiaki, Mark L.

1989-01-01

The algorithm's objective is to efficiently solve Dynamic Linear Programs (DLP) by taking advantage of their special staircase structure. This algorithm constitutes a stepping stone to an improved algorithm for solving Dynamic Quadratic Programs, which, in turn, would make the nonlinear programming method of Successive Quadratic Programs more practical for solving trajectory optimization problems. The ultimate goal is to being trajectory optimization solution speeds into the realm of real-time control. The algorithm exploits the staircase nature of the large constraint matrix of the equality-constrained DLPs encountered when solving inequality-constrained DLPs by an active set approach. A numerically-stable, staircase QL factorization of the staircase constraint matrix is carried out starting from its last rows and columns. The resulting recursion is like the time-varying Riccati equation from multi-stage LQR theory. The resulting factorization increases the efficiency of all of the typical LP solution operations over that of a dense matrix LP code. At the same time numerical stability is ensured. The algorithm also takes advantage of dynamic programming ideas about the cost-to-go by relaxing active pseudo constraints in a backwards sweeping process. This further decreases the cost per update of the LP rank-1 updating procedure, although it may result in more changes of the active set that if pseudo constraints were relaxed in a non-stagewise fashion. The usual stability of closed-loop Linear/Quadratic optimally-controlled systems, if it carries over to strictly linear cost functions, implies that the saving due to reduced factor update effort may outweigh the cost of an increased number of updates. An aerospace example is presented in which a ground-to-ground rocket's distance is maximized. This example demonstrates the applicability of this class of algorithms to aerospace guidance. It also sheds light on the efficacy of the proposed pseudo constraint relaxation scheme.

A new universal dynamic model to describe eating rate and cumulative intake curves123

PubMed Central

Paynter, Jonathan; Peterson, Courtney M; Heymsfield, Steven B

2017-01-01

Background: Attempts to model cumulative intake curves with quadratic functions have not simultaneously taken gustatory stimulation, satiation, and maximal food intake into account. Objective: Our aim was to develop a dynamic model for cumulative intake curves that captures gustatory stimulation, satiation, and maximal food intake. Design: We developed a first-principles model describing cumulative intake that universally describes gustatory stimulation, satiation, and maximal food intake using 3 key parameters: 1) the initial eating rate, 2) the effective duration of eating, and 3) the maximal food intake. These model parameters were estimated in a study (n = 49) where eating rates were deliberately changed. Baseline data was used to determine the quality of model's fit to data compared with the quadratic model. The 3 parameters were also calculated in a second study consisting of restrained and unrestrained eaters. Finally, we calculated when the gustatory stimulation phase is short or absent. Results: The mean sum squared error for the first-principles model was 337.1 ± 240.4 compared with 581.6 ± 563.5 for the quadratic model, or a 43% improvement in fit. Individual comparison demonstrated lower errors for 94% of the subjects. Both sex (P = 0.002) and eating duration (P = 0.002) were associated with the initial eating rate (adjusted R2 = 0.23). Sex was also associated (P = 0.03 and P = 0.012) with the effective eating duration and maximum food intake (adjusted R2 = 0.06 and 0.11). In participants directed to eat as much as they could compared with as much as they felt comfortable with, the maximal intake parameter was approximately double the amount. The model found that certain parameter regions resulted in both stimulation and satiation phases, whereas others only produced a satiation phase. Conclusions: The first-principles model better quantifies interindividual differences in food intake, shows how aspects of food intake differ across subpopulations, and can be applied to determine how eating behavior factors influence total food intake. PMID:28077377

Data Modeling Using Finite Differences

ERIC Educational Resources Information Center

Rhoads, Kathryn; Mendoza Epperson, James A.

2017-01-01

The Common Core State Standards for Mathematics (CCSSM) states that high school students should be able to recognize patterns of growth in linear, quadratic, and exponential functions and construct such functions from tables of data (CCSSI 2010). In their work with practicing secondary teachers, the authors found that teachers may make some tacit…

University of Chicago School Mathematics Project (UCSMP) Algebra. WWC Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2009

2009-01-01

University of Chicago School Mathematics Project (UCSMP) Algebra is a one-year course covering three primary topics: (1) linear and quadratic expressions, sentences, and functions; (2) exponential expressions and functions; and (3) linear systems. Topics from geometry, probability, and statistics are integrated with the appropriate algebra.…

Does integration of HIV and SRH services achieve economies of scale and scope in practice? A cost function analysis of the Integra Initiative

PubMed Central

Obure, Carol Dayo; Guinness, Lorna; Sweeney, Sedona; Initiative, Integra; Vassall, Anna

2016-01-01

Objective Policy-makers have long argued about the potential efficiency gains and cost savings from integrating HIV and sexual reproductive health (SRH) services, particularly in resource-constrained settings with generalised HIV epidemics. However, until now, little empirical evidence exists on whether the hypothesised efficiency gains associated with such integration can be achieved in practice. Methods We estimated a quadratic cost function using data obtained from 40 health facilities, over a 2-year-period, in Kenya and Swaziland. The quadratic specification enables us to determine the existence of economies of scale and scope. Findings The empirical results reveal that at the current output levels, only HIV counselling and testing services are characterised by service-specific economies of scale. However, no overall economies of scale exist as all outputs are increased. The results also indicate cost complementarities between cervical cancer screening and HIV care; post-natal care and HIV care and family planning and sexually transmitted infection treatment combinations only. Conclusions The results from this analysis reveal that contrary to expectation, efficiency gains from the integration of HIV and SRH services, if any, are likely to be modest. Efficiency gains are likely to be most achievable in settings that are currently delivering HIV and SRH services at a low scale with high levels of fixed costs. The presence of cost complementarities for only three service combinations implies that careful consideration of setting-specific clinical practices and the extent to which they can be combined should be made when deciding which services to integrate. Trial registration number NCT01694862. PMID:26438349

Fusion of multiple quadratic penalty function support vector machines (QPFSVM) for automated sea mine detection and classification

NASA Astrophysics Data System (ADS)

Dobeck, Gerald J.; Cobb, J. Tory

2002-08-01

The high-resolution sonar is one of the principal sensors used by the Navy to detect and classify sea mines in minehunting operations. For such sonar systems, substantial effort has been devoted to the development of automated detection and classification (D/C) algorithms. These have been spurred by several factors including (1) aids for operators to reduce work overload, (2) more optimal use of all available data, and (3) the introduction of unmanned minehunting systems. The environments where sea mines are typically laid (harbor areas, shipping lanes, and the littorals) give rise to many false alarms caused by natural, biologic, and man-made clutter. The objective of the automated D/C algorithms is to eliminate most of these false alarms while still maintaining a very high probability of mine detection and classification (PdPc). In recent years, the benefits of fusing the outputs of multiple D/C algorithms have been studied. We refer to this as Algorithm Fusion. The results have been remarkable, including reliable robustness to new environments. The Quadratic Penalty Function Support Vector Machine (QPFSVM) algorithm to aid in the automated detection and classification of sea mines is introduced in this paper. The QPFSVM algorithm is easy to train, simple to implement, and robust to feature space dimension. Outputs of successive SVM algorithms are cascaded in stages (fused) to improve the Probability of Classification (Pc) and reduce the number of false alarms. Even though our experience has been gained in the area of sea mine detection and classification, the principles described herein are general and can be applied to fusion of any D/C problem (e.g., automated medical diagnosis or automatic target recognition for ballistic missile defense).

Inexact nonlinear improved fuzzy chance-constrained programming model for irrigation water management under uncertainty

NASA Astrophysics Data System (ADS)

Zhang, Chenglong; Zhang, Fan; Guo, Shanshan; Liu, Xiao; Guo, Ping

2018-01-01

An inexact nonlinear mλ-measure fuzzy chance-constrained programming (INMFCCP) model is developed for irrigation water allocation under uncertainty. Techniques of inexact quadratic programming (IQP), mλ-measure, and fuzzy chance-constrained programming (FCCP) are integrated into a general optimization framework. The INMFCCP model can deal with not only nonlinearities in the objective function, but also uncertainties presented as discrete intervals in the objective function, variables and left-hand side constraints and fuzziness in the right-hand side constraints. Moreover, this model improves upon the conventional fuzzy chance-constrained programming by introducing a linear combination of possibility measure and necessity measure with varying preference parameters. To demonstrate its applicability, the model is then applied to a case study in the middle reaches of Heihe River Basin, northwest China. An interval regression analysis method is used to obtain interval crop water production functions in the whole growth period under uncertainty. Therefore, more flexible solutions can be generated for optimal irrigation water allocation. The variation of results can be examined by giving different confidence levels and preference parameters. Besides, it can reflect interrelationships among system benefits, preference parameters, confidence levels and the corresponding risk levels. Comparison between interval crop water production functions and deterministic ones based on the developed INMFCCP model indicates that the former is capable of reflecting more complexities and uncertainties in practical application. These results can provide more reliable scientific basis for supporting irrigation water management in arid areas.

Longitudinal Models of Reading Achievement of Students with Learning Disabilities and without Disabilities

ERIC Educational Resources Information Center

Sullivan, Amanda L.; Kohli, Nidhi; Farnsworth, Elyse M.; Sadeh, Shanna; Jones, Leila

2017-01-01

Objective: Accurate estimation of developmental trajectories can inform instruction and intervention. We compared the fit of linear, quadratic, and piecewise mixed-effects models of reading development among students with learning disabilities relative to their typically developing peers. Method: We drew an analytic sample of 1,990 students from…

Using a Model to Describe Students' Inductive Reasoning in Problem Solving

ERIC Educational Resources Information Center

Canadas, Maria C.; Castro, Encarnacion; Castro, Enrique

2009-01-01

Introduction: We present some aspects of a wider investigation (Canadas, 2007), whose main objective is to describe and characterize inductive reasoning used by Spanish students in years 9 and 10 when they work on problems that involved linear and quadratic sequences. Method: We produced a test composed of six problems with different…

Acceleration-Augmented LQG Control of an Active Magnetic Bearing

NASA Technical Reports Server (NTRS)

Feeley, Joseph J.

1993-01-01

A linear-quadratic-gaussian (LQG) regulator controller design for an acceleration-augmented active magnetic bearing (AMB) is outlined. Acceleration augmentation is a key feature in providing improved dynamic performance of the controller. The optimal control formulation provides a convenient method of trading-off fast transient response and force attenuation as control objectives.

Nested Conjugate Gradient Algorithm with Nested Preconditioning for Non-linear Image Restoration.

PubMed

Skariah, Deepak G; Arigovindan, Muthuvel

2017-06-19

We develop a novel optimization algorithm, which we call Nested Non-Linear Conjugate Gradient algorithm (NNCG), for image restoration based on quadratic data fitting and smooth non-quadratic regularization. The algorithm is constructed as a nesting of two conjugate gradient (CG) iterations. The outer iteration is constructed as a preconditioned non-linear CG algorithm; the preconditioning is performed by the inner CG iteration that is linear. The inner CG iteration, which performs preconditioning for outer CG iteration, itself is accelerated by an another FFT based non-iterative preconditioner. We prove that the method converges to a stationary point for both convex and non-convex regularization functionals. We demonstrate experimentally that proposed method outperforms the well-known majorization-minimization method used for convex regularization, and a non-convex inertial-proximal method for non-convex regularization functional.

Multi-piecewise quadratic nonlinearity memristor and its 2N-scroll and 2N + 1-scroll chaotic attractors system.

PubMed

Wang, Chunhua; Liu, Xiaoming; Xia, Hu

2017-03-01

In this paper, two kinds of novel ideal active flux-controlled smooth multi-piecewise quadratic nonlinearity memristors with multi-piecewise continuous memductance function are presented. The pinched hysteresis loop characteristics of the two memristor models are verified by building a memristor emulator circuit. Using the two memristor models establish a new memristive multi-scroll Chua's circuit, which can generate 2N-scroll and 2N+1-scroll chaotic attractors without any other ordinary nonlinear function. Furthermore, coexisting multi-scroll chaotic attractors are found in the proposed memristive multi-scroll Chua's circuit. Phase portraits, Lyapunov exponents, bifurcation diagrams, and equilibrium point analysis have been used to research the basic dynamics of the memristive multi-scroll Chua's circuit. The consistency of circuit implementation and numerical simulation verifies the effectiveness of the system design.

Linear Approximation SAR Azimuth Processing Study

NASA Technical Reports Server (NTRS)

Lindquist, R. B.; Masnaghetti, R. K.; Belland, E.; Hance, H. V.; Weis, W. G.

1979-01-01

A segmented linear approximation of the quadratic phase function that is used to focus the synthetic antenna of a SAR was studied. Ideal focusing, using a quadratic varying phase focusing function during the time radar target histories are gathered, requires a large number of complex multiplications. These can be largely eliminated by using linear approximation techniques. The result is a reduced processor size and chip count relative to ideally focussed processing and a correspondingly increased feasibility for spaceworthy implementation. A preliminary design and sizing for a spaceworthy linear approximation SAR azimuth processor meeting requirements similar to those of the SEASAT-A SAR was developed. The study resulted in a design with approximately 1500 IC's, 1.2 cubic feet of volume, and 350 watts of power for a single look, 4000 range cell azimuth processor with 25 meters resolution.

A quadratically regularized functional canonical correlation analysis for identifying the global structure of pleiotropy with NGS data

PubMed Central

Zhu, Yun; Fan, Ruzong; Xiong, Momiao

2017-01-01

Investigating the pleiotropic effects of genetic variants can increase statistical power, provide important information to achieve deep understanding of the complex genetic structures of disease, and offer powerful tools for designing effective treatments with fewer side effects. However, the current multiple phenotype association analysis paradigm lacks breadth (number of phenotypes and genetic variants jointly analyzed at the same time) and depth (hierarchical structure of phenotype and genotypes). A key issue for high dimensional pleiotropic analysis is to effectively extract informative internal representation and features from high dimensional genotype and phenotype data. To explore correlation information of genetic variants, effectively reduce data dimensions, and overcome critical barriers in advancing the development of novel statistical methods and computational algorithms for genetic pleiotropic analysis, we proposed a new statistic method referred to as a quadratically regularized functional CCA (QRFCCA) for association analysis which combines three approaches: (1) quadratically regularized matrix factorization, (2) functional data analysis and (3) canonical correlation analysis (CCA). Large-scale simulations show that the QRFCCA has a much higher power than that of the ten competing statistics while retaining the appropriate type 1 errors. To further evaluate performance, the QRFCCA and ten other statistics are applied to the whole genome sequencing dataset from the TwinsUK study. We identify a total of 79 genes with rare variants and 67 genes with common variants significantly associated with the 46 traits using QRFCCA. The results show that the QRFCCA substantially outperforms the ten other statistics. PMID:29040274

A prospective study of change in bone mass with age in postmenopausal women.

PubMed

Hui, S L; Wiske, P S; Norton, J A; Johnston, C C

1982-01-01

For the first time a model for age-related bone loss has been developed from prospective data utilizing a new weighted least squares method. Two hundred and sixty-eight Caucasian women ranging in age from 50 to 95 were studied. A quadratic function best fit the data, and correcting for body weight and bone width reduced variance. The derived equation is: bone mass = (0.6032) (bone width) (cm) + (0.003059) (body weight) (kg) - (0.0163) (age - 50) + (0.0002249) (age - 50)2. Analysis of cross-sectional data on 583 Caucasian women of similar age showed a quadratic function with very similar coefficients. This quadratic function predicts an increase in bone mass after age 86, therefore 42 women over age 70 who had been followed for at least 2.5 yr were identified to test for this effect. of these, 13 had significantly positive regression coefficients of bone mass on age, and rate of change in bone width was positive in 40 of 42 individuals, of which 5 were significant. Since photon absorptiometry measures net changes on all bone envelopes, the most likely explanation for the observed changes is an early exponential loss of endosteal bone which ultimately slows or perhaps stops. There is a positive balance on the periosteal envelope which only becomes apparent in later years when the endosteal loss stops. These new statistical methods allow the development of models utilizing data collected at irregular intervals. The methods used are applicable to other biological data collected prospectively.

Technical report. The application of probability-generating functions to linear-quadratic radiation survival curves.

PubMed

Kendal, W S

2000-04-01

To illustrate how probability-generating functions (PGFs) can be employed to derive a simple probabilistic model for clonogenic survival after exposure to ionizing irradiation. Both repairable and irreparable radiation damage to DNA were assumed to occur by independent (Poisson) processes, at intensities proportional to the irradiation dose. Also, repairable damage was assumed to be either repaired or further (lethally) injured according to a third (Bernoulli) process, with the probability of lethal conversion being directly proportional to dose. Using the algebra of PGFs, these three processes were combined to yield a composite PGF that described the distribution of lethal DNA lesions in irradiated cells. The composite PGF characterized a Poisson distribution with mean, chiD+betaD2, where D was dose and alpha and beta were radiobiological constants. This distribution yielded the conventional linear-quadratic survival equation. To test the composite model, the derived distribution was used to predict the frequencies of multiple chromosomal aberrations in irradiated human lymphocytes. The predictions agreed well with observation. This probabilistic model was consistent with single-hit mechanisms, but it was not consistent with binary misrepair mechanisms. A stochastic model for radiation survival has been constructed from elementary PGFs that exactly yields the linear-quadratic relationship. This approach can be used to investigate other simple probabilistic survival models.

On the Convergence Analysis of the Optimized Gradient Method.

PubMed

Kim, Donghwan; Fessler, Jeffrey A

2017-01-01

This paper considers the problem of unconstrained minimization of smooth convex functions having Lipschitz continuous gradients with known Lipschitz constant. We recently proposed the optimized gradient method for this problem and showed that it has a worst-case convergence bound for the cost function decrease that is twice as small as that of Nesterov's fast gradient method, yet has a similarly efficient practical implementation. Drori showed recently that the optimized gradient method has optimal complexity for the cost function decrease over the general class of first-order methods. This optimality makes it important to study fully the convergence properties of the optimized gradient method. The previous worst-case convergence bound for the optimized gradient method was derived for only the last iterate of a secondary sequence. This paper provides an analytic convergence bound for the primary sequence generated by the optimized gradient method. We then discuss additional convergence properties of the optimized gradient method, including the interesting fact that the optimized gradient method has two types of worstcase functions: a piecewise affine-quadratic function and a quadratic function. These results help complete the theory of an optimal first-order method for smooth convex minimization.

On the Convergence Analysis of the Optimized Gradient Method

PubMed Central

Kim, Donghwan; Fessler, Jeffrey A.

2016-01-01

This paper considers the problem of unconstrained minimization of smooth convex functions having Lipschitz continuous gradients with known Lipschitz constant. We recently proposed the optimized gradient method for this problem and showed that it has a worst-case convergence bound for the cost function decrease that is twice as small as that of Nesterov’s fast gradient method, yet has a similarly efficient practical implementation. Drori showed recently that the optimized gradient method has optimal complexity for the cost function decrease over the general class of first-order methods. This optimality makes it important to study fully the convergence properties of the optimized gradient method. The previous worst-case convergence bound for the optimized gradient method was derived for only the last iterate of a secondary sequence. This paper provides an analytic convergence bound for the primary sequence generated by the optimized gradient method. We then discuss additional convergence properties of the optimized gradient method, including the interesting fact that the optimized gradient method has two types of worstcase functions: a piecewise affine-quadratic function and a quadratic function. These results help complete the theory of an optimal first-order method for smooth convex minimization. PMID:28461707

Fast Spatial Resolution Analysis of Quadratic Penalized Least-Squares Image Reconstruction With Separate Real and Imaginary Roughness Penalty: Application to fMRI.

PubMed

Olafsson, Valur T; Noll, Douglas C; Fessler, Jeffrey A

2018-02-01

Penalized least-squares iterative image reconstruction algorithms used for spatial resolution-limited imaging, such as functional magnetic resonance imaging (fMRI), commonly use a quadratic roughness penalty to regularize the reconstructed images. When used for complex-valued images, the conventional roughness penalty regularizes the real and imaginary parts equally. However, these imaging methods sometimes benefit from separate penalties for each part. The spatial smoothness from the roughness penalty on the reconstructed image is dictated by the regularization parameter(s). One method to set the parameter to a desired smoothness level is to evaluate the full width at half maximum of the reconstruction method's local impulse response. Previous work has shown that when using the conventional quadratic roughness penalty, one can approximate the local impulse response using an FFT-based calculation. However, that acceleration method cannot be applied directly for separate real and imaginary regularization. This paper proposes a fast and stable calculation for this case that also uses FFT-based calculations to approximate the local impulse responses of the real and imaginary parts. This approach is demonstrated with a quadratic image reconstruction of fMRI data that uses separate roughness penalties for the real and imaginary parts.

The Factorability of Quadratics: Motivation for More Techniques

ERIC Educational Resources Information Center

Bosse, Michael J.; Nandakumar, N. R.

2005-01-01

Typically, secondary and college algebra students attempt to utilize either completing the square or the quadratic formula as techniques to solve a quadratic equation only after frustration with factoring has arisen. While both completing the square and the quadratic formula are techniques which can determine solutions for all quadratic equations,…

Solution of monotone complementarity and general convex programming problems using a modified potential reduction interior point method

DOE PAGES

Huang, Kuo -Ling; Mehrotra, Sanjay

2016-11-08

We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition (SLC) is satisfied. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation in iOptimize maintains global linear and polynomial time convergence properties, while achieving practical performance. It either successfully solves the problem, or concludes that the SLC is not satisfied. When compared with the mature software package MOSEK (barrier solver version 6.0.0.106), iOptimize solves convex quadraticmore » programming problems, convex quadratically constrained quadratic programming problems, and general convex programming problems in fewer iterations. Moreover, several problems for which MOSEK fails are solved to optimality. In addition, we also find that iOptimize detects infeasibility more reliably than the general nonlinear solvers Ipopt (version 3.9.2) and Knitro (version 8.0).« less

Coherence solution for bidirectional reflectance distributions of surfaces with wavelength-scale statistics.

PubMed

Hoover, Brian G; Gamiz, Victor L

2006-02-01

The scalar bidirectional reflectance distribution function (BRDF) due to a perfectly conducting surface with roughness and autocorrelation width comparable with the illumination wavelength is derived from coherence theory on the assumption of a random reflective phase screen and an expansion valid for large effective roughness. A general quadratic expansion of the two-dimensional isotropic surface autocorrelation function near the origin yields representative Cauchy and Gaussian BRDF solutions and an intermediate general solution as the sum of an incoherent component and a nonspecular coherent component proportional to an integral of the plasma dispersion function in the complex plane. Plots illustrate agreement of the derived general solution with original bistatic BRDF data due to a machined aluminum surface, and comparisons are drawn with previously published data in the examination of variations with incident angle, roughness, illumination wavelength, and autocorrelation coefficients in the bistatic and monostatic geometries. The general quadratic autocorrelation expansion provides a BRDF solution that smoothly interpolates between the well-known results of the linear and parabolic approximations.

[Effects of fundamental frequency and speech rate on impression formation].

PubMed

Uchida, Teruhisa; Nakaune, Naoko

2004-12-01

This study investigated the systematic relationship between nonverbal features of speech and personality trait ratings of the speaker. In Study 1, fundamental frequency (F0) in original speech was converted into five levels from 64% to 156.25%. Then 132 undergraduates rated each of the converted speeches in terms of personality traits. In Study 2 134 undergraduates similarly rated the speech stimuli, which had five speech rate levels as well as two F0 levels. Results showed that listener ratings along Big Five dimensions were mostly independent. Each dimension had a slightly different change profile over the five levels of F0 and speech rate. A quadratic regression equation provided a good approximation for each rating as a function of F0 or speech rate. The quadratic regression equations put together would provide us with a rough estimate of personality trait impression as a function of prosodic features. The functional relationship among F0, speech rate, and trait ratings was shown as a curved surface in the three-dimensional space.

High-order Newton-penalty algorithms

NASA Astrophysics Data System (ADS)

Dussault, Jean-Pierre

2005-10-01

Recent efforts in differentiable non-linear programming have been focused on interior point methods, akin to penalty and barrier algorithms. In this paper, we address the classical equality constrained program solved using the simple quadratic loss penalty function/algorithm. The suggestion to use extrapolations to track the differentiable trajectory associated with penalized subproblems goes back to the classic monograph of Fiacco & McCormick. This idea was further developed by Gould who obtained a two-steps quadratically convergent algorithm using prediction steps and Newton correction. Dussault interpreted the prediction step as a combined extrapolation with respect to the penalty parameter and the residual of the first order optimality conditions. Extrapolation with respect to the residual coincides with a Newton step.We explore here higher-order extrapolations, thus higher-order Newton-like methods. We first consider high-order variants of the Newton-Raphson method applied to non-linear systems of equations. Next, we obtain improved asymptotic convergence results for the quadratic loss penalty algorithm by using high-order extrapolation steps.

de la Vallée-Poussin means of Fourier series for the quadratic spectrum and for spectra with power-like density

NASA Astrophysics Data System (ADS)

Bochkarev, S. V.

2014-02-01

A new method is proposed and elaborated for investigating complex or real trigonometric series with various spectra. It is based on new multiplicative inequalities which give a lower bound for the integral norm of the de la Vallée-Poussin means and are themselves based on results establishing corresponding analogues of the Littlewood-Paley theorem in the BMO, Hardy, and Lorentz spaces. For spectra with power-like density a description of the class of absolute values of coefficients such that the corresponding complex or real trigonometric series are Fourier series is found which depends on the arithmetic characteristics of the spectrum and is sharp in limiting cases. Furthermore, for the quadratic spectrum some results of Hardy and Littlewood on elliptic theta functions are generalized and refined. For the quadratic spectrum and power-like spectra with non-integer exponents new lower bounds are found for the integral norms of exponential sums. Bibliography: 41 titles.

Application of stochastic particle swarm optimization algorithm to determine the graded refractive index distribution in participating media

NASA Astrophysics Data System (ADS)

Wei, Lin-Yang; Qi, Hong; Ren, Ya-Tao; Ruan, Li-Ming

2016-11-01

Inverse estimation of the refractive index distribution in one-dimensional participating media with graded refractive index (GRI) is investigated. The forward radiative transfer problem is solved by the Chebyshev collocation spectral method. The stochastic particle swarm optimization (SPSO) algorithm is employed to retrieve three kinds of GRI distribution, i.e. the linear, sinusoidal and quadratic GRI distribution. The retrieval accuracy of GRI distribution with different wall emissivity, optical thickness, absorption coefficients and scattering coefficients are discussed thoroughly. To improve the retrieval accuracy of quadratic GRI distribution, a double-layer model is proposed to supply more measurement information. The influence of measurement errors upon the precision of estimated results is also investigated. Considering the GRI distribution is unknown beforehand in practice, a quadratic function is employed to retrieve the linear GRI by SPSO algorithm. All the results show that the SPSO algorithm is applicable to retrieve different GRI distributions in participating media accurately even with noisy data.

AESOP- INTERACTIVE DESIGN OF LINEAR QUADRATIC REGULATORS AND KALMAN FILTERS

NASA Technical Reports Server (NTRS)

Lehtinen, B.

1994-01-01

AESOP was developed to solve a number of problems associated with the design of controls and state estimators for linear time-invariant systems. The systems considered are modeled in state-variable form by a set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are the linear quadratic regulator (LQR) design problem and the steady-state Kalman filter design problem. AESOP is designed to be used in an interactive manner. The user can solve design problems and analyze the solutions in a single interactive session. Both numerical and graphical information are available to the user during the session. The AESOP program is structured around a list of predefined functions. Each function performs a single computation associated with control, estimation, or system response determination. AESOP contains over sixty functions and permits the easy inclusion of user defined functions. The user accesses these functions either by inputting a list of desired functions in the order they are to be performed, or by specifying a single function to be performed. The latter case is used when the choice of function and function order depends on the results of previous functions. The available AESOP functions are divided into several general areas including: 1) program control, 2) matrix input and revision, 3) matrix formation, 4) open-loop system analysis, 5) frequency response, 6) transient response, 7) transient function zeros, 8) LQR and Kalman filter design, 9) eigenvalues and eigenvectors, 10) covariances, and 11) user-defined functions. The most important functions are those that design linear quadratic regulators and Kalman filters. The user interacts with AESOP when using these functions by inputting design weighting parameters and by viewing displays of designed system response. Support functions obtain system transient and frequency responses, transfer functions, and covariance matrices. AESOP can also provide the user with open-loop system information including stability, controllability, and observability. The AESOP program is written in FORTRAN IV for interactive execution and has been implemented on an IBM 3033 computer using TSS 370. As currently configured, AESOP has a central memory requirement of approximately 2 Megs of 8 bit bytes. Memory requirements can be reduced by redimensioning arrays in the AESOP program. Graphical output requires adaptation of the AESOP plot routines to whatever device is available. The AESOP program was developed in 1984.

Interpolation and Polynomial Curve Fitting

ERIC Educational Resources Information Center

Yang, Yajun; Gordon, Sheldon P.

2014-01-01

Two points determine a line. Three noncollinear points determine a quadratic function. Four points that do not lie on a lower-degree polynomial curve determine a cubic function. In general, n + 1 points uniquely determine a polynomial of degree n, presuming that they do not fall onto a polynomial of lower degree. The process of finding such a…

The Inverted Student Density and Test Scores.

ERIC Educational Resources Information Center

Boldt, Robert F.

The inverted density is one whose contour lines are spheroidal as in the normal distribution, but whose moments differ from those of the normal in that its conditional arrays are not homoscedastic, being quadratic functions of the values of the linear regression functions. It is also platykurtic, its measure of kurtosis ranging from that of the…

State Spending on Higher Education Capital Outlays

ERIC Educational Resources Information Center

Delaney, Jennifer A.; Doyle, William R.

2014-01-01

This paper explores the role that state spending on higher education capital outlays plays in state budgets by considering the functional form of the relationship between state spending on higher education capital outlays and four types of state expenditures. Three possible functional forms are tested: a linear model, a quadratic model, and the…

An Authentic Task That Models Quadratics

ERIC Educational Resources Information Center

Baron, Lorraine M.

2015-01-01

As students develop algebraic reasoning in grades 5 to 9, they learn to recognize patterns and understand expressions, equations, and variables. Linear functions are a focus in eighth-grade mathematics, and by algebra 1, students must make sense of functions that are not linear. This article describes how students worked through a classroom task…

Smoothing of Transport Plans with Fixed Marginals and Rigorous Semiclassical Limit of the Hohenberg-Kohn Functional

NASA Astrophysics Data System (ADS)

Cotar, Codina; Friesecke, Gero; Klüppelberg, Claudia

2018-06-01

We prove rigorously that the exact N-electron Hohenberg-Kohn density functional converges in the strongly interacting limit to the strictly correlated electrons (SCE) functional, and that the absolute value squared of the associated constrained search wavefunction tends weakly in the sense of probability measures to a minimizer of the multi-marginal optimal transport problem with Coulomb cost associated to the SCE functional. This extends our previous work for N = 2 ( Cotar etal. in Commun Pure Appl Math 66:548-599, 2013). The correct limit problem has been derived in the physics literature by Seidl (Phys Rev A 60 4387-4395, 1999) and Seidl, Gorigiorgi and Savin (Phys Rev A 75:042511 1-12, 2007); in these papers the lack of a rigorous proofwas pointed out.We also give amathematical counterexample to this type of result, by replacing the constraint of given one-body density—an infinite dimensional quadratic expression in the wavefunction—by an infinite-dimensional quadratic expression in the wavefunction and its gradient. Connections with the Lawrentiev phenomenon in the calculus of variations are indicated.

Joint Optimization of Fluence Field Modulation and Regularization in Task-Driven Computed Tomography.

PubMed

Gang, G J; Siewerdsen, J H; Stayman, J W

2017-02-11

This work presents a task-driven joint optimization of fluence field modulation (FFM) and regularization in quadratic penalized-likelihood (PL) reconstruction. Conventional FFM strategies proposed for filtered-backprojection (FBP) are evaluated in the context of PL reconstruction for comparison. We present a task-driven framework that leverages prior knowledge of the patient anatomy and imaging task to identify FFM and regularization. We adopted a maxi-min objective that ensures a minimum level of detectability index ( d' ) across sample locations in the image volume. The FFM designs were parameterized by 2D Gaussian basis functions to reduce dimensionality of the optimization and basis function coefficients were estimated using the covariance matrix adaptation evolutionary strategy (CMA-ES) algorithm. The FFM was jointly optimized with both space-invariant and spatially-varying regularization strength ( β ) - the former via an exhaustive search through discrete values and the latter using an alternating optimization where β was exhaustively optimized locally and interpolated to form a spatially-varying map. The optimal FFM inverts as β increases, demonstrating the importance of a joint optimization. For the task and object investigated, the optimal FFM assigns more fluence through less attenuating views, counter to conventional FFM schemes proposed for FBP. The maxi-min objective homogenizes detectability throughout the image and achieves a higher minimum detectability than conventional FFM strategies. The task-driven FFM designs found in this work are counter to conventional patterns for FBP and yield better performance in terms of the maxi-min objective, suggesting opportunities for improved image quality and/or dose reduction when model-based reconstructions are applied in conjunction with FFM.

Discrete-time pilot model. [human dynamics and digital simulation

NASA Technical Reports Server (NTRS)

Cavalli, D.

1978-01-01

Pilot behavior is considered as a discrete-time process where the decision making has a sequential nature. This model differs from both the quasilinear model which follows from classical control theory and from the optimal control model which considers the human operator as a Kalman estimator-predictor. An additional factor considered is that the pilot's objective may not be adequately formulated as a quadratic cost functional to be minimized, but rather as a more fuzzy measure of the closeness with which the aircraft follows a reference trajectory. All model parameters, in the digital program simulating the pilot's behavior, were successfully compared in terms of standard-deviation and performance with those of professional pilots in IFR configuration. The first practical application of the model was in the study of its performance degradation when the aircraft model static margin decreases.

Evaluation of the Williams-type model for barley yields in North Dakota and Minnesota

NASA Technical Reports Server (NTRS)

Barnett, T. L. (Principal Investigator)

1981-01-01

The Williams-type yield model is based on multiple regression analysis of historial time series data at CRD level pooled to regional level (groups of similar CRDs). Basic variables considered in the analysis include USDA yield, monthly mean temperature, monthly precipitation, soil texture and topographic information, and variables derived from these. Technologic trend is represented by piecewise linear and/or quadratic functions of year. Indicators of yield reliability obtained from a ten-year bootstrap test (1970-1979) demonstrate that biases are small and performance based on root mean square appears to be acceptable for the intended AgRISTARS large area applications. The model is objective, adequate, timely, simple, and not costly. It consideres scientific knowledge on a broad scale but not in detail, and does not provide a good current measure of modeled yield reliability.

Quadratic Forms and Semiclassical Eigenfunction Hypothesis for Flat Tori

NASA Astrophysics Data System (ADS)

T. Sardari, Naser

2018-03-01

Let Q( X) be any integral primitive positive definite quadratic form in k variables, where {k≥4}, and discriminant D. For any integer n, we give an upper bound on the number of integral solutions of Q( X) = n in terms of n, k, and D. As a corollary, we prove a conjecture of Lester and Rudnick on the small scale equidistribution of almost all functions belonging to any orthonormal basis of a given eigenspace of the Laplacian on the flat torus {T^d} for {d≥ 5}. This conjecture is motivated by the work of Berry [2,3] on the semiclassical eigenfunction hypothesis.

A Monte Carlo study of the spin-1 Blume-Emery-Griffiths phase diagrams within biquadratic exchange anisotropy

NASA Astrophysics Data System (ADS)

Dani, Ibtissam; Tahiri, Najim; Ez-Zahraouy, Hamid; Benyoussef, Abdelilah

2014-08-01

The effect of the bi-quadratic exchange coupling anisotropy on the phase diagram of the spin-1 Blume-Emery-Griffiths model on simple-cubic lattice is investigated using mean field theory (MFT) and Monte Carlo simulation (MC). It is found that the anisotropy of the biquadratic coupling favors the stability of the ferromagnetic phase. By decreasing the parallel and/or perpendicular bi-quadratic coupling, the ferrimagnetic and the antiquadrupolar phases broaden in contrast, the ferromagnetic and the disordered phases become narrow. The behavior of magnetization and quadrupolar moment as a function of temperature is also computed, especially in the ferrimagnetic phase.

Quadratic stark effect in the fullerene C60 at low symmetry orientation in the field

NASA Astrophysics Data System (ADS)

Tuchin, A. V.; Bityutskaya, L. A.; Bormontov, E. N.

2014-08-01

Results of numeric simulation of the influence of the electric field E = 0 - 1 V/Å on the electronic structure of the neutral fullerene C60 taking into account orientational deformation of its carbon cage at arbitrary orientations in the electric field including low symmetry orientations are presented. Splitting of the frontier t 1 u - and h u -levels of the molecule due to the quadratic Stark effect has been investigated. Dependencies of the effective electron work function and the energy gap between the lowest unoccupied and highest occupied molecular orbitals on the strengths of the electric field have been determined.

Effects of Phytoecdysteroids (PEDS) Extracted from Cyanotis arachnoidea on Rumen Fermentation, Enzyme Activity and Microbial Efficiency in a Continuous-Culture System.

PubMed

Li, Deyong; Zhang, Yawei; Cui, Zhenliang; He, Liwen; Chen, Wanbao; Meng, Qingxiang; Ren, Liping

2016-01-01

The objective of this study was to evaluate the effects of supplementation of phytoecdysteroids (PEDS) extracted from Cyanotis arachnoidea on rumen fermentation, enzymes activity and microbial efficiency in a dual flow continuous-culture system. A single-factor experimental design was used with twelve fermenters in 4 groups with 3 replicates each. Fermenters were incubated for a total of 7 days that included first 4 days for adaptation and last 3 days for sampling. PEDS was added at levels of zero (as control), 5, 10, and 15 mg/g of the substrate (DM). The results showed that increasing supplementation levels of PEDS resulted in incremental digestibility of dry matter (DMD) (quadratic, P = 0.001) and organic matter (OMD) (quadratic, P = 0.031), but unchanged digestibility of neutral detergent fiber (NDFD), crude protein (CPD) and acid detergent acid (ADFD). As supplementation levels of PEDS increased, there were decreased response in the concentration of ammonia nitrogen (NH3-N) (linear, P = 0.015) and increased response in molar proportions of butyrate (linear, P = 0.004), but unchanged response in total volatile fatty acid (TVFA) and the molar proportion of acetate and propionate, respectively. Increasing PEDS supplementation levels decreased the ratio of acetate to propionate (linear, P = 0.038), suggesting an alteration of rumen fermentation pattern occurring due to PEDS supplementation in the diet. Supplementation of PEDS significantly increased activities of glutamate dehydrogenase (quadratic, P = 0.001), alanine dehydrogenase (quadratic, P = 0.004), glutamate synthase (linear, P = 0.038), glutamine synthetase (quadratic, P = 0.011), respectively. There were no discernible differences in the activity of carboxymethyl cellulose (CMCase), xylanase and protease regardless of the treatments. The daily production of microbial nitrogen (linear, P = 0.002) and microbial efficiency (MOEEF) (linear, P = 0.001) increased linearly as supplementation levels of PEDS increased. The decreased response of fluid NH3-N and the increased response of MN indicated that PEDS positively increased the synthesis of microbial proteins.

Frictional Torque on a Rotating Disc

ERIC Educational Resources Information Center

Mungan, Carl E.

2012-01-01

Resistance to motion often includes a dry frictional term independent of the speed of an object and a fluid drag term varying linearly with speed in the viscous limit. (At higher speeds, quadratic drag can also occur.) Here, measurements are performed for an aluminium disc mounted on bearings that is given an initial twist and allowed to spin…

Measuring Human Performance on Clustering Problems: Some Potential Objective Criteria and Experimental Research Opportunities

ERIC Educational Resources Information Center

Brusco, Michael J.

2007-01-01

The study of human performance on discrete optimization problems has a considerable history that spans various disciplines. The two most widely studied problems are the Euclidean traveling salesperson problem and the quadratic assignment problem. The purpose of this paper is to outline a program of study for the measurement of human performance on…

Optical Pattern Recognition

NASA Astrophysics Data System (ADS)

Yu, Francis T. S.; Jutamulia, Suganda

2008-10-01

Contributors; Preface; 1. Pattern recognition with optics Francis T. S. Yu and Don A. Gregory; 2. Hybrid neural networks for nonlinear pattern recognition Taiwei Lu; 3. Wavelets, optics, and pattern recognition Yao Li and Yunglong Sheng; 4. Applications of the fractional Fourier transform to optical pattern recognition David Mendlovic, Zeev Zalesky and Haldum M. Oxaktas; 5. Optical implementation of mathematical morphology Tien-Hsin Chao; 6. Nonlinear optical correlators with improved discrimination capability for object location and recognition Leonid P. Yaroslavsky; 7. Distortion-invariant quadratic filters Gregory Gheen; 8. Composite filter synthesis as applied to pattern recognition Shizhou Yin and Guowen Lu; 9. Iterative procedures in electro-optical pattern recognition Joseph Shamir; 10. Optoelectronic hybrid system for three-dimensional object pattern recognition Guoguang Mu, Mingzhe Lu and Ying Sun; 11. Applications of photrefractive devices in optical pattern recognition Ziangyang Yang; 12. Optical pattern recognition with microlasers Eung-Gi Paek; 13. Optical properties and applications of bacteriorhodopsin Q. Wang Song and Yu-He Zhang; 14. Liquid-crystal spatial light modulators Aris Tanone and Suganda Jutamulia; 15. Representations of fully complex functions on real-time spatial light modulators Robert W. Cohn and Laurence G. Hassbrook; Index.

Decomposition method for zonal resource allocation problems in telecommunication networks

NASA Astrophysics Data System (ADS)

Konnov, I. V.; Kashuba, A. Yu

2016-11-01

We consider problems of optimal resource allocation in telecommunication networks. We first give an optimization formulation for the case where the network manager aims to distribute some homogeneous resource (bandwidth) among users of one region with quadratic charge and fee functions and present simple and efficient solution methods. Next, we consider a more general problem for a provider of a wireless communication network divided into zones (clusters) with common capacity constraints. We obtain a convex quadratic optimization problem involving capacity and balance constraints. By using the dual Lagrangian method with respect to the capacity constraint, we suggest to reduce the initial problem to a single-dimensional optimization problem, but calculation of the cost function value leads to independent solution of zonal problems, which coincide with the above single region problem. Some results of computational experiments confirm the applicability of the new methods.

Neural-genetic synthesis for state-space controllers based on linear quadratic regulator design for eigenstructure assignment.

PubMed

da Fonseca Neto, João Viana; Abreu, Ivanildo Silva; da Silva, Fábio Nogueira

2010-04-01

Toward the synthesis of state-space controllers, a neural-genetic model based on the linear quadratic regulator design for the eigenstructure assignment of multivariable dynamic systems is presented. The neural-genetic model represents a fusion of a genetic algorithm and a recurrent neural network (RNN) to perform the selection of the weighting matrices and the algebraic Riccati equation solution, respectively. A fourth-order electric circuit model is used to evaluate the convergence of the computational intelligence paradigms and the control design method performance. The genetic search convergence evaluation is performed in terms of the fitness function statistics and the RNN convergence, which is evaluated by landscapes of the energy and norm, as a function of the parameter deviations. The control problem solution is evaluated in the time and frequency domains by the impulse response, singular values, and modal analysis.

Ingestive Behavior of Heifers Supplemented with Glycerin in Substitution of Corn on Brachiaria brizantha Pasture

PubMed Central

Facuri, L. M. A. M.; Silva, R. R.; da Silva, F. F.; de Carvalho, G. G. P.; Sampaio, C. B.; Mendes, F. B. L.; Lisboa, M. M.; Barroso, D. S.; Carvalho, V. M.; Pereira, M. M. S.

2014-01-01

The objective was to evaluate the ingestive behavior of crossbred heifers finished on a Brachiaria brizantha cv. Marandu pasture receiving four levels of glycerin in their supplementation. Thirty-six crossbred heifers with average initial weight of 264.83±3.83 kg and 20 months of age were distributed into a completely randomized design with four treatments and nine replications: control (0%), 4.82%, 10.12%, and 15.56% glycerin in the dry matter. The grazing time reduced linearly (p<0.05), whereas the time spent on activities like rumination, idleness, trough and total chewing time were quadratically affected (p<0.05). Bite rate and number of bites/day were quadratically influenced (p<0.05). The number of bites/swallowed cud and the number of bites/minute, however, increased linearly (p<0.05). Although the time spent on each cud and number of chews per cud were not affected (p>0.05). The number of rumination periods reduced linearly (p<0.05), whereas the number of grazing, idle and trough periods, and the times per grazing, idle, rumination and trough periods were quadratically affected (p<0.05). The feed and rumination efficiencies of the dry matter, non-fibrous carbohydrates, pasture dry matter and concentrate were quadratically affected (p>0.05) whereas the feed efficiency of neutral detergent fiber reduced linearly (p<0.05). Addition of glycerin in substitution of corn in supplements for animals managed on pastures does not influenced feed intake, but reduces the grazing time and increases the idle time. The supplementation also improves feed and rumination efficiencies. PMID:25358318

Species composition, monitoring, and feeding injury of stink bugs (Heteroptera: Pentatomidae) in blackberry.

PubMed

Brennan, S A; Liburd, O E; Eger, J E; Rhodes, E M

2013-04-01

Blackberry (Rubus spp.) production in Florida has increased > 100% within the past two decades. and several insect pests, including stink bugs (Heteroptera: Pentatomidae), have been observed feeding on this crop. The objectives for this study were to determine the stink bug species present in blackberry; to develop monitoring tools for stink bugs in blackberry; and to describe feeding injury to blackberries by Euschistus quadrator Rolston, a relatively new stink bug pest to Florida, that has spread throughout the state. In a field survey, E. quadrator was the most abundant stink bug species, followed by Euschistus servus Say, Euschistus obscurus (Palisot de Beauvois), Thyanta custator (F.), Proxys punctulatus (Palisot de Beauvois), and Podisus maculiventris Say. Yellow pyramid traps caught more stink bugs than tube traps with or without the addition of Euschistus spp. pheromone lures. There were no statistical differences between traps baited with a Trécé Pherocon Centrum lure, a Suterra Scenturion lure, and an unbaited trap. These results were supported by Y-tube olfactometer assays with E. quadrator where there were no differences between pheromone baited lures and a control. Injury to berries caused by E. quadrator adults and third instars was similar, and both adults and third instars fed more on green berries compared with turning berries. In addition, adults fed more on green berries compared with ripe fruit. The most common injury to green berries was discoloration. In contrast, misshapen drupelets were commonly seen on turning and ripe berries. The potential for managing stink bugs in blackberries to prevent them from reaching damaging levels is discussed.

Convergence of neural networks for programming problems via a nonsmooth Lojasiewicz inequality.

PubMed

Forti, Mauro; Nistri, Paolo; Quincampoix, Marc

2006-11-01

This paper considers a class of neural networks (NNs) for solving linear programming (LP) problems, convex quadratic programming (QP) problems, and nonconvex QP problems where an indefinite quadratic objective function is subject to a set of affine constraints. The NNs are characterized by constraint neurons modeled by ideal diodes with vertical segments in their characteristic, which enable to implement an exact penalty method. A new method is exploited to address convergence of trajectories, which is based on a nonsmooth Lojasiewicz inequality for the generalized gradient vector field describing the NN dynamics. The method permits to prove that each forward trajectory of the NN has finite length, and as a consequence it converges toward a singleton. Furthermore, by means of a quantitative evaluation of the Lojasiewicz exponent at the equilibrium points, the following results on convergence rate of trajectories are established: (1) for nonconvex QP problems, each trajectory is either exponentially convergent, or convergent in finite time, toward a singleton belonging to the set of constrained critical points; (2) for convex QP problems, the same result as in (1) holds; moreover, the singleton belongs to the set of global minimizers; and (3) for LP problems, each trajectory converges in finite time to a singleton belonging to the set of global minimizers. These results, which improve previous results obtained via the Lyapunov approach, are true independently of the nature of the set of equilibrium points, and in particular they hold even when the NN possesses infinitely many nonisolated equilibrium points.

Photometric Follow-up Transit (Primary Eclipse) Observations of WASP-43 b and TrES-3b and A Study on Their Transit Timing Variations

NASA Astrophysics Data System (ADS)

Zhao, Sun; Jiang-hui, Ji; Yao, Dong

2018-01-01

Two photometric follow-up transit (primary eclipse) observations on WASP-43 b and four observations on TrES-3 b are performed using the Xuyi Near-Earth Object Survey Telescope. After differential photometry and light curve analysis, the physical parameters of the two systems are obtained and are in good match with the literature. Combining with transit data from a lot of literature, the residuals (O - C) of transit observations of both systems are fitted with the linear and quadratic functions. With the linear fitting, the periods and transit timing variations (TTVs) of the planets are obtained, and no obvious periodic TTV signal is found in both systems after an analysis. The maximum mass of a perturbing planet located at the 1:2 mean motion resonance (MMR) for WASP-43 b and TrES-3 b is estimated to be 1.826 and 1.504 Earth mass, respectively. By quadratic fitting, it is confirmed that WASP-43 b may have a long-term TTV which means an orbital decay. The decay rate is shown to be Ṗ = (-0.005248 ± 0.001714) s·yr-1, and compared with the previous results. Based on this, the lower limit of the stellar tidal quality parameter of WASP-43 is calculated to be Q‧* ≥ 1.5 × 105 , and the remaining lifetimes of the planets are presented for the different Q‧* values of the two systems, correspondingly.

Multi-Product Total Cost Functions for Higher Education: The Case of Chinese Research Universities

ERIC Educational Resources Information Center

Longlong, Hou; Fengliang, Li; Weifang, Min

2009-01-01

This paper empirically investigates the economies of scale and economies of scope for the Chinese research universities by employing the flexible fixed cost quadratic (FFCQ) function. The empirical results show that both economies of scale and economies of scope exist in the Chinese higher education system and support the common belief of…

An Improved Correction for Range Restricted Correlations Under Extreme, Monotonic Quadratic Nonlinearity and Heteroscedasticity.

PubMed

Culpepper, Steven Andrew

2016-06-01

Standardized tests are frequently used for selection decisions, and the validation of test scores remains an important area of research. This paper builds upon prior literature about the effect of nonlinearity and heteroscedasticity on the accuracy of standard formulas for correcting correlations in restricted samples. Existing formulas for direct range restriction require three assumptions: (1) the criterion variable is missing at random; (2) a linear relationship between independent and dependent variables; and (3) constant error variance or homoscedasticity. The results in this paper demonstrate that the standard approach for correcting restricted correlations is severely biased in cases of extreme monotone quadratic nonlinearity and heteroscedasticity. This paper offers at least three significant contributions to the existing literature. First, a method from the econometrics literature is adapted to provide more accurate estimates of unrestricted correlations. Second, derivations establish bounds on the degree of bias attributed to quadratic functions under the assumption of a monotonic relationship between test scores and criterion measurements. New results are presented on the bias associated with using the standard range restriction correction formula, and the results show that the standard correction formula yields estimates of unrestricted correlations that deviate by as much as 0.2 for high to moderate selectivity. Third, Monte Carlo simulation results demonstrate that the new procedure for correcting restricted correlations provides more accurate estimates in the presence of quadratic and heteroscedastic test score and criterion relationships.

Validation of drift and diffusion coefficients from experimental data

NASA Astrophysics Data System (ADS)

Riera, R.; Anteneodo, C.

2010-04-01

Many fluctuation phenomena, in physics and other fields, can be modeled by Fokker-Planck or stochastic differential equations whose coefficients, associated with drift and diffusion components, may be estimated directly from the observed time series. Its correct characterization is crucial to determine the system quantifiers. However, due to the finite sampling rates of real data, the empirical estimates may significantly differ from their true functional forms. In the literature, low-order corrections, or even no corrections, have been applied to the finite-time estimates. A frequent outcome consists of linear drift and quadratic diffusion coefficients. For this case, exact corrections have been recently found, from Itô-Taylor expansions. Nevertheless, model validation constitutes a necessary step before determining and applying the appropriate corrections. Here, we exploit the consequences of the exact theoretical results obtained for the linear-quadratic model. In particular, we discuss whether the observed finite-time estimates are actually a manifestation of that model. The relevance of this analysis is put into evidence by its application to two contrasting real data examples in which finite-time linear drift and quadratic diffusion coefficients are observed. In one case the linear-quadratic model is readily rejected while in the other, although the model constitutes a very good approximation, low-order corrections are inappropriate. These examples give warning signs about the proper interpretation of finite-time analysis even in more general diffusion processes.

A wavelet-based adaptive fusion algorithm of infrared polarization imaging

NASA Astrophysics Data System (ADS)

Yang, Wei; Gu, Guohua; Chen, Qian; Zeng, Haifang

2011-08-01

The purpose of infrared polarization image is to highlight man-made target from a complex natural background. For the infrared polarization images can significantly distinguish target from background with different features, this paper presents a wavelet-based infrared polarization image fusion algorithm. The method is mainly for image processing of high-frequency signal portion, as for the low frequency signal, the original weighted average method has been applied. High-frequency part is processed as follows: first, the source image of the high frequency information has been extracted by way of wavelet transform, then signal strength of 3*3 window area has been calculated, making the regional signal intensity ration of source image as a matching measurement. Extraction method and decision mode of the details are determined by the decision making module. Image fusion effect is closely related to the setting threshold of decision making module. Compared to the commonly used experiment way, quadratic interpolation optimization algorithm is proposed in this paper to obtain threshold. Set the endpoints and midpoint of the threshold searching interval as initial interpolation nodes, and compute the minimum quadratic interpolation function. The best threshold can be obtained by comparing the minimum quadratic interpolation function. A series of image quality evaluation results show this method has got improvement in fusion effect; moreover, it is not only effective for some individual image, but also for a large number of images.

Alterations in plant community niche hypervolume and functional group representation to accommodate extreme drought

NASA Astrophysics Data System (ADS)

Mao, W.; Sun, Z.; Felton, A. J.; Zhao, X.; Zhang, T.; Li, Y.; Smith, M. D.

2017-12-01

We used the method of `niche hypervolume' to study how plant communities accommodate extreme environmental changes. Due to the gradual decreases in precipitation, the desert-steppe ecotone in western of Inner Mongolia, an already arid region, has large shifts in species composition within short geographical ranges. Based on precipitation and species composition, we divided this study area into four categories: desert area (D), partial desert area (pD), partial steppe area (pS) and steppe area(S). We sampled along a climatic gradient of precipitation. We selected four transects, in each transect 100-125 quadrats were randomly selected, with 425 quadrats sampled in total. We assessed species composition of each sampling quadrat, and collected leaves of every species that appeared in every quadrat. We also studied the change of plant community weighted means of leaf traits (CWM) along the precipitation gradient. Leaf traits (phenotypic traits, i.e. SLA, LDMC and stoichiometry traits, i.e. LNC, LCC) were used to calculate the changes in `niche hypervolume'. Our results show that: 1) with decreases in precipitation, species richness and functional group types (PFTs) change. Species richness and functional groups were the highest in the pD area, while the species richness and functional groups in the desert area were the lowest. 2), CWM-SLA in the desert area was relatively small, while CWM-SLA in pD area, the pS area, and the steppe area are more similar. CWM-LNC decreases as precipitation decreases, consistent with CWM-LCC trends. While CWM-LDMC of the desert area was the highest, and CWM-LDMC in desert area was the lowest. The dynamics of CWM traits suggests that species in the desert region have slower growth rates, while species in the transitional zone and steppe area have relatively higher growth rates. Finally, the pD area had the highest niche hypervolume, while the steppe area had the lowest hypervolume, which may be closely related to the high level of PFTs. These results suggest that even in drought-prone ecosystems, plants yield multiple life strategies to adapt to stressful environments. While under extreme drought conditions, environmental filters will remove species with unsuitable traits, like perennial species in this study, leaving shrubs and other drought tolerant species to survive.

Seven Wonders of the Ancient and Modern Quadratic World.

ERIC Educational Resources Information Center

Taylor, Sharon E.; Mittag, Kathleen Cage

2001-01-01

Presents four methods for solving a quadratic equation using graphing calculator technology: (1) graphing with the CALC feature; (2) quadratic formula program; (3) table; and (4) solver. Includes a worksheet for a lab activity on factoring quadratic equations. (KHR)

Some simple solutions of Schrödinger's equation for a free particle or for an oscillator

NASA Astrophysics Data System (ADS)

Andrews, Mark

2018-05-01

For a non-relativistic free particle, we show that the evolution of some simple initial wave functions made up of linear segments can be expressed in terms of Fresnel integrals. Examples include the square wave function and the triangular wave function. The method is then extended to wave functions made from quadratic elements. The evolution of all these initial wave functions can also be found for the harmonic oscillator by a transformation of the free evolutions.

Impedance Eduction in Sound Fields With Peripherally Varying Liners and Flow

NASA Technical Reports Server (NTRS)

Watson, W. R.; Jones, M. G.

2015-01-01

A two-dimensional impedance eduction theory is extended to three-dimensional sound fields and peripherally varying duct liners. The approach is to first measure the acoustic pressure field at a series of flush-mounted wall microphones located around the periphery of the flow duct. The numerical solution for the acoustic pressure field at these microphones is also obtained by solving the three-dimensional convected Helmholtz equation using the finite element method. A quadratic objective function based on the difference between the measured and finite element solution is constructed and the unknown impedance function is obtained by minimizing this objective function. Impedance spectra educed for two uniform-structure liners (a wire-mesh and a conventional liner) and a hard-soft-hard peripherally varying liner (for which the soft segment is that of the conventional liner) are presented. Results are presented at three mean flow Mach numbers and fourteen sound source frequencies. The impedance spectra of the uniform-structure liners are also computed using a two-dimensional impedance eduction theory. The primary conclusions of the study are: 1) when measured data is used with the uniform-structure liners, the three-dimensional theory reproduces the same impedance spectra as the two-dimensional theory except for frequencies corresponding to very low or very high liner attenuation; and 2) good agreement between the educed impedance spectra of the uniform structure conventional liner and the soft segment of the peripherally varying liner is obtained.

THE EFFECTIVENESS OF QUADRATS FOR MEASURING VASCULAR PLANT DIVERSITY

EPA Science Inventory

Quadrats are widely used for measuring characteristics of vascular plant communities. It is well recognized that quadrat size affects measurements of frequency and cover. The ability of quadrats of varying sizes to adequately measure diversity has not been established. An exha...

Analysis of the Electrohydrodynamic Flow in a Symmetric System of Electrodes by the Method of Dynamic Current-Voltage Characteristics

NASA Astrophysics Data System (ADS)

Stishkov, Yu. K.; Zakir'yanova, R. E.

2018-04-01

We have solved the problem of injection-type through electrohydrodynamic (EHD) flow in a closed channel. We have considered a model of a liquid with four types of ions. It is shown that a through EHD flow without internal vortices in the electrode gap is formed for the ratio 2 : 1 of the initial injection current from the electrodes in the channel. The structure of the flow in different parts of the channel and the integral characteristics of the flow have been analyzed. It is shown that for a quadratic function of injection at the electrodes, the current-voltage characteristic of the flow is also quadratic.

A sequential quadratic programming algorithm using an incomplete solution of the subproblem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Murray, W.; Prieto, F.J.

1993-05-01

We analyze sequential quadratic programming (SQP) methods to solve nonlinear constrained optimization problems that are more flexible in their definition than standard SQP methods. The type of flexibility introduced is motivated by the necessity to deviate from the standard approach when solving large problems. Specifically we no longer require a minimizer of the QP subproblem to be determined or particular Lagrange multiplier estimates to be used. Our main focus is on an SQP algorithm that uses a particular augmented Lagrangian merit function. New results are derived for this algorithm under weaker conditions than previously assumed; in particular, it is notmore » assumed that the iterates lie on a compact set.« less

An Algebraic Construction of the First Integrals of the Stationary KdV Hierarchy

NASA Astrophysics Data System (ADS)

Matsushima, Masatomo; Ohmiya, Mayumi

2009-09-01

The stationary KdV hierarchy is constructed using a kind of recursion operator called Λ-operator. The notion of the maximal solution of the n-th stationary KdV equation is introduced. Using this maximal solution, a specific differential polynomial with the auxiliary spectral parameter called the spectral M-function is constructed as the quadratic form of the fundamental system of the eigenvalue problem for the 2-nd order linear ordinary differential equation which is related to the linearizing operator of the hierarchy. By calculating a perfect square condition of the quadratic form by an elementary algebraic method, the complete set of first integrals of this hierarchy is constructed.

Linear quadratic tracking problems in Hilbert space - Application to optimal active noise suppression

NASA Technical Reports Server (NTRS)

Banks, H. T.; Silcox, R. J.; Keeling, S. L.; Wang, C.

1989-01-01

A unified treatment of the linear quadratic tracking (LQT) problem, in which a control system's dynamics are modeled by a linear evolution equation with a nonhomogeneous component that is linearly dependent on the control function u, is presented; the treatment proceeds from the theoretical formulation to a numerical approximation framework. Attention is given to two categories of LQT problems in an infinite time interval: the finite energy and the finite average energy. The behavior of the optimal solution for finite time-interval problems as the length of the interval tends to infinity is discussed. Also presented are the formulations and properties of LQT problems in a finite time interval.

Optical neural network system for pose determination of spinning satellites

NASA Technical Reports Server (NTRS)

Lee, Andrew; Casasent, David

1990-01-01

An optical neural network architecture and algorithm based on a Hopfield optimization network are presented for multitarget tracking. This tracker utilizes a neuron for every possible target track, and a quadratic energy function of neural activities which is minimized using gradient descent neural evolution. The neural net tracker is demonstrated as part of a system for determining position and orientation (pose) of spinning satellites with respect to a robotic spacecraft. The input to the system is time sequence video from a single camera. Novelty detection and filtering are utilized to locate and segment novel regions from the input images. The neural net multitarget tracker determines the correspondences (or tracks) of the novel regions as a function of time, and hence the paths of object (satellite) parts. The path traced out by a given part or region is approximately elliptical in image space, and the position, shape and orientation of the ellipse are functions of the satellite geometry and its pose. Having a geometric model of the satellite, and the elliptical path of a part in image space, the three-dimensional pose of the satellite is determined. Digital simulation results using this algorithm are presented for various satellite poses and lighting conditions.

Transfer as a function of exploration and stabilization in original practice.

PubMed

Pacheco, Matheus M; Newell, Karl M

2015-12-01

The identification of practice conditions that provide flexibility to perform successfully in transfer is a long-standing issue in motor learning but is still not well understood. Here we investigated the hypothesis that a search strategy that encompasses both exploration and stabilization of the perceptual-motor workspace will enhance performance in transfer. Twenty-two participants practiced a virtual projection task (120 trials on each of 3 days) and subsequently performed two transfer conditions (20 trials/condition) with different constraints in the angle to project the object. The findings revealed a quadratic relation between exploration in practice (indexed by autocorrelation and distribution of error) and subsequent performance error in transfer. The integration of exploration and stabilization of the perceptual-motor workspace enhances transfer to tasks with different constraints on the scaling of motor output. Copyright © 2015 Elsevier B.V. All rights reserved.

Numerical study of steady dissipative mixed convection optically-thick micropolar flow with thermal radiation effects

NASA Astrophysics Data System (ADS)

Gupta, Diksha; Kumar, Lokendra; Bég, O. Anwar; Singh, Bani

2017-10-01

The objective of this paper is to study theoretically and numerically the effect of thermal radiation on mixed convection boundary layer flow of a dissipative micropolar non-Newtonian fluid from a continuously moving vertical porous sheet. The governing partial differential equations are transformed into a set of non-linear differential equations by using similarity transformations. These equations are solved iteratively with the Bellman-Kalaba quasi-linearization algorithm. This method converges quadratically and the solution is valid for a large range of parameters. The effects of transpiration (suction or injection) parameter, buoyancy parameter, radiation parameter and Eckert number on velocity, microrotation and temperature functions have been studied. Under a special case comparison of the present numerical results is made with the results available in the literature and an excellent agreement is found. Additionally skin friction and rate of heat transfer have also been computed. The study has applications in polymer processing.

Optimized Quasi-Interpolators for Image Reconstruction.

PubMed

Sacht, Leonardo; Nehab, Diego

2015-12-01

We propose new quasi-interpolators for the continuous reconstruction of sampled images, combining a narrowly supported piecewise-polynomial kernel and an efficient digital filter. In other words, our quasi-interpolators fit within the generalized sampling framework and are straightforward to use. We go against standard practice and optimize for approximation quality over the entire Nyquist range, rather than focusing exclusively on the asymptotic behavior as the sample spacing goes to zero. In contrast to previous work, we jointly optimize with respect to all degrees of freedom available in both the kernel and the digital filter. We consider linear, quadratic, and cubic schemes, offering different tradeoffs between quality and computational cost. Experiments with compounded rotations and translations over a range of input images confirm that, due to the additional degrees of freedom and the more realistic objective function, our new quasi-interpolators perform better than the state of the art, at a similar computational cost.

The period function of the generalized Lotka-Volterra centers

NASA Astrophysics Data System (ADS)

Villadelprat, J.

2008-05-01

The present paper deals with the period function of the quadratic centers. In the literature different terminologies are used to classify these centers, but essentially there are four families: Hamiltonian, reversible , codimension four Q4 and generalized Lotka-Volterra systems . Chicone [C. Chicone, Review in MathSciNet, Ref. 94h:58072] conjectured that the reversible centers have at most two critical periods, and that the centers of the three other families have a monotonic period function. With regard to the second part of this conjecture, only the monotonicity of the Hamiltonian and Q4 families [W.A. Coppel, L. Gavrilov, The period function of a Hamiltonian quadratic system, Differential Integral Equations 6 (1993) 1357-1365; Y. Zhao, The monotonicity of period function for codimension four quadratic system Q4, J. Differential Equations 185 (2002) 370-387] has been proved. Concerning the family, no substantial progress has been made since the middle 80s, when several authors showed independently the monotonicity of the classical Lotka-Volterra centers [F. Rothe, The periods of the Volterra-Lokta system, J. Reine Angew. Math. 355 (1985) 129-138; R. Schaaf, Global behaviour of solution branches for some Neumann problems depending on one or several parameters, J. Reine Angew. Math. 346 (1984) 1-31; J. Waldvogel, The period in the Lotka-Volterra system is monotonic, J. Math. Anal. Appl. 114 (1986) 178-184]. By means of the first period constant one can easily conclude that the period function of the centers in the family is monotone increasing near the inner boundary of its period annulus (i.e., the center itself). Thus, according to Chicone's conjecture, it should be also monotone increasing near the outer boundary, which in the Poincaré disc is a polycycle. In this paper we show that this is true. In addition we prove that, except for a zero measure subset of the parameter plane, there is no bifurcation of critical periods from the outer boundary. Finally we show that the period function is globally (i.e., in the whole period annulus) monotone increasing in two other cases different from the classical one.

Backward Transfer: An Investigation of the Influence of Quadratic Functions Instruction on Students' Prior Ways of Reasoning about Linear Functions

ERIC Educational Resources Information Center

Hohensee, Charles

2014-01-01

The transfer of learning has been the subject of much scientific inquiry in the social sciences. However, mathematics education research has given little attention to a subclass called backward transfer, which is when learning about new concepts influences learners' ways of reasoning about previously encountered concepts. This study examined when…

MPC Design for Rapid Pump-Attenuation and Expedited Hyperglycemia Response to Treat T1DM with an Artificial Pancreas

PubMed Central

Gondhalekar, Ravi; Dassau, Eyal; Doyle, Francis J.

2016-01-01

The design of a Model Predictive Control (MPC) strategy for the closed-loop operation of an Artificial Pancreas (AP) for treating Type 1 Diabetes Mellitus (T1DM) is considered in this paper. The contribution of this paper is to propose two changes to the usual structure of the MPC problems typically considered for control of an AP. The first proposed change is to replace the symmetric, quadratic input cost function with an asymmetric, quadratic function, allowing negative control inputs to be penalized less than positive ones. This facilitates rapid pump-suspensions in response to predicted hypoglycemia, while simultaneously permitting the design of a conservative response to hyperglycemia. The second proposed change is to penalize the velocity of the predicted glucose level, where this velocity penalty is based on a cost function that is again asymmetric, but additionally state-dependent. This facilitates the accelerated response to acute, persistent hyperglycemic events, e.g., as induced by unannounced meals. The novel functionality is demonstrated by numerical examples, and the efficacy of the proposed MPC strategy verified using the University of Padova/Virginia metabolic simulator. PMID:28479660

A Novel Finite-Sum Inequality-Based Method for Robust H∞ Control of Uncertain Discrete-Time Takagi-Sugeno Fuzzy Systems With Interval-Like Time-Varying Delays.

PubMed

Zhang, Xian-Ming; Han, Qing-Long; Ge, Xiaohua

2017-09-22

This paper is concerned with the problem of robust H∞ control of an uncertain discrete-time Takagi-Sugeno fuzzy system with an interval-like time-varying delay. A novel finite-sum inequality-based method is proposed to provide a tighter estimation on the forward difference of certain Lyapunov functional, leading to a less conservative result. First, an auxiliary vector function is used to establish two finite-sum inequalities, which can produce tighter bounds for the finite-sum terms appearing in the forward difference of the Lyapunov functional. Second, a matrix-based quadratic convex approach is employed to equivalently convert the original matrix inequality including a quadratic polynomial on the time-varying delay into two boundary matrix inequalities, which delivers a less conservative bounded real lemma (BRL) for the resultant closed-loop system. Third, based on the BRL, a novel sufficient condition on the existence of suitable robust H∞ fuzzy controllers is derived. Finally, two numerical examples and a computer-simulated truck-trailer system are provided to show the effectiveness of the obtained results.

Effect of Evolutionary Anisotropy on Earing Prediction in Cylindrical Cup Drawing

NASA Astrophysics Data System (ADS)

Choi, H. J.; Lee, K. J.; Choi, Y.; Bae, G.; Ahn, D.-C.; Lee, M.-G.

2017-05-01

The formability of sheet metals is associated with their planar anisotropy, and finite element simulations have been applied to the sheet metal-forming process by describing the anisotropic behaviors using yield functions and hardening models. In this study, the evaluation of anisotropic constitutive models was performed based on the non-uniform height profile or earing in circular cylindrical cup drawing. Two yield functions, a quadratic Hill1948 and a non-quadratic Yld2000-2d model, were used under non-associated and associated flow rules, respectively, to simultaneously capture directional differences in yield stress and r value. The effect of the evolution of anisotropy on the earing prediction was also investigated by employing simplified equivalent plastic strain rate-dependent anisotropic coefficients. The computational results were in good agreement with experiments when the proper choice of the yield function and flow rule, which predicts the planar anisotropy, was made. Moreover, the accuracy of the earing profile could be significantly enhanced if the evolution of anisotropy between uniaxial and biaxial stress states was additionally considered.

Linear quadratic stochastic control of atomic hydrogen masers.

PubMed

Koppang, P; Leland, R

1999-01-01

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

Linear-Quadratic-Gaussian Regulator Developed for a Magnetic Bearing

NASA Technical Reports Server (NTRS)

Choi, Benjamin B.

2002-01-01

Linear-Quadratic-Gaussian (LQG) control is a modern state-space technique for designing optimal dynamic regulators. It enables us to trade off regulation performance and control effort, and to take into account process and measurement noise. The Structural Mechanics and Dynamics Branch at the NASA Glenn Research Center has developed an LQG control for a fault-tolerant magnetic bearing suspension rig to optimize system performance and to reduce the sensor and processing noise. The LQG regulator consists of an optimal state-feedback gain and a Kalman state estimator. The first design step is to seek a state-feedback law that minimizes the cost function of regulation performance, which is measured by a quadratic performance criterion with user-specified weighting matrices, and to define the tradeoff between regulation performance and control effort. The next design step is to derive a state estimator using a Kalman filter because the optimal state feedback cannot be implemented without full state measurement. Since the Kalman filter is an optimal estimator when dealing with Gaussian white noise, it minimizes the asymptotic covariance of the estimation error.

Joint Optimization of Fluence Field Modulation and Regularization in Task-Driven Computed Tomography

PubMed Central

Gang, G. J.; Siewerdsen, J. H.; Stayman, J. W.

2017-01-01

Purpose This work presents a task-driven joint optimization of fluence field modulation (FFM) and regularization in quadratic penalized-likelihood (PL) reconstruction. Conventional FFM strategies proposed for filtered-backprojection (FBP) are evaluated in the context of PL reconstruction for comparison. Methods We present a task-driven framework that leverages prior knowledge of the patient anatomy and imaging task to identify FFM and regularization. We adopted a maxi-min objective that ensures a minimum level of detectability index (d′) across sample locations in the image volume. The FFM designs were parameterized by 2D Gaussian basis functions to reduce dimensionality of the optimization and basis function coefficients were estimated using the covariance matrix adaptation evolutionary strategy (CMA-ES) algorithm. The FFM was jointly optimized with both space-invariant and spatially-varying regularization strength (β) - the former via an exhaustive search through discrete values and the latter using an alternating optimization where β was exhaustively optimized locally and interpolated to form a spatially-varying map. Results The optimal FFM inverts as β increases, demonstrating the importance of a joint optimization. For the task and object investigated, the optimal FFM assigns more fluence through less attenuating views, counter to conventional FFM schemes proposed for FBP. The maxi-min objective homogenizes detectability throughout the image and achieves a higher minimum detectability than conventional FFM strategies. Conclusions The task-driven FFM designs found in this work are counter to conventional patterns for FBP and yield better performance in terms of the maxi-min objective, suggesting opportunities for improved image quality and/or dose reduction when model-based reconstructions are applied in conjunction with FFM. PMID:28626290

Joint optimization of fluence field modulation and regularization in task-driven computed tomography

NASA Astrophysics Data System (ADS)

Gang, G. J.; Siewerdsen, J. H.; Stayman, J. W.

2017-03-01

Purpose: This work presents a task-driven joint optimization of fluence field modulation (FFM) and regularization in quadratic penalized-likelihood (PL) reconstruction. Conventional FFM strategies proposed for filtered-backprojection (FBP) are evaluated in the context of PL reconstruction for comparison. Methods: We present a task-driven framework that leverages prior knowledge of the patient anatomy and imaging task to identify FFM and regularization. We adopted a maxi-min objective that ensures a minimum level of detectability index (d') across sample locations in the image volume. The FFM designs were parameterized by 2D Gaussian basis functions to reduce dimensionality of the optimization and basis function coefficients were estimated using the covariance matrix adaptation evolutionary strategy (CMA-ES) algorithm. The FFM was jointly optimized with both space-invariant and spatially-varying regularization strength (β) - the former via an exhaustive search through discrete values and the latter using an alternating optimization where β was exhaustively optimized locally and interpolated to form a spatially-varying map. Results: The optimal FFM inverts as β increases, demonstrating the importance of a joint optimization. For the task and object investigated, the optimal FFM assigns more fluence through less attenuating views, counter to conventional FFM schemes proposed for FBP. The maxi-min objective homogenizes detectability throughout the image and achieves a higher minimum detectability than conventional FFM strategies. Conclusions: The task-driven FFM designs found in this work are counter to conventional patterns for FBP and yield better performance in terms of the maxi-min objective, suggesting opportunities for improved image quality and/or dose reduction when model-based reconstructions are applied in conjunction with FFM.

An EOQ model of time quadratic and inventory dependent demand for deteriorated items with partially backlogged shortages under trade credit

NASA Astrophysics Data System (ADS)

Singh, Pushpinder; Mishra, Nitin Kumar; Singh, Vikramjeet; Saxena, Seema

2017-07-01

In this paper a single buyer, single supplier inventory model with time quadratic and stock dependent demand for a finite planning horizon has been studied. Single deteriorating item which suffers shortage, with partial backlogging and some lost sales is considered. Model is divided into two scenarios, one with non permissible delay in payment and other with permissible delay in payment. Latter is called, centralized system, where supplier offers trade credit to retailer. In the centralized system cost saving is shared amongst the two. The objective is to study the difference in minimum costs borne by retailer and supplier, under two scenarios including the above mentioned parameters. To obtain optimal solution of the problem the model is solved analytically. Numerical example and a comparative study are then discussed supported by sensitivity analysis of each parameter.

B-spline goal-oriented error estimators for geometrically nonlinear rods

DTIC Science & Technology

2011-04-01

respectively, for the output functionals q2–q4 (linear and nonlinear with the trigonometric functions sine and cosine) in all the tests considered...of the errors resulting from the linear, quadratic and nonlinear (with trigonometric functions sine and cosine) outputs and for p = 1, 2. If the... Portugal . References [1] A.T. Adams. Sobolev Spaces. Academic Press, Boston, 1975. [2] M. Ainsworth and J.T. Oden. A posteriori error estimation in

Locally optimal control under unknown dynamics with learnt cost function: application to industrial robot positioning

NASA Astrophysics Data System (ADS)

Guérin, Joris; Gibaru, Olivier; Thiery, Stéphane; Nyiri, Eric

2017-01-01

Recent methods of Reinforcement Learning have enabled to solve difficult, high dimensional, robotic tasks under unknown dynamics using iterative Linear Quadratic Gaussian control theory. These algorithms are based on building a local time-varying linear model of the dynamics from data gathered through interaction with the environment. In such tasks, the cost function is often expressed directly in terms of the state and control variables so that it can be locally quadratized to run the algorithm. If the cost is expressed in terms of other variables, a model is required to compute the cost function from the variables manipulated. We propose a method to learn the cost function directly from the data, in the same way as for the dynamics. This way, the cost function can be defined in terms of any measurable quantity and thus can be chosen more appropriately for the task to be carried out. With our method, any sensor information can be used to design the cost function. We demonstrate the efficiency of this method through simulating, with the V-REP software, the learning of a Cartesian positioning task on several industrial robots with different characteristics. The robots are controlled in joint space and no model is provided a priori. Our results are compared with another model free technique, consisting in writing the cost function as a state variable.

Mathematics in the Real World.

ERIC Educational Resources Information Center

Borenstein, Matt

1997-01-01

The abstract nature of algebra causes difficulties for many students. Describes "Real-World Data," an algebra course designed for students with low grades in algebra and provides multidisciplinary experiments (linear functions and variations; quadratic, square-root, and inverse relations; and exponential and periodic variation)…

QAPgrid: A Two Level QAP-Based Approach for Large-Scale Data Analysis and Visualization

PubMed Central

Inostroza-Ponta, Mario; Berretta, Regina; Moscato, Pablo

2011-01-01

Background The visualization of large volumes of data is a computationally challenging task that often promises rewarding new insights. There is great potential in the application of new algorithms and models from combinatorial optimisation. Datasets often contain “hidden regularities” and a combined identification and visualization method should reveal these structures and present them in a way that helps analysis. While several methodologies exist, including those that use non-linear optimization algorithms, severe limitations exist even when working with only a few hundred objects. Methodology/Principal Findings We present a new data visualization approach (QAPgrid) that reveals patterns of similarities and differences in large datasets of objects for which a similarity measure can be computed. Objects are assigned to positions on an underlying square grid in a two-dimensional space. We use the Quadratic Assignment Problem (QAP) as a mathematical model to provide an objective function for assignment of objects to positions on the grid. We employ a Memetic Algorithm (a powerful metaheuristic) to tackle the large instances of this NP-hard combinatorial optimization problem, and we show its performance on the visualization of real data sets. Conclusions/Significance Overall, the results show that QAPgrid algorithm is able to produce a layout that represents the relationships between objects in the data set. Furthermore, it also represents the relationships between clusters that are feed into the algorithm. We apply the QAPgrid on the 84 Indo-European languages instance, producing a near-optimal layout. Next, we produce a layout of 470 world universities with an observed high degree of correlation with the score used by the Academic Ranking of World Universities compiled in the The Shanghai Jiao Tong University Academic Ranking of World Universities without the need of an ad hoc weighting of attributes. Finally, our Gene Ontology-based study on Saccharomyces cerevisiae fully demonstrates the scalability and precision of our method as a novel alternative tool for functional genomics. PMID:21267077

QAPgrid: a two level QAP-based approach for large-scale data analysis and visualization.

PubMed

Inostroza-Ponta, Mario; Berretta, Regina; Moscato, Pablo

2011-01-18

The visualization of large volumes of data is a computationally challenging task that often promises rewarding new insights. There is great potential in the application of new algorithms and models from combinatorial optimisation. Datasets often contain "hidden regularities" and a combined identification and visualization method should reveal these structures and present them in a way that helps analysis. While several methodologies exist, including those that use non-linear optimization algorithms, severe limitations exist even when working with only a few hundred objects. We present a new data visualization approach (QAPgrid) that reveals patterns of similarities and differences in large datasets of objects for which a similarity measure can be computed. Objects are assigned to positions on an underlying square grid in a two-dimensional space. We use the Quadratic Assignment Problem (QAP) as a mathematical model to provide an objective function for assignment of objects to positions on the grid. We employ a Memetic Algorithm (a powerful metaheuristic) to tackle the large instances of this NP-hard combinatorial optimization problem, and we show its performance on the visualization of real data sets. Overall, the results show that QAPgrid algorithm is able to produce a layout that represents the relationships between objects in the data set. Furthermore, it also represents the relationships between clusters that are feed into the algorithm. We apply the QAPgrid on the 84 Indo-European languages instance, producing a near-optimal layout. Next, we produce a layout of 470 world universities with an observed high degree of correlation with the score used by the Academic Ranking of World Universities compiled in the The Shanghai Jiao Tong University Academic Ranking of World Universities without the need of an ad hoc weighting of attributes. Finally, our Gene Ontology-based study on Saccharomyces cerevisiae fully demonstrates the scalability and precision of our method as a novel alternative tool for functional genomics.

The Fisher-Markov selector: fast selecting maximally separable feature subset for multiclass classification with applications to high-dimensional data.

PubMed

Cheng, Qiang; Zhou, Hongbo; Cheng, Jie

2011-06-01

Selecting features for multiclass classification is a critically important task for pattern recognition and machine learning applications. Especially challenging is selecting an optimal subset of features from high-dimensional data, which typically have many more variables than observations and contain significant noise, missing components, or outliers. Existing methods either cannot handle high-dimensional data efficiently or scalably, or can only obtain local optimum instead of global optimum. Toward the selection of the globally optimal subset of features efficiently, we introduce a new selector--which we call the Fisher-Markov selector--to identify those features that are the most useful in describing essential differences among the possible groups. In particular, in this paper we present a way to represent essential discriminating characteristics together with the sparsity as an optimization objective. With properly identified measures for the sparseness and discriminativeness in possibly high-dimensional settings, we take a systematic approach for optimizing the measures to choose the best feature subset. We use Markov random field optimization techniques to solve the formulated objective functions for simultaneous feature selection. Our results are noncombinatorial, and they can achieve the exact global optimum of the objective function for some special kernels. The method is fast; in particular, it can be linear in the number of features and quadratic in the number of observations. We apply our procedure to a variety of real-world data, including mid--dimensional optical handwritten digit data set and high-dimensional microarray gene expression data sets. The effectiveness of our method is confirmed by experimental results. In pattern recognition and from a model selection viewpoint, our procedure says that it is possible to select the most discriminating subset of variables by solving a very simple unconstrained objective function which in fact can be obtained with an explicit expression.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gang, G; Siewerdsen, J; Stayman, J

Purpose: There has been increasing interest in integrating fluence field modulation (FFM) devices with diagnostic CT scanners for dose reduction purposes. Conventional FFM strategies, however, are often either based on heuristics or the analysis of filtered-backprojection (FBP) performance. This work investigates a prospective task-driven optimization of FFM for model-based iterative reconstruction (MBIR) in order to improve imaging performance at the same total dose as conventional strategies. Methods: The task-driven optimization framework utilizes an ultra-low dose 3D scout as a patient-specific anatomical model and a mathematical formation of the imaging task. The MBIR method investigated is quadratically penalized-likelihood reconstruction. The FFMmore » objective function uses detectability index, d’, computed as a function of the predicted spatial resolution and noise in the image. To optimize performance throughout the object, a maxi-min objective was adopted where the minimum d’ over multiple locations is maximized. To reduce the dimensionality of the problem, FFM is parameterized as a linear combination of 2D Gaussian basis functions over horizontal detector pixels and projection angles. The coefficients of these bases are found using the covariance matrix adaptation evolution strategy (CMA-ES) algorithm. The task-driven design was compared with three other strategies proposed for FBP reconstruction for a calcification cluster discrimination task in an abdomen phantom. Results: The task-driven optimization yielded FFM that was significantly different from those designed for FBP. Comparing all four strategies, the task-based design achieved the highest minimum d’ with an 8–48% improvement, consistent with the maxi-min objective. In addition, d’ was improved to a greater extent over a larger area within the entire phantom. Conclusion: Results from this investigation suggests the need to re-evaluate conventional FFM strategies for MBIR. The task-based optimization framework provides a promising approach that maximizes imaging performance under the same total dose constraint.« less

Estimating population size with correlated sampling unit estimates

Treesearch

David C. Bowden; Gary C. White; Alan B. Franklin; Joseph L. Ganey

2003-01-01

Finite population sampling theory is useful in estimating total population size (abundance) from abundance estimates of each sampled unit (quadrat). We develop estimators that allow correlated quadrat abundance estimates, even for quadrats in different sampling strata. Correlated quadrat abundance estimates based on mark–recapture or distance sampling methods occur...

Quadratic soliton self-reflection at a quadratically nonlinear interface

NASA Astrophysics Data System (ADS)

Jankovic, Ladislav; Kim, Hongki; Stegeman, George; Carrasco, Silvia; Torner, Lluis; Katz, Mordechai

2003-11-01

The reflection of bulk quadratic solutions incident onto a quadratically nonlinear interface in periodically poled potassium titanyl phosphate was observed. The interface consisted of the boundary between two quasi-phase-matched regions displaced from each other by a half-period. At high intensities and small angles of incidence the soliton is reflected.

Self-Replicating Quadratics

ERIC Educational Resources Information Center

Withers, Christopher S.; Nadarajah, Saralees

2012-01-01

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

Measurement of pediatric regional cerebral blood flow from 6 months to 15 years of age in a clinical population.

PubMed

Carsin-Vu, Aline; Corouge, Isabelle; Commowick, Olivier; Bouzillé, Guillaume; Barillot, Christian; Ferré, Jean-Christophe; Proisy, Maia

2018-04-01

To investigate changes in cerebral blood flow (CBF) in gray matter (GM) between 6 months and 15 years of age and to provide CBF values for the brain, GM, white matter (WM), hemispheres and lobes. Between 2013 and 2016, we retrospectively included all clinical MRI examinations with arterial spin labeling (ASL). We excluded subjects with a condition potentially affecting brain perfusion. For each subject, mean values of CBF in the brain, GM, WM, hemispheres and lobes were calculated. GM CBF was fitted using linear, quadratic and cubic polynomial regression against age. Regression models were compared with Akaike's information criterion (AIC), and Likelihood Ratio tests. 84 children were included (44 females/40 males). Mean CBF values were 64.2 ± 13.8 mL/100 g/min in GM, and 29.3 ± 10.0 mL/100 g/min in WM. The best-fit model of brain perfusion was the cubic polynomial function (AIC = 672.7, versus respectively AIC = 673.9 and AIC = 674.1 with the linear negative function and the quadratic polynomial function). A statistically significant difference between the tested models demonstrating the superiority of the quadratic (p = 0.18) or cubic polynomial model (p = 0.06), over the negative linear regression model was not found. No effect of general anesthesia (p = 0.34) or of gender (p = 0.16) was found. we provided values for ASL CBF in the brain, GM, WM, hemispheres, and lobes over a wide pediatric age range, approximately showing inverted U-shaped changes in GM perfusion over the course of childhood. Copyright © 2018 Elsevier B.V. All rights reserved.

Equivalent uniform dose concept evaluated by theoretical dose volume histograms for thoracic irradiation.

PubMed

Dumas, J L; Lorchel, F; Perrot, Y; Aletti, P; Noel, A; Wolf, D; Courvoisier, P; Bosset, J F

2007-03-01

The goal of our study was to quantify the limits of the EUD models for use in score functions in inverse planning software, and for clinical application. We focused on oesophagus cancer irradiation. Our evaluation was based on theoretical dose volume histograms (DVH), and we analyzed them using volumetric and linear quadratic EUD models, average and maximum dose concepts, the linear quadratic model and the differential area between each DVH. We evaluated our models using theoretical and more complex DVHs for the above regions of interest. We studied three types of DVH for the target volume: the first followed the ICRU dose homogeneity recommendations; the second was built out of the first requirements and the same average dose was built in for all cases; the third was truncated by a small dose hole. We also built theoretical DVHs for the organs at risk, in order to evaluate the limits of, and the ways to use both EUD(1) and EUD/LQ models, comparing them to the traditional ways of scoring a treatment plan. For each volume of interest we built theoretical treatment plans with differences in the fractionation. We concluded that both volumetric and linear quadratic EUDs should be used. Volumetric EUD(1) takes into account neither hot-cold spot compensation nor the differences in fractionation, but it is more sensitive to the increase of the irradiated volume. With linear quadratic EUD/LQ, a volumetric analysis of fractionation variation effort can be performed.

Task-Driven Optimization of Fluence Field and Regularization for Model-Based Iterative Reconstruction in Computed Tomography.

PubMed

Gang, Grace J; Siewerdsen, Jeffrey H; Stayman, J Webster

2017-12-01

This paper presents a joint optimization of dynamic fluence field modulation (FFM) and regularization in quadratic penalized-likelihood reconstruction that maximizes a task-based imaging performance metric. We adopted a task-driven imaging framework for prospective designs of the imaging parameters. A maxi-min objective function was adopted to maximize the minimum detectability index ( ) throughout the image. The optimization algorithm alternates between FFM (represented by low-dimensional basis functions) and local regularization (including the regularization strength and directional penalty weights). The task-driven approach was compared with three FFM strategies commonly proposed for FBP reconstruction (as well as a task-driven TCM strategy) for a discrimination task in an abdomen phantom. The task-driven FFM assigned more fluence to less attenuating anteroposterior views and yielded approximately constant fluence behind the object. The optimal regularization was almost uniform throughout image. Furthermore, the task-driven FFM strategy redistribute fluence across detector elements in order to prescribe more fluence to the more attenuating central region of the phantom. Compared with all strategies, the task-driven FFM strategy not only improved minimum by at least 17.8%, but yielded higher over a large area inside the object. The optimal FFM was highly dependent on the amount of regularization, indicating the importance of a joint optimization. Sample reconstructions of simulated data generally support the performance estimates based on computed . The improvements in detectability show the potential of the task-driven imaging framework to improve imaging performance at a fixed dose, or, equivalently, to provide a similar level of performance at reduced dose.

Orthogonality preserving infinite dimensional quadratic stochastic operators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Akın, Hasan; Mukhamedov, Farrukh

In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.

Graphical Solution of the Monic Quadratic Equation with Complex Coefficients

ERIC Educational Resources Information Center

Laine, A. D.

2015-01-01

There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…

The significance of the quadratic Doppler effect for space travel and astrophysics

NASA Astrophysics Data System (ADS)

Boehm, M.

1985-09-01

It is shown that a distinct frame of reference exists for light for which the Kennedy-Thorndike experiment provides unequivocal evidence. This leads to the postulate of a rotating instead of an expanding universe. It is shown that the cosmic red shift can be understood as the result of a Coriolis acceleration of the light propagating between two arbitrary points of different gravitational potential. Methods for determining the angular velocity of the rotating universe are given, and it is discussed whether the speed of light and the gravitational constant are universal constants or whether they are functions of distance from the center of the universe. Suggestions are made for further experimental studies and for practical application of the quadratic Doppler effect.

Quadratic resonance in the three-dimensional oscillations of inviscid drops with surface tension

NASA Technical Reports Server (NTRS)

Natarajan, R.; Brown, R. A.

1986-01-01

The moderate-amplitude, three-dimensional oscillations of an inviscid drop are described in terms of spherical harmonics. Specific oscillation modes are resonantly coupled by quadratic nonlinearities caused by inertia, capillarity, and drop deformation. The equations describing the interactions of these modes are derived from the variational principle for the appropriate Lagrangian by expressing the modal amplitudes to be functions of a slow time scale and by preaveraging the Lagrangian over the time scale of the primary oscillations. Stochastic motions are predicted for nonaxisymmetric deformations starting from most initial conditions, even those arbitrarily close to the axisymmetric shapes. The stochasticity is characterized by a redistribution of the energy contained in the initial deformation over all the degrees of freedom of the interacting modes.

Estimation of regions of attraction and ultimate boundedness for multiloop LQ regulators. [Linear Quadratic

NASA Technical Reports Server (NTRS)

Joshi, S. M.

1984-01-01

Closed-loop stability is investigated for multivariable linear time-invariant systems controlled by optimal full state feedback linear quadratic (LQ) regulators, with nonlinear gains present in the feedback channels. Estimates are obtained for the region of attraction when the nonlinearities escape the (0.5, infinity) sector in regions away from the origin and for the region of ultimate boundedness when the nonlinearities escape the sector near the origin. The expressions for these regions also provide methods for selecting the performance function parameters in order to obtain LQ designs with better tolerance for nonlinearities. The analytical results are illustrated by applying them to the problem of controlling the rigid-body pitch angle and elastic motion of a large, flexible space antenna.

Unsteady Propeller Hydrodynamics

DTIC Science & Technology

2001-06-01

coupling routines, making the code more robust while decreasing the computation burden over currect methods. Finally, a higher order quadratic influence ... function technique was implemented within the wake to more accurately define the induction velocity at the trailing edge which has suffered in the past due to lack of discretization.

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for high Reynolds number laminar flows

NASA Technical Reports Server (NTRS)

Kim, Sang-Wook

1988-01-01

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables were interpolated using complete quadratic shape functions and the pressure was interpolated using linear shape functions. For the two dimensional case, the pressure is defined on a triangular element which is contained inside the complete biquadratic element for velocity variables; and for the three dimensional case, the pressure is defined on a tetrahedral element which is again contained inside the complete tri-quadratic element. Thus the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow for Reynolds number of 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorable with those of the finite difference methods as well as experimental data available. A finite elememt computer program for incompressible, laminar flows is presented.

Atomistic and molecular effects in electric double layers at high surface charges

DOE PAGES

Templeton, Jeremy Alan; Lee, Jonathan; Mani, Ali

2015-06-16

Here, the Poisson–Boltzmann theory for electrolytes near a charged surface is known to be invalid due to unaccounted physics associated with high ion concentration regimes. In order to investigate this regime, fluids density functional theory (f-DFT) and molecular dynamics (MD) simulations were used to determine electric surface potential as a function of surface charge. Based on these detailed computations, for electrolytes with nonpolar solvent, the surface potential is shown to depend quadratically on the surface charge in the high charge limit. We demonstrate that modified Poisson–Boltzmann theories can model this limit if they are augmented with atomic packing densities providedmore » by MD. However, when the solvent is a highly polar molecule water an intermediate regime is identified in which a constant capacitance is realized. Simulation results demonstrate the mechanism underlying this regime, and for the salt water system studied here, it persists throughout the range of physically realistic surface charge densities so the potential’s quadratic surface charge dependence is not obtained.« less

Robust Stabilization of Uncertain Systems Based on Energy Dissipation Concepts

NASA Technical Reports Server (NTRS)

Gupta, Sandeep

1996-01-01

Robust stability conditions obtained through generalization of the notion of energy dissipation in physical systems are discussed in this report. Linear time-invariant (LTI) systems which dissipate energy corresponding to quadratic power functions are characterized in the time-domain and the frequency-domain, in terms of linear matrix inequalities (LMls) and algebraic Riccati equations (ARE's). A novel characterization of strictly dissipative LTI systems is introduced in this report. Sufficient conditions in terms of dissipativity and strict dissipativity are presented for (1) stability of the feedback interconnection of dissipative LTI systems, (2) stability of dissipative LTI systems with memoryless feedback nonlinearities, and (3) quadratic stability of uncertain linear systems. It is demonstrated that the framework of dissipative LTI systems investigated in this report unifies and extends small gain, passivity, and sector conditions for stability. Techniques for selecting power functions for characterization of uncertain plants and robust controller synthesis based on these stability results are introduced. A spring-mass-damper example is used to illustrate the application of these methods for robust controller synthesis.

Optimization of Fish Protection System to Increase Technosphere Safety

NASA Astrophysics Data System (ADS)

Khetsuriani, E. D.; Fesenko, L. N.; Larin, D. S.

2017-11-01

The article is concerned with field study data. Drawing upon prior information and considering structural features of fish protection devices, we decided to conduct experimental research while changing three parameters: process pressure PCT, stream velocity Vp and washer nozzle inclination angle αc. The variability intervals of examined factors are shown in the Table 1. The conicity angle was assumed as a constant one. The box design B3 was chosen as a baseline being close to D-optimal designs in its statistical characteristics. The number of device rotations and its fish fry protection efficiency were accepted as the output functions of optimization. The numerical values of regression coefficients of quadratic equations describing the behavior of optimization functions Y1 and Y2 and their formulaic errors were calculated upon the test results in accordance with the planning matrix. The adequacy or inadequacy of the obtained quadratic regression model is judged via checking the condition whether Fexp ≤ Ftheor.

Probabilistic dual heuristic programming-based adaptive critic

NASA Astrophysics Data System (ADS)

Herzallah, Randa

2010-02-01

Adaptive critic (AC) methods have common roots as generalisations of dynamic programming for neural reinforcement learning approaches. Since they approximate the dynamic programming solutions, they are potentially suitable for learning in noisy, non-linear and non-stationary environments. In this study, a novel probabilistic dual heuristic programming (DHP)-based AC controller is proposed. Distinct to current approaches, the proposed probabilistic (DHP) AC method takes uncertainties of forward model and inverse controller into consideration. Therefore, it is suitable for deterministic and stochastic control problems characterised by functional uncertainty. Theoretical development of the proposed method is validated by analytically evaluating the correct value of the cost function which satisfies the Bellman equation in a linear quadratic control problem. The target value of the probabilistic critic network is then calculated and shown to be equal to the analytically derived correct value. Full derivation of the Riccati solution for this non-standard stochastic linear quadratic control problem is also provided. Moreover, the performance of the proposed probabilistic controller is demonstrated on linear and non-linear control examples.

Fast Algorithms for Designing Unimodular Waveform(s) With Good Correlation Properties

NASA Astrophysics Data System (ADS)

Li, Yongzhe; Vorobyov, Sergiy A.

2018-03-01

In this paper, we develop new fast and efficient algorithms for designing single/multiple unimodular waveforms/codes with good auto- and cross-correlation or weighted correlation properties, which are highly desired in radar and communication systems. The waveform design is based on the minimization of the integrated sidelobe level (ISL) and weighted ISL (WISL) of waveforms. As the corresponding optimization problems can quickly grow to large scale with increasing the code length and number of waveforms, the main issue turns to be the development of fast large-scale optimization techniques. The difficulty is also that the corresponding optimization problems are non-convex, but the required accuracy is high. Therefore, we formulate the ISL and WISL minimization problems as non-convex quartic optimization problems in frequency domain, and then simplify them into quadratic problems by utilizing the majorization-minimization technique, which is one of the basic techniques for addressing large-scale and/or non-convex optimization problems. While designing our fast algorithms, we find out and use inherent algebraic structures in the objective functions to rewrite them into quartic forms, and in the case of WISL minimization, to derive additionally an alternative quartic form which allows to apply the quartic-quadratic transformation. Our algorithms are applicable to large-scale unimodular waveform design problems as they are proved to have lower or comparable computational burden (analyzed theoretically) and faster convergence speed (confirmed by comprehensive simulations) than the state-of-the-art algorithms. In addition, the waveforms designed by our algorithms demonstrate better correlation properties compared to their counterparts.

The Effect of Detector Nonlinearity on WFIRST PSF Profiles for Weak Gravitational Lensing Measurements

NASA Astrophysics Data System (ADS)

Plazas, A. A.; Shapiro, C.; Kannawadi, A.; Mandelbaum, R.; Rhodes, J.; Smith, R.

2016-10-01

Weak gravitational lensing (WL) is one of the most powerful techniques to learn about the dark sector of the universe. To extract the WL signal from astronomical observations, galaxy shapes must be measured and corrected for the point-spread function (PSF) of the imaging system with extreme accuracy. Future WL missions—such as NASA’s Wide-Field Infrared Survey Telescope (WFIRST)—will use a family of hybrid near-infrared complementary metal-oxide-semiconductor detectors (HAWAII-4RG) that are untested for accurate WL measurements. Like all image sensors, these devices are subject to conversion gain nonlinearities (voltage response to collected photo-charge) that bias the shape and size of bright objects such as reference stars that are used in PSF determination. We study this type of detector nonlinearity (NL) and show how to derive requirements on it from WFIRST PSF size and ellipticity requirements. We simulate the PSF optical profiles expected for WFIRST and measure the fractional error in the PSF size (ΔR/R) and the absolute error in the PSF ellipticity (Δe) as a function of star magnitude and the NL model. For our nominal NL model (a quadratic correction), we find that, uncalibrated, NL can induce an error of ΔR/R = 1 × 10-2 and Δe 2 = 1.75 × 10-3 in the H158 bandpass for the brightest unsaturated stars in WFIRST. In addition, our simulations show that to limit the bias of ΔR/R and Δe in the H158 band to ˜10% of the estimated WFIRST error budget, the quadratic NL model parameter β must be calibrated to ˜1% and ˜2.4%, respectively. We present a fitting formula that can be used to estimate WFIRST detector NL requirements once a true PSF error budget is established.

Mediterranean diet score and left ventricular structure and function: the Multi-Ethnic Study of Atherosclerosis12

PubMed Central

Levitan, Emily B; Ahmed, Ali; Arnett, Donna K; Polak, Joseph F; Hundley, W Gregory; Bluemke, David A; Heckbert, Susan R; Jacobs, David R; Nettleton, Jennifer A

2016-01-01

Background: Data are limited on the relation between dietary patterns and left ventricular (LV) structure and function. Objective: We examined cross-sectional associations of a diet-score assessment of a Mediterranean dietary pattern with LV mass, volume, mass-to-volume ratio, stroke volume, and ejection fraction. Design: We measured LV variables with the use of cardiac MRI in 4497 participants in the Multi-Ethnic Study of Atherosclerosis study who were aged 45–84 y and without clinical cardiovascular disease. We calculated a Mediterranean diet score from intakes of fruit, vegetables, nuts, legumes, whole grains, fish, red meat, the monounsaturated fat:saturated fat ratio, and alcohol that were self-reported with the use of a food-frequency questionnaire. We used linear regression with adjustment for body size, physical activity, and cardiovascular disease risk factors to model associations and assess the shape of these associations (linear or quadratic). Results: The Mediterranean diet score had a slight U-shaped association with LV mass (adjusted means: 146, 145, 146, and 147 g across quartiles of diet score, respectively; P-quadratic trend = 0.04). The score was linearly associated with LV volume, stroke volume, and ejection fraction: for each +1-U difference in score, LV volume was 0.4 mL higher (95% CI: 0.0, 0.8 mL higher), the stroke volume was 0.5 mL higher (95% CI: 0.2, 0.8 mL higher), and the ejection fraction was 0.2 percentage points higher (95% CI: 0.1, 0.3 percentage points higher). The score was not associated with the mass-to-volume ratio. Conclusions: A higher Mediterranean diet score is cross-sectionally associated with a higher LV mass, which is balanced by a higher LV volume as well as a higher ejection fraction and stroke volume. Participants in this healthy, multiethnic sample whose dietary patterns most closely conformed to a Mediterranean-type pattern had a modestly better LV structure and function than did participants with less–Mediterranean-like dietary patterns. This trial was registered at clinicaltrials.gov as NCT00005487. PMID:27488238

Hidden supersymmetry and quadratic deformations of the space-time conformal superalgebra

NASA Astrophysics Data System (ADS)

Yates, L. A.; Jarvis, P. D.

2018-04-01

We analyze the structure of the family of quadratic superalgebras, introduced in Jarvis et al (2011 J. Phys. A: Math. Theor. 44 235205), for the quadratic deformations of N  =  1 space-time conformal supersymmetry. We characterize in particular the ‘zero-step’ modules for this case. In such modules, the odd generators vanish identically, and the quadratic superalgebra is realized on a single irreducible representation of the even subalgebra (which is a Lie algebra). In the case under study, the quadratic deformations of N  =  1 space-time conformal supersymmetry, it is shown that each massless positive energy unitary irreducible representation (in the standard classification of Mack), forms such a zero-step module, for an appropriate parameter choice amongst the quadratic family (with vanishing central charge). For these massless particle multiplets therefore, quadratic supersymmetry is unbroken, in that the supersymmetry generators annihilate all physical states (including the vacuum state), while at the same time, superpartners do not exist.

Linear state feedback, quadratic weights, and closed loop eigenstructures. M.S. Thesis

NASA Technical Reports Server (NTRS)

Thompson, P. M.

1979-01-01

Results are given on the relationships between closed loop eigenstructures, state feedback gain matrices of the linear state feedback problem, and quadratic weights of the linear quadratic regulator. Equations are derived for the angles of general multivariable root loci and linear quadratic optimal root loci, including angles of departure and approach. The generalized eigenvalue problem is used for the first time to compute angles of approach. Equations are also derived to find the sensitivity of closed loop eigenvalues and the directional derivatives of closed loop eigenvectors (with respect to a scalar multiplying the feedback gain matrix or the quadratic control weight). An equivalence class of quadratic weights that produce the same asymptotic eigenstructure is defined, sufficient conditions to be in it are given, a canonical element is defined, and an algorithm to find it is given. The behavior of the optimal root locus in the nonasymptotic region is shown to be different for quadratic weights with the same asymptotic properties.

Using Visualization to Generalize on Quadratic Patterning Tasks

ERIC Educational Resources Information Center

Kirwan, J. Vince

2017-01-01

Patterning tasks engage students in a core aspect of algebraic thinking-generalization (Kaput 2008). The National Council of Teachers of Mathematics (NCTM) Algebra Standard states that students in grades 9-12 should "generalize patterns using explicitly defined and recursively defined functions" (NCTM 2000, p. 296). Although educators…

Solution of Thermoelectricity Problems Energy Method

NASA Astrophysics Data System (ADS)

Niyazbek, Muheyat; Nogaybaeva, M. O.; Talp, Kuenssaule; Kudaikulov, A. A.

2018-06-01

On the basis of the fundamental laws of conservation of energy in conjunction with local quadratic spline functions was developed a universal computing algorithm, a method and associated software, which allows to investigate the Thermophysical insulated rod, with limited length, influenced by local heat flow, heat transfer and temperature

Design of a model observer to evaluate calcification detectability in breast tomosynthesis and application to smoothing prior optimization.

PubMed

Michielsen, Koen; Nuyts, Johan; Cockmartin, Lesley; Marshall, Nicholas; Bosmans, Hilde

2016-12-01

In this work, the authors design and validate a model observer that can detect groups of microcalcifications in a four-alternative forced choice experiment and use it to optimize a smoothing prior for detectability of microcalcifications. A channelized Hotelling observer (CHO) with eight Laguerre-Gauss channels was designed to detect groups of five microcalcifications in a background of acrylic spheres by adding the CHO log-likelihood ratios calculated at the expected locations of the five calcifications. This model observer is then applied to optimize the detectability of the microcalcifications as a function of the smoothing prior. The authors examine the quadratic and total variation (TV) priors, and a combination of both. A selection of these reconstructions was then evaluated by human observers to validate the correct working of the model observer. The authors found a clear maximum for the detectability of microcalcification when using the total variation prior with weight β TV = 35. Detectability only varied over a small range for the quadratic and combined quadratic-TV priors when weight β Q of the quadratic prior was changed by two orders of magnitude. Spearman correlation with human observers was good except for the highest value of β for the quadratic and TV priors. Excluding those, the authors found ρ = 0.93 when comparing detection fractions, and ρ = 0.86 for the fitted detection threshold diameter. The authors successfully designed a model observer that was able to predict human performance over a large range of settings of the smoothing prior, except for the highest values of β which were outside the useful range for good image quality. Since detectability only depends weakly on the strength of the combined prior, it is not possible to pick an optimal smoothness based only on this criterion. On the other hand, such choice can now be made based on other criteria without worrying about calcification detectability.

Functional properties of models for direction selectivity in the retina.

PubMed

Grzywacz, N M; Koch, C

1987-01-01

Poggio and Reichardt (Kybernetik, 13:223-227, 1973) showed that if the average response of a visual system to a moving stimulus is directionally selective, then this sensitivity must be mediated by a nonlinear operation. In particular, it has been proposed that at the behavioral level, motion-sensitive biological systems are implemented by quadratic nonlinearities (Hassenstein and Reichardt: Z. Naturforsch., 11b:513-524, 1956; van Santen and Sperling: J. Opt. Soc. Am. [A] 1:451-473, 1984; Adelson and Bergen: J. Opt. Soc. Am. [A], 2:284-299, 1985). This paper analyzes theoretically two nonlinear neural mechanisms that possibly underlie retinal direction selectivity and explores the conditions under which they behave as a quadratic nonlinearity. The first mechanism is shunting inhibition (Torre and Poggio: Proc. R. Soc. Lond. [Biol.], 202:409-416, 1978), and the second consists of the linear combination of the outputs of a depolarizing and a hyperpolarizing synapse, followed by a threshold operation. It was found that although sometimes possible, it is in practice hard to approximate the Shunting Inhibition and the Threshold models for direction selectivity by quadratic systems. For instance, the level of the threshold on the Threshold model must be close to the steady-state level of the cell's combined synaptic input. Furthermore, for both the Shunting and the Threshold models, the approximation by a quadratic system is only possible for a small range of low contrast stimuli and for situations where the rectifications due to the ON-OFF mechanisms, and to the ganglion cells' action potentials, can be linearized. The main question that this paper leaves open is, how do we account for the apparent quadratic properties of motion perception given that the same properties seem so fragile at the single cell level? Finally, as a result of this study, some system analysis experiments were proposed that can distinguish between different instances of the models.

Short-term forecasting of meteorological time series using Nonparametric Functional Data Analysis (NPFDA)

NASA Astrophysics Data System (ADS)

Curceac, S.; Ternynck, C.; Ouarda, T.

2015-12-01

Over the past decades, a substantial amount of research has been conducted to model and forecast climatic variables. In this study, Nonparametric Functional Data Analysis (NPFDA) methods are applied to forecast air temperature and wind speed time series in Abu Dhabi, UAE. The dataset consists of hourly measurements recorded for a period of 29 years, 1982-2010. The novelty of the Functional Data Analysis approach is in expressing the data as curves. In the present work, the focus is on daily forecasting and the functional observations (curves) express the daily measurements of the above mentioned variables. We apply a non-linear regression model with a functional non-parametric kernel estimator. The computation of the estimator is performed using an asymmetrical quadratic kernel function for local weighting based on the bandwidth obtained by a cross validation procedure. The proximities between functional objects are calculated by families of semi-metrics based on derivatives and Functional Principal Component Analysis (FPCA). Additionally, functional conditional mode and functional conditional median estimators are applied and the advantages of combining their results are analysed. A different approach employs a SARIMA model selected according to the minimum Akaike (AIC) and Bayessian (BIC) Information Criteria and based on the residuals of the model. The performance of the models is assessed by calculating error indices such as the root mean square error (RMSE), relative RMSE, BIAS and relative BIAS. The results indicate that the NPFDA models provide more accurate forecasts than the SARIMA models. Key words: Nonparametric functional data analysis, SARIMA, time series forecast, air temperature, wind speed

Density Functional Theory Calculations of the Dissociation of H[2] on (100) 2H-MoS[2] Surfaces: A Key Step in the Hydroprocessing of Crude Oil

ERIC Educational Resources Information Center

Todorova, Teodora; Alexiev, Valentin; Weber, Thomas

2006-01-01

Hydrogen activation on the (100) surface of MoS[2] structures was investigated by means of density functional theory calculations. Linear and quadratic synchronous transit methods with a conjugate gradient refinement of the saddle point were used to localize transition states. The calculations include heterolytic and homolytic dissociation of…

Exact and quasi-classical density matrix and Wigner functions for a particle in the box and half space

NASA Technical Reports Server (NTRS)

Akhundova, E. A.; Dodonov, V. V.; Manko, V. I.

1993-01-01

The exact expressions for density matrix and Wigner functions of quantum systems are known only in special cases. Corresponding Hamiltonians are quadratic forms of Euclidean coordinates and momenta. In this paper we consider the problem of one-dimensional free particle movement in the bounded region 0 is less than x is less than a (including the case a = infinity).

Dynamical correlation functions of the quadratic coupling spin-Boson model

NASA Astrophysics Data System (ADS)

Zheng, Da-Chuan; Tong, Ning-Hua

2017-06-01

The spin-boson model with quadratic coupling is studied using the bosonic numerical renormalization group method. We focus on the dynamical auto-correlation functions {C}O(ω ), with the operator \\hat{O} taken as {\\hat{{{σ }}}}x, {\\hat{{{σ }}}}z, and \\hat{X}, respectively. In the weak-coupling regime α < {α }{{c}}, these functions show power law ω-dependence in the small frequency limit, with the powers 1+2s, 1+2s, and s, respectively. At the critical point α ={α }{{c}} of the boson-unstable quantum phase transition, the critical exponents y O of these correlation functions are obtained as {y}{{{σ }}x}={y}{{{σ }}z}=1-2s and {y}X=-s, respectively. Here s is the bath index and X is the boson displacement operator. Close to the spin flip point, the high frequency peak of {C}{{{σ }}x}(ω ) is broadened significantly and the line shape changes qualitatively, showing enhanced dephasing at the spin flip point. Project supported by the National Key Basic Research Program of China (Grant No. 2012CB921704), the National Natural Science Foundation of China (Grant No. 11374362), the Fundamental Research Funds for the Central Universities, China, and the Research Funds of Renmin University of China (Grant No. 15XNLQ03).

Approximate likelihood approaches for detecting the influence of primordial gravitational waves in cosmic microwave background polarization

NASA Astrophysics Data System (ADS)

Pan, Zhen; Anderes, Ethan; Knox, Lloyd

2018-05-01

One of the major targets for next-generation cosmic microwave background (CMB) experiments is the detection of the primordial B-mode signal. Planning is under way for Stage-IV experiments that are projected to have instrumental noise small enough to make lensing and foregrounds the dominant source of uncertainty for estimating the tensor-to-scalar ratio r from polarization maps. This makes delensing a crucial part of future CMB polarization science. In this paper we present a likelihood method for estimating the tensor-to-scalar ratio r from CMB polarization observations, which combines the benefits of a full-scale likelihood approach with the tractability of the quadratic delensing technique. This method is a pixel space, all order likelihood analysis of the quadratic delensed B modes, and it essentially builds upon the quadratic delenser by taking into account all order lensing and pixel space anomalies. Its tractability relies on a crucial factorization of the pixel space covariance matrix of the polarization observations which allows one to compute the full Gaussian approximate likelihood profile, as a function of r , at the same computational cost of a single likelihood evaluation.

Functional Form of the Radiometric Equation for the SNPP VIIRS Reflective Solar Bands: An Initial Study

NASA Technical Reports Server (NTRS)

Lei, Ning; Xiong, Xiaoxiong

2016-01-01

The Visible Infrared Imaging Radiometer Suite (VIIRS) aboard the Suomi National Polar-orbiting Partnership (SNPP) satellite is a passive scanning radiometer and an imager, observing radiative energy from the Earth in 22 spectral bands from 0.41 to 12 microns which include 14 reflective solar bands (RSBs). Extending the formula used by the Moderate Resolution Imaging Spectroradiometer instruments, currently the VIIRS determines the sensor aperture spectral radiance through a quadratic polynomial of its detector digital count. It has been known that for the RSBs the quadratic polynomial is not adequate in the design specified spectral radiance region and using a quadratic polynomial could drastically increase the errors in the polynomial coefficients, leading to possible large errors in the determined aperture spectral radiance. In addition, it is very desirable to be able to extend the radiance calculation formula to correctly retrieve the aperture spectral radiance with the level beyond the design specified range. In order to more accurately determine the aperture spectral radiance from the observed digital count, we examine a few polynomials of the detector digital count to calculate the sensor aperture spectral radiance.

Lyapunov functions for a class of nonlinear systems using Caputo derivative

NASA Astrophysics Data System (ADS)

Fernandez-Anaya, G.; Nava-Antonio, G.; Jamous-Galante, J.; Muñoz-Vega, R.; Hernández-Martínez, E. G.

2017-02-01

This paper presents an extension of recent results that allow proving the stability of Caputo nonlinear and time-varying systems, by means of the fractional order Lyapunov direct method, using quadratic Lyapunov functions. This article introduces a new way of building polynomial Lyapunov functions of any positive integer order as a way of determining the stability of a greater variety of systems when the order of the derivative is 0 < α < 1. Some examples are given to validate these results.

Quadratic Solid⁻Shell Finite Elements for Geometrically Nonlinear Analysis of Functionally Graded Material Plates.

PubMed

Chalal, Hocine; Abed-Meraim, Farid

2018-06-20

In the current contribution, prismatic and hexahedral quadratic solid⁻shell (SHB) finite elements are proposed for the geometrically nonlinear analysis of thin structures made of functionally graded material (FGM). The proposed SHB finite elements are developed within a purely 3D framework, with displacements as the only degrees of freedom. Also, the in-plane reduced-integration technique is combined with the assumed-strain method to alleviate various locking phenomena. Furthermore, an arbitrary number of integration points are placed along a special direction, which represents the thickness. The developed elements are coupled with functionally graded behavior for the modeling of thin FGM plates. To this end, the Young modulus of the FGM plate is assumed to vary gradually in the thickness direction, according to a volume fraction distribution. The resulting formulations are implemented into the quasi-static ABAQUS/Standard finite element software in the framework of large displacements and rotations. Popular nonlinear benchmark problems are considered to assess the performance and accuracy of the proposed SHB elements. Comparisons with reference solutions from the literature demonstrate the good capabilities of the developed SHB elements for the 3D simulation of thin FGM plates.

Securing Digital Audio using Complex Quadratic Map

NASA Astrophysics Data System (ADS)

Suryadi, MT; Satria Gunawan, Tjandra; Satria, Yudi

2018-03-01

In This digital era, exchanging data are common and easy to do, therefore it is vulnerable to be attacked and manipulated from unauthorized parties. One data type that is vulnerable to attack is digital audio. So, we need data securing method that is not vulnerable and fast. One of the methods that match all of those criteria is securing the data using chaos function. Chaos function that is used in this research is complex quadratic map (CQM). There are some parameter value that causing the key stream that is generated by CQM function to pass all 15 NIST test, this means that the key stream that is generated using this CQM is proven to be random. In addition, samples of encrypted digital sound when tested using goodness of fit test are proven to be uniform, so securing digital audio using this method is not vulnerable to frequency analysis attack. The key space is very huge about 8.1×l031 possible keys and the key sensitivity is very small about 10-10, therefore this method is also not vulnerable against brute-force attack. And finally, the processing speed for both encryption and decryption process on average about 450 times faster that its digital audio duration.

Regions of absolute ultimate boundedness for discrete-time systems.

NASA Technical Reports Server (NTRS)

Siljak, D. D.; Weissenberger, S.

1972-01-01

This paper considers discrete-time systems of the Lur'e-Postnikov class where the linear part is not asymptotically stable and the nonlinear characteristic satisfies only partially the usual sector condition. Estimates of the resulting finite regions of absolute ultimate boundedness are calculated by means of a quadratic Liapunov function.

Prediction of infection risk of hop by Pseudoperonspora humuli

USDA-ARS?s Scientific Manuscript database

Downy mildew, caused by Pseudoperonospora humuli, is one of the most destructive diseases of hop. Weather factors associated with infection risk by P. humuli in the maritime region of western Oregon were examined for 24 and 48-h periods and quadratic discriminant function models were developed to c...

The Shock and Vibration Digest. Volume 18, Number 6

DTIC Science & Technology

1986-06-01

linear, quadratic, or cubic. Bessel function Reed [124] reported a method for computing solutions were obtained for a truncated pyramid amplitudes of a...86-1198 A. Ragab, Chung C. Fu Seismic Analysis of a Large LMFBR with Flu- Cairo Univ., Giza , Egypt . . *. id-Structure Imteractions Computers Struc

Probability, Problem Solving, and "The Price is Right."

ERIC Educational Resources Information Center

Wood, Eric

1992-01-01

This article discusses the analysis of a decision-making process faced by contestants on the television game show "The Price is Right". The included analyses of the original and related problems concern pattern searching, inductive reasoning, quadratic functions, and graphing. Computer simulation programs in BASIC and tables of…

Interactive Spreadsheets in JCE Webware

ERIC Educational Resources Information Center

Coleman, William F.; Fedosky, Edward W.

2005-01-01

A description of the Microsoft Excel spreadsheet simulation, Anharmonicity.xls that can be used to smoothly and continuously switch a plotted function and its quadratic approximation is presented. It can be used in a classroom demonstration or incorporated into a student-centered computer-laboratory exercise to examine the qualitative behavior of…

Pre-Service Teachers' Perceptions and Beliefs of Technological Pedagogical Content Knowledge on Algebra

ERIC Educational Resources Information Center

Lin, Cheng-Yao; Kuo, Yu-Chun; Ko, Yi-Yin

2015-01-01

The purpose of this study was to investigate elementary pre-service teachers' content knowledge in algebra (Linear Equation, Quadratic Equation, Functions, System Equations and Polynomials) as well as their technological pedagogical content knowledge (TPACK) in teaching algebra. Participants were 79 undergraduate pre-service teachers who were…

On Partial Fraction Decompositions by Repeated Polynomial Divisions

ERIC Educational Resources Information Center

Man, Yiu-Kwong

2017-01-01

We present a method for finding partial fraction decompositions of rational functions with linear or quadratic factors in the denominators by means of repeated polynomial divisions. This method does not involve differentiation or solving linear equations for obtaining the unknown partial fraction coefficients, which is very suitable for either…

Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models.

PubMed

Bignardi, A B; El Faro, L; Cardoso, V L; Machado, P F; Albuquerque, L G

2009-09-01

The objective of the present study was to estimate milk yield genetic parameters applying random regression models and parametric correlation functions combined with a variance function to model animal permanent environmental effects. A total of 152,145 test-day milk yields from 7,317 first lactations of Holstein cows belonging to herds located in the southeastern region of Brazil were analyzed. Test-day milk yields were divided into 44 weekly classes of days in milk. Contemporary groups were defined by herd-test-day comprising a total of 2,539 classes. The model included direct additive genetic, permanent environmental, and residual random effects. The following fixed effects were considered: contemporary group, age of cow at calving (linear and quadratic regressions), and the population average lactation curve modeled by fourth-order orthogonal Legendre polynomial. Additive genetic effects were modeled by random regression on orthogonal Legendre polynomials of days in milk, whereas permanent environmental effects were estimated using a stationary or nonstationary parametric correlation function combined with a variance function of different orders. The structure of residual variances was modeled using a step function containing 6 variance classes. The genetic parameter estimates obtained with the model using a stationary correlation function associated with a variance function to model permanent environmental effects were similar to those obtained with models employing orthogonal Legendre polynomials for the same effect. A model using a sixth-order polynomial for additive effects and a stationary parametric correlation function associated with a seventh-order variance function to model permanent environmental effects would be sufficient for data fitting.

Scaling Laws for the Multidimensional Burgers Equation with Quadratic External Potential

NASA Astrophysics Data System (ADS)

Leonenko, N. N.; Ruiz-Medina, M. D.

2006-07-01

The reordering of the multidimensional exponential quadratic operator in coordinate-momentum space (see X. Wang, C.H. Oh and L.C. Kwek (1998). J. Phys. A.: Math. Gen. 31:4329-4336) is applied to derive an explicit formulation of the solution to the multidimensional heat equation with quadratic external potential and random initial conditions. The solution to the multidimensional Burgers equation with quadratic external potential under Gaussian strongly dependent scenarios is also obtained via the Hopf-Cole transformation. The limiting distributions of scaling solutions to the multidimensional heat and Burgers equations with quadratic external potential are then obtained under such scenarios.

Molecular density functional theory of water describing hydrophobicity at short and long length scales

NASA Astrophysics Data System (ADS)

Jeanmairet, Guillaume; Levesque, Maximilien; Borgis, Daniel

2013-10-01

We present an extension of our recently introduced molecular density functional theory of water [G. Jeanmairet et al., J. Phys. Chem. Lett. 4, 619 (2013)] to the solvation of hydrophobic solutes of various sizes, going from angstroms to nanometers. The theory is based on the quadratic expansion of the excess free energy in terms of two classical density fields: the particle density and the multipolar polarization density. Its implementation requires as input a molecular model of water and three measurable bulk properties, namely, the structure factor and the k-dependent longitudinal and transverse dielectric susceptibilities. The fine three-dimensional water structure around small hydrophobic molecules is found to be well reproduced. In contrast, the computed solvation free-energies appear overestimated and do not exhibit the correct qualitative behavior when the hydrophobic solute is grown in size. These shortcomings are corrected, in the spirit of the Lum-Chandler-Weeks theory, by complementing the functional with a truncated hard-sphere functional acting beyond quadratic order in density, and making the resulting functional compatible with the Van-der-Waals theory of liquid-vapor coexistence at long range. Compared to available molecular simulations, the approach yields reasonable solvation structure and free energy of hard or soft spheres of increasing size, with a correct qualitative transition from a volume-driven to a surface-driven regime at the nanometer scale.

Effects of pea chips on pig performance, carcass quality and composition, and palatability of pork.

PubMed

Newman, D J; Harris, E K; Lepper, A N; Berg, E P; Stein, H H

2011-10-01

Pea chips are produced as a by-product when field peas are processed to produce split peas for human consumption. The objective of this experiment was to test the hypothesis that inclusion of pea chips in diets fed to finishing pigs does not negatively influence pig growth performance, carcass composition, and the palatability of pork. A total of 24 barrows (initial BW: 58.0 ± 6.6 kg) were allotted to 1 of 4 treatments and fed early finishing diets for 35 d and late finishing diets for 35 d. A corn-soybean meal (SBM) control diet and 3 diets containing pea chips were formulated for each phase. Pea chips replaced 33.3, 66.6, or 100% of the SBM in the control diet. Pigs were housed individually, and all pigs were slaughtered at the conclusion of the experiment. Overall, there were no differences (P > 0.11) in final BW, ADFI, and G:F of pigs among treatments, but there was a quadratic response in ADG (P = 0.04), with the smallest value observed in pigs fed the control diet. Dressing percentage linearly decreased (P = 0.04) as pea chips replaced SBM in diets, but there were no differences (P > 0.20) among treatments in HCW, LM area, 10th-rib backfat, lean meat percentage, and marbling. Likewise, pH in loin and ham, drip loss, and purge loss were not influenced (P > 0.13) by treatment. However, there was a quadratic response (P = 0.08) in 24-h pH in the shoulder, with the smallest value present in pigs fed the diet, in which 66.6% of the SBM was replaced by pea chips. Subjective LM color and Japanese color score standard were reduced (quadratic, P = 0.03 and 0.05, respectively) and LM b* values and hue angle were increased (quadratic, P = 0.09 and 0.10, respectively) when pea chips replaced SBM in the diets. Ham L* (quadratic, P = 0.04), a* (linear, P = 0.02), b* (quadratic, P = 0.07), color saturation (linear, P = 0.02), and hue angle (quadratic, P = 0.05) were increased when pea chips replaced SBM. However, there were no differences (P > 0.16) in shoulder and fat color. Moreover, cook loss percentage, shear force, juiciness, and pork flavor of pork chops were not different (P > 0.10) among treatments, but tenderness of pork chops linearly decreased (P = 0.04) as SBM replaced pea chips. It is concluded that all the SBM in diets fed to growing-finishing pigs may be replaced by pea chips without negatively influencing growth performance or carcass composition. However, pigs fed pea chips will have pork chops and hams that are lighter, and chops may be less tender if pigs are fed pea chips rather than corn and SBM.

Parametric optimal control of uncertain systems under an optimistic value criterion

NASA Astrophysics Data System (ADS)

Li, Bo; Zhu, Yuanguo

2018-01-01

It is well known that the optimal control of a linear quadratic model is characterized by the solution of a Riccati differential equation. In many cases, the corresponding Riccati differential equation cannot be solved exactly such that the optimal feedback control may be a complex time-oriented function. In this article, a parametric optimal control problem of an uncertain linear quadratic model under an optimistic value criterion is considered for simplifying the expression of optimal control. Based on the equation of optimality for the uncertain optimal control problem, an approximation method is presented to solve it. As an application, a two-spool turbofan engine optimal control problem is given to show the utility of the proposed model and the efficiency of the presented approximation method.

Dolan Grady relations and noncommutative quasi-exactly solvable systems

NASA Astrophysics Data System (ADS)

Klishevich, Sergey M.; Plyushchay, Mikhail S.

2003-11-01

We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives obeying the nonlinear Dolan-Grady relations. This restricts the structure function of the deformed oscillator algebra to a quadratic polynomial. The cases when the coordinates form the {\\mathfrak{su}}(2) and {\\mathfrak{sl}}(2,{\\bb {R}}) algebras are investigated in detail. Reducing the Hamiltonian to 1D finite-difference quasi-exactly solvable operators, we demonstrate partial algebraization of the spectrum of the corresponding systems on the fuzzy sphere and noncommutative hyperbolic plane. A completely covariant method based on the notion of intrinsic algebra is proposed to deal with the spectral problem of such systems.

TH-A-BRD-01: Radiation Biology for Radiation Therapy Physicists

DOE Office of Scientific and Technical Information (OSTI.GOV)

Orton, C; Borras, C; Carlson, D

Mechanisms by which radiation kills cells and ways cell damage can be repaired will be reviewed. The radiobiological parameters of dose, fractionation, delivery time, dose rate, and LET will be discussed. The linear-quadratic model for cell survival for high and low dose rate treatments and the effect of repopulation will be presented and discussed. The rationale for various radiotherapy techniques such as conventional fractionation, hyperfractionation, hypofractionation, and low and high dose rate brachytherapy, including permanent implants, will be presented. The radiobiological principles underlying radiation protection guidelines and the different radiation dosimetry terms used in radiation biology and in radiation protectionmore » will be reviewed. Human data on radiation induced cancer, including increases in the risk of second cancers following radiation therapy, as well as data on radiation induced tissue reactions, such as cardiovascular effects, for follow up times up to 20–40 years, published by ICRP, NCRP and BEIR Committees, will be examined. The latest risk estimates per unit dose will be presented. Their adoption in recent radiation protection standards and guidelines and their impact on patient and workers safety in radiotherapy will be discussed. Biologically-guided radiotherapy (BGRT) provides a systematic method to derive prescription doses that integrate patient-specific information about tumor and normal tissue biology. Treatment individualization based on patient-specific biology requires the identification of biological objective functions to facilitate the design and comparison of competing treatment modalities. Biological objectives provide a more direct approach to plan optimization instead of relying solely on dose-based surrogates and can incorporate factors that alter radiation response, such as DNA repair, tumor hypoxia, and relative biological effectiveness. We review concepts motivating biological objectives and provide examples of how they might be used to address clinically relevant problems. Underlying assumptions and limitations of existing models and their proper application will be discussed. This multidisciplinary educational session combines the fundamentals of radiobiology for radiation therapy and radiation protection with the practical application of biophysical models for treatment planning and evaluation. Learning Objectives: To understand fractionation in teletherapy and dose rate techniques in brachytherapy. To understand how the linear-quadratic models the effect of radiobiological parameters for radiotherapy. To understand the radiobiological basis of radiation protection standards applied to radiotherapy. To distinguish between stochastic effects and tissue reactions. To learn how to apply concepts of biological effective dose and RBE-weighted dose and to incorporate biological factors that alter radiation response. To discuss clinical strategies to increase therapeutic ratio, i.e., maximize local control while minimizing the risk of acute and late normal tissue effects.« less

Geometric Approaches to Quadratic Equations from Other Times and Places.

ERIC Educational Resources Information Center

Allaire, Patricia R.; Bradley, Robert E.

2001-01-01

Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)

Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle, and Popov theorems and their application to robust stability

NASA Technical Reports Server (NTRS)

Haddad, Wassim M.; Bernstein, Dennis S.

1991-01-01

Lyapunov function proofs of sufficient conditions for asymptotic stability are given for feedback interconnections of bounded real and positive real transfer functions. Two cases are considered: (1) a proper bounded real (resp., positive real) transfer function with a bounded real (resp., positive real) time-varying memoryless nonlinearity; and (2) two strictly proper bounded real (resp., positive real) transfer functions. A similar treatment is given for the circle and Popov theorems. Application of these results to robust stability with time-varying bounded real, positive real, and sector-bounded uncertainty is discussed.

On non-autonomous dynamical systems

NASA Astrophysics Data System (ADS)

Anzaldo-Meneses, A.

2015-04-01

In usual realistic classical dynamical systems, the Hamiltonian depends explicitly on time. In this work, a class of classical systems with time dependent nonlinear Hamiltonians is analyzed. This type of problems allows to find invariants by a family of Veronese maps. The motivation to develop this method results from the observation that the Poisson-Lie algebra of monomials in the coordinates and momenta is clearly defined in terms of its brackets and leads naturally to an infinite linear set of differential equations, under certain circumstances. To perform explicit analytic and numerical calculations, two examples are presented to estimate the trajectories, the first given by a nonlinear problem and the second by a quadratic Hamiltonian with three time dependent parameters. In the nonlinear problem, the Veronese approach using jets is shown to be equivalent to a direct procedure using elliptic functions identities, and linear invariants are constructed. For the second example, linear and quadratic invariants as well as stability conditions are given. Explicit solutions are also obtained for stepwise constant forces. For the quadratic Hamiltonian, an appropriated set of coordinates relates the geometric setting to that of the three dimensional manifold of central conic sections. It is shown further that the quantum mechanical problem of scattering in a superlattice leads to mathematically equivalent equations for the wave function, if the classical time is replaced by the space coordinate along a superlattice. The mathematical method used to compute the trajectories for stepwise constant parameters can be applied to both problems. It is the standard method in quantum scattering calculations, as known for locally periodic systems including a space dependent effective mass.

Linkages between Snow Cover Seasonality, Terrain, and Land Surface Phenology in the Highland Pastures of Kyrgyzstan

NASA Astrophysics Data System (ADS)

Henebry, Geoffrey; Tomaszewska, Monika; Kelgenbaeva, Kamilya

2017-04-01

In the highlands of Kyrgyzstan, vertical transhumance is the foundation of montane agropastoralism. Terrain attributes, such as elevation, slope, and aspect, affect snow cover seasonality, which is a key influence on the timing of plant growth and forage availability. Our study areas include the highland pastures in Central Tien Shan mountains, specifically in the rayons of Naryn and At-Bashy in Naryn oblast, and Alay and Chong-Alay rayons in Osh oblast. To explore the linkages between snow cover seasonality and land surface phenology as modulated by terrain and variations in thermal time, we use 16 years (2001-2016) of Landsat surface reflectance data at 30 m resolution with MODIS land surface temperature and snow cover products at 1 km and 500 m resolution, respectively, and two digital elevation models, SRTM and ASTER GDEM. We model snow cover seasonality using frost degree-days and land surface phenology using growing degree-days as quadratic functions of thermal time: a convex quadratic (CxQ) model for land surface phenology and a concave quadratic (CvQ) model for snow cover seasonality. From the fitted parameter coefficients, we calculated phenometrics, including "peak height" and "thermal time to peak" for the CxQ models and "trough depth" and "thermal time to trough" for the CvQ models. We explore how these phenometrics change as a function of elevation and slope-aspect interactions and due to interannual variability. Further, we examine how snow cover duration and timing affects the subsequent peak height and thermal time to peak in wetter, drier, and normal years.

Reconfigurable Flight Control Design using a Robust Servo LQR and Radial Basis Function Neural Networks

NASA Technical Reports Server (NTRS)

Burken, John J.

2005-01-01

This viewgraph presentation reviews the use of a Robust Servo Linear Quadratic Regulator (LQR) and a Radial Basis Function (RBF) Neural Network in reconfigurable flight control designs in adaptation to a aircraft part failure. The method uses a robust LQR servomechanism design with model Reference adaptive control, and RBF neural networks. During the failure the LQR servomechanism behaved well, and using the neural networks improved the tracking.

Optimal Water-Power Flow Problem: Formulation and Distributed Optimal Solution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dall-Anese, Emiliano; Zhao, Changhong; Zamzam, Admed S.

This paper formalizes an optimal water-power flow (OWPF) problem to optimize the use of controllable assets across power and water systems while accounting for the couplings between the two infrastructures. Tanks and pumps are optimally managed to satisfy water demand while improving power grid operations; {for the power network, an AC optimal power flow formulation is augmented to accommodate the controllability of water pumps.} Unfortunately, the physics governing the operation of the two infrastructures and coupling constraints lead to a nonconvex (and, in fact, NP-hard) problem; however, after reformulating OWPF as a nonconvex, quadratically-constrained quadratic problem, a feasible point pursuit-successivemore » convex approximation approach is used to identify feasible and optimal solutions. In addition, a distributed solver based on the alternating direction method of multipliers enables water and power operators to pursue individual objectives while respecting the couplings between the two networks. The merits of the proposed approach are demonstrated for the case of a distribution feeder coupled with a municipal water distribution network.« less

Nonlinear predictive control of a boiler-turbine unit: A state-space approach with successive on-line model linearisation and quadratic optimisation.

PubMed

Ławryńczuk, Maciej

2017-03-01

This paper details development of a Model Predictive Control (MPC) algorithm for a boiler-turbine unit, which is a nonlinear multiple-input multiple-output process. The control objective is to follow set-point changes imposed on two state (output) variables and to satisfy constraints imposed on three inputs and one output. In order to obtain a computationally efficient control scheme, the state-space model is successively linearised on-line for the current operating point and used for prediction. In consequence, the future control policy is easily calculated from a quadratic optimisation problem. For state estimation the extended Kalman filter is used. It is demonstrated that the MPC strategy based on constant linear models does not work satisfactorily for the boiler-turbine unit whereas the discussed algorithm with on-line successive model linearisation gives practically the same trajectories as the truly nonlinear MPC controller with nonlinear optimisation repeated at each sampling instant. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Combined control-structure optimization

NASA Technical Reports Server (NTRS)

Salama, M.; Milman, M.; Bruno, R.; Scheid, R.; Gibson, S.

1989-01-01

An approach for combined control-structure optimization keyed to enhancing early design trade-offs is outlined and illustrated by numerical examples. The approach employs a homotopic strategy and appears to be effective for generating families of designs that can be used in these early trade studies. Analytical results were obtained for classes of structure/control objectives with linear quadratic Gaussian (LQG) and linear quadratic regulator (LQR) costs. For these, researchers demonstrated that global optima can be computed for small values of the homotopy parameter. Conditions for local optima along the homotopy path were also given. Details of two numerical examples employing the LQR control cost were given showing variations of the optimal design variables along the homotopy path. The results of the second example suggest that introducing a second homotopy parameter relating the two parts of the control index in the LQG/LQR formulation might serve to enlarge the family of Pareto optima, but its effect on modifying the optimal structural shapes may be analogous to the original parameter lambda.

Modification of Perioral Stiffness in Patients With Repaired Cleft Lip and Palate

PubMed Central

Barlow, Steven M.; Trotman, Carroll-Ann; Chu, Shin-Ying; Lee, Jaehoon

2013-01-01

Objective To measure and compare the perioral stiffness among three groups of pediatric subjects: a group of patients with a repaired cleft lip (and palate) who had a secondary lip revision surgery (revision), another group of patients with repaired cleft lip (and palate) who did not have secondary surgery (nonrevision), and a group of noncleft “normal” patients (noncleft). Design A parallel, three-group, nonrandomized clinical trial. Participants A total of 16 patients with repaired cleft lip/palate who did not have lip revision, 13 patients with repaired cleft lip/palate who had lip revision surgery and were tested at 18 to 24 months postsurgery, and 27 noncleft patients. Analysis Nonparticipatory perioral stiffness was sampled using a recently developed face-referenced measurement technology known as OroSTIFF. Perioral stiffness, derived as a quotient from resultant force and interangle lip span, was modeled with multilevel regression techniques. Real-time calculation of the perioral stiffness function demonstrated a significant quadratic relation between imposed interangle stretch and resultant force for each of the three groups. Results This nonlinear stiffness growth function was significantly elevated in the nonrevision patients compared with the noncleft controls and is likely due to the presence of scar tissue in the upper lip; it was significantly lower among patients with cleft lip/palate who completed lip revision surgery. Conclusion This study demonstrates the efficacy of applying an objective measurement to map differences in perioral tissue biomechanics among patients born with orofacial clefts. PMID:21247345

A Stochastic Inversion Method for Potential Field Data: Ant Colony Optimization

NASA Astrophysics Data System (ADS)

Liu, Shuang; Hu, Xiangyun; Liu, Tianyou

2014-07-01

Simulating natural ants' foraging behavior, the ant colony optimization (ACO) algorithm performs excellently in combinational optimization problems, for example the traveling salesman problem and the quadratic assignment problem. However, the ACO is seldom used to inverted for gravitational and magnetic data. On the basis of the continuous and multi-dimensional objective function for potential field data optimization inversion, we present the node partition strategy ACO (NP-ACO) algorithm for inversion of model variables of fixed shape and recovery of physical property distributions of complicated shape models. We divide the continuous variables into discrete nodes and ants directionally tour the nodes by use of transition probabilities. We update the pheromone trails by use of Gaussian mapping between the objective function value and the quantity of pheromone. It can analyze the search results in real time and promote the rate of convergence and precision of inversion. Traditional mapping, including the ant-cycle system, weaken the differences between ant individuals and lead to premature convergence. We tested our method by use of synthetic data and real data from scenarios involving gravity and magnetic anomalies. The inverted model variables and recovered physical property distributions were in good agreement with the true values. The ACO algorithm for binary representation imaging and full imaging can recover sharper physical property distributions than traditional linear inversion methods. The ACO has good optimization capability and some excellent characteristics, for example robustness, parallel implementation, and portability, compared with other stochastic metaheuristics.

Polyspectral signal analysis techniques for condition based maintenance of helicopter drive-train system

NASA Astrophysics Data System (ADS)

Hassan Mohammed, Mohammed Ahmed

For an efficient maintenance of a diverse fleet of air- and rotorcraft, effective condition based maintenance (CBM) must be established based on rotating components monitored vibration signals. In this dissertation, we present theory and applications of polyspectral signal processing techniques for condition monitoring of critical components in the AH-64D helicopter tail rotor drive train system. Currently available vibration-monitoring tools are mostly built around auto- and cross-power spectral analysis which have limited performance in detecting frequency correlations higher than second order. Studying higher order correlations and their Fourier transforms, higher order spectra, provides more information about the vibration signals which helps in building more accurate diagnostic models of the mechanical system. Based on higher order spectral analysis, different signal processing techniques are developed to assess health conditions of different critical rotating-components in the AH-64D helicopter drive-train. Based on cross-bispectrum, quadratic nonlinear transfer function is presented to model second order nonlinearity in a drive-shaft running between the two hanger bearings. Then, quadratic-nonlinearity coupling coefficient between frequency harmonics of the rotating shaft is used as condition metric to study different seeded shaft faults compared to baseline case, namely: shaft misalignment, shaft imbalance, and combination of shaft misalignment and imbalance. The proposed quadratic-nonlinearity metric shows better capabilities in distinguishing the four studied shaft settings than the conventional linear coupling based on cross-power spectrum. We also develop a new concept of Quadratic-Nonlinearity Power-Index spectrum, QNLPI(f), that can be used in signal detection and classification, based on bicoherence spectrum. The proposed QNLPI(f) is derived as a projection of the three-dimensional bicoherence spectrum into two-dimensional spectrum that quantitatively describes how much of the mean square power at certain frequency f is generated due to nonlinear quadratic interaction between different frequency components. The proposed index, QNLPI(f), can be used to simplify the study of bispectrum and bicoherence signal spectra. It also inherits useful characteristics from the bicoherence such as high immunity to additive Gaussian noise, high capability of nonlinear-systems identifications, and amplification invariance. The quadratic-nonlinear power spectral density PQNL(f) and percentage of quadratic nonlinear power PQNLP are also introduced based on the QNLPI(f). Concept of the proposed indices and their computational considerations are discussed first using computer generated data, and then applied to real-world vibration data to assess health conditions of different rotating components in the drive train including drive-shaft, gearbox, and hanger bearing faults. The QNLPI(f) spectrum enables us to gain more details about nonlinear harmonic generation patterns that can be used to distinguish between different cases of mechanical faults, which in turn helps to gaining more diagnostic/prognostic capabilities.

A Posteriori Bounds for Linear-Functional Outputs of Crouzeix-Raviart Finite Element Discretizations of the Incompressible Stokes Problem

NASA Technical Reports Server (NTRS)

Patera, Anthony T.; Paraschivoiu, Marius

1998-01-01

We present a finite element technique for the efficient generation of lower and upper bounds to outputs which are linear functionals of the solutions to the incompressible Stokes equations in two space dimensions; the finite element discretization is effected by Crouzeix-Raviart elements, the discontinuous pressure approximation of which is central to our approach. The bounds are based upon the construction of an augmented Lagrangian: the objective is a quadratic "energy" reformulation of the desired output; the constraints are the finite element equilibrium equations (including the incompressibility constraint), and the intersubdomain continuity conditions on velocity. Appeal to the dual max-min problem for appropriately chosen candidate Lagrange multipliers then yields inexpensive bounds for the output associated with a fine-mesh discretization; the Lagrange multipliers are generated by exploiting an associated coarse-mesh approximation. In addition to the requisite coarse-mesh calculations, the bound technique requires solution only of local subdomain Stokes problems on the fine-mesh. The method is illustrated for the Stokes equations, in which the outputs of interest are the flowrate past, and the lift force on, a body immersed in a channel.

A General Family of Limited Information Goodness-of-Fit Statistics for Multinomial Data

ERIC Educational Resources Information Center

Joe, Harry; Maydeu-Olivares, Alberto

2010-01-01

Maydeu-Olivares and Joe (J. Am. Stat. Assoc. 100:1009-1020, "2005"; Psychometrika 71:713-732, "2006") introduced classes of chi-square tests for (sparse) multidimensional multinomial data based on low-order marginal proportions. Our extension provides general conditions under which quadratic forms in linear functions of cell residuals are…

Using Challenging Tasks for Formative Assessment on Quadratic Functions with Senior Secondary Students

ERIC Educational Resources Information Center

Wilkie, Karina J.

2016-01-01

Senior secondary mathematics students who develop conceptual understanding that moves them beyond "rules without reasons" to connections between related concepts are in a strong place to tackle the more difficult mathematics application problems. Current research is examining how the use of challenging tasks at different levels of…

Polynomial Graphs and Symmetry

ERIC Educational Resources Information Center

Goehle, Geoff; Kobayashi, Mitsuo

2013-01-01

Most quadratic functions are not even, but every parabola has symmetry with respect to some vertical line. Similarly, every cubic has rotational symmetry with respect to some point, though most cubics are not odd. We show that every polynomial has at most one point of symmetry and give conditions under which the polynomial has rotational or…

Learning Mathematics with Interactive Whiteboards and Computer-Based Graphing Utility

ERIC Educational Resources Information Center

Erbas, Ayhan Kursat; Ince, Muge; Kaya, Sukru

2015-01-01

The purpose of this study was to explore the effect of a technology-supported learning environment utilizing an interactive whiteboard (IWB) and NuCalc graphing software compared to a traditional direct instruction-based environment on student achievement in graphs of quadratic functions and attitudes towards mathematics and technology. Sixty-five…

A Historical Perspective from "a" to "c"

ERIC Educational Resources Information Center

Edwards, Thomas G.; Ozgun-Koca, S. Asli

2010-01-01

Evolving technology has played an important part in a common quadratic-function lesson. Having been mentioned repeatedly in numerous reform documents, a recurring lesson has involved changing the parameters in f(x) = ax[superscript 2] + bx + c and studying the effects on the graph. In both NCTM Yearbooks and NCTM Standards documents, technology is…

Bicycles, Birds, Bats and Balloons: New Applications for Algebra Classes.

ERIC Educational Resources Information Center

Yoshiwara, Bruce; Yoshiwara, Kathy

This collection of activities is intended to enhance the teaching of college algebra through the use of modeling. The problems use real data and involve the representation and interpretation of the data. The concepts addressed include rates of change, linear and quadratic regression, and functions. The collection consists of eight problems, four…

Self-Efficacy and Interest: Experimental Studies of Optimal Incompetence.

ERIC Educational Resources Information Center

Silvia, Paul J.

2003-01-01

To test the optimal incompetence hypothesis (high self-efficacy lowers task interest), 30 subjects rated interest, perceived difficulty, and confidence of success in different tasks. In study 2, 33 subjects completed a dart-game task in easy, moderate, and difficult conditions. In both, interest was a quadratic function of self-efficacy,…

Effect of Cabri-Assisted Instruction on Secondary School Students' Misconceptions about Graphs of Quadratic Functions

ERIC Educational Resources Information Center

Koklu, Oguz; Topcu, Abdullah

2012-01-01

Pre-existing misconceptions are serious impediments to learning in mathematics. Means for detecting and correcting them have received much attention in the literature of educational research. Dynamic geometry software has been tried at different grade levels. This quasi-experimental study investigates the effect of Cabri-assisted instruction on…

Deriving the Quadratic Regression Equation Using Algebra

ERIC Educational Resources Information Center

Gordon, Sheldon P.; Gordon, Florence S.

2004-01-01

In discussions with leading educators from many different fields, MAA's CRAFTY (Curriculum Renewal Across the First Two Years) committee found that one of the most common mathematical themes in those other disciplines is the idea of fitting a function to a set of data in the least squares sense. The representatives of those partner disciplines…

Synchronization of Lienard-Type Oscillators in Uniform Electrical Networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sinha, Mohit; Dorfler, Florian; Johnson, Brian B.

2016-08-01

This paper presents a condition for global asymptotic synchronization of Lienard-type nonlinear oscillators in uniform LTI electrical networks with series R-L circuits modeling interconnections. By uniform electrical networks, we mean that the per-unit-length impedances are identical for the interconnecting lines. We derive conditions for global asymptotic synchronization for a particular feedback architecture where the derivative of the oscillator output current supplements the innate current feedback induced by simply interconnecting the oscillator to the network. Our proof leverages a coordinate transformation to a set of differential coordinates that emphasizes signal differences and the particular form of feedback permits the formulation ofmore » a quadratic Lyapunov function for this class of networks. This approach is particularly interesting since synchronization conditions are difficult to obtain by means of quadratic Lyapunov functions when only current feedback is used and for networks composed of series R-L circuits. Our synchronization condition depends on the algebraic connectivity of the underlying network, and reiterates the conventional wisdom from Lyapunov- and passivity-based arguments that strong coupling is required to ensure synchronization.« less

Offline handwritten word recognition using MQDF-HMMs

NASA Astrophysics Data System (ADS)

Ramachandrula, Sitaram; Hambarde, Mangesh; Patial, Ajay; Sahoo, Dushyant; Kochar, Shaivi

2015-01-01

We propose an improved HMM formulation for offline handwriting recognition (HWR). The main contribution of this work is using modified quadratic discriminant function (MQDF) [1] within HMM framework. In an MQDF-HMM the state observation likelihood is calculated by a weighted combination of MQDF likelihoods of individual Gaussians of GMM (Gaussian Mixture Model). The quadratic discriminant function (QDF) of a multivariate Gaussian can be rewritten by avoiding the inverse of covariance matrix by using the Eigen values and Eigen vectors of it. The MQDF is derived from QDF by substituting few of badly estimated lower-most Eigen values by an appropriate constant. The estimation errors of non-dominant Eigen vectors and Eigen values of covariance matrix for which the training data is insufficient can be controlled by this approach. MQDF has been successfully shown to improve the character recognition performance [1]. The usage of MQDF in HMM improves the computation, storage and modeling power of HMM when there is limited training data. We have got encouraging results on offline handwritten character (NIST database) and word recognition in English using MQDF HMMs.

Calculation of the electron wave function in a graded-channel double-heterojunction modulation-doped field-effect transistor

NASA Technical Reports Server (NTRS)

Mui, D. S. L.; Patil, M. B.; Morkoc, H.

1989-01-01

Three double-heterojunction modulation-doped field-effect transistor structures with different channel composition are investigated theoretically. All of these transistors have an In(x)Ga(1-x)As channel sandwiched between two doped Al(0.3)Ga(0.7)As barriers with undoped spacer layers. In one of the structures, x varies from 0 from either heterojunction to 0.15 at the center of the channel quadratically; in the other two, constant values of x of 0 and 0.15 are used. The Poisson and Schroedinger equations are solved self-consistently for the electron wave function in all three cases. The results showed that the two-dimensional electron gas (2DEG) concentration in the channel of the quadratically graded structure is higher than the x = 0 one and slightly lower than the x = 0.15 one, and the mean distance of the 2DEG is closer to the center of the channel for this transistor than the other two. These two effects have important implications on the electron mobility in the channel.

Hemoglobin level in older persons and incident Alzheimer disease

PubMed Central

Buchman, A.S.; Wilson, R.S.; Leurgans, S.E.; Bennett, D.A.

2011-01-01

Objective: To test the hypothesis that level of hemoglobin is associated with incident Alzheimer disease (AD). Methods: A total of 881 community-dwelling older persons participating in the Rush Memory and Aging Project without dementia and a measure of hemoglobin level underwent annual cognitive assessments and clinical evaluations for AD. Results: During an average of 3.3 years of follow-up, 113 persons developed AD. In a Cox proportional hazards model adjusted for age, sex, and education, there was a nonlinear relationship between baseline level of hemoglobin such that higher and lower levels of hemoglobin were associated with AD risk (hazard ratio [HR] for the quadratic of hemoglobin 1.06, 95% confidence interval [CI] 1.01–1.11). Findings were unchanged after controlling for multiple covariates. When compared to participants with clinically normal hemoglobin (n = 717), participants with anemia (n = 154) had a 60% increased hazard for developing AD (95% CI 1.02–2.52), as did participants with clinically high hemoglobin (n = 10, HR 3.39, 95% CI 1.25–9.20). Linear mixed-effects models showed that lower and higher hemoglobin levels were associated with a greater rate of global cognitive decline (parameter estimate for quadratic of hemoglobin = −0.008, SE −0.002, p < 0.001). Compared to participants with clinically normal hemoglobin, participants with anemia had a −0.061 z score unit annual decline in global cognitive function (SE 0.012, p < 0.001), as did participants with clinically high hemoglobin (−0.090 unit/year, SE 0.038, p = 0.018). Conclusions: In older persons without dementia, both lower and higher hemoglobin levels are associated with an increased hazard for developing AD and more rapid cognitive decline. PMID:21753176

Comparison of joint space versus task force load distribution optimization for a multiarm manipulator system

NASA Technical Reports Server (NTRS)

Soloway, Donald I.; Alberts, Thomas E.

1989-01-01

It is often proposed that the redundancy in choosing a force distribution for multiple arms grasping a single object should be handled by minimizing a quadratic performance index. The performance index may be formulated in terms of joint torques or in terms of the Cartesian space force/torque applied to the body by the grippers. The former seeks to minimize power consumption while the latter minimizes body stresses. Because the cost functions are related to each other by a joint angle dependent transformation on the weight matrix, it might be argued that either method tends to reduce power consumption, but clearly the joint space minimization is optimal. A comparison of these two options is presented with consideration given to computational cost and power consumption. Simulation results using a two arm robot system are presented to show the savings realized by employing the joint space optimization. These savings are offset by additional complexity, computation time and in some cases processor power consumption.

To construct a stable and tunable optical trap in the focal region of a high numerical aperture lens

NASA Astrophysics Data System (ADS)

Kandasamy, Gokulakrishnan; Ponnan, Suresh; Sivasubramonia Pillai, T. V.; Balasundaram, Rajesh K.

2014-05-01

Based on the diffraction theory, the focusing properties of a radially polarized quadratic Bessel-Gaussian beam (QBG) with on-axis radial phase variance wavefront are investigated theoretically in the focal region of a high numerical aperture (NA) objective lens. The phase wavefront C and pupil beam parameter μ of QBG are the functions of the radial coordinate. The detailed numerical calculation of the focusing property of a QBG beam is presented. The numerical calculation shows that the beam parameter μ and phase parameter C have greater effect on the total electric field intensity distribution. It is observed that under the condition of different μ, evolution principle of focal pattern differs very remarkably on increasing C. Also, some different focal shapes may appear, including rhombic shape, quadrangular shape, two-spherical crust focus shape, two-peak shape, one dark hollow focus, two dark hollow focuses pattern, and triangle dark hollow focus, which find wide optical applications such as optical trapping and nanopatterning.

Quadratic polynomial interpolation on triangular domain

NASA Astrophysics Data System (ADS)

Li, Ying; Zhang, Congcong; Yu, Qian

2018-04-01

In the simulation of natural terrain, the continuity of sample points are not in consonance with each other always, traditional interpolation methods often can't faithfully reflect the shape information which lie in data points. So, a new method for constructing the polynomial interpolation surface on triangular domain is proposed. Firstly, projected the spatial scattered data points onto a plane and then triangulated them; Secondly, A C1 continuous piecewise quadric polynomial patch was constructed on each vertex, all patches were required to be closed to the line-interpolation one as far as possible. Lastly, the unknown quantities were gotten by minimizing the object functions, and the boundary points were treated specially. The result surfaces preserve as many properties of data points as possible under conditions of satisfying certain accuracy and continuity requirements, not too convex meantime. New method is simple to compute and has a good local property, applicable to shape fitting of mines and exploratory wells and so on. The result of new surface is given in experiments.

Vehicle trajectory linearisation to enable efficient optimisation of the constant speed racing line

NASA Astrophysics Data System (ADS)

Timings, Julian P.; Cole, David J.

2012-06-01

A driver model is presented capable of optimising the trajectory of a simple dynamic nonlinear vehicle, at constant forward speed, so that progression along a predefined track is maximised as a function of time. In doing so, the model is able to continually operate a vehicle at its lateral-handling limit, maximising vehicle performance. The technique used forms a part of the solution to the motor racing objective of minimising lap time. A new approach of formulating the minimum lap time problem is motivated by the need for a more computationally efficient and robust tool-set for understanding on-the-limit driving behaviour. This has been achieved through set point-dependent linearisation of the vehicle model and coupling the vehicle-track system using an intrinsic coordinate description. Through this, the geometric vehicle trajectory had been linearised relative to the track reference, leading to new path optimisation algorithm which can be formed as a computationally efficient convex quadratic programming problem.

Application of multivariate statistics to vestibular testing: discriminating between Meniere's disease and migraine associated dizziness

NASA Technical Reports Server (NTRS)

Dimitri, P. S.; Wall, C. 3rd; Oas, J. G.; Rauch, S. D.

2001-01-01

Meniere's disease (MD) and migraine associated dizziness (MAD) are two disorders that can have similar symptomatologies, but differ vastly in treatment. Vestibular testing is sometimes used to help differentiate between these disorders, but the inefficiency of a human interpreter analyzing a multitude of variables independently decreases its utility. Our hypothesis was that we could objectively discriminate between patients with MD and those with MAD using select variables from the vestibular test battery. Sinusoidal harmonic acceleration test variables were reduced to three vestibulo-ocular reflex physiologic parameters: gain, time constant, and asymmetry. A combination of these parameters plus a measurement of reduced vestibular response from caloric testing allowed us to achieve a joint classification rate of 91%, independent quadratic classification algorithm. Data from posturography were not useful for this type of differentiation. Overall, our classification function can be used as an unbiased assistant to discriminate between MD and MAD and gave us insight into the pathophysiologic differences between the two disorders.

Multi-Task Learning with Low Rank Attribute Embedding for Multi-Camera Person Re-Identification.

PubMed

Su, Chi; Yang, Fan; Zhang, Shiliang; Tian, Qi; Davis, Larry Steven; Gao, Wen

2018-05-01

We propose Multi-Task Learning with Low Rank Attribute Embedding (MTL-LORAE) to address the problem of person re-identification on multi-cameras. Re-identifications on different cameras are considered as related tasks, which allows the shared information among different tasks to be explored to improve the re-identification accuracy. The MTL-LORAE framework integrates low-level features with mid-level attributes as the descriptions for persons. To improve the accuracy of such description, we introduce the low-rank attribute embedding, which maps original binary attributes into a continuous space utilizing the correlative relationship between each pair of attributes. In this way, inaccurate attributes are rectified and missing attributes are recovered. The resulting objective function is constructed with an attribute embedding error and a quadratic loss concerning class labels. It is solved by an alternating optimization strategy. The proposed MTL-LORAE is tested on four datasets and is validated to outperform the existing methods with significant margins.

Expected value analysis for integrated supplier selection and inventory control of multi-product inventory system with fuzzy cost

NASA Astrophysics Data System (ADS)

Sutrisno, Widowati, Tjahjana, R. Heru

2017-12-01

The future cost in many industrial problem is obviously uncertain. Then a mathematical analysis for a problem with uncertain cost is needed. In this article, we deals with the fuzzy expected value analysis to solve an integrated supplier selection and supplier selection problem with uncertain cost where the costs uncertainty is approached by a fuzzy variable. We formulate the mathematical model of the problems fuzzy expected value based quadratic optimization with total cost objective function and solve it by using expected value based fuzzy programming. From the numerical examples result performed by the authors, the supplier selection problem was solved i.e. the optimal supplier was selected for each time period where the optimal product volume of all product that should be purchased from each supplier for each time period was determined and the product stock level was controlled as decided by the authors i.e. it was followed the given reference level.

Retrieve polarization aberration from image degradation: a new measurement method in DUV lithography

NASA Astrophysics Data System (ADS)

Xiang, Zhongbo; Li, Yanqiu

2017-10-01

Detailed knowledge of polarization aberration (PA) of projection lens in higher-NA DUV lithographic imaging is necessary due to its impact to imaging degradations, and precise measurement of PA is conductive to computational lithography techniques such as RET and OPC. Current in situ measurement method of PA thorough the detection of degradations of aerial images need to do linear approximation and apply the assumption of 3-beam/2-beam interference condition. The former approximation neglects the coupling effect of the PA coefficients, which would significantly influence the accuracy of PA retrieving. The latter assumption restricts the feasible pitch of test masks in higher-NA system, conflicts with the Kirhhoff diffraction model of test mask used in retrieving model, and introduces 3D mask effect as a source of retrieving error. In this paper, a new in situ measurement method of PA is proposed. It establishes the analytical quadratic relation between the PA coefficients and the degradations of aerial images of one-dimensional dense lines in coherent illumination through vector aerial imaging, which does not rely on the assumption of 3-beam/2- beam interference and linear approximation. In this case, the retrieval of PA from image degradation can be convert from the nonlinear system of m-quadratic equations to a multi-objective quadratic optimization problem, and finally be solved by nonlinear least square method. Some preliminary simulation results are given to demonstrate the correctness and accuracy of the new PA retrieving model.

Bias of cylinder diameter estimation from ground-based laser scanners with different beam widths: A simulation study

NASA Astrophysics Data System (ADS)

Forsman, Mona; Börlin, Niclas; Olofsson, Kenneth; Reese, Heather; Holmgren, Johan

2018-01-01

In this study we have investigated why diameters of tree stems, which are approximately cylindrical, are often overestimated by mobile laser scanning. This paper analyzes the physical processes when using ground-based laser scanning that may contribute to a bias when estimating cylinder diameters using circle-fit methods. A laser scanner simulator was implemented and used to evaluate various properties, such as distance, cylinder diameter, and beam width of a laser scanner-cylinder system to find critical conditions. The simulation results suggest that a positive bias of the diameter estimation is expected. Furthermore, the bias follows a quadratic function of one parameter - the relative footprint, i.e., the fraction of the cylinder width illuminated by the laser beam. The quadratic signature opens up a possibility to construct a compensation model for the bias.

Robust decentralised stabilisation of uncertain large-scale interconnected nonlinear descriptor systems via proportional plus derivative feedback

NASA Astrophysics Data System (ADS)

Li, Jian; Zhang, Qingling; Ren, Junchao; Zhang, Yanhao

2017-10-01

This paper studies the problem of robust stability and stabilisation for uncertain large-scale interconnected nonlinear descriptor systems via proportional plus derivative state feedback or proportional plus derivative output feedback. The basic idea of this work is to use the well-known differential mean value theorem to deal with the nonlinear model such that the considered nonlinear descriptor systems can be transformed into linear parameter varying systems. By using a parameter-dependent Lyapunov function, a decentralised proportional plus derivative state feedback controller and decentralised proportional plus derivative output feedback controller are designed, respectively such that the closed-loop system is quadratically normal and quadratically stable. Finally, a hypersonic vehicle practical simulation example and numerical example are given to illustrate the effectiveness of the results obtained in this paper.

Stochastic Control of Energy Efficient Buildings: A Semidefinite Programming Approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ma, Xiao; Dong, Jin; Djouadi, Seddik M

2015-01-01

The key goal in energy efficient buildings is to reduce energy consumption of Heating, Ventilation, and Air- Conditioning (HVAC) systems while maintaining a comfortable temperature and humidity in the building. This paper proposes a novel stochastic control approach for achieving joint performance and power control of HVAC. We employ a constrained Stochastic Linear Quadratic Control (cSLQC) by minimizing a quadratic cost function with a disturbance assumed to be Gaussian. The problem is formulated to minimize the expected cost subject to a linear constraint and a probabilistic constraint. By using cSLQC, the problem is reduced to a semidefinite optimization problem, wheremore » the optimal control can be computed efficiently by Semidefinite programming (SDP). Simulation results are provided to demonstrate the effectiveness and power efficiency by utilizing the proposed control approach.« less

Thermodynamics of charged Lifshitz black holes with quadratic corrections

NASA Astrophysics Data System (ADS)

Bravo-Gaete, Moisés; Hassaïne, Mokhtar

2015-03-01

In arbitrary dimension, we consider the Einstein-Maxwell Lagrangian supplemented by the more general quadratic-curvature corrections. For this model, we derive four classes of charged Lifshitz black hole solutions for which the metric function is shown to depend on a unique integration constant. The masses of these solutions are computed using the quasilocal formalism based on the relation established between the off-shell Abbott-Deser-Tekin and Noether potentials. Among these four solutions, three of them are interpreted as extremal in the sense that their masses vanish identically. For the last family of solutions, both the quasilocal mass and the electric charge are shown to depend on the integration constant. Finally, we verify that the first law of thermodynamics holds for each solution and a Smarr formula is also established for the four solutions.

Approximating the linear quadratic optimal control law for hereditary systems with delays in the control

NASA Technical Reports Server (NTRS)

Milman, Mark H.

1987-01-01

The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary systems. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.

Ambiguity resolution for satellite Doppler positioning systems

NASA Technical Reports Server (NTRS)

Argentiero, P. D.; Marini, J. W.

1977-01-01

A test for ambiguity resolution was derived which was the most powerful in the sense that it maximized the probability of a correct decision. When systematic error sources were properly included in the least squares reduction process to yield an optimal solution, the test reduced to choosing the solution which provided the smaller valuation of the least squares loss function. When systematic error sources were ignored in the least squares reduction, the most powerful test was a quadratic form comparison with the weighting matrix of the quadratic form obtained by computing the pseudo-inverse of a reduced rank square matrix. A formula is presented for computing the power of the most powerful test. A numerical example is included in which the power of the test is computed for a situation which may occur during an actual satellite aided search and rescue mission.

Biological effects and equivalent doses in radiotherapy: A software solution

PubMed Central

Voyant, Cyril; Julian, Daniel; Roustit, Rudy; Biffi, Katia; Lantieri, Céline

2013-01-01

Background The limits of TDF (time, dose, and fractionation) and linear quadratic models have been known for a long time. Medical physicists and physicians are required to provide fast and reliable interpretations regarding delivered doses or any future prescriptions relating to treatment changes. Aim We, therefore, propose a calculation interface under the GNU license to be used for equivalent doses, biological doses, and normal tumor complication probability (Lyman model). Materials and methods The methodology used draws from several sources: the linear-quadratic-linear model of Astrahan, the repopulation effects of Dale, and the prediction of multi-fractionated treatments of Thames. Results and conclusions The results are obtained from an algorithm that minimizes an ad-hoc cost function, and then compared to an equivalent dose computed using standard calculators in seven French radiotherapy centers. PMID:24936319

Approximating the linear quadratic optimal control law for hereditary systems with delays in the control

NASA Technical Reports Server (NTRS)

Milman, Mark H.

1988-01-01

The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary schemes. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.

Weight Vector Fluctuations in Adaptive Antenna Arrays Tuned Using the Least-Mean-Square Error Algorithm with Quadratic Constraint

NASA Astrophysics Data System (ADS)

Zimina, S. V.

2015-06-01

We present the results of statistical analysis of an adaptive antenna array tuned using the least-mean-square error algorithm with quadratic constraint on the useful-signal amplification with allowance for the weight-coefficient fluctuations. Using the perturbation theory, the expressions for the correlation function and power of the output signal of the adaptive antenna array, as well as the formula for the weight-vector covariance matrix are obtained in the first approximation. The fluctuations are shown to lead to the signal distortions at the antenna-array output. The weight-coefficient fluctuations result in the appearance of additional terms in the statistical characteristics of the antenna array. It is also shown that the weight-vector fluctuations are isotropic, i.e., identical in all directions of the weight-coefficient space.

Accurate evaluation of exchange fields in finite element micromagnetic solvers

NASA Astrophysics Data System (ADS)

Chang, R.; Escobar, M. A.; Li, S.; Lubarda, M. V.; Lomakin, V.

2012-04-01

Quadratic basis functions (QBFs) are implemented for solving the Landau-Lifshitz-Gilbert equation via the finite element method. This involves the introduction of a set of special testing functions compatible with the QBFs for evaluating the Laplacian operator. The results by using QBFs are significantly more accurate than those via linear basis functions. QBF approach leads to significantly more accurate results than conventionally used approaches based on linear basis functions. Importantly QBFs allow reducing the error of computing the exchange field by increasing the mesh density for structured and unstructured meshes. Numerical examples demonstrate the feasibility of the method.

Some New Estimation Methods for Weighted Regression When There are Possible Outliers.

DTIC Science & Technology

1985-01-01

about influential points, and to add to our understanding of the structure of the data In Section 2 we show, by considering the influence function , why... influence function lampel; 1968, 1974) for the maximum likelihood esti- mator is proportional to (EP-l)h(x), where £= (y-x’B)exp[-h’(x)e], and is thus...unbounded. Since the influence function for the MLE is quadratic in the residual c, in theory a point with a sufficiently large residual can have an

Substitution of starch by soluble fiber and Saccharomyces cerevisiae dose response on nutrient digestion and blood metabolites for precision-fed dairy heifers.

PubMed

Lascano, G J; Heinrichs, A J; Tricarico, J M

2012-06-01

The objective of this experiment was to determine the effects of 2 levels of dietary starch and the dose at which the effects of yeast culture (YC) derived from Saccharomyces cerevisiae (Yea-Sacc¹⁰²⁶, Alltech Inc., Nicholasville, KY) were maximized based on nutrient total-tract digestibility (AD), N utilization, and blood metabolites of precision-fed dairy heifers. A split-plot design with starch level as the whole plot and YC dose as subplot was administered in a 4-period (21 d), 4 × 4 Latin square. Eight Holstein heifers (432.49 ± 6.81 kg of body weight) were allocated to 2 starch treatments (28% starch, high starch, HS, or 17% starch, low starch, LS) and to a sequence of YC doses (0, 10, 30, and 50 g/d). Dry matter (DM) and neutral detergent fiber (NDF) AD were not different between HS and LS; however, HS decreased acid detergent fiber (ADF) and increased hemicellulose AD. Digestibility of DM and organic matter (OM) increased quadratically in response to increasing YC dose. Hemicellulose, NDF, and ADF AD increased or tended to increase quadratically with increasing YC dose. No significant effects were noted on fecal or urine output between dietary starch concentrations; YC decreased wet and dry fecal output corresponding to the effect in DM and OM. Apparent N digestibility was greater in the LS group. As YC dose increased, fecal N output decreased quadratically and was lowest at 30 g/d YC. A corresponding quadratic increase was observed for N retention expressed as a percentage of N digested: N output in urine tended to increase with increasing YC dose, resulting in no differences in retained N (g/d). Dietary starch concentration did not affect blood glucose, triglyceride, creatinine, or lactate concentration. However, HS increased plasma urea N concentration. Glucose concentration tended to increase quadratically with daily YC dose in both starch treatments, with the greatest response at 30 g/d. For triglycerides, dietary starch concentration and YC dose interacted, decreasing quadratically in the LS group and increasing in the HS group (lowest and highest value for 10 g/d respectively). We observed a significant time effect for all blood metabolites measured. We conclude that starch level did not affect DM AD, but influenced ADF and hemicellulose AD. Yeast culture had the greatest effect on DM, NDF, ADF, and hemicellulose AD when added at 30 g/d. Addition of YC influenced glucose and triglyceride concentrations differently according to the dietary starch concentration of the diet. Copyright © 2012 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Quadratic Damping

ERIC Educational Resources Information Center

Fay, Temple H.

2012-01-01

Quadratic friction involves a discontinuous damping term in equations of motion in order that the frictional force always opposes the direction of the motion. Perhaps for this reason this topic is usually omitted from beginning texts in differential equations and physics. However, quadratic damping is more realistic than viscous damping in many…

Visualising the Roots of Quadratic Equations with Complex Coefficients

ERIC Educational Resources Information Center

Bardell, Nicholas S.

2014-01-01

This paper is a natural extension of the root visualisation techniques first presented by Bardell (2012) for quadratic equations with real coefficients. Consideration is now given to the familiar quadratic equation "y = ax[superscript 2] + bx + c" in which the coefficients "a," "b," "c" are generally…

Simply Prairie Homepage

Science.gov Websites

Ed Home - Data Home PRAIRIE ADVOCATES Project - QUADRAT STUDY Project Answer research questions multi-state quadrat study. Bob Lootens, Fermilab Join us! Check out the Quadrat Study Project. Prairie study a prairie "expert" to facilitate your research student Internet access an e-mail address

Role of orbital filling on nonlinear ionic Raman scattering in perovskite titanates

NASA Astrophysics Data System (ADS)

Gu, Mingqiang; Rondinelli, James M.

2017-01-01

The linear and nonlinear phononic interactions between an optically excited infrared (IR) or hyper-Raman mode and a driven Raman mode are computed for the d0 (CaTiO3) and d1 (LaTiO3) titanates within a first-principles density functional framework. We calculate the potential energy surface expanded in terms of the Ag or B1 g mode amplitudes coupled to the Au or the B3 u mode and determine the coupling coefficients for these multimode interactions. We find that the linear-quadratic coupling dominates the anharmonicities over the quadratic-quadratic interaction in the perovskite titanates. The IR and Raman modes both modify the electronic structure with the former being more significant but occurring on a different time scale; furthermore, the coupled-mode interactions lead to sizable perturbations to the valence bandwidth (˜100 meV ) and band gap (˜50 meV). By comparing the coupling coefficients of undoped CaTiO3 and LaTiO3 to those for electron-doped (CaTiO3) and hole-doped (LaTiO3) titanates, we isolate the role of orbital filling in the nonlinear coupling process. We find that with increasing occupancy of the d manifold, the linear-quadratic interaction decreases by approximately 30% with minor changes induced by the cation chemistry (that mainly affect the phonon mode frequencies) or by electron correlation. We identify the importance of the Ti-O bond stiffness, which depends on the orbital filling, in governing the lattice anharmonicitiy. This microscopic understanding can be used to increase the nonlinear coupling coefficient to facilitate more facile access of nonequilibrium structures and properties through ionic Raman scattering processes.

Kinematic parameters of internal waves of the second mode in the South China Sea

NASA Astrophysics Data System (ADS)

Kurkina, Oxana; Talipova, Tatyana; Soomere, Tarmo; Giniyatullin, Ayrat; Kurkin, Andrey

2017-10-01

Spatial distributions of the main properties of the mode function and kinematic and non-linear parameters of internal waves of the second mode are derived for the South China Sea for typical summer conditions in July. The calculations are based on the Generalized Digital Environmental Model (GDEM) climatology of hydrological variables, from which the local stratification is evaluated. The focus is on the phase speed of long internal waves and the coefficients at the dispersive, quadratic and cubic terms of the weakly non-linear Gardner model. Spatial distributions of these parameters, except for the coefficient at the cubic term, are qualitatively similar for waves of both modes. The dispersive term of Gardner's equation and phase speed for internal waves of the second mode are about a quarter and half, respectively, of those for waves of the first mode. Similarly to the waves of the first mode, the coefficients at the quadratic and cubic terms of Gardner's equation are practically independent of water depth. In contrast to the waves of the first mode, for waves of the second mode the quadratic term is mostly negative. The results can serve as a basis for expressing estimates of the expected parameters of internal waves for the South China Sea.

Analysis of Maneuvering Targets with Complex Motions by Two-Dimensional Product Modified Lv's Distribution for Quadratic Frequency Modulation Signals.

PubMed

Jing, Fulong; Jiao, Shuhong; Hou, Changbo; Si, Weijian; Wang, Yu

2017-06-21

For targets with complex motion, such as ships fluctuating with oceanic waves and high maneuvering airplanes, azimuth echo signals can be modeled as multicomponent quadratic frequency modulation (QFM) signals after migration compensation and phase adjustment. For the QFM signal model, the chirp rate (CR) and the quadratic chirp rate (QCR) are two important physical quantities, which need to be estimated. For multicomponent QFM signals, the cross terms create a challenge for detection, which needs to be addressed. In this paper, by employing a novel multi-scale parametric symmetric self-correlation function (PSSF) and modified scaled Fourier transform (mSFT), an effective parameter estimation algorithm is proposed-referred to as the Two-Dimensional product modified Lv's distribution (2D-PMLVD)-for QFM signals. The 2D-PMLVD is simple and can be easily implemented by using fast Fourier transform (FFT) and complex multiplication. These measures are analyzed in the paper, including the principle, the cross term, anti-noise performance, and computational complexity. Compared to the other three representative methods, the 2D-PMLVD can achieve better anti-noise performance. The 2D-PMLVD, which is free of searching and has no identifiability problems, is more suitable for multicomponent situations. Through several simulations and analyses, the effectiveness of the proposed estimation algorithm is verified.

Formalism for the solution of quadratic Hamiltonians with large cosine terms

NASA Astrophysics Data System (ADS)

Ganeshan, Sriram; Levin, Michael

2016-02-01

We consider quantum Hamiltonians of the form H =H0-U ∑jcos(Cj) , where H0 is a quadratic function of position and momentum variables {x1,p1,x2,p2,⋯} and the Cj's are linear in these variables. We allow H0 and Cj to be completely general with only two restrictions: we require that (1) the Cj's are linearly independent and (2) [Cj,Ck] is an integer multiple of 2 π i for all j ,k so that the different cosine terms commute with one another. Our main result is a recipe for solving these Hamiltonians and obtaining their exact low-energy spectrum in the limit U →∞ . This recipe involves constructing creation and annihilation operators and is similar in spirit to the procedure for diagonalizing quadratic Hamiltonians. In addition to our exact solution in the infinite U limit, we also discuss how to analyze these systems when U is large but finite. Our results are relevant to a number of different physical systems, but one of the most natural applications is to understanding the effects of electron scattering on quantum Hall edge modes. To demonstrate this application, we use our formalism to solve a toy model for a fractional quantum spin Hall edge with different types of impurities.

Geometric quadratic stochastic operator on countable infinite set

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar

2015-02-03

In this paper we construct the family of Geometric quadratic stochastic operators defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. Such operators can be reinterpreted in terms of of evolutionary operator of free population. We show that Geometric quadratic stochastic operators are regular transformations.

Estimating factors influencing the detection probability of semiaquatic freshwater snails using quadrat survey methods

USGS Publications Warehouse

Roesler, Elizabeth L.; Grabowski, Timothy B.

2018-01-01

Developing effective monitoring methods for elusive, rare, or patchily distributed species requires extra considerations, such as imperfect detection. Although detection is frequently modeled, the opportunity to assess it empirically is rare, particularly for imperiled species. We used Pecos assiminea (Assiminea pecos), an endangered semiaquatic snail, as a case study to test detection and accuracy issues surrounding quadrat searches. Quadrats (9 × 20 cm; n = 12) were placed in suitable Pecos assiminea habitat and randomly assigned a treatment, defined as the number of empty snail shells (0, 3, 6, or 9). Ten observers rotated through each quadrat, conducting 5-min visual searches for shells. The probability of detecting a shell when present was 67.4 ± 3.0%, but it decreased with the increasing litter depth and fewer number of shells present. The mean (± SE) observer accuracy was 25.5 ± 4.3%. Accuracy was positively correlated to the number of shells in the quadrat and negatively correlated to the number of times a quadrat was searched. The results indicate quadrat surveys likely underrepresent true abundance, but accurately determine the presence or absence. Understanding detection and accuracy of elusive, rare, or imperiled species improves density estimates and aids in monitoring and conservation efforts.

Clarifying functional roles: algal removal by the surgeonfishes Ctenochaetus striatus and Acanthurus nigrofuscus

NASA Astrophysics Data System (ADS)

Tebbett, Sterling B.; Goatley, Christopher H. R.; Bellwood, David R.

2017-09-01

The lined bristletooth, Ctenochaetus striatus, and the brown surgeonfish, Acanthurus nigrofuscus, are among the most abundant surgeonfishes on Indo-Pacific coral reefs. Yet, the functional role of these species has been the focus of an ongoing debate lasting at least six decades. Specifically, to what extent are C. striatus herbivorous like the visually similar A. nigrofuscus? To address this question, we used natural feeding surfaces, covered with late successional stage reef-grown algal turfs, to examine turf algal removal by the two species. Surfaces exposed to C. striatus in laboratory experiments exhibited no significant reductions in turf length or area covered by turfing algae. In marked contrast, A. nigrofuscus reduced turf length by 51% and area covered by turfing algae by 15% in 1 h. The gut contents of specimens from the reef revealed that A. nigrofuscus predominantly ingests algae (the dominant item in 79.6-94.7% of gut content quadrats), while C. striatus ingests detritus and sediments (dominant in 99.6-100% of quadrats). Therefore, C. striatus ingests detritus and sediment, leaving mature algal turfs relatively intact, while A. nigrofuscus directly removes and ingests turf algae. The function of C. striatus differs from cropping herbivorous surgeonfishes such as A. nigrofuscus. On coral reefs, C. striatus brush detrital aggregates from algal turfs, removing microorganisms, organic detritus and inorganic sediment. Confusion over the functional role of C. striatus may stem from an inability to fit it into a single functional category.

Price-Dynamics of Shares and Bohmian Mechanics: Deterministic or Stochastic Model?

NASA Astrophysics Data System (ADS)

Choustova, Olga

2007-02-01

We apply the mathematical formalism of Bohmian mechanics to describe dynamics of shares. The main distinguishing feature of the financial Bohmian model is the possibility to take into account market psychology by describing expectations of traders by the pilot wave. We also discuss some objections (coming from conventional financial mathematics of stochastic processes) against the deterministic Bohmian model. In particular, the objection that such a model contradicts to the efficient market hypothesis which is the cornerstone of the modern market ideology. Another objection is of pure mathematical nature: it is related to the quadratic variation of price trajectories. One possibility to reply to this critique is to consider the stochastic Bohm-Vigier model, instead of the deterministic one. We do this in the present note.

An efficient inverse radiotherapy planning method for VMAT using quadratic programming optimization.

PubMed

Hoegele, W; Loeschel, R; Merkle, N; Zygmanski, P

2012-01-01

The purpose of this study is to investigate the feasibility of an inverse planning optimization approach for the Volumetric Modulated Arc Therapy (VMAT) based on quadratic programming and the projection method. The performance of this method is evaluated against a reference commercial planning system (eclipse(TM) for rapidarc(TM)) for clinically relevant cases. The inverse problem is posed in terms of a linear combination of basis functions representing arclet dose contributions and their respective linear coefficients as degrees of freedom. MLC motion is decomposed into basic motion patterns in an intuitive manner leading to a system of equations with a relatively small number of equations and unknowns. These equations are solved using quadratic programming under certain limiting physical conditions for the solution, such as the avoidance of negative dose during optimization and Monitor Unit reduction. The modeling by the projection method assures a unique treatment plan with beneficial properties, such as the explicit relation between organ weightings and the final dose distribution. Clinical cases studied include prostate and spine treatments. The optimized plans are evaluated by comparing isodose lines, DVH profiles for target and normal organs, and Monitor Units to those obtained by the clinical treatment planning system eclipse(TM). The resulting dose distributions for a prostate (with rectum and bladder as organs at risk), and for a spine case (with kidneys, liver, lung and heart as organs at risk) are presented. Overall, the results indicate that similar plan qualities for quadratic programming (QP) and rapidarc(TM) could be achieved at significantly more efficient computational and planning effort using QP. Additionally, results for the quasimodo phantom [Bohsung et al., "IMRT treatment planning: A comparative inter-system and inter-centre planning exercise of the estro quasimodo group," Radiother. Oncol. 76(3), 354-361 (2005)] are presented as an example for an extreme concave case. Quadratic programming is an alternative approach for inverse planning which generates clinically satisfying plans in comparison to the clinical system and constitutes an efficient optimization process characterized by uniqueness and reproducibility of the solution.

Extremal entanglement witnesses

NASA Astrophysics Data System (ADS)

Hansen, Leif Ove; Hauge, Andreas; Myrheim, Jan; Sollid, Per Øyvind

2015-02-01

We present a study of extremal entanglement witnesses on a bipartite composite quantum system. We define the cone of witnesses as the dual of the set of separable density matrices, thus TrΩρ≥0 when Ω is a witness and ρ is a pure product state, ρ=ψψ† with ψ=ϕ⊗χ. The set of witnesses of unit trace is a compact convex set, uniquely defined by its extremal points. The expectation value f(ϕ,χ)=TrΩρ as a function of vectors ϕ and χ is a positive semidefinite biquadratic form. Every zero of f(ϕ,χ) imposes strong real-linear constraints on f and Ω. The real and symmetric Hessian matrix at the zero must be positive semidefinite. Its eigenvectors with zero eigenvalue, if such exist, we call Hessian zeros. A zero of f(ϕ,χ) is quadratic if it has no Hessian zeros, otherwise it is quartic. We call a witness quadratic if it has only quadratic zeros, and quartic if it has at least one quartic zero. A main result we prove is that a witness is extremal if and only if no other witness has the same, or a larger, set of zeros and Hessian zeros. A quadratic extremal witness has a minimum number of isolated zeros depending on dimensions. If a witness is not extremal, then the constraints defined by its zeros and Hessian zeros determine all directions in which we may search for witnesses having more zeros or Hessian zeros. A finite number of iterated searches in random directions, by numerical methods, leads to an extremal witness which is nearly always quadratic and has the minimum number of zeros. We discuss briefly some topics related to extremal witnesses, in particular the relation between the facial structures of the dual sets of witnesses and separable states. We discuss the relation between extremality and optimality of witnesses, and a conjecture of separability of the so-called structural physical approximation (SPA) of an optimal witness. Finally, we discuss how to treat the entanglement witnesses on a complex Hilbert space as a subset of the witnesses on a real Hilbert space.

Explicit asymmetric bounds for robust stability of continuous and discrete-time systems

NASA Technical Reports Server (NTRS)

Gao, Zhiqiang; Antsaklis, Panos J.

1993-01-01

The problem of robust stability in linear systems with parametric uncertainties is considered. Explicit stability bounds on uncertain parameters are derived and expressed in terms of linear inequalities for continuous systems, and inequalities with quadratic terms for discrete-times systems. Cases where system parameters are nonlinear functions of an uncertainty are also examined.

Orientations toward Mathematical Processes of Prospective Secondary Mathematics Teachers as Related to Work with Tasks

ERIC Educational Resources Information Center

Cannon, Tenille

2016-01-01

Mathematics can be conceptualized in different ways. Policy documents such as the National Council of Teachers of Mathematics (NCTM) (2000) and the Common Core State Standards Initiative (CCSSI) (2010), classify mathematics in terms of mathematical content (e.g., quadratic functions, Pythagorean theorem) and mathematical activity in the form of…

Compact Numerical Function Generators Based on Quadratic Approximation: Architecture and Synthesis Method

DTIC Science & Technology

2006-12-01

Specifi- cation described by Scilab [19], a MATLAB-like software, into HDL code. The Design Specification consists of a func- tion f (x), a domain over x...In- ter. Conf. on Field Programmable Logic and Applications (FPL’05), pp.118–123, Tampere, Finland, Aug. 2005. [19] Scilab 3.0, INRIA-ENPC, France

Programmable Numerical Function Generators Based on Quadratic Approximation: Architecture and Synthesis Method

DTIC Science & Technology

2006-01-01

experts. Fig. 1 shows the synthesis flow for the NFG. It converts the Design Specification described by Scilab [18], a MATLAB-like software, into HDL...Tam- pare, Finland, pp. 118–123, Aug. 2005. [18] Scilab 3.0, INRIA-ENPC, France, http://scilabsoft.inria.fr/ [19] M. J. Schulte and J. E. Stine

An Application of Quadratic Functions to Australian Government Policy on Funding Schools

ERIC Educational Resources Information Center

Nillsen, Rodney

2007-01-01

In the "Sydney Morning Herald" of 23 March 2005, Ross Gittins argued that the funding arrangements for private schools positively encourage parents to move their children from the state system. The then Federal Minister for Education, Dr Brendan Nelson, in a letter to the "Herald" of 25-27 March, responded by saying that 68% of…

Analytical Description of Ascending Motion of Rockets in the Atmosphere

ERIC Educational Resources Information Center

Rodrigues, H.; de Pinho, M. O.; Portes, D., Jr.; Santiago, A.

2009-01-01

In continuation of a previous work, we present an analytic study of ascending vertical motion of a rocket subjected to a quadratic drag for the case where the mass-variation law is a linear function of time. We discuss the detailed analytical solution of the model differential equations in closed form. Examples of application are presented and…

Effects of gypsy moth infestation on near-view aesthetic preferences and recreation behavior intentions

Treesearch

S.J. Hollenhorst; S.M. Brock; W.A. Freimund; M.J. Twery

1991-01-01

Using the Scenic Beauty Estimator (SBE) approach, near-view color photographs were taken of 25 forested sites exhibiting gypsy moth induced tree mortality from 6% - 97%. A quadratic function of tree mortality by preference rating best described the variability in ratings ( R2 = .60). The effect of flowering mountain laurel flowers was also...

On deformation of complex continuum immersed in a plane space

NASA Astrophysics Data System (ADS)

Kovalev, V. A.; Murashkin, E. V.; Radayev, Y. N.

2018-05-01

The present paper is devoted to mathematical modelling of complex continua deformations considered as immersed in an external plane space. The complex continuum is defined as a differential manifold supplied with metrics induced by the external space. A systematic derivation of strain tensors by notion of isometric immersion of the complex continuum into a plane space of a higher dimension is proposed. Problem of establishing complete systems of irreducible objective strain and extrastrain tensors for complex continuum immersed in an external plane space is resolved. The solution to the problem is obtained by methods of the field theory and the theory of rational algebraic invariants. Strain tensors of the complex continuum are derived as irreducible algebraic invariants of contravariant vectors of the external space emerging as functional arguments in the complex continuum action density. Present analysis is restricted to rational algebraic invariants. Completeness of the considered systems of rational algebraic invariants is established for micropolar elastic continua. Rational syzygies for non-quadratic invariants are discussed. Objective strain tensors (indifferent to frame rotations in the external plane space) for micropolar continuum are alternatively obtained by properly combining multipliers of polar decompositions of deformation and extra-deformation gradients. The latter is realized only for continua immersed in a plane space of the equal mathematical dimension.

Optimization of LED light spectrum to enhance colorfulness of illuminated objects with white light constraints.

PubMed

Wu, Haining; Dong, Jianfei; Qi, Gaojin; Zhang, Guoqi

2015-07-01

Enhancing the colorfulness of illuminated objects is a promising application of LED lighting for commercial, exhibiting, and scientific purposes. This paper proposes a method to enhance the color of illuminated objects for a given polychromatic lamp. Meanwhile, the light color is restricted to white. We further relax the white light constraints by introducing soft margins. Based on the spectral and electrical characteristics of LEDs and object surface properties, we determine the optimal mixing of the LED light spectrum by solving a numerical optimization problem, which is a quadratic fractional programming problem by formulation. Simulation studies show that the trade-off between the white light constraint and the level of the color enhancement can be adjusted by tuning an upper limit value of the soft margin. Furthermore, visual evaluation experiments are performed to evaluate human perception of the color enhancement. The experiments have verified the effectiveness of the proposed method.

Some Paradoxical Results for the Quadratically Weighted Kappa

ERIC Educational Resources Information Center

Warrens, Matthijs J.

2012-01-01

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

Quadratic elongation: A quantitative measure of distortion in coordination polyhedra

USGS Publications Warehouse

Robinson, Kelly F.; Gibbs, G.V.; Ribbe, P.H.

1971-01-01

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

Analysis of Students' Error in Learning of Quadratic Equations

ERIC Educational Resources Information Center

Zakaria, Effandi; Ibrahim; Maat, Siti Mistima

2010-01-01

The purpose of the study was to determine the students' error in learning quadratic equation. The samples were 30 form three students from a secondary school in Jambi, Indonesia. Diagnostic test was used as the instrument of this study that included three components: factorization, completing the square and quadratic formula. Diagnostic interview…

No Evidence of Causal Effects of Blood Pressure on Cognition in the Population at Large.

PubMed

Swagerman, Suzanne C; van Bergen, Elsje; Kan, Kees-Jan; Koenis, Marinka M G; Hulshoff Pol, Hilleke E; Boomsma, Dorret I; de Geus, Eco J C

2016-02-01

The large body of literature on the association between blood pressure (BP) and cognitive functioning has yielded mixed results, possibly due to the presence of non-linear effects across age, or because BP affects specific brain areas differently, impacting more on some cognitive skills than on others. If a robust association was detected among BP and specific cognitive tasks, the causal nature of reported associations between BP and cognition could be investigated in twin data, which allow a test of alternative explanations, including genetic pleiotropy. The present study first examines the association between BP and cognition in a sample of 1,140 participants with an age range between 10 and 86 years. Linear and quadratic effects of systolic BP (SBP) and diastolic BP (DBP) on cognitive functioning were examined for 17 tests across five functions. Associations were corrected for effects of sex and linear and quadratic effects of age. Second, to test a causal model, data from 123 monozygotic (MZ) twin pairs were analyzed to test whether cognitive functioning of the twins with the higher BP was different from that of the co-twins with lower BP. Associations between BP and cognitive functioning were absent for the majority of the cognitive tests, with the exception of a lower speed of emotion identification and verbal reasoning in subjects with high diastolic BP. In the MZ twin pair analyses, no effects of BP on cognition were found. We conclude that in the population at large, BP level is not associated with cognitive functioning in a clinically meaningful way.

Steepest descent with momentum for quadratic functions is a version of the conjugate gradient method.

PubMed

Bhaya, Amit; Kaszkurewicz, Eugenius

2004-01-01

It is pointed out that the so called momentum method, much used in the neural network literature as an acceleration of the backpropagation method, is a stationary version of the conjugate gradient method. Connections with the continuous optimization method known as heavy ball with friction are also made. In both cases, adaptive (dynamic) choices of the so called learning rate and momentum parameters are obtained using a control Liapunov function analysis of the system.

Graded-index fibers, Wigner-distribution functions, and the fractional Fourier transform.

PubMed

Mendlovic, D; Ozaktas, H M; Lohmann, A W

1994-09-10

Two definitions of a fractional Fourier transform have been proposed previously. One is based on the propagation of a wave field through a graded-index medium, and the other is based on rotating a function's Wigner distribution. It is shown that both definitions are equivalent. An important result of this equivalency is that the Wigner distribution of a wave field rotates as the wave field propagates through a quadratic graded-index medium. The relation with ray-optics phase space is discussed.

Number Theoretic Background

NASA Astrophysics Data System (ADS)

Rudnick, Z.

Contents: 1. Introduction 2. Divisibility 2.1. Basics on Divisibility 2.2. The Greatest Common Divisor 2.3. The Euclidean Algorithm 2.4. The Diophantine Equation ax+by=c 3. Prime Numbers 3.1. The Fundamental Theorem of Arithmetic 3.2. There Are Infinitely Many Primes 3.3. The Density of Primes 3.4. Primes in Arithmetic Progressions 4. Continued Fractions 5. Modular Arithmetic 5.1. Congruences 5.2. Modular Inverses 5.3. The Chinese Remainder Theorem 5.4. The Structure of the Multiplicative Group (Z/NZ)^* 5.5. Primitive Roots 6. Quadratic Congruences 6.1. Euler's Criterion 6.2. The Legendre Symbol and Quadratic Reciprocity 7. Pell's Equation 7.1. The Group Law 7.2. Integer Solutions 7.3. Finding the Fundamental Solution 8. The Riemann Zeta Function 8.1 Analytic Continuation and Functinal Equation of ζ(s) 8.2 Connecting the Primes and the Zeros of ζ(s) 8.3 The Riemann Hypothesis References

Limit Cycle Bifurcations Near a Piecewise Smooth Generalized Homoclinic Loop with a Saddle-Fold Point

NASA Astrophysics Data System (ADS)

Liang, Feng; Wang, Dechang

In this paper, we suppose that a planar piecewise Hamiltonian system, with a straight line of separation, has a piecewise generalized homoclinic loop passing through a Saddle-Fold point, and assume that there exists a family of piecewise smooth periodic orbits near the loop. By studying the asymptotic expansion of the first order Melnikov function corresponding to the period annulus, we obtain the formulas of the first six coefficients in the expansion, based on which, we provide a lower bound for the maximal number of limit cycles bifurcated from the period annulus. As applications, two concrete systems are considered. Especially, the first one reveals that a quadratic piecewise Hamiltonian system can have five limit cycles near a generalized homoclinic loop under a quadratic piecewise smooth perturbation. Compared with the smooth case [Horozov & Iliev, 1994; Han et al., 1999], three more limit cycles are found.

Stochastic Multiresonance for a Fractional Linear Oscillator with Quadratic Trichotomous Noise

NASA Astrophysics Data System (ADS)

Zhu, Jian-Qu; Jin, Wei-Dong; Zheng, Gao; Guo, Feng

2017-11-01

The stochastic multiresonance behavior for a fractional linear oscillator with random system frequency is investigated. The fluctuation of the system frequency is a quadratic trichotomous noise, the memory kernel of the fractional oscillator is modeled as a Mittag-Leffler function. Based on linear system theory, applying Laplace transform and the definition of fractional derivative, the expression of the system output amplitude (SPA) is obtained. Stochastic multiresonance phenomenon is found on the curves of SPA versus the memory time and the memory exponent of the fractional oscillator, as well as versus the trichotomous noise amplitude. The SPA depends non-monotonically on the stationary probability of the trichotomous noise, on the viscous damping coefficient and system characteristic frequency of the oscillator, as well as on the driving frequency of external force. Supported by National Natural Science Foundation of China under Grant No. 61134002

Microgravity vibration isolation: An optimal control law for the one-dimensional case

NASA Technical Reports Server (NTRS)

Hampton, Richard D.; Grodsinsky, Carlos M.; Allaire, Paul E.; Lewis, David W.; Knospe, Carl R.

1991-01-01

Certain experiments contemplated for space platforms must be isolated from the accelerations of the platform. An optimal active control is developed for microgravity vibration isolation, using constant state feedback gains (identical to those obtained from the Linear Quadratic Regulator (LQR) approach) along with constant feedforward gains. The quadratic cost function for this control algorithm effectively weights external accelerations of the platform disturbances by a factor proportional to (1/omega) exp 4. Low frequency accelerations are attenuated by greater than two orders of magnitude. The control relies on the absolute position and velocity feedback of the experiment and the absolute position and velocity feedforward of the platform, and generally derives the stability robustness characteristics guaranteed by the LQR approach to optimality. The method as derived is extendable to the case in which only the relative positions and velocities and the absolute accelerations of the experiment and space platform are available.

Cylindrically symmetric cosmological model of the universe in modified gravity

NASA Astrophysics Data System (ADS)

Mishra, B.; Vadrevu, Samhita

2017-02-01

In this paper, we have constructed the cosmological models of the universe in a cylindrically symmetric space time in two classes of f(R,T) gravity (Harko et al. in Phys. Rev. D 84:024020, 2011). We have discussed two cases: one in the linear form and the other in the quadratic form of R. The matter is considered to be in the form of perfect fluid. It is observed that in the first case, the pressure and energy density remain the same, which reduces to a Zeldovich fluid. In the second case we have studied the quadratic function of f(R,T) gravity in the form f(R)=λ(R+R2) and f(T)=λ T. In the second case the pressure is in the negative domain and the energy density is in the positive domain, which confirms that the equation of state parameter is negative. The physical properties of the constructed models are studied.

2dFLenS and KiDS: determining source redshift distributions with cross-correlations

NASA Astrophysics Data System (ADS)

Johnson, Andrew; Blake, Chris; Amon, Alexandra; Erben, Thomas; Glazebrook, Karl; Harnois-Deraps, Joachim; Heymans, Catherine; Hildebrandt, Hendrik; Joudaki, Shahab; Klaes, Dominik; Kuijken, Konrad; Lidman, Chris; Marin, Felipe A.; McFarland, John; Morrison, Christopher B.; Parkinson, David; Poole, Gregory B.; Radovich, Mario; Wolf, Christian

2017-03-01

We develop a statistical estimator to infer the redshift probability distribution of a photometric sample of galaxies from its angular cross-correlation in redshift bins with an overlapping spectroscopic sample. This estimator is a minimum-variance weighted quadratic function of the data: a quadratic estimator. This extends and modifies the methodology presented by McQuinn & White. The derived source redshift distribution is degenerate with the source galaxy bias, which must be constrained via additional assumptions. We apply this estimator to constrain source galaxy redshift distributions in the Kilo-Degree imaging survey through cross-correlation with the spectroscopic 2-degree Field Lensing Survey, presenting results first as a binned step-wise distribution in the range z < 0.8, and then building a continuous distribution using a Gaussian process model. We demonstrate the robustness of our methodology using mock catalogues constructed from N-body simulations, and comparisons with other techniques for inferring the redshift distribution.

Influence of salinity and temperature on acute toxicity of cadmium to Mysidopsis bahia molenock

DOE Office of Scientific and Technical Information (OSTI.GOV)

Voyer, R.A.; Modica, G.

1990-01-01

Acute toxicity tests were conducted to compare estimates of toxicity, as modified by salinity and temperature, based on response surface techniques with those derived using conventional test methods, and to compare effect of a single episodic exposure to cadmium as a function of salinity with that of continuous exposure. Regression analysis indicated that mortality following continuous 96-hr exposure is related to linear and quadratic effects of salinity and cadmium at 20 C, and to the linear and quadratic effects of cadmium only at 25C. LC50s decreased with increases in temperature and decreases in salinity. Based on the regression model developed,more » 96-hr LC50s ranged from 15.5 to 28.0 micro Cd/L at 10 and 30% salinities, respectively, at 25C; and from 47 to 85 microgram Cd/L at these salinities at 20C.« less

Nonparametric entropy estimation using kernel densities.

PubMed

Lake, Douglas E

2009-01-01

The entropy of experimental data from the biological and medical sciences provides additional information over summary statistics. Calculating entropy involves estimates of probability density functions, which can be effectively accomplished using kernel density methods. Kernel density estimation has been widely studied and a univariate implementation is readily available in MATLAB. The traditional definition of Shannon entropy is part of a larger family of statistics, called Renyi entropy, which are useful in applications that require a measure of the Gaussianity of data. Of particular note is the quadratic entropy which is related to the Friedman-Tukey (FT) index, a widely used measure in the statistical community. One application where quadratic entropy is very useful is the detection of abnormal cardiac rhythms, such as atrial fibrillation (AF). Asymptotic and exact small-sample results for optimal bandwidth and kernel selection to estimate the FT index are presented and lead to improved methods for entropy estimation.

Quadratic time dependent Hamiltonians and separation of variables

NASA Astrophysics Data System (ADS)

Anzaldo-Meneses, A.

2017-06-01

Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green's function is obtained and a comparison with the classical Hamilton-Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei-Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü-Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems.

Regions of attraction and ultimate boundedness for linear quadratic regulators with nonlinearities

NASA Technical Reports Server (NTRS)

Joshi, S. M.

1984-01-01

The closed-loop stability of multivariable linear time-invariant systems controlled by optimal linear quadratic (LQ) regulators is investigated for the case when the feedback loops have nonlinearities N(sigma) that violate the standard stability condition, sigma N(sigma) or = 0.5 sigma(2). The violations of the condition are assumed to occur either (1) for values of sigma away from the origin (sigma = 0) or (2) for values of sigma in a neighborhood of the origin. It is proved that there exists a region of attraction for case (1) and a region of ultimate boundedness for case (2), and estimates are obtained for these regions. The results provide methods for selecting the performance function parameters to design LQ regulators with better tolerance to nonlinearities. The results are demonstrated by application to the problem of attitude and vibration control of a large, flexible space antenna in the presence of actuator nonlinearities.

Microgravity vibration isolation: An optimal control law for the one-dimensional case

NASA Technical Reports Server (NTRS)

Hampton, R. D.; Grodsinsky, C. M.; Allaire, P. E.; Lewis, D. W.; Knospe, C. R.

1991-01-01

Certain experiments contemplated for space platforms must be isolated from the accelerations of the platforms. An optimal active control is developed for microgravity vibration isolation, using constant state feedback gains (identical to those obtained from the Linear Quadratic Regulator (LQR) approach) along with constant feedforward (preview) gains. The quadratic cost function for this control algorithm effectively weights external accelerations of the platform disturbances by a factor proportional to (1/omega)(exp 4). Low frequency accelerations (less than 50 Hz) are attenuated by greater than two orders of magnitude. The control relies on the absolute position and velocity feedback of the experiment and the absolute position and velocity feedforward of the platform, and generally derives the stability robustness characteristics guaranteed by the LQR approach to optimality. The method as derived is extendable to the case in which only the relative positions and velocities and the absolute accelerations of the experiment and space platform are available.

Analysis of mutagenic DNA repair in a thermoconditional mutant of Saccharomyces cerevisiae. III. Dose-response pattern of mutation induction in UV-irradiated rev2ts cells.

PubMed

Siede, W; Eckardt, F

1986-01-01

Recent studies regarding the influence of cycloheximide on the temperature-dependent increase in survival and mutation frequencies of a thermoconditional rev2 mutant lead to the suggestion that the REV2-coded mutagenic repair function is UV-inducible. In the present study we show that stationary-phase rev2ts cells are characterized by a biphasic linear-quadratic dose-dependence of mutation induction ("mutation kinetics") of ochre alleles at 23 degrees C (permissive temperature) but linear kinetics at the restrictive temperature of 36 degrees C. Mathematical analysis using a model based on Poisson statistics and a further mathematical procedure, the calculation of "apparent survival", support the assumption that the quadratic component of the reverse mutation kinetics investigated can be attributed to a UV-inducible component of mutagenic DNA repair controlled by the REV2 gene.

Portfolio optimization using fuzzy linear programming

NASA Astrophysics Data System (ADS)

Pandit, Purnima K.

2013-09-01

Portfolio Optimization (PO) is a problem in Finance, in which investor tries to maximize return and minimize risk by carefully choosing different assets. Expected return and risk are the most important parameters with regard to optimal portfolios. In the simple form PO can be modeled as quadratic programming problem which can be put into equivalent linear form. PO problems with the fuzzy parameters can be solved as multi-objective fuzzy linear programming problem. In this paper we give the solution to such problems with an illustrative example.

A multilevel control approach for a modular structured space platform

NASA Technical Reports Server (NTRS)

Chichester, F. D.; Borelli, M. T.

1981-01-01

A three axis mathematical representation of a modular assembled space platform consisting of interconnected discrete masses, including a deployable truss module, was derived for digital computer simulation. The platform attitude control system as developed to provide multilevel control utilizing the Gauss-Seidel second level formulation along with an extended form of linear quadratic regulator techniques. The objectives of the multilevel control are to decouple the space platform's spatial axes and to accommodate the modification of the platform's configuration for each of the decoupled axes.

Effects of Classroom Instruction on Students' Understanding of Quadratic Equations

ERIC Educational Resources Information Center

Vaiyavutjamai, Pongchawee; Clements, M. A.

2006-01-01

Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of…

Sketching the General Quadratic Equation Using Dynamic Geometry Software

ERIC Educational Resources Information Center

Stols, G. H.

2005-01-01

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

Wilson polynomials/functions and intertwining operators for the generic quantum superintegrable system on the 2-sphere

NASA Astrophysics Data System (ADS)

Miller, W., Jr.; Li, Q.

2015-04-01

The Wilson and Racah polynomials can be characterized as basis functions for irreducible representations of the quadratic symmetry algebra of the quantum superintegrable system on the 2-sphere, HΨ = EΨ, with generic 3-parameter potential. Clearly, the polynomials are expansion coefficients for one eigenbasis of a symmetry operator L2 of H in terms of an eigenbasis of another symmetry operator L1, but the exact relationship appears not to have been made explicit. We work out the details of the expansion to show, explicitly, how the polynomials arise and how the principal properties of these functions: the measure, 3-term recurrence relation, 2nd order difference equation, duality of these relations, permutation symmetry, intertwining operators and an alternate derivation of Wilson functions - follow from the symmetry of this quantum system. This paper is an exercise to show that quantum mechancal concepts and recurrence relations for Gausian hypergeometrc functions alone suffice to explain these properties; we make no assumptions about the structure of Wilson polynomial/functions, but derive them from quantum principles. There is active interest in the relation between multivariable Wilson polynomials and the quantum superintegrable system on the n-sphere with generic potential, and these results should aid in the generalization. Contracting function space realizations of irreducible representations of this quadratic algebra to the other superintegrable systems one can obtain the full Askey scheme of orthogonal hypergeometric polynomials. All of these contractions of superintegrable systems with potential are uniquely induced by Wigner Lie algebra contractions of so(3, C) and e(2,C). All of the polynomials produced are interpretable as quantum expansion coefficients. It is important to extend this process to higher dimensions.

A transformation method for constrained-function minimization

NASA Technical Reports Server (NTRS)

Park, S. K.

1975-01-01

A direct method for constrained-function minimization is discussed. The method involves the construction of an appropriate function mapping all of one finite dimensional space onto the region defined by the constraints. Functions which produce such a transformation are constructed for a variety of constraint regions including, for example, those arising from linear and quadratic inequalities and equalities. In addition, the computational performance of this method is studied in the situation where the Davidon-Fletcher-Powell algorithm is used to solve the resulting unconstrained problem. Good performance is demonstrated for 19 test problems by achieving rapid convergence to a solution from several widely separated starting points.

Two-dimensional, phase modulated lattice sums with application to the Helmholtz Green’s function

DOE Office of Scientific and Technical Information (OSTI.GOV)

Linton, C. M., E-mail: C.M.Linton@lboro.ac.uk

2015-01-15

A class of two-dimensional phase modulated lattice sums in which the denominator is an indefinite quadratic polynomial Q is expressed in terms of a single, exponentially convergent series of elementary functions. This expression provides an extremely efficient method for the computation of the quasi-periodic Green’s function for the Helmholtz equation that arises in a number of physical contexts when studying wave propagation through a doubly periodic medium. For a class of sums in which Q is positive definite, our new result can be used to generate representations in terms of θ-functions which are significant generalisations of known results.

A study of parameter identification

NASA Technical Reports Server (NTRS)

Herget, C. J.; Patterson, R. E., III

1978-01-01

A set of definitions for deterministic parameter identification ability were proposed. Deterministic parameter identificability properties are presented based on four system characteristics: direct parameter recoverability, properties of the system transfer function, properties of output distinguishability, and uniqueness properties of a quadratic cost functional. Stochastic parameter identifiability was defined in terms of the existence of an estimation sequence for the unknown parameters which is consistent in probability. Stochastic parameter identifiability properties are presented based on the following characteristics: convergence properties of the maximum likelihood estimate, properties of the joint probability density functions of the observations, and properties of the information matrix.

Decoupled and linear quadratic regulator control of a large, flexible space antenna with an observer in the control loop

NASA Technical Reports Server (NTRS)

Hamer, H. A.; Johnson, K. G.; Young, J. W.

1985-01-01

An analysis is performed to compare decoupled and linear quadratic regulator (LQR) procedures for the control of a large, flexible space antenna. Control objectives involve: (1) commanding changes in the rigid-body modes, (2) nulling initial disturbances in the rigid-body modes, or (3) nulling initial disturbances in the first three flexible modes. Control is achieved with two three-axis control-moment gyros located on the antenna column. Results are presented to illustrate various effects on control requirements for the two procedures. These effects include errors in the initial estimates of state variables, variations in the type, number, and location of sensors, and deletions of state-variable estimates for certain flexible modes after control activation. The advantages of incorporating a time lag in the control feedback are also illustrated. In addition, the effects of inoperative-control situations are analyzed with regard to control requirements and resultant modal responses. Comparisons are included which show the effects of perfect state feedback with no residual modes (ideal case). Time-history responses are presented to illustrate the various effects on the control procedures.

Optimal control of the gear shifting process for shift smoothness in dual-clutch transmissions

NASA Astrophysics Data System (ADS)

Li, Guoqiang; Görges, Daniel

2018-03-01

The control of the transmission system in vehicles is significant for the driving comfort. In order to design a controller for smooth shifting and comfortable driving, a dynamic model of a dual-clutch transmission is presented in this paper. A finite-time linear quadratic regulator is proposed for the optimal control of the two friction clutches in the torque phase for the upshift process. An integral linear quadratic regulator is introduced to regulate the relative speed difference between the engine and the slipping clutch under the optimization of the input torque during the inertia phase. The control objective focuses on smoothing the upshift process so as to improve the driving comfort. Considering the available sensors in vehicles for feedback control, an observer design is presented to track the immeasurable variables. Simulation results show that the jerk can be reduced both in the torque phase and inertia phase, indicating good shift performance. Furthermore, compared with conventional controllers for the upshift process, the proposed control method can reduce shift jerk and improve shift quality.

Wing box transonic-flutter suppression using piezoelectric self-sensing actuators attached to skin

NASA Astrophysics Data System (ADS)

Otiefy, R. A. H.; Negm, H. M.

2010-12-01

The main objective of this research is to study the capability of piezoelectric (PZT) self-sensing actuators to suppress the transonic wing box flutter, which is a flow-structure interaction phenomenon. The unsteady general frequency modified transonic small disturbance (TSD) equation is used to model the transonic flow about the wing. The wing box structure and piezoelectric actuators are modeled using the equivalent plate method, which is based on the first order shear deformation plate theory (FSDPT). The piezoelectric actuators are bonded to the skin. The optimal electromechanical coupling conditions between the piezoelectric actuators and the wing are collected from previous work. Three main different control strategies, a linear quadratic Gaussian (LQG) which combines the linear quadratic regulator (LQR) with the Kalman filter estimator (KFE), an optimal static output feedback (SOF), and a classic feedback controller (CFC), are studied and compared. The optimum actuator and sensor locations are determined using the norm of feedback control gains (NFCG) and norm of Kalman filter estimator gains (NKFEG) respectively. A genetic algorithm (GA) optimization technique is used to calculate the controller and estimator parameters to achieve a target response.

Analysis of explicit model predictive control for path-following control

PubMed Central

2018-01-01

In this paper, explicit Model Predictive Control(MPC) is employed for automated lane-keeping systems. MPC has been regarded as the key to handle such constrained systems. However, the massive computational complexity of MPC, which employs online optimization, has been a major drawback that limits the range of its target application to relatively small and/or slow problems. Explicit MPC can reduce this computational burden using a multi-parametric quadratic programming technique(mp-QP). The control objective is to derive an optimal front steering wheel angle at each sampling time so that autonomous vehicles travel along desired paths, including straight, circular, and clothoid parts, at high entry speeds. In terms of the design of the proposed controller, a method of choosing weighting matrices in an optimization problem and the range of horizons for path-following control are described through simulations. For the verification of the proposed controller, simulation results obtained using other control methods such as MPC, Linear-Quadratic Regulator(LQR), and driver model are employed, and CarSim, which reflects the features of a vehicle more realistically than MATLAB/Simulink, is used for reliable demonstration. PMID:29534080

Analysis of explicit model predictive control for path-following control.

PubMed

Lee, Junho; Chang, Hyuk-Jun

2018-01-01

In this paper, explicit Model Predictive Control(MPC) is employed for automated lane-keeping systems. MPC has been regarded as the key to handle such constrained systems. However, the massive computational complexity of MPC, which employs online optimization, has been a major drawback that limits the range of its target application to relatively small and/or slow problems. Explicit MPC can reduce this computational burden using a multi-parametric quadratic programming technique(mp-QP). The control objective is to derive an optimal front steering wheel angle at each sampling time so that autonomous vehicles travel along desired paths, including straight, circular, and clothoid parts, at high entry speeds. In terms of the design of the proposed controller, a method of choosing weighting matrices in an optimization problem and the range of horizons for path-following control are described through simulations. For the verification of the proposed controller, simulation results obtained using other control methods such as MPC, Linear-Quadratic Regulator(LQR), and driver model are employed, and CarSim, which reflects the features of a vehicle more realistically than MATLAB/Simulink, is used for reliable demonstration.

Optimal helicopter trajectory planning for terrain following flight

NASA Technical Reports Server (NTRS)

Menon, P. K. A.

1990-01-01

Helicopters operating in high threat areas have to fly close to the earth surface to minimize the risk of being detected by the adversaries. Techniques are presented for low altitude helicopter trajectory planning. These methods are based on optimal control theory and appear to be implementable onboard in realtime. Second order necessary conditions are obtained to provide a criterion for finding the optimal trajectory when more than one extremal passes through a given point. A second trajectory planning method incorporating a quadratic performance index is also discussed. Trajectory planning problem is formulated as a differential game. The objective is to synthesize optimal trajectories in the presence of an actively maneuvering adversary. Numerical methods for obtaining solutions to these problems are outlined. As an alternative to numerical method, feedback linearizing transformations are combined with the linear quadratic game results to synthesize explicit nonlinear feedback strategies for helicopter pursuit-evasion. Some of the trajectories generated from this research are evaluated on a six-degree-of-freedom helicopter simulation incorporating an advanced autopilot. The optimal trajectory planning methods presented are also useful for autonomous land vehicle guidance.

Evaluation of oxidant and antioxidant status in infants with hyperbilirubinemia and kernicterus.

PubMed

Doğan, Murat; Peker, Erdal; Kirimi, Ercan; Sal, Ertan; Akbayram, Sinan; Erel, Ozcan; Ocak, Ali Riza; Tuncer, Oguz

2011-11-01

The objective of the present study was to determine oxidant and antioxidant status in infants with hyperbilirubinemia and/or kernicterus and to find whether there is a relationship between bilirubin level and oxidant/antioxidant status. The study includes 69 full-term newborns (neonates with hyperbilirubinemia needing phototherapy [Group 1, n = 36] and neonates with kernicterus [Group 2, n = 33]) and 25 age-matched healthy newborn. Plasma total antioxidant capacity (TAC) and serum total oxidant status (TOS) were significantly higher in Groups 1 and 2 than the control group. There was a significant difference between Group 1 and control cases for malondialdehyde (MDA; p < 0.001). Total free sulfhydryl group (TTHI) values were significantly elevated in Group 1 compared to Group 2 and control cases. Correlation analysis showed that the correlation between total bilirubin (TB) and TAC, TOS, MDA and oxidative stress index may be expressed by a quadratic curve. After phototherapy, a statistically significant increase in nitrite level was observed. We demonstrated that the relationship between serum TB and antioxidants and oxidative stress could be expressed by a quadratic correlation curve.

Predicting out-of-office blood pressure level using repeated measurements in the clinic: an observational cohort study

PubMed Central

Sheppard, James P.; Holder, Roger; Nichols, Linda; Bray, Emma; Hobbs, F.D. Richard; Mant, Jonathan; Little, Paul; Williams, Bryan; Greenfield, Sheila; McManus, Richard J.

2014-01-01

Objectives: Identification of people with lower (white-coat effect) or higher (masked effect) blood pressure at home compared to the clinic usually requires ambulatory or home monitoring. This study assessed whether changes in SBP with repeated measurement at a single clinic predict subsequent differences between clinic and home measurements. Methods: This study used an observational cohort design and included 220 individuals aged 35–84 years, receiving treatment for hypertension, but whose SBP was not controlled. The characteristics of change in SBP over six clinic readings were defined as the SBP drop, the slope and the quadratic coefficient using polynomial regression modelling. The predictive abilities of these characteristics for lower or higher home SBP readings were investigated with logistic regression and repeated operating characteristic analysis. Results: The single clinic SBP drop was predictive of the white-coat effect with a sensitivity of 90%, specificity of 50%, positive predictive value of 56% and negative predictive value of 88%. Predictive values for the masked effect and those of the slope and quadratic coefficient were slightly lower, but when the slope and quadratic variables were combined, the sensitivity, specificity, positive and negative predictive values for the masked effect were improved to 91, 48, 24 and 97%, respectively. Conclusion: Characteristics obtainable from multiple SBP measurements in a single clinic in patients with treated hypertension appear to reasonably predict those unlikely to have a large white-coat or masked effect, potentially allowing better targeting of out-of-office monitoring in routine clinical practice. PMID:25144295

Tangent Lines without Derivatives for Quadratic and Cubic Equations

ERIC Educational Resources Information Center

Carroll, William J.

2009-01-01

In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)

Geometrical Solutions of Some Quadratic Equations with Non-Real Roots

ERIC Educational Resources Information Center

Pathak, H. K.; Grewal, A. S.

2002-01-01

This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the…

Acetate Dose-Dependently Stimulates Milk Fat Synthesis in Lactating Dairy Cows.

PubMed

Urrutia, Natalie L; Harvatine, Kevin J

2017-05-01

Background: Acetate is a short-chain fatty acid (FA) that is especially important to cows because it is the major substrate for de novo FA synthesis. However, the effect of acetate supply on mammary lipid synthesis is not clear. Objective: The objective of this experiment was to determine the effect of increasing acetate supply on milk fat synthesis in lactating dairy cows. Methods: Six multiparous lactating Holstein cows were randomly assigned to treatments in a replicated design to investigate the effect of acetate supply on milk fat synthesis. Treatments were 0 (control), 5, 10, and 15 mol acetate/d continuously infused into the rumen for 4 d. Rumen short-chain FAs, plasma hormones and metabolites, milk fat concentration, and milk FA profile were analyzed on day 4 of each treatment. Polynomial contrasts were used to test the linear and quadratic effects of increasing acetate supply. Results: Acetate increased milk fat yield quadratically ( P < 0.01) by 7%, 16%, and 14% and increased milk fat concentration linearly ( P < 0.001) by 6%, 9%, and 11% for 5, 10, and 15 mol acetate/d, respectively, compared with the control treatment. Increased milk fat yield predominantly was due to a linear increase in 16-carbon FAs ( P < 0.001) and a quadratic increase in de novo synthesized FAs (<16-carbon FAs; P < 0.01), indicating that there was stimulation of de novo synthesis pathways. Apparent transfer of acetate to milk fat was 33.4%, 36.2%, and 20.6% for 5, 10, and 15 mol/d, respectively. Acetate infusion linearly increased the relative concentration of rumen acetate ( P < 0.001) before feeding, but not after feeding. Acetate linearly increased plasma ß-hydroxybutyric acid by 29%, 50%, and 78%, respectively, after feeding compared with the control treatment ( P < 0.01). Conclusions: Increasing acetate supply to lactating cows increases milk fat synthesis, suggesting that nutritional strategies that increase ruminal acetate absorption would be expected to increase milk fat by increasing de novo FA synthesis. © 2017 American Society for Nutrition.

Tip-tilt disturbance model identification based on non-linear least squares fitting for Linear Quadratic Gaussian control

NASA Astrophysics Data System (ADS)

Yang, Kangjian; Yang, Ping; Wang, Shuai; Dong, Lizhi; Xu, Bing

2018-05-01

We propose a method to identify tip-tilt disturbance model for Linear Quadratic Gaussian control. This identification method based on Levenberg-Marquardt method conducts with a little prior information and no auxiliary system and it is convenient to identify the tip-tilt disturbance model on-line for real-time control. This identification method makes it easy that Linear Quadratic Gaussian control runs efficiently in different adaptive optics systems for vibration mitigation. The validity of the Linear Quadratic Gaussian control associated with this tip-tilt disturbance model identification method is verified by experimental data, which is conducted in replay mode by simulation.

Exponential approximations in optimal design

NASA Technical Reports Server (NTRS)

Belegundu, A. D.; Rajan, S. D.; Rajgopal, J.

1990-01-01

One-point and two-point exponential functions have been developed and proved to be very effective approximations of structural response. The exponential has been compared to the linear, reciprocal and quadratic fit methods. Four test problems in structural analysis have been selected. The use of such approximations is attractive in structural optimization to reduce the numbers of exact analyses which involve computationally expensive finite element analysis.

Dynamic Geometry Software and Tracing Tangents in the Context of the Mean Value Theorem: Technique and Theory Production

ERIC Educational Resources Information Center

Martínez-Hernández, Cesar; Ulloa-Azpeitia, Ricardo

2017-01-01

Based on the theoretical elements of the instrumental approach to tool use known as Task-Technique-Theory (Artigue, 2002), this paper analyses and discusses the performance of graduate students enrolled in a Teacher Training program. The latter performance relates to tracing tangent lines to the curve of a quadratic function in Dynamic Geometry…

Comparison of yellow poplar growth models on the basis of derived growth analysis variables

Treesearch

Keith F. Jensen; Daniel A. Yaussy

1986-01-01

Quadratic and cubic polynomials, and Gompertz and Richards asymptotic models were fitted to yellow poplar growth data. These data included height, leaf area, leaf weight and new shoot height for 23 weeks. Seven growth analysis variables were estimated from each function. The Gompertz and Richards models fitted the data best and provided the most accurate derived...

The Application of Various Nonlinear Models to Describe Academic Growth Trajectories: An Empirical Analysis Using Four-Wave Longitudinal Achievement Data from a Large Urban School District

ERIC Educational Resources Information Center

Shin, Tacksoo

2012-01-01

This study introduced various nonlinear growth models, including the quadratic conventional polynomial model, the fractional polynomial model, the Sigmoid model, the growth model with negative exponential functions, the multidimensional scaling technique, and the unstructured growth curve model. It investigated which growth models effectively…

Are Public Master's Institutions Cost Efficient? A Stochastic Frontier and Spatial Analysis

ERIC Educational Resources Information Center

Titus, Marvin A.; Vamosiu, Adriana; McClure, Kevin R.

2017-01-01

The current study examines costs, measured by educational and general (E&G) spending, and cost efficiency at 252 public master's institutions in the United States over a nine-year (2004-2012) period. We use a multi-product quadratic cost function and results from a random-effects model with a first-order autoregressive (AR1) disturbance term…

The Impact of Computer Use on Learning of Quadratic Functions

ERIC Educational Resources Information Center

Pihlap, Sirje

2017-01-01

Studies of the impact of various types of computer use on the results of learning and student motivation have indicated that the use of computers can increase learning motivation, and that computers can have a positive effect, a negative effect, or no effect at all on learning outcomes. Some results indicate that it is not computer use itself that…

Multifractal Analysis for Nutritional Assessment

PubMed Central

Park, Youngja; Lee, Kichun; Ziegler, Thomas R.; Martin, Greg S.; Hebbar, Gautam; Vidakovic, Brani; Jones, Dean P.

2013-01-01

The concept of multifractality is currently used to describe self-similar and complex scaling properties observed in numerous biological signals. Fractals are geometric objects or dynamic variations which exhibit some degree of similarity (irregularity) to the original object in a wide range of scales. This approach determines irregularity of biologic signal as an indicator of adaptability, the capability to respond to unpredictable stress, and health. In the present work, we propose the application of multifractal analysis of wavelet-transformed proton nuclear magnetic resonance (1H NMR) spectra of plasma to determine nutritional insufficiency. For validation of this method on 1H NMR signal of human plasma, standard deviation from classical statistical approach and Hurst exponent (H), left slope and partition function from multifractal analysis were extracted from 1H NMR spectra to test whether multifractal indices could discriminate healthy subjects from unhealthy, intensive care unit patients. After validation, the multifractal approach was applied to spectra of plasma from a modified crossover study of sulfur amino acid insufficiency and tested for associations with blood lipids. The results showed that standard deviation and H, but not left slope, were significantly different for sulfur amino acid sufficiency and insufficiency. Quadratic discriminant analysis of H, left slope and the partition function showed 78% overall classification accuracy according to sulfur amino acid status. Triglycerides and apolipoprotein C3 were significantly correlated with a multifractal model containing H, left slope, and standard deviation, and cholesterol and high-sensitivity C-reactive protein were significantly correlated to H. In conclusion, multifractal analysis of 1H NMR spectra provides a new approach to characterize nutritional status. PMID:23990878